TPTP Problem File: SEV668+1.p
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%------------------------------------------------------------------------------
% File : SEV668+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - Redblack T neq E
% 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 : Redblack.T.neq.E.p [Kal26]
% Status : Theorem
% Rating : 0.30 v9.3.0
% Syntax : Number of formulae : 2821 ( 991 unt; 0 def)
% Number of atoms : 10300 (3260 equ)
% Maximal formula atoms : 369 ( 3 avg)
% Number of connectives : 7944 ( 465 ~; 846 |;1851 &)
% (1149 <=>;3633 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 501 ( 500 usr; 0 prp; 1-23 aty)
% Number of functors : 1671 (1671 usr;1083 con; 0-22 aty)
% Number of variables : 9049 (8285 !; 764 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.bool$36738',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__8)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__9)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__10)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__11)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__12)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436799___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436738___24a14(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13) = cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__6,Vv__CANONICAL__13) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436799___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436738___24a14(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$36799',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__8)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__9)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__10)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436840___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436799___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__5,Vv__CANONICAL__11) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436840___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436799___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$36840',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__8)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436865___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436840___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9) = cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__4,Vv__CANONICAL__9) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436865___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436840___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$36865',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436878___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436865___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__3,Vv__CANONICAL__7) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436878___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436865___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$36878',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436883___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436878___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__5) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436883___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436878___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$36883',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( ( cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436883___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) )
| ( cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436883___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$59791',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
& ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459791___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) )
| ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
& ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459791___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$63580',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2463580___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__63581] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63581)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__63581)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2463580___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__63581)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$63602',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2463602___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__63603] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63603)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__63603)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2463602___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__63603)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$56717',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__56730___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__56722] :
( t(Vvar__2___24Anonymous__56722,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__56723] :
( t(Vvar__3___24Anonymous__56723,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__56722,Vvar__3___24Anonymous__56723)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2456717___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__56722)),Vvar__3___24Anonymous__56723)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Specif.sumbool$3367',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( c_24__type__114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__3 = Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__3379___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__3380___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_243367___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__let__var__var__7__n__3336__3340__3349___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)) )
| ( Vv__CANONICAL__3 != Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__3381___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__3382___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_243367___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__let__var__var__7__n__3336__3340__3349___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$63597',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2463602___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2463597___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__63598] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63598)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2463602___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__63598)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2463597___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__63598) )
| ? [Vvar__0___24Anonymous__63599] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63599)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2463602___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__63599)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2463597___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__63599) ) ) ) ).
fof('$_def_$_let_11_subst_l_51852',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__51852___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_var_6_p_52252_52255',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__52251] : c_24__let__var__6__p__52252__52255___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__52251) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__52251) ).
fof('$_def_$_let_var_6_p_52254_52256',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__52253] : c_24__let__var__6__p__52254__52256___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__52253) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__52253) ).
fof('$_def_$_let_var_var_7_n_3336_3340_3349',axiom,
! [V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__3333] : c_24__let__var__var__7__n__3336__3340__3349___24a4(V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__3333) = cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,Vvar__2___24Anonymous__3333,V4__x) ).
fof('$_def_Coq.Arith.Between.in_int',axiom,
! [V0__p,V1__q,V2__r] :
( cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r)
<=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__p,V2__r)
& cCoq_2eInit_2ePeano_2elt___24a2(V2__r,V1__q) ) ) ).
fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__61475] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__61475)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__61475)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__61476] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__61476)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__61476)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__61479] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__61479)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__61479)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__61476,Vvar__0___24Anonymous__61479) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.Factorial.fact',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__4405] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4405)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4405)
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4405),cCoq_2eArith_2eFactorial_2efact___24a1(Vvar__0___24Anonymous__4405)) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.Even',axiom,
! [V0__n] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eEven___24a1(V0__n)
<=> ? [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
& V0__n = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__m) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.clearbit',axiom,
! [V0__a,V1__n] : cCoq_2eArith_2ePeanoNat_2eNat_2eclearbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eNat_2eldiff___24a2(V0__a,cCoq_2eInit_2eNat_2eshiftl___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),V1__n)) ).
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.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.Sumbool.sumbool_not',axiom,
! [V0__A,V1__B,V2__H1] :
( cProp___24t(V0__A)
=> ( cProp___24t(V1__B)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V2__H1)
=> ( ( p(V0__A)
& V2__H1 = cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B)
& cCoq_2eBool_2eSumbool_2esumbool__not___24a3(V0__A,V1__B,V2__H1) = cCoq_2eInit_2eSpecif_2eright___24a2(V1__B,V0__A) )
| ( p(V1__B)
& V2__H1 = cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B)
& cCoq_2eBool_2eSumbool_2esumbool__not___24a3(V0__A,V1__B,V2__H1) = cCoq_2eInit_2eSpecif_2eleft___24a2(V1__B,V0__A) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Zerob.zerob',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__59793] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59793)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59793)
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V0__s)
<=> ! [V1__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__a)
=> ~ p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__a,V0__s)) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s))
<=> p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27)) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( p(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('$_def_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s))
=> p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27)) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.add',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& ( ? [Vvar__0___24Anonymous__61061] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61061)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__61061)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__61061,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf)) )
| ? [Vvar__0___24Anonymous__61062] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61062)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__61062)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__61062,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf),cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ) ) ) )
| ? [Vvar__0___24Anonymous__61063] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__61063)
& ? [Vvar__1___24Anonymous__61064] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__61064)
& ? [Vvar__2___24Anonymous__61065] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__61065)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61063,Vvar__1___24Anonymous__61064,Vvar__2___24Anonymous__61065)
& ( ? [Vvar__0___24Anonymous__61078] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61078)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__61078)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61063,Vvar__1___24Anonymous__61064,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__61078,Vvar__2___24Anonymous__61065)) )
| ? [Vvar__0___24Anonymous__61079] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61079)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__61079)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__61079,Vvar__0___24Anonymous__61063),Vvar__1___24Anonymous__61064,Vvar__2___24Anonymous__61065) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61063,cCoq_2eInit_2eDatatypes_2etrue,Vvar__2___24Anonymous__61065) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__4243] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__4243)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__4243) ) ).
fof('$_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__61040] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__61040)
& ? [Vvar__1___24Anonymous__61041] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__61041)
& ? [Vvar__2___24Anonymous__61042] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__61042)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61040,Vvar__1___24Anonymous__61041,Vvar__2___24Anonymous__61042)
& ( ? [Vvar__0___24Anonymous__61055] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61055)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__61055)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__61055,Vvar__2___24Anonymous__61042) )
| ? [Vvar__0___24Anonymous__61056] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61056)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__61056)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__61056,Vvar__0___24Anonymous__61040) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__61041 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.node',axiom,
! [V0__l,V1__b,V2__r] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( ( V1__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(V0__l,V1__b,V2__r) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V0__l,V1__b,V2__r) )
| ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__l)
=> ( V1__b = cCoq_2eInit_2eDatatypes_2efalse
& ( ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__r)
=> ( V0__l = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& ( ( V2__r = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(V0__l,V1__b,V2__r) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf )
| ? [Vvar__0___24Anonymous__61081] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__61081)
& ? [Vvar__1___24Anonymous__61082] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__61082)
& ? [Vvar__2___24Anonymous__61083] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__61083)
& V2__r = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61081,Vvar__1___24Anonymous__61082,Vvar__2___24Anonymous__61083)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(V0__l,V1__b,V2__r) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V0__l,cCoq_2eInit_2eDatatypes_2efalse,V2__r) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__61087] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__61087)
& ? [Vvar__1___24Anonymous__61088] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__61088)
& ? [Vvar__2___24Anonymous__61089] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__61089)
& V0__l = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61087,Vvar__1___24Anonymous__61088,Vvar__2___24Anonymous__61089)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(V0__l,V1__b,V2__r) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V0__l,cCoq_2eInit_2eDatatypes_2efalse,V2__r) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.remove',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf )
| ? [Vvar__0___24Anonymous__4246] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__4246)
& ? [Vvar__1___24Anonymous__4247] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__4247)
& ? [Vvar__2___24Anonymous__4248] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__4248)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__4246,Vvar__1___24Anonymous__4247,Vvar__2___24Anonymous__4248)
& ( ? [Vvar__0___24Anonymous__4261] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4261)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4261)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(Vvar__0___24Anonymous__4246,Vvar__1___24Anonymous__4247,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(Vvar__0___24Anonymous__4261,Vvar__2___24Anonymous__4248)) )
| ? [Vvar__0___24Anonymous__4262] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4262)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__4262)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(Vvar__0___24Anonymous__4262,Vvar__0___24Anonymous__4246),Vvar__1___24Anonymous__4247,Vvar__2___24Anonymous__4248) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(Vvar__0___24Anonymous__4246,cCoq_2eInit_2eDatatypes_2efalse,Vvar__2___24Anonymous__4248) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.singleton',axiom,
! [V0__i] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esingleton___24a1(V0__i) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V0__i,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__4244] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__4244)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__4244) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.union',axiom,
! [V1__m,V2__m_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__m)
=> ( ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V1__m,V2__m_27) = V2__m_27 )
| ? [Vvar__0___24Anonymous__61099] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__61099)
& ? [Vvar__1___24Anonymous__61100] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__61100)
& ? [Vvar__2___24Anonymous__61101] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__61101)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m_27)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61099,Vvar__1___24Anonymous__61100,Vvar__2___24Anonymous__61101)
& ( ( V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V1__m,V2__m_27) = V1__m )
| ? [Vvar__0___24Anonymous__61117] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__61117)
& ? [Vvar__1___24Anonymous__61118] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__61118)
& ? [Vvar__2___24Anonymous__61119] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__61119)
& V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61117,Vvar__1___24Anonymous__61118,Vvar__2___24Anonymous__61119)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(Vvar__0___24Anonymous__61099,Vvar__0___24Anonymous__61117),cCoq_2eInit_2eDatatypes_2eorb___24a2(Vvar__1___24Anonymous__61100,Vvar__1___24Anonymous__61118),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(Vvar__2___24Anonymous__61101,Vvar__2___24Anonymous__61119)) ) ) ) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.Init.Datatypes.andb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_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__38227] :
( t(Vvar__1___24Anonymous__38227,V0__A)
& ? [Vvar__2___24Anonymous__38228] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__38228)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__38227,Vvar__2___24Anonymous__38228)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__38227,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__38228,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.bool_rec',axiom,
! [V0__P] : cCoq_2eInit_2eDatatypes_2ebool__rec___24a1(V0__P) = cCoq_2eInit_2eDatatypes_2ebool__rect___24a1(V0__P) ).
fof('$_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__38168] :
( t(Vvar__2___24Anonymous__38168,V0__A)
& ? [Vvar__3___24Anonymous__38169] :
( t(Vvar__3___24Anonymous__38169,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__38168,Vvar__3___24Anonymous__38169)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__38168 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__4312] :
( t(Vvar__1___24Anonymous__4312,V0__A)
& ? [Vvar__2___24Anonymous__4313] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4313)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4312,Vvar__2___24Anonymous__4313)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__4313)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.list_rec',axiom,
! [V0__A,V1__P] : cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V0__A,V1__P) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V0__A,V1__P) ).
fof('$_def_Coq.Init.Datatypes.list_rect',axiom,
! [V0__A,V1__P,V2__f,V3__f,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__38198___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = V2__f )
| ? [Vvar__1___24Anonymous__38192] :
( t(Vvar__1___24Anonymous__38192,V0__A)
& ? [Vvar__2___24Anonymous__38193] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__38193)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__38192,Vvar__2___24Anonymous__38193)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = happ(happ(happ(V3__f,Vvar__1___24Anonymous__38192),Vvar__2___24Anonymous__38193),cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,Vvar__2___24Anonymous__38193)) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rec',axiom,
! [V0__P] : cCoq_2eInit_2eDatatypes_2enat__rec___24a1(V0__P) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V0__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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__38180] :
( t(Vvar__2___24Anonymous__38180,V0__A)
& ? [Vvar__3___24Anonymous__38181] :
( t(Vvar__3___24Anonymous__38181,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__38180,Vvar__3___24Anonymous__38181)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__38181 ) ) ) ) ) ).
fof('$_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__4014] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4014)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4014)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__4014,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.compare',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__120] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__121] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__121)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__121)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__124] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__124)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__124)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__121,Vvar__0___24Anonymous__124) ) ) ) ) ) ) ) ).
fof('$_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__63285] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63285)
& V1__y = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__63285)
& 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__63285,cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__63285)) ) ) ) ).
fof('$_def_Coq.Init.Nat.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__4429] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4429)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4429)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__4430] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4430)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4430)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__4433] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4433)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4433)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__4430,Vvar__0___24Anonymous__4433) ) ) ) ) ) ) ) ).
fof('$_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__63281] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63281)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63281)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__63281)
& ( ( Vvar__0___24Anonymous__63281 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__63284] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63284)
& Vvar__0___24Anonymous__63281 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__63284)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__63284) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.gcd',axiom,
! [V1__a,V2__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__a)
=> ( ( V1__a = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = V2__b )
| ? [Vvar__0___24Anonymous__63288] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63288)
& V1__a = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__63288)
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = cCoq_2eInit_2eNat_2egcd___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V2__b,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__63288)),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__63288)) ) ) ) ).
fof('$_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__42639] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42639)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42639)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__42642] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42642)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42642)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__42639,Vvar__0___24Anonymous__42642) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__63275] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63275)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__63275)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__63278] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63278)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__63278)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__63275,Vvar__0___24Anonymous__63278)) ) ) ) ) ) ) ) ).
fof('$_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__42630] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42630)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42630)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__42630,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__4019] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4019)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4019)
& 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__4019)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__42628] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42628)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42628)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__42628 ) ) ) ).
fof('$_def_Coq.Init.Nat.shiftl',axiom,
! [V0__a] : cCoq_2eInit_2eNat_2eshiftl___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__63290,V0__a,c_24__lam__63291) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__42633] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42633)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42633)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__42636] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42636)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42636)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__42633,Vvar__0___24Anonymous__42636) ) ) ) ) ) ) ) ).
fof('$_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__42646] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42646)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42646)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__42646) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).
fof('$_def_Coq.Init.Specif.sumbool_rec',axiom,
! [V0__A,V1__B,V2__P] : cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V0__A,V1__B,V2__P) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V0__A,V1__B,V2__P) ).
fof('$_def_Coq.Init.Wf.well_founded',axiom,
! [V0__A,V1__R] :
( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).
fof('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__3320] :
( t(Vvar__1___24Anonymous__3320,V0__A)
& ? [Vvar__2___24Anonymous__3321] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3321)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3320,Vvar__2___24Anonymous__3321)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> ( Vvar__1___24Anonymous__3320 = V2__a
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__3321)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.count_occ',axiom,
! [V0__A,V1__eq__dec,V3__l,V4__x] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__3332] :
( t(Vvar__1___24Anonymous__3332,V0__A)
& ? [Vvar__2___24Anonymous__3333] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3333)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3332,Vvar__2___24Anonymous__3333)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_243367___24a5(V0__A,V1__eq__dec,V4__x,Vvar__1___24Anonymous__3332,Vvar__2___24Anonymous__3333) ) ) ) ) ) ).
fof('$_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__42462] :
( t(Vvar__1___24Anonymous__42462,V1__B)
& ? [Vvar__2___24Anonymous__42463] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__42463)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__42462,Vvar__2___24Anonymous__42463)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__42462),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__42463)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd_error',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__41588] :
( t(Vvar__1___24Anonymous__41588,V0__A)
& ? [Vvar__2___24Anonymous__41589] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__41589)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__41588,Vvar__2___24Anonymous__41589)
& cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__41588) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.incl',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m)) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__63190] :
( t(Vvar__1___24Anonymous__63190,V0__A)
& ? [Vvar__2___24Anonymous__63191] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__63191)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__63191)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__63190,Vvar__2___24Anonymous__63191)
& ( ( Vvar__2___24Anonymous__63191 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__63190 )
| ? [Vvar__1___24Anonymous__63202] :
( t(Vvar__1___24Anonymous__63202,V0__A)
& ? [Vvar__2___24Anonymous__63203] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__63203)
& Vvar__2___24Anonymous__63191 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__63202,Vvar__2___24Anonymous__63203)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__63191,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__42441] :
( t(Vvar__1___24Anonymous__42441,V0__A)
& ? [Vvar__2___24Anonymous__42442] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__42442)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__42441,Vvar__2___24Anonymous__42442)
& 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__42441),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__42442)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_error',axiom,
! [V0__A,V2__l,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__4410] :
( t(Vvar__1___24Anonymous__4410,V0__A)
& ? [Vvar__2___24Anonymous__4411] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4411)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4410,Vvar__2___24Anonymous__4411)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__4410) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__4413] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4413)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4413)
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__4420] :
( t(Vvar__1___24Anonymous__4420,V0__A)
& ? [Vvar__2___24Anonymous__4421] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4421)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4420,Vvar__2___24Anonymous__4421)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,Vvar__2___24Anonymous__4421,Vvar__0___24Anonymous__4413) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.remove',axiom,
! [V0__A,V1__eq__dec,V3__x,V4__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__41598] :
( t(Vvar__1___24Anonymous__41598,V0__A)
& ? [Vvar__2___24Anonymous__41599] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__41599)
& ( cType___24t(V0__A)
=> ( c_24__type__114___24t(V0__A,V1__eq__dec)
=> ( t(V3__x,V0__A)
=> ( t(Vvar__1___24Anonymous__41598,V0__A)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__41598,Vvar__2___24Anonymous__41599)
& ( ( V3__x = Vvar__1___24Anonymous__41598
& happ(happ(V1__eq__dec,V3__x),Vvar__1___24Anonymous__41598) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__41618___24a3(V0__A,V3__x,Vvar__1___24Anonymous__41598),c_24__prop__41619___24a3(V0__A,V3__x,Vvar__1___24Anonymous__41598))
& cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V4__l) = cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,Vvar__2___24Anonymous__41599) )
| ( V3__x != Vvar__1___24Anonymous__41598
& happ(happ(V1__eq__dec,V3__x),Vvar__1___24Anonymous__41598) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__41620___24a3(V0__A,V3__x,Vvar__1___24Anonymous__41598),c_24__prop__41621___24a3(V0__A,V3__x,Vvar__1___24Anonymous__41598))
& cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__41598,cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,Vvar__2___24Anonymous__41599)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.ListDec.In_dec',axiom,
! [V0__A,V1__dec] : cCoq_2eLists_2eListDec_2eIn__dec___24a2(V0__A,V1__dec) = cCoq_2eLists_2eList_2ein__dec___24a2(V0__A,V1__dec) ).
fof('$_def_Coq.Lists.SetoidList.equivlistA',axiom,
! [V0__A,V1__eqA,V2__l,V3__l_27] :
( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l)
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l_27) ) ) ) ).
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('$_def_Coq.Logic.EqdepFacts.Eq_rect_eq',axiom,
! [V0__U] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V0__U)
<=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__61506___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V0__U,V1__p,V2__Q,V3__x) ) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.EqDec',axiom,
! [V0__A] : cCoq_2eLogic_2eFinFun_2eEqDec___24a1(V0__A) = c_24__type__114___24a1(V0__A) ).
fof('$_def_Coq.NArith.BinNat.N.clearbit',axiom,
! [V0__a,V1__n] : cCoq_2eNArith_2eBinNat_2eN_2eclearbit___24a2(V0__a,V1__n) = cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V0__a,cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__n)) ).
fof('$_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('$_def_Coq.NArith.BinNat.N.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNat.N.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__6160] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6160)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6160)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__6163] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6163)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6163)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__6160,Vvar__0___24Anonymous__6163)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.compare',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__3496] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3496)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3496)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__3497] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3497)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3497)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__3500] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3500)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3500)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__3497,Vvar__0___24Anonymous__3500) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.NArith.BinNatDef.N.double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__64704] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64704)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__64704)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64704)) ) ) ) ).
fof('$_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__60736] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60736)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60736)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__60737] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60737)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60737)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__60740] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60740)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60740)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__60737,Vvar__0___24Anonymous__60740) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__64705] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64705)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64705)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__64705)
& ( ? [Vvar__0___24Anonymous__64709] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64709)
& Vvar__0___24Anonymous__64705 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64709)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__64710] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64710)
& Vvar__0___24Anonymous__64705 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64710)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__64705 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_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__64721] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64721)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__64721)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = V0__a )
| ? [Vvar__0___24Anonymous__64724] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64724)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__64724)
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__64721,Vvar__0___24Anonymous__64724)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_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__64713] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64713)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64713)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__64713)
& ( ? [Vvar__0___24Anonymous__64717] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64717)
& Vvar__0___24Anonymous__64713 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64717)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__64717)) )
| ? [Vvar__0___24Anonymous__64718] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64718)
& Vvar__0___24Anonymous__64713 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64718)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__64718)) )
| ( Vvar__0___24Anonymous__64713 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
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__60730] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60730)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60730)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__60733] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60733)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60733)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__60730,Vvar__0___24Anonymous__60733)) ) ) ) ) ) ) ) ).
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__60746] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60746)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60746)
& ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__60749] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60749)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60749)
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(Vvar__0___24Anonymous__60749,Vvar__0___24Anonymous__60746)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__60719] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60719)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60719)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__60719) ) ) ) ).
fof('$_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__60720] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60720)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60720)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__60725] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60725)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60720)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60725)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60725)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__60720,Vvar__0___24Anonymous__60725) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__60728] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60728)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__60720,Vvar__0___24Anonymous__60725) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__60728)
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60728) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__60720,Vvar__0___24Anonymous__60725) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__6157] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6157)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__6157)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__6157)) ) ) ) ).
fof('$_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__64703] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64703)
& V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__64703)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64703)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__60751] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60751)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60751)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__60751,V1__n) ) ) ) ).
fof('$_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__64726] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64726)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__64726)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__64726) ) ) ) ).
fof('$_def_Coq.NArith.Ndigits.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eNdigits_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.Numbers.BinNums.N_rec',axiom,
! [V0__P] : cCoq_2eNumbers_2eBinNums_2eN__rec___24a1(V0__P) = cCoq_2eNumbers_2eBinNums_2eN__rect___24a1(V0__P) ).
fof('$_def_Coq.Numbers.BinNums.Z_rec',axiom,
! [V0__P] : cCoq_2eNumbers_2eBinNums_2eZ__rec___24a1(V0__P) = cCoq_2eNumbers_2eBinNums_2eZ__rect___24a1(V0__P) ).
fof('$_def_Coq.Numbers.BinNums.positive_rec',axiom,
! [V0__P] : cCoq_2eNumbers_2eBinNums_2epositive__rec___24a1(V0__P) = cCoq_2eNumbers_2eBinNums_2epositive__rect___24a1(V0__P) ).
fof('$_def_Coq.PArith.BinPos.Pos.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ege___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2egt___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.le',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_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.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__60953] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60953)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60953)
& ( ? [Vvar__0___24Anonymous__60957] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60957)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60957)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__60952__1__add__carry___24a2(Vvar__0___24Anonymous__60953,Vvar__0___24Anonymous__60957)) )
| ? [Vvar__0___24Anonymous__60958] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60958)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60958)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__60953,Vvar__0___24Anonymous__60958)) )
| ( 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__60953)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__60959] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60959)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60959)
& ( ? [Vvar__0___24Anonymous__60963] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60963)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60963)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__60959,Vvar__0___24Anonymous__60963)) )
| ? [Vvar__0___24Anonymous__60964] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60964)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60964)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__60959,Vvar__0___24Anonymous__60964)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60959) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__60965] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60965)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60965)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__60965)) )
| ? [Vvar__0___24Anonymous__60966] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60966)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60966)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60966) )
| ( 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.compare_cont',axiom,
! [V1__r,V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__6176] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6176)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__6176)
& ( ? [Vvar__0___24Anonymous__6180] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6180)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__6180)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,Vvar__0___24Anonymous__6176,Vvar__0___24Anonymous__6180) )
| ? [Vvar__0___24Anonymous__6181] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6181)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__6181)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(cCoq_2eInit_2eDatatypes_2eGt,Vvar__0___24Anonymous__6176,Vvar__0___24Anonymous__6181) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__6182] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6182)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__6182)
& ( ? [Vvar__0___24Anonymous__6186] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6186)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__6186)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(cCoq_2eInit_2eDatatypes_2eLt,Vvar__0___24Anonymous__6182,Vvar__0___24Anonymous__6186) )
| ? [Vvar__0___24Anonymous__6187] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6187)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__6187)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,Vvar__0___24Anonymous__6182,Vvar__0___24Anonymous__6187) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__6188] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6188)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__6188)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__6189] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6189)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__6189)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = V1__r ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.eqb',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__60995] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60995)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60995)
& ( ? [Vvar__0___24Anonymous__60999] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60999)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60999)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__60995,Vvar__0___24Anonymous__60999) )
| ? [Vvar__0___24Anonymous__61000] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61000)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__61000)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__61001] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61001)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__61001)
& ( ? [Vvar__0___24Anonymous__61005] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61005)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__61005)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__61006] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61006)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__61006)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__61001,Vvar__0___24Anonymous__61006) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__61007] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61007)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__61007)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__61008] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61008)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__61008)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__60988] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60988)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60988)
& 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__60988,V2__y))) )
| ? [Vvar__0___24Anonymous__60989] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60989)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60989)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__60989,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__64771] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__64771)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__64771)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__64771)
& ( ( Vvar__0___24Anonymous__64771 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__64774] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__64774)
& Vvar__0___24Anonymous__64771 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__64774)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__64771)) ) ) ) ) ) ) ) ).
fof('$_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__64778] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__64778)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__64778)
& 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__64778)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( ? [Vvar__0___24Anonymous__64736] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64736)
& V0__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64736)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64736) )
| ? [Vvar__0___24Anonymous__64737] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64737)
& V0__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64737)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__64737) )
| ( V0__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__60985] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60985)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60985)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60985)) )
| ? [Vvar__0___24Anonymous__60986] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60986)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60986)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__60986)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__64738] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64738)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__64738)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__64738 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__60950] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60950)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60950)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__60950)) )
| ? [Vvar__0___24Anonymous__60951] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60951)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60951)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60951) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__64741] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64741)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64741)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__64754___24a1(Vvar__0___24Anonymous__64741) )
| ? [Vvar__0___24Anonymous__64745] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64745)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64745)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__64761___24a1(Vvar__0___24Anonymous__64745) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__64765 ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
! [V0__x] : cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd,V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('$_def_Coq.QArith.QArith_base.Qcompare',axiom,
! [V0__p,V1__q] : cCoq_2eQArith_2eQArith__base_2eQcompare___24a2(V0__p,V1__q) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__p),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__q))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__q),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__p)))) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__4450] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__4450)
& ? [Vvar__1__Qden__4451] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__4451)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__4450,Vvar__1__Qden__4451)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__4451 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qeq',axiom,
! [V0__p,V1__q] :
( cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__p,V1__q)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__p),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__q))) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__q),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__p))) ) ).
fof('$_def_Coq.QArith.QArith_base.Qeq_bool',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)))) ).
fof('$_def_Coq.QArith.QArith_base.Qle',axiom,
! [V0__x,V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQle___24a2(V0__x,V1__y)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x))))) ) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__4445] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__4445)
& ? [Vvar__1__Qden__4446] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__4446)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__4445,Vvar__1__Qden__4446)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__4445 ) ) ) ).
fof('$_def_Coq.Reals.RIneq.Rsqr',axiom,
! [V0__r] : cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r) ).
fof('$_def_Coq.Reals.RIneq.nonzero',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V0__n)
=> ? [Vvar__0__nonzero__43937] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__43937)
& Vvar__0__nonzero__43937 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V0__n = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__43937)
& cCoq_2eReals_2eRIneq_2enonzero___24a1(V0__n) = Vvar__0__nonzero__43937 ) ) ).
fof('$_def_Coq.Reals.R_Ifp.frac_part',axiom,
! [V0__r] : cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eReals_2eR__Ifp_2eInt__part___24a1(V0__r))) ).
fof('$_def_Coq.Reals.Raxioms.INR',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__43950] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43950)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43950)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43950)
& ( ( Vvar__0___24Anonymous__43950 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__43953] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43953)
& Vvar__0___24Anonymous__43950 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43953)
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(Vvar__0___24Anonymous__43950),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rabs',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__r) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) )
| ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__r) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = V0__r ) ) ) ).
fof('$_def_Coq.Reals.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__4031] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4031)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4031)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__4031) )
| ? [Vvar__0___24Anonymous__4032] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4032)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4032)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__4032)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rfunctions.powerRZ',axiom,
! [V0__x,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__4035] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4035)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4035)
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__4035)) )
| ? [Vvar__0___24Anonymous__4036] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4036)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4036)
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__4036))) ) ) ) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__4041] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4041)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4041)
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r,cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,Vvar__0___24Anonymous__4041)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__39236___24a1(V0__A) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Strings.Ascii.ascii_rec',axiom,
! [V0__P] : cCoq_2eStrings_2eAscii_2eascii__rec___24a1(V0__P) = cCoq_2eStrings_2eAscii_2eascii__rect___24a1(V0__P) ).
fof('$_def_Coq.Strings.Ascii.eqb',axiom,
! [V0__a,V1__b] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V0__a)
=> ? [Vvar__0___24Anonymous__36398] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__36398)
& ? [Vvar__1___24Anonymous__36399] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__36399)
& ? [Vvar__2___24Anonymous__36400] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__36400)
& ? [Vvar__3___24Anonymous__36401] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__36401)
& ? [Vvar__4___24Anonymous__36402] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__36402)
& ? [Vvar__5___24Anonymous__36403] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__36403)
& ? [Vvar__6___24Anonymous__36404] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__36404)
& ? [Vvar__7___24Anonymous__36405] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__36405)
& ( cCoq_2eStrings_2eAscii_2eascii___24t(V1__b)
=> ( V0__a = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__36398,Vvar__1___24Anonymous__36399,Vvar__2___24Anonymous__36400,Vvar__3___24Anonymous__36401,Vvar__4___24Anonymous__36402,Vvar__5___24Anonymous__36403,Vvar__6___24Anonymous__36404,Vvar__7___24Anonymous__36405)
& ? [Vvar__0___24Anonymous__36562] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__36562)
& ? [Vvar__1___24Anonymous__36563] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__36563)
& ? [Vvar__2___24Anonymous__36564] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__36564)
& ? [Vvar__3___24Anonymous__36565] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__36565)
& ? [Vvar__4___24Anonymous__36566] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__36566)
& ? [Vvar__5___24Anonymous__36567] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__36567)
& ? [Vvar__6___24Anonymous__36568] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__36568)
& ? [Vvar__7___24Anonymous__36569] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__36569)
& ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__36398)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__36399)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__36400)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__36401)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__36402)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__36403)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__36404)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__36562)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__36563)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__36564)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__36565)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__36566)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__36567)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__36568)
=> ( V1__b = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__36562,Vvar__1___24Anonymous__36563,Vvar__2___24Anonymous__36564,Vvar__3___24Anonymous__36565,Vvar__4___24Anonymous__36566,Vvar__5___24Anonymous__36567,Vvar__6___24Anonymous__36568,Vvar__7___24Anonymous__36569)
& ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436738___24a14(Vvar__0___24Anonymous__36398,Vvar__1___24Anonymous__36399,Vvar__2___24Anonymous__36400,Vvar__3___24Anonymous__36401,Vvar__4___24Anonymous__36402,Vvar__5___24Anonymous__36403,Vvar__6___24Anonymous__36404,Vvar__0___24Anonymous__36562,Vvar__1___24Anonymous__36563,Vvar__2___24Anonymous__36564,Vvar__3___24Anonymous__36565,Vvar__4___24Anonymous__36566,Vvar__5___24Anonymous__36567,Vvar__6___24Anonymous__36568) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eStrings_2eAscii_2eeqb___24a2(V0__a,V1__b) = cCoq_2eBool_2eBool_2eeqb___24a2(Vvar__7___24Anonymous__36405,Vvar__7___24Anonymous__36569) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436738___24a14(Vvar__0___24Anonymous__36398,Vvar__1___24Anonymous__36399,Vvar__2___24Anonymous__36400,Vvar__3___24Anonymous__36401,Vvar__4___24Anonymous__36402,Vvar__5___24Anonymous__36403,Vvar__6___24Anonymous__36404,Vvar__0___24Anonymous__36562,Vvar__1___24Anonymous__36563,Vvar__2___24Anonymous__36564,Vvar__3___24Anonymous__36565,Vvar__4___24Anonymous__36566,Vvar__5___24Anonymous__36567,Vvar__6___24Anonymous__36568) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eStrings_2eAscii_2eeqb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Strings.String.eqb',axiom,
! [V1__s1,V2__s2] :
( cCoq_2eStrings_2eString_2estring___24t(V1__s1)
=> ( ( cCoq_2eStrings_2eString_2estring___24t(V2__s2)
=> ( V1__s1 = cCoq_2eStrings_2eString_2eEmptyString
& ( ( V2__s2 = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2eeqb___24a2(V1__s1,V2__s2) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__58795] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__58795)
& ? [Vvar__1___24Anonymous__58796] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__58796)
& V2__s2 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__58795,Vvar__1___24Anonymous__58796)
& cCoq_2eStrings_2eString_2eeqb___24a2(V1__s1,V2__s2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__58798] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__58798)
& ? [Vvar__1___24Anonymous__58799] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__58799)
& ( cCoq_2eStrings_2eString_2estring___24t(V2__s2)
=> ( V1__s1 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__58798,Vvar__1___24Anonymous__58799)
& ( ( V2__s2 = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2eeqb___24a2(V1__s1,V2__s2) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__58809] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__58809)
& ? [Vvar__1___24Anonymous__58810] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__58810)
& ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__58798)
=> ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__58809)
=> ( V2__s2 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__58809,Vvar__1___24Anonymous__58810)
& ( ( cCoq_2eStrings_2eAscii_2eeqb___24a2(Vvar__0___24Anonymous__58798,Vvar__0___24Anonymous__58809) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eStrings_2eString_2eeqb___24a2(V1__s1,V2__s2) = cCoq_2eStrings_2eString_2eeqb___24a2(Vvar__1___24Anonymous__58799,Vvar__1___24Anonymous__58810) )
| ( cCoq_2eStrings_2eAscii_2eeqb___24a2(Vvar__0___24Anonymous__58798,Vvar__0___24Anonymous__58809) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eStrings_2eString_2eeqb___24a2(V1__s1,V2__s2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Strings.String.length',axiom,
! [V1__s] :
( cCoq_2eStrings_2eString_2estring___24t(V1__s)
=> ( ( V1__s = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2elength___24a1(V1__s) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__3433] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__3433)
& ? [Vvar__1___24Anonymous__3434] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__3434)
& V1__s = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__3433,Vvar__1___24Anonymous__3434)
& cCoq_2eStrings_2eString_2elength___24a1(V1__s) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eStrings_2eString_2elength___24a1(Vvar__1___24Anonymous__3434)) ) ) ) ) ).
fof('$_def_Coq.Strings.String.prefix',axiom,
! [V1__s1,V2__s2] :
( cCoq_2eStrings_2eString_2estring___24t(V1__s1)
=> ( ( V1__s1 = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2eprefix___24a2(V1__s1,V2__s2) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__4058] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__4058)
& ? [Vvar__1___24Anonymous__4059] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__4059)
& ( cCoq_2eStrings_2eString_2estring___24t(V2__s2)
=> ( V1__s1 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__4058,Vvar__1___24Anonymous__4059)
& ( ( V2__s2 = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2eprefix___24a2(V1__s1,V2__s2) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__4073] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__4073)
& ? [Vvar__1___24Anonymous__4074] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__4074)
& ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__4058)
=> ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__4073)
=> ( V2__s2 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__4073,Vvar__1___24Anonymous__4074)
& ( ( Vvar__0___24Anonymous__4058 = Vvar__0___24Anonymous__4073
& cCoq_2eStrings_2eAscii_2eascii__dec___24a2(Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__4090___24a2(Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073),c_24__prop__4091___24a2(Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073))
& cCoq_2eStrings_2eString_2eprefix___24a2(V1__s1,V2__s2) = cCoq_2eStrings_2eString_2eprefix___24a2(Vvar__1___24Anonymous__4059,Vvar__1___24Anonymous__4074) )
| ( Vvar__0___24Anonymous__4058 != Vvar__0___24Anonymous__4073
& cCoq_2eStrings_2eAscii_2eascii__dec___24a2(Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__4092___24a2(Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073),c_24__prop__4093___24a2(Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073))
& cCoq_2eStrings_2eString_2eprefix___24a2(V1__s1,V2__s2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Strings.String.string_rec',axiom,
! [V0__P] : cCoq_2eStrings_2eString_2estring__rec___24a1(V0__P) = cCoq_2eStrings_2eString_2estring__rect___24a1(V0__P) ).
fof('$_def_Coq.Strings.String.substring',axiom,
! [V1__n,V2__m,V3__s] :
( 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_2eStrings_2eString_2esubstring___24a3(V1__n,V2__m,V3__s) = cCoq_2eStrings_2eString_2eEmptyString )
| ? [Vvar__0___24Anonymous__3439] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3439)
& ( cCoq_2eStrings_2eString_2estring___24t(V3__s)
=> ( V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3439)
& ( ( V3__s = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2esubstring___24a3(V1__n,V2__m,V3__s) = V3__s )
| ? [Vvar__0___24Anonymous__3443] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__3443)
& ? [Vvar__1___24Anonymous__3444] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__3444)
& V3__s = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__3443,Vvar__1___24Anonymous__3444)
& cCoq_2eStrings_2eString_2esubstring___24a3(V1__n,V2__m,V3__s) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__3443,cCoq_2eStrings_2eString_2esubstring___24a3(cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__3439,Vvar__1___24Anonymous__3444)) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__3446] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3446)
& ( cCoq_2eStrings_2eString_2estring___24t(V3__s)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3446)
& ( ( V3__s = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2esubstring___24a3(V1__n,V2__m,V3__s) = V3__s )
| ? [Vvar__0___24Anonymous__3450] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__3450)
& ? [Vvar__1___24Anonymous__3451] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__3451)
& V3__s = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__3450,Vvar__1___24Anonymous__3451)
& cCoq_2eStrings_2eString_2esubstring___24a3(V1__n,V2__m,V3__s) = cCoq_2eStrings_2eString_2esubstring___24a3(Vvar__0___24Anonymous__3446,V2__m,Vvar__1___24Anonymous__3451) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.eq_dec',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq__dec = cCoq_2eNArith_2eBinNat_2eN_2eeq__dec ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq_dec',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq__dec = cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt = cCoq_2eInit_2ePeano_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__64733] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__64733)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__64733) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__64684] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64684)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64684)
& ( ? [Vvar__0___24Anonymous__64688] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64688)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64688)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__64684,Vvar__0___24Anonymous__64688) ) )
| ? [Vvar__0___24Anonymous__64689] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64689)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64689)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__64690] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64690)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64690)
& ( ? [Vvar__0___24Anonymous__64694] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64694)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64694)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__64695] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64695)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64695)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__64690,Vvar__0___24Anonymous__64695) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__64696] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64696)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64696)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__64697] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64697)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64697)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt = cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__64681] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__64681)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__64681) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq_dec',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq__dec = cCoq_2ePArith_2eBinPos_2ePos_2eeq__dec ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt = cCoq_2ePArith_2eBinPos_2ePos_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__64782] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__64782)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__64782) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq = c_3d___24a1(cCoq_2eStrings_2eString_2estring) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.eq_dec',axiom,
! [V0__x,V1__y] : cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq__dec___24a2(V0__x,V1__y) = cCoq_2eStrings_2eString_2estring__dec___24a2(V0__x,V1__y) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt = cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__64785] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__64785)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__64785) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq_dec',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq__dec = cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec ).
fof('$_def_Coq.Vectors.Fin.eqb',axiom,
! [V1__m,V2__n,V3__p,V4__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eVectors_2eFin_2et___24t(V1__m,V3__p)
=> ( ? [Vvar__0__n__41237] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__41237)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eVectors_2eFin_2et___24t(V2__n,V4__q)
=> ( V3__p = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__41237)
& ( ? [Vvar__0__n__41244] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__41244)
& V4__q = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__41244)
& cCoq_2eVectors_2eFin_2eeqb___24a4(V1__m,V2__n,V3__p,V4__q) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0__n__41237,Vvar__0__n__41244) )
| ? [Vvar__0__n__41245] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__41245)
& ? [Vvar__1___24Anonymous__41246] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__41245,Vvar__1___24Anonymous__41246)
& V4__q = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__41245,Vvar__1___24Anonymous__41246)
& cCoq_2eVectors_2eFin_2eeqb___24a4(V1__m,V2__n,V3__p,V4__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__0__n__41248] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__41248)
& ? [Vvar__1___24Anonymous__41249] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__41248,Vvar__1___24Anonymous__41249)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eVectors_2eFin_2et___24t(V2__n,V4__q)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__41248)
=> ( V3__p = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__41248,Vvar__1___24Anonymous__41249)
& ( ? [Vvar__0__n__41262] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__41262)
& V4__q = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__41262)
& cCoq_2eVectors_2eFin_2eeqb___24a4(V1__m,V2__n,V3__p,V4__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0__n__41263] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__41263)
& ? [Vvar__1___24Anonymous__41264] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__41263,Vvar__1___24Anonymous__41264)
& V4__q = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__41263,Vvar__1___24Anonymous__41264)
& cCoq_2eVectors_2eFin_2eeqb___24a4(V1__m,V2__n,V3__p,V4__q) = cCoq_2eVectors_2eFin_2eeqb___24a4(Vvar__0__n__41248,Vvar__0__n__41263,Vvar__1___24Anonymous__41249,Vvar__1___24Anonymous__41264) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorEq.eqb',axiom,
! [V0__A,V1__A__beq,V3__m,V4__n,V5__v1,V6__v2] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__m,V5__v1)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V6__v2)
=> ( V5__v1 = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& ( ( V6__v2 = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,V3__m,V4__n,V5__v1,V6__v2) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1__h__58914] :
( t(Vvar__1__h__58914,V0__A)
& ? [Vvar__2__n__58915] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__58915)
& ? [Vvar__3___24Anonymous__58916] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__58915,Vvar__3___24Anonymous__58916)
& V6__v2 = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__58914,Vvar__2__n__58915,Vvar__3___24Anonymous__58916)
& cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,V3__m,V4__n,V5__v1,V6__v2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1__h__58921] :
( t(Vvar__1__h__58921,V0__A)
& ? [Vvar__2__n__58922] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__58922)
& ? [Vvar__3___24Anonymous__58923] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__58922,Vvar__3___24Anonymous__58923)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V6__v2)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__58922)
=> ( V5__v1 = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__58921,Vvar__2__n__58922,Vvar__3___24Anonymous__58923)
& ( ( V6__v2 = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,V3__m,V4__n,V5__v1,V6__v2) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1__h__58946] :
( t(Vvar__1__h__58946,V0__A)
& ? [Vvar__2__n__58947] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__58947)
& ? [Vvar__3___24Anonymous__58948] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__58947,Vvar__3___24Anonymous__58948)
& V6__v2 = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__58946,Vvar__2__n__58947,Vvar__3___24Anonymous__58948)
& cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,V3__m,V4__n,V5__v1,V6__v2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(happ(V1__A__beq,Vvar__1__h__58921),Vvar__1__h__58946),cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,Vvar__2__n__58922,Vvar__2__n__58947,Vvar__3___24Anonymous__58923,Vvar__3___24Anonymous__58948)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.clearbit',axiom,
! [V0__a,V1__n] : cCoq_2eZArith_2eBinInt_2eZ_2eclearbit___24a2(V0__a,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eldiff___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__n)) ).
fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__61287] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61287)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61287)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61287) )
| ? [Vvar__0___24Anonymous__61288] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61288)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61288)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61288) ) ) ) ).
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__61264] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61264)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61264)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__61268] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61268)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61268)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__61264,Vvar__0___24Anonymous__61268)) )
| ? [Vvar__0___24Anonymous__61269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61269)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61269)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__61264,Vvar__0___24Anonymous__61269) ) ) ) ) )
| ? [Vvar__0___24Anonymous__61270] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61270)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61270)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__61274] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61274)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61274)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__61274,Vvar__0___24Anonymous__61270) )
| ? [Vvar__0___24Anonymous__61275] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61275)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61275)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__61270,Vvar__0___24Anonymous__61275)) ) ) ) ) ) ) ) ).
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__6694] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6694)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__6694)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__6695] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6695)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__6695)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__6696] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6696)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__6696)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__6700] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6700)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__6700)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__6696,Vvar__0___24Anonymous__6700) )
| ? [Vvar__0___24Anonymous__6701] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6701)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__6701)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__6702] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6702)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__6702)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__6706] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6706)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__6706)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__6707] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6707)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__6707)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__6702,Vvar__0___24Anonymous__6707)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__64818] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__64818)
& ? [Vvar__3___24Anonymous__64819] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__64819)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__64818,Vvar__3___24Anonymous__64819)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__64818 ) ) ) ) ).
fof('$_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__6712] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6712)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__6712)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__6713] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6713)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__6713)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__6714] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6714)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__6714)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__6718] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6718)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__6718)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__6714,Vvar__0___24Anonymous__6718) )
| ? [Vvar__0___24Anonymous__6719] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6719)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__6719)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__6720] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6720)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__6720)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__6724] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6724)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__6724)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__6725] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6725)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__6725)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__6720,Vvar__0___24Anonymous__6725) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.even',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__64823] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64823)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64823)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__64823)
& ( ? [Vvar__0___24Anonymous__64827] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64827)
& Vvar__0___24Anonymous__64823 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64827)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__64828] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64828)
& Vvar__0___24Anonymous__64823 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64828)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__64823 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__64829] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64829)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64829)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__64829)
& ( ? [Vvar__0___24Anonymous__64833] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64833)
& Vvar__0___24Anonymous__64829 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64833)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__64834] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64834)
& Vvar__0___24Anonymous__64829 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64834)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__64829 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
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__61365] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61365)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61365)
& ( ( 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__61369] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61369)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61369)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__61365,Vvar__0___24Anonymous__61369)) )
| ? [Vvar__0___24Anonymous__61370] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61370)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61370)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__61365,Vvar__0___24Anonymous__61370)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__61371] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61371)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61371)
& ( ( 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__61375] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61375)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61375)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__61371,Vvar__0___24Anonymous__61375)) )
| ? [Vvar__0___24Anonymous__61376] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61376)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61376)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__61371,Vvar__0___24Anonymous__61376)) ) ) ) ) ) ) ) ).
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__64847] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64847)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64847)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__64847)
& ( ? [Vvar__0___24Anonymous__64851] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64851)
& Vvar__0___24Anonymous__64847 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64851)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__64851)) )
| ? [Vvar__0___24Anonymous__64852] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64852)
& Vvar__0___24Anonymous__64847 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64852)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__64852)) )
| ( Vvar__0___24Anonymous__64847 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
| ? [Vvar__0___24Anonymous__64853] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64853)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__64853)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.ltb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__61293] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__61293)
& ? [Vvar__3___24Anonymous__61294] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__61294)
& 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__61293,Vvar__3___24Anonymous__61294)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__61294 ) ) ) ) ).
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__6679] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6679)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__6679)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__6683] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6683)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__6683)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__6679,Vvar__0___24Anonymous__6683)) )
| ? [Vvar__0___24Anonymous__6684] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6684)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__6684)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__6679,Vvar__0___24Anonymous__6684)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__6685] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6685)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__6685)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__6689] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6689)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__6689)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__6685,Vvar__0___24Anonymous__6689)) )
| ? [Vvar__0___24Anonymous__6690] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6690)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__6690)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__6685,Vvar__0___24Anonymous__6690)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.odd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__64835] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64835)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64835)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__64835)
& ( ? [Vvar__0___24Anonymous__64839] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64839)
& Vvar__0___24Anonymous__64835 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64839)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__64840] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64840)
& Vvar__0___24Anonymous__64835 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64840)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__64835 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__64841] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64841)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64841)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__64841)
& ( ? [Vvar__0___24Anonymous__64845] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64845)
& Vvar__0___24Anonymous__64841 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64845)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__64846] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64846)
& Vvar__0___24Anonymous__64841 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64846)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__64841 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__64811] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64811)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__64811)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__64811) ) ) ) ).
fof('$_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__64808] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__64808)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__64808)
& 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__64808)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__61277] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61277)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61277)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61277) )
| ? [Vvar__0___24Anonymous__61278] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61278)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61278)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61278) ) ) ) ).
fof('$_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__61280] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61280)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61280)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__61280) )
| ? [Vvar__0___24Anonymous__61281] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61281)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61281)
& 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.quotrem',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__61297] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61297)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61297)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__61307] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61307)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61297)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61307)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61307)
& ? [Vvar__2___24Anonymous__61315] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__61315)
& ? [Vvar__3___24Anonymous__61316] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__61316)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__61297,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__61307)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__61315,Vvar__3___24Anonymous__61316)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__61315),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__61316)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__61318] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61318)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61297)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61318)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61318)
& ? [Vvar__2___24Anonymous__61326] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__61326)
& ? [Vvar__3___24Anonymous__61327] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__61327)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__61297,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__61318)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__61326,Vvar__3___24Anonymous__61327)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__61326)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__61327)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__61329] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61329)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61329)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__61339] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61339)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61329)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61339)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61339)
& ? [Vvar__2___24Anonymous__61347] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__61347)
& ? [Vvar__3___24Anonymous__61348] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__61348)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__61329,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__61339)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__61347,Vvar__3___24Anonymous__61348)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__61347)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__61348))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__61350] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61350)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61329)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61350)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61350)
& ? [Vvar__2___24Anonymous__61358] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__61358)
& ? [Vvar__3___24Anonymous__61359] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__61359)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__61329,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__61350)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__61358,Vvar__3___24Anonymous__61359)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__61358),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__61359))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.ZArith.BinIntDef.Z.sgn',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__61283] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61283)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61283)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__61284] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61284)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61284)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__61378] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61378)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61378)
& ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__61382] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61382)
& V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__61382)
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__61382,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__61378)) )
| ? [Vvar__0___24Anonymous__61383] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61383)
& V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61383)
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__61383),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__61378))) ) ) ) ) )
| ? [Vvar__0___24Anonymous__61384] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__61384)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61384)
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__64804] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64804)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__64804)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__64804) )
| ? [Vvar__0___24Anonymous__64805] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64805)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__64805)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.ZArith.ZArith_dec.Z_zerop',axiom,
! [V0__x] : cCoq_2eZArith_2eZArith__dec_2eZ__zerop___24a1(V0__x) = cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('$_def_Coq.ZArith.Zbool.Z_eq_bool',axiom,
! [V0__x,V1__y] : cCoq_2eZArith_2eZbool_2eZ__eq__bool___24a2(V0__x,V1__y) = cCoq_2eBool_2eSumbool_2ebool__of__sumbool___24a3(c_24__prop__4655___24a2(V0__x,V1__y),c_24__prop__4656___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec___24a2(V0__x,V1__y)) ).
fof('$_def_Coq.ZArith.Zbool.Z_noteq_bool',axiom,
! [V0__x,V1__y] : cCoq_2eZArith_2eZbool_2eZ__noteq__bool___24a2(V0__x,V1__y) = cCoq_2eBool_2eSumbool_2ebool__of__sumbool___24a3(c_24__prop__59773___24a2(V0__x,V1__y),c_24__prop__59774___24a2(V0__x,V1__y),cCoq_2eZArith_2eZArith__dec_2eZ__noteq__dec___24a2(V0__x,V1__y)) ).
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))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__r,V1__b)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V0__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__r,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ).
fof('$_def_Coq.ZArith.Zdiv.Remainder_alt',axiom,
! [V0__r,V1__b] :
( cCoq_2eZArith_2eZdiv_2eRemainder__alt___24a2(V0__r,V1__b)
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__r),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__b)))
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__r) != cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V1__b)) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zeven',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__64654] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64654)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64654)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__64654)
& ( ? [Vvar__0___24Anonymous__64658] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64658)
& Vvar__0___24Anonymous__64654 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64658)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__64659] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64659)
& Vvar__0___24Anonymous__64654 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64659)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__64654 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__64660] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64660)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64660)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__64660)
& ( ? [Vvar__0___24Anonymous__64664] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64664)
& Vvar__0___24Anonymous__64660 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64664)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__64665] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64665)
& Vvar__0___24Anonymous__64660 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64665)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__64660 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zodd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__64666] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64666)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64666)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__64666)
& ( ? [Vvar__0___24Anonymous__64670] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64670)
& Vvar__0___24Anonymous__64666 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64670)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__64671] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64671)
& Vvar__0___24Anonymous__64666 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64671)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__64666 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__64672] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64672)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64672)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__64672)
& ( ? [Vvar__0___24Anonymous__64676] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64676)
& Vvar__0___24Anonymous__64672 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64676)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__64677] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64677)
& Vvar__0___24Anonymous__64672 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64677)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__64672 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.Is_power',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__64679] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64679)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__64679)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__64680] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64680)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__64680)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__64680) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.ZArith.Znat.neq',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.Znumtheory.rel_prime',axiom,
! [V0__a,V1__b] :
( cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b)
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
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.RMicromega.Reval_op2',axiom,
! [V0__o] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V0__o)
=> ( ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR) )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = c_24__lam__43943 )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = cCoq_2eReals_2eRdefinitions_2eRle )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = cCoq_2eReals_2eRdefinitions_2eRge )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = cCoq_2eReals_2eRdefinitions_2eRlt )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = cCoq_2eReals_2eRdefinitions_2eRgt ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_conj',axiom,
! [V1__A,V2__eval,V3__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__43990] :
( t(Vvar__1___24Anonymous__43990,V1__A)
& ? [Vvar__2___24Anonymous__43991] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__43991)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__43991)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__43990,Vvar__2___24Anonymous__43991)
& ( ( Vvar__2___24Anonymous__43991 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(happ(V2__eval,Vvar__1___24Anonymous__43990)) ) )
| ? [Vvar__1___24Anonymous__44002] :
( t(Vvar__1___24Anonymous__44002,V1__A)
& ? [Vvar__2___24Anonymous__44003] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__44003)
& Vvar__2___24Anonymous__43991 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__44002,Vvar__2___24Anonymous__44003)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__43990))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__43991) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.NFormula',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C) = cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_def_Coq.micromega.RingMicromega.PolC',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).
fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).
fof('$_def_Coq.micromega.RingMicromega.cneqb',axiom,
! [V0__C,V1__ceqb,V2__x,V3__y] : cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V0__C,V1__ceqb,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2enegb___24a1(happ(happ(V1__ceqb,V2__x),V3__y)) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op1',axiom,
! [V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V5__o)
=> ( ( V5__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__49929___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__49937___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__49945___24a3(V0__R,V1__rO,V4__rlt) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__49953___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op2',axiom,
! [V0__R,V1__req,V2__rle,V3__rlt,V4__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V4__o)
=> ( ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V1__req )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__63652___24a2(V0__R,V1__req) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V2__rle )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__63660___24a2(V0__R,V2__rle) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__63668___24a2(V0__R,V3__rlt) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__63676___24a2(V0__R,V3__rlt) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.clause',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.eval_f',axiom,
! [V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f] :
( cType___24t(V0__TA)
=> ( cType___24t(V1__TX)
=> ( cType___24t(V2__AA)
=> ( cType___24t(V3__AF)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,V7__f)
=> ( ( V7__f = cCoq_2emicromega_2eTauto_2eTT___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24True) ) )
| ( V7__f = cCoq_2emicromega_2eTauto_2eFF___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24False) ) )
| ? [Vvar__4___24Anonymous__64567] :
( t(Vvar__4___24Anonymous__64567,V1__TX)
& V7__f = cCoq_2emicromega_2eTauto_2eX___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__64567)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(happ(V4__ex,Vvar__4___24Anonymous__64567)) ) )
| ? [Vvar__4___24Anonymous__64572] :
( t(Vvar__4___24Anonymous__64572,V0__TA)
& ? [Vvar__5___24Anonymous__64573] :
( t(Vvar__5___24Anonymous__64573,V2__AA)
& V7__f = cCoq_2emicromega_2eTauto_2eA___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__64572,Vvar__5___24Anonymous__64573)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(happ(V5__ea,Vvar__4___24Anonymous__64572)) ) ) )
| ? [Vvar__4___24Anonymous__64579] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__64579)
& ? [Vvar__5___24Anonymous__64580] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__64580)
& V7__f = cCoq_2emicromega_2eTauto_2eCj___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__64579,Vvar__5___24Anonymous__64580)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__64579)
& cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__64580) ) ) ) )
| ? [Vvar__4___24Anonymous__64586] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__64586)
& ? [Vvar__5___24Anonymous__64587] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__64587)
& V7__f = cCoq_2emicromega_2eTauto_2eD___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__64586,Vvar__5___24Anonymous__64587)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__64586)
| cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__64587) ) ) ) )
| ? [Vvar__4___24Anonymous__64593] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__64593)
& V7__f = cCoq_2emicromega_2eTauto_2eN___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__64593)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ~ cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__64593) ) )
| ? [Vvar__4___24Anonymous__64598] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__64598)
& ? [Vvar__5___24Anonymous__64599] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V3__AF,Vvar__5___24Anonymous__64599)
& ? [Vvar__6___24Anonymous__64600] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__64600)
& V7__f = cCoq_2emicromega_2eTauto_2eI___24a7(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__64598,Vvar__5___24Anonymous__64599,Vvar__6___24Anonymous__64600)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__64598)
=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__6___24Anonymous__64600) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.eval_tt',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt] :
( cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt)
<=> p(happ(happ(V3__eval_27,V4__env),cCoq_2eInit_2eDatatypes_2efst___24a3(V1__Term_27,V2__Annot,V5__tt))) ) ).
fof('$_def_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
! [V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp] : cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a6(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.eqb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( V0__x = V1__y
& cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__60386___24a2(V0__x,V1__y),c_24__prop__60387___24a2(V0__x,V1__y))
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__x != V1__y
& cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__60388___24a2(V0__x,V1__y),c_24__prop__60389___24a2(V0__x,V1__y))
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.Zeval_op1',axiom,
! [V0__o] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V0__o)
=> ( ( V0__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eZMicromega_2eZeval__op1___24a1(V0__o) = c_24__lam__59762 )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eZMicromega_2eZeval__op1___24a1(V0__o) = c_24__lam__59763 )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eZMicromega_2eZeval__op1___24a1(V0__o) = c_24__lam__59764 )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eZMicromega_2eZeval__op1___24a1(V0__o) = c_24__lam__59765 ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.Zeval_op2',axiom,
! [V0__o] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V0__o)
=> ( ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = c_24__lam__59756 )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2ele )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2ege )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2elt )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2egt ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.isZ0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__59769] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__59769)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__59769)
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__59770] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__59770)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__59770)
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_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__39851] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__39851)
& ? [Vvar__2___24Anonymous__39852] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__39852)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__39851,Vvar__2___24Anonymous__39852)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__39851),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__39852,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.PCond',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__le)
=> ( ( V15__le = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__39557] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__39557)
& ? [Vvar__2___24Anonymous__39558] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__39558)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__39558)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__39557,Vvar__2___24Anonymous__39558)
& ( ( Vvar__2___24Anonymous__39558 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__39557)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__39569] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__39569)
& ? [Vvar__2___24Anonymous__39570] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__39570)
& Vvar__2___24Anonymous__39558 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__39569,Vvar__2___24Anonymous__39570)
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ( ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__39557)),V1__rO))
& cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__39558) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__61948] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__61948)
& ? [Vvar__2__denum__61949] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__61949)
& ? [Vvar__3__condition__61950] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__61950)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__61948,Vvar__2__denum__61949,Vvar__3__condition__61950)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__61950 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__61939] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__61939)
& ? [Vvar__2__denum__61940] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__61940)
& ? [Vvar__3__condition__61941] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__61941)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__61939,Vvar__2__denum__61940,Vvar__3__condition__61941)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__61940 ) ) ) ) ) ).
fof('$_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__61928] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__61928)
& ? [Vvar__2__denum__61929] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__61929)
& ? [Vvar__3__condition__61930] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__61930)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__61928,Vvar__2__denum__61929,Vvar__3__condition__61930)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__61928 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__63108] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63108)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63108)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__63108)
& ( ? [Vvar__0___24Anonymous__63112] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63112)
& Vvar__0___24Anonymous__63108 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__63112)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__63108))) )
| ? [Vvar__0___24Anonymous__63113] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63113)
& Vvar__0___24Anonymous__63108 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__63113)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__63108))) )
| ( Vvar__0___24Anonymous__63108 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V2__radd,V1__rI),V1__rI)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__63114] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63114)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63114)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__63114)
& ( ? [Vvar__0___24Anonymous__63118] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63118)
& Vvar__0___24Anonymous__63114 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__63118)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__63114)) )
| ? [Vvar__0___24Anonymous__63119] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63119)
& Vvar__0___24Anonymous__63114 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__63119)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__63114)) )
| ( Vvar__0___24Anonymous__63114 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),V1__rI) ) ) ) ) ) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__41553] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41553)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__41553)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__41553))) )
| ? [Vvar__0___24Anonymous__41554] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41554)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__41554)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__41554)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__63142] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63142)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__63142)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__63142) )
| ? [Vvar__0___24Anonymous__63143] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__63143)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__63143)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__63143)) ) ) ) ) ).
fof('$_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__51640] :
( t(Vvar__1___24Anonymous__51640,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__51640)
& 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__51640) )
| ? [Vvar__1___24Anonymous__51642] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__51642)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__51642)
& 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__51642,V13__l) )
| ? [Vvar__1___24Anonymous__51644] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__51644)
& ? [Vvar__2___24Anonymous__51645] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__51645)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__51644,Vvar__2___24Anonymous__51645)
& 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__51644)),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__51645)) ) )
| ? [Vvar__1___24Anonymous__51648] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__51648)
& ? [Vvar__2___24Anonymous__51649] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__51649)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__51648,Vvar__2___24Anonymous__51649)
& 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__51648)),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__51649)) ) )
| ? [Vvar__1___24Anonymous__51652] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__51652)
& ? [Vvar__2___24Anonymous__51653] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__51653)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__51652,Vvar__2___24Anonymous__51653)
& 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__51652)),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__51653)) ) )
| ? [Vvar__1___24Anonymous__51656] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__51656)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__51656)
& 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__51656)) )
| ? [Vvar__1___24Anonymous__51658] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__51658)
& ? [Vvar__2___24Anonymous__51659] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__51659)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__51658,Vvar__2___24Anonymous__51659)
& 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__51658)),happ(V10__Cp__phi,Vvar__2___24Anonymous__51659)) ) ) ) ) ) ) ) ).
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__51214] :
( t(Vvar__1___24Anonymous__51214,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__51214)
& ( ? [Vvar__1___24Anonymous__51224] :
( t(Vvar__1___24Anonymous__51224,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__51224)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__51214),Vvar__1___24Anonymous__51224) )
| ? [Vvar__1___24Anonymous__51226] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__51226)
& ? [Vvar__2___24Anonymous__51227] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__51227)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__51226,Vvar__2___24Anonymous__51227)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__51230] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__51230)
& ? [Vvar__2___24Anonymous__51231] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__51231)
& ? [Vvar__3___24Anonymous__51232] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__51232)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__51230,Vvar__2___24Anonymous__51231,Vvar__3___24Anonymous__51232)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__51237] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__51237)
& ? [Vvar__2___24Anonymous__51238] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__51238)
& ( 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__51237,Vvar__2___24Anonymous__51238)
& ( ? [Vvar__1___24Anonymous__51258] :
( t(Vvar__1___24Anonymous__51258,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__51258)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__51260] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__51260)
& ? [Vvar__2___24Anonymous__51261] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__51261)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__51237)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__51260)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__51260,Vvar__2___24Anonymous__51261)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__51237,Vvar__1___24Anonymous__51260) = 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__51238,Vvar__2___24Anonymous__51261) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__51237,Vvar__1___24Anonymous__51260) = 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__51237,Vvar__1___24Anonymous__51260) = 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__51266] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__51266)
& ? [Vvar__2___24Anonymous__51267] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__51267)
& ? [Vvar__3___24Anonymous__51268] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__51268)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__51266,Vvar__2___24Anonymous__51267,Vvar__3___24Anonymous__51268)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__51273] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__51273)
& ? [Vvar__2___24Anonymous__51274] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__51274)
& ? [Vvar__3___24Anonymous__51275] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__51275)
& ( 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__51273,Vvar__2___24Anonymous__51274,Vvar__3___24Anonymous__51275)
& ( ? [Vvar__1___24Anonymous__51308] :
( t(Vvar__1___24Anonymous__51308,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__51308)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__51310] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__51310)
& ? [Vvar__2___24Anonymous__51311] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__51311)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__51310,Vvar__2___24Anonymous__51311)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__51314] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__51314)
& ? [Vvar__2___24Anonymous__51315] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__51315)
& ? [Vvar__3___24Anonymous__51316] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__51316)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__51274)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__51315)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__51314,Vvar__2___24Anonymous__51315,Vvar__3___24Anonymous__51316)
& ( ( cType___24t(V0__C)
=> ( c_24__type__39494___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__51273)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__51314)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__51274,Vvar__2___24Anonymous__51315) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__51273,Vvar__1___24Anonymous__51314) = 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__51275,Vvar__3___24Anonymous__51316) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__51273,Vvar__1___24Anonymous__51314) = 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__51274,Vvar__2___24Anonymous__51315) = 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__51274,Vvar__2___24Anonymous__51315) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__51924___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.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__52271] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__52271)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__52271)
& 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__52271) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__52251] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__52251)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__52251)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__52252__52255___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__52251)),c_24__let__var__6__p__52252__52255___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__52251))) )
| ? [Vvar__0___24Anonymous__52253] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__52253)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__52253)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__52254__52256___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__52253)),c_24__let__var__6__p__52254__52256___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__52253)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_Redblack.TREES.balance',axiom,
! [V0__rb,V1__t1,V2__k,V3__vk,V4__t2] :
( cRedblack_2ecolor___24t(V0__rb)
=> ( ( V0__rb = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,V1__t1,V2__k,V3__vk,V4__t2) )
| ( cRedblack_2eTREES_2etree___24t(V1__t1)
=> ( V0__rb = cRedblack_2eBlack
& ( ( cRedblack_2eTREES_2etree___24t(V4__t2)
=> ( V1__t1 = cRedblack_2eTREES_2eE
& ( ( V4__t2 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__192] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__192)
& ? [Vvar__1___24Anonymous__193] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__193)
& ? [Vvar__2___24Anonymous__194] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__194)
& ? [Vvar__3___24Anonymous__195] :
( cV___24t(Vvar__3___24Anonymous__195)
& ? [Vvar__4___24Anonymous__196] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__196)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__192)
=> ( V4__t2 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__192,Vvar__1___24Anonymous__193,Vvar__2___24Anonymous__194,Vvar__3___24Anonymous__195,Vvar__4___24Anonymous__196)
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__193)
=> ( Vvar__0___24Anonymous__192 = cRedblack_2eRed
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__196)
=> ( Vvar__1___24Anonymous__193 = cRedblack_2eTREES_2eE
& ( ( Vvar__4___24Anonymous__196 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__317] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__317)
& ? [Vvar__1___24Anonymous__318] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__318)
& ? [Vvar__2___24Anonymous__319] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__319)
& ? [Vvar__3___24Anonymous__320] :
( cV___24t(Vvar__3___24Anonymous__320)
& ? [Vvar__4___24Anonymous__321] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__321)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__317)
=> ( Vvar__4___24Anonymous__196 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__317,Vvar__1___24Anonymous__318,Vvar__2___24Anonymous__319,Vvar__3___24Anonymous__320,Vvar__4___24Anonymous__321)
& ( ( Vvar__0___24Anonymous__317 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__193),Vvar__2___24Anonymous__194,Vvar__3___24Anonymous__195,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__318,Vvar__2___24Anonymous__319,Vvar__3___24Anonymous__320,Vvar__4___24Anonymous__321)) )
| ( Vvar__0___24Anonymous__317 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__337] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__337)
& ? [Vvar__1___24Anonymous__338] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__338)
& ? [Vvar__2___24Anonymous__339] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__339)
& ? [Vvar__3___24Anonymous__340] :
( cV___24t(Vvar__3___24Anonymous__340)
& ? [Vvar__4___24Anonymous__341] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__341)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__337)
=> ( Vvar__1___24Anonymous__193 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__337,Vvar__1___24Anonymous__338,Vvar__2___24Anonymous__339,Vvar__3___24Anonymous__340,Vvar__4___24Anonymous__341)
& ( ( Vvar__0___24Anonymous__337 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__338),Vvar__2___24Anonymous__339,Vvar__3___24Anonymous__340,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__4___24Anonymous__341,Vvar__2___24Anonymous__194,Vvar__3___24Anonymous__195,Vvar__4___24Anonymous__196)) )
| ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__196)
=> ( Vvar__0___24Anonymous__337 = cRedblack_2eBlack
& ( ( Vvar__4___24Anonymous__196 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__392] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__392)
& ? [Vvar__1___24Anonymous__393] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__393)
& ? [Vvar__2___24Anonymous__394] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__394)
& ? [Vvar__3___24Anonymous__395] :
( cV___24t(Vvar__3___24Anonymous__395)
& ? [Vvar__4___24Anonymous__396] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__396)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__392)
=> ( Vvar__4___24Anonymous__196 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__392,Vvar__1___24Anonymous__393,Vvar__2___24Anonymous__394,Vvar__3___24Anonymous__395,Vvar__4___24Anonymous__396)
& ( ( Vvar__0___24Anonymous__392 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__193),Vvar__2___24Anonymous__194,Vvar__3___24Anonymous__195,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__393,Vvar__2___24Anonymous__394,Vvar__3___24Anonymous__395,Vvar__4___24Anonymous__396)) )
| ( Vvar__0___24Anonymous__392 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( Vvar__0___24Anonymous__192 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__412] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__412)
& ? [Vvar__1___24Anonymous__413] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__413)
& ? [Vvar__2___24Anonymous__414] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__414)
& ? [Vvar__3___24Anonymous__415] :
( cV___24t(Vvar__3___24Anonymous__415)
& ? [Vvar__4___24Anonymous__416] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__416)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__412)
=> ( V1__t1 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__412,Vvar__1___24Anonymous__413,Vvar__2___24Anonymous__414,Vvar__3___24Anonymous__415,Vvar__4___24Anonymous__416)
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__413)
=> ( Vvar__0___24Anonymous__412 = cRedblack_2eRed
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__416)
=> ( Vvar__1___24Anonymous__413 = cRedblack_2eTREES_2eE
& ( ( cRedblack_2eTREES_2etree___24t(V4__t2)
=> ( Vvar__4___24Anonymous__416 = cRedblack_2eTREES_2eE
& ( ( V4__t2 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__1237] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1237)
& ? [Vvar__1___24Anonymous__1238] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1238)
& ? [Vvar__2___24Anonymous__1239] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__1239)
& ? [Vvar__3___24Anonymous__1240] :
( cV___24t(Vvar__3___24Anonymous__1240)
& ? [Vvar__4___24Anonymous__1241] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1241)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1237)
=> ( V4__t2 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__1237,Vvar__1___24Anonymous__1238,Vvar__2___24Anonymous__1239,Vvar__3___24Anonymous__1240,Vvar__4___24Anonymous__1241)
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1238)
=> ( Vvar__0___24Anonymous__1237 = cRedblack_2eRed
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1241)
=> ( Vvar__1___24Anonymous__1238 = cRedblack_2eTREES_2eE
& ( ( Vvar__4___24Anonymous__1241 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__1362] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1362)
& ? [Vvar__1___24Anonymous__1363] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1363)
& ? [Vvar__2___24Anonymous__1364] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__1364)
& ? [Vvar__3___24Anonymous__1365] :
( cV___24t(Vvar__3___24Anonymous__1365)
& ? [Vvar__4___24Anonymous__1366] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1366)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1362)
=> ( Vvar__4___24Anonymous__1241 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__1362,Vvar__1___24Anonymous__1363,Vvar__2___24Anonymous__1364,Vvar__3___24Anonymous__1365,Vvar__4___24Anonymous__1366)
& ( ( Vvar__0___24Anonymous__1362 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__1238),Vvar__2___24Anonymous__1239,Vvar__3___24Anonymous__1240,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__1363,Vvar__2___24Anonymous__1364,Vvar__3___24Anonymous__1365,Vvar__4___24Anonymous__1366)) )
| ( Vvar__0___24Anonymous__1362 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__1382] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1382)
& ? [Vvar__1___24Anonymous__1383] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1383)
& ? [Vvar__2___24Anonymous__1384] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__1384)
& ? [Vvar__3___24Anonymous__1385] :
( cV___24t(Vvar__3___24Anonymous__1385)
& ? [Vvar__4___24Anonymous__1386] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1386)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1382)
=> ( Vvar__1___24Anonymous__1238 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__1382,Vvar__1___24Anonymous__1383,Vvar__2___24Anonymous__1384,Vvar__3___24Anonymous__1385,Vvar__4___24Anonymous__1386)
& ( ( Vvar__0___24Anonymous__1382 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__1383),Vvar__2___24Anonymous__1384,Vvar__3___24Anonymous__1385,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__4___24Anonymous__1386,Vvar__2___24Anonymous__1239,Vvar__3___24Anonymous__1240,Vvar__4___24Anonymous__1241)) )
| ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1241)
=> ( Vvar__0___24Anonymous__1382 = cRedblack_2eBlack
& ( ( Vvar__4___24Anonymous__1241 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__1437] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1437)
& ? [Vvar__1___24Anonymous__1438] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1438)
& ? [Vvar__2___24Anonymous__1439] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__1439)
& ? [Vvar__3___24Anonymous__1440] :
( cV___24t(Vvar__3___24Anonymous__1440)
& ? [Vvar__4___24Anonymous__1441] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1441)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1437)
=> ( Vvar__4___24Anonymous__1241 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__1437,Vvar__1___24Anonymous__1438,Vvar__2___24Anonymous__1439,Vvar__3___24Anonymous__1440,Vvar__4___24Anonymous__1441)
& ( ( Vvar__0___24Anonymous__1437 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__1238),Vvar__2___24Anonymous__1239,Vvar__3___24Anonymous__1240,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__1438,Vvar__2___24Anonymous__1439,Vvar__3___24Anonymous__1440,Vvar__4___24Anonymous__1441)) )
| ( Vvar__0___24Anonymous__1437 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( Vvar__0___24Anonymous__1237 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__1457] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1457)
& ? [Vvar__1___24Anonymous__1458] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1458)
& ? [Vvar__2___24Anonymous__1459] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__1459)
& ? [Vvar__3___24Anonymous__1460] :
( cV___24t(Vvar__3___24Anonymous__1460)
& ? [Vvar__4___24Anonymous__1461] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1461)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1457)
=> ( Vvar__4___24Anonymous__416 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__1457,Vvar__1___24Anonymous__1458,Vvar__2___24Anonymous__1459,Vvar__3___24Anonymous__1460,Vvar__4___24Anonymous__1461)
& ( ( Vvar__0___24Anonymous__1457 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__413,Vvar__2___24Anonymous__414,Vvar__3___24Anonymous__415,Vvar__1___24Anonymous__1458),Vvar__2___24Anonymous__1459,Vvar__3___24Anonymous__1460,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__4___24Anonymous__1461,V2__k,V3__vk,V4__t2)) )
| ( cRedblack_2eTREES_2etree___24t(V4__t2)
=> ( Vvar__0___24Anonymous__1457 = cRedblack_2eBlack
& ( ( V4__t2 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__1617] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1617)
& ? [Vvar__1___24Anonymous__1618] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1618)
& ? [Vvar__2___24Anonymous__1619] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__1619)
& ? [Vvar__3___24Anonymous__1620] :
( cV___24t(Vvar__3___24Anonymous__1620)
& ? [Vvar__4___24Anonymous__1621] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1621)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1617)
=> ( V4__t2 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__1617,Vvar__1___24Anonymous__1618,Vvar__2___24Anonymous__1619,Vvar__3___24Anonymous__1620,Vvar__4___24Anonymous__1621)
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1618)
=> ( Vvar__0___24Anonymous__1617 = cRedblack_2eRed
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1621)
=> ( Vvar__1___24Anonymous__1618 = cRedblack_2eTREES_2eE
& ( ( Vvar__4___24Anonymous__1621 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__1742] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1742)
& ? [Vvar__1___24Anonymous__1743] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1743)
& ? [Vvar__2___24Anonymous__1744] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__1744)
& ? [Vvar__3___24Anonymous__1745] :
( cV___24t(Vvar__3___24Anonymous__1745)
& ? [Vvar__4___24Anonymous__1746] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1746)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1742)
=> ( Vvar__4___24Anonymous__1621 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__1742,Vvar__1___24Anonymous__1743,Vvar__2___24Anonymous__1744,Vvar__3___24Anonymous__1745,Vvar__4___24Anonymous__1746)
& ( ( Vvar__0___24Anonymous__1742 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__1618),Vvar__2___24Anonymous__1619,Vvar__3___24Anonymous__1620,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__1743,Vvar__2___24Anonymous__1744,Vvar__3___24Anonymous__1745,Vvar__4___24Anonymous__1746)) )
| ( Vvar__0___24Anonymous__1742 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__1762] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1762)
& ? [Vvar__1___24Anonymous__1763] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1763)
& ? [Vvar__2___24Anonymous__1764] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__1764)
& ? [Vvar__3___24Anonymous__1765] :
( cV___24t(Vvar__3___24Anonymous__1765)
& ? [Vvar__4___24Anonymous__1766] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1766)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1762)
=> ( Vvar__1___24Anonymous__1618 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__1762,Vvar__1___24Anonymous__1763,Vvar__2___24Anonymous__1764,Vvar__3___24Anonymous__1765,Vvar__4___24Anonymous__1766)
& ( ( Vvar__0___24Anonymous__1762 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__1763),Vvar__2___24Anonymous__1764,Vvar__3___24Anonymous__1765,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__4___24Anonymous__1766,Vvar__2___24Anonymous__1619,Vvar__3___24Anonymous__1620,Vvar__4___24Anonymous__1621)) )
| ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1621)
=> ( Vvar__0___24Anonymous__1762 = cRedblack_2eBlack
& ( ( Vvar__4___24Anonymous__1621 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__1817] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1817)
& ? [Vvar__1___24Anonymous__1818] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1818)
& ? [Vvar__2___24Anonymous__1819] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__1819)
& ? [Vvar__3___24Anonymous__1820] :
( cV___24t(Vvar__3___24Anonymous__1820)
& ? [Vvar__4___24Anonymous__1821] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1821)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1817)
=> ( Vvar__4___24Anonymous__1621 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__1817,Vvar__1___24Anonymous__1818,Vvar__2___24Anonymous__1819,Vvar__3___24Anonymous__1820,Vvar__4___24Anonymous__1821)
& ( ( Vvar__0___24Anonymous__1817 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__1618),Vvar__2___24Anonymous__1619,Vvar__3___24Anonymous__1620,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__1818,Vvar__2___24Anonymous__1819,Vvar__3___24Anonymous__1820,Vvar__4___24Anonymous__1821)) )
| ( Vvar__0___24Anonymous__1817 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( Vvar__0___24Anonymous__1617 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__1837] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1837)
& ? [Vvar__1___24Anonymous__1838] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__1838)
& ? [Vvar__2___24Anonymous__1839] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__1839)
& ? [Vvar__3___24Anonymous__1840] :
( cV___24t(Vvar__3___24Anonymous__1840)
& ? [Vvar__4___24Anonymous__1841] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__1841)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__1837)
=> ( Vvar__1___24Anonymous__413 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__1837,Vvar__1___24Anonymous__1838,Vvar__2___24Anonymous__1839,Vvar__3___24Anonymous__1840,Vvar__4___24Anonymous__1841)
& ( ( Vvar__0___24Anonymous__1837 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__1838,Vvar__2___24Anonymous__1839,Vvar__3___24Anonymous__1840,Vvar__4___24Anonymous__1841),Vvar__2___24Anonymous__414,Vvar__3___24Anonymous__415,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__4___24Anonymous__416,V2__k,V3__vk,V4__t2)) )
| ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__416)
=> ( Vvar__0___24Anonymous__1837 = cRedblack_2eBlack
& ( ( cRedblack_2eTREES_2etree___24t(V4__t2)
=> ( Vvar__4___24Anonymous__416 = cRedblack_2eTREES_2eE
& ( ( V4__t2 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__2172] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2172)
& ? [Vvar__1___24Anonymous__2173] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2173)
& ? [Vvar__2___24Anonymous__2174] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2174)
& ? [Vvar__3___24Anonymous__2175] :
( cV___24t(Vvar__3___24Anonymous__2175)
& ? [Vvar__4___24Anonymous__2176] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2176)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2172)
=> ( V4__t2 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2172,Vvar__1___24Anonymous__2173,Vvar__2___24Anonymous__2174,Vvar__3___24Anonymous__2175,Vvar__4___24Anonymous__2176)
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2173)
=> ( Vvar__0___24Anonymous__2172 = cRedblack_2eRed
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2176)
=> ( Vvar__1___24Anonymous__2173 = cRedblack_2eTREES_2eE
& ( ( Vvar__4___24Anonymous__2176 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__2297] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2297)
& ? [Vvar__1___24Anonymous__2298] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2298)
& ? [Vvar__2___24Anonymous__2299] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2299)
& ? [Vvar__3___24Anonymous__2300] :
( cV___24t(Vvar__3___24Anonymous__2300)
& ? [Vvar__4___24Anonymous__2301] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2301)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2297)
=> ( Vvar__4___24Anonymous__2176 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2297,Vvar__1___24Anonymous__2298,Vvar__2___24Anonymous__2299,Vvar__3___24Anonymous__2300,Vvar__4___24Anonymous__2301)
& ( ( Vvar__0___24Anonymous__2297 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__2173),Vvar__2___24Anonymous__2174,Vvar__3___24Anonymous__2175,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__2298,Vvar__2___24Anonymous__2299,Vvar__3___24Anonymous__2300,Vvar__4___24Anonymous__2301)) )
| ( Vvar__0___24Anonymous__2297 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2317] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2317)
& ? [Vvar__1___24Anonymous__2318] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2318)
& ? [Vvar__2___24Anonymous__2319] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2319)
& ? [Vvar__3___24Anonymous__2320] :
( cV___24t(Vvar__3___24Anonymous__2320)
& ? [Vvar__4___24Anonymous__2321] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2321)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2317)
=> ( Vvar__1___24Anonymous__2173 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2317,Vvar__1___24Anonymous__2318,Vvar__2___24Anonymous__2319,Vvar__3___24Anonymous__2320,Vvar__4___24Anonymous__2321)
& ( ( Vvar__0___24Anonymous__2317 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__2318),Vvar__2___24Anonymous__2319,Vvar__3___24Anonymous__2320,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__4___24Anonymous__2321,Vvar__2___24Anonymous__2174,Vvar__3___24Anonymous__2175,Vvar__4___24Anonymous__2176)) )
| ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2176)
=> ( Vvar__0___24Anonymous__2317 = cRedblack_2eBlack
& ( ( Vvar__4___24Anonymous__2176 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__2372] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2372)
& ? [Vvar__1___24Anonymous__2373] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2373)
& ? [Vvar__2___24Anonymous__2374] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2374)
& ? [Vvar__3___24Anonymous__2375] :
( cV___24t(Vvar__3___24Anonymous__2375)
& ? [Vvar__4___24Anonymous__2376] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2376)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2372)
=> ( Vvar__4___24Anonymous__2176 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2372,Vvar__1___24Anonymous__2373,Vvar__2___24Anonymous__2374,Vvar__3___24Anonymous__2375,Vvar__4___24Anonymous__2376)
& ( ( Vvar__0___24Anonymous__2372 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__2173),Vvar__2___24Anonymous__2174,Vvar__3___24Anonymous__2175,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__2373,Vvar__2___24Anonymous__2374,Vvar__3___24Anonymous__2375,Vvar__4___24Anonymous__2376)) )
| ( Vvar__0___24Anonymous__2372 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( Vvar__0___24Anonymous__2172 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2392] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2392)
& ? [Vvar__1___24Anonymous__2393] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2393)
& ? [Vvar__2___24Anonymous__2394] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2394)
& ? [Vvar__3___24Anonymous__2395] :
( cV___24t(Vvar__3___24Anonymous__2395)
& ? [Vvar__4___24Anonymous__2396] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2396)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2392)
=> ( Vvar__4___24Anonymous__416 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2392,Vvar__1___24Anonymous__2393,Vvar__2___24Anonymous__2394,Vvar__3___24Anonymous__2395,Vvar__4___24Anonymous__2396)
& ( ( Vvar__0___24Anonymous__2392 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__413,Vvar__2___24Anonymous__414,Vvar__3___24Anonymous__415,Vvar__1___24Anonymous__2393),Vvar__2___24Anonymous__2394,Vvar__3___24Anonymous__2395,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__4___24Anonymous__2396,V2__k,V3__vk,V4__t2)) )
| ( cRedblack_2eTREES_2etree___24t(V4__t2)
=> ( Vvar__0___24Anonymous__2392 = cRedblack_2eBlack
& ( ( V4__t2 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__2552] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2552)
& ? [Vvar__1___24Anonymous__2553] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2553)
& ? [Vvar__2___24Anonymous__2554] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2554)
& ? [Vvar__3___24Anonymous__2555] :
( cV___24t(Vvar__3___24Anonymous__2555)
& ? [Vvar__4___24Anonymous__2556] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2556)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2552)
=> ( V4__t2 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2552,Vvar__1___24Anonymous__2553,Vvar__2___24Anonymous__2554,Vvar__3___24Anonymous__2555,Vvar__4___24Anonymous__2556)
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2553)
=> ( Vvar__0___24Anonymous__2552 = cRedblack_2eRed
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2556)
=> ( Vvar__1___24Anonymous__2553 = cRedblack_2eTREES_2eE
& ( ( Vvar__4___24Anonymous__2556 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__2677] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2677)
& ? [Vvar__1___24Anonymous__2678] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2678)
& ? [Vvar__2___24Anonymous__2679] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2679)
& ? [Vvar__3___24Anonymous__2680] :
( cV___24t(Vvar__3___24Anonymous__2680)
& ? [Vvar__4___24Anonymous__2681] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2681)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2677)
=> ( Vvar__4___24Anonymous__2556 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2677,Vvar__1___24Anonymous__2678,Vvar__2___24Anonymous__2679,Vvar__3___24Anonymous__2680,Vvar__4___24Anonymous__2681)
& ( ( Vvar__0___24Anonymous__2677 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__2553),Vvar__2___24Anonymous__2554,Vvar__3___24Anonymous__2555,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__2678,Vvar__2___24Anonymous__2679,Vvar__3___24Anonymous__2680,Vvar__4___24Anonymous__2681)) )
| ( Vvar__0___24Anonymous__2677 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2697] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2697)
& ? [Vvar__1___24Anonymous__2698] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2698)
& ? [Vvar__2___24Anonymous__2699] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2699)
& ? [Vvar__3___24Anonymous__2700] :
( cV___24t(Vvar__3___24Anonymous__2700)
& ? [Vvar__4___24Anonymous__2701] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2701)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2697)
=> ( Vvar__1___24Anonymous__2553 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2697,Vvar__1___24Anonymous__2698,Vvar__2___24Anonymous__2699,Vvar__3___24Anonymous__2700,Vvar__4___24Anonymous__2701)
& ( ( Vvar__0___24Anonymous__2697 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__2698),Vvar__2___24Anonymous__2699,Vvar__3___24Anonymous__2700,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__4___24Anonymous__2701,Vvar__2___24Anonymous__2554,Vvar__3___24Anonymous__2555,Vvar__4___24Anonymous__2556)) )
| ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2556)
=> ( Vvar__0___24Anonymous__2697 = cRedblack_2eBlack
& ( ( Vvar__4___24Anonymous__2556 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__2752] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2752)
& ? [Vvar__1___24Anonymous__2753] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2753)
& ? [Vvar__2___24Anonymous__2754] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2754)
& ? [Vvar__3___24Anonymous__2755] :
( cV___24t(Vvar__3___24Anonymous__2755)
& ? [Vvar__4___24Anonymous__2756] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2756)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2752)
=> ( Vvar__4___24Anonymous__2556 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2752,Vvar__1___24Anonymous__2753,Vvar__2___24Anonymous__2754,Vvar__3___24Anonymous__2755,Vvar__4___24Anonymous__2756)
& ( ( Vvar__0___24Anonymous__2752 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__2553),Vvar__2___24Anonymous__2554,Vvar__3___24Anonymous__2555,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__2753,Vvar__2___24Anonymous__2754,Vvar__3___24Anonymous__2755,Vvar__4___24Anonymous__2756)) )
| ( Vvar__0___24Anonymous__2752 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( Vvar__0___24Anonymous__2552 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( cRedblack_2eTREES_2etree___24t(V4__t2)
=> ( Vvar__0___24Anonymous__412 = cRedblack_2eBlack
& ( ( V4__t2 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__2772] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2772)
& ? [Vvar__1___24Anonymous__2773] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2773)
& ? [Vvar__2___24Anonymous__2774] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2774)
& ? [Vvar__3___24Anonymous__2775] :
( cV___24t(Vvar__3___24Anonymous__2775)
& ? [Vvar__4___24Anonymous__2776] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2776)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2772)
=> ( V4__t2 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2772,Vvar__1___24Anonymous__2773,Vvar__2___24Anonymous__2774,Vvar__3___24Anonymous__2775,Vvar__4___24Anonymous__2776)
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2773)
=> ( Vvar__0___24Anonymous__2772 = cRedblack_2eRed
& ( ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2776)
=> ( Vvar__1___24Anonymous__2773 = cRedblack_2eTREES_2eE
& ( ( Vvar__4___24Anonymous__2776 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__2897] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2897)
& ? [Vvar__1___24Anonymous__2898] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2898)
& ? [Vvar__2___24Anonymous__2899] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2899)
& ? [Vvar__3___24Anonymous__2900] :
( cV___24t(Vvar__3___24Anonymous__2900)
& ? [Vvar__4___24Anonymous__2901] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2901)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2897)
=> ( Vvar__4___24Anonymous__2776 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2897,Vvar__1___24Anonymous__2898,Vvar__2___24Anonymous__2899,Vvar__3___24Anonymous__2900,Vvar__4___24Anonymous__2901)
& ( ( Vvar__0___24Anonymous__2897 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__2773),Vvar__2___24Anonymous__2774,Vvar__3___24Anonymous__2775,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__2898,Vvar__2___24Anonymous__2899,Vvar__3___24Anonymous__2900,Vvar__4___24Anonymous__2901)) )
| ( Vvar__0___24Anonymous__2897 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2917] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2917)
& ? [Vvar__1___24Anonymous__2918] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2918)
& ? [Vvar__2___24Anonymous__2919] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2919)
& ? [Vvar__3___24Anonymous__2920] :
( cV___24t(Vvar__3___24Anonymous__2920)
& ? [Vvar__4___24Anonymous__2921] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2921)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2917)
=> ( Vvar__1___24Anonymous__2773 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2917,Vvar__1___24Anonymous__2918,Vvar__2___24Anonymous__2919,Vvar__3___24Anonymous__2920,Vvar__4___24Anonymous__2921)
& ( ( Vvar__0___24Anonymous__2917 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__2918),Vvar__2___24Anonymous__2919,Vvar__3___24Anonymous__2920,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__4___24Anonymous__2921,Vvar__2___24Anonymous__2774,Vvar__3___24Anonymous__2775,Vvar__4___24Anonymous__2776)) )
| ( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2776)
=> ( Vvar__0___24Anonymous__2917 = cRedblack_2eBlack
& ( ( Vvar__4___24Anonymous__2776 = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) )
| ? [Vvar__0___24Anonymous__2972] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2972)
& ? [Vvar__1___24Anonymous__2973] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__2973)
& ? [Vvar__2___24Anonymous__2974] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__2974)
& ? [Vvar__3___24Anonymous__2975] :
( cV___24t(Vvar__3___24Anonymous__2975)
& ? [Vvar__4___24Anonymous__2976] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__2976)
& ( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__2972)
=> ( Vvar__4___24Anonymous__2776 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__2972,Vvar__1___24Anonymous__2973,Vvar__2___24Anonymous__2974,Vvar__3___24Anonymous__2975,Vvar__4___24Anonymous__2976)
& ( ( Vvar__0___24Anonymous__2972 = cRedblack_2eRed
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,Vvar__1___24Anonymous__2773),Vvar__2___24Anonymous__2774,Vvar__3___24Anonymous__2775,cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__2973,Vvar__2___24Anonymous__2974,Vvar__3___24Anonymous__2975,Vvar__4___24Anonymous__2976)) )
| ( Vvar__0___24Anonymous__2972 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( Vvar__0___24Anonymous__2772 = cRedblack_2eBlack
& cRedblack_2eTREES_2ebalance___24a5(V0__rb,V1__t1,V2__k,V3__vk,V4__t2) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,V1__t1,V2__k,V3__vk,V4__t2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Redblack.TREES.empty_tree',axiom,
cRedblack_2eTREES_2eempty__tree = cRedblack_2eTREES_2eE ).
fof('$_def_Redblack.TREES.ins',axiom,
! [V1__x,V2__vx,V3__s] :
( cRedblack_2eTREES_2etree___24t(V3__s)
=> ( ( V3__s = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2eins___24a3(V1__x,V2__vx,V3__s) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eRed,cRedblack_2eTREES_2eE,V1__x,V2__vx,cRedblack_2eTREES_2eE) )
| ? [Vvar__0___24Anonymous__147] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__147)
& ? [Vvar__1___24Anonymous__148] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__148)
& ? [Vvar__2___24Anonymous__149] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__149)
& ? [Vvar__3___24Anonymous__150] :
( cV___24t(Vvar__3___24Anonymous__150)
& ? [Vvar__4___24Anonymous__151] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__151)
& ( cRedblack_2ekey___24t(V1__x)
=> ( cRedblack_2ekey___24t(Vvar__2___24Anonymous__149)
=> ( V3__s = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__147,Vvar__1___24Anonymous__148,Vvar__2___24Anonymous__149,Vvar__3___24Anonymous__150,Vvar__4___24Anonymous__151)
& ( ( cVFA_2eExtract_2eltb___24a2(V1__x,Vvar__2___24Anonymous__149) = cCoq_2eInit_2eDatatypes_2etrue
& cRedblack_2eTREES_2eins___24a3(V1__x,V2__vx,V3__s) = cRedblack_2eTREES_2ebalance___24a5(Vvar__0___24Anonymous__147,cRedblack_2eTREES_2eins___24a3(V1__x,V2__vx,Vvar__1___24Anonymous__148),Vvar__2___24Anonymous__149,Vvar__3___24Anonymous__150,Vvar__4___24Anonymous__151) )
| ( cRedblack_2ekey___24t(V1__x)
=> ( cRedblack_2ekey___24t(Vvar__2___24Anonymous__149)
=> ( cVFA_2eExtract_2eltb___24a2(V1__x,Vvar__2___24Anonymous__149) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( cVFA_2eExtract_2eltb___24a2(Vvar__2___24Anonymous__149,V1__x) = cCoq_2eInit_2eDatatypes_2etrue
& cRedblack_2eTREES_2eins___24a3(V1__x,V2__vx,V3__s) = cRedblack_2eTREES_2ebalance___24a5(Vvar__0___24Anonymous__147,Vvar__1___24Anonymous__148,Vvar__2___24Anonymous__149,Vvar__3___24Anonymous__150,cRedblack_2eTREES_2eins___24a3(V1__x,V2__vx,Vvar__4___24Anonymous__151)) )
| ( cVFA_2eExtract_2eltb___24a2(Vvar__2___24Anonymous__149,V1__x) = cCoq_2eInit_2eDatatypes_2efalse
& cRedblack_2eTREES_2eins___24a3(V1__x,V2__vx,V3__s) = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__147,Vvar__1___24Anonymous__148,V1__x,V2__vx,Vvar__4___24Anonymous__151) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Redblack.TREES.insert',axiom,
! [V0__x,V1__vx,V2__s] : cRedblack_2eTREES_2einsert___24a3(V0__x,V1__vx,V2__s) = cRedblack_2eTREES_2emakeBlack___24a1(cRedblack_2eTREES_2eins___24a3(V0__x,V1__vx,V2__s)) ).
fof('$_def_Redblack.TREES.lookup',axiom,
! [V1__x,V2__t] :
( cRedblack_2eTREES_2etree___24t(V2__t)
=> ( ( V2__t = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2elookup___24a2(V1__x,V2__t) = cdefault )
| ? [Vvar__0___24Anonymous__3005] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__3005)
& ? [Vvar__1___24Anonymous__3006] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__3006)
& ? [Vvar__2___24Anonymous__3007] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__3007)
& ? [Vvar__3___24Anonymous__3008] :
( cV___24t(Vvar__3___24Anonymous__3008)
& ? [Vvar__4___24Anonymous__3009] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__3009)
& ( cRedblack_2ekey___24t(V1__x)
=> ( cRedblack_2ekey___24t(Vvar__2___24Anonymous__3007)
=> ( V2__t = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3005,Vvar__1___24Anonymous__3006,Vvar__2___24Anonymous__3007,Vvar__3___24Anonymous__3008,Vvar__4___24Anonymous__3009)
& ( ( cVFA_2eExtract_2eltb___24a2(V1__x,Vvar__2___24Anonymous__3007) = cCoq_2eInit_2eDatatypes_2etrue
& cRedblack_2eTREES_2elookup___24a2(V1__x,V2__t) = cRedblack_2eTREES_2elookup___24a2(V1__x,Vvar__1___24Anonymous__3006) )
| ( cRedblack_2ekey___24t(V1__x)
=> ( cRedblack_2ekey___24t(Vvar__2___24Anonymous__3007)
=> ( cVFA_2eExtract_2eltb___24a2(V1__x,Vvar__2___24Anonymous__3007) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( cVFA_2eExtract_2eltb___24a2(Vvar__2___24Anonymous__3007,V1__x) = cCoq_2eInit_2eDatatypes_2etrue
& cRedblack_2eTREES_2elookup___24a2(V1__x,V2__t) = cRedblack_2eTREES_2elookup___24a2(V1__x,Vvar__4___24Anonymous__3009) )
| ( cVFA_2eExtract_2eltb___24a2(Vvar__2___24Anonymous__3007,V1__x) = cCoq_2eInit_2eDatatypes_2efalse
& cRedblack_2eTREES_2elookup___24a2(V1__x,V2__t) = Vvar__3___24Anonymous__3008 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Redblack.TREES.makeBlack',axiom,
! [V0__t] :
( cRedblack_2eTREES_2etree___24t(V0__t)
=> ( ( V0__t = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2emakeBlack___24a1(V0__t) = cRedblack_2eTREES_2eE )
| ? [Vvar__0___24Anonymous__175] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__175)
& ? [Vvar__1___24Anonymous__176] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__176)
& ? [Vvar__2___24Anonymous__177] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__177)
& ? [Vvar__3___24Anonymous__178] :
( cV___24t(Vvar__3___24Anonymous__178)
& ? [Vvar__4___24Anonymous__179] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__179)
& V0__t = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__175,Vvar__1___24Anonymous__176,Vvar__2___24Anonymous__177,Vvar__3___24Anonymous__178,Vvar__4___24Anonymous__179)
& cRedblack_2eTREES_2emakeBlack___24a1(V0__t) = cRedblack_2eTREES_2eT___24a5(cRedblack_2eBlack,Vvar__1___24Anonymous__176,Vvar__2___24Anonymous__177,Vvar__3___24Anonymous__178,Vvar__4___24Anonymous__179) ) ) ) ) ) ) ) ).
fof('$_def_Redblack.TREES.tree_rec',axiom,
! [V0__P] : cRedblack_2eTREES_2etree__rec___24a1(V0__P) = cRedblack_2eTREES_2etree__rect___24a1(V0__P) ).
fof('$_def_Redblack.TREES.tree_rect',axiom,
! [V0__P,V1__f,V2__f,V4__t] :
( c_24__type__3134___24t(V0__P,V0__P)
=> ( cRedblack_2eTREES_2etree___24t(V4__t)
=> ( ( V4__t = cRedblack_2eTREES_2eE
& cRedblack_2eTREES_2etree__rect___24a4(V0__P,V1__f,V2__f,V4__t) = V1__f )
| ? [Vvar__0___24Anonymous__3118] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__3118)
& ? [Vvar__1___24Anonymous__3119] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__3119)
& ? [Vvar__2___24Anonymous__3120] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__3120)
& ? [Vvar__3___24Anonymous__3121] :
( cV___24t(Vvar__3___24Anonymous__3121)
& ? [Vvar__4___24Anonymous__3122] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__3122)
& V4__t = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3118,Vvar__1___24Anonymous__3119,Vvar__2___24Anonymous__3120,Vvar__3___24Anonymous__3121,Vvar__4___24Anonymous__3122)
& cRedblack_2eTREES_2etree__rect___24a4(V0__P,V1__f,V2__f,V4__t) = happ(happ(happ(happ(happ(happ(happ(V2__f,Vvar__0___24Anonymous__3118),Vvar__1___24Anonymous__3119),cRedblack_2eTREES_2etree__rect___24a4(V0__P,V1__f,V2__f,Vvar__1___24Anonymous__3119)),Vvar__2___24Anonymous__3120),Vvar__3___24Anonymous__3121),Vvar__4___24Anonymous__3122),cRedblack_2eTREES_2etree__rect___24a4(V0__P,V1__f,V2__f,Vvar__4___24Anonymous__3122)) ) ) ) ) ) ) ) ) ).
fof('$_def_Redblack.color_rec',axiom,
! [V0__P] : cRedblack_2ecolor__rec___24a1(V0__P) = cRedblack_2ecolor__rect___24a1(V0__P) ).
fof('$_def_Redblack.color_rect',axiom,
! [V0__P,V1__f,V2__f,V3__c] :
( c_24__type__3221___24t(V0__P,V0__P)
=> ( cRedblack_2ecolor___24t(V3__c)
=> ( ( V3__c = cRedblack_2eRed
& cRedblack_2ecolor__rect___24a4(V0__P,V1__f,V2__f,V3__c) = V1__f )
| ( V3__c = cRedblack_2eBlack
& cRedblack_2ecolor__rect___24a4(V0__P,V1__f,V2__f,V3__c) = V2__f ) ) ) ) ).
fof('$_def_Redblack.key',axiom,
! [Vvar__3230] :
( cRedblack_2ekey___24t(Vvar__3230)
<=> cVFA_2eExtract_2eint___24t(Vvar__3230) ) ).
fof('$_def_VFA.Extract.IntMaps.total_map',axiom,
! [V0__A] : cVFA_2eExtract_2eIntMaps_2etotal__map___24a1(V0__A) = c_24__type__64701___24a1(V0__A) ).
fof('$_def_VFA.Maps.t_empty',axiom,
! [V0__A,V1__v,V2___24Anonymous] : cVFA_2eMaps_2et__empty___24a3(V0__A,V1__v,V2___24Anonymous) = V1__v ).
fof('$_def_VFA.Maps.t_update',axiom,
! [V0__A,V1__m,V2__x,V3__v,V4__x_27] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__x_27)
=> ( ( cCoq_2eInit_2eNat_2eeqb___24a2(V2__x,V4__x_27) = cCoq_2eInit_2eDatatypes_2etrue
& cVFA_2eMaps_2et__update___24a5(V0__A,V1__m,V2__x,V3__v,V4__x_27) = V3__v )
| ( cCoq_2eInit_2eNat_2eeqb___24a2(V2__x,V4__x_27) = cCoq_2eInit_2eDatatypes_2efalse
& cVFA_2eMaps_2et__update___24a5(V0__A,V1__m,V2__x,V3__v,V4__x_27) = happ(V1__m,V4__x_27) ) ) ) ) ) ).
fof('$_def_VFA.Maps.total_map',axiom,
! [V0__A] : cVFA_2eMaps_2etotal__map___24a1(V0__A) = c_24__type__4022___24a1(V0__A) ).
fof('$_def_VFA.SearchTree.key',axiom,
! [Vvar__57010] :
( cVFA_2eSearchTree_2ekey___24t(Vvar__57010)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__57010) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__37223,Vvar__1___24Anonymous__37224,Vvar__0__P__37225,Vvar__1___24Anonymous__37226] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__37223) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__37225) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__61018,Vvar__1___24Anonymous__61019,Vvar__2___24Anonymous__61020] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61018,Vvar__1___24Anonymous__61019,Vvar__2___24Anonymous__61020) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__4] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__3997,Vvar__1___24Anonymous__3998,Vvar__0__A__3999] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3997,Vvar__1___24Anonymous__3998) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3999) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__3257,Vvar__0__A__3258,Vvar__1___24Anonymous__3259,Vvar__2___24Anonymous__3260] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3257) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3258,Vvar__1___24Anonymous__3259,Vvar__2___24Anonymous__3260) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__4568,Vvar__1__B__4569,Vvar__2___24Anonymous__4570,Vvar__0__A__4571,Vvar__1__B__4572,Vvar__2___24Anonymous__4573] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__4568,Vvar__1__B__4569,Vvar__2___24Anonymous__4570) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__4571,Vvar__1__B__4572) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__3409,Vvar__1__B__3410,Vvar__2___24Anonymous__3411,Vvar__0__A__3412,Vvar__1__B__3413,Vvar__2___24Anonymous__3414] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3409,Vvar__1__B__3410) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3412,Vvar__1__B__3413) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__3233] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3233) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__3242] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3242) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__3964,Vvar__0___24Anonymous__3965] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3964) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3965) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__63622,Vvar__1___24Anonymous__63623,Vvar__0__x__63624,Vvar__1__n__63625,Vvar__2___24Anonymous__63626] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__63622) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__63624,Vvar__1__n__63625) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__4048,Vvar__1___24Anonymous__4049] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__4048,Vvar__1___24Anonymous__4049) ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__41226,Vvar__0__n__41227,Vvar__1___24Anonymous__41228] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__41226) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__41227,Vvar__1___24Anonymous__41228) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__58891,Vvar__0__A__58892,Vvar__1__h__58893,Vvar__2__n__58894,Vvar__3___24Anonymous__58895] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__58891) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__58892,Vvar__1__h__58893,Vvar__2__n__58894,Vvar__3___24Anonymous__58895) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__38376,Vvar__1___24Anonymous__38377,Vvar__0__C__38378,Vvar__1___24Anonymous__38379] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__38376,Vvar__1___24Anonymous__38377) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__38378,Vvar__1___24Anonymous__38379) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__38440,Vvar__1___24Anonymous__38441,Vvar__0__C__38442,Vvar__1___24Anonymous__38443,Vvar__2___24Anonymous__38444] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__38440,Vvar__1___24Anonymous__38441) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__38442,Vvar__1___24Anonymous__38443,Vvar__2___24Anonymous__38444) ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__64456,Vvar__1__TX__64457,Vvar__2__AA__64458,Vvar__3__AF__64459,Vvar__0__TA__64460,Vvar__1__TX__64461,Vvar__2__AA__64462,Vvar__3__AF__64463] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__64456,Vvar__1__TX__64457,Vvar__2__AA__64458,Vvar__3__AF__64459) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__64460,Vvar__1__TX__64461,Vvar__2__AA__64462,Vvar__3__AF__64463) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__61831,Vvar__0__C__61832] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__61831) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__61832) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__51544,Vvar__0__C__51545] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__51544) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__51545) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__51188,Vvar__1___24Anonymous__51189,Vvar__0__C__51190,Vvar__1___24Anonymous__51191,Vvar__2___24Anonymous__51192] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__51188,Vvar__1___24Anonymous__51189) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__51190,Vvar__1___24Anonymous__51191,Vvar__2___24Anonymous__51192) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__51354,Vvar__1___24Anonymous__51355] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__51354,Vvar__1___24Anonymous__51355) ).
fof('$_discrim_Redblack.Red$Redblack.Black',axiom,
cRedblack_2eRed != cRedblack_2eBlack ).
fof('$_discrim_Redblack.TREES.E$Redblack.TREES.T',axiom,
! [Vvar__0___24Anonymous__3183,Vvar__1___24Anonymous__3184,Vvar__2___24Anonymous__3185,Vvar__3___24Anonymous__3186,Vvar__4___24Anonymous__3187] : cRedblack_2eTREES_2eE != cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3183,Vvar__1___24Anonymous__3184,Vvar__2___24Anonymous__3185,Vvar__3___24Anonymous__3186,Vvar__4___24Anonymous__3187) ).
fof('$_discrim_VFA.SearchTree.E$VFA.SearchTree.T',axiom,
! [Vvar__0__V__57019,Vvar__0__V__57020,Vvar__1___24Anonymous__57021,Vvar__2___24Anonymous__57022,Vvar__3___24Anonymous__57023,Vvar__4___24Anonymous__57024] : cVFA_2eSearchTree_2eE___24a1(Vvar__0__V__57019) != cVFA_2eSearchTree_2eT___24a5(Vvar__0__V__57020,Vvar__1___24Anonymous__57021,Vvar__2___24Anonymous__57022,Vvar__3___24Anonymous__57023,Vvar__4___24Anonymous__57024) ).
fof('$_fix_60952_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__60967] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60967)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60967)
& ( ? [Vvar__0___24Anonymous__60971] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60971)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60971)
& c_24__fix__60952__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__60952__1__add__carry___24a2(Vvar__0___24Anonymous__60967,Vvar__0___24Anonymous__60971)) )
| ? [Vvar__0___24Anonymous__60972] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60972)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60972)
& c_24__fix__60952__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__60952__1__add__carry___24a2(Vvar__0___24Anonymous__60967,Vvar__0___24Anonymous__60972)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__60952__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__60967)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__60973] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60973)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60973)
& ( ? [Vvar__0___24Anonymous__60977] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60977)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60977)
& c_24__fix__60952__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__60952__1__add__carry___24a2(Vvar__0___24Anonymous__60973,Vvar__0___24Anonymous__60977)) )
| ? [Vvar__0___24Anonymous__60978] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60978)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60978)
& c_24__fix__60952__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__60973,Vvar__0___24Anonymous__60978)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__60952__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__60973)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__60979] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60979)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60979)
& c_24__fix__60952__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__60979)) )
| ? [Vvar__0___24Anonymous__60980] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60980)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60980)
& c_24__fix__60952__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__60980)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__60952__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__37231,Vvar__0__P__37232,Vvar__1___24Anonymous__37233,Vvar__1___24Anonymous__37234] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__37231) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__37232)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__37231 = Vvar__0__P__37232 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__37227,Vvar__0__P__37228,Vvar__1___24Anonymous__37229,Vvar__1___24Anonymous__37230] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__37227) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__37228)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__37227 = Vvar__0__P__37228 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__61021,Vvar__0___24Anonymous__61022,Vvar__1___24Anonymous__61023,Vvar__1___24Anonymous__61024,Vvar__2___24Anonymous__61025,Vvar__2___24Anonymous__61026] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61021,Vvar__1___24Anonymous__61023,Vvar__2___24Anonymous__61025) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61022,Vvar__1___24Anonymous__61024,Vvar__2___24Anonymous__61026)
=> ( Vvar__2___24Anonymous__61025 = Vvar__2___24Anonymous__61026
& Vvar__1___24Anonymous__61023 = Vvar__1___24Anonymous__61024
& Vvar__0___24Anonymous__61021 = Vvar__0___24Anonymous__61022 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__4004,Vvar__0__A__4005] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4004) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4005)
=> Vvar__0__A__4004 = Vvar__0__A__4005 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__5,Vvar__0___24Anonymous__6] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6)
=> Vvar__0___24Anonymous__5 = Vvar__0___24Anonymous__6 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__4000,Vvar__0__A__4001,Vvar__1___24Anonymous__4002,Vvar__1___24Anonymous__4003] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4000,Vvar__1___24Anonymous__4002) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4001,Vvar__1___24Anonymous__4003)
=> ( Vvar__1___24Anonymous__4002 = Vvar__1___24Anonymous__4003
& Vvar__0__A__4000 = Vvar__0__A__4001 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__3263,Vvar__0__A__3264,Vvar__1___24Anonymous__3265,Vvar__1___24Anonymous__3266,Vvar__2___24Anonymous__3267,Vvar__2___24Anonymous__3268] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3263,Vvar__1___24Anonymous__3265,Vvar__2___24Anonymous__3267) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3264,Vvar__1___24Anonymous__3266,Vvar__2___24Anonymous__3268)
=> ( Vvar__2___24Anonymous__3267 = Vvar__2___24Anonymous__3268
& Vvar__1___24Anonymous__3265 = Vvar__1___24Anonymous__3266
& Vvar__0__A__3263 = Vvar__0__A__3264 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__3261,Vvar__0__A__3262] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3261) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3262)
=> Vvar__0__A__3261 = Vvar__0__A__3262 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__38148,Vvar__0__A__38149,Vvar__1__B__38150,Vvar__1__B__38151,Vvar__2___24Anonymous__38152,Vvar__2___24Anonymous__38153,Vvar__3___24Anonymous__38154,Vvar__3___24Anonymous__38155] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__38148,Vvar__1__B__38150,Vvar__2___24Anonymous__38152,Vvar__3___24Anonymous__38154) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__38149,Vvar__1__B__38151,Vvar__2___24Anonymous__38153,Vvar__3___24Anonymous__38155)
=> ( Vvar__3___24Anonymous__38154 = Vvar__3___24Anonymous__38155
& Vvar__2___24Anonymous__38152 = Vvar__2___24Anonymous__38153
& Vvar__1__B__38150 = Vvar__1__B__38151
& Vvar__0__A__38148 = Vvar__0__A__38149 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__4498,Vvar__0__A__4499,Vvar__1__P__4500,Vvar__1__P__4501,Vvar__2__x__4502,Vvar__2__x__4503,Vvar__3___24Anonymous__4504,Vvar__3___24Anonymous__4505] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__4498,Vvar__1__P__4500,Vvar__2__x__4502) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__4499,Vvar__1__P__4501,Vvar__2__x__4503)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__4502 = Vvar__2__x__4503
& Vvar__1__P__4500 = Vvar__1__P__4501
& Vvar__0__A__4498 = Vvar__0__A__4499 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__64089,Vvar__0__A__64090,Vvar__1__P__64091,Vvar__1__P__64092,Vvar__2__x__64093,Vvar__2__x__64094,Vvar__3___24Anonymous__64095,Vvar__3___24Anonymous__64096] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__64089,Vvar__1__P__64091,Vvar__2__x__64093,Vvar__3___24Anonymous__64095) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__64090,Vvar__1__P__64092,Vvar__2__x__64094,Vvar__3___24Anonymous__64096)
=> ( Vvar__3___24Anonymous__64095 = Vvar__3___24Anonymous__64096
& Vvar__2__x__64093 = Vvar__2__x__64094
& Vvar__1__P__64091 = Vvar__1__P__64092
& Vvar__0__A__64089 = Vvar__0__A__64090 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__4574,Vvar__0__A__4575,Vvar__1__B__4576,Vvar__1__B__4577,Vvar__2___24Anonymous__4578,Vvar__2___24Anonymous__4579] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__4574,Vvar__1__B__4576,Vvar__2___24Anonymous__4578) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__4575,Vvar__1__B__4577,Vvar__2___24Anonymous__4579)
=> ( Vvar__2___24Anonymous__4578 = Vvar__2___24Anonymous__4579
& Vvar__1__B__4576 = Vvar__1__B__4577
& Vvar__0__A__4574 = Vvar__0__A__4575 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__4580,Vvar__0__A__4581,Vvar__1__B__4582,Vvar__1__B__4583,Vvar__2___24Anonymous__4584,Vvar__2___24Anonymous__4585] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__4580,Vvar__1__B__4582) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__4581,Vvar__1__B__4583)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__4582 = Vvar__1__B__4583
& Vvar__0__A__4580 = Vvar__0__A__4581 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__3415,Vvar__0__A__3416,Vvar__1__B__3417,Vvar__1__B__3418,Vvar__2___24Anonymous__3419,Vvar__2___24Anonymous__3420] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3415,Vvar__1__B__3417) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3416,Vvar__1__B__3418)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__3417 = Vvar__1__B__3418
& Vvar__0__A__3415 = Vvar__0__A__3416 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__3421,Vvar__0__A__3422,Vvar__1__B__3423,Vvar__1__B__3424,Vvar__2___24Anonymous__3425,Vvar__2___24Anonymous__3426] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3421,Vvar__1__B__3423) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3422,Vvar__1__B__3424)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__3423 = Vvar__1__B__3424
& Vvar__0__A__3421 = Vvar__0__A__3422 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__3234,Vvar__0___24Anonymous__3235] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3234) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3235)
=> Vvar__0___24Anonymous__3234 = Vvar__0___24Anonymous__3235 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__3245,Vvar__0___24Anonymous__3246] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3245) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3246)
=> Vvar__0___24Anonymous__3245 = Vvar__0___24Anonymous__3246 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__3243,Vvar__0___24Anonymous__3244] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3243) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3244)
=> Vvar__0___24Anonymous__3243 = Vvar__0___24Anonymous__3244 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__3966,Vvar__0___24Anonymous__3967] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3966) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3967)
=> Vvar__0___24Anonymous__3966 = Vvar__0___24Anonymous__3967 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__3968,Vvar__0___24Anonymous__3969] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3968) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3969)
=> Vvar__0___24Anonymous__3968 = Vvar__0___24Anonymous__3969 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__4441,Vvar__0__Qnum__4442,Vvar__1__Qden__4443,Vvar__1__Qden__4444] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__4441,Vvar__1__Qden__4443) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__4442,Vvar__1__Qden__4444)
=> ( Vvar__1__Qden__4443 = Vvar__1__Qden__4444
& Vvar__0__Qnum__4441 = Vvar__0__Qnum__4442 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__43933,Vvar__0__nonzero__43934,Vvar__1__cond__nonzero__43935,Vvar__1__cond__nonzero__43936] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__43933) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__43934)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__43933 = Vvar__0__nonzero__43934 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__63637,Vvar__0__x__63638,Vvar__1__n__63639,Vvar__1__n__63640,Vvar__2___24Anonymous__63641,Vvar__2___24Anonymous__63642] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__63637,Vvar__1__n__63639) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__63638,Vvar__1__n__63640)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__63639 = Vvar__1__n__63640
& Vvar__0__x__63637 = Vvar__0__x__63638 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__63627,Vvar__0__x__63628,Vvar__1___24Anonymous__63629,Vvar__1___24Anonymous__63630] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__63627) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__63628)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__63627 = Vvar__0__x__63628 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__63631,Vvar__0__x__63632,Vvar__1__n__63633,Vvar__1__n__63634,Vvar__2___24Anonymous__63635,Vvar__2___24Anonymous__63636] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__63631,Vvar__1__n__63633) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__63632,Vvar__1__n__63634)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__63633 = Vvar__1__n__63634
& Vvar__0__x__63631 = Vvar__0__x__63632 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__3943,Vvar__0___24Anonymous__3944,Vvar__1___24Anonymous__3945,Vvar__1___24Anonymous__3946,Vvar__2___24Anonymous__3947,Vvar__2___24Anonymous__3948,Vvar__3___24Anonymous__3949,Vvar__3___24Anonymous__3950,Vvar__4___24Anonymous__3951,Vvar__4___24Anonymous__3952,Vvar__5___24Anonymous__3953,Vvar__5___24Anonymous__3954,Vvar__6___24Anonymous__3955,Vvar__6___24Anonymous__3956,Vvar__7___24Anonymous__3957,Vvar__7___24Anonymous__3958] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__3943,Vvar__1___24Anonymous__3945,Vvar__2___24Anonymous__3947,Vvar__3___24Anonymous__3949,Vvar__4___24Anonymous__3951,Vvar__5___24Anonymous__3953,Vvar__6___24Anonymous__3955,Vvar__7___24Anonymous__3957) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__3944,Vvar__1___24Anonymous__3946,Vvar__2___24Anonymous__3948,Vvar__3___24Anonymous__3950,Vvar__4___24Anonymous__3952,Vvar__5___24Anonymous__3954,Vvar__6___24Anonymous__3956,Vvar__7___24Anonymous__3958)
=> ( Vvar__7___24Anonymous__3957 = Vvar__7___24Anonymous__3958
& Vvar__6___24Anonymous__3955 = Vvar__6___24Anonymous__3956
& Vvar__5___24Anonymous__3953 = Vvar__5___24Anonymous__3954
& Vvar__4___24Anonymous__3951 = Vvar__4___24Anonymous__3952
& Vvar__3___24Anonymous__3949 = Vvar__3___24Anonymous__3950
& Vvar__2___24Anonymous__3947 = Vvar__2___24Anonymous__3948
& Vvar__1___24Anonymous__3945 = Vvar__1___24Anonymous__3946
& Vvar__0___24Anonymous__3943 = Vvar__0___24Anonymous__3944 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__4050,Vvar__0___24Anonymous__4051,Vvar__1___24Anonymous__4052,Vvar__1___24Anonymous__4053] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__4050,Vvar__1___24Anonymous__4052) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__4051,Vvar__1___24Anonymous__4053)
=> ( Vvar__1___24Anonymous__4052 = Vvar__1___24Anonymous__4053
& Vvar__0___24Anonymous__4050 = Vvar__0___24Anonymous__4051 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__41229,Vvar__0__n__41230] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__41229) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__41230)
=> Vvar__0__n__41229 = Vvar__0__n__41230 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__41231,Vvar__0__n__41232,Vvar__1___24Anonymous__41233,Vvar__1___24Anonymous__41234] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__41231,Vvar__1___24Anonymous__41233) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__41232,Vvar__1___24Anonymous__41234)
=> ( Vvar__1___24Anonymous__41233 = Vvar__1___24Anonymous__41234
& Vvar__0__n__41231 = Vvar__0__n__41232 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__58898,Vvar__0__A__58899,Vvar__1__h__58900,Vvar__1__h__58901,Vvar__2__n__58902,Vvar__2__n__58903,Vvar__3___24Anonymous__58904,Vvar__3___24Anonymous__58905] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__58898,Vvar__1__h__58900,Vvar__2__n__58902,Vvar__3___24Anonymous__58904) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__58899,Vvar__1__h__58901,Vvar__2__n__58903,Vvar__3___24Anonymous__58905)
=> ( Vvar__3___24Anonymous__58904 = Vvar__3___24Anonymous__58905
& Vvar__2__n__58902 = Vvar__2__n__58903
& Vvar__1__h__58900 = Vvar__1__h__58901
& Vvar__0__A__58898 = Vvar__0__A__58899 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__58896,Vvar__0__A__58897] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__58896) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__58897)
=> Vvar__0__A__58896 = Vvar__0__A__58897 ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__38384,Vvar__0__C__38385,Vvar__1___24Anonymous__38386,Vvar__1___24Anonymous__38387] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__38384,Vvar__1___24Anonymous__38386) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__38385,Vvar__1___24Anonymous__38387)
=> ( Vvar__1___24Anonymous__38386 = Vvar__1___24Anonymous__38387
& Vvar__0__C__38384 = Vvar__0__C__38385 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__38388,Vvar__0__C__38389,Vvar__1___24Anonymous__38390,Vvar__1___24Anonymous__38391,Vvar__2___24Anonymous__38392,Vvar__2___24Anonymous__38393] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__38388,Vvar__1___24Anonymous__38390,Vvar__2___24Anonymous__38392) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__38389,Vvar__1___24Anonymous__38391,Vvar__2___24Anonymous__38393)
=> ( Vvar__2___24Anonymous__38392 = Vvar__2___24Anonymous__38393
& Vvar__1___24Anonymous__38390 = Vvar__1___24Anonymous__38391
& Vvar__0__C__38388 = Vvar__0__C__38389 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__38380,Vvar__0__C__38381,Vvar__1___24Anonymous__38382,Vvar__1___24Anonymous__38383] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__38380,Vvar__1___24Anonymous__38382) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__38381,Vvar__1___24Anonymous__38383)
=> ( Vvar__1___24Anonymous__38382 = Vvar__1___24Anonymous__38383
& Vvar__0__C__38380 = Vvar__0__C__38381 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__38400,Vvar__0__C__38401,Vvar__1___24Anonymous__38402,Vvar__1___24Anonymous__38403,Vvar__2___24Anonymous__38404,Vvar__2___24Anonymous__38405] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__38400,Vvar__1___24Anonymous__38402,Vvar__2___24Anonymous__38404) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__38401,Vvar__1___24Anonymous__38403,Vvar__2___24Anonymous__38405)
=> ( Vvar__2___24Anonymous__38404 = Vvar__2___24Anonymous__38405
& Vvar__1___24Anonymous__38402 = Vvar__1___24Anonymous__38403
& Vvar__0__C__38400 = Vvar__0__C__38401 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__38406,Vvar__0__C__38407,Vvar__1___24Anonymous__38408,Vvar__1___24Anonymous__38409] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__38406,Vvar__1___24Anonymous__38408) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__38407,Vvar__1___24Anonymous__38409)
=> ( Vvar__1___24Anonymous__38408 = Vvar__1___24Anonymous__38409
& Vvar__0__C__38406 = Vvar__0__C__38407 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__38410,Vvar__0__C__38411,Vvar__1___24Anonymous__38412,Vvar__1___24Anonymous__38413,Vvar__2___24Anonymous__38414,Vvar__2___24Anonymous__38415] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__38410,Vvar__1___24Anonymous__38412,Vvar__2___24Anonymous__38414) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__38411,Vvar__1___24Anonymous__38413,Vvar__2___24Anonymous__38415)
=> ( Vvar__2___24Anonymous__38414 = Vvar__2___24Anonymous__38415
& Vvar__1___24Anonymous__38412 = Vvar__1___24Anonymous__38413
& Vvar__0__C__38410 = Vvar__0__C__38411 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__38394,Vvar__0__C__38395,Vvar__1___24Anonymous__38396,Vvar__1___24Anonymous__38397,Vvar__2___24Anonymous__38398,Vvar__2___24Anonymous__38399] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__38394,Vvar__1___24Anonymous__38396,Vvar__2___24Anonymous__38398) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__38395,Vvar__1___24Anonymous__38397,Vvar__2___24Anonymous__38399)
=> ( Vvar__2___24Anonymous__38398 = Vvar__2___24Anonymous__38399
& Vvar__1___24Anonymous__38396 = Vvar__1___24Anonymous__38397
& Vvar__0__C__38394 = Vvar__0__C__38395 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__38455,Vvar__0__C__38456,Vvar__1___24Anonymous__38457,Vvar__1___24Anonymous__38458,Vvar__2___24Anonymous__38459,Vvar__2___24Anonymous__38460,Vvar__3___24Anonymous__38461,Vvar__3___24Anonymous__38462] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__38455,Vvar__1___24Anonymous__38457,Vvar__2___24Anonymous__38459,Vvar__3___24Anonymous__38461) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__38456,Vvar__1___24Anonymous__38458,Vvar__2___24Anonymous__38460,Vvar__3___24Anonymous__38462)
=> ( Vvar__3___24Anonymous__38461 = Vvar__3___24Anonymous__38462
& Vvar__2___24Anonymous__38459 = Vvar__2___24Anonymous__38460
& Vvar__1___24Anonymous__38457 = Vvar__1___24Anonymous__38458
& Vvar__0__C__38455 = Vvar__0__C__38456 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__38445,Vvar__0__C__38446,Vvar__1___24Anonymous__38447,Vvar__1___24Anonymous__38448] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__38445,Vvar__1___24Anonymous__38447) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__38446,Vvar__1___24Anonymous__38448)
=> ( Vvar__1___24Anonymous__38447 = Vvar__1___24Anonymous__38448
& Vvar__0__C__38445 = Vvar__0__C__38446 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__38449,Vvar__0__C__38450,Vvar__1___24Anonymous__38451,Vvar__1___24Anonymous__38452,Vvar__2___24Anonymous__38453,Vvar__2___24Anonymous__38454] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__38449,Vvar__1___24Anonymous__38451,Vvar__2___24Anonymous__38453) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__38450,Vvar__1___24Anonymous__38452,Vvar__2___24Anonymous__38454)
=> ( Vvar__2___24Anonymous__38453 = Vvar__2___24Anonymous__38454
& Vvar__1___24Anonymous__38451 = Vvar__1___24Anonymous__38452
& Vvar__0__C__38449 = Vvar__0__C__38450 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__50416,Vvar__0__T__50417,Vvar__1__Flhs__50418,Vvar__1__Flhs__50419,Vvar__2__Fop__50420,Vvar__2__Fop__50421,Vvar__3__Frhs__50422,Vvar__3__Frhs__50423] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__50416,Vvar__1__Flhs__50418,Vvar__2__Fop__50420,Vvar__3__Frhs__50422) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__50417,Vvar__1__Flhs__50419,Vvar__2__Fop__50421,Vvar__3__Frhs__50423)
=> ( Vvar__3__Frhs__50422 = Vvar__3__Frhs__50423
& Vvar__2__Fop__50420 = Vvar__2__Fop__50421
& Vvar__1__Flhs__50418 = Vvar__1__Flhs__50419
& Vvar__0__T__50416 = Vvar__0__T__50417 ) ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__64490,Vvar__0__TA__64491,Vvar__1__TX__64492,Vvar__1__TX__64493,Vvar__2__AA__64494,Vvar__2__AA__64495,Vvar__3__AF__64496,Vvar__3__AF__64497,Vvar__4___24Anonymous__64498,Vvar__4___24Anonymous__64499,Vvar__5___24Anonymous__64500,Vvar__5___24Anonymous__64501] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__64490,Vvar__1__TX__64492,Vvar__2__AA__64494,Vvar__3__AF__64496,Vvar__4___24Anonymous__64498,Vvar__5___24Anonymous__64500) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__64491,Vvar__1__TX__64493,Vvar__2__AA__64495,Vvar__3__AF__64497,Vvar__4___24Anonymous__64499,Vvar__5___24Anonymous__64501)
=> ( Vvar__5___24Anonymous__64500 = Vvar__5___24Anonymous__64501
& Vvar__4___24Anonymous__64498 = Vvar__4___24Anonymous__64499
& Vvar__3__AF__64496 = Vvar__3__AF__64497
& Vvar__2__AA__64494 = Vvar__2__AA__64495
& Vvar__1__TX__64492 = Vvar__1__TX__64493
& Vvar__0__TA__64490 = Vvar__0__TA__64491 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__64502,Vvar__0__TA__64503,Vvar__1__TX__64504,Vvar__1__TX__64505,Vvar__2__AA__64506,Vvar__2__AA__64507,Vvar__3__AF__64508,Vvar__3__AF__64509,Vvar__4___24Anonymous__64510,Vvar__4___24Anonymous__64511,Vvar__5___24Anonymous__64512,Vvar__5___24Anonymous__64513] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__64502,Vvar__1__TX__64504,Vvar__2__AA__64506,Vvar__3__AF__64508,Vvar__4___24Anonymous__64510,Vvar__5___24Anonymous__64512) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__64503,Vvar__1__TX__64505,Vvar__2__AA__64507,Vvar__3__AF__64509,Vvar__4___24Anonymous__64511,Vvar__5___24Anonymous__64513)
=> ( Vvar__5___24Anonymous__64512 = Vvar__5___24Anonymous__64513
& Vvar__4___24Anonymous__64510 = Vvar__4___24Anonymous__64511
& Vvar__3__AF__64508 = Vvar__3__AF__64509
& Vvar__2__AA__64506 = Vvar__2__AA__64507
& Vvar__1__TX__64504 = Vvar__1__TX__64505
& Vvar__0__TA__64502 = Vvar__0__TA__64503 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__64514,Vvar__0__TA__64515,Vvar__1__TX__64516,Vvar__1__TX__64517,Vvar__2__AA__64518,Vvar__2__AA__64519,Vvar__3__AF__64520,Vvar__3__AF__64521,Vvar__4___24Anonymous__64522,Vvar__4___24Anonymous__64523,Vvar__5___24Anonymous__64524,Vvar__5___24Anonymous__64525] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__64514,Vvar__1__TX__64516,Vvar__2__AA__64518,Vvar__3__AF__64520,Vvar__4___24Anonymous__64522,Vvar__5___24Anonymous__64524) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__64515,Vvar__1__TX__64517,Vvar__2__AA__64519,Vvar__3__AF__64521,Vvar__4___24Anonymous__64523,Vvar__5___24Anonymous__64525)
=> ( Vvar__5___24Anonymous__64524 = Vvar__5___24Anonymous__64525
& Vvar__4___24Anonymous__64522 = Vvar__4___24Anonymous__64523
& Vvar__3__AF__64520 = Vvar__3__AF__64521
& Vvar__2__AA__64518 = Vvar__2__AA__64519
& Vvar__1__TX__64516 = Vvar__1__TX__64517
& Vvar__0__TA__64514 = Vvar__0__TA__64515 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__64472,Vvar__0__TA__64473,Vvar__1__TX__64474,Vvar__1__TX__64475,Vvar__2__AA__64476,Vvar__2__AA__64477,Vvar__3__AF__64478,Vvar__3__AF__64479] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__64472,Vvar__1__TX__64474,Vvar__2__AA__64476,Vvar__3__AF__64478) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__64473,Vvar__1__TX__64475,Vvar__2__AA__64477,Vvar__3__AF__64479)
=> ( Vvar__3__AF__64478 = Vvar__3__AF__64479
& Vvar__2__AA__64476 = Vvar__2__AA__64477
& Vvar__1__TX__64474 = Vvar__1__TX__64475
& Vvar__0__TA__64472 = Vvar__0__TA__64473 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__64536,Vvar__0__TA__64537,Vvar__1__TX__64538,Vvar__1__TX__64539,Vvar__2__AA__64540,Vvar__2__AA__64541,Vvar__3__AF__64542,Vvar__3__AF__64543,Vvar__4___24Anonymous__64544,Vvar__4___24Anonymous__64545,Vvar__5___24Anonymous__64546,Vvar__5___24Anonymous__64547,Vvar__6___24Anonymous__64548,Vvar__6___24Anonymous__64549] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__64536,Vvar__1__TX__64538,Vvar__2__AA__64540,Vvar__3__AF__64542,Vvar__4___24Anonymous__64544,Vvar__5___24Anonymous__64546,Vvar__6___24Anonymous__64548) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__64537,Vvar__1__TX__64539,Vvar__2__AA__64541,Vvar__3__AF__64543,Vvar__4___24Anonymous__64545,Vvar__5___24Anonymous__64547,Vvar__6___24Anonymous__64549)
=> ( Vvar__6___24Anonymous__64548 = Vvar__6___24Anonymous__64549
& Vvar__5___24Anonymous__64546 = Vvar__5___24Anonymous__64547
& Vvar__4___24Anonymous__64544 = Vvar__4___24Anonymous__64545
& Vvar__3__AF__64542 = Vvar__3__AF__64543
& Vvar__2__AA__64540 = Vvar__2__AA__64541
& Vvar__1__TX__64538 = Vvar__1__TX__64539
& Vvar__0__TA__64536 = Vvar__0__TA__64537 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__64526,Vvar__0__TA__64527,Vvar__1__TX__64528,Vvar__1__TX__64529,Vvar__2__AA__64530,Vvar__2__AA__64531,Vvar__3__AF__64532,Vvar__3__AF__64533,Vvar__4___24Anonymous__64534,Vvar__4___24Anonymous__64535] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__64526,Vvar__1__TX__64528,Vvar__2__AA__64530,Vvar__3__AF__64532,Vvar__4___24Anonymous__64534) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__64527,Vvar__1__TX__64529,Vvar__2__AA__64531,Vvar__3__AF__64533,Vvar__4___24Anonymous__64535)
=> ( Vvar__4___24Anonymous__64534 = Vvar__4___24Anonymous__64535
& Vvar__3__AF__64532 = Vvar__3__AF__64533
& Vvar__2__AA__64530 = Vvar__2__AA__64531
& Vvar__1__TX__64528 = Vvar__1__TX__64529
& Vvar__0__TA__64526 = Vvar__0__TA__64527 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__64464,Vvar__0__TA__64465,Vvar__1__TX__64466,Vvar__1__TX__64467,Vvar__2__AA__64468,Vvar__2__AA__64469,Vvar__3__AF__64470,Vvar__3__AF__64471] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__64464,Vvar__1__TX__64466,Vvar__2__AA__64468,Vvar__3__AF__64470) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__64465,Vvar__1__TX__64467,Vvar__2__AA__64469,Vvar__3__AF__64471)
=> ( Vvar__3__AF__64470 = Vvar__3__AF__64471
& Vvar__2__AA__64468 = Vvar__2__AA__64469
& Vvar__1__TX__64466 = Vvar__1__TX__64467
& Vvar__0__TA__64464 = Vvar__0__TA__64465 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__64480,Vvar__0__TA__64481,Vvar__1__TX__64482,Vvar__1__TX__64483,Vvar__2__AA__64484,Vvar__2__AA__64485,Vvar__3__AF__64486,Vvar__3__AF__64487,Vvar__4___24Anonymous__64488,Vvar__4___24Anonymous__64489] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__64480,Vvar__1__TX__64482,Vvar__2__AA__64484,Vvar__3__AF__64486,Vvar__4___24Anonymous__64488) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__64481,Vvar__1__TX__64483,Vvar__2__AA__64485,Vvar__3__AF__64487,Vvar__4___24Anonymous__64489)
=> ( Vvar__4___24Anonymous__64488 = Vvar__4___24Anonymous__64489
& Vvar__3__AF__64486 = Vvar__3__AF__64487
& Vvar__2__AA__64484 = Vvar__2__AA__64485
& Vvar__1__TX__64482 = Vvar__1__TX__64483
& Vvar__0__TA__64480 = Vvar__0__TA__64481 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__61835,Vvar__0__C__61836] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__61835) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__61836)
=> Vvar__0__C__61835 = Vvar__0__C__61836 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__61833,Vvar__0__C__61834] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__61833) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__61834)
=> Vvar__0__C__61833 = Vvar__0__C__61834 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__61841,Vvar__0__C__61842,Vvar__1___24Anonymous__61843,Vvar__1___24Anonymous__61844] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__61841,Vvar__1___24Anonymous__61843) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__61842,Vvar__1___24Anonymous__61844)
=> ( Vvar__1___24Anonymous__61843 = Vvar__1___24Anonymous__61844
& Vvar__0__C__61841 = Vvar__0__C__61842 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__61845,Vvar__0__C__61846,Vvar__1___24Anonymous__61847,Vvar__1___24Anonymous__61848,Vvar__2___24Anonymous__61849,Vvar__2___24Anonymous__61850] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__61845,Vvar__1___24Anonymous__61847,Vvar__2___24Anonymous__61849) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__61846,Vvar__1___24Anonymous__61848,Vvar__2___24Anonymous__61850)
=> ( Vvar__2___24Anonymous__61849 = Vvar__2___24Anonymous__61850
& Vvar__1___24Anonymous__61847 = Vvar__1___24Anonymous__61848
& Vvar__0__C__61845 = Vvar__0__C__61846 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__61837,Vvar__0__C__61838,Vvar__1___24Anonymous__61839,Vvar__1___24Anonymous__61840] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__61837,Vvar__1___24Anonymous__61839) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__61838,Vvar__1___24Anonymous__61840)
=> ( Vvar__1___24Anonymous__61839 = Vvar__1___24Anonymous__61840
& Vvar__0__C__61837 = Vvar__0__C__61838 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__61871,Vvar__0__C__61872,Vvar__1___24Anonymous__61873,Vvar__1___24Anonymous__61874,Vvar__2___24Anonymous__61875,Vvar__2___24Anonymous__61876] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__61871,Vvar__1___24Anonymous__61873,Vvar__2___24Anonymous__61875) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__61872,Vvar__1___24Anonymous__61874,Vvar__2___24Anonymous__61876)
=> ( Vvar__2___24Anonymous__61875 = Vvar__2___24Anonymous__61876
& Vvar__1___24Anonymous__61873 = Vvar__1___24Anonymous__61874
& Vvar__0__C__61871 = Vvar__0__C__61872 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__61867,Vvar__0__C__61868,Vvar__1___24Anonymous__61869,Vvar__1___24Anonymous__61870] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__61867,Vvar__1___24Anonymous__61869) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__61868,Vvar__1___24Anonymous__61870)
=> ( Vvar__1___24Anonymous__61869 = Vvar__1___24Anonymous__61870
& Vvar__0__C__61867 = Vvar__0__C__61868 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__61857,Vvar__0__C__61858,Vvar__1___24Anonymous__61859,Vvar__1___24Anonymous__61860,Vvar__2___24Anonymous__61861,Vvar__2___24Anonymous__61862] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__61857,Vvar__1___24Anonymous__61859,Vvar__2___24Anonymous__61861) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__61858,Vvar__1___24Anonymous__61860,Vvar__2___24Anonymous__61862)
=> ( Vvar__2___24Anonymous__61861 = Vvar__2___24Anonymous__61862
& Vvar__1___24Anonymous__61859 = Vvar__1___24Anonymous__61860
& Vvar__0__C__61857 = Vvar__0__C__61858 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__61863,Vvar__0__C__61864,Vvar__1___24Anonymous__61865,Vvar__1___24Anonymous__61866] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__61863,Vvar__1___24Anonymous__61865) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__61864,Vvar__1___24Anonymous__61866)
=> ( Vvar__1___24Anonymous__61865 = Vvar__1___24Anonymous__61866
& Vvar__0__C__61863 = Vvar__0__C__61864 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__61877,Vvar__0__C__61878,Vvar__1___24Anonymous__61879,Vvar__1___24Anonymous__61880,Vvar__2___24Anonymous__61881,Vvar__2___24Anonymous__61882] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__61877,Vvar__1___24Anonymous__61879,Vvar__2___24Anonymous__61881) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__61878,Vvar__1___24Anonymous__61880,Vvar__2___24Anonymous__61882)
=> ( Vvar__2___24Anonymous__61881 = Vvar__2___24Anonymous__61882
& Vvar__1___24Anonymous__61879 = Vvar__1___24Anonymous__61880
& Vvar__0__C__61877 = Vvar__0__C__61878 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__61851,Vvar__0__C__61852,Vvar__1___24Anonymous__61853,Vvar__1___24Anonymous__61854,Vvar__2___24Anonymous__61855,Vvar__2___24Anonymous__61856] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__61851,Vvar__1___24Anonymous__61853,Vvar__2___24Anonymous__61855) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__61852,Vvar__1___24Anonymous__61854,Vvar__2___24Anonymous__61856)
=> ( Vvar__2___24Anonymous__61855 = Vvar__2___24Anonymous__61856
& Vvar__1___24Anonymous__61853 = Vvar__1___24Anonymous__61854
& Vvar__0__C__61851 = Vvar__0__C__61852 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__61910,Vvar__0__C__61911,Vvar__1__num__61912,Vvar__1__num__61913,Vvar__2__denum__61914,Vvar__2__denum__61915,Vvar__3__condition__61916,Vvar__3__condition__61917] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__61910,Vvar__1__num__61912,Vvar__2__denum__61914,Vvar__3__condition__61916) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__61911,Vvar__1__num__61913,Vvar__2__denum__61915,Vvar__3__condition__61917)
=> ( Vvar__3__condition__61916 = Vvar__3__condition__61917
& Vvar__2__denum__61914 = Vvar__2__denum__61915
& Vvar__1__num__61912 = Vvar__1__num__61913
& Vvar__0__C__61910 = Vvar__0__C__61911 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__51548,Vvar__0__C__51549] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__51548) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__51549)
=> Vvar__0__C__51548 = Vvar__0__C__51549 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__51546,Vvar__0__C__51547] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__51546) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__51547)
=> Vvar__0__C__51546 = Vvar__0__C__51547 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__51554,Vvar__0__C__51555,Vvar__1___24Anonymous__51556,Vvar__1___24Anonymous__51557] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__51554,Vvar__1___24Anonymous__51556) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__51555,Vvar__1___24Anonymous__51557)
=> ( Vvar__1___24Anonymous__51556 = Vvar__1___24Anonymous__51557
& Vvar__0__C__51554 = Vvar__0__C__51555 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__51558,Vvar__0__C__51559,Vvar__1___24Anonymous__51560,Vvar__1___24Anonymous__51561,Vvar__2___24Anonymous__51562,Vvar__2___24Anonymous__51563] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__51558,Vvar__1___24Anonymous__51560,Vvar__2___24Anonymous__51562) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__51559,Vvar__1___24Anonymous__51561,Vvar__2___24Anonymous__51563)
=> ( Vvar__2___24Anonymous__51562 = Vvar__2___24Anonymous__51563
& Vvar__1___24Anonymous__51560 = Vvar__1___24Anonymous__51561
& Vvar__0__C__51558 = Vvar__0__C__51559 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__51550,Vvar__0__C__51551,Vvar__1___24Anonymous__51552,Vvar__1___24Anonymous__51553] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__51550,Vvar__1___24Anonymous__51552) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__51551,Vvar__1___24Anonymous__51553)
=> ( Vvar__1___24Anonymous__51552 = Vvar__1___24Anonymous__51553
& Vvar__0__C__51550 = Vvar__0__C__51551 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__51570,Vvar__0__C__51571,Vvar__1___24Anonymous__51572,Vvar__1___24Anonymous__51573,Vvar__2___24Anonymous__51574,Vvar__2___24Anonymous__51575] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__51570,Vvar__1___24Anonymous__51572,Vvar__2___24Anonymous__51574) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__51571,Vvar__1___24Anonymous__51573,Vvar__2___24Anonymous__51575)
=> ( Vvar__2___24Anonymous__51574 = Vvar__2___24Anonymous__51575
& Vvar__1___24Anonymous__51572 = Vvar__1___24Anonymous__51573
& Vvar__0__C__51570 = Vvar__0__C__51571 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__51576,Vvar__0__C__51577,Vvar__1___24Anonymous__51578,Vvar__1___24Anonymous__51579] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__51576,Vvar__1___24Anonymous__51578) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__51577,Vvar__1___24Anonymous__51579)
=> ( Vvar__1___24Anonymous__51578 = Vvar__1___24Anonymous__51579
& Vvar__0__C__51576 = Vvar__0__C__51577 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__51580,Vvar__0__C__51581,Vvar__1___24Anonymous__51582,Vvar__1___24Anonymous__51583,Vvar__2___24Anonymous__51584,Vvar__2___24Anonymous__51585] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__51580,Vvar__1___24Anonymous__51582,Vvar__2___24Anonymous__51584) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__51581,Vvar__1___24Anonymous__51583,Vvar__2___24Anonymous__51585)
=> ( Vvar__2___24Anonymous__51584 = Vvar__2___24Anonymous__51585
& Vvar__1___24Anonymous__51582 = Vvar__1___24Anonymous__51583
& Vvar__0__C__51580 = Vvar__0__C__51581 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__51564,Vvar__0__C__51565,Vvar__1___24Anonymous__51566,Vvar__1___24Anonymous__51567,Vvar__2___24Anonymous__51568,Vvar__2___24Anonymous__51569] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__51564,Vvar__1___24Anonymous__51566,Vvar__2___24Anonymous__51568) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__51565,Vvar__1___24Anonymous__51567,Vvar__2___24Anonymous__51569)
=> ( Vvar__2___24Anonymous__51568 = Vvar__2___24Anonymous__51569
& Vvar__1___24Anonymous__51566 = Vvar__1___24Anonymous__51567
& Vvar__0__C__51564 = Vvar__0__C__51565 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__51203,Vvar__0__C__51204,Vvar__1___24Anonymous__51205,Vvar__1___24Anonymous__51206,Vvar__2___24Anonymous__51207,Vvar__2___24Anonymous__51208,Vvar__3___24Anonymous__51209,Vvar__3___24Anonymous__51210] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__51203,Vvar__1___24Anonymous__51205,Vvar__2___24Anonymous__51207,Vvar__3___24Anonymous__51209) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__51204,Vvar__1___24Anonymous__51206,Vvar__2___24Anonymous__51208,Vvar__3___24Anonymous__51210)
=> ( Vvar__3___24Anonymous__51209 = Vvar__3___24Anonymous__51210
& Vvar__2___24Anonymous__51207 = Vvar__2___24Anonymous__51208
& Vvar__1___24Anonymous__51205 = Vvar__1___24Anonymous__51206
& Vvar__0__C__51203 = Vvar__0__C__51204 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__51193,Vvar__0__C__51194,Vvar__1___24Anonymous__51195,Vvar__1___24Anonymous__51196] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__51193,Vvar__1___24Anonymous__51195) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__51194,Vvar__1___24Anonymous__51196)
=> ( Vvar__1___24Anonymous__51195 = Vvar__1___24Anonymous__51196
& Vvar__0__C__51193 = Vvar__0__C__51194 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__51197,Vvar__0__C__51198,Vvar__1___24Anonymous__51199,Vvar__1___24Anonymous__51200,Vvar__2___24Anonymous__51201,Vvar__2___24Anonymous__51202] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__51197,Vvar__1___24Anonymous__51199,Vvar__2___24Anonymous__51201) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__51198,Vvar__1___24Anonymous__51200,Vvar__2___24Anonymous__51202)
=> ( Vvar__2___24Anonymous__51201 = Vvar__2___24Anonymous__51202
& Vvar__1___24Anonymous__51199 = Vvar__1___24Anonymous__51200
& Vvar__0__C__51197 = Vvar__0__C__51198 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__51360,Vvar__0___24Anonymous__51361,Vvar__1___24Anonymous__51362,Vvar__1___24Anonymous__51363] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__51360,Vvar__1___24Anonymous__51362) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__51361,Vvar__1___24Anonymous__51363)
=> ( Vvar__1___24Anonymous__51362 = Vvar__1___24Anonymous__51363
& Vvar__0___24Anonymous__51360 = Vvar__0___24Anonymous__51361 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__51356,Vvar__0___24Anonymous__51357,Vvar__1___24Anonymous__51358,Vvar__1___24Anonymous__51359] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__51356,Vvar__1___24Anonymous__51358) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__51357,Vvar__1___24Anonymous__51359)
=> ( Vvar__1___24Anonymous__51358 = Vvar__1___24Anonymous__51359
& Vvar__0___24Anonymous__51356 = Vvar__0___24Anonymous__51357 ) ) ).
fof('$_inj_Redblack.TREES.T',axiom,
! [Vvar__0___24Anonymous__3188,Vvar__0___24Anonymous__3189,Vvar__1___24Anonymous__3190,Vvar__1___24Anonymous__3191,Vvar__2___24Anonymous__3192,Vvar__2___24Anonymous__3193,Vvar__3___24Anonymous__3194,Vvar__3___24Anonymous__3195,Vvar__4___24Anonymous__3196,Vvar__4___24Anonymous__3197] :
( cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3188,Vvar__1___24Anonymous__3190,Vvar__2___24Anonymous__3192,Vvar__3___24Anonymous__3194,Vvar__4___24Anonymous__3196) = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3189,Vvar__1___24Anonymous__3191,Vvar__2___24Anonymous__3193,Vvar__3___24Anonymous__3195,Vvar__4___24Anonymous__3197)
=> ( Vvar__4___24Anonymous__3196 = Vvar__4___24Anonymous__3197
& Vvar__3___24Anonymous__3194 = Vvar__3___24Anonymous__3195
& Vvar__2___24Anonymous__3192 = Vvar__2___24Anonymous__3193
& Vvar__1___24Anonymous__3190 = Vvar__1___24Anonymous__3191
& Vvar__0___24Anonymous__3188 = Vvar__0___24Anonymous__3189 ) ) ).
fof('$_inj_VFA.SearchTree.E',axiom,
! [Vvar__0__V__57025,Vvar__0__V__57026] :
( cVFA_2eSearchTree_2eE___24a1(Vvar__0__V__57025) = cVFA_2eSearchTree_2eE___24a1(Vvar__0__V__57026)
=> Vvar__0__V__57025 = Vvar__0__V__57026 ) ).
fof('$_inj_VFA.SearchTree.T',axiom,
! [Vvar__0__V__57027,Vvar__0__V__57028,Vvar__1___24Anonymous__57029,Vvar__1___24Anonymous__57030,Vvar__2___24Anonymous__57031,Vvar__2___24Anonymous__57032,Vvar__3___24Anonymous__57033,Vvar__3___24Anonymous__57034,Vvar__4___24Anonymous__57035,Vvar__4___24Anonymous__57036] :
( cVFA_2eSearchTree_2eT___24a5(Vvar__0__V__57027,Vvar__1___24Anonymous__57029,Vvar__2___24Anonymous__57031,Vvar__3___24Anonymous__57033,Vvar__4___24Anonymous__57035) = cVFA_2eSearchTree_2eT___24a5(Vvar__0__V__57028,Vvar__1___24Anonymous__57030,Vvar__2___24Anonymous__57032,Vvar__3___24Anonymous__57034,Vvar__4___24Anonymous__57036)
=> ( Vvar__4___24Anonymous__57035 = Vvar__4___24Anonymous__57036
& Vvar__3___24Anonymous__57033 = Vvar__3___24Anonymous__57034
& Vvar__2___24Anonymous__57031 = Vvar__2___24Anonymous__57032
& Vvar__1___24Anonymous__57029 = Vvar__1___24Anonymous__57030
& Vvar__0__V__57027 = Vvar__0__V__57028 ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__61394,Vvar__1__k__61396,Vvar__2___24Anonymous__61397] :
( c_24__type__61411___24t(Vvar__0__P__61394,Vvar__1__k__61396,Vvar__2___24Anonymous__61397,Vvar__0__P__61394)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__61396)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__61397)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__61394,Vvar__1__k__61396,Vvar__2___24Anonymous__61397)
=> ( Vvar__2___24Anonymous__61397 = Vvar__1__k__61396
| ? [Vvar__2__l__61405] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__61405)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__61394,Vvar__1__k__61396,Vvar__2__l__61405)
& p(happ(Vvar__0__P__61394,Vvar__2__l__61405))
& Vvar__2___24Anonymous__61397 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__61405) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__61413,Vvar__1__k__61415,Vvar__2___24Anonymous__61416] :
( c_24__type__61432___24t(Vvar__0__Q__61413,Vvar__1__k__61415,Vvar__2___24Anonymous__61416,Vvar__0__Q__61413)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__61415)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__61416)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__61413,Vvar__1__k__61415,Vvar__2___24Anonymous__61416)
=> ( ? [Vvar__2__l__61421] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__61421)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__61413,Vvar__1__k__61415,Vvar__2__l__61421)
& Vvar__2___24Anonymous__61416 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__61421) )
| ? [Vvar__2__l__61426] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__61426)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__61415,Vvar__2__l__61426)
& p(happ(Vvar__0__Q__61413,Vvar__2__l__61426))
& Vvar__2___24Anonymous__61416 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__61426) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__37213,Vvar__1___24Anonymous__37214,VX37215] :
( cProp___24t(Vvar__0__P__37213)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__37214)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__37213,Vvar__1___24Anonymous__37214,VX37215)
=> ( ( p(Vvar__0__P__37213)
& Vvar__1___24Anonymous__37214 = cCoq_2eInit_2eDatatypes_2etrue
& VX37215 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__37213) )
| ( ~ p(Vvar__0__P__37213)
& Vvar__1___24Anonymous__37214 = cCoq_2eInit_2eDatatypes_2efalse
& VX37215 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__37213) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX61014] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX61014)
=> ( VX61014 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__61015] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__61015)
& ? [Vvar__1___24Anonymous__61016] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__61016)
& ? [Vvar__2___24Anonymous__61017] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__61017)
& VX61014 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__61015,Vvar__1___24Anonymous__61016,Vvar__2___24Anonymous__61017) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX37420] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX37420)
=> ( VX37420 = cCoq_2eInit_2eByte_2ex00
| VX37420 = cCoq_2eInit_2eByte_2ex01
| VX37420 = cCoq_2eInit_2eByte_2ex02
| VX37420 = cCoq_2eInit_2eByte_2ex03
| VX37420 = cCoq_2eInit_2eByte_2ex04
| VX37420 = cCoq_2eInit_2eByte_2ex05
| VX37420 = cCoq_2eInit_2eByte_2ex06
| VX37420 = cCoq_2eInit_2eByte_2ex07
| VX37420 = cCoq_2eInit_2eByte_2ex08
| VX37420 = cCoq_2eInit_2eByte_2ex09
| VX37420 = cCoq_2eInit_2eByte_2ex0a
| VX37420 = cCoq_2eInit_2eByte_2ex0b
| VX37420 = cCoq_2eInit_2eByte_2ex0c
| VX37420 = cCoq_2eInit_2eByte_2ex0d
| VX37420 = cCoq_2eInit_2eByte_2ex0e
| VX37420 = cCoq_2eInit_2eByte_2ex0f
| VX37420 = cCoq_2eInit_2eByte_2ex10
| VX37420 = cCoq_2eInit_2eByte_2ex11
| VX37420 = cCoq_2eInit_2eByte_2ex12
| VX37420 = cCoq_2eInit_2eByte_2ex13
| VX37420 = cCoq_2eInit_2eByte_2ex14
| VX37420 = cCoq_2eInit_2eByte_2ex15
| VX37420 = cCoq_2eInit_2eByte_2ex16
| VX37420 = cCoq_2eInit_2eByte_2ex17
| VX37420 = cCoq_2eInit_2eByte_2ex18
| VX37420 = cCoq_2eInit_2eByte_2ex19
| VX37420 = cCoq_2eInit_2eByte_2ex1a
| VX37420 = cCoq_2eInit_2eByte_2ex1b
| VX37420 = cCoq_2eInit_2eByte_2ex1c
| VX37420 = cCoq_2eInit_2eByte_2ex1d
| VX37420 = cCoq_2eInit_2eByte_2ex1e
| VX37420 = cCoq_2eInit_2eByte_2ex1f
| VX37420 = cCoq_2eInit_2eByte_2ex20
| VX37420 = cCoq_2eInit_2eByte_2ex21
| VX37420 = cCoq_2eInit_2eByte_2ex22
| VX37420 = cCoq_2eInit_2eByte_2ex23
| VX37420 = cCoq_2eInit_2eByte_2ex24
| VX37420 = cCoq_2eInit_2eByte_2ex25
| VX37420 = cCoq_2eInit_2eByte_2ex26
| VX37420 = cCoq_2eInit_2eByte_2ex27
| VX37420 = cCoq_2eInit_2eByte_2ex28
| VX37420 = cCoq_2eInit_2eByte_2ex29
| VX37420 = cCoq_2eInit_2eByte_2ex2a
| VX37420 = cCoq_2eInit_2eByte_2ex2b
| VX37420 = cCoq_2eInit_2eByte_2ex2c
| VX37420 = cCoq_2eInit_2eByte_2ex2d
| VX37420 = cCoq_2eInit_2eByte_2ex2e
| VX37420 = cCoq_2eInit_2eByte_2ex2f
| VX37420 = cCoq_2eInit_2eByte_2ex30
| VX37420 = cCoq_2eInit_2eByte_2ex31
| VX37420 = cCoq_2eInit_2eByte_2ex32
| VX37420 = cCoq_2eInit_2eByte_2ex33
| VX37420 = cCoq_2eInit_2eByte_2ex34
| VX37420 = cCoq_2eInit_2eByte_2ex35
| VX37420 = cCoq_2eInit_2eByte_2ex36
| VX37420 = cCoq_2eInit_2eByte_2ex37
| VX37420 = cCoq_2eInit_2eByte_2ex38
| VX37420 = cCoq_2eInit_2eByte_2ex39
| VX37420 = cCoq_2eInit_2eByte_2ex3a
| VX37420 = cCoq_2eInit_2eByte_2ex3b
| VX37420 = cCoq_2eInit_2eByte_2ex3c
| VX37420 = cCoq_2eInit_2eByte_2ex3d
| VX37420 = cCoq_2eInit_2eByte_2ex3e
| VX37420 = cCoq_2eInit_2eByte_2ex3f
| VX37420 = cCoq_2eInit_2eByte_2ex40
| VX37420 = cCoq_2eInit_2eByte_2ex41
| VX37420 = cCoq_2eInit_2eByte_2ex42
| VX37420 = cCoq_2eInit_2eByte_2ex43
| VX37420 = cCoq_2eInit_2eByte_2ex44
| VX37420 = cCoq_2eInit_2eByte_2ex45
| VX37420 = cCoq_2eInit_2eByte_2ex46
| VX37420 = cCoq_2eInit_2eByte_2ex47
| VX37420 = cCoq_2eInit_2eByte_2ex48
| VX37420 = cCoq_2eInit_2eByte_2ex49
| VX37420 = cCoq_2eInit_2eByte_2ex4a
| VX37420 = cCoq_2eInit_2eByte_2ex4b
| VX37420 = cCoq_2eInit_2eByte_2ex4c
| VX37420 = cCoq_2eInit_2eByte_2ex4d
| VX37420 = cCoq_2eInit_2eByte_2ex4e
| VX37420 = cCoq_2eInit_2eByte_2ex4f
| VX37420 = cCoq_2eInit_2eByte_2ex50
| VX37420 = cCoq_2eInit_2eByte_2ex51
| VX37420 = cCoq_2eInit_2eByte_2ex52
| VX37420 = cCoq_2eInit_2eByte_2ex53
| VX37420 = cCoq_2eInit_2eByte_2ex54
| VX37420 = cCoq_2eInit_2eByte_2ex55
| VX37420 = cCoq_2eInit_2eByte_2ex56
| VX37420 = cCoq_2eInit_2eByte_2ex57
| VX37420 = cCoq_2eInit_2eByte_2ex58
| VX37420 = cCoq_2eInit_2eByte_2ex59
| VX37420 = cCoq_2eInit_2eByte_2ex5a
| VX37420 = cCoq_2eInit_2eByte_2ex5b
| VX37420 = cCoq_2eInit_2eByte_2ex5c
| VX37420 = cCoq_2eInit_2eByte_2ex5d
| VX37420 = cCoq_2eInit_2eByte_2ex5e
| VX37420 = cCoq_2eInit_2eByte_2ex5f
| VX37420 = cCoq_2eInit_2eByte_2ex60
| VX37420 = cCoq_2eInit_2eByte_2ex61
| VX37420 = cCoq_2eInit_2eByte_2ex62
| VX37420 = cCoq_2eInit_2eByte_2ex63
| VX37420 = cCoq_2eInit_2eByte_2ex64
| VX37420 = cCoq_2eInit_2eByte_2ex65
| VX37420 = cCoq_2eInit_2eByte_2ex66
| VX37420 = cCoq_2eInit_2eByte_2ex67
| VX37420 = cCoq_2eInit_2eByte_2ex68
| VX37420 = cCoq_2eInit_2eByte_2ex69
| VX37420 = cCoq_2eInit_2eByte_2ex6a
| VX37420 = cCoq_2eInit_2eByte_2ex6b
| VX37420 = cCoq_2eInit_2eByte_2ex6c
| VX37420 = cCoq_2eInit_2eByte_2ex6d
| VX37420 = cCoq_2eInit_2eByte_2ex6e
| VX37420 = cCoq_2eInit_2eByte_2ex6f
| VX37420 = cCoq_2eInit_2eByte_2ex70
| VX37420 = cCoq_2eInit_2eByte_2ex71
| VX37420 = cCoq_2eInit_2eByte_2ex72
| VX37420 = cCoq_2eInit_2eByte_2ex73
| VX37420 = cCoq_2eInit_2eByte_2ex74
| VX37420 = cCoq_2eInit_2eByte_2ex75
| VX37420 = cCoq_2eInit_2eByte_2ex76
| VX37420 = cCoq_2eInit_2eByte_2ex77
| VX37420 = cCoq_2eInit_2eByte_2ex78
| VX37420 = cCoq_2eInit_2eByte_2ex79
| VX37420 = cCoq_2eInit_2eByte_2ex7a
| VX37420 = cCoq_2eInit_2eByte_2ex7b
| VX37420 = cCoq_2eInit_2eByte_2ex7c
| VX37420 = cCoq_2eInit_2eByte_2ex7d
| VX37420 = cCoq_2eInit_2eByte_2ex7e
| VX37420 = cCoq_2eInit_2eByte_2ex7f
| VX37420 = cCoq_2eInit_2eByte_2ex80
| VX37420 = cCoq_2eInit_2eByte_2ex81
| VX37420 = cCoq_2eInit_2eByte_2ex82
| VX37420 = cCoq_2eInit_2eByte_2ex83
| VX37420 = cCoq_2eInit_2eByte_2ex84
| VX37420 = cCoq_2eInit_2eByte_2ex85
| VX37420 = cCoq_2eInit_2eByte_2ex86
| VX37420 = cCoq_2eInit_2eByte_2ex87
| VX37420 = cCoq_2eInit_2eByte_2ex88
| VX37420 = cCoq_2eInit_2eByte_2ex89
| VX37420 = cCoq_2eInit_2eByte_2ex8a
| VX37420 = cCoq_2eInit_2eByte_2ex8b
| VX37420 = cCoq_2eInit_2eByte_2ex8c
| VX37420 = cCoq_2eInit_2eByte_2ex8d
| VX37420 = cCoq_2eInit_2eByte_2ex8e
| VX37420 = cCoq_2eInit_2eByte_2ex8f
| VX37420 = cCoq_2eInit_2eByte_2ex90
| VX37420 = cCoq_2eInit_2eByte_2ex91
| VX37420 = cCoq_2eInit_2eByte_2ex92
| VX37420 = cCoq_2eInit_2eByte_2ex93
| VX37420 = cCoq_2eInit_2eByte_2ex94
| VX37420 = cCoq_2eInit_2eByte_2ex95
| VX37420 = cCoq_2eInit_2eByte_2ex96
| VX37420 = cCoq_2eInit_2eByte_2ex97
| VX37420 = cCoq_2eInit_2eByte_2ex98
| VX37420 = cCoq_2eInit_2eByte_2ex99
| VX37420 = cCoq_2eInit_2eByte_2ex9a
| VX37420 = cCoq_2eInit_2eByte_2ex9b
| VX37420 = cCoq_2eInit_2eByte_2ex9c
| VX37420 = cCoq_2eInit_2eByte_2ex9d
| VX37420 = cCoq_2eInit_2eByte_2ex9e
| VX37420 = cCoq_2eInit_2eByte_2ex9f
| VX37420 = cCoq_2eInit_2eByte_2exa0
| VX37420 = cCoq_2eInit_2eByte_2exa1
| VX37420 = cCoq_2eInit_2eByte_2exa2
| VX37420 = cCoq_2eInit_2eByte_2exa3
| VX37420 = cCoq_2eInit_2eByte_2exa4
| VX37420 = cCoq_2eInit_2eByte_2exa5
| VX37420 = cCoq_2eInit_2eByte_2exa6
| VX37420 = cCoq_2eInit_2eByte_2exa7
| VX37420 = cCoq_2eInit_2eByte_2exa8
| VX37420 = cCoq_2eInit_2eByte_2exa9
| VX37420 = cCoq_2eInit_2eByte_2exaa
| VX37420 = cCoq_2eInit_2eByte_2exab
| VX37420 = cCoq_2eInit_2eByte_2exac
| VX37420 = cCoq_2eInit_2eByte_2exad
| VX37420 = cCoq_2eInit_2eByte_2exae
| VX37420 = cCoq_2eInit_2eByte_2exaf
| VX37420 = cCoq_2eInit_2eByte_2exb0
| VX37420 = cCoq_2eInit_2eByte_2exb1
| VX37420 = cCoq_2eInit_2eByte_2exb2
| VX37420 = cCoq_2eInit_2eByte_2exb3
| VX37420 = cCoq_2eInit_2eByte_2exb4
| VX37420 = cCoq_2eInit_2eByte_2exb5
| VX37420 = cCoq_2eInit_2eByte_2exb6
| VX37420 = cCoq_2eInit_2eByte_2exb7
| VX37420 = cCoq_2eInit_2eByte_2exb8
| VX37420 = cCoq_2eInit_2eByte_2exb9
| VX37420 = cCoq_2eInit_2eByte_2exba
| VX37420 = cCoq_2eInit_2eByte_2exbb
| VX37420 = cCoq_2eInit_2eByte_2exbc
| VX37420 = cCoq_2eInit_2eByte_2exbd
| VX37420 = cCoq_2eInit_2eByte_2exbe
| VX37420 = cCoq_2eInit_2eByte_2exbf
| VX37420 = cCoq_2eInit_2eByte_2exc0
| VX37420 = cCoq_2eInit_2eByte_2exc1
| VX37420 = cCoq_2eInit_2eByte_2exc2
| VX37420 = cCoq_2eInit_2eByte_2exc3
| VX37420 = cCoq_2eInit_2eByte_2exc4
| VX37420 = cCoq_2eInit_2eByte_2exc5
| VX37420 = cCoq_2eInit_2eByte_2exc6
| VX37420 = cCoq_2eInit_2eByte_2exc7
| VX37420 = cCoq_2eInit_2eByte_2exc8
| VX37420 = cCoq_2eInit_2eByte_2exc9
| VX37420 = cCoq_2eInit_2eByte_2exca
| VX37420 = cCoq_2eInit_2eByte_2excb
| VX37420 = cCoq_2eInit_2eByte_2excc
| VX37420 = cCoq_2eInit_2eByte_2excd
| VX37420 = cCoq_2eInit_2eByte_2exce
| VX37420 = cCoq_2eInit_2eByte_2excf
| VX37420 = cCoq_2eInit_2eByte_2exd0
| VX37420 = cCoq_2eInit_2eByte_2exd1
| VX37420 = cCoq_2eInit_2eByte_2exd2
| VX37420 = cCoq_2eInit_2eByte_2exd3
| VX37420 = cCoq_2eInit_2eByte_2exd4
| VX37420 = cCoq_2eInit_2eByte_2exd5
| VX37420 = cCoq_2eInit_2eByte_2exd6
| VX37420 = cCoq_2eInit_2eByte_2exd7
| VX37420 = cCoq_2eInit_2eByte_2exd8
| VX37420 = cCoq_2eInit_2eByte_2exd9
| VX37420 = cCoq_2eInit_2eByte_2exda
| VX37420 = cCoq_2eInit_2eByte_2exdb
| VX37420 = cCoq_2eInit_2eByte_2exdc
| VX37420 = cCoq_2eInit_2eByte_2exdd
| VX37420 = cCoq_2eInit_2eByte_2exde
| VX37420 = cCoq_2eInit_2eByte_2exdf
| VX37420 = cCoq_2eInit_2eByte_2exe0
| VX37420 = cCoq_2eInit_2eByte_2exe1
| VX37420 = cCoq_2eInit_2eByte_2exe2
| VX37420 = cCoq_2eInit_2eByte_2exe3
| VX37420 = cCoq_2eInit_2eByte_2exe4
| VX37420 = cCoq_2eInit_2eByte_2exe5
| VX37420 = cCoq_2eInit_2eByte_2exe6
| VX37420 = cCoq_2eInit_2eByte_2exe7
| VX37420 = cCoq_2eInit_2eByte_2exe8
| VX37420 = cCoq_2eInit_2eByte_2exe9
| VX37420 = cCoq_2eInit_2eByte_2exea
| VX37420 = cCoq_2eInit_2eByte_2exeb
| VX37420 = cCoq_2eInit_2eByte_2exec
| VX37420 = cCoq_2eInit_2eByte_2exed
| VX37420 = cCoq_2eInit_2eByte_2exee
| VX37420 = cCoq_2eInit_2eByte_2exef
| VX37420 = cCoq_2eInit_2eByte_2exf0
| VX37420 = cCoq_2eInit_2eByte_2exf1
| VX37420 = cCoq_2eInit_2eByte_2exf2
| VX37420 = cCoq_2eInit_2eByte_2exf3
| VX37420 = cCoq_2eInit_2eByte_2exf4
| VX37420 = cCoq_2eInit_2eByte_2exf5
| VX37420 = cCoq_2eInit_2eByte_2exf6
| VX37420 = cCoq_2eInit_2eByte_2exf7
| VX37420 = cCoq_2eInit_2eByte_2exf8
| VX37420 = cCoq_2eInit_2eByte_2exf9
| VX37420 = cCoq_2eInit_2eByte_2exfa
| VX37420 = cCoq_2eInit_2eByte_2exfb
| VX37420 = cCoq_2eInit_2eByte_2exfc
| VX37420 = cCoq_2eInit_2eByte_2exfd
| VX37420 = cCoq_2eInit_2eByte_2exfe
| VX37420 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__61442,Vvar__1__Q__61443,Vvar__2___24Anonymous__61444] :
( cProp___24t(Vvar__0__P__61442)
=> ( cProp___24t(Vvar__1__Q__61443)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__61444)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__61442,Vvar__1__Q__61443,Vvar__2___24Anonymous__61444)
=> ( ( p(Vvar__0__P__61442)
& Vvar__2___24Anonymous__61444 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__61443)
& Vvar__2___24Anonymous__61444 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__61452,Vvar__1__Plt__61453,Vvar__2__Pgt__61454,Vvar__3___24Anonymous__61455] :
( cProp___24t(Vvar__0__Peq__61452)
=> ( cProp___24t(Vvar__1__Plt__61453)
=> ( cProp___24t(Vvar__2__Pgt__61454)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__61455)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__61452,Vvar__1__Plt__61453,Vvar__2__Pgt__61454,Vvar__3___24Anonymous__61455)
=> ( ( p(Vvar__0__Peq__61452)
& Vvar__3___24Anonymous__61455 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__61453)
& Vvar__3___24Anonymous__61455 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__61454)
& Vvar__3___24Anonymous__61455 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX1)
=> ( VX1 = cCoq_2eInit_2eDatatypes_2etrue
| VX1 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX7] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX7)
=> ( VX7 = cCoq_2eInit_2eDatatypes_2eEq
| VX7 = cCoq_2eInit_2eDatatypes_2eLt
| VX7 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__3249,VX3250] :
( cType___24t(Vvar__0__A__3249)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3249,VX3250)
=> ( VX3250 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3249)
| ? [Vvar__1___24Anonymous__3253] :
( t(Vvar__1___24Anonymous__3253,Vvar__0__A__3249)
& ? [Vvar__2___24Anonymous__3254] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3249,Vvar__2___24Anonymous__3254)
& VX3250 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3249,Vvar__1___24Anonymous__3253,Vvar__2___24Anonymous__3254) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX2)
=> ( VX2 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3)
& VX2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__3992,VX3993] :
( cType___24t(Vvar__0__A__3992)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__3992,VX3993)
=> ( ? [Vvar__1___24Anonymous__3995] :
( t(Vvar__1___24Anonymous__3995,Vvar__0__A__3992)
& VX3993 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3992,Vvar__1___24Anonymous__3995) )
| VX3993 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3992) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__38138,Vvar__1__B__38139,VX38140] :
( cType___24t(Vvar__0__A__38138)
=> ( cType___24t(Vvar__1__B__38139)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__38138,Vvar__1__B__38139,VX38140)
=> ? [Vvar__2___24Anonymous__38143] :
( t(Vvar__2___24Anonymous__38143,Vvar__0__A__38138)
& ? [Vvar__3___24Anonymous__38144] :
( t(Vvar__3___24Anonymous__38144,Vvar__1__B__38139)
& VX38140 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__38138,Vvar__1__B__38139,Vvar__2___24Anonymous__38143,Vvar__3___24Anonymous__38144) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX4299] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX4299)
=> VX4299 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__4024,Vvar__1___24Anonymous__4025] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__4024)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__4025)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__4024,Vvar__1___24Anonymous__4025)
=> ( Vvar__1___24Anonymous__4025 = Vvar__0__n__4024
| ? [Vvar__1__m__4029] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__4029)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__4024,Vvar__1__m__4029)
& Vvar__1___24Anonymous__4025 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__4029) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__4475,Vvar__1__P__4476,VX4479] :
( cType___24t(Vvar__0__A__4475)
=> ( c_24__type__4489___24t(Vvar__0__A__4475,Vvar__1__P__4476,Vvar__1__P__4476)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__4475,Vvar__1__P__4476,VX4479)
=> ? [Vvar__2__x__4484] :
( t(Vvar__2__x__4484,Vvar__0__A__4475)
& p(happ(Vvar__1__P__4476,Vvar__2__x__4484))
& VX4479 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__4475,Vvar__1__P__4476,Vvar__2__x__4484) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__64068,Vvar__1__P__64069,VX64072] :
( cType___24t(Vvar__0__A__64068)
=> ( c_24__type__64082___24t(Vvar__0__A__64068,Vvar__1__P__64069,Vvar__1__P__64069)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__64068,Vvar__1__P__64069,VX64072)
=> ? [Vvar__2__x__64077] :
( t(Vvar__2__x__64077,Vvar__0__A__64068)
& ? [Vvar__3___24Anonymous__64078] :
( t(Vvar__3___24Anonymous__64078,happ(Vvar__1__P__64069,Vvar__2__x__64077))
& VX64072 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__64068,Vvar__1__P__64069,Vvar__2__x__64077,Vvar__3___24Anonymous__64078) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__3397,Vvar__1__B__3398,VX3399] :
( cProp___24t(Vvar__0__A__3397)
=> ( cProp___24t(Vvar__1__B__3398)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__3397,Vvar__1__B__3398,VX3399)
=> ( ( p(Vvar__0__A__3397)
& VX3399 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3397,Vvar__1__B__3398) )
| ( p(Vvar__1__B__3398)
& VX3399 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3397,Vvar__1__B__3398) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__4556,Vvar__1__B__4557,VX4558] :
( cType___24t(Vvar__0__A__4556)
=> ( cProp___24t(Vvar__1__B__4557)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__4556,Vvar__1__B__4557,VX4558)
=> ( ? [Vvar__2___24Anonymous__4561] :
( t(Vvar__2___24Anonymous__4561,Vvar__0__A__4556)
& VX4558 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__4556,Vvar__1__B__4557,Vvar__2___24Anonymous__4561) )
| ( p(Vvar__1__B__4557)
& VX4558 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__4556,Vvar__1__B__4557) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__63210,Vvar__1__a__63211,Vvar__2___24Anonymous__63212,Vvar__3___24Anonymous__63213] :
( cType___24t(Vvar__0__A__63210)
=> ( t(Vvar__1__a__63211,Vvar__0__A__63210)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63210,Vvar__2___24Anonymous__63212)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63210,Vvar__3___24Anonymous__63213)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__63210,Vvar__1__a__63211,Vvar__2___24Anonymous__63212,Vvar__3___24Anonymous__63213)
=> ( ? [Vvar__2__l__63217] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63210,Vvar__2__l__63217)
& Vvar__3___24Anonymous__63213 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63210,Vvar__1__a__63211,Vvar__2__l__63217)
& Vvar__2___24Anonymous__63212 = Vvar__2__l__63217 )
| ? [Vvar__2__x__63220] :
( t(Vvar__2__x__63220,Vvar__0__A__63210)
& ? [Vvar__3__l__63221] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63210,Vvar__3__l__63221)
& ? [Vvar__4__l_27__63222] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63210,Vvar__4__l_27__63222)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__63210,Vvar__1__a__63211,Vvar__3__l__63221,Vvar__4__l_27__63222)
& Vvar__3___24Anonymous__63213 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63210,Vvar__2__x__63220,Vvar__4__l_27__63222)
& Vvar__2___24Anonymous__63212 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63210,Vvar__2__x__63220,Vvar__3__l__63221) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__63224,Vvar__1__P__63225,Vvar__2___24Anonymous__63228] :
( cType___24t(Vvar__0__A__63224)
=> ( c_24__type__63248___24t(Vvar__0__A__63224,Vvar__1__P__63225,Vvar__2___24Anonymous__63228,Vvar__1__P__63225)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63224,Vvar__2___24Anonymous__63228)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__63224,Vvar__1__P__63225,Vvar__2___24Anonymous__63228)
=> ( ? [Vvar__2__x__63234] :
( t(Vvar__2__x__63234,Vvar__0__A__63224)
& ? [Vvar__3__l__63235] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63224,Vvar__3__l__63235)
& p(happ(Vvar__1__P__63225,Vvar__2__x__63234))
& Vvar__2___24Anonymous__63228 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63224,Vvar__2__x__63234,Vvar__3__l__63235) ) )
| ? [Vvar__2__x__63241] :
( t(Vvar__2__x__63241,Vvar__0__A__63224)
& ? [Vvar__3__l__63242] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63224,Vvar__3__l__63242)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__63224,Vvar__1__P__63225,Vvar__3__l__63242)
& Vvar__2___24Anonymous__63228 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63224,Vvar__2__x__63241,Vvar__3__l__63242) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__63250,Vvar__1__P__63251,Vvar__2___24Anonymous__63254] :
( cType___24t(Vvar__0__A__63250)
=> ( c_24__type__63272___24t(Vvar__0__A__63250,Vvar__1__P__63251,Vvar__2___24Anonymous__63254,Vvar__1__P__63251)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63250,Vvar__2___24Anonymous__63254)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__63250,Vvar__1__P__63251,Vvar__2___24Anonymous__63254)
=> ( Vvar__2___24Anonymous__63254 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__63250)
| ? [Vvar__2__x__63264] :
( t(Vvar__2__x__63264,Vvar__0__A__63250)
& ? [Vvar__3__l__63265] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63250,Vvar__3__l__63265)
& p(happ(Vvar__1__P__63251,Vvar__2__x__63264))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__63250,Vvar__1__P__63251,Vvar__3__l__63265)
& Vvar__2___24Anonymous__63254 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63250,Vvar__2__x__63264,Vvar__3__l__63265) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__42513,Vvar__1___24Anonymous__42514] :
( cType___24t(Vvar__0__A__42513)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42513,Vvar__1___24Anonymous__42514)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__42513,Vvar__1___24Anonymous__42514)
=> ( Vvar__1___24Anonymous__42514 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__42513)
| ? [Vvar__1__x__42518] :
( t(Vvar__1__x__42518,Vvar__0__A__42513)
& ? [Vvar__2__l__42519] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42513,Vvar__2__l__42519)
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__42513,Vvar__1__x__42518,Vvar__2__l__42519))
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__42513,Vvar__2__l__42519)
& Vvar__1___24Anonymous__42514 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__42513,Vvar__1__x__42518,Vvar__2__l__42519) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__57190,Vvar__1__eqA__57191,Vvar__2__x__57196,Vvar__3___24Anonymous__57197] :
( cType___24t(Vvar__0__A__57190)
=> ( c_24__type__57230___24t(Vvar__0__A__57190,Vvar__1__eqA__57191,Vvar__2__x__57196,Vvar__3___24Anonymous__57197,Vvar__1__eqA__57191)
=> ( t(Vvar__2__x__57196,Vvar__0__A__57190)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__57190,Vvar__3___24Anonymous__57197)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__57190,Vvar__1__eqA__57191,Vvar__2__x__57196,Vvar__3___24Anonymous__57197)
=> ( ? [Vvar__3__y__57206] :
( t(Vvar__3__y__57206,Vvar__0__A__57190)
& ? [Vvar__4__l__57207] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__57190,Vvar__4__l__57207)
& p(happ(happ(Vvar__1__eqA__57191,Vvar__2__x__57196),Vvar__3__y__57206))
& Vvar__3___24Anonymous__57197 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__57190,Vvar__3__y__57206,Vvar__4__l__57207) ) )
| ? [Vvar__3__y__57216] :
( t(Vvar__3__y__57216,Vvar__0__A__57190)
& ? [Vvar__4__l__57217] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__57190,Vvar__4__l__57217)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__57190,Vvar__1__eqA__57191,Vvar__2__x__57196,Vvar__4__l__57217)
& Vvar__3___24Anonymous__57197 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__57190,Vvar__3__y__57216,Vvar__4__l__57217) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__57244,Vvar__1__eqA__57245,Vvar__2___24Anonymous__57250] :
( cType___24t(Vvar__0__A__57244)
=> ( c_24__type__57277___24t(Vvar__0__A__57244,Vvar__1__eqA__57245,Vvar__2___24Anonymous__57250,Vvar__1__eqA__57245)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__57244,Vvar__2___24Anonymous__57250)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__57244,Vvar__1__eqA__57245,Vvar__2___24Anonymous__57250)
=> ( Vvar__2___24Anonymous__57250 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__57244)
| ? [Vvar__2__x__57264] :
( t(Vvar__2__x__57264,Vvar__0__A__57244)
& ? [Vvar__3__l__57265] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__57244,Vvar__3__l__57265)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__57244,Vvar__1__eqA__57245,Vvar__2__x__57264,Vvar__3__l__57265)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__57244,Vvar__1__eqA__57245,Vvar__3__l__57265)
& Vvar__2___24Anonymous__57250 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__57244,Vvar__2__x__57264,Vvar__3__l__57265) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__61481,Vvar__1__P__61482,Vvar__2__p__61485,Vvar__3__x__61486,Vvar__4__q__61487,Vvar__5___24Anonymous__61488] :
( cType___24t(Vvar__0__U__61481)
=> ( c_24__type__61503___24t(Vvar__0__U__61481,Vvar__1__P__61482,Vvar__2__p__61485,Vvar__3__x__61486,Vvar__4__q__61487,Vvar__5___24Anonymous__61488,Vvar__1__P__61482)
=> ( t(Vvar__2__p__61485,Vvar__0__U__61481)
=> ( t(Vvar__3__x__61486,happ(Vvar__1__P__61482,Vvar__2__p__61485))
=> ( t(Vvar__4__q__61487,Vvar__0__U__61481)
=> ( t(Vvar__5___24Anonymous__61488,happ(Vvar__1__P__61482,Vvar__4__q__61487))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__61481,Vvar__1__P__61482,Vvar__2__p__61485,Vvar__3__x__61486,Vvar__4__q__61487,Vvar__5___24Anonymous__61488)
=> ( Vvar__5___24Anonymous__61488 = Vvar__3__x__61486
& Vvar__4__q__61487 = Vvar__2__p__61485 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX3231] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX3231)
=> ( VX3231 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__3232] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3232)
& VX3231 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3232) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX3236] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX3236)
=> ( VX3236 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__3237] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3237)
& VX3236 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3237) )
| ? [Vvar__0___24Anonymous__3238] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3238)
& VX3236 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3238) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX3959] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX3959)
=> ( ? [Vvar__0___24Anonymous__3960] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3960)
& VX3959 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3960) )
| ? [Vvar__0___24Anonymous__3961] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3961)
& VX3959 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3961) )
| VX3959 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX4438] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX4438)
=> ? [Vvar__0__Qnum__4439] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__4439)
& ? [Vvar__1__Qden__4440] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__4440)
& VX4438 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__4439,Vvar__1__Qden__4440) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX43930] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX43930)
=> ? [Vvar__0__nonzero__43931] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__43931)
& Vvar__0__nonzero__43931 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX43930 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__43931) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__63554,Vvar__1___24Anonymous__63555,VX63556] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__63554)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__63555)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__63554,Vvar__1___24Anonymous__63555,VX63556)
=> ( ( Vvar__0__x__63554 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__63555 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX63556 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__63554) )
| ? [Vvar__1__n__63560] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__63560)
& Vvar__0__x__63554 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__63560)
& Vvar__1___24Anonymous__63555 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2463580___24a3(Vvar__0__x__63554,Vvar__1___24Anonymous__63555,Vvar__1__n__63560)
& VX63556 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__63554,Vvar__1__n__63560) )
| ? [Vvar__1__n__63565] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__63565)
& Vvar__0__x__63554 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__63565))
& Vvar__1___24Anonymous__63555 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2463597___24a3(Vvar__0__x__63554,Vvar__1___24Anonymous__63555,Vvar__1__n__63565)
& VX63556 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__63554,Vvar__1__n__63565) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__63525,Vvar__1___24Anonymous__63526,Vvar__2___24Anonymous__63527] :
( cType___24t(Vvar__0__A__63525)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63525,Vvar__1___24Anonymous__63526)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63525,Vvar__2___24Anonymous__63527)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__63525,Vvar__1___24Anonymous__63526,Vvar__2___24Anonymous__63527)
=> ( ( Vvar__2___24Anonymous__63527 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__63525)
& Vvar__1___24Anonymous__63526 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__63525) )
| ? [Vvar__1__x__63531] :
( t(Vvar__1__x__63531,Vvar__0__A__63525)
& ? [Vvar__2__l__63532] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63525,Vvar__2__l__63532)
& ? [Vvar__3__l_27__63533] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63525,Vvar__3__l_27__63533)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__63525,Vvar__2__l__63532,Vvar__3__l_27__63533)
& Vvar__2___24Anonymous__63527 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63525,Vvar__1__x__63531,Vvar__3__l_27__63533)
& Vvar__1___24Anonymous__63526 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63525,Vvar__1__x__63531,Vvar__2__l__63532) ) ) )
| ? [Vvar__1__x__63536] :
( t(Vvar__1__x__63536,Vvar__0__A__63525)
& ? [Vvar__2__y__63537] :
( t(Vvar__2__y__63537,Vvar__0__A__63525)
& ? [Vvar__3__l__63538] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63525,Vvar__3__l__63538)
& Vvar__2___24Anonymous__63527 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63525,Vvar__1__x__63536,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63525,Vvar__2__y__63537,Vvar__3__l__63538))
& Vvar__1___24Anonymous__63526 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63525,Vvar__2__y__63537,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__63525,Vvar__1__x__63536,Vvar__3__l__63538)) ) ) )
| ? [Vvar__1__l__63540] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63525,Vvar__1__l__63540)
& ? [Vvar__2__l_27__63541] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63525,Vvar__2__l_27__63541)
& ? [Vvar__3__l_27_27__63542] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__63525,Vvar__3__l_27_27__63542)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__63525,Vvar__1__l__63540,Vvar__2__l_27__63541)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__63525,Vvar__2__l_27__63541,Vvar__3__l_27_27__63542)
& Vvar__2___24Anonymous__63527 = Vvar__3__l_27_27__63542
& Vvar__1___24Anonymous__63526 = Vvar__1__l__63540 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX3934] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX3934)
=> ? [Vvar__0___24Anonymous__3935] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__3935)
& ? [Vvar__1___24Anonymous__3936] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__3936)
& ? [Vvar__2___24Anonymous__3937] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__3937)
& ? [Vvar__3___24Anonymous__3938] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__3938)
& ? [Vvar__4___24Anonymous__3939] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__3939)
& ? [Vvar__5___24Anonymous__3940] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__3940)
& ? [Vvar__6___24Anonymous__3941] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__3941)
& ? [Vvar__7___24Anonymous__3942] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__3942)
& VX3934 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__3935,Vvar__1___24Anonymous__3936,Vvar__2___24Anonymous__3937,Vvar__3___24Anonymous__3938,Vvar__4___24Anonymous__3939,Vvar__5___24Anonymous__3940,Vvar__6___24Anonymous__3941,Vvar__7___24Anonymous__3942) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX4045] :
( cCoq_2eStrings_2eString_2estring___24t(VX4045)
=> ( VX4045 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__4046] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__4046)
& ? [Vvar__1___24Anonymous__4047] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__4047)
& VX4045 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__4046,Vvar__1___24Anonymous__4047) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__64789,Vvar__1___24Anonymous__64790] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__64789)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__64790)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__64789,Vvar__1___24Anonymous__64790)
=> ( ? [Vvar__0__a__64792] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__64792)
& ? [Vvar__1__s__64793] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__64793)
& Vvar__1___24Anonymous__64790 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__64792,Vvar__1__s__64793)
& Vvar__0___24Anonymous__64789 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__64794] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__64794)
& ? [Vvar__1__s1__64795] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__64795)
& ? [Vvar__2__s2__64796] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__64796)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__64795,Vvar__2__s2__64796)
& Vvar__1___24Anonymous__64790 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__64794,Vvar__2__s2__64796)
& Vvar__0___24Anonymous__64789 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__64794,Vvar__1__s1__64795) ) ) )
| ? [Vvar__0__a__64798] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__64798)
& ? [Vvar__1__b__64799] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__64799)
& ? [Vvar__2__s1__64800] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__64800)
& ? [Vvar__3__s2__64801] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__64801)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__64798),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__64799))
& Vvar__1___24Anonymous__64790 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__64799,Vvar__3__s2__64801)
& Vvar__0___24Anonymous__64789 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__64798,Vvar__2__s1__64800) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__41221,VX41222] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__41221)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__41221,VX41222)
=> ( ? [Vvar__0__n__41223] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__41223)
& Vvar__0___24Anonymous__41221 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__41223)
& VX41222 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__41223) )
| ? [Vvar__0__n__41224] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__41224)
& ? [Vvar__1___24Anonymous__41225] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__41224,Vvar__1___24Anonymous__41225)
& Vvar__0___24Anonymous__41221 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__41224)
& VX41222 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__41224,Vvar__1___24Anonymous__41225) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__58880,Vvar__1___24Anonymous__58881,VX58882] :
( cType___24t(Vvar__0__A__58880)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__58881)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__58880,Vvar__1___24Anonymous__58881,VX58882)
=> ( ( Vvar__1___24Anonymous__58881 = cCoq_2eInit_2eDatatypes_2eO
& VX58882 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__58880) )
| ? [Vvar__1__h__58885] :
( t(Vvar__1__h__58885,Vvar__0__A__58880)
& ? [Vvar__2__n__58886] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__58886)
& ? [Vvar__3___24Anonymous__58887] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__58880,Vvar__2__n__58886,Vvar__3___24Anonymous__58887)
& Vvar__1___24Anonymous__58881 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__58886)
& VX58882 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__58880,Vvar__1__h__58885,Vvar__2__n__58886,Vvar__3___24Anonymous__58887) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__59986,Vvar__1__b__59987,Vvar__2__g__59988] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__59986)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__59987)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__59988)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__59986,Vvar__1__b__59987,Vvar__2__g__59988)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__59988,Vvar__0__a__59986)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__59988,Vvar__1__b__59987)
& ! [Vvar__var__var__var__var__5__x__59996__59999__60002__60005__60008] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__59996__59999__60002__60005__60008)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__59996__59999__60002__60005__60008,Vvar__0__a__59986)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__59996__59999__60002__60005__60008,Vvar__1__b__59987)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__59996__59999__60002__60005__60008,Vvar__2__g__59988) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__60018] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__60018)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__60018)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__60018))
& ! [Vvar__var__var__2__n__60023__60025__60027] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__60023__60025__60027)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__60023__60025__60027))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__60023__60025__60027,Vvar__0__p__60018)) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__60023__60025__60027,Vvar__0__p__60018) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__38252,VX38253] :
( cType___24t(Vvar__0__C__38252)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__38252,VX38253)
=> ( ? [Vvar__1___24Anonymous__38255] :
( t(Vvar__1___24Anonymous__38255,Vvar__0__C__38252)
& VX38253 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__38252,Vvar__1___24Anonymous__38255) )
| ? [Vvar__1___24Anonymous__38257] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__38257)
& VX38253 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__38252,Vvar__1___24Anonymous__38257) )
| ? [Vvar__1___24Anonymous__38259] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__38252,Vvar__1___24Anonymous__38259)
& ? [Vvar__2___24Anonymous__38260] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__38252,Vvar__2___24Anonymous__38260)
& VX38253 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__38252,Vvar__1___24Anonymous__38259,Vvar__2___24Anonymous__38260) ) )
| ? [Vvar__1___24Anonymous__38262] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__38252,Vvar__1___24Anonymous__38262)
& ? [Vvar__2___24Anonymous__38263] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__38252,Vvar__2___24Anonymous__38263)
& VX38253 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__38252,Vvar__1___24Anonymous__38262,Vvar__2___24Anonymous__38263) ) )
| ? [Vvar__1___24Anonymous__38265] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__38252,Vvar__1___24Anonymous__38265)
& ? [Vvar__2___24Anonymous__38266] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__38252,Vvar__2___24Anonymous__38266)
& VX38253 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__38252,Vvar__1___24Anonymous__38265,Vvar__2___24Anonymous__38266) ) )
| ? [Vvar__1___24Anonymous__38268] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__38252,Vvar__1___24Anonymous__38268)
& VX38253 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__38252,Vvar__1___24Anonymous__38268) )
| ? [Vvar__1___24Anonymous__38270] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__38252,Vvar__1___24Anonymous__38270)
& ? [Vvar__2___24Anonymous__38271] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__38271)
& VX38253 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__38252,Vvar__1___24Anonymous__38270,Vvar__2___24Anonymous__38271) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__38416,VX38417] :
( cType___24t(Vvar__0__C__38416)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__38416,VX38417)
=> ( ? [Vvar__1___24Anonymous__38419] :
( t(Vvar__1___24Anonymous__38419,Vvar__0__C__38416)
& VX38417 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__38416,Vvar__1___24Anonymous__38419) )
| ? [Vvar__1___24Anonymous__38421] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__38421)
& ? [Vvar__2___24Anonymous__38422] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__38416,Vvar__2___24Anonymous__38422)
& VX38417 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__38416,Vvar__1___24Anonymous__38421,Vvar__2___24Anonymous__38422) ) )
| ? [Vvar__1___24Anonymous__38424] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__38416,Vvar__1___24Anonymous__38424)
& ? [Vvar__2___24Anonymous__38425] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__38425)
& ? [Vvar__3___24Anonymous__38426] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__38416,Vvar__3___24Anonymous__38426)
& VX38417 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__38416,Vvar__1___24Anonymous__38424,Vvar__2___24Anonymous__38425,Vvar__3___24Anonymous__38426) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__42650,Vvar__1__rO__42651,Vvar__2__rI__42652,Vvar__3__rplus__42653,Vvar__4__rtimes__42658,Vvar__5__rminus__42663,Vvar__6__ropp__42668,Vvar__7__req__42671,Vvar__8__rle__42676,Vvar__9__rlt__42681] :
( cType___24t(Vvar__0__R__42650)
=> ( t(Vvar__1__rO__42651,Vvar__0__R__42650)
=> ( t(Vvar__2__rI__42652,Vvar__0__R__42650)
=> ( c_24__type__43082___24t(Vvar__0__R__42650,Vvar__1__rO__42651,Vvar__2__rI__42652,Vvar__3__rplus__42653,Vvar__4__rtimes__42658,Vvar__5__rminus__42663,Vvar__6__ropp__42668,Vvar__7__req__42671,Vvar__8__rle__42676,Vvar__9__rlt__42681,Vvar__3__rplus__42653)
=> ( c_24__type__43183___24t(Vvar__0__R__42650,Vvar__1__rO__42651,Vvar__2__rI__42652,Vvar__3__rplus__42653,Vvar__4__rtimes__42658,Vvar__5__rminus__42663,Vvar__6__ropp__42668,Vvar__7__req__42671,Vvar__8__rle__42676,Vvar__9__rlt__42681,Vvar__4__rtimes__42658)
=> ( c_24__type__43284___24t(Vvar__0__R__42650,Vvar__1__rO__42651,Vvar__2__rI__42652,Vvar__3__rplus__42653,Vvar__4__rtimes__42658,Vvar__5__rminus__42663,Vvar__6__ropp__42668,Vvar__7__req__42671,Vvar__8__rle__42676,Vvar__9__rlt__42681,Vvar__5__rminus__42663)
=> ( c_24__type__43374___24t(Vvar__0__R__42650,Vvar__1__rO__42651,Vvar__2__rI__42652,Vvar__3__rplus__42653,Vvar__4__rtimes__42658,Vvar__5__rminus__42663,Vvar__6__ropp__42668,Vvar__7__req__42671,Vvar__8__rle__42676,Vvar__9__rlt__42681,Vvar__6__ropp__42668)
=> ( c_24__type__43475___24t(Vvar__0__R__42650,Vvar__1__rO__42651,Vvar__2__rI__42652,Vvar__3__rplus__42653,Vvar__4__rtimes__42658,Vvar__5__rminus__42663,Vvar__6__ropp__42668,Vvar__7__req__42671,Vvar__8__rle__42676,Vvar__9__rlt__42681,Vvar__7__req__42671)
=> ( c_24__type__43576___24t(Vvar__0__R__42650,Vvar__1__rO__42651,Vvar__2__rI__42652,Vvar__3__rplus__42653,Vvar__4__rtimes__42658,Vvar__5__rminus__42663,Vvar__6__ropp__42668,Vvar__7__req__42671,Vvar__8__rle__42676,Vvar__9__rlt__42681,Vvar__8__rle__42676)
=> ( c_24__type__43677___24t(Vvar__0__R__42650,Vvar__1__rO__42651,Vvar__2__rI__42652,Vvar__3__rplus__42653,Vvar__4__rtimes__42658,Vvar__5__rminus__42663,Vvar__6__ropp__42668,Vvar__7__req__42671,Vvar__8__rle__42676,Vvar__9__rlt__42681,Vvar__9__rlt__42681)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__42650,Vvar__1__rO__42651,Vvar__2__rI__42652,Vvar__3__rplus__42653,Vvar__4__rtimes__42658,Vvar__5__rminus__42663,Vvar__6__ropp__42668,Vvar__7__req__42671,Vvar__8__rle__42676,Vvar__9__rlt__42681)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__42650,Vvar__7__req__42671)
& ! [Vvar__var__var__var__var__11__x1__42725__42731__42836__42842__42848] :
( t(Vvar__var__var__var__var__11__x1__42725__42731__42836__42842__42848,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__12__x2__42726__42732__42837__42843__42849] :
( t(Vvar__var__var__var__var__12__x2__42726__42732__42837__42843__42849,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__11__x1__42725__42731__42836__42842__42848),Vvar__var__var__var__var__12__x2__42726__42732__42837__42843__42849))
=> ! [Vvar__var__var__var__var__14__y1__42727__42733__42838__42844__42850] :
( t(Vvar__var__var__var__var__14__y1__42727__42733__42838__42844__42850,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__15__y2__42728__42734__42839__42845__42851] :
( t(Vvar__var__var__var__var__15__y2__42728__42734__42839__42845__42851,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__14__y1__42727__42733__42838__42844__42850),Vvar__var__var__var__var__15__y2__42728__42734__42839__42845__42851))
=> p(happ(happ(Vvar__7__req__42671,happ(happ(Vvar__3__rplus__42653,Vvar__var__var__var__var__11__x1__42725__42731__42836__42842__42848),Vvar__var__var__var__var__14__y1__42727__42733__42838__42844__42850)),happ(happ(Vvar__3__rplus__42653,Vvar__var__var__var__var__12__x2__42726__42732__42837__42843__42849),Vvar__var__var__var__var__15__y2__42728__42734__42839__42845__42851))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__42738__42744__42854__42860__42866] :
( t(Vvar__var__var__var__var__12__x1__42738__42744__42854__42860__42866,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__13__x2__42739__42745__42855__42861__42867] :
( t(Vvar__var__var__var__var__13__x2__42739__42745__42855__42861__42867,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__12__x1__42738__42744__42854__42860__42866),Vvar__var__var__var__var__13__x2__42739__42745__42855__42861__42867))
=> ! [Vvar__var__var__var__var__15__y1__42740__42746__42856__42862__42868] :
( t(Vvar__var__var__var__var__15__y1__42740__42746__42856__42862__42868,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__16__y2__42741__42747__42857__42863__42869] :
( t(Vvar__var__var__var__var__16__y2__42741__42747__42857__42863__42869,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__15__y1__42740__42746__42856__42862__42868),Vvar__var__var__var__var__16__y2__42741__42747__42857__42863__42869))
=> p(happ(happ(Vvar__7__req__42671,happ(happ(Vvar__4__rtimes__42658,Vvar__var__var__var__var__12__x1__42738__42744__42854__42860__42866),Vvar__var__var__var__var__15__y1__42740__42746__42856__42862__42868)),happ(happ(Vvar__4__rtimes__42658,Vvar__var__var__var__var__13__x2__42739__42745__42855__42861__42867),Vvar__var__var__var__var__16__y2__42741__42747__42857__42863__42869))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__42751__42754__42872__42875__42878] :
( t(Vvar__var__var__var__var__13__x1__42751__42754__42872__42875__42878,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__14__x2__42752__42755__42873__42876__42879] :
( t(Vvar__var__var__var__var__14__x2__42752__42755__42873__42876__42879,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__13__x1__42751__42754__42872__42875__42878),Vvar__var__var__var__var__14__x2__42752__42755__42873__42876__42879))
=> p(happ(happ(Vvar__7__req__42671,happ(Vvar__6__ropp__42668,Vvar__var__var__var__var__13__x1__42751__42754__42872__42875__42878)),happ(Vvar__6__ropp__42668,Vvar__var__var__var__var__14__x2__42752__42755__42873__42876__42879))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__42758__42764__42881__42887__42893] :
( t(Vvar__var__var__var__var__14__x1__42758__42764__42881__42887__42893,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__15__x2__42759__42765__42882__42888__42894] :
( t(Vvar__var__var__var__var__15__x2__42759__42765__42882__42888__42894,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__14__x1__42758__42764__42881__42887__42893),Vvar__var__var__var__var__15__x2__42759__42765__42882__42888__42894))
=> ! [Vvar__var__var__var__var__17__y1__42760__42766__42883__42889__42895] :
( t(Vvar__var__var__var__var__17__y1__42760__42766__42883__42889__42895,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__18__y2__42761__42767__42884__42890__42896] :
( t(Vvar__var__var__var__var__18__y2__42761__42767__42884__42890__42896,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__17__y1__42760__42766__42883__42889__42895),Vvar__var__var__var__var__18__y2__42761__42767__42884__42890__42896))
=> ( p(happ(happ(Vvar__8__rle__42676,Vvar__var__var__var__var__14__x1__42758__42764__42881__42887__42893),Vvar__var__var__var__var__17__y1__42760__42766__42883__42889__42895))
<=> p(happ(happ(Vvar__8__rle__42676,Vvar__var__var__var__var__15__x2__42759__42765__42882__42888__42894),Vvar__var__var__var__var__18__y2__42761__42767__42884__42890__42896)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__42771__42777__42899__42905__42911] :
( t(Vvar__var__var__var__var__15__x1__42771__42777__42899__42905__42911,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__16__x2__42772__42778__42900__42906__42912] :
( t(Vvar__var__var__var__var__16__x2__42772__42778__42900__42906__42912,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__15__x1__42771__42777__42899__42905__42911),Vvar__var__var__var__var__16__x2__42772__42778__42900__42906__42912))
=> ! [Vvar__var__var__var__var__18__y1__42773__42779__42901__42907__42913] :
( t(Vvar__var__var__var__var__18__y1__42773__42779__42901__42907__42913,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__19__y2__42774__42780__42902__42908__42914] :
( t(Vvar__var__var__var__var__19__y2__42774__42780__42902__42908__42914,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__18__y1__42773__42779__42901__42907__42913),Vvar__var__var__var__var__19__y2__42774__42780__42902__42908__42914))
=> ( p(happ(happ(Vvar__9__rlt__42681,Vvar__var__var__var__var__15__x1__42771__42777__42899__42905__42911),Vvar__var__var__var__var__18__y1__42773__42779__42901__42907__42913))
<=> p(happ(happ(Vvar__9__rlt__42681,Vvar__var__var__var__var__16__x2__42772__42778__42900__42906__42912),Vvar__var__var__var__var__19__y2__42774__42780__42902__42908__42914)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__42650,Vvar__1__rO__42651,Vvar__2__rI__42652,Vvar__3__rplus__42653,Vvar__4__rtimes__42658,Vvar__5__rminus__42663,Vvar__6__ropp__42668,Vvar__7__req__42671)
& ! [Vvar__var__var__var__17__n__42785__42786__42917__42918] :
( t(Vvar__var__var__var__17__n__42785__42786__42917__42918,Vvar__0__R__42650)
=> p(happ(happ(Vvar__8__rle__42676,Vvar__var__var__var__17__n__42785__42786__42917__42918),Vvar__var__var__var__17__n__42785__42786__42917__42918)) )
& ! [Vvar__var__var__var__var__18__n__42788__42792__42919__42923__42927] :
( t(Vvar__var__var__var__var__18__n__42788__42792__42919__42923__42927,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__19__m__42789__42793__42920__42924__42928] :
( t(Vvar__var__var__var__var__19__m__42789__42793__42920__42924__42928,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__8__rle__42676,Vvar__var__var__var__var__18__n__42788__42792__42919__42923__42927),Vvar__var__var__var__var__19__m__42789__42793__42920__42924__42928))
=> ( p(happ(happ(Vvar__8__rle__42676,Vvar__var__var__var__var__19__m__42789__42793__42920__42924__42928),Vvar__var__var__var__var__18__n__42788__42792__42919__42923__42927))
=> p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__18__n__42788__42792__42919__42923__42927),Vvar__var__var__var__var__19__m__42789__42793__42920__42924__42928)) ) ) ) )
& ! [Vvar__var__var__var__19__n__42797__42802__42931__42936] :
( t(Vvar__var__var__var__19__n__42797__42802__42931__42936,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__20__m__42798__42803__42932__42937] :
( t(Vvar__var__var__var__20__m__42798__42803__42932__42937,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__21__p__42799__42804__42933__42938] :
( t(Vvar__var__var__var__21__p__42799__42804__42933__42938,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__8__rle__42676,Vvar__var__var__var__19__n__42797__42802__42931__42936),Vvar__var__var__var__20__m__42798__42803__42932__42937))
=> ( p(happ(happ(Vvar__8__rle__42676,Vvar__var__var__var__20__m__42798__42803__42932__42937),Vvar__var__var__var__21__p__42799__42804__42933__42938))
=> p(happ(happ(Vvar__8__rle__42676,Vvar__var__var__var__19__n__42797__42802__42931__42936),Vvar__var__var__var__21__p__42799__42804__42933__42938)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__42808__42810__42941__42943__42945__42947] :
( t(Vvar__var__var__var__var__var__20__n__42808__42810__42941__42943__42945__42947,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__var__21__m__42809__42811__42942__42944__42946__42948] :
( t(Vvar__var__var__var__var__var__21__m__42809__42811__42942__42944__42946__42948,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__9__rlt__42681,Vvar__var__var__var__var__var__20__n__42808__42810__42941__42943__42945__42947),Vvar__var__var__var__var__var__21__m__42809__42811__42942__42944__42946__42948))
<=> ( p(happ(happ(Vvar__8__rle__42676,Vvar__var__var__var__var__var__20__n__42808__42810__42941__42943__42945__42947),Vvar__var__var__var__var__var__21__m__42809__42811__42942__42944__42946__42948))
& ~ p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__var__20__n__42808__42810__42941__42943__42945__42947),Vvar__var__var__var__var__var__21__m__42809__42811__42942__42944__42946__42948)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__42813__42815__42949__42951__42953] :
( t(Vvar__var__var__var__var__21__n__42813__42815__42949__42951__42953,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__22__m__42814__42816__42950__42952__42954] :
( t(Vvar__var__var__var__var__22__m__42814__42816__42950__42952__42954,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__9__rlt__42681,Vvar__var__var__var__var__21__n__42813__42815__42949__42951__42953),Vvar__var__var__var__var__22__m__42814__42816__42950__42952__42954))
| p(happ(happ(Vvar__7__req__42671,Vvar__var__var__var__var__21__n__42813__42815__42949__42951__42953),Vvar__var__var__var__var__22__m__42814__42816__42950__42952__42954))
| p(happ(happ(Vvar__9__rlt__42681,Vvar__var__var__var__var__22__m__42814__42816__42950__42952__42954),Vvar__var__var__var__var__21__n__42813__42815__42949__42951__42953)) ) ) )
& ! [Vvar__var__var__var__var__22__n__42818__42822__42955__42959__42963] :
( t(Vvar__var__var__var__var__22__n__42818__42822__42955__42959__42963,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__23__m__42819__42823__42956__42960__42964] :
( t(Vvar__var__var__var__var__23__m__42819__42823__42956__42960__42964,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__24__p__42820__42824__42957__42961__42965] :
( t(Vvar__var__var__var__var__24__p__42820__42824__42957__42961__42965,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__8__rle__42676,Vvar__var__var__var__var__22__n__42818__42822__42955__42959__42963),Vvar__var__var__var__var__23__m__42819__42823__42956__42960__42964))
=> p(happ(happ(Vvar__8__rle__42676,happ(happ(Vvar__3__rplus__42653,Vvar__var__var__var__var__24__p__42820__42824__42957__42961__42965),Vvar__var__var__var__var__22__n__42818__42822__42955__42959__42963)),happ(happ(Vvar__3__rplus__42653,Vvar__var__var__var__var__24__p__42820__42824__42957__42961__42965),Vvar__var__var__var__var__23__m__42819__42823__42956__42960__42964))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__42827__42831__42967__42971__42975__42979] :
( t(Vvar__var__var__var__var__var__23__n__42827__42831__42967__42971__42975__42979,Vvar__0__R__42650)
=> ! [Vvar__var__var__var__var__var__24__m__42828__42832__42968__42972__42976__42980] :
( t(Vvar__var__var__var__var__var__24__m__42828__42832__42968__42972__42976__42980,Vvar__0__R__42650)
=> ( p(happ(happ(Vvar__9__rlt__42681,Vvar__1__rO__42651),Vvar__var__var__var__var__var__23__n__42827__42831__42967__42971__42975__42979))
=> ( p(happ(happ(Vvar__9__rlt__42681,Vvar__1__rO__42651),Vvar__var__var__var__var__var__24__m__42828__42832__42968__42972__42976__42980))
=> p(happ(happ(Vvar__9__rlt__42681,Vvar__1__rO__42651),happ(happ(Vvar__4__rtimes__42658,Vvar__var__var__var__var__var__23__n__42827__42831__42967__42971__42975__42979),Vvar__var__var__var__var__var__24__m__42828__42832__42968__42972__42976__42980))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__42671,Vvar__1__rO__42651),Vvar__2__rI__42652))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__50410,VX50411] :
( cType___24t(Vvar__0__T__50410)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__50410,VX50411)
=> ? [Vvar__1__Flhs__50413] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__50410,Vvar__1__Flhs__50413)
& ? [Vvar__2__Fop__50414] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__50414)
& ? [Vvar__3__Frhs__50415] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__50410,Vvar__3__Frhs__50415)
& VX50411 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__50410,Vvar__1__Flhs__50413,Vvar__2__Fop__50414,Vvar__3__Frhs__50415) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX49921] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX49921)
=> ( VX49921 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX49921 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX49921 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX49921 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX50267] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX50267)
=> ( VX50267 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX50267 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX50267 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX50267 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX50267 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX50267 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081] :
( cType___24t(Vvar__0__R__44012)
=> ( t(Vvar__1__rO__44013,Vvar__0__R__44012)
=> ( t(Vvar__2__rI__44014,Vvar__0__R__44012)
=> ( c_24__type__44545___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__3__rplus__44015)
=> ( c_24__type__44891___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__4__rtimes__44020)
=> ( c_24__type__45237___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__5__rminus__44025)
=> ( c_24__type__45560___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__6__ropp__44030)
=> ( c_24__type__45906___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__7__req__44033)
=> ( c_24__type__46252___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__8__rle__44038)
=> ( cType___24t(Vvar__9__C__44043)
=> ( t(Vvar__10__cO__44044,Vvar__9__C__44043)
=> ( t(Vvar__11__cI__44045,Vvar__9__C__44043)
=> ( c_24__type__46598___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__12__cplus__44046)
=> ( c_24__type__46944___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__13__ctimes__44051)
=> ( c_24__type__47290___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__14__cminus__44056)
=> ( c_24__type__47613___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__15__copp__44061)
=> ( c_24__type__47959___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__16__ceqb__44064)
=> ( c_24__type__48305___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__17__cleb__44069)
=> ( c_24__type__48628___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__18__phi__44074)
=> ( cType___24t(Vvar__19__E__44077)
=> ( c_24__type__48951___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__20__pow__phi__44078)
=> ( c_24__type__49297___24t(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081,Vvar__21__rpow__44081)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__8__rle__44038,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__17__cleb__44069,Vvar__18__phi__44074,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__44012,Vvar__1__rO__44013,Vvar__2__rI__44014,Vvar__3__rplus__44015,Vvar__4__rtimes__44020,Vvar__5__rminus__44025,Vvar__6__ropp__44030,Vvar__7__req__44033,Vvar__9__C__44043,Vvar__10__cO__44044,Vvar__11__cI__44045,Vvar__12__cplus__44046,Vvar__13__ctimes__44051,Vvar__14__cminus__44056,Vvar__15__copp__44061,Vvar__16__ceqb__44064,Vvar__18__phi__44074)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__44012,Vvar__2__rI__44014,Vvar__4__rtimes__44020,Vvar__7__req__44033,Vvar__19__E__44077,Vvar__20__pow__phi__44078,Vvar__21__rpow__44081)
& ! [Vvar__var__var__var__var__var__24__x__44164__44167__44177__44180__44183__44186] :
( t(Vvar__var__var__var__var__var__24__x__44164__44167__44177__44180__44183__44186,Vvar__9__C__44043)
=> ! [Vvar__var__var__var__var__var__25__y__44165__44168__44178__44181__44184__44187] :
( t(Vvar__var__var__var__var__var__25__y__44165__44168__44178__44181__44184__44187,Vvar__9__C__44043)
=> ( happ(happ(Vvar__16__ceqb__44064,Vvar__var__var__var__var__var__24__x__44164__44167__44177__44180__44183__44186),Vvar__var__var__var__var__var__25__y__44165__44168__44178__44181__44184__44187) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__44033,happ(Vvar__18__phi__44074,Vvar__var__var__var__var__var__24__x__44164__44167__44177__44180__44183__44186)),happ(Vvar__18__phi__44074,Vvar__var__var__var__var__var__25__y__44165__44168__44178__44181__44184__44187))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__44171__44174__44189__44192__44195__44198] :
( t(Vvar__var__var__var__var__var__25__x__44171__44174__44189__44192__44195__44198,Vvar__9__C__44043)
=> ! [Vvar__var__var__var__var__var__26__y__44172__44175__44190__44193__44196__44199] :
( t(Vvar__var__var__var__var__var__26__y__44172__44175__44190__44193__44196__44199,Vvar__9__C__44043)
=> ( happ(happ(Vvar__17__cleb__44069,Vvar__var__var__var__var__var__25__x__44171__44174__44189__44192__44195__44198),Vvar__var__var__var__var__var__26__y__44172__44175__44190__44193__44196__44199) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__44038,happ(Vvar__18__phi__44074,Vvar__var__var__var__var__var__25__x__44171__44174__44189__44192__44195__44198)),happ(Vvar__18__phi__44074,Vvar__var__var__var__var__var__26__y__44172__44175__44190__44193__44196__44199))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,VX64111] :
( cType___24t(Vvar__0__TA__64107)
=> ( cType___24t(Vvar__1__TX__64108)
=> ( cType___24t(Vvar__2__AA__64109)
=> ( cType___24t(Vvar__3__AF__64110)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,VX64111)
=> ( VX64111 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110)
| VX64111 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110)
| ? [Vvar__4___24Anonymous__64124] :
( t(Vvar__4___24Anonymous__64124,Vvar__1__TX__64108)
& VX64111 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__4___24Anonymous__64124) )
| ? [Vvar__4___24Anonymous__64129] :
( t(Vvar__4___24Anonymous__64129,Vvar__0__TA__64107)
& ? [Vvar__5___24Anonymous__64130] :
( t(Vvar__5___24Anonymous__64130,Vvar__2__AA__64109)
& VX64111 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__4___24Anonymous__64129,Vvar__5___24Anonymous__64130) ) )
| ? [Vvar__4___24Anonymous__64135] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__4___24Anonymous__64135)
& ? [Vvar__5___24Anonymous__64136] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__5___24Anonymous__64136)
& VX64111 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__4___24Anonymous__64135,Vvar__5___24Anonymous__64136) ) )
| ? [Vvar__4___24Anonymous__64141] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__4___24Anonymous__64141)
& ? [Vvar__5___24Anonymous__64142] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__5___24Anonymous__64142)
& VX64111 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__4___24Anonymous__64141,Vvar__5___24Anonymous__64142) ) )
| ? [Vvar__4___24Anonymous__64147] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__4___24Anonymous__64147)
& VX64111 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__4___24Anonymous__64147) )
| ? [Vvar__4___24Anonymous__64152] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__4___24Anonymous__64152)
& ? [Vvar__5___24Anonymous__64153] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__64110,Vvar__5___24Anonymous__64153)
& ? [Vvar__6___24Anonymous__64154] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__6___24Anonymous__64154)
& VX64111 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__64107,Vvar__1__TX__64108,Vvar__2__AA__64109,Vvar__3__AF__64110,Vvar__4___24Anonymous__64152,Vvar__5___24Anonymous__64153,Vvar__6___24Anonymous__64154) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__60393] :
( cProp___24t(Vvar__0___24Anonymous__60393)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__60393)
=> ( ? [Vvar__0__S__60395] :
( cType___24t(Vvar__0__S__60395)
& ? [Vvar__1__x__60396] :
( t(Vvar__1__x__60396,Vvar__0__S__60395)
& ? [Vvar__2__y__60397] :
( t(Vvar__2__y__60397,Vvar__0__S__60395)
& Vvar__0___24Anonymous__60393 = c_24__prop__60417___24a4(Vvar__0___24Anonymous__60393,Vvar__0__S__60395,Vvar__1__x__60396,Vvar__2__y__60397) ) ) )
| ? [Vvar__0__x__60398] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__60398)
& ? [Vvar__1__y__60399] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__60399)
& Vvar__0___24Anonymous__60393 = c_24__prop__60418___24a3(Vvar__0___24Anonymous__60393,Vvar__0__x__60398,Vvar__1__y__60399) ) )
| ? [Vvar__0__x__60400] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__60400)
& ? [Vvar__1__s__60401] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__60401)
& Vvar__0___24Anonymous__60393 = c_24__prop__60419___24a3(Vvar__0___24Anonymous__60393,Vvar__0__x__60400,Vvar__1__s__60401) ) )
| Vvar__0___24Anonymous__60393 = c_24True
| Vvar__0___24Anonymous__60393 = c_24False
| ? [Vvar__0__P__60402] :
( cProp___24t(Vvar__0__P__60402)
& ? [Vvar__1__Q__60403] :
( cProp___24t(Vvar__1__Q__60403)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__60402)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__60403)
& Vvar__0___24Anonymous__60393 = c_24__prop__60420___24a3(Vvar__0___24Anonymous__60393,Vvar__0__P__60402,Vvar__1__Q__60403) ) )
| ? [Vvar__0__P__60406] :
( cProp___24t(Vvar__0__P__60406)
& ? [Vvar__1__Q__60407] :
( cProp___24t(Vvar__1__Q__60407)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__60406)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__60407)
& Vvar__0___24Anonymous__60393 = c_24__prop__60421___24a3(Vvar__0___24Anonymous__60393,Vvar__0__P__60406,Vvar__1__Q__60407) ) )
| ? [Vvar__0__P__60410] :
( cProp___24t(Vvar__0__P__60410)
& ? [Vvar__1__Q__60411] :
( cProp___24t(Vvar__1__Q__60411)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__60410)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__60411)
& Vvar__0___24Anonymous__60393 = c_24__prop__60422___24a3(Vvar__0___24Anonymous__60393,Vvar__0__P__60410,Vvar__1__Q__60411) ) )
| ? [Vvar__0__P__60415] :
( cProp___24t(Vvar__0__P__60415)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__60415)
& Vvar__0___24Anonymous__60393 = c_24__prop__60423___24a2(Vvar__0___24Anonymous__60393,Vvar__0__P__60415) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__61556,VX61557] :
( cType___24t(Vvar__0__C__61556)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,VX61557)
=> ( VX61557 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__61556)
| VX61557 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__61556)
| ? [Vvar__1___24Anonymous__61561] :
( t(Vvar__1___24Anonymous__61561,Vvar__0__C__61556)
& VX61557 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__61556,Vvar__1___24Anonymous__61561) )
| ? [Vvar__1___24Anonymous__61563] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__61563)
& VX61557 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__61556,Vvar__1___24Anonymous__61563) )
| ? [Vvar__1___24Anonymous__61565] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,Vvar__1___24Anonymous__61565)
& ? [Vvar__2___24Anonymous__61566] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,Vvar__2___24Anonymous__61566)
& VX61557 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__61556,Vvar__1___24Anonymous__61565,Vvar__2___24Anonymous__61566) ) )
| ? [Vvar__1___24Anonymous__61568] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,Vvar__1___24Anonymous__61568)
& ? [Vvar__2___24Anonymous__61569] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,Vvar__2___24Anonymous__61569)
& VX61557 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__61556,Vvar__1___24Anonymous__61568,Vvar__2___24Anonymous__61569) ) )
| ? [Vvar__1___24Anonymous__61571] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,Vvar__1___24Anonymous__61571)
& ? [Vvar__2___24Anonymous__61572] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,Vvar__2___24Anonymous__61572)
& VX61557 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__61556,Vvar__1___24Anonymous__61571,Vvar__2___24Anonymous__61572) ) )
| ? [Vvar__1___24Anonymous__61574] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,Vvar__1___24Anonymous__61574)
& VX61557 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__61556,Vvar__1___24Anonymous__61574) )
| ? [Vvar__1___24Anonymous__61576] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,Vvar__1___24Anonymous__61576)
& VX61557 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__61556,Vvar__1___24Anonymous__61576) )
| ? [Vvar__1___24Anonymous__61578] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,Vvar__1___24Anonymous__61578)
& ? [Vvar__2___24Anonymous__61579] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,Vvar__2___24Anonymous__61579)
& VX61557 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__61556,Vvar__1___24Anonymous__61578,Vvar__2___24Anonymous__61579) ) )
| ? [Vvar__1___24Anonymous__61581] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__61556,Vvar__1___24Anonymous__61581)
& ? [Vvar__2___24Anonymous__61582] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__61582)
& VX61557 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__61556,Vvar__1___24Anonymous__61581,Vvar__2___24Anonymous__61582) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__38479,Vvar__1__rO__38480,Vvar__2__rI__38481,Vvar__3__radd__38482,Vvar__4__rmul__38487,Vvar__5__rsub__38492,Vvar__6__ropp__38497,Vvar__7__rdiv__38500,Vvar__8__rinv__38505,Vvar__9__req__38508] :
( cType___24t(Vvar__0__R__38479)
=> ( t(Vvar__1__rO__38480,Vvar__0__R__38479)
=> ( t(Vvar__2__rI__38481,Vvar__0__R__38479)
=> ( c_24__type__38673___24t(Vvar__0__R__38479,Vvar__1__rO__38480,Vvar__2__rI__38481,Vvar__3__radd__38482,Vvar__4__rmul__38487,Vvar__5__rsub__38492,Vvar__6__ropp__38497,Vvar__7__rdiv__38500,Vvar__8__rinv__38505,Vvar__9__req__38508,Vvar__3__radd__38482)
=> ( c_24__type__38766___24t(Vvar__0__R__38479,Vvar__1__rO__38480,Vvar__2__rI__38481,Vvar__3__radd__38482,Vvar__4__rmul__38487,Vvar__5__rsub__38492,Vvar__6__ropp__38497,Vvar__7__rdiv__38500,Vvar__8__rinv__38505,Vvar__9__req__38508,Vvar__4__rmul__38487)
=> ( c_24__type__38859___24t(Vvar__0__R__38479,Vvar__1__rO__38480,Vvar__2__rI__38481,Vvar__3__radd__38482,Vvar__4__rmul__38487,Vvar__5__rsub__38492,Vvar__6__ropp__38497,Vvar__7__rdiv__38500,Vvar__8__rinv__38505,Vvar__9__req__38508,Vvar__5__rsub__38492)
=> ( c_24__type__38941___24t(Vvar__0__R__38479,Vvar__1__rO__38480,Vvar__2__rI__38481,Vvar__3__radd__38482,Vvar__4__rmul__38487,Vvar__5__rsub__38492,Vvar__6__ropp__38497,Vvar__7__rdiv__38500,Vvar__8__rinv__38505,Vvar__9__req__38508,Vvar__6__ropp__38497)
=> ( c_24__type__39034___24t(Vvar__0__R__38479,Vvar__1__rO__38480,Vvar__2__rI__38481,Vvar__3__radd__38482,Vvar__4__rmul__38487,Vvar__5__rsub__38492,Vvar__6__ropp__38497,Vvar__7__rdiv__38500,Vvar__8__rinv__38505,Vvar__9__req__38508,Vvar__7__rdiv__38500)
=> ( c_24__type__39116___24t(Vvar__0__R__38479,Vvar__1__rO__38480,Vvar__2__rI__38481,Vvar__3__radd__38482,Vvar__4__rmul__38487,Vvar__5__rsub__38492,Vvar__6__ropp__38497,Vvar__7__rdiv__38500,Vvar__8__rinv__38505,Vvar__9__req__38508,Vvar__8__rinv__38505)
=> ( c_24__type__39209___24t(Vvar__0__R__38479,Vvar__1__rO__38480,Vvar__2__rI__38481,Vvar__3__radd__38482,Vvar__4__rmul__38487,Vvar__5__rsub__38492,Vvar__6__ropp__38497,Vvar__7__rdiv__38500,Vvar__8__rinv__38505,Vvar__9__req__38508,Vvar__9__req__38508)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__38479,Vvar__1__rO__38480,Vvar__2__rI__38481,Vvar__3__radd__38482,Vvar__4__rmul__38487,Vvar__5__rsub__38492,Vvar__6__ropp__38497,Vvar__7__rdiv__38500,Vvar__8__rinv__38505,Vvar__9__req__38508)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__38479,Vvar__1__rO__38480,Vvar__2__rI__38481,Vvar__3__radd__38482,Vvar__4__rmul__38487,Vvar__5__rsub__38492,Vvar__6__ropp__38497,Vvar__9__req__38508)
& ~ p(happ(happ(Vvar__9__req__38508,Vvar__2__rI__38481),Vvar__1__rO__38480))
& ! [Vvar__var__var__var__var__var__var__12__p__38551__38553__38560__38562__38564__38566__38568] :
( t(Vvar__var__var__var__var__var__var__12__p__38551__38553__38560__38562__38564__38566__38568,Vvar__0__R__38479)
=> ! [Vvar__var__var__var__var__var__var__13__q__38552__38554__38561__38563__38565__38567__38569] :
( t(Vvar__var__var__var__var__var__var__13__q__38552__38554__38561__38563__38565__38567__38569,Vvar__0__R__38479)
=> p(happ(happ(Vvar__9__req__38508,happ(happ(Vvar__7__rdiv__38500,Vvar__var__var__var__var__var__var__12__p__38551__38553__38560__38562__38564__38566__38568),Vvar__var__var__var__var__var__var__13__q__38552__38554__38561__38563__38565__38567__38569)),happ(happ(Vvar__4__rmul__38487,Vvar__var__var__var__var__var__var__12__p__38551__38553__38560__38562__38564__38566__38568),happ(Vvar__8__rinv__38505,Vvar__var__var__var__var__var__var__13__q__38552__38554__38561__38563__38565__38567__38569)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__38556__38558__38570__38572__38574__38576__38578__38580] :
( t(Vvar__var__var__var__var__var__var__var__13__p__38556__38558__38570__38572__38574__38576__38578__38580,Vvar__0__R__38479)
=> ( ~ p(happ(happ(Vvar__9__req__38508,Vvar__var__var__var__var__var__var__var__13__p__38556__38558__38570__38572__38574__38576__38578__38580),Vvar__1__rO__38480))
=> p(happ(happ(Vvar__9__req__38508,happ(happ(Vvar__4__rmul__38487,happ(Vvar__8__rinv__38505,Vvar__var__var__var__var__var__var__var__13__p__38556__38558__38570__38572__38574__38576__38578__38580)),Vvar__var__var__var__var__var__var__var__13__p__38556__38558__38570__38572__38574__38576__38578__38580)),Vvar__2__rI__38481)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__61957,Vvar__1__rO__61958,Vvar__2__rI__61959,Vvar__3__radd__61960,Vvar__4__rmul__61965,Vvar__5__rsub__61970,Vvar__6__ropp__61975,Vvar__7__rdiv__61978,Vvar__8__rinv__61983,Vvar__9__req__61986] :
( cType___24t(Vvar__0__R__61957)
=> ( t(Vvar__1__rO__61958,Vvar__0__R__61957)
=> ( t(Vvar__2__rI__61959,Vvar__0__R__61957)
=> ( c_24__type__62151___24t(Vvar__0__R__61957,Vvar__1__rO__61958,Vvar__2__rI__61959,Vvar__3__radd__61960,Vvar__4__rmul__61965,Vvar__5__rsub__61970,Vvar__6__ropp__61975,Vvar__7__rdiv__61978,Vvar__8__rinv__61983,Vvar__9__req__61986,Vvar__3__radd__61960)
=> ( c_24__type__62244___24t(Vvar__0__R__61957,Vvar__1__rO__61958,Vvar__2__rI__61959,Vvar__3__radd__61960,Vvar__4__rmul__61965,Vvar__5__rsub__61970,Vvar__6__ropp__61975,Vvar__7__rdiv__61978,Vvar__8__rinv__61983,Vvar__9__req__61986,Vvar__4__rmul__61965)
=> ( c_24__type__62337___24t(Vvar__0__R__61957,Vvar__1__rO__61958,Vvar__2__rI__61959,Vvar__3__radd__61960,Vvar__4__rmul__61965,Vvar__5__rsub__61970,Vvar__6__ropp__61975,Vvar__7__rdiv__61978,Vvar__8__rinv__61983,Vvar__9__req__61986,Vvar__5__rsub__61970)
=> ( c_24__type__62419___24t(Vvar__0__R__61957,Vvar__1__rO__61958,Vvar__2__rI__61959,Vvar__3__radd__61960,Vvar__4__rmul__61965,Vvar__5__rsub__61970,Vvar__6__ropp__61975,Vvar__7__rdiv__61978,Vvar__8__rinv__61983,Vvar__9__req__61986,Vvar__6__ropp__61975)
=> ( c_24__type__62512___24t(Vvar__0__R__61957,Vvar__1__rO__61958,Vvar__2__rI__61959,Vvar__3__radd__61960,Vvar__4__rmul__61965,Vvar__5__rsub__61970,Vvar__6__ropp__61975,Vvar__7__rdiv__61978,Vvar__8__rinv__61983,Vvar__9__req__61986,Vvar__7__rdiv__61978)
=> ( c_24__type__62594___24t(Vvar__0__R__61957,Vvar__1__rO__61958,Vvar__2__rI__61959,Vvar__3__radd__61960,Vvar__4__rmul__61965,Vvar__5__rsub__61970,Vvar__6__ropp__61975,Vvar__7__rdiv__61978,Vvar__8__rinv__61983,Vvar__9__req__61986,Vvar__8__rinv__61983)
=> ( c_24__type__62687___24t(Vvar__0__R__61957,Vvar__1__rO__61958,Vvar__2__rI__61959,Vvar__3__radd__61960,Vvar__4__rmul__61965,Vvar__5__rsub__61970,Vvar__6__ropp__61975,Vvar__7__rdiv__61978,Vvar__8__rinv__61983,Vvar__9__req__61986,Vvar__9__req__61986)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__61957,Vvar__1__rO__61958,Vvar__2__rI__61959,Vvar__3__radd__61960,Vvar__4__rmul__61965,Vvar__5__rsub__61970,Vvar__6__ropp__61975,Vvar__7__rdiv__61978,Vvar__8__rinv__61983,Vvar__9__req__61986)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__61957,Vvar__1__rO__61958,Vvar__2__rI__61959,Vvar__3__radd__61960,Vvar__4__rmul__61965,Vvar__5__rsub__61970,Vvar__6__ropp__61975,Vvar__9__req__61986)
& ~ p(happ(happ(Vvar__9__req__61986,Vvar__2__rI__61959),Vvar__1__rO__61958))
& ! [Vvar__var__var__var__var__var__var__12__p__62029__62031__62038__62040__62042__62044__62046] :
( t(Vvar__var__var__var__var__var__var__12__p__62029__62031__62038__62040__62042__62044__62046,Vvar__0__R__61957)
=> ! [Vvar__var__var__var__var__var__var__13__q__62030__62032__62039__62041__62043__62045__62047] :
( t(Vvar__var__var__var__var__var__var__13__q__62030__62032__62039__62041__62043__62045__62047,Vvar__0__R__61957)
=> p(happ(happ(Vvar__9__req__61986,happ(happ(Vvar__7__rdiv__61978,Vvar__var__var__var__var__var__var__12__p__62029__62031__62038__62040__62042__62044__62046),Vvar__var__var__var__var__var__var__13__q__62030__62032__62039__62041__62043__62045__62047)),happ(happ(Vvar__4__rmul__61965,Vvar__var__var__var__var__var__var__12__p__62029__62031__62038__62040__62042__62044__62046),happ(Vvar__8__rinv__61983,Vvar__var__var__var__var__var__var__13__q__62030__62032__62039__62041__62043__62045__62047)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__62034__62036__62048__62050__62052__62054__62056__62058] :
( t(Vvar__var__var__var__var__var__var__var__13__p__62034__62036__62048__62050__62052__62054__62056__62058,Vvar__0__R__61957)
=> ( ~ p(happ(happ(Vvar__9__req__61986,Vvar__var__var__var__var__var__var__var__13__p__62034__62036__62048__62050__62052__62054__62056__62058),Vvar__1__rO__61958))
=> p(happ(happ(Vvar__9__req__61986,happ(happ(Vvar__4__rmul__61965,happ(Vvar__8__rinv__61983,Vvar__var__var__var__var__var__var__var__13__p__62034__62036__62048__62050__62052__62054__62056__62058)),Vvar__var__var__var__var__var__var__var__13__p__62034__62036__62048__62050__62052__62054__62056__62058)),Vvar__2__rI__61959)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__61904,VX61905] :
( cType___24t(Vvar__0__C__61904)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__61904,VX61905)
=> ? [Vvar__1__num__61907] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__61904,Vvar__1__num__61907)
& ? [Vvar__2__denum__61908] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__61904,Vvar__2__denum__61908)
& ? [Vvar__3__condition__61909] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__61904),Vvar__3__condition__61909)
& VX61905 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__61904,Vvar__1__num__61907,Vvar__2__denum__61908,Vvar__3__condition__61909) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__62710,Vvar__1__rO__62711,Vvar__2__rI__62712,Vvar__3__radd__62713,Vvar__4__rmul__62718,Vvar__5__rdiv__62723,Vvar__6__rinv__62728,Vvar__7__req__62731] :
( cType___24t(Vvar__0__R__62710)
=> ( t(Vvar__1__rO__62711,Vvar__0__R__62710)
=> ( t(Vvar__2__rI__62712,Vvar__0__R__62710)
=> ( c_24__type__62858___24t(Vvar__0__R__62710,Vvar__1__rO__62711,Vvar__2__rI__62712,Vvar__3__radd__62713,Vvar__4__rmul__62718,Vvar__5__rdiv__62723,Vvar__6__rinv__62728,Vvar__7__req__62731,Vvar__3__radd__62713)
=> ( c_24__type__62921___24t(Vvar__0__R__62710,Vvar__1__rO__62711,Vvar__2__rI__62712,Vvar__3__radd__62713,Vvar__4__rmul__62718,Vvar__5__rdiv__62723,Vvar__6__rinv__62728,Vvar__7__req__62731,Vvar__4__rmul__62718)
=> ( c_24__type__62984___24t(Vvar__0__R__62710,Vvar__1__rO__62711,Vvar__2__rI__62712,Vvar__3__radd__62713,Vvar__4__rmul__62718,Vvar__5__rdiv__62723,Vvar__6__rinv__62728,Vvar__7__req__62731,Vvar__5__rdiv__62723)
=> ( c_24__type__63038___24t(Vvar__0__R__62710,Vvar__1__rO__62711,Vvar__2__rI__62712,Vvar__3__radd__62713,Vvar__4__rmul__62718,Vvar__5__rdiv__62723,Vvar__6__rinv__62728,Vvar__7__req__62731,Vvar__6__rinv__62728)
=> ( c_24__type__63101___24t(Vvar__0__R__62710,Vvar__1__rO__62711,Vvar__2__rI__62712,Vvar__3__radd__62713,Vvar__4__rmul__62718,Vvar__5__rdiv__62723,Vvar__6__rinv__62728,Vvar__7__req__62731,Vvar__7__req__62731)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__62710,Vvar__1__rO__62711,Vvar__2__rI__62712,Vvar__3__radd__62713,Vvar__4__rmul__62718,Vvar__5__rdiv__62723,Vvar__6__rinv__62728,Vvar__7__req__62731)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__62710,Vvar__1__rO__62711,Vvar__2__rI__62712,Vvar__3__radd__62713,Vvar__4__rmul__62718,Vvar__7__req__62731)
& ~ p(happ(happ(Vvar__7__req__62731,Vvar__2__rI__62712),Vvar__1__rO__62711))
& ! [Vvar__var__var__var__var__var__var__10__p__62766__62768__62775__62777__62779__62781__62783] :
( t(Vvar__var__var__var__var__var__var__10__p__62766__62768__62775__62777__62779__62781__62783,Vvar__0__R__62710)
=> ! [Vvar__var__var__var__var__var__var__11__q__62767__62769__62776__62778__62780__62782__62784] :
( t(Vvar__var__var__var__var__var__var__11__q__62767__62769__62776__62778__62780__62782__62784,Vvar__0__R__62710)
=> p(happ(happ(Vvar__7__req__62731,happ(happ(Vvar__5__rdiv__62723,Vvar__var__var__var__var__var__var__10__p__62766__62768__62775__62777__62779__62781__62783),Vvar__var__var__var__var__var__var__11__q__62767__62769__62776__62778__62780__62782__62784)),happ(happ(Vvar__4__rmul__62718,Vvar__var__var__var__var__var__var__10__p__62766__62768__62775__62777__62779__62781__62783),happ(Vvar__6__rinv__62728,Vvar__var__var__var__var__var__var__11__q__62767__62769__62776__62778__62780__62782__62784)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__62771__62773__62785__62787__62789__62791__62793__62795] :
( t(Vvar__var__var__var__var__var__var__var__11__p__62771__62773__62785__62787__62789__62791__62793__62795,Vvar__0__R__62710)
=> ( ~ p(happ(happ(Vvar__7__req__62731,Vvar__var__var__var__var__var__var__var__11__p__62771__62773__62785__62787__62789__62791__62793__62795),Vvar__1__rO__62711))
=> p(happ(happ(Vvar__7__req__62731,happ(happ(Vvar__4__rmul__62718,happ(Vvar__6__rinv__62728,Vvar__var__var__var__var__var__var__var__11__p__62771__62773__62785__62787__62789__62791__62793__62795)),Vvar__var__var__var__var__var__var__var__11__p__62771__62773__62785__62787__62789__62791__62793__62795)),Vvar__2__rI__62712)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX51343] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX51343)
=> ( VX51343 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__51344] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__51344)
& ? [Vvar__1___24Anonymous__51345] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__51345)
& VX51343 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__51344,Vvar__1___24Anonymous__51345) ) )
| ? [Vvar__0___24Anonymous__51346] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__51346)
& ? [Vvar__1___24Anonymous__51347] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__51347)
& VX51343 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__51346,Vvar__1___24Anonymous__51347) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__51364,VX51365] :
( cType___24t(Vvar__0__C__51364)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__51364,VX51365)
=> ( VX51365 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__51364)
| VX51365 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__51364)
| ? [Vvar__1___24Anonymous__51369] :
( t(Vvar__1___24Anonymous__51369,Vvar__0__C__51364)
& VX51365 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__51364,Vvar__1___24Anonymous__51369) )
| ? [Vvar__1___24Anonymous__51371] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__51371)
& VX51365 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__51364,Vvar__1___24Anonymous__51371) )
| ? [Vvar__1___24Anonymous__51373] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__51364,Vvar__1___24Anonymous__51373)
& ? [Vvar__2___24Anonymous__51374] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__51364,Vvar__2___24Anonymous__51374)
& VX51365 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__51364,Vvar__1___24Anonymous__51373,Vvar__2___24Anonymous__51374) ) )
| ? [Vvar__1___24Anonymous__51376] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__51364,Vvar__1___24Anonymous__51376)
& ? [Vvar__2___24Anonymous__51377] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__51364,Vvar__2___24Anonymous__51377)
& VX51365 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__51364,Vvar__1___24Anonymous__51376,Vvar__2___24Anonymous__51377) ) )
| ? [Vvar__1___24Anonymous__51379] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__51364,Vvar__1___24Anonymous__51379)
& ? [Vvar__2___24Anonymous__51380] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__51364,Vvar__2___24Anonymous__51380)
& VX51365 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__51364,Vvar__1___24Anonymous__51379,Vvar__2___24Anonymous__51380) ) )
| ? [Vvar__1___24Anonymous__51382] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__51364,Vvar__1___24Anonymous__51382)
& VX51365 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__51364,Vvar__1___24Anonymous__51382) )
| ? [Vvar__1___24Anonymous__51384] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__51364,Vvar__1___24Anonymous__51384)
& ? [Vvar__2___24Anonymous__51385] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__51385)
& VX51365 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__51364,Vvar__1___24Anonymous__51384,Vvar__2___24Anonymous__51385) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__51164,VX51165] :
( cType___24t(Vvar__0__C__51164)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__51164,VX51165)
=> ( ? [Vvar__1___24Anonymous__51167] :
( t(Vvar__1___24Anonymous__51167,Vvar__0__C__51164)
& VX51165 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__51164,Vvar__1___24Anonymous__51167) )
| ? [Vvar__1___24Anonymous__51169] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__51169)
& ? [Vvar__2___24Anonymous__51170] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__51164,Vvar__2___24Anonymous__51170)
& VX51165 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__51164,Vvar__1___24Anonymous__51169,Vvar__2___24Anonymous__51170) ) )
| ? [Vvar__1___24Anonymous__51172] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__51164,Vvar__1___24Anonymous__51172)
& ? [Vvar__2___24Anonymous__51173] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__51173)
& ? [Vvar__3___24Anonymous__51174] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__51164,Vvar__3___24Anonymous__51174)
& VX51165 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__51164,Vvar__1___24Anonymous__51172,Vvar__2___24Anonymous__51173,Vvar__3___24Anonymous__51174) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__52292,Vvar__1__rO__52293,Vvar__2__rI__52294,Vvar__3__radd__52295,Vvar__4__rmul__52300,Vvar__5__rsub__52305,Vvar__6__ropp__52310,Vvar__7__req__52313] :
( cType___24t(Vvar__0__R__52292)
=> ( t(Vvar__1__rO__52293,Vvar__0__R__52292)
=> ( t(Vvar__2__rI__52294,Vvar__0__R__52292)
=> ( c_24__type__52541___24t(Vvar__0__R__52292,Vvar__1__rO__52293,Vvar__2__rI__52294,Vvar__3__radd__52295,Vvar__4__rmul__52300,Vvar__5__rsub__52305,Vvar__6__ropp__52310,Vvar__7__req__52313,Vvar__3__radd__52295)
=> ( c_24__type__52604___24t(Vvar__0__R__52292,Vvar__1__rO__52293,Vvar__2__rI__52294,Vvar__3__radd__52295,Vvar__4__rmul__52300,Vvar__5__rsub__52305,Vvar__6__ropp__52310,Vvar__7__req__52313,Vvar__4__rmul__52300)
=> ( c_24__type__52667___24t(Vvar__0__R__52292,Vvar__1__rO__52293,Vvar__2__rI__52294,Vvar__3__radd__52295,Vvar__4__rmul__52300,Vvar__5__rsub__52305,Vvar__6__ropp__52310,Vvar__7__req__52313,Vvar__5__rsub__52305)
=> ( c_24__type__52721___24t(Vvar__0__R__52292,Vvar__1__rO__52293,Vvar__2__rI__52294,Vvar__3__radd__52295,Vvar__4__rmul__52300,Vvar__5__rsub__52305,Vvar__6__ropp__52310,Vvar__7__req__52313,Vvar__6__ropp__52310)
=> ( c_24__type__52784___24t(Vvar__0__R__52292,Vvar__1__rO__52293,Vvar__2__rI__52294,Vvar__3__radd__52295,Vvar__4__rmul__52300,Vvar__5__rsub__52305,Vvar__6__ropp__52310,Vvar__7__req__52313,Vvar__7__req__52313)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__52292,Vvar__1__rO__52293,Vvar__2__rI__52294,Vvar__3__radd__52295,Vvar__4__rmul__52300,Vvar__5__rsub__52305,Vvar__6__ropp__52310,Vvar__7__req__52313)
=> ( ! [Vvar__var__var__var__var__var__8__x__52346__52347__52400__52401__52402__52403] :
( t(Vvar__var__var__var__var__var__8__x__52346__52347__52400__52401__52402__52403,Vvar__0__R__52292)
=> p(happ(happ(Vvar__7__req__52313,happ(happ(Vvar__3__radd__52295,Vvar__1__rO__52293),Vvar__var__var__var__var__var__8__x__52346__52347__52400__52401__52402__52403)),Vvar__var__var__var__var__var__8__x__52346__52347__52400__52401__52402__52403)) )
& ! [Vvar__var__var__var__var__9__x__52349__52351__52404__52406__52408] :
( t(Vvar__var__var__var__var__9__x__52349__52351__52404__52406__52408,Vvar__0__R__52292)
=> ! [Vvar__var__var__var__var__10__y__52350__52352__52405__52407__52409] :
( t(Vvar__var__var__var__var__10__y__52350__52352__52405__52407__52409,Vvar__0__R__52292)
=> p(happ(happ(Vvar__7__req__52313,happ(happ(Vvar__3__radd__52295,Vvar__var__var__var__var__9__x__52349__52351__52404__52406__52408),Vvar__var__var__var__var__10__y__52350__52352__52405__52407__52409)),happ(happ(Vvar__3__radd__52295,Vvar__var__var__var__var__10__y__52350__52352__52405__52407__52409),Vvar__var__var__var__var__9__x__52349__52351__52404__52406__52408))) ) )
& ! [Vvar__var__var__var__var__10__x__52354__52357__52410__52413__52416] :
( t(Vvar__var__var__var__var__10__x__52354__52357__52410__52413__52416,Vvar__0__R__52292)
=> ! [Vvar__var__var__var__var__11__y__52355__52358__52411__52414__52417] :
( t(Vvar__var__var__var__var__11__y__52355__52358__52411__52414__52417,Vvar__0__R__52292)
=> ! [Vvar__var__var__var__var__12__z__52356__52359__52412__52415__52418] :
( t(Vvar__var__var__var__var__12__z__52356__52359__52412__52415__52418,Vvar__0__R__52292)
=> p(happ(happ(Vvar__7__req__52313,happ(happ(Vvar__3__radd__52295,Vvar__var__var__var__var__10__x__52354__52357__52410__52413__52416),happ(happ(Vvar__3__radd__52295,Vvar__var__var__var__var__11__y__52355__52358__52411__52414__52417),Vvar__var__var__var__var__12__z__52356__52359__52412__52415__52418))),happ(happ(Vvar__3__radd__52295,happ(happ(Vvar__3__radd__52295,Vvar__var__var__var__var__10__x__52354__52357__52410__52413__52416),Vvar__var__var__var__var__11__y__52355__52358__52411__52414__52417)),Vvar__var__var__var__var__12__z__52356__52359__52412__52415__52418))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__52361__52362__52419__52420__52421__52422] :
( t(Vvar__var__var__var__var__var__11__x__52361__52362__52419__52420__52421__52422,Vvar__0__R__52292)
=> p(happ(happ(Vvar__7__req__52313,happ(happ(Vvar__4__rmul__52300,Vvar__2__rI__52294),Vvar__var__var__var__var__var__11__x__52361__52362__52419__52420__52421__52422)),Vvar__var__var__var__var__var__11__x__52361__52362__52419__52420__52421__52422)) )
& ! [Vvar__var__var__var__var__var__12__x__52364__52365__52423__52424__52425__52426] :
( t(Vvar__var__var__var__var__var__12__x__52364__52365__52423__52424__52425__52426,Vvar__0__R__52292)
=> p(happ(happ(Vvar__7__req__52313,happ(happ(Vvar__4__rmul__52300,Vvar__1__rO__52293),Vvar__var__var__var__var__var__12__x__52364__52365__52423__52424__52425__52426)),Vvar__1__rO__52293)) )
& ! [Vvar__var__var__var__var__13__x__52367__52369__52427__52429__52431] :
( t(Vvar__var__var__var__var__13__x__52367__52369__52427__52429__52431,Vvar__0__R__52292)
=> ! [Vvar__var__var__var__var__14__y__52368__52370__52428__52430__52432] :
( t(Vvar__var__var__var__var__14__y__52368__52370__52428__52430__52432,Vvar__0__R__52292)
=> p(happ(happ(Vvar__7__req__52313,happ(happ(Vvar__4__rmul__52300,Vvar__var__var__var__var__13__x__52367__52369__52427__52429__52431),Vvar__var__var__var__var__14__y__52368__52370__52428__52430__52432)),happ(happ(Vvar__4__rmul__52300,Vvar__var__var__var__var__14__y__52368__52370__52428__52430__52432),Vvar__var__var__var__var__13__x__52367__52369__52427__52429__52431))) ) )
& ! [Vvar__var__var__var__var__14__x__52372__52375__52433__52436__52439] :
( t(Vvar__var__var__var__var__14__x__52372__52375__52433__52436__52439,Vvar__0__R__52292)
=> ! [Vvar__var__var__var__var__15__y__52373__52376__52434__52437__52440] :
( t(Vvar__var__var__var__var__15__y__52373__52376__52434__52437__52440,Vvar__0__R__52292)
=> ! [Vvar__var__var__var__var__16__z__52374__52377__52435__52438__52441] :
( t(Vvar__var__var__var__var__16__z__52374__52377__52435__52438__52441,Vvar__0__R__52292)
=> p(happ(happ(Vvar__7__req__52313,happ(happ(Vvar__4__rmul__52300,Vvar__var__var__var__var__14__x__52372__52375__52433__52436__52439),happ(happ(Vvar__4__rmul__52300,Vvar__var__var__var__var__15__y__52373__52376__52434__52437__52440),Vvar__var__var__var__var__16__z__52374__52377__52435__52438__52441))),happ(happ(Vvar__4__rmul__52300,happ(happ(Vvar__4__rmul__52300,Vvar__var__var__var__var__14__x__52372__52375__52433__52436__52439),Vvar__var__var__var__var__15__y__52373__52376__52434__52437__52440)),Vvar__var__var__var__var__16__z__52374__52377__52435__52438__52441))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__52379__52382__52442__52445__52448__52451] :
( t(Vvar__var__var__var__var__var__15__x__52379__52382__52442__52445__52448__52451,Vvar__0__R__52292)
=> ! [Vvar__var__var__var__var__var__16__y__52380__52383__52443__52446__52449__52452] :
( t(Vvar__var__var__var__var__var__16__y__52380__52383__52443__52446__52449__52452,Vvar__0__R__52292)
=> ! [Vvar__var__var__var__var__var__17__z__52381__52384__52444__52447__52450__52453] :
( t(Vvar__var__var__var__var__var__17__z__52381__52384__52444__52447__52450__52453,Vvar__0__R__52292)
=> p(happ(happ(Vvar__7__req__52313,happ(happ(Vvar__4__rmul__52300,happ(happ(Vvar__3__radd__52295,Vvar__var__var__var__var__var__15__x__52379__52382__52442__52445__52448__52451),Vvar__var__var__var__var__var__16__y__52380__52383__52443__52446__52449__52452)),Vvar__var__var__var__var__var__17__z__52381__52384__52444__52447__52450__52453)),happ(happ(Vvar__3__radd__52295,happ(happ(Vvar__4__rmul__52300,Vvar__var__var__var__var__var__15__x__52379__52382__52442__52445__52448__52451),Vvar__var__var__var__var__var__17__z__52381__52384__52444__52447__52450__52453)),happ(happ(Vvar__4__rmul__52300,Vvar__var__var__var__var__var__16__y__52380__52383__52443__52446__52449__52452),Vvar__var__var__var__var__var__17__z__52381__52384__52444__52447__52450__52453)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__52386__52388__52454__52456__52458__52460] :
( t(Vvar__var__var__var__var__var__16__x__52386__52388__52454__52456__52458__52460,Vvar__0__R__52292)
=> ! [Vvar__var__var__var__var__var__17__y__52387__52389__52455__52457__52459__52461] :
( t(Vvar__var__var__var__var__var__17__y__52387__52389__52455__52457__52459__52461,Vvar__0__R__52292)
=> p(happ(happ(Vvar__7__req__52313,happ(Vvar__6__ropp__52310,happ(happ(Vvar__4__rmul__52300,Vvar__var__var__var__var__var__16__x__52386__52388__52454__52456__52458__52460),Vvar__var__var__var__var__var__17__y__52387__52389__52455__52457__52459__52461))),happ(happ(Vvar__4__rmul__52300,happ(Vvar__6__ropp__52310,Vvar__var__var__var__var__var__16__x__52386__52388__52454__52456__52458__52460)),Vvar__var__var__var__var__var__17__y__52387__52389__52455__52457__52459__52461))) ) )
& ! [Vvar__var__var__var__var__var__17__x__52391__52393__52462__52464__52466__52468] :
( t(Vvar__var__var__var__var__var__17__x__52391__52393__52462__52464__52466__52468,Vvar__0__R__52292)
=> ! [Vvar__var__var__var__var__var__18__y__52392__52394__52463__52465__52467__52469] :
( t(Vvar__var__var__var__var__var__18__y__52392__52394__52463__52465__52467__52469,Vvar__0__R__52292)
=> p(happ(happ(Vvar__7__req__52313,happ(Vvar__6__ropp__52310,happ(happ(Vvar__3__radd__52295,Vvar__var__var__var__var__var__17__x__52391__52393__52462__52464__52466__52468),Vvar__var__var__var__var__var__18__y__52392__52394__52463__52465__52467__52469))),happ(happ(Vvar__3__radd__52295,happ(Vvar__6__ropp__52310,Vvar__var__var__var__var__var__17__x__52391__52393__52462__52464__52466__52468)),happ(Vvar__6__ropp__52310,Vvar__var__var__var__var__var__18__y__52392__52394__52463__52465__52467__52469)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__52396__52398__52470__52472__52474__52476__52478] :
( t(Vvar__var__var__var__var__var__var__18__x__52396__52398__52470__52472__52474__52476__52478,Vvar__0__R__52292)
=> ! [Vvar__var__var__var__var__var__var__19__y__52397__52399__52471__52473__52475__52477__52479] :
( t(Vvar__var__var__var__var__var__var__19__y__52397__52399__52471__52473__52475__52477__52479,Vvar__0__R__52292)
=> p(happ(happ(Vvar__7__req__52313,happ(happ(Vvar__5__rsub__52305,Vvar__var__var__var__var__var__var__18__x__52396__52398__52470__52472__52474__52476__52478),Vvar__var__var__var__var__var__var__19__y__52397__52399__52471__52473__52475__52477__52479)),happ(happ(Vvar__3__radd__52295,Vvar__var__var__var__var__var__var__18__x__52396__52398__52470__52472__52474__52476__52478),happ(Vvar__6__ropp__52310,Vvar__var__var__var__var__var__var__19__y__52397__52399__52471__52473__52475__52477__52479)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__56322,Vvar__1__req__56323,Vvar__2__C__56328,Vvar__3__cadd__56329,Vvar__4__cmul__56334,Vvar__5__phi__56339,Vvar__6__cdiv__56342] :
( cType___24t(Vvar__0__R__56322)
=> ( c_24__type__56462___24t(Vvar__0__R__56322,Vvar__1__req__56323,Vvar__2__C__56328,Vvar__3__cadd__56329,Vvar__4__cmul__56334,Vvar__5__phi__56339,Vvar__6__cdiv__56342,Vvar__1__req__56323)
=> ( cType___24t(Vvar__2__C__56328)
=> ( c_24__type__56512___24t(Vvar__0__R__56322,Vvar__1__req__56323,Vvar__2__C__56328,Vvar__3__cadd__56329,Vvar__4__cmul__56334,Vvar__5__phi__56339,Vvar__6__cdiv__56342,Vvar__3__cadd__56329)
=> ( c_24__type__56562___24t(Vvar__0__R__56322,Vvar__1__req__56323,Vvar__2__C__56328,Vvar__3__cadd__56329,Vvar__4__cmul__56334,Vvar__5__phi__56339,Vvar__6__cdiv__56342,Vvar__4__cmul__56334)
=> ( c_24__type__56604___24t(Vvar__0__R__56322,Vvar__1__req__56323,Vvar__2__C__56328,Vvar__3__cadd__56329,Vvar__4__cmul__56334,Vvar__5__phi__56339,Vvar__6__cdiv__56342,Vvar__5__phi__56339)
=> ( c_24__type__56654___24t(Vvar__0__R__56322,Vvar__1__req__56323,Vvar__2__C__56328,Vvar__3__cadd__56329,Vvar__4__cmul__56334,Vvar__5__phi__56339,Vvar__6__cdiv__56342,Vvar__6__cdiv__56342)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__56322,Vvar__1__req__56323,Vvar__2__C__56328,Vvar__3__cadd__56329,Vvar__4__cmul__56334,Vvar__5__phi__56339,Vvar__6__cdiv__56342)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__56374__56379__56384__56389__56394__56399__56404__56409] :
( t(Vvar__var__var__var__var__var__var__var__7__a__56374__56379__56384__56389__56394__56399__56404__56409,Vvar__2__C__56328)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__56375__56380__56385__56390__56395__56400__56405__56410] :
( t(Vvar__var__var__var__var__var__var__var__8__b__56375__56380__56385__56390__56395__56400__56405__56410,Vvar__2__C__56328)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2456717___24a9(Vvar__0__R__56322,Vvar__1__req__56323,Vvar__2__C__56328,Vvar__3__cadd__56329,Vvar__4__cmul__56334,Vvar__5__phi__56339,Vvar__6__cdiv__56342,Vvar__var__var__var__var__var__var__var__7__a__56374__56379__56384__56389__56394__56399__56404__56409,Vvar__var__var__var__var__var__var__var__8__b__56375__56380__56385__56390__56395__56400__56405__56410) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__56737,Vvar__1__rI__56738,Vvar__2__rmul__56739,Vvar__3__req__56744,Vvar__4__Cpow__56749,Vvar__5__Cp__phi__56750,Vvar__6__rpow__56753] :
( cType___24t(Vvar__0__R__56737)
=> ( t(Vvar__1__rI__56738,Vvar__0__R__56737)
=> ( c_24__type__56839___24t(Vvar__0__R__56737,Vvar__1__rI__56738,Vvar__2__rmul__56739,Vvar__3__req__56744,Vvar__4__Cpow__56749,Vvar__5__Cp__phi__56750,Vvar__6__rpow__56753,Vvar__2__rmul__56739)
=> ( c_24__type__56883___24t(Vvar__0__R__56737,Vvar__1__rI__56738,Vvar__2__rmul__56739,Vvar__3__req__56744,Vvar__4__Cpow__56749,Vvar__5__Cp__phi__56750,Vvar__6__rpow__56753,Vvar__3__req__56744)
=> ( cType___24t(Vvar__4__Cpow__56749)
=> ( c_24__type__56919___24t(Vvar__0__R__56737,Vvar__1__rI__56738,Vvar__2__rmul__56739,Vvar__3__req__56744,Vvar__4__Cpow__56749,Vvar__5__Cp__phi__56750,Vvar__6__rpow__56753,Vvar__5__Cp__phi__56750)
=> ( c_24__type__56963___24t(Vvar__0__R__56737,Vvar__1__rI__56738,Vvar__2__rmul__56739,Vvar__3__req__56744,Vvar__4__Cpow__56749,Vvar__5__Cp__phi__56750,Vvar__6__rpow__56753,Vvar__6__rpow__56753)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__56737,Vvar__1__rI__56738,Vvar__2__rmul__56739,Vvar__3__req__56744,Vvar__4__Cpow__56749,Vvar__5__Cp__phi__56750,Vvar__6__rpow__56753)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__56781__56783__56785__56787__56789__56791__56793__56795] :
( t(Vvar__var__var__var__var__var__var__var__7__r__56781__56783__56785__56787__56789__56791__56793__56795,Vvar__0__R__56737)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__56782__56784__56786__56788__56790__56792__56794__56796] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__56782__56784__56786__56788__56790__56792__56794__56796)
=> p(happ(happ(Vvar__3__req__56744,happ(happ(Vvar__6__rpow__56753,Vvar__var__var__var__var__var__var__var__7__r__56781__56783__56785__56787__56789__56791__56793__56795),happ(Vvar__5__Cp__phi__56750,Vvar__var__var__var__var__var__var__var__8__n__56782__56784__56786__56788__56790__56792__56794__56796))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__56737,Vvar__1__rI__56738,Vvar__2__rmul__56739,Vvar__var__var__var__var__var__var__var__7__r__56781__56783__56785__56787__56789__56791__56793__56795,Vvar__var__var__var__var__var__var__var__8__n__56782__56784__56786__56788__56790__56792__56794__56796))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__53360,Vvar__1__radd__53361,Vvar__2__rmul__53366,Vvar__3__ropp__53371,Vvar__4__req__53374] :
( cType___24t(Vvar__0__R__53360)
=> ( c_24__type__53465___24t(Vvar__0__R__53360,Vvar__1__radd__53361,Vvar__2__rmul__53366,Vvar__3__ropp__53371,Vvar__4__req__53374,Vvar__1__radd__53361)
=> ( c_24__type__53495___24t(Vvar__0__R__53360,Vvar__1__radd__53361,Vvar__2__rmul__53366,Vvar__3__ropp__53371,Vvar__4__req__53374,Vvar__2__rmul__53366)
=> ( c_24__type__53519___24t(Vvar__0__R__53360,Vvar__1__radd__53361,Vvar__2__rmul__53366,Vvar__3__ropp__53371,Vvar__4__req__53374,Vvar__3__ropp__53371)
=> ( c_24__type__53549___24t(Vvar__0__R__53360,Vvar__1__radd__53361,Vvar__2__rmul__53366,Vvar__3__ropp__53371,Vvar__4__req__53374,Vvar__4__req__53374)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__53360,Vvar__1__radd__53361,Vvar__2__rmul__53366,Vvar__3__ropp__53371,Vvar__4__req__53374)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__53579___24a5(Vvar__0__R__53360,Vvar__1__radd__53361,Vvar__2__rmul__53366,Vvar__3__ropp__53371,Vvar__4__req__53374),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__53360,c_24__type__53603___24a5(Vvar__0__R__53360,Vvar__1__radd__53361,Vvar__2__rmul__53366,Vvar__3__ropp__53371,Vvar__4__req__53374),Vvar__4__req__53374,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__53360,Vvar__0__R__53360,Vvar__4__req__53374,Vvar__4__req__53374)),Vvar__1__radd__53361)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__53636___24a5(Vvar__0__R__53360,Vvar__1__radd__53361,Vvar__2__rmul__53366,Vvar__3__ropp__53371,Vvar__4__req__53374),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__53360,c_24__type__53660___24a5(Vvar__0__R__53360,Vvar__1__radd__53361,Vvar__2__rmul__53366,Vvar__3__ropp__53371,Vvar__4__req__53374),Vvar__4__req__53374,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__53360,Vvar__0__R__53360,Vvar__4__req__53374,Vvar__4__req__53374)),Vvar__2__rmul__53366)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__53687___24a5(Vvar__0__R__53360,Vvar__1__radd__53361,Vvar__2__rmul__53366,Vvar__3__ropp__53371,Vvar__4__req__53374),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__53360,Vvar__0__R__53360,Vvar__4__req__53374,Vvar__4__req__53374),Vvar__3__ropp__53371)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742] :
( cType___24t(Vvar__0__R__53690)
=> ( t(Vvar__1__rO__53691,Vvar__0__R__53690)
=> ( t(Vvar__2__rI__53692,Vvar__0__R__53690)
=> ( c_24__type__54086___24t(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742,Vvar__3__radd__53693)
=> ( c_24__type__54299___24t(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742,Vvar__4__rmul__53698)
=> ( c_24__type__54512___24t(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742,Vvar__5__rsub__53703)
=> ( c_24__type__54707___24t(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742,Vvar__6__ropp__53708)
=> ( c_24__type__54920___24t(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742,Vvar__7__req__53711)
=> ( cType___24t(Vvar__8__C__53716)
=> ( t(Vvar__9__cO__53717,Vvar__8__C__53716)
=> ( t(Vvar__10__cI__53718,Vvar__8__C__53716)
=> ( c_24__type__55133___24t(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742,Vvar__11__cadd__53719)
=> ( c_24__type__55346___24t(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742,Vvar__12__cmul__53724)
=> ( c_24__type__55559___24t(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742,Vvar__13__csub__53729)
=> ( c_24__type__55754___24t(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742,Vvar__14__copp__53734)
=> ( c_24__type__55967___24t(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742,Vvar__15__ceqb__53737)
=> ( c_24__type__56162___24t(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742,Vvar__16__phi__53742)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__53690,Vvar__1__rO__53691,Vvar__2__rI__53692,Vvar__3__radd__53693,Vvar__4__rmul__53698,Vvar__5__rsub__53703,Vvar__6__ropp__53708,Vvar__7__req__53711,Vvar__8__C__53716,Vvar__9__cO__53717,Vvar__10__cI__53718,Vvar__11__cadd__53719,Vvar__12__cmul__53724,Vvar__13__csub__53729,Vvar__14__copp__53734,Vvar__15__ceqb__53737,Vvar__16__phi__53742)
=> ( p(happ(happ(Vvar__7__req__53711,happ(Vvar__16__phi__53742,Vvar__9__cO__53717)),Vvar__1__rO__53691))
& p(happ(happ(Vvar__7__req__53711,happ(Vvar__16__phi__53742,Vvar__10__cI__53718)),Vvar__2__rI__53692))
& ! [Vvar__var__var__var__var__var__var__19__x__53804__53806__53828__53830__53832__53834__53836] :
( t(Vvar__var__var__var__var__var__var__19__x__53804__53806__53828__53830__53832__53834__53836,Vvar__8__C__53716)
=> ! [Vvar__var__var__var__var__var__var__20__y__53805__53807__53829__53831__53833__53835__53837] :
( t(Vvar__var__var__var__var__var__var__20__y__53805__53807__53829__53831__53833__53835__53837,Vvar__8__C__53716)
=> p(happ(happ(Vvar__7__req__53711,happ(Vvar__16__phi__53742,happ(happ(Vvar__11__cadd__53719,Vvar__var__var__var__var__var__var__19__x__53804__53806__53828__53830__53832__53834__53836),Vvar__var__var__var__var__var__var__20__y__53805__53807__53829__53831__53833__53835__53837))),happ(happ(Vvar__3__radd__53693,happ(Vvar__16__phi__53742,Vvar__var__var__var__var__var__var__19__x__53804__53806__53828__53830__53832__53834__53836)),happ(Vvar__16__phi__53742,Vvar__var__var__var__var__var__var__20__y__53805__53807__53829__53831__53833__53835__53837)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__53809__53811__53838__53840__53842__53844__53846] :
( t(Vvar__var__var__var__var__var__var__20__x__53809__53811__53838__53840__53842__53844__53846,Vvar__8__C__53716)
=> ! [Vvar__var__var__var__var__var__var__21__y__53810__53812__53839__53841__53843__53845__53847] :
( t(Vvar__var__var__var__var__var__var__21__y__53810__53812__53839__53841__53843__53845__53847,Vvar__8__C__53716)
=> p(happ(happ(Vvar__7__req__53711,happ(Vvar__16__phi__53742,happ(happ(Vvar__13__csub__53729,Vvar__var__var__var__var__var__var__20__x__53809__53811__53838__53840__53842__53844__53846),Vvar__var__var__var__var__var__var__21__y__53810__53812__53839__53841__53843__53845__53847))),happ(happ(Vvar__5__rsub__53703,happ(Vvar__16__phi__53742,Vvar__var__var__var__var__var__var__20__x__53809__53811__53838__53840__53842__53844__53846)),happ(Vvar__16__phi__53742,Vvar__var__var__var__var__var__var__21__y__53810__53812__53839__53841__53843__53845__53847)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__53814__53816__53848__53850__53852__53854__53856] :
( t(Vvar__var__var__var__var__var__var__21__x__53814__53816__53848__53850__53852__53854__53856,Vvar__8__C__53716)
=> ! [Vvar__var__var__var__var__var__var__22__y__53815__53817__53849__53851__53853__53855__53857] :
( t(Vvar__var__var__var__var__var__var__22__y__53815__53817__53849__53851__53853__53855__53857,Vvar__8__C__53716)
=> p(happ(happ(Vvar__7__req__53711,happ(Vvar__16__phi__53742,happ(happ(Vvar__12__cmul__53724,Vvar__var__var__var__var__var__var__21__x__53814__53816__53848__53850__53852__53854__53856),Vvar__var__var__var__var__var__var__22__y__53815__53817__53849__53851__53853__53855__53857))),happ(happ(Vvar__4__rmul__53698,happ(Vvar__16__phi__53742,Vvar__var__var__var__var__var__var__21__x__53814__53816__53848__53850__53852__53854__53856)),happ(Vvar__16__phi__53742,Vvar__var__var__var__var__var__var__22__y__53815__53817__53849__53851__53853__53855__53857)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__53819__53820__53858__53859__53860__53861__53862] :
( t(Vvar__var__var__var__var__var__var__22__x__53819__53820__53858__53859__53860__53861__53862,Vvar__8__C__53716)
=> p(happ(happ(Vvar__7__req__53711,happ(Vvar__16__phi__53742,happ(Vvar__14__copp__53734,Vvar__var__var__var__var__var__var__22__x__53819__53820__53858__53859__53860__53861__53862))),happ(Vvar__6__ropp__53708,happ(Vvar__16__phi__53742,Vvar__var__var__var__var__var__var__22__x__53819__53820__53858__53859__53860__53861__53862)))) )
& ! [Vvar__var__var__var__var__var__23__x__53822__53825__53863__53866__53869__53872] :
( t(Vvar__var__var__var__var__var__23__x__53822__53825__53863__53866__53869__53872,Vvar__8__C__53716)
=> ! [Vvar__var__var__var__var__var__24__y__53823__53826__53864__53867__53870__53873] :
( t(Vvar__var__var__var__var__var__24__y__53823__53826__53864__53867__53870__53873,Vvar__8__C__53716)
=> ( happ(happ(Vvar__15__ceqb__53737,Vvar__var__var__var__var__var__23__x__53822__53825__53863__53866__53869__53872),Vvar__var__var__var__var__var__24__y__53823__53826__53864__53867__53870__53873) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__53711,happ(Vvar__16__phi__53742,Vvar__var__var__var__var__var__23__x__53822__53825__53863__53866__53869__53872)),happ(Vvar__16__phi__53742,Vvar__var__var__var__var__var__24__y__53823__53826__53864__53867__53870__53873))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__52873,Vvar__1__rO__52874,Vvar__2__rI__52875,Vvar__3__radd__52876,Vvar__4__rmul__52881,Vvar__5__rsub__52886,Vvar__6__ropp__52891,Vvar__7__req__52894] :
( cType___24t(Vvar__0__R__52873)
=> ( t(Vvar__1__rO__52874,Vvar__0__R__52873)
=> ( t(Vvar__2__rI__52875,Vvar__0__R__52873)
=> ( c_24__type__53097___24t(Vvar__0__R__52873,Vvar__1__rO__52874,Vvar__2__rI__52875,Vvar__3__radd__52876,Vvar__4__rmul__52881,Vvar__5__rsub__52886,Vvar__6__ropp__52891,Vvar__7__req__52894,Vvar__3__radd__52876)
=> ( c_24__type__53160___24t(Vvar__0__R__52873,Vvar__1__rO__52874,Vvar__2__rI__52875,Vvar__3__radd__52876,Vvar__4__rmul__52881,Vvar__5__rsub__52886,Vvar__6__ropp__52891,Vvar__7__req__52894,Vvar__4__rmul__52881)
=> ( c_24__type__53223___24t(Vvar__0__R__52873,Vvar__1__rO__52874,Vvar__2__rI__52875,Vvar__3__radd__52876,Vvar__4__rmul__52881,Vvar__5__rsub__52886,Vvar__6__ropp__52891,Vvar__7__req__52894,Vvar__5__rsub__52886)
=> ( c_24__type__53277___24t(Vvar__0__R__52873,Vvar__1__rO__52874,Vvar__2__rI__52875,Vvar__3__radd__52876,Vvar__4__rmul__52881,Vvar__5__rsub__52886,Vvar__6__ropp__52891,Vvar__7__req__52894,Vvar__6__ropp__52891)
=> ( c_24__type__53340___24t(Vvar__0__R__52873,Vvar__1__rO__52874,Vvar__2__rI__52875,Vvar__3__radd__52876,Vvar__4__rmul__52881,Vvar__5__rsub__52886,Vvar__6__ropp__52891,Vvar__7__req__52894,Vvar__7__req__52894)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__52873,Vvar__1__rO__52874,Vvar__2__rI__52875,Vvar__3__radd__52876,Vvar__4__rmul__52881,Vvar__5__rsub__52886,Vvar__6__ropp__52891,Vvar__7__req__52894)
=> ( ! [Vvar__var__var__var__var__var__8__x__52927__52928__52971__52972__52973__52974] :
( t(Vvar__var__var__var__var__var__8__x__52927__52928__52971__52972__52973__52974,Vvar__0__R__52873)
=> p(happ(happ(Vvar__7__req__52894,happ(happ(Vvar__3__radd__52876,Vvar__1__rO__52874),Vvar__var__var__var__var__var__8__x__52927__52928__52971__52972__52973__52974)),Vvar__var__var__var__var__var__8__x__52927__52928__52971__52972__52973__52974)) )
& ! [Vvar__var__var__var__var__9__x__52930__52932__52975__52977__52979] :
( t(Vvar__var__var__var__var__9__x__52930__52932__52975__52977__52979,Vvar__0__R__52873)
=> ! [Vvar__var__var__var__var__10__y__52931__52933__52976__52978__52980] :
( t(Vvar__var__var__var__var__10__y__52931__52933__52976__52978__52980,Vvar__0__R__52873)
=> p(happ(happ(Vvar__7__req__52894,happ(happ(Vvar__3__radd__52876,Vvar__var__var__var__var__9__x__52930__52932__52975__52977__52979),Vvar__var__var__var__var__10__y__52931__52933__52976__52978__52980)),happ(happ(Vvar__3__radd__52876,Vvar__var__var__var__var__10__y__52931__52933__52976__52978__52980),Vvar__var__var__var__var__9__x__52930__52932__52975__52977__52979))) ) )
& ! [Vvar__var__var__var__var__10__x__52935__52938__52981__52984__52987] :
( t(Vvar__var__var__var__var__10__x__52935__52938__52981__52984__52987,Vvar__0__R__52873)
=> ! [Vvar__var__var__var__var__11__y__52936__52939__52982__52985__52988] :
( t(Vvar__var__var__var__var__11__y__52936__52939__52982__52985__52988,Vvar__0__R__52873)
=> ! [Vvar__var__var__var__var__12__z__52937__52940__52983__52986__52989] :
( t(Vvar__var__var__var__var__12__z__52937__52940__52983__52986__52989,Vvar__0__R__52873)
=> p(happ(happ(Vvar__7__req__52894,happ(happ(Vvar__3__radd__52876,Vvar__var__var__var__var__10__x__52935__52938__52981__52984__52987),happ(happ(Vvar__3__radd__52876,Vvar__var__var__var__var__11__y__52936__52939__52982__52985__52988),Vvar__var__var__var__var__12__z__52937__52940__52983__52986__52989))),happ(happ(Vvar__3__radd__52876,happ(happ(Vvar__3__radd__52876,Vvar__var__var__var__var__10__x__52935__52938__52981__52984__52987),Vvar__var__var__var__var__11__y__52936__52939__52982__52985__52988)),Vvar__var__var__var__var__12__z__52937__52940__52983__52986__52989))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__52942__52943__52990__52991__52992__52993] :
( t(Vvar__var__var__var__var__var__11__x__52942__52943__52990__52991__52992__52993,Vvar__0__R__52873)
=> p(happ(happ(Vvar__7__req__52894,happ(happ(Vvar__4__rmul__52881,Vvar__2__rI__52875),Vvar__var__var__var__var__var__11__x__52942__52943__52990__52991__52992__52993)),Vvar__var__var__var__var__var__11__x__52942__52943__52990__52991__52992__52993)) )
& ! [Vvar__var__var__var__var__12__x__52945__52947__52994__52996__52998] :
( t(Vvar__var__var__var__var__12__x__52945__52947__52994__52996__52998,Vvar__0__R__52873)
=> ! [Vvar__var__var__var__var__13__y__52946__52948__52995__52997__52999] :
( t(Vvar__var__var__var__var__13__y__52946__52948__52995__52997__52999,Vvar__0__R__52873)
=> p(happ(happ(Vvar__7__req__52894,happ(happ(Vvar__4__rmul__52881,Vvar__var__var__var__var__12__x__52945__52947__52994__52996__52998),Vvar__var__var__var__var__13__y__52946__52948__52995__52997__52999)),happ(happ(Vvar__4__rmul__52881,Vvar__var__var__var__var__13__y__52946__52948__52995__52997__52999),Vvar__var__var__var__var__12__x__52945__52947__52994__52996__52998))) ) )
& ! [Vvar__var__var__var__var__13__x__52950__52953__53000__53003__53006] :
( t(Vvar__var__var__var__var__13__x__52950__52953__53000__53003__53006,Vvar__0__R__52873)
=> ! [Vvar__var__var__var__var__14__y__52951__52954__53001__53004__53007] :
( t(Vvar__var__var__var__var__14__y__52951__52954__53001__53004__53007,Vvar__0__R__52873)
=> ! [Vvar__var__var__var__var__15__z__52952__52955__53002__53005__53008] :
( t(Vvar__var__var__var__var__15__z__52952__52955__53002__53005__53008,Vvar__0__R__52873)
=> p(happ(happ(Vvar__7__req__52894,happ(happ(Vvar__4__rmul__52881,Vvar__var__var__var__var__13__x__52950__52953__53000__53003__53006),happ(happ(Vvar__4__rmul__52881,Vvar__var__var__var__var__14__y__52951__52954__53001__53004__53007),Vvar__var__var__var__var__15__z__52952__52955__53002__53005__53008))),happ(happ(Vvar__4__rmul__52881,happ(happ(Vvar__4__rmul__52881,Vvar__var__var__var__var__13__x__52950__52953__53000__53003__53006),Vvar__var__var__var__var__14__y__52951__52954__53001__53004__53007)),Vvar__var__var__var__var__15__z__52952__52955__53002__53005__53008))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__52957__52960__53009__53012__53015__53018] :
( t(Vvar__var__var__var__var__var__14__x__52957__52960__53009__53012__53015__53018,Vvar__0__R__52873)
=> ! [Vvar__var__var__var__var__var__15__y__52958__52961__53010__53013__53016__53019] :
( t(Vvar__var__var__var__var__var__15__y__52958__52961__53010__53013__53016__53019,Vvar__0__R__52873)
=> ! [Vvar__var__var__var__var__var__16__z__52959__52962__53011__53014__53017__53020] :
( t(Vvar__var__var__var__var__var__16__z__52959__52962__53011__53014__53017__53020,Vvar__0__R__52873)
=> p(happ(happ(Vvar__7__req__52894,happ(happ(Vvar__4__rmul__52881,happ(happ(Vvar__3__radd__52876,Vvar__var__var__var__var__var__14__x__52957__52960__53009__53012__53015__53018),Vvar__var__var__var__var__var__15__y__52958__52961__53010__53013__53016__53019)),Vvar__var__var__var__var__var__16__z__52959__52962__53011__53014__53017__53020)),happ(happ(Vvar__3__radd__52876,happ(happ(Vvar__4__rmul__52881,Vvar__var__var__var__var__var__14__x__52957__52960__53009__53012__53015__53018),Vvar__var__var__var__var__var__16__z__52959__52962__53011__53014__53017__53020)),happ(happ(Vvar__4__rmul__52881,Vvar__var__var__var__var__var__15__y__52958__52961__53010__53013__53016__53019),Vvar__var__var__var__var__var__16__z__52959__52962__53011__53014__53017__53020)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__52964__52966__53021__53023__53025__53027__53029] :
( t(Vvar__var__var__var__var__var__var__15__x__52964__52966__53021__53023__53025__53027__53029,Vvar__0__R__52873)
=> ! [Vvar__var__var__var__var__var__var__16__y__52965__52967__53022__53024__53026__53028__53030] :
( t(Vvar__var__var__var__var__var__var__16__y__52965__52967__53022__53024__53026__53028__53030,Vvar__0__R__52873)
=> p(happ(happ(Vvar__7__req__52894,happ(happ(Vvar__5__rsub__52886,Vvar__var__var__var__var__var__var__15__x__52964__52966__53021__53023__53025__53027__53029),Vvar__var__var__var__var__var__var__16__y__52965__52967__53022__53024__53026__53028__53030)),happ(happ(Vvar__3__radd__52876,Vvar__var__var__var__var__var__var__15__x__52964__52966__53021__53023__53025__53027__53029),happ(Vvar__6__ropp__52891,Vvar__var__var__var__var__var__var__16__y__52965__52967__53022__53024__53026__53028__53030)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__52969__52970__53031__53032__53033__53034__53035] :
( t(Vvar__var__var__var__var__var__var__16__x__52969__52970__53031__53032__53033__53034__53035,Vvar__0__R__52873)
=> p(happ(happ(Vvar__7__req__52894,happ(happ(Vvar__3__radd__52876,Vvar__var__var__var__var__var__var__16__x__52969__52970__53031__53032__53033__53034__53035),happ(Vvar__6__ropp__52891,Vvar__var__var__var__var__var__var__16__x__52969__52970__53031__53032__53033__53034__53035))),Vvar__1__rO__52874)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__63724,Vvar__1__rO__63725,Vvar__2__rI__63726,Vvar__3__radd__63727,Vvar__4__rmul__63732,Vvar__5__req__63737] :
( cType___24t(Vvar__0__R__63724)
=> ( t(Vvar__1__rO__63725,Vvar__0__R__63724)
=> ( t(Vvar__2__rI__63726,Vvar__0__R__63724)
=> ( c_24__type__63892___24t(Vvar__0__R__63724,Vvar__1__rO__63725,Vvar__2__rI__63726,Vvar__3__radd__63727,Vvar__4__rmul__63732,Vvar__5__req__63737,Vvar__3__radd__63727)
=> ( c_24__type__63931___24t(Vvar__0__R__63724,Vvar__1__rO__63725,Vvar__2__rI__63726,Vvar__3__radd__63727,Vvar__4__rmul__63732,Vvar__5__req__63737,Vvar__4__rmul__63732)
=> ( c_24__type__63970___24t(Vvar__0__R__63724,Vvar__1__rO__63725,Vvar__2__rI__63726,Vvar__3__radd__63727,Vvar__4__rmul__63732,Vvar__5__req__63737,Vvar__5__req__63737)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__63724,Vvar__1__rO__63725,Vvar__2__rI__63726,Vvar__3__radd__63727,Vvar__4__rmul__63732,Vvar__5__req__63737)
=> ( ! [Vvar__var__var__var__var__var__6__n__63762__63763__63801__63802__63803__63804] :
( t(Vvar__var__var__var__var__var__6__n__63762__63763__63801__63802__63803__63804,Vvar__0__R__63724)
=> p(happ(happ(Vvar__5__req__63737,happ(happ(Vvar__3__radd__63727,Vvar__1__rO__63725),Vvar__var__var__var__var__var__6__n__63762__63763__63801__63802__63803__63804)),Vvar__var__var__var__var__var__6__n__63762__63763__63801__63802__63803__63804)) )
& ! [Vvar__var__var__var__var__7__n__63765__63767__63805__63807__63809] :
( t(Vvar__var__var__var__var__7__n__63765__63767__63805__63807__63809,Vvar__0__R__63724)
=> ! [Vvar__var__var__var__var__8__m__63766__63768__63806__63808__63810] :
( t(Vvar__var__var__var__var__8__m__63766__63768__63806__63808__63810,Vvar__0__R__63724)
=> p(happ(happ(Vvar__5__req__63737,happ(happ(Vvar__3__radd__63727,Vvar__var__var__var__var__7__n__63765__63767__63805__63807__63809),Vvar__var__var__var__var__8__m__63766__63768__63806__63808__63810)),happ(happ(Vvar__3__radd__63727,Vvar__var__var__var__var__8__m__63766__63768__63806__63808__63810),Vvar__var__var__var__var__7__n__63765__63767__63805__63807__63809))) ) )
& ! [Vvar__var__var__var__var__8__n__63770__63773__63811__63814__63817] :
( t(Vvar__var__var__var__var__8__n__63770__63773__63811__63814__63817,Vvar__0__R__63724)
=> ! [Vvar__var__var__var__var__9__m__63771__63774__63812__63815__63818] :
( t(Vvar__var__var__var__var__9__m__63771__63774__63812__63815__63818,Vvar__0__R__63724)
=> ! [Vvar__var__var__var__var__10__p__63772__63775__63813__63816__63819] :
( t(Vvar__var__var__var__var__10__p__63772__63775__63813__63816__63819,Vvar__0__R__63724)
=> p(happ(happ(Vvar__5__req__63737,happ(happ(Vvar__3__radd__63727,Vvar__var__var__var__var__8__n__63770__63773__63811__63814__63817),happ(happ(Vvar__3__radd__63727,Vvar__var__var__var__var__9__m__63771__63774__63812__63815__63818),Vvar__var__var__var__var__10__p__63772__63775__63813__63816__63819))),happ(happ(Vvar__3__radd__63727,happ(happ(Vvar__3__radd__63727,Vvar__var__var__var__var__8__n__63770__63773__63811__63814__63817),Vvar__var__var__var__var__9__m__63771__63774__63812__63815__63818)),Vvar__var__var__var__var__10__p__63772__63775__63813__63816__63819))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__63777__63778__63820__63821__63822__63823] :
( t(Vvar__var__var__var__var__var__9__n__63777__63778__63820__63821__63822__63823,Vvar__0__R__63724)
=> p(happ(happ(Vvar__5__req__63737,happ(happ(Vvar__4__rmul__63732,Vvar__2__rI__63726),Vvar__var__var__var__var__var__9__n__63777__63778__63820__63821__63822__63823)),Vvar__var__var__var__var__var__9__n__63777__63778__63820__63821__63822__63823)) )
& ! [Vvar__var__var__var__var__var__10__n__63780__63781__63824__63825__63826__63827] :
( t(Vvar__var__var__var__var__var__10__n__63780__63781__63824__63825__63826__63827,Vvar__0__R__63724)
=> p(happ(happ(Vvar__5__req__63737,happ(happ(Vvar__4__rmul__63732,Vvar__1__rO__63725),Vvar__var__var__var__var__var__10__n__63780__63781__63824__63825__63826__63827)),Vvar__1__rO__63725)) )
& ! [Vvar__var__var__var__var__11__n__63783__63785__63828__63830__63832] :
( t(Vvar__var__var__var__var__11__n__63783__63785__63828__63830__63832,Vvar__0__R__63724)
=> ! [Vvar__var__var__var__var__12__m__63784__63786__63829__63831__63833] :
( t(Vvar__var__var__var__var__12__m__63784__63786__63829__63831__63833,Vvar__0__R__63724)
=> p(happ(happ(Vvar__5__req__63737,happ(happ(Vvar__4__rmul__63732,Vvar__var__var__var__var__11__n__63783__63785__63828__63830__63832),Vvar__var__var__var__var__12__m__63784__63786__63829__63831__63833)),happ(happ(Vvar__4__rmul__63732,Vvar__var__var__var__var__12__m__63784__63786__63829__63831__63833),Vvar__var__var__var__var__11__n__63783__63785__63828__63830__63832))) ) )
& ! [Vvar__var__var__var__var__12__n__63788__63791__63834__63837__63840] :
( t(Vvar__var__var__var__var__12__n__63788__63791__63834__63837__63840,Vvar__0__R__63724)
=> ! [Vvar__var__var__var__var__13__m__63789__63792__63835__63838__63841] :
( t(Vvar__var__var__var__var__13__m__63789__63792__63835__63838__63841,Vvar__0__R__63724)
=> ! [Vvar__var__var__var__var__14__p__63790__63793__63836__63839__63842] :
( t(Vvar__var__var__var__var__14__p__63790__63793__63836__63839__63842,Vvar__0__R__63724)
=> p(happ(happ(Vvar__5__req__63737,happ(happ(Vvar__4__rmul__63732,Vvar__var__var__var__var__12__n__63788__63791__63834__63837__63840),happ(happ(Vvar__4__rmul__63732,Vvar__var__var__var__var__13__m__63789__63792__63835__63838__63841),Vvar__var__var__var__var__14__p__63790__63793__63836__63839__63842))),happ(happ(Vvar__4__rmul__63732,happ(happ(Vvar__4__rmul__63732,Vvar__var__var__var__var__12__n__63788__63791__63834__63837__63840),Vvar__var__var__var__var__13__m__63789__63792__63835__63838__63841)),Vvar__var__var__var__var__14__p__63790__63793__63836__63839__63842))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__63795__63798__63843__63846__63849__63852] :
( t(Vvar__var__var__var__var__var__13__n__63795__63798__63843__63846__63849__63852,Vvar__0__R__63724)
=> ! [Vvar__var__var__var__var__var__14__m__63796__63799__63844__63847__63850__63853] :
( t(Vvar__var__var__var__var__var__14__m__63796__63799__63844__63847__63850__63853,Vvar__0__R__63724)
=> ! [Vvar__var__var__var__var__var__15__p__63797__63800__63845__63848__63851__63854] :
( t(Vvar__var__var__var__var__var__15__p__63797__63800__63845__63848__63851__63854,Vvar__0__R__63724)
=> p(happ(happ(Vvar__5__req__63737,happ(happ(Vvar__4__rmul__63732,happ(happ(Vvar__3__radd__63727,Vvar__var__var__var__var__var__13__n__63795__63798__63843__63846__63849__63852),Vvar__var__var__var__var__var__14__m__63796__63799__63844__63847__63850__63853)),Vvar__var__var__var__var__var__15__p__63797__63800__63845__63848__63851__63854)),happ(happ(Vvar__3__radd__63727,happ(happ(Vvar__4__rmul__63732,Vvar__var__var__var__var__var__13__n__63795__63798__63843__63846__63849__63852),Vvar__var__var__var__var__var__15__p__63797__63800__63845__63848__63851__63854)),happ(happ(Vvar__4__rmul__63732,Vvar__var__var__var__var__var__14__m__63796__63799__63844__63847__63850__63853),Vvar__var__var__var__var__var__15__p__63797__63800__63845__63848__63851__63854)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Redblack.TREES.tree',axiom,
! [VX3177] :
( cRedblack_2eTREES_2etree___24t(VX3177)
=> ( VX3177 = cRedblack_2eTREES_2eE
| ? [Vvar__0___24Anonymous__3178] :
( cRedblack_2ecolor___24t(Vvar__0___24Anonymous__3178)
& ? [Vvar__1___24Anonymous__3179] :
( cRedblack_2eTREES_2etree___24t(Vvar__1___24Anonymous__3179)
& ? [Vvar__2___24Anonymous__3180] :
( cRedblack_2ekey___24t(Vvar__2___24Anonymous__3180)
& ? [Vvar__3___24Anonymous__3181] :
( cV___24t(Vvar__3___24Anonymous__3181)
& ? [Vvar__4___24Anonymous__3182] :
( cRedblack_2eTREES_2etree___24t(Vvar__4___24Anonymous__3182)
& VX3177 = cRedblack_2eTREES_2eT___24a5(Vvar__0___24Anonymous__3178,Vvar__1___24Anonymous__3179,Vvar__2___24Anonymous__3180,Vvar__3___24Anonymous__3181,Vvar__4___24Anonymous__3182) ) ) ) ) ) ) ) ).
fof('$_inversion_Redblack.color',axiom,
! [VX3229] :
( cRedblack_2ecolor___24t(VX3229)
=> ( VX3229 = cRedblack_2eRed
| VX3229 = cRedblack_2eBlack ) ) ).
fof('$_inversion_VFA.SearchTree.Abs',axiom,
! [Vvar__0__V__57084,Vvar__1__default__57085,Vvar__2___24Anonymous__57086,Vvar__3___24Anonymous__57087] :
( cType___24t(Vvar__0__V__57084)
=> ( t(Vvar__1__default__57085,Vvar__0__V__57084)
=> ( cVFA_2eSearchTree_2etree___24t(Vvar__0__V__57084,Vvar__2___24Anonymous__57086)
=> ( cVFA_2eMaps_2etotal__map___24t(Vvar__0__V__57084,Vvar__3___24Anonymous__57087)
=> ( cVFA_2eSearchTree_2eAbs___24a4(Vvar__0__V__57084,Vvar__1__default__57085,Vvar__2___24Anonymous__57086,Vvar__3___24Anonymous__57087)
=> ( ( Vvar__3___24Anonymous__57087 = c_24__lam__57115___24a4(Vvar__0__V__57084,Vvar__1__default__57085,Vvar__2___24Anonymous__57086,Vvar__3___24Anonymous__57087)
& Vvar__2___24Anonymous__57086 = cVFA_2eSearchTree_2eE___24a1(Vvar__0__V__57084) )
| ? [Vvar__2__a__57095] :
( cVFA_2eMaps_2etotal__map___24t(Vvar__0__V__57084,Vvar__2__a__57095)
& ? [Vvar__3__b__57096] :
( cVFA_2eMaps_2etotal__map___24t(Vvar__0__V__57084,Vvar__3__b__57096)
& ? [Vvar__4__l__57097] :
( cVFA_2eSearchTree_2etree___24t(Vvar__0__V__57084,Vvar__4__l__57097)
& ? [Vvar__5__k__57098] :
( cVFA_2eSearchTree_2ekey___24t(Vvar__5__k__57098)
& ? [Vvar__6__v__57099] :
( t(Vvar__6__v__57099,Vvar__0__V__57084)
& ? [Vvar__7__r__57100] :
( cVFA_2eSearchTree_2etree___24t(Vvar__0__V__57084,Vvar__7__r__57100)
& cVFA_2eSearchTree_2eAbs___24a4(Vvar__0__V__57084,Vvar__1__default__57085,Vvar__4__l__57097,Vvar__2__a__57095)
& cVFA_2eSearchTree_2eAbs___24a4(Vvar__0__V__57084,Vvar__1__default__57085,Vvar__7__r__57100,Vvar__3__b__57096)
& Vvar__3___24Anonymous__57087 = c_24__lam__57152___24a8(Vvar__0__V__57084,Vvar__1__default__57085,Vvar__2___24Anonymous__57086,Vvar__3___24Anonymous__57087,Vvar__2__a__57095,Vvar__3__b__57096,Vvar__5__k__57098,Vvar__6__v__57099)
& Vvar__2___24Anonymous__57086 = cVFA_2eSearchTree_2eT___24a5(Vvar__0__V__57084,Vvar__4__l__57097,Vvar__5__k__57098,Vvar__6__v__57099,Vvar__7__r__57100) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_VFA.SearchTree.tree',axiom,
! [Vvar__0__V__57011,VX57012] :
( cType___24t(Vvar__0__V__57011)
=> ( cVFA_2eSearchTree_2etree___24t(Vvar__0__V__57011,VX57012)
=> ( VX57012 = cVFA_2eSearchTree_2eE___24a1(Vvar__0__V__57011)
| ? [Vvar__1___24Anonymous__57015] :
( cVFA_2eSearchTree_2etree___24t(Vvar__0__V__57011,Vvar__1___24Anonymous__57015)
& ? [Vvar__2___24Anonymous__57016] :
( cVFA_2eSearchTree_2ekey___24t(Vvar__2___24Anonymous__57016)
& ? [Vvar__3___24Anonymous__57017] :
( t(Vvar__3___24Anonymous__57017,Vvar__0__V__57011)
& ? [Vvar__4___24Anonymous__57018] :
( cVFA_2eSearchTree_2etree___24t(Vvar__0__V__57011,Vvar__4___24Anonymous__57018)
& VX57012 = cVFA_2eSearchTree_2eT___24a5(Vvar__0__V__57011,Vvar__1___24Anonymous__57015,Vvar__2___24Anonymous__57016,Vvar__3___24Anonymous__57017,Vvar__4___24Anonymous__57018) ) ) ) ) ) ) ) ).
fof('$_lam_4337',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__4337___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> Vv__CANONICAL__2 = Vv__CANONICAL__1 ) ).
fof('$_lam_43943',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__43943___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_lam_4670',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2etrue
& ( c_24__lam__4670___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) )
| ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2efalse
& ( c_24__lam__4670___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ) ) ) ).
fof('$_lam_49929',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__49929___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_49937',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__49937___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_49945',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__49945___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_49953',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__49953___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_51924',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11] : c_24__lam__51924___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = c_24__let__11__subst__l__51852___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__11)) ).
fof('$_lam_57115',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__57115___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 ).
fof('$_lam_57152',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cVFA_2eSearchTree_2ekey___24t(Vv__CANONICAL__6)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__8)
=> ( ( cCoq_2eInit_2eNat_2eeqb___24a2(Vv__CANONICAL__6,Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__lam__57152___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8) = Vv__CANONICAL__7 )
| ( cType___24t(Vv__CANONICAL__0)
=> ( cVFA_2eSearchTree_2ekey___24t(Vv__CANONICAL__6)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__8)
=> ( cCoq_2eInit_2eNat_2eeqb___24a2(Vv__CANONICAL__6,Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( cCoq_2eInit_2eNat_2eltb___24a2(Vv__CANONICAL__8,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__lam__57152___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8) = happ(Vv__CANONICAL__4,Vv__CANONICAL__8) )
| ( cCoq_2eInit_2eNat_2eltb___24a2(Vv__CANONICAL__8,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__lam__57152___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8) = happ(Vv__CANONICAL__5,Vv__CANONICAL__8) ) ) ) ) ) ) ) ) ) ) ).
fof('$_lam_59756',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__59756___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_lam_59762',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__59762___24a1(Vv__CANONICAL__0)
<=> Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_lam_59763',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__59763___24a1(Vv__CANONICAL__0)
<=> Vv__CANONICAL__0 != cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_lam_59764',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__59764___24a1(Vv__CANONICAL__0)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__0)) ) ).
fof('$_lam_59765',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__59765___24a1(Vv__CANONICAL__0)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__0)) ) ).
fof('$_lam_59788',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2etrue
& ( c_24__lam__59788___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) )
| ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2efalse
& ( c_24__lam__59788___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ) ) ) ).
fof('$_lam_63290',axiom,
! [Vv__CANONICAL__0] : c_24__lam__63290___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enat ).
fof('$_lam_63291',axiom,
! [Vv__CANONICAL__0] : c_24__lam__63291___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eNat_2edouble ).
fof('$_lam_63652',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__63652___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('$_lam_63660',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__63660___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_63668',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__63668___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('$_lam_63676',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__63676___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_64754',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__64754___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__64755] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__64755)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__64755)
& c_24__lam__64754___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__64755) ) ) ) ).
fof('$_lam_64761',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__64761___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__64762] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__64762)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__64762)
& c_24__lam__64761___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__64762) ) ) ) ).
fof('$_lam_64765',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__64765___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__64766] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__64766)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__64766)
& c_24__lam__64765___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_prop_116',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__116___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__2 ) ).
fof('$_prop_117',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__117___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__2 ) ).
fof('$_prop_118',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__118___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ).
fof('$_prop_3379',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__3379___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_3380',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__3380___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_3381',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__3381___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_3382',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__3382___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_37114',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__37114___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_3931',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__3931___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_3932',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__3932___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_4090',axiom,
! [Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073] :
( p(c_24__prop__4090___24a2(Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073))
<=> Vvar__0___24Anonymous__4058 = Vvar__0___24Anonymous__4073 ) ).
fof('$_prop_4091',axiom,
! [Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073] :
( p(c_24__prop__4091___24a2(Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073))
<=> Vvar__0___24Anonymous__4058 != Vvar__0___24Anonymous__4073 ) ).
fof('$_prop_4092',axiom,
! [Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073] :
( p(c_24__prop__4092___24a2(Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073))
<=> Vvar__0___24Anonymous__4058 = Vvar__0___24Anonymous__4073 ) ).
fof('$_prop_4093',axiom,
! [Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073] :
( p(c_24__prop__4093___24a2(Vvar__0___24Anonymous__4058,Vvar__0___24Anonymous__4073))
<=> Vvar__0___24Anonymous__4058 != Vvar__0___24Anonymous__4073 ) ).
fof('$_prop_4112',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__4112___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_4113',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__4113___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 != cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_4117',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__4117___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_4118',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__4118___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_41618',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__41598] :
( p(c_24__prop__41618___24a3(V0__A,V3__x,Vvar__1___24Anonymous__41598))
<=> V3__x = Vvar__1___24Anonymous__41598 ) ).
fof('$_prop_41619',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__41598] :
( p(c_24__prop__41619___24a3(V0__A,V3__x,Vvar__1___24Anonymous__41598))
<=> V3__x != Vvar__1___24Anonymous__41598 ) ).
fof('$_prop_41620',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__41598] :
( p(c_24__prop__41620___24a3(V0__A,V3__x,Vvar__1___24Anonymous__41598))
<=> V3__x = Vvar__1___24Anonymous__41598 ) ).
fof('$_prop_41621',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__41598] :
( p(c_24__prop__41621___24a3(V0__A,V3__x,Vvar__1___24Anonymous__41598))
<=> V3__x != Vvar__1___24Anonymous__41598 ) ).
fof('$_prop_4233',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__4233___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_4234',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__4234___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_4235',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__4235___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_43922',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__43922___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_43928',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__43928___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_43929',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__43929___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_4470',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__4470___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_4655',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__4655___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_4656',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__4656___24a2(V0__x,V1__y))
<=> V0__x != V1__y ) ).
fof('$_prop_58792',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__58792___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_58793',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__58793___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_58818',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__58818___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_59664',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__59664___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 != cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_59665',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__59665___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_59773',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__59773___24a2(V0__x,V1__y))
<=> V0__x != V1__y ) ).
fof('$_prop_59774',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__59774___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_60386',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__60386___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_60387',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__60387___24a2(V0__x,V1__y))
<=> V0__x != V1__y ) ).
fof('$_prop_60388',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__60388___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_60389',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__60389___24a2(V0__x,V1__y))
<=> V0__x != V1__y ) ).
fof('$_prop_60417',axiom,
! [Vvar__0___24Anonymous__60393,Vvar__0__S__60395,Vvar__1__x__60396,Vvar__2__y__60397] :
( p(c_24__prop__60417___24a4(Vvar__0___24Anonymous__60393,Vvar__0__S__60395,Vvar__1__x__60396,Vvar__2__y__60397))
<=> Vvar__1__x__60396 = Vvar__2__y__60397 ) ).
fof('$_prop_60418',axiom,
! [Vvar__0___24Anonymous__60393,Vvar__0__x__60398,Vvar__1__y__60399] :
( p(c_24__prop__60418___24a3(Vvar__0___24Anonymous__60393,Vvar__0__x__60398,Vvar__1__y__60399))
<=> Vvar__0__x__60398 = Vvar__1__y__60399 ) ).
fof('$_prop_60419',axiom,
! [Vvar__0___24Anonymous__60393,Vvar__0__x__60400,Vvar__1__s__60401] :
( p(c_24__prop__60419___24a3(Vvar__0___24Anonymous__60393,Vvar__0__x__60400,Vvar__1__s__60401))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__60400,Vvar__1__s__60401) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_60420',axiom,
! [Vvar__0___24Anonymous__60393,Vvar__0__P__60402,Vvar__1__Q__60403] :
( p(c_24__prop__60420___24a3(Vvar__0___24Anonymous__60393,Vvar__0__P__60402,Vvar__1__Q__60403))
<=> ( p(Vvar__0__P__60402)
& p(Vvar__1__Q__60403) ) ) ).
fof('$_prop_60421',axiom,
! [Vvar__0___24Anonymous__60393,Vvar__0__P__60406,Vvar__1__Q__60407] :
( p(c_24__prop__60421___24a3(Vvar__0___24Anonymous__60393,Vvar__0__P__60406,Vvar__1__Q__60407))
<=> ( p(Vvar__0__P__60406)
| p(Vvar__1__Q__60407) ) ) ).
fof('$_prop_60422',axiom,
! [Vvar__0___24Anonymous__60393,Vvar__0__P__60410,Vvar__1__Q__60411] :
( p(c_24__prop__60422___24a3(Vvar__0___24Anonymous__60393,Vvar__0__P__60410,Vvar__1__Q__60411))
<=> ( p(Vvar__0__P__60410)
=> p(Vvar__1__Q__60411) ) ) ).
fof('$_prop_60423',axiom,
! [Vvar__0___24Anonymous__60393,Vvar__0__P__60415] :
( p(c_24__prop__60423___24a2(Vvar__0___24Anonymous__60393,Vvar__0__P__60415))
<=> ~ p(Vvar__0__P__60415) ) ).
fof('$_prop_60917',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__60917___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_60918',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__60918___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_60919',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__60919___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_61392',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__61392___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_61469',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__61469___24a2(V0__A,V1__B))
<=> ( p(V0__A)
& p(V1__B) ) ) ).
fof('$_prop_61470',axiom,
! [V0__A] :
( p(c_24__prop__61470___24a1(V0__A))
<=> ~ p(V0__A) ) ).
fof('$_prop_64699',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__64699___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_6677',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__6677___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_6678',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__6678___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_type_109',axiom,
! [Vvar__110] :
( c_24__type__109___24t(Vvar__110)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eLists_2eList_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__118___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(Vvar__110,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_114',axiom,
! [Vv__CANONICAL__0,Vvar__115] :
( c_24__type__114___24t(Vv__CANONICAL__0,Vvar__115)
<=> ! [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__116___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__117___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(Vvar__115,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_126',axiom,
! [Vvar__127] :
( c_24__type__126___24t(Vvar__127)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__127,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_129',axiom,
! [Vvar__130] :
( c_24__type__129___24t(Vvar__130)
<=> ! [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__130,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_134',axiom,
! [Vvar__135] :
( c_24__type__134___24t(Vvar__135)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__135,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_139',axiom,
! [Vvar__140] :
( c_24__type__139___24t(Vvar__140)
<=> ! [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__140,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_144',axiom,
! [Vvar__145] :
( c_24__type__144___24t(Vvar__145)
<=> ! [Vv__CANONICAL__0] :
( cRedblack_2ekey___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cV___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cRedblack_2eTREES_2etree___24t(Vv__CANONICAL__2)
=> cRedblack_2eTREES_2etree___24t(happ(happ(happ(Vvar__145,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_190',axiom,
! [Vvar__191] :
( c_24__type__190___24t(Vvar__191)
<=> ! [Vv__CANONICAL__0] :
( cRedblack_2eTREES_2etree___24t(Vv__CANONICAL__0)
=> cRedblack_2eTREES_2etree___24t(happ(Vvar__191,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3002',axiom,
! [Vvar__3003] :
( c_24__type__3002___24t(Vvar__3003)
<=> ! [Vv__CANONICAL__0] :
( cRedblack_2ecolor___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cRedblack_2eTREES_2etree___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cRedblack_2ekey___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cV___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cRedblack_2eTREES_2etree___24t(Vv__CANONICAL__4)
=> cRedblack_2eTREES_2etree___24t(happ(happ(happ(happ(happ(Vvar__3003,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_3031',axiom,
! [Vvar__3032] :
( c_24__type__3031___24t(Vvar__3032)
<=> ! [Vv__CANONICAL__0] :
( cRedblack_2ekey___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cRedblack_2eTREES_2etree___24t(Vv__CANONICAL__1)
=> cV___24t(happ(happ(Vvar__3032,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3074',axiom,
! [Vvar__3075] :
( c_24__type__3074___24t(Vvar__3075)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__3076___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cRedblack_2eTREES_2eE))
=> ! [Vv__CANONICAL__2] :
( c_24__type__3106___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cRedblack_2eTREES_2etree___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__3075,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3076',axiom,
! [Vvar__3077] :
( c_24__type__3076___24t(Vvar__3077)
<=> ! [Vv__CANONICAL__0] :
( cRedblack_2eTREES_2etree___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__3077,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3106',axiom,
! [Vv__CANONICAL__0,Vvar__3107] :
( c_24__type__3106___24t(Vv__CANONICAL__0,Vvar__3107)
<=> ! [Vv__CANONICAL__1] :
( cRedblack_2ecolor___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cRedblack_2eTREES_2etree___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__2))
=> ! [Vv__CANONICAL__4] :
( cRedblack_2ekey___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cV___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cRedblack_2eTREES_2etree___24t(Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,happ(Vv__CANONICAL__0,Vv__CANONICAL__6))
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__3107,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),happ(Vv__CANONICAL__0,cRedblack_2eTREES_2eT___24a5(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6))) ) ) ) ) ) ) ) ) ).
fof('$_type_3108',axiom,
! [Vvar__3109] :
( c_24__type__3108___24t(Vvar__3109)
<=> ! [Vv__CANONICAL__0] :
( cRedblack_2eTREES_2etree___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3109,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3134',axiom,
! [Vv__CANONICAL__0,Vvar__3135] :
( c_24__type__3134___24t(Vv__CANONICAL__0,Vvar__3135)
<=> ! [Vv__CANONICAL__1] :
( cRedblack_2eTREES_2etree___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__3135,Vv__CANONICAL__1)) ) ) ).
fof('$_type_3214',axiom,
! [Vvar__3215] :
( c_24__type__3214___24t(Vvar__3215)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__3216___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cRedblack_2eRed))
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,cRedblack_2eBlack))
=> ! [Vv__CANONICAL__3] :
( cRedblack_2ecolor___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__3215,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3216',axiom,
! [Vvar__3217] :
( c_24__type__3216___24t(Vvar__3217)
<=> ! [Vv__CANONICAL__0] :
( cRedblack_2ecolor___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__3217,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3218',axiom,
! [Vvar__3219] :
( c_24__type__3218___24t(Vvar__3219)
<=> ! [Vv__CANONICAL__0] :
( cRedblack_2ecolor___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3219,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3221',axiom,
! [Vv__CANONICAL__0,Vvar__3222] :
( c_24__type__3221___24t(Vv__CANONICAL__0,Vvar__3222)
<=> ! [Vv__CANONICAL__1] :
( cRedblack_2ecolor___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__3222,Vv__CANONICAL__1)) ) ) ).
fof('$_type_3247',axiom,
! [Vvar__3248] :
( c_24__type__3247___24t(Vvar__3248)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__3248,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3255',axiom,
! [Vvar__3256] :
( c_24__type__3255___24t(Vvar__3256)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__3256,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3269',axiom,
! [Vvar__3270] :
( c_24__type__3269___24t(Vvar__3270)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__3270,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3274',axiom,
! [Vvar__3275] :
( c_24__type__3274___24t(Vvar__3275)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__3275,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3299',axiom,
! [Vvar__3300] :
( c_24__type__3299___24t(Vvar__3300)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3302___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__3314___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__3300,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_3302',axiom,
! [Vv__CANONICAL__0,Vvar__3303] :
( c_24__type__3302___24t(Vv__CANONICAL__0,Vvar__3303)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__3303,Vv__CANONICAL__1)) ) ) ).
fof('$_type_3314',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3315] :
( c_24__type__3314___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3315)
<=> ! [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__3315,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('$_type_3326',axiom,
! [Vvar__3327] :
( c_24__type__3326___24t(Vvar__3327)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__3327,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3392',axiom,
! [Vvar__3393] :
( c_24__type__3392___24t(Vvar__3393)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__3393,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3407',axiom,
! [Vvar__3408] :
( c_24__type__3407___24t(Vvar__3408)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__3408,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3427',axiom,
! [Vvar__3428] :
( c_24__type__3427___24t(Vvar__3428)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3428,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3436',axiom,
! [Vvar__3437] :
( c_24__type__3436___24t(Vvar__3437)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__3437,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3456',axiom,
! [Vvar__3457] :
( c_24__type__3456___24t(Vvar__3457)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(happ(Vvar__3457,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3502',axiom,
! [Vvar__3503] :
( c_24__type__3502___24t(Vvar__3503)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__3503,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3505',axiom,
! [Vvar__3506] :
( c_24__type__3505___24t(Vvar__3506)
<=> ! [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__3506,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3507',axiom,
! [Vvar__3508] :
( c_24__type__3507___24t(Vvar__3508)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__3508,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37109',axiom,
! [Vvar__37110] :
( c_24__type__37109___24t(Vvar__37110)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__37110,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37112',axiom,
! [Vvar__37113] :
( c_24__type__37112___24t(Vvar__37113)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__1)
=> cCoq_2eBool_2eBool_2ereflect___24t(c_24__prop__37114___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eStrings_2eAscii_2eeqb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__37113,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37116',axiom,
! [Vvar__37117] :
( c_24__type__37116___24t(Vvar__37117)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__37117,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37140',axiom,
! [Vvar__37141] :
( c_24__type__37140___24t(Vvar__37141)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__37142___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__37147___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__37152___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__37141,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_37142',axiom,
! [Vvar__37143] :
( c_24__type__37142___24t(Vvar__37143)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__37143,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37147',axiom,
! [Vv__CANONICAL__0,Vvar__37148] :
( c_24__type__37147___24t(Vv__CANONICAL__0,Vvar__37148)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__37148,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2exI___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_37152',axiom,
! [Vv__CANONICAL__0,Vvar__37153] :
( c_24__type__37152___24t(Vv__CANONICAL__0,Vvar__37153)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__37153,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2exO___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_37154',axiom,
! [Vvar__37155] :
( c_24__type__37154___24t(Vvar__37155)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__37155,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37164',axiom,
! [Vvar__37165] :
( c_24__type__37164___24t(Vvar__37165)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__37166___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eN0))
=> ! [Vv__CANONICAL__2] :
( c_24__type__37169___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__37165,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_37166',axiom,
! [Vvar__37167] :
( c_24__type__37166___24t(Vvar__37167)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__37167,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37169',axiom,
! [Vv__CANONICAL__0,Vvar__37170] :
( c_24__type__37169___24t(Vv__CANONICAL__0,Vvar__37170)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__37170,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_type_37221',axiom,
! [Vvar__37222] :
( c_24__type__37221___24t(Vvar__37222)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__37222,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37236',axiom,
! [Vvar__37237] :
( c_24__type__37236___24t(Vvar__37237)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2etrue,happ(Vvar__37237,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_37239',axiom,
! [Vvar__37240] :
( c_24__type__37239___24t(Vvar__37240)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ( ~ p(Vv__CANONICAL__0)
=> cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2efalse,happ(Vvar__37240,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_38131',axiom,
! [Vvar__38132] :
( c_24__type__38131___24t(Vvar__38132)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__38133___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2etrue))
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2efalse))
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__38132,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_38133',axiom,
! [Vvar__38134] :
( c_24__type__38133___24t(Vvar__38134)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__38134,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38136',axiom,
! [Vvar__38137] :
( c_24__type__38136___24t(Vvar__38137)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__38137,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38146',axiom,
! [Vvar__38147] :
( c_24__type__38146___24t(Vvar__38147)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__38147,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38162',axiom,
! [Vvar__38163] :
( c_24__type__38162___24t(Vvar__38163)
<=> ! [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__38163,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_38174',axiom,
! [Vvar__38175] :
( c_24__type__38174___24t(Vvar__38175)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__38175,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_38186',axiom,
! [Vvar__38187] :
( c_24__type__38186___24t(Vvar__38187)
<=> ! [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__38187,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_38198',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38199] :
( c_24__type__38198___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38199)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__38199,Vv__CANONICAL__2)) ) ) ).
fof('$_type_38233',axiom,
! [Vvar__38234] :
( c_24__type__38233___24t(Vvar__38234)
<=> ! [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__38234,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38242',axiom,
! [Vvar__38243] :
( c_24__type__38242___24t(Vvar__38243)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__38243,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_38464',axiom,
! [Vvar__38465] :
( c_24__type__38464___24t(Vvar__38465)
<=> ! [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__38465,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38469',axiom,
! [Vvar__38470] :
( c_24__type__38469___24t(Vvar__38470)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__38470,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38477',axiom,
! [Vvar__38478] :
( c_24__type__38477___24t(Vvar__38478)
<=> ! [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__38478,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_38673',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__38674] :
( c_24__type__38673___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__38674)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38674,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_38766',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__38767] :
( c_24__type__38766___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__38767)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38767,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_38859',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__38860] :
( c_24__type__38859___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__38860)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38860,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_38941',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__38942] :
( c_24__type__38941___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__38942)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__38942,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_39034',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__39035] :
( c_24__type__39034___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__39035)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__39035,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_39116',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__39117] :
( c_24__type__39116___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__39117)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__39117,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_39209',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__39210] :
( c_24__type__39209___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__39210)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__39210,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_39218',axiom,
! [Vv__CANONICAL__0,Vvar__39219] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vvar__39219)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__39219,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_39227',axiom,
! [Vv__CANONICAL__0,Vvar__39228] :
( c_24__type__39227___24t(Vv__CANONICAL__0,Vvar__39228)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__39228,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_39236',axiom,
! [Vv__CANONICAL__0,Vvar__39237] :
( c_24__type__39236___24t(Vv__CANONICAL__0,Vvar__39237)
<=> ! [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__39237,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_3929',axiom,
! [Vvar__3930] :
( c_24__type__3929___24t(Vvar__3930)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__3931___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__3932___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__3930,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_39353',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39354] :
( c_24__type__39353___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39354)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__39354,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_39358',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39359] :
( c_24__type__39358___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39359)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__39359,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_39367',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39368] :
( c_24__type__39367___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39368)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__39368,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_39494',axiom,
! [Vv__CANONICAL__0,Vvar__39495] :
( c_24__type__39494___24t(Vv__CANONICAL__0,Vvar__39495)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__39495,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_39518',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39519] :
( c_24__type__39518___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39519)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__39519,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_39532',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39533] :
( c_24__type__39532___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39533)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__39533,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_39539',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39540] :
( c_24__type__39539___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39540)
<=> ! [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__39540,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_3970',axiom,
! [Vvar__3971] :
( c_24__type__3970___24t(Vvar__3971)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__3971,Vv__CANONICAL__0)) ) ) ).
fof('$_type_39770',axiom,
! [Vvar__39771] :
( c_24__type__39770___24t(Vvar__39771)
<=> ! [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__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__39227___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__39236___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__39353___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__39358___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__39367___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__39771,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_3983',axiom,
! [Vvar__3984] :
( c_24__type__3983___24t(Vvar__3984)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__3985___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__3990___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__3984,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3985',axiom,
! [Vvar__3986] :
( c_24__type__3985___24t(Vvar__3986)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__3986,Vv__CANONICAL__0)) ) ) ).
fof('$_type_39863',axiom,
! [Vvar__39864] :
( c_24__type__39863___24t(Vvar__39864)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__39868___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__39864,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_39868',axiom,
! [Vv__CANONICAL__0,Vvar__39869] :
( c_24__type__39868___24t(Vv__CANONICAL__0,Vvar__39869)
<=> ! [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__39869,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_3990',axiom,
! [Vv__CANONICAL__0,Vvar__3991] :
( c_24__type__3990___24t(Vv__CANONICAL__0,Vvar__3991)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__3991,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_4007',axiom,
! [Vvar__4008] :
( c_24__type__4007___24t(Vvar__4008)
<=> ! [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__4008,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4009',axiom,
! [Vvar__4010] :
( c_24__type__4009___24t(Vvar__4010)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__4010,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4011',axiom,
! [Vvar__4012] :
( c_24__type__4011___24t(Vvar__4012)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4012,Vv__CANONICAL__0)) ) ) ).
fof('$_type_40140',axiom,
! [Vv__CANONICAL__0,Vvar__40141] :
( c_24__type__40140___24t(Vv__CANONICAL__0,Vvar__40141)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__40141,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_4016',axiom,
! [Vvar__4017] :
( c_24__type__4016___24t(Vvar__4017)
<=> ! [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__4017,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4022',axiom,
! [Vv__CANONICAL__0,Vvar__4023] :
( c_24__type__4022___24t(Vv__CANONICAL__0,Vvar__4023)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__4023,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_4033',axiom,
! [Vvar__4034] :
( c_24__type__4033___24t(Vvar__4034)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__4034,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4038',axiom,
! [Vvar__4039] :
( c_24__type__4038___24t(Vvar__4039)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__4039,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4043',axiom,
! [Vvar__4044] :
( c_24__type__4043___24t(Vvar__4044)
<=> ! [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__4044,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4055',axiom,
! [Vvar__4056] :
( c_24__type__4055___24t(Vvar__4056)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__4056,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4095',axiom,
! [Vvar__4096] :
( c_24__type__4095___24t(Vvar__4096)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__4096,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4108',axiom,
! [Vvar__4109] :
( c_24__type__4108___24t(Vvar__4109)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,happ(happ(happ(Vvar__4109,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4110',axiom,
! [Vvar__4111] :
( c_24__type__4110___24t(Vvar__4111)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__4112___24a1(Vv__CANONICAL__0),c_24__prop__4113___24a1(Vv__CANONICAL__0),happ(Vvar__4111,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4115',axiom,
! [Vvar__4116] :
( c_24__type__4115___24t(Vvar__4116)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__4117___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__4118___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__4116,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4120',axiom,
! [Vvar__4121] :
( c_24__type__4120___24t(Vvar__4121)
<=> ! [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__4121,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_41272',axiom,
! [Vvar__41273] :
( c_24__type__41272___24t(Vvar__41273)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__41273,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_41577',axiom,
! [Vvar__41578] :
( c_24__type__41577___24t(Vvar__41578)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__41578,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_41592',axiom,
! [Vvar__41593] :
( c_24__type__41592___24t(Vvar__41593)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__41593,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_41631',axiom,
! [Vvar__41632] :
( c_24__type__41631___24t(Vvar__41632)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__41632,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4231',axiom,
! [Vvar__4232] :
( c_24__type__4231___24t(Vvar__4232)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__4233___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__4234___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__4232,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4236',axiom,
! [Vvar__4237] :
( c_24__type__4236___24t(Vvar__4237)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4237,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4241',axiom,
! [Vvar__4242] :
( c_24__type__4241___24t(Vvar__4242)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__4242,Vv__CANONICAL__0)) ) ) ).
fof('$_type_42452',axiom,
! [Vvar__42453] :
( c_24__type__42452___24t(Vvar__42453)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__42456___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__42453,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_42456',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42457] :
( c_24__type__42456___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42457)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__42457,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_42480',axiom,
! [Vvar__42481] :
( c_24__type__42480___24t(Vvar__42481)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__42487___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__42481,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_42487',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42488] :
( c_24__type__42487___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42488)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__42488,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_42511',axiom,
! [Vvar__42512] :
( c_24__type__42511___24t(Vvar__42512)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__42512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_42614',axiom,
! [Vvar__42615] :
( c_24__type__42614___24t(Vvar__42615)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cVFA_2eMaps_2etotal__map___24t(Vv__CANONICAL__0,happ(happ(Vvar__42615,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42626',axiom,
! [Vvar__42627] :
( c_24__type__42626___24t(Vvar__42627)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cVFA_2eMaps_2etotal__map___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__42627,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_4264',axiom,
! [Vvar__4265] :
( c_24__type__4264___24t(Vvar__4265)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(happ(Vvar__4265,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42648',axiom,
! [Vvar__42649] :
( c_24__type__42648___24t(Vvar__42649)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__42649,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4267',axiom,
! [Vvar__4268] :
( c_24__type__4267___24t(Vvar__4268)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4268,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4269',axiom,
! [Vvar__4270] :
( c_24__type__4269___24t(Vvar__4270)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__4270,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4286',axiom,
! [Vvar__4287] :
( c_24__type__4286___24t(Vvar__4287)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__4288___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ! [Vv__CANONICAL__2] :
( c_24__type__4291___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__4294___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__4287,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_4288',axiom,
! [Vvar__4289] :
( c_24__type__4288___24t(Vvar__4289)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__4289,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4291',axiom,
! [Vv__CANONICAL__0,Vvar__4292] :
( c_24__type__4291___24t(Vv__CANONICAL__0,Vvar__4292)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__4292,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_type_4294',axiom,
! [Vv__CANONICAL__0,Vvar__4295] :
( c_24__type__4294___24t(Vv__CANONICAL__0,Vvar__4295)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__4295,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_type_4297',axiom,
! [Vvar__4298] :
( c_24__type__4297___24t(Vvar__4298)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__4298,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4303',axiom,
! [Vv__CANONICAL__0,Vvar__4304] :
( c_24__type__4303___24t(Vv__CANONICAL__0,Vvar__4304)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__4304,Vv__CANONICAL__1)) ) ) ).
fof('$_type_43082',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43083] :
( c_24__type__43082___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43083)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__43083,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4316',axiom,
! [Vvar__4317] :
( c_24__type__4316___24t(Vvar__4317)
<=> ! [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__4317,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4318',axiom,
! [Vvar__4319] :
( c_24__type__4318___24t(Vvar__4319)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__4319,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43183',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__43184] :
( c_24__type__43183___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__43184)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__43184,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_43284',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43285] :
( c_24__type__43284___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43285)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__43285,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_43374',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__43375] :
( c_24__type__43374___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__43375)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__43375,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_43475',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43476] :
( c_24__type__43475___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43476)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__43476,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_43576',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__43577] :
( c_24__type__43576___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__43577)
<=> ! [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__43577,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_43677',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43678] :
( c_24__type__43677___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43678)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__43678,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_43920',axiom,
! [Vvar__43921] :
( c_24__type__43920___24t(Vvar__43921)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__43922___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__43921,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43923',axiom,
! [Vvar__43924] :
( c_24__type__43923___24t(Vvar__43924)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__43924,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43926',axiom,
! [Vvar__43927] :
( c_24__type__43926___24t(Vvar__43927)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__43928___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__43929___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__43927,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43940',axiom,
! [Vvar__43941] :
( c_24__type__43940___24t(Vvar__43941)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__43941,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43947',axiom,
! [Vvar__43948] :
( c_24__type__43947___24t(Vvar__43948)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__43948,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_43954',axiom,
! [Vvar__43955] :
( c_24__type__43954___24t(Vvar__43955)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__43955,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43967',axiom,
! [Vvar__43968] :
( c_24__type__43967___24t(Vvar__43968)
<=> ! [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__43968,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43969',axiom,
! [Vvar__43970] :
( c_24__type__43969___24t(Vvar__43970)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),happ(Vvar__43970,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44009',axiom,
! [Vvar__44010] :
( c_24__type__44009___24t(Vvar__44010)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4496___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__44010,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4426',axiom,
! [Vvar__4427] :
( c_24__type__4426___24t(Vvar__4427)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__4427,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4435',axiom,
! [Vvar__4436] :
( c_24__type__4435___24t(Vvar__4436)
<=> ! [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__4436,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4448',axiom,
! [Vvar__4449] :
( c_24__type__4448___24t(Vvar__4449)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__4449,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4453',axiom,
! [Vvar__4454] :
( c_24__type__4453___24t(Vvar__4454)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__4454,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44545',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__44546] :
( c_24__type__44545___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__44546)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__44546,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4456',axiom,
! [Vvar__4457] :
( c_24__type__4456___24t(Vvar__4457)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4457,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4460',axiom,
! [Vvar__4461] :
( c_24__type__4460___24t(Vvar__4461)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__4461,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4463',axiom,
! [Vvar__4464] :
( c_24__type__4463___24t(Vvar__4464)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__4464,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4468',axiom,
! [Vvar__4469] :
( c_24__type__4468___24t(Vvar__4469)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__4470___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eReals_2eRdefinitions_2eRgt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__4469,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4472',axiom,
! [Vvar__4473] :
( c_24__type__4472___24t(Vvar__4473)
<=> ! [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__4473,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4489',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4490] :
( c_24__type__4489___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4490)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4490,Vv__CANONICAL__2)) ) ) ).
fof('$_type_44891',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__44892] :
( c_24__type__44891___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__44892)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__44892,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4493',axiom,
! [Vvar__4494] :
( c_24__type__4493___24t(Vvar__4494)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4496___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__4494,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4496',axiom,
! [Vv__CANONICAL__0,Vvar__4497] :
( c_24__type__4496___24t(Vv__CANONICAL__0,Vvar__4497)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4497,Vv__CANONICAL__1)) ) ) ).
fof('$_type_4508',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4509] :
( c_24__type__4508___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4509)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__4509,Vv__CANONICAL__2)) ) ) ).
fof('$_type_45237',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__45238] :
( c_24__type__45237___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__45238)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__45238,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4536',axiom,
! [Vvar__4537] :
( c_24__type__4536___24t(Vvar__4537)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4540___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__4547___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__4554___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__4537,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_4540',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4541] :
( c_24__type__4540___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4541)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__4541,Vv__CANONICAL__2)) ) ) ).
fof('$_type_4547',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__4548] :
( c_24__type__4547___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__4548)
<=> ( p(Vv__CANONICAL__0)
=> t(Vvar__4548,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_4554',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__4555] :
( c_24__type__4554___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__4555)
<=> ( p(Vv__CANONICAL__1)
=> t(Vvar__4555,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_45560',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__45561] :
( c_24__type__45560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__45561)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__45561,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_4566',axiom,
! [Vvar__4567] :
( c_24__type__4566___24t(Vvar__4567)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__4567,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45906',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__45907] :
( c_24__type__45906___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__45907)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__45907,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_46252',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__46253] :
( c_24__type__46252___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__46253)
<=> ! [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__46253,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_46598',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__46599] :
( c_24__type__46598___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__46599)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__46599,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_4663',axiom,
! [Vvar__4664] :
( c_24__type__4663___24t(Vvar__4664)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2ebool,c_24__lam__4670___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__4664,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46944',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__46945] :
( c_24__type__46944___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__46945)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__46945,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_47290',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__47291] :
( c_24__type__47290___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__47291)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__47291,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_47613',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__47614] :
( c_24__type__47613___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__47614)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__47614,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_47959',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__47960] :
( c_24__type__47959___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__47960)
<=> ! [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__47960,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_48305',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48306] :
( c_24__type__48305___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48306)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__48306,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_48628',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__48629] :
( c_24__type__48628___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__48629)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__48629,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_48951',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48952] :
( c_24__type__48951___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48952)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__48952,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_49297',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__49298] :
( c_24__type__49297___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__49298)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__49298,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_49679',axiom,
! [Vvar__49680] :
( c_24__type__49679___24t(Vvar__49680)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__39494___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__49680,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_49996',axiom,
! [Vvar__49997] :
( c_24__type__49996___24t(Vvar__49997)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__39236___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__39236___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__39236___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__49997,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_51338',axiom,
! [Vvar__51339] :
( c_24__type__51338___24t(Vvar__51339)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__39494___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__51339,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_51586',axiom,
! [Vvar__51587] :
( c_24__type__51586___24t(Vvar__51587)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__51587,Vv__CANONICAL__0)) ) ) ).
fof('$_type_51589',axiom,
! [Vvar__51590] :
( c_24__type__51589___24t(Vvar__51590)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__51590,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_51592',axiom,
! [Vvar__51593] :
( c_24__type__51592___24t(Vvar__51593)
<=> ! [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__51593,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_51597',axiom,
! [Vvar__51598] :
( c_24__type__51597___24t(Vvar__51598)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__51598,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_51606',axiom,
! [Vvar__51607] :
( c_24__type__51606___24t(Vvar__51607)
<=> ! [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__51607,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_51611',axiom,
! [Vvar__51612] :
( c_24__type__51611___24t(Vvar__51612)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__51612,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_51826',axiom,
! [Vvar__51827] :
( c_24__type__51826___24t(Vvar__51827)
<=> ! [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__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__39227___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__39353___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__39358___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__39367___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__51827,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__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('$_type_52056',axiom,
! [Vvar__52057] :
( c_24__type__52056___24t(Vvar__52057)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__39227___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__39494___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__40140___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__52057,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_52266',axiom,
! [Vvar__52267] :
( c_24__type__52266___24t(Vvar__52267)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__39218___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__52267,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_52287',axiom,
! [Vvar__52288] :
( c_24__type__52287___24t(Vvar__52288)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__52288,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_52541',axiom,
! [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__52542] :
( c_24__type__52541___24t(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__52542)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__52542,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_52604',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__52605] :
( c_24__type__52604___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__52605)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__52605,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_52667',axiom,
! [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__52668] :
( c_24__type__52667___24t(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__52668)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__52668,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_52721',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__52722] :
( c_24__type__52721___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__52722)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__52722,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_52784',axiom,
! [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__52785] :
( c_24__type__52784___24t(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__52785)
<=> ! [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__52785,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_53097',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__53098] :
( c_24__type__53097___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__53098)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__53098,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53160',axiom,
! [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__53161] :
( c_24__type__53160___24t(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__53161)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__53161,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53223',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__53224] :
( c_24__type__53223___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__53224)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__53224,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53277',axiom,
! [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__53278] :
( c_24__type__53277___24t(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__53278)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__53278,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_53340',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__53341] :
( c_24__type__53340___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__53341)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__53341,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_53465',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53466] :
( c_24__type__53465___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53466)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__53466,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53495',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53496] :
( c_24__type__53495___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53496)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__53496,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53519',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53520] :
( c_24__type__53519___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53520)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__53520,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_53549',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53550] :
( c_24__type__53549___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53550)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__53550,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_53579',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53580] :
( c_24__type__53579___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53580)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__53580,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53603',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53604] :
( c_24__type__53603___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53604)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__53604,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_53636',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53637] :
( c_24__type__53636___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53637)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__53637,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53660',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53661] :
( c_24__type__53660___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53661)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__53661,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_53687',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53688] :
( c_24__type__53687___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__53688)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__53688,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_54086',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54087] :
( c_24__type__54086___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54087)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__54087,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_54299',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__54300] :
( c_24__type__54299___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__54300)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__54300,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_54512',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54513] :
( c_24__type__54512___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54513)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__54513,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_54707',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__54708] :
( c_24__type__54707___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__54708)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__54708,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_54920',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54921] :
( c_24__type__54920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54921)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__54921,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_55133',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__55134] :
( c_24__type__55133___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__55134)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__55134,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_55346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__55347] :
( c_24__type__55346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__55347)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__55347,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_55559',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__55560] :
( c_24__type__55559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__55560)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__55560,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_55754',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__55755] :
( c_24__type__55754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__55755)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__55755,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_55967',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__55968] :
( c_24__type__55967___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__55968)
<=> ! [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__55968,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_56162',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__56163] :
( c_24__type__56162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__56163)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__56163,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_56462',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56463] :
( c_24__type__56462___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56463)
<=> ! [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__56463,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_56512',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56513] :
( c_24__type__56512___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56513)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__56513,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_56562',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56563] :
( c_24__type__56562___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56563)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__56563,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_56604',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56605] :
( c_24__type__56604___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56605)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__56605,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_56654',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56655] :
( c_24__type__56654___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56655)
<=> ! [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__56655,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_56730',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56731] :
( c_24__type__56730___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56731)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__56731,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_56839',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56840] :
( c_24__type__56839___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56840)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__56840,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_56883',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56884] :
( c_24__type__56883___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56884)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__56884,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_56919',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56920] :
( c_24__type__56919___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56920)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__56920,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_56963',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56964] :
( c_24__type__56963___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__56964)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__56964,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_56975',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56976] :
( c_24__type__56975___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56976)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__56976,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_56982',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56983] :
( c_24__type__56982___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56983)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__56983,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_57037',axiom,
! [Vvar__57038] :
( c_24__type__57037___24t(Vvar__57038)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cVFA_2eSearchTree_2etree___24t(Vv__CANONICAL__0,happ(Vvar__57038,Vv__CANONICAL__0)) ) ) ).
fof('$_type_57049',axiom,
! [Vvar__57050] :
( c_24__type__57049___24t(Vvar__57050)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cVFA_2eSearchTree_2etree___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cVFA_2eSearchTree_2ekey___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cVFA_2eSearchTree_2etree___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> cVFA_2eSearchTree_2etree___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(Vvar__57050,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_57188',axiom,
! [Vvar__57189] :
( c_24__type__57188___24t(Vvar__57189)
<=> ! [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__57189,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_57230',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__57231] :
( c_24__type__57230___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__57231)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__57231,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_57277',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__57278] :
( c_24__type__57277___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__57278)
<=> ! [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__57278,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_58129',axiom,
! [Vvar__58130] :
( c_24__type__58129___24t(Vvar__58130)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__58130,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_58134',axiom,
! [Vvar__58135] :
( c_24__type__58134___24t(Vvar__58135)
<=> ! [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__58135,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_58151',axiom,
! [Vvar__58152] :
( c_24__type__58151___24t(Vvar__58152)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__58153___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eStrings_2eString_2eEmptyString))
=> ! [Vv__CANONICAL__2] :
( c_24__type__58161___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__58152,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_58153',axiom,
! [Vvar__58154] :
( c_24__type__58153___24t(Vvar__58154)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__58154,Vv__CANONICAL__0)) ) ) ).
fof('$_type_58161',axiom,
! [Vv__CANONICAL__0,Vvar__58162] :
( c_24__type__58161___24t(Vv__CANONICAL__0,Vvar__58162)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__2))
=> t(happ(happ(happ(Vvar__58162,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,cCoq_2eStrings_2eString_2eString___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_type_58790',axiom,
! [Vvar__58791] :
( c_24__type__58790___24t(Vvar__58791)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__58792___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__58793___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__58791,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_58816',axiom,
! [Vvar__58817] :
( c_24__type__58816___24t(Vvar__58817)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eBool_2eBool_2ereflect___24t(c_24__prop__58818___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eStrings_2eString_2eeqb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__58817,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_58842',axiom,
! [Vvar__58843] :
( c_24__type__58842___24t(Vvar__58843)
<=> ! [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__58849___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__58843,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_58849',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__58850] :
( c_24__type__58849___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__58850)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__58850,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_58889',axiom,
! [Vvar__58890] :
( c_24__type__58889___24t(Vvar__58890)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__58890,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_58970',axiom,
! [Vvar__58971] :
( c_24__type__58970___24t(Vvar__58971)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__39494___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__5)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(happ(happ(Vvar__58971,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_59434',axiom,
! [Vvar__59435] :
( c_24__type__59434___24t(Vvar__59435)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__4288___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ! [Vv__CANONICAL__2] :
( c_24__type__59442___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__3)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__3))
=> t(happ(happ(happ(happ(Vvar__59435,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ) ).
fof('$_type_59442',axiom,
! [Vv__CANONICAL__0,Vvar__59443] :
( c_24__type__59442___24t(Vv__CANONICAL__0,Vvar__59443)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__59443,Vv__CANONICAL__1),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(Vv__CANONICAL__1))) ) ) ) ) ).
fof('$_type_59662',axiom,
! [Vvar__59663] :
( c_24__type__59662___24t(Vvar__59663)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__59664___24a1(Vv__CANONICAL__0),c_24__prop__59665___24a1(Vv__CANONICAL__0),happ(Vvar__59663,Vv__CANONICAL__0)) ) ) ).
fof('$_type_59708',axiom,
! [Vvar__59709] :
( c_24__type__59708___24t(Vvar__59709)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__39218___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__39227___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__59709,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_59760',axiom,
! [Vvar__59761] :
( c_24__type__59760___24t(Vvar__59761)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___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__59761,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_59767',axiom,
! [Vvar__59768] :
( c_24__type__59767___24t(Vvar__59768)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__59768,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_59771',axiom,
! [Vvar__59772] :
( c_24__type__59771___24t(Vvar__59772)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__59772,Vv__CANONICAL__0)) ) ) ).
fof('$_type_59781',axiom,
! [Vvar__59782] :
( c_24__type__59781___24t(Vvar__59782)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2ebool,c_24__lam__59788___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__59782,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_59794',axiom,
! [Vvar__59795] :
( c_24__type__59794___24t(Vvar__59795)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__59795,Vv__CANONICAL__0)) ) ) ).
fof('$_type_60391',axiom,
! [Vvar__60392] :
( c_24__type__60391___24t(Vvar__60392)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__60392,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_60742',axiom,
! [Vvar__60743] :
( c_24__type__60742___24t(Vvar__60743)
<=> ! [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__60743,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_60915',axiom,
! [Vvar__60916] :
( c_24__type__60915___24t(Vvar__60916)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__60917___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__60918___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__60916,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_60982',axiom,
! [Vvar__60983] :
( c_24__type__60982___24t(Vvar__60983)
<=> ! [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__60983,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_60992',axiom,
! [Vvar__60993] :
( c_24__type__60992___24t(Vvar__60993)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__60993,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_61030',axiom,
! [Vvar__61031] :
( c_24__type__61030___24t(Vvar__61031)
<=> ! [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__61031,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_61058',axiom,
! [Vvar__61059] :
( c_24__type__61058___24t(Vvar__61059)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__61059,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_61096',axiom,
! [Vvar__61097] :
( c_24__type__61096___24t(Vvar__61097)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(happ(happ(Vvar__61097,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_61124',axiom,
! [Vvar__61125] :
( c_24__type__61124___24t(Vvar__61125)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(happ(Vvar__61125,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_61243',axiom,
! [Vvar__61244] :
( c_24__type__61243___24t(Vvar__61244)
<=> ! [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__61244,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_61245',axiom,
! [Vvar__61246] :
( c_24__type__61245___24t(Vvar__61246)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__61246,Vv__CANONICAL__0)) ) ) ).
fof('$_type_61362',axiom,
! [Vvar__61363] :
( c_24__type__61362___24t(Vvar__61363)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__61363,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_61411',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__61412] :
( c_24__type__61411___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__61412)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__61412,Vv__CANONICAL__3)) ) ) ).
fof('$_type_61432',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__61433] :
( c_24__type__61432___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__61433)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__61433,Vv__CANONICAL__3)) ) ) ).
fof('$_type_61437',axiom,
! [Vvar__61438] :
( c_24__type__61437___24t(Vvar__61438)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__61438,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_61439',axiom,
! [Vvar__61440] :
( c_24__type__61439___24t(Vvar__61440)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__61440,Vv__CANONICAL__0)) ) ) ).
fof('$_type_61503',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__61504] :
( c_24__type__61503___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__61504)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__61504,Vv__CANONICAL__6)) ) ) ).
fof('$_type_61506',axiom,
! [Vv__CANONICAL__0,Vvar__61507] :
( c_24__type__61506___24t(Vv__CANONICAL__0,Vvar__61507)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__61507,Vv__CANONICAL__1)) ) ) ).
fof('$_type_61508',axiom,
! [Vvar__61509] :
( c_24__type__61508___24t(Vvar__61509)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__61509,Vv__CANONICAL__0)) ) ) ).
fof('$_type_61514',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__61515] :
( c_24__type__61514___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__61515)
<=> ( Vv__CANONICAL__1 = Vv__CANONICAL__1
=> cProp___24t(Vvar__61515) ) ) ).
fof('$_type_6158',axiom,
! [Vvar__6159] :
( c_24__type__6158___24t(Vvar__6159)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__6159,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6165',axiom,
! [Vvar__6166] :
( c_24__type__6165___24t(Vvar__6166)
<=> ! [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__6166,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6169',axiom,
! [Vvar__6170] :
( c_24__type__6169___24t(Vvar__6170)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__6170,Vv__CANONICAL__0)) ) ) ).
fof('$_type_61884',axiom,
! [Vvar__61885] :
( c_24__type__61884___24t(Vvar__61885)
<=> ! [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__61885,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_61887',axiom,
! [Vvar__61888] :
( c_24__type__61887___24t(Vvar__61888)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__61888,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_61892',axiom,
! [Vvar__61893] :
( c_24__type__61892___24t(Vvar__61893)
<=> ! [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__61893,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_61901',axiom,
! [Vvar__61902] :
( c_24__type__61901___24t(Vvar__61902)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__61902,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_61924',axiom,
! [Vvar__61925] :
( c_24__type__61924___24t(Vvar__61925)
<=> ! [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__61925,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_6193',axiom,
! [Vvar__6194] :
( c_24__type__6193___24t(Vvar__6194)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(happ(Vvar__6194,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_61935',axiom,
! [Vvar__61936] :
( c_24__type__61935___24t(Vvar__61936)
<=> ! [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__61936,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_61955',axiom,
! [Vvar__61956] :
( c_24__type__61955___24t(Vvar__61956)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__61956,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6196',axiom,
! [Vvar__6197] :
( c_24__type__6196___24t(Vvar__6197)
<=> ! [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__6197,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_62151',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__62152] :
( c_24__type__62151___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__62152)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__62152,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_62244',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__62245] :
( c_24__type__62244___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__62245)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__62245,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_62337',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__62338] :
( c_24__type__62337___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__62338)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__62338,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_62419',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__62420] :
( c_24__type__62419___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__62420)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__62420,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_62512',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__62513] :
( c_24__type__62512___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__62513)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__62513,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_62594',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__62595] :
( c_24__type__62594___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__62595)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__62595,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_62687',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__62688] :
( c_24__type__62687___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__62688)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__62688,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_62858',axiom,
! [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__62859] :
( c_24__type__62858___24t(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__62859)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__62859,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_62921',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__62922] :
( c_24__type__62921___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__62922)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__62922,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_62984',axiom,
! [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__62985] :
( c_24__type__62984___24t(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__62985)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__62985,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_63038',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__63039] :
( c_24__type__63038___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__63039)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__63039,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_63101',axiom,
! [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__63102] :
( c_24__type__63101___24t(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__63102)
<=> ! [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__63102,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_63208',axiom,
! [Vvar__63209] :
( c_24__type__63208___24t(Vvar__63209)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__63209,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_63248',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__63249] :
( c_24__type__63248___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__63249)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__63249,Vv__CANONICAL__3)) ) ) ).
fof('$_type_63272',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__63273] :
( c_24__type__63272___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__63273)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__63273,Vv__CANONICAL__3)) ) ) ).
fof('$_type_63295',axiom,
! [Vvar__63296] :
( c_24__type__63295___24t(Vvar__63296)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__59794___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__59794___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__63296,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_63546',axiom,
! [Vvar__63547] :
( c_24__type__63546___24t(Vvar__63547)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__63547,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_63548',axiom,
! [Vvar__63549] :
( c_24__type__63548___24t(Vvar__63549)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__63549,Vv__CANONICAL__0)) ) ) ).
fof('$_type_63609',axiom,
! [Vvar__63610] :
( c_24__type__63609___24t(Vvar__63610)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__63610,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_63643',axiom,
! [Vvar__63644] :
( c_24__type__63643___24t(Vvar__63644)
<=> ! [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__63644,Vv__CANONICAL__0)) ) ) ).
fof('$_type_63713',axiom,
! [Vvar__63714] :
( c_24__type__63713___24t(Vvar__63714)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__39236___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__39236___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__39236___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__63714,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_63892',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__63893] :
( c_24__type__63892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__63893)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__63893,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_63931',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__63932] :
( c_24__type__63931___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__63932)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__63932,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_63970',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__63971] :
( c_24__type__63970___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__63971)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__63971,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_64023',axiom,
! [Vvar__64024] :
( c_24__type__64023___24t(Vvar__64024)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__39236___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__64024,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_64046',axiom,
! [Vvar__64047] :
( c_24__type__64046___24t(Vvar__64047)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__39236___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__64056___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__64047,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_64056',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__64057] :
( c_24__type__64056___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__64057)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__64057,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_64065',axiom,
! [Vvar__64066] :
( c_24__type__64065___24t(Vvar__64066)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4496___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__64066,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_64082',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__64083] :
( c_24__type__64082___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__64083)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__64083,Vv__CANONICAL__2)) ) ) ).
fof('$_type_64086',axiom,
! [Vvar__64087] :
( c_24__type__64086___24t(Vvar__64087)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__61506___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__64087,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64104',axiom,
! [Vvar__64105] :
( c_24__type__64104___24t(Vvar__64105)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__61506___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__64105,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_64161',axiom,
! [Vvar__64162] :
( c_24__type__64161___24t(Vvar__64162)
<=> ! [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__64162,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_64637',axiom,
! [Vvar__64638] :
( c_24__type__64637___24t(Vvar__64638)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__4496___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__64642___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__64638,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_64642',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__64643] :
( c_24__type__64642___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__64643)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__64643,Vv__CANONICAL__2)) ) ) ).
fof('$_type_64648',axiom,
! [Vvar__64649] :
( c_24__type__64648___24t(Vvar__64649)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__39236___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__64649,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64701',axiom,
! [Vv__CANONICAL__0,Vvar__64702] :
( c_24__type__64701___24t(Vv__CANONICAL__0,Vvar__64702)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__64702,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_64711',axiom,
! [Vvar__64712] :
( c_24__type__64711___24t(Vvar__64712)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__64712,Vv__CANONICAL__0)) ) ) ).
fof('$_type_64727',axiom,
! [Vvar__64728] :
( c_24__type__64727___24t(Vvar__64728)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__64728,Vv__CANONICAL__0)) ) ) ).
fof('$_type_64768',axiom,
! [Vvar__64769] :
( c_24__type__64768___24t(Vvar__64769)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__64769,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64775',axiom,
! [Vvar__64776] :
( c_24__type__64775___24t(Vvar__64776)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__64776,Vv__CANONICAL__0)) ) ) ).
fof('$_type_64779',axiom,
! [Vvar__64780] :
( c_24__type__64779___24t(Vvar__64780)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(Vvar__64780,Vv__CANONICAL__0)) ) ) ).
fof('$_type_64787',axiom,
! [Vvar__64788] :
( c_24__type__64787___24t(Vvar__64788)
<=> ! [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__64788,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64806',axiom,
! [Vvar__64807] :
( c_24__type__64806___24t(Vvar__64807)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__64807,Vv__CANONICAL__0)) ) ) ).
fof('$_type_64809',axiom,
! [Vvar__64810] :
( c_24__type__64809___24t(Vvar__64810)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__64810,Vv__CANONICAL__0)) ) ) ).
fof('$_type_64812',axiom,
! [Vvar__64813] :
( c_24__type__64812___24t(Vvar__64813)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__64813,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6675',axiom,
! [Vvar__6676] :
( c_24__type__6675___24t(Vvar__6676)
<=> ! [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__6677___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__6678___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__6676,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6692',axiom,
! [Vvar__6693] :
( c_24__type__6692___24t(Vvar__6693)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__6693,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6709',axiom,
! [Vvar__6710] :
( c_24__type__6709___24t(Vvar__6710)
<=> ! [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__6710,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6728',axiom,
! [Vvar__6729] :
( c_24__type__6728___24t(Vvar__6729)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__6729,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6761',axiom,
! [Vvar__6762] :
( c_24__type__6761___24t(Vvar__6762)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> cCoq_2eStrings_2eAscii_2eascii___24t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__6762,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_6802',axiom,
! [Vvar__6803] :
( c_24__type__6802___24t(Vvar__6803)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__6804___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6842___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__6803,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6804',axiom,
! [Vvar__6805] :
( c_24__type__6804___24t(Vvar__6805)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__6805,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6842',axiom,
! [Vv__CANONICAL__0,Vvar__6843] :
( c_24__type__6842___24t(Vv__CANONICAL__0,Vvar__6843)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__8)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__6843,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),happ(Vv__CANONICAL__0,cCoq_2eStrings_2eAscii_2eAscii___24a8(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8))) ) ) ) ) ) ) ) ) ) ).
fof('$_type_9',axiom,
! [Vvar__10] :
( c_24__type__9___24t(Vvar__10)
<=> ! [Vv__CANONICAL__0] :
( cVFA_2eExtract_2eint___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cVFA_2eExtract_2eint___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__10,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_typeof_Coq.Arith.Between.in_int',axiom,
c_24__type__61437___24t(cCoq_2eArith_2eBetween_2ein__int) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__129___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.Factorial.fact',axiom,
c_24__type__3247___24t(cCoq_2eArith_2eFactorial_2efact) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.Even',axiom,
c_24__type__4236___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eEven) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.clearbit',axiom,
c_24__type__4016___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eclearbit) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__129___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__61439___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.ReflectF',axiom,
c_24__type__37239___24t(cCoq_2eBool_2eBool_2eReflectF) ).
fof('$_typeof_Coq.Bool.Bool.ReflectT',axiom,
c_24__type__37236___24t(cCoq_2eBool_2eBool_2eReflectT) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__4297___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__37221___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Sumbool.sumbool_not',axiom,
c_24__type__4108___24t(cCoq_2eBool_2eSumbool_2esumbool__not) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__59794___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
c_24__type__61245___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
c_24__type__61243___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__4267___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__61030___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
c_24__type__61243___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.add',axiom,
c_24__type__4264___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd) ).
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('$_typeof_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
c_24__type__61243___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__61058___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.node',axiom,
c_24__type__61096___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.remove',axiom,
c_24__type__4264___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.singleton',axiom,
c_24__type__64779___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esingleton) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.union',axiom,
c_24__type__61124___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__4318___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__4009___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__3247___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__4007___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__4297___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__38233___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_typeof_Coq.Init.Datatypes.bool',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_typeof_Coq.Init.Datatypes.bool_rec',axiom,
c_24__type__38131___24t(cCoq_2eInit_2eDatatypes_2ebool__rec) ).
fof('$_typeof_Coq.Init.Datatypes.comparison',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2ecomparison) ).
fof('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__3274___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__38174___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__4316___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__3255___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.list_rec',axiom,
c_24__type__3299___24t(cCoq_2eInit_2eDatatypes_2elist__rec) ).
fof('$_typeof_Coq.Init.Datatypes.list_rect',axiom,
c_24__type__3299___24t(cCoq_2eInit_2eDatatypes_2elist__rect) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rec',axiom,
c_24__type__3983___24t(cCoq_2eInit_2eDatatypes_2enat__rec) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__38136___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__3269___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__3255___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__4297___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__38162___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__38146___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__38186___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
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.Nat.add',axiom,
c_24__type__4016___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__126___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div',axiom,
c_24__type__4016___24t(cCoq_2eInit_2eNat_2ediv) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__4435___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__59794___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.gcd',axiom,
c_24__type__4016___24t(cCoq_2eInit_2eNat_2egcd) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__4435___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__4016___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__4016___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.odd',axiom,
c_24__type__59794___24t(cCoq_2eInit_2eNat_2eodd) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__4016___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__3247___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.shiftl',axiom,
c_24__type__4016___24t(cCoq_2eInit_2eNat_2eshiftl) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__4016___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__4435___24t(cCoq_2eInit_2eNat_2etestbit) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__129___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__129___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__129___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__64065___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__64104___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__58129___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__58134___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__134___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__139___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__4493___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__64086___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__3407___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
c_24__type__4536___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__4566___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__64648___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__3326___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.count_occ',axiom,
c_24__type__3392___24t(cCoq_2eLists_2eList_2ecount__occ) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__42480___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.hd_error',axiom,
c_24__type__41592___24t(cCoq_2eLists_2eList_2ehd__error) ).
fof('$_typeof_Coq.Lists.List.incl',axiom,
c_24__type__42511___24t(cCoq_2eLists_2eList_2eincl) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__63208___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__42452___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nth_error',axiom,
c_24__type__4426___24t(cCoq_2eLists_2eList_2enth__error) ).
fof('$_typeof_Coq.Lists.List.remove',axiom,
c_24__type__41631___24t(cCoq_2eLists_2eList_2eremove) ).
fof('$_typeof_Coq.Lists.ListDec.In_dec',axiom,
c_24__type__109___24t(cCoq_2eLists_2eListDec_2eIn__dec) ).
fof('$_typeof_Coq.Lists.SetoidList.equivlistA',axiom,
c_24__type__64023___24t(cCoq_2eLists_2eSetoidList_2eequivlistA) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__64046___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__4011___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq',axiom,
c_24__type__61508___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq) ).
fof('$_typeof_Coq.Logic.FinFun.EqDec',axiom,
c_24__type__3255___24t(cCoq_2eLogic_2eFinFun_2eEqDec) ).
fof('$_typeof_Coq.NArith.BinNat.N.clearbit',axiom,
c_24__type__6165___24t(cCoq_2eNArith_2eBinNat_2eN_2eclearbit) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__3505___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.ge',axiom,
c_24__type__3505___24t(cCoq_2eNArith_2eBinNat_2eN_2ege) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__3505___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__3505___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__6165___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
c_24__type__3502___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div',axiom,
c_24__type__6165___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__6158___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__60742___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__64711___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.gcd',axiom,
c_24__type__6165___24t(cCoq_2eNArith_2eBinNatDef_2eN_2egcd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.leb',axiom,
c_24__type__60742___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eleb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.log2',axiom,
c_24__type__6158___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elog2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.modulo',axiom,
c_24__type__6165___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__6165___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.odd',axiom,
c_24__type__64711___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eodd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pow',axiom,
c_24__type__6165___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epow) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__6158___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sub',axiom,
c_24__type__6165___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esub) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__6158___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
c_24__type__6158___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__60742___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__64727___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__63295___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.N_rec',axiom,
c_24__type__37164___24t(cCoq_2eNumbers_2eBinNums_2eN__rec) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__37154___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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.Z_rec',axiom,
c_24__type__4286___24t(cCoq_2eNumbers_2eBinNums_2eZ__rec) ).
fof('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__3970___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__3970___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_typeof_Coq.Numbers.BinNums.positive',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_typeof_Coq.Numbers.BinNums.positive_rec',axiom,
c_24__type__37140___24t(cCoq_2eNumbers_2eBinNums_2epositive__rec) ).
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__4269___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__4269___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.ge',axiom,
c_24__type__6196___24t(cCoq_2ePArith_2eBinPos_2ePos_2ege) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.gt',axiom,
c_24__type__6196___24t(cCoq_2ePArith_2eBinPos_2ePos_2egt) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__6196___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__6196___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__60982___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__60992___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare_cont',axiom,
c_24__type__6193___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__60391___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.leb',axiom,
c_24__type__60391___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eleb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__60982___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
c_24__type__64775___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__64775___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred',axiom,
c_24__type__4269___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
c_24__type__4269___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__60982___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__4269___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
c_24__type__64768___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
c_24__type__4241___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qcompare',axiom,
c_24__type__4460___24t(cCoq_2eQArith_2eQArith__base_2eQcompare) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__4453___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq',axiom,
c_24__type__4456___24t(cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq_bool',axiom,
c_24__type__4463___24t(cCoq_2eQArith_2eQArith__base_2eQeq__bool) ).
fof('$_typeof_Coq.QArith.QArith_base.Qle',axiom,
c_24__type__4456___24t(cCoq_2eQArith_2eQArith__base_2eQle) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__63546___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__4448___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.Reals.RIneq.Req_EM_T',axiom,
c_24__type__43926___24t(cCoq_2eReals_2eRIneq_2eReq__EM__T) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_dec',axiom,
c_24__type__43920___24t(cCoq_2eReals_2eRIneq_2eRle__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__43923___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.nonzero',axiom,
c_24__type__43940___24t(cCoq_2eReals_2eRIneq_2enonzero) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.R_Ifp.frac_part',axiom,
c_24__type__43923___24t(cCoq_2eReals_2eR__Ifp_2efrac__part) ).
fof('$_typeof_Coq.Reals.Raxioms.INR',axiom,
c_24__type__43954___24t(cCoq_2eReals_2eRaxioms_2eINR) ).
fof('$_typeof_Coq.Reals.Raxioms.total_order_T',axiom,
c_24__type__4468___24t(cCoq_2eReals_2eRaxioms_2etotal__order__T) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rabs',axiom,
c_24__type__43923___24t(cCoq_2eReals_2eRbasic__fun_2eRabs) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rcase_abs',axiom,
c_24__type__43969___24t(cCoq_2eReals_2eRbasic__fun_2eRcase__abs) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__4033___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__43967___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__4472___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__4472___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__43923___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__4472___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__4472___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__43967___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__43967___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__43923___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__43967___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__63548___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__63609___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rfunctions.intP',axiom,
c_24__type__63643___24t(cCoq_2eReals_2eRfunctions_2eintP) ).
fof('$_typeof_Coq.Reals.Rfunctions.powerRZ',axiom,
c_24__type__4038___24t(cCoq_2eReals_2eRfunctions_2epowerRZ) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__4043___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__3255___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__57188___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
c_24__type__6761___24t(cCoq_2eStrings_2eAscii_2eAscii) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.Ascii.ascii_rec',axiom,
c_24__type__6802___24t(cCoq_2eStrings_2eAscii_2eascii__rec) ).
fof('$_typeof_Coq.Strings.Ascii.eqb',axiom,
c_24__type__37109___24t(cCoq_2eStrings_2eAscii_2eeqb) ).
fof('$_typeof_Coq.Strings.Ascii.eqb_spec',axiom,
c_24__type__37112___24t(cCoq_2eStrings_2eAscii_2eeqb__spec) ).
fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).
fof('$_typeof_Coq.Strings.String.String',axiom,
c_24__type__4055___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.eqb',axiom,
c_24__type__4095___24t(cCoq_2eStrings_2eString_2eeqb) ).
fof('$_typeof_Coq.Strings.String.eqb_spec',axiom,
c_24__type__58816___24t(cCoq_2eStrings_2eString_2eeqb__spec) ).
fof('$_typeof_Coq.Strings.String.length',axiom,
c_24__type__3436___24t(cCoq_2eStrings_2eString_2elength) ).
fof('$_typeof_Coq.Strings.String.prefix',axiom,
c_24__type__4095___24t(cCoq_2eStrings_2eString_2eprefix) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Strings.String.string_rec',axiom,
c_24__type__58151___24t(cCoq_2eStrings_2eString_2estring__rec) ).
fof('$_typeof_Coq.Strings.String.substring',axiom,
c_24__type__3456___24t(cCoq_2eStrings_2eString_2esubstring) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq_dec',axiom,
c_24__type__60915___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq__dec) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__129___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq_dec',axiom,
c_24__type__4231___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq__dec) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__129___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
c_24__type__6196___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__6196___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec',axiom,
c_24__type__6675___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
c_24__type__6196___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
c_24__type__6196___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq_dec',axiom,
c_24__type__6675___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq__dec) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__6196___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
c_24__type__64787___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.eq_dec',axiom,
c_24__type__58790___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq__dec) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
c_24__type__64787___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq_dec',axiom,
c_24__type__3929___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq__dec) ).
fof('$_typeof_Coq.Vectors.Fin.eqb',axiom,
c_24__type__41272___24t(cCoq_2eVectors_2eFin_2eeqb) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__3985___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__58889___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.Vectors.VectorEq.eqb',axiom,
c_24__type__58970___24t(cCoq_2eVectors_2eVectorEq_2eeqb) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.clearbit',axiom,
c_24__type__6692___24t(cCoq_2eZArith_2eBinInt_2eZ_2eclearbit) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__6728___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__6728___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__6728___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__6728___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__6728___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__6728___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__3507___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__6692___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__6709___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__6692___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.eqb',axiom,
c_24__type__4120___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__59771___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gcd',axiom,
c_24__type__6692___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__4120___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.log2',axiom,
c_24__type__3507___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.ltb',axiom,
c_24__type__4120___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__6692___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__6692___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__59771___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__64812___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__64809___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__3507___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__6692___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__3507___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quot',axiom,
c_24__type__6692___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equot) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__61362___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.rem',axiom,
c_24__type__6692___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2erem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sgn',axiom,
c_24__type__3507___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__6692___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__3507___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.testbit',axiom,
c_24__type__4120___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
c_24__type__64806___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).
fof('$_typeof_Coq.ZArith.Wf_Z.natlike_rec',axiom,
c_24__type__59434___24t(cCoq_2eZArith_2eWf__Z_2enatlike__rec) ).
fof('$_typeof_Coq.ZArith.ZArith_dec.Z_noteq_dec',axiom,
c_24__type__4115___24t(cCoq_2eZArith_2eZArith__dec_2eZ__noteq__dec) ).
fof('$_typeof_Coq.ZArith.ZArith_dec.Z_notzerop',axiom,
c_24__type__59662___24t(cCoq_2eZArith_2eZArith__dec_2eZ__notzerop) ).
fof('$_typeof_Coq.ZArith.ZArith_dec.Z_zerop',axiom,
c_24__type__4110___24t(cCoq_2eZArith_2eZArith__dec_2eZ__zerop) ).
fof('$_typeof_Coq.ZArith.Zbool.Z_eq_bool',axiom,
c_24__type__4663___24t(cCoq_2eZArith_2eZbool_2eZ__eq__bool) ).
fof('$_typeof_Coq.ZArith.Zbool.Z_noteq_bool',axiom,
c_24__type__59781___24t(cCoq_2eZArith_2eZbool_2eZ__noteq__bool) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__4120___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zdiv.Remainder',axiom,
c_24__type__6728___24t(cCoq_2eZArith_2eZdiv_2eRemainder) ).
fof('$_typeof_Coq.ZArith.Zdiv.Remainder_alt',axiom,
c_24__type__6728___24t(cCoq_2eZArith_2eZdiv_2eRemainder__alt) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__42648___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__42648___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__37116___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Znat.neq',axiom,
c_24__type__129___24t(cCoq_2eZArith_2eZnat_2eneq) ).
fof('$_typeof_Coq.ZArith.Znumtheory.rel_prime',axiom,
c_24__type__6728___24t(cCoq_2eZArith_2eZnumtheory_2erel__prime) ).
fof('$_typeof_Coq.micromega.Env.jump',axiom,
c_24__type__38242___24t(cCoq_2emicromega_2eEnv_2ejump) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__3255___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__38477___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__38464___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__38469___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__3255___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.RMicromega.Reval_op2',axiom,
c_24__type__43947___24t(cCoq_2emicromega_2eRMicromega_2eReval__op2) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__44009___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__3255___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__3255___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpNEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__3255___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__3255___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.cneqb',axiom,
c_24__type__49679___24t(cCoq_2emicromega_2eRingMicromega_2ecneqb) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
c_24__type__49996___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op2',axiom,
c_24__type__63713___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op2) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__64161___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__38146___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.Tauto.eval_f',axiom,
c_24__type__64637___24t(cCoq_2emicromega_2eTauto_2eeval__f) ).
fof('$_typeof_Coq.micromega.Tauto.eval_tt',axiom,
c_24__type__58842___24t(cCoq_2emicromega_2eTauto_2eeval__tt) ).
fof('$_typeof_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
c_24__type__59708___24t(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.eqb',axiom,
c_24__type__60391___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb) ).
fof('$_typeof_Coq.micromega.ZMicromega.Zeval_op1',axiom,
c_24__type__59767___24t(cCoq_2emicromega_2eZMicromega_2eZeval__op1) ).
fof('$_typeof_Coq.micromega.ZMicromega.Zeval_op2',axiom,
c_24__type__59760___24t(cCoq_2emicromega_2eZMicromega_2eZeval__op2) ).
fof('$_typeof_Coq.micromega.ZMicromega.isZ0',axiom,
c_24__type__59771___24t(cCoq_2emicromega_2eZMicromega_2eisZ0) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__61887___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__61892___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__61884___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__61901___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__61892___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__61901___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__61892___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__3255___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__39863___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__39770___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__61955___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__61935___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__3255___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__61924___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__61935___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__41577___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__41577___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__59708___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
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__51586___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__51586___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__51592___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__51597___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__51589___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__51826___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__51597___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__51606___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__51611___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__51597___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__3255___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__51338___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__3255___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__52056___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__52287___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__52266___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Redblack.Black',axiom,
cRedblack_2ecolor___24t(cRedblack_2eBlack) ).
fof('$_typeof_Redblack.Red',axiom,
cRedblack_2ecolor___24t(cRedblack_2eRed) ).
fof('$_typeof_Redblack.TREES.E',axiom,
cRedblack_2eTREES_2etree___24t(cRedblack_2eTREES_2eE) ).
fof('$_typeof_Redblack.TREES.T',axiom,
c_24__type__3002___24t(cRedblack_2eTREES_2eT) ).
fof('$_typeof_Redblack.TREES.balance',axiom,
c_24__type__3002___24t(cRedblack_2eTREES_2ebalance) ).
fof('$_typeof_Redblack.TREES.empty_tree',axiom,
cRedblack_2eTREES_2etree___24t(cRedblack_2eTREES_2eempty__tree) ).
fof('$_typeof_Redblack.TREES.ins',axiom,
c_24__type__144___24t(cRedblack_2eTREES_2eins) ).
fof('$_typeof_Redblack.TREES.insert',axiom,
c_24__type__144___24t(cRedblack_2eTREES_2einsert) ).
fof('$_typeof_Redblack.TREES.lookup',axiom,
c_24__type__3031___24t(cRedblack_2eTREES_2elookup) ).
fof('$_typeof_Redblack.TREES.makeBlack',axiom,
c_24__type__190___24t(cRedblack_2eTREES_2emakeBlack) ).
fof('$_typeof_Redblack.TREES.tree',axiom,
cType___24t(cRedblack_2eTREES_2etree) ).
fof('$_typeof_Redblack.TREES.tree_rec',axiom,
c_24__type__3074___24t(cRedblack_2eTREES_2etree__rec) ).
fof('$_typeof_Redblack.TREES.tree_rect',axiom,
c_24__type__3074___24t(cRedblack_2eTREES_2etree__rect) ).
fof('$_typeof_Redblack.color',axiom,
cType___24t(cRedblack_2ecolor) ).
fof('$_typeof_Redblack.color_rec',axiom,
c_24__type__3214___24t(cRedblack_2ecolor__rec) ).
fof('$_typeof_Redblack.color_rect',axiom,
c_24__type__3214___24t(cRedblack_2ecolor__rect) ).
fof('$_typeof_Redblack.key',axiom,
cType___24t(cRedblack_2ekey) ).
fof('$_typeof_V',axiom,
cType___24t(cV) ).
fof('$_typeof_VFA.Extract.IntMaps.total_map',axiom,
c_24__type__3255___24t(cVFA_2eExtract_2eIntMaps_2etotal__map) ).
fof('$_typeof_VFA.Extract.ltb',axiom,
c_24__type__9___24t(cVFA_2eExtract_2eltb) ).
fof('$_typeof_VFA.Maps.t_empty',axiom,
c_24__type__42614___24t(cVFA_2eMaps_2et__empty) ).
fof('$_typeof_VFA.Maps.t_update',axiom,
c_24__type__42626___24t(cVFA_2eMaps_2et__update) ).
fof('$_typeof_VFA.Maps.total_map',axiom,
c_24__type__3255___24t(cVFA_2eMaps_2etotal__map) ).
fof('$_typeof_VFA.SearchTree.E',axiom,
c_24__type__57037___24t(cVFA_2eSearchTree_2eE) ).
fof('$_typeof_VFA.SearchTree.T',axiom,
c_24__type__57049___24t(cVFA_2eSearchTree_2eT) ).
fof('$_typeof_VFA.SearchTree.key',axiom,
cType___24t(cVFA_2eSearchTree_2ekey) ).
fof('$_typeof_VFA.SearchTree.tree',axiom,
c_24__type__3255___24t(cVFA_2eSearchTree_2etree) ).
fof('$_typeof_default',axiom,
cV___24t(cdefault) ).
fof('Coq.Arith.Compare_dec.leb_compare',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eNat_2eleb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> cCoq_2eInit_2eNat_2ecompare___24a2(V0__n,V1__m) != cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).
fof('Coq.Arith.Compare_dec.nat_compare_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_2eInit_2eNat_2ecompare___24a2(V0__n,V1__m) != cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).
fof('Coq.Arith.Compare_dec.nat_compare_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2eNat_2ecompare___24a2(V0__n,V1__m) != cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).
fof('Coq.Arith.Compare_dec.not_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.Arith.EqNat.beq_nat_false',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eNat_2eeqb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2efalse
=> V0__n != V1__m ) ) ) ).
fof('Coq.Arith.Factorial.fact_neq_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eArith_2eFactorial_2efact___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.Factorial.lt_O_fact',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eArith_2eFactorial_2efact___24a1(V0__n)) ) ).
fof('Coq.Arith.Gt.gt_S_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Gt.gt_irrefl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V0__n) ) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Gt.gt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
=> ~ cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Le.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_or_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.Lt.le_not_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.Lt.lt_0_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)
=> cCoq_2eInit_2eDatatypes_2eO != V0__n ) ) ).
fof('Coq.Arith.Lt.lt_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Lt.lt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Lt.lt_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.Lt.nat_total_order',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.Arith.Mult.odd_even_lem',axiom,
! [V0__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__q)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V0__p),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) != cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__q) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Even_Odd_False',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ( cCoq_2eArith_2ePeanoNat_2eNat_2eEven___24a1(V0__x)
=> ( cCoq_2eArith_2ePeanoNat_2eNat_2eOdd___24a1(V0__x)
=> p(c_24False) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_NZPow.pow_0_l\'',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ( V0__a != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eNat_2epow___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__a) = cCoq_2eInit_2eDatatypes_2eO ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_NZPow.pow_eq_0',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V1__b)
=> ( cCoq_2eInit_2eNat_2epow___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2eO
=> V0__a = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_NZPow.pow_eq_0_iff',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( cCoq_2eInit_2eNat_2epow___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2eO
<=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__b,cCoq_2eInit_2eDatatypes_2eO)
| ( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V1__b)
& V0__a = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_NZPow.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_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V1__b)
=> cCoq_2eInit_2eNat_2epow___24a2(V0__a,V1__b) != cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.IsTotal.lt_total',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_lt',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
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V2__z)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V2__z)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V2__z)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Parity.Odd_0',axiom,
~ cCoq_2eArith_2ePeanoNat_2eNat_2eOdd___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
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_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_succ_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4016,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__3247,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.case_analysis',axiom,
! [V0__A] :
( c_24__type__4236___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4236,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e),V0__A)
=> ( p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n))) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(happ(V0__A,V4__n)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.clearbit_iff',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eArith_2ePeanoNat_2eNat_2eclearbit___24a2(V0__a,V1__n),V2__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> ( cCoq_2eInit_2eNat_2etestbit___24a2(V0__a,V2__m) = cCoq_2eInit_2eDatatypes_2etrue
& V1__n != V2__m ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.compare_antisym',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2ecompare___24a2(V1__m,V0__n) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2eInit_2eNat_2ecompare___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.compare_ge_iff',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2eNat_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.compare_gt_iff',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2eNat_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.compare_le_iff',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eNat_2ecompare___24a2(V0__n,V1__m) != cCoq_2eInit_2eDatatypes_2eGt
<=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.compare_lt_iff',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eNat_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
<=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.compare_ngt_iff',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2eNat_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt
<=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.compare_nlt_iff',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2eNat_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt
<=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__4235___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_dne',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ ( V0__n != V1__m )
<=> V0__n = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.eq_mul_0',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_2eDatatypes_2eO
<=> ( V0__n = cCoq_2eInit_2eDatatypes_2eO
| V1__m = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eqb_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eNat_2eeqb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> V0__n = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eqb_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2eNat_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> V0__x != 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.induction',axiom,
! [V0__A] :
( c_24__type__4236___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4236,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e),V0__A)
=> ( p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(happ(V0__A,V3__n))
=> p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n))) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(happ(V0__A,V4__n)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
& V0__n != V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ngt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
<=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2ele) ).
fof('Coq.Arith.PeanoNat.Nat.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__129,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__4236,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.leb_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eNat_2eleb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_1',axiom,
cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_1_2',axiom,
cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ).
fof('Coq.Arith.PeanoNat.Nat.lt_asymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
<=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
<=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> V0__n != V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_nge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_total',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__129,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__4236,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.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_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__4016,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__3247,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',axiom,
~ ! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_0_lt_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
<=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
<=> ? [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_mul_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ( V0__n != cCoq_2eInit_2eDatatypes_2eO
& V1__m != cCoq_2eInit_2eDatatypes_2eO )
<=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) != cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(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.nle_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.nlt_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.PeanoNat.Nat.nlt_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('Coq.Arith.PeanoNat.Nat.pow_eq_0_iff',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( cCoq_2eInit_2eNat_2epow___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2eO
<=> ( V1__b != cCoq_2eInit_2eDatatypes_2eO
& V0__a = 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.pow_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4016,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__3247,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_2epow) ).
fof('Coq.Arith.PeanoNat.Nat.pred_0',axiom,
cCoq_2eInit_2eNat_2epred___24a1(cCoq_2eInit_2eDatatypes_2eO) = 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.pred_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3247,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_2epred) ).
fof('Coq.Arith.PeanoNat.Nat.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m) != cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) = cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4016,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__3247,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2esub) ).
fof('Coq.Arith.PeanoNat.Nat.succ_add_discr',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> V1__m != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_inj',axiom,
! [V0__n1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n2)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n2)
=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_inj_wd',axiom,
! [V0__n1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n2)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n2)
<=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_inj_wd_neg',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)
<=> V0__n != V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3247,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.Arith.Plus.n_SSSSn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)))) ) ).
fof('Coq.Arith.Plus.n_SSSn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.Plus.n_SSn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.Plus.succ_plus_discr',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n)) ) ) ).
fof('Coq.Bool.Bool.absurd_eq_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( p(c_24False)
=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.Bool.Bool.andb_true_iff',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue
<=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
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.diff_true_false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('Coq.Bool.Bool.eqb_false_iff',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eBool_2eBool_2eeqb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efalse
<=> V0__a != V1__b ) ) ) ).
fof('Coq.Bool.Bool.negb_true_iff',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue
<=> V0__b = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.Bool.Bool.no_fixpoint_negb',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) != V0__b ) ).
fof('Coq.Bool.Bool.not_false_iff_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_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_iff_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.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.Zerob.zerob_false_elim',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse
=> V0__n != cCoq_2eInit_2eDatatypes_2eO ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.remove_1',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
=> ~ p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__x,V0__s))) ) ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.remove_2',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
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,V0__s))
=> p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__x,V0__s))) ) ) ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.remove_3',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)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__x,V0__s)))
=> p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,V0__s)) ) ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.remove_spec',axiom,
! [V0__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__y)
=> ! [V2__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__s)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V0__x,V2__s)))
<=> ( V0__x != V1__y
& p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__y,V2__s)) ) ) ) ) ) ).
fof('Coq.Init.Datatypes.CompOpp_iff',axiom,
! [V0__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__c)
=> ! [V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__c) = V1__c_27
<=> V0__c = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V1__c_27) ) ) ) ).
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__4303___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__4236___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.O_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Init.Peano.eq_add_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Init.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__4022___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_0_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).
fof('Coq.Init.Peano.le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Init.Peano.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.Init.Peano.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Init.Peano.n_Sn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Init.Peano.nat_double_ind',axiom,
! [V0__R] :
( c_24__type__129___24t(V0__R)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eO),V1__n)) )
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)),cCoq_2eInit_2eDatatypes_2eO)) )
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( p(happ(happ(V0__R,V3__n),V4__m))
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ).
fof('Coq.Init.Peano.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.sumbool_ind',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__4508___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ).
fof('Coq.Lists.List.app_cons_not_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__y)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) != cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__y)) ) ) ) ) ).
fof('Coq.Lists.List.in_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ).
fof('Coq.Lists.List.nil_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) != cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l) ) ) ) ).
fof('Coq.Lists.List.not_in_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)))
<=> ( V1__x != V2__a
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__61469___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__61470___24a1(V0__A)) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.imp_simp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( p(V0__A)
=> p(V1__B) )
=> ( ~ p(V0__A)
| p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
& p(V1__B) )
=> ( ~ p(V0__A)
| ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
& p(V1__B) )
=> p(c_24False) )
<=> ( p(V0__A)
=> ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_imp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
=> p(V1__B) )
=> ( p(V0__A)
& ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_not_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( ( p(V0__A)
=> p(c_24False) )
=> p(c_24False) )
<=> p(V0__A) ) ) ) ).
fof('Coq.Logic.Decidable.not_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ~ ( p(V0__A)
| p(V1__B) )
=> ( ~ p(V0__A)
& ~ p(V1__B) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
| p(V1__B) )
=> p(c_24False) )
<=> ( ( p(V0__A)
=> p(c_24False) )
& ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.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__61514___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__61514___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__114___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_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.Eqdep_dec.nu_left_inv_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
=> cCoq_2eInit_2eLogic_2eeq__ind___24a6(V0__A,V1__x,c_24__lam__4337___24a2(V0__A,V3__y),c_24__generic__case__4394,V1__x,c_24__generic__case__4403) = c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.trans_sym_eq',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
=> cCoq_2eInit_2eLogic_2eeq__ind___24a4(V0__A,V1__x,c_24__lam__4337___24a2(V0__A,V2__y),V2__y) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V2__y) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_NZPow.pow_0_l\'',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eN0
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__a) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ).
fof('Coq.NArith.BinNat.N.Private_NZPow.pow_eq_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V1__b)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eN0
=> V0__a = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_NZPow.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_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V1__b)
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_lt',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
=> ( 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.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_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_2ele___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.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_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_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.add_succ_r',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,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.add_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6165,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__6158,cCoq_2eNArith_2eBinNat_2eN_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNat_2eN_2eeq,cCoq_2eNArith_2eBinNat_2eN_2eeq)),cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('Coq.NArith.BinNat.N.case_analysis',axiom,
! [V0__A] :
( c_24__type__6169___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6169,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e),V0__A)
=> ( p(happ(V0__A,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> p(happ(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n))) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__n)
=> p(happ(V0__A,V4__n)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.clearbit_iff',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNArith_2eBinNat_2eN_2eclearbit___24a2(V0__a,V1__n),V2__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> ( cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V2__m) = cCoq_2eInit_2eDatatypes_2etrue
& V1__n != V2__m ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.compare_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('Coq.NArith.BinNat.N.compare_antisym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V1__m,V0__n) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.compare_ge_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.NArith.BinNat.N.compare_le_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) != cCoq_2eInit_2eDatatypes_2eGt
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.compare_lt_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.compare_ngt_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt
<=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.NArith.BinNat.N.compare_nlt_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt
<=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__60919___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.eq_dne',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( ~ ( V0__n != V1__m )
<=> V0__n = V1__m ) ) ) ).
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_mul_0',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_2eNumbers_2eBinNums_2eN0
<=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
| V1__m = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ).
fof('Coq.NArith.BinNat.N.eqb_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> V0__n = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.eqb_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> V0__x != V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.induction',axiom,
! [V0__A] :
( c_24__type__6169___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6169,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e),V0__A)
=> ( p(happ(V0__A,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> ( p(happ(V0__A,V3__n))
=> p(happ(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n))) ) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__n)
=> p(happ(V0__A,V4__n)) ) ) ) ) ) ).
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_neq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
<=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
& V0__n != V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_ngt',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_succ_l',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(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m)
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3505,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__6169,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_0_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) ) ).
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_asymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
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_gt_cases',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_2elt___24a2(V0__n,V1__m)
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.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.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_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_neq',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 ) ) ) ).
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_succ_r',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,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
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.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3505,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__6169,cCoq_2eNArith_2eBinNat_2eN_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,cCoq_2eNArith_2eBinNat_2eN_2eeq,c_3c_3d_3e)),cCoq_2eNArith_2eBinNat_2eN_2elt) ).
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_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = 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_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.mul_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6165,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__6158,cCoq_2eNArith_2eBinNat_2eN_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNat_2eN_2eeq,cCoq_2eNArith_2eBinNat_2eN_2eeq)),cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('Coq.NArith.BinNat.N.neq_0',axiom,
~ ! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> V0__n = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
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_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eN0
<=> ? [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
& V0__n = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.neq_0_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) ) ).
fof('Coq.NArith.BinNat.N.neq_mul_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( ( V0__n != cCoq_2eNumbers_2eBinNums_2eN0
& V1__m != cCoq_2eNumbers_2eBinNums_2eN0 )
<=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) != cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.neq_succ_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) != cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.neq_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) != V0__n ) ).
fof('Coq.NArith.BinNat.N.neq_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> V0__n != cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(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.nlt_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) ) ).
fof('Coq.NArith.BinNat.N.pow_eq_0_iff',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eN0
<=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eN0
& V0__a = 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_0',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(cCoq_2eNumbers_2eBinNums_2eN0) = 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.NArith.BinNat.N.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = V0__n ) ).
fof('Coq.NArith.BinNat.N.sub_gt',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(V1__m,V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) != cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.sub_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) ) ) ).
fof('Coq.NArith.BinNat.N.succ_0_discr',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) != cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.succ_add_discr',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> V1__m != cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.succ_inj',axiom,
! [V0__n1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n2)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__n2)
=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.NArith.BinNat.N.succ_inj_wd',axiom,
! [V0__n1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n2)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__n2)
<=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.NArith.BinNat.N.succ_inj_wd_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) != cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m)
<=> V0__n != V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6158,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNat_2eN_2eeq,cCoq_2eNArith_2eBinNat_2eN_2eeq),cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__37116___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_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.add_no_neutral',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) != V0__p ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_antisym',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V1__q,V0__p) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__q)) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_cont_Gt_not_Gt',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(cCoq_2eInit_2eDatatypes_2eGt,V0__p,V1__q) != cCoq_2eInit_2eDatatypes_2eGt
<=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,V1__q) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_cont_Lt_not_Gt',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(cCoq_2eInit_2eDatatypes_2eLt,V0__p,V1__q) != cCoq_2eInit_2eDatatypes_2eGt
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__p,V1__q) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_cont_Lt_not_Lt',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(cCoq_2eInit_2eDatatypes_2eLt,V0__p,V1__q) != cCoq_2eInit_2eDatatypes_2eLt
<=> cCoq_2ePArith_2eBinPos_2ePos_2egt___24a2(V0__p,V1__q) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
=> V0__x = V1__y ) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_ge_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_le_iff',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__q) != cCoq_2eInit_2eDatatypes_2eGt
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__p,V1__q) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_lt_iff',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__q) = cCoq_2eInit_2eDatatypes_2eLt
<=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,V1__q) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_ngt_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt
<=> ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_nlt_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt
<=> ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V0__x) = cCoq_2eInit_2eDatatypes_2eEq ) ).
fof('Coq.PArith.BinPos.Pos.eqb_eq',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V0__p,V1__q) = cCoq_2eInit_2eDatatypes_2etrue
<=> V0__p = V1__q ) ) ) ).
fof('Coq.PArith.BinPos.Pos.eqb_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> V0__x != V1__y ) ) ) ).
fof('Coq.PArith.BinPos.Pos.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.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.BinPos.Pos.lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__m,V2__p)
=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.mul_xI_mul_xO_discr',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__r)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2eNumbers_2eBinNums_2exI___24a1(V0__p),V2__r) != cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2eNumbers_2eBinNums_2exO___24a1(V1__q),V2__r) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.mul_xO_discr',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2eNumbers_2eBinNums_2exO___24a1(V0__p),V1__q) != V1__q ) ) ).
fof('Coq.PArith.BinPos.Pos.mul_xO_r',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V0__p,cCoq_2eNumbers_2eBinNums_2exO___24a1(V1__q)) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V0__p,V1__q)) ) ) ).
fof('Coq.PArith.BinPos.Pos.nlt_1_r',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,cCoq_2eNumbers_2eBinNums_2exH) ) ).
fof('Coq.PArith.BinPos.Pos.pred_double_xO_discr',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V0__p) != cCoq_2eNumbers_2eBinNums_2exO___24a1(V0__p) ) ).
fof('Coq.PArith.BinPos.Pos.succ_discr',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> V0__p != cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V0__p) ) ).
fof('Coq.PArith.BinPos.Pos.succ_not_1',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V0__p) != cCoq_2eNumbers_2eBinNums_2exH ) ).
fof('Coq.QArith.QArith_base.Q_Setoid',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('Coq.QArith.QArith_base.Qeq_bool_neq',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.QArith.QArith_base.Qge_alt',axiom,
! [V0__p] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__q)
=> ( cCoq_2eQArith_2eQArith__base_2eQle___24a2(V1__q,V0__p)
<=> cCoq_2eQArith_2eQArith__base_2eQcompare___24a2(V0__p,V1__q) != cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).
fof('Coq.QArith.QArith_base.Qle_alt',axiom,
! [V0__p] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__q)
=> ( cCoq_2eQArith_2eQArith__base_2eQle___24a2(V0__p,V1__q)
<=> cCoq_2eQArith_2eQArith__base_2eQcompare___24a2(V0__p,V1__q) != cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).
fof('Coq.QArith.Qreals.IZR_nz',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.QArith.Qreals.eqR_Qeq',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQreals_2eQ2R___24a1(V0__x) = cCoq_2eQArith_2eQreals_2eQ2R___24a1(V1__y)
=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Reals.ArithProp.minus_neq_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__i,V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__i) != cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('Coq.Reals.RIneq.INR_not_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__n != cCoq_2eInit_2eDatatypes_2eO ) ) ).
fof('Coq.Reals.RIneq.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_dec',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
| V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rge_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_not_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_irrefl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r,V0__r)) ) ).
fof('Coq.Reals.RIneq.Rgt_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_not_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_neq_0_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.Rle_antisym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1))
=> V0__r1 = V1__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_dichotomy_converse',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) )
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_irrefl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,V0__r)) ) ).
fof('Coq.Reals.RIneq.Rlt_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_diag_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_diag_uniq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_eq_contra',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_not_eq_right',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_eq_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
| V1__r2 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_integral',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
| V1__r2 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_integral_contrapositive',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_integral_contrapositive_currified',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_neq_0_reg',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_involutive',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) = V0__r ) ).
fof('Coq.Reals.RIneq.Ropp_neq_0_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.Rplus_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rplus_lt_le_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rsqr_0',axiom,
cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.RIneq.cond_nonzero',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V0__n)
=> cCoq_2eReals_2eRIneq_2enonzero___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.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.lt_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.not_0_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.not_0_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.not_1_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ).
fof('Coq.Reals.RIneq.not_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) != cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m) ) ) ) ).
fof('Coq.Reals.RIneq.pos_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n))) ) ).
fof('Coq.Reals.RIneq.tech_Rplus',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__s] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__s)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__s))
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__s) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.R_Ifp.R0_fp_O',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) != cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) != V0__r ) ) ).
fof('Coq.Reals.R_Ifp.fp_R0',axiom,
cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.R_sqr.Rsqr_gt_0_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x)))
=> V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Raxioms.R1_neq_R0',axiom,
cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Raxioms.Rlt_asym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_no_R0',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Rfunctions.INR_fact_neq_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(V0__n)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.Rfunctions.pow_nonzero',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_NOR',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__z) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.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.Strings.Ascii.eqb_neq',axiom,
! [V0__x] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V1__y)
=> ( cCoq_2eStrings_2eAscii_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> V0__x != V1__y ) ) ) ).
fof('Coq.Strings.Byte.eqb_false',axiom,
! [V0__x] :
( cCoq_2eInit_2eByte_2ebyte___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eByte_2ebyte___24t(V1__y)
=> ( cCoq_2eStrings_2eByte_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> V0__x != V1__y ) ) ) ).
fof('Coq.Strings.String.eqb_neq',axiom,
! [V0__x] :
( cCoq_2eStrings_2eString_2estring___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eStrings_2eString_2estring___24t(V1__y)
=> ( cCoq_2eStrings_2eString_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> V0__x != V1__y ) ) ) ).
fof('Coq.Strings.String.string_ind',axiom,
! [V0__P] :
( c_24__type__3427___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eStrings_2eString_2eEmptyString))
=> ( ! [V2__a] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V2__a)
=> ! [V3__s] :
( cCoq_2eStrings_2eString_2estring___24t(V3__s)
=> ( p(happ(V0__P,V3__s))
=> p(happ(V0__P,cCoq_2eStrings_2eString_2eString___24a2(V2__a,V3__s))) ) ) )
=> ! [V3__s] :
( cCoq_2eStrings_2eString_2estring___24t(V3__s)
=> p(happ(V0__P,V3__s)) ) ) ) ) ).
fof('Coq.Structures.OrderedTypeEx.N_as_OT.lt_not_eq',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 ) ) ) ).
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.Structures.OrderedTypeEx.Z_as_OT.lt_not_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> V0__x != V1__y ) ) ) ).
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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.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))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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_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
=> p(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)
=> ~ p(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_0_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
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.abs_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n))) ) ).
fof('Coq.ZArith.BinInt.Z.abs_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n)))
<=> V0__n != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
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_move_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> V1__m = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_shuffle0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6692,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__3507,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eZArith_2eBinInt_2eZ_2eeq)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('Coq.ZArith.BinInt.Z.clearbit_iff',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinInt_2eZ_2eclearbit___24a2(V0__a,V1__n),V2__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__m) = cCoq_2eInit_2eDatatypes_2etrue
& V1__n != V2__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.compare_antisym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V1__m,V0__n) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.compare_ge_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.compare_le_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) != cCoq_2eInit_2eDatatypes_2eGt
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.compare_lt_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.compare_ngt_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.compare_nlt_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__61392___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_dne',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ ( V0__n != V1__m )
<=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
| V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__m != cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_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.eqb_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eqb_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> V0__x != V1__y ) ) ) ).
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.ge_le',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(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ge_le_iff',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(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gt_lt_iff',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_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_neq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
& V0__n != V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ngt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('Coq.ZArith.BinInt.Z.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6728,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__42648,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e)),cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('Coq.ZArith.BinInt.Z.lt_0_1',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.ZArith.BinInt.Z.lt_1_2',axiom,
p(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_asymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_gt_cases',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_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_neq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> V0__n != V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_nge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_pred_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n),V0__n)) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n))) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6728,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__42648,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,cCoq_2eZArith_2eBinInt_2eZ_2eeq,c_3c_3d_3e)),cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('Coq.ZArith.BinInt.Z.mod_divide',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V1__b,V0__a) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_sign',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b)) != cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_add_distr_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_lt_mono_pos_r',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V2__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__n,V0__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__m,V0__p))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_nonneg_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pos_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_reg_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_shuffle0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_shuffle3',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6692,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__3507,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eZArith_2eBinInt_2eZ_2eeq)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('Coq.ZArith.BinInt.Z.neg_pos_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.neq_mul_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
& V1__m != cCoq_2eNumbers_2eBinNums_2eZ0 )
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.neq_pred_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n) != V0__n ) ).
fof('Coq.ZArith.BinInt.Z.neq_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n) != V0__n ) ).
fof('Coq.ZArith.BinInt.Z.neq_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> V0__n != cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n) ) ).
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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_eq_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__a = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_sign',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b)) != cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__a)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.sgn_null_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3507,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).
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_inj_wd',axiom,
! [V0__n1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n2)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__n2)
<=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.succ_inj_wd_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n) != cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m)
<=> V0__n != V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3507,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eZArith_2eBinInt_2eZ_2eeq),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('Coq.ZArith.BinInt.Z.two_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.ZArith.Zbool.Zeq_bool_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_bool_if',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459791___24a2(V0__x,V1__y) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_bool_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> V0__x != V1__y ) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_is_eq_bool',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
<=> cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_intro',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__g] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__g)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V1__b)
=> ( ! [V5__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V2__g) ) ) )
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V2__g) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zrel_prime_neq_mod_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__b))
=> ( cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.not_rel_prime_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n))
=> ~ cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) ) ) ).
fof('Coq.ZArith.Znumtheory.prime_dec_aux_subproof',axiom,
! [V0__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__m)) ) ) ).
fof('Coq.ZArith.Zorder.Zgt_irrefl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V0__n) ) ).
fof('Coq.ZArith.Zorder.Zle_not_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.Zorder.Zlt_not_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_gt_le',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(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_le_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_lt_ge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___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
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(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.Zle_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zne_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.micromega.OrderedRing.Req_em',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V7__req,V11__n),V12__m))
| ~ p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_gt_cases',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_lt_trans',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_ngt',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
<=> ~ p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_le_neq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
<=> ( p(happ(happ(V8__rle,V11__n),V12__m))
& ~ p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_le_trans',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_neq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ~ p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_nge',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
<=> ~ p(happ(happ(V8__rle,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_trichotomy',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
| p(happ(happ(V7__req,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rneq_0_1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ~ p(happ(happ(V7__req,V1__rO),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rneq_symm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( ~ p(happ(happ(V7__req,V11__n),V12__m))
=> ~ p(happ(happ(V7__req,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V12__m)),happ(happ(V4__rtimes,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_neg_neg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V1__rO))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_neq_0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( ( ~ p(happ(happ(V7__req,V11__n),V1__rO))
& ~ p(happ(happ(V7__req,V12__m),V1__rO)) )
=> ~ p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V12__m)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_neg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,happ(happ(V4__rtimes,V11__n),V12__m)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_pos',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__39218___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__39218___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__39218___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__39236___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__39236___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RMicromega.Qeq_false',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eQArith_2eQreals_2eQ2R___24a1(V0__x) != cCoq_2eQArith_2eQreals_2eQ2R___24a1(V1__y) ) ) ) ).
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.add_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)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__x,V0__s)))
<=> ( V1__x = V2__y
| p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,V0__s)) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.remove_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)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__x,V0__s)))
<=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,V0__s))
& V1__x != V2__y ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.union_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ! [V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__x)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V0__s,V1__s_27)))
<=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V0__s))
| p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V1__s_27)) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.In_elt_prop',axiom,
! [V0__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V0__x)
=> ! [V1__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s)
=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__x,V1__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__64699___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.micromega.ZMicromega.isZ0_n0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse
<=> V0__x != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA4',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_2egt___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__y,V0__x)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V1__y),V0__x) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA7',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ! [V3__t] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__t)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__z,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V3__t,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V3__t)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_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__42648___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_OMEGA15',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k2)
=> ! [V6__P] :
( c_24__type__42648___24t(V6__P)
=> ( p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__c1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V5__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V5__k2)))))
=> p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V5__k2)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__42648___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_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__42648___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_comm',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__42648___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V0__x)))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__42648___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_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__42648___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__42648___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.new_var',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& V0__x = V1__y ) ) ).
fof('Coq.setoid_ring.Field_theory.AF_1_neq_0',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__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__39218___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__39227___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__39236___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ~ p(happ(happ(V9__req,V2__rI),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AF_AR',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__39218___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__39227___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__39236___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AFdiv_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__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__39218___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__39227___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__39236___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ! [V12__q] :
( t(V12__q,V0__R)
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V11__p),V12__q)),happ(happ(V4__rmul,V11__p),happ(V8__rinv,V12__q)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AFinv_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__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__39218___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__39227___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__39236___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V11__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V11__p)),V11__p)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.F_R',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__39218___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__39227___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__39236___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__39218___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__39218___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__39227___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__39236___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__39218___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__39227___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.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__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___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__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___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__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___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__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___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__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___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__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___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__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V9__x),V10__y))),happ(happ(V4__rmul,happ(V6__ropp,V9__x)),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARsub_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___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.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__39218___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__39218___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__39218___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__39227___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__39236___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__39518___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__39518___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__39518___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__39532___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__39539___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__39353___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.rpow_pow_N',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__39218___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__39236___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__56975___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__56982___24t(V0__R,V4__Cpow,V6__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V1__rI,V2__rmul,V3__req,V4__Cpow,V5__Cp__phi,V6__rpow)
=> ! [V8__r] :
( t(V8__r,V0__R)
=> ! [V9__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V9__n)
=> p(happ(happ(V3__req,happ(happ(V6__rpow,V8__r),happ(V5__Cp__phi,V9__n))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V8__r,V9__n))) ) ) ) ) ) ) ) ) ) ) ).
fof('Redblack.TREES.tree_ind',axiom,
! [V0__P] :
( c_24__type__3108___24t(V0__P)
=> ( p(happ(V0__P,cRedblack_2eTREES_2eE))
=> ( ! [V2__c] :
( cRedblack_2ecolor___24t(V2__c)
=> ! [V3__t] :
( cRedblack_2eTREES_2etree___24t(V3__t)
=> ( p(happ(V0__P,V3__t))
=> ! [V5__k] :
( cRedblack_2ekey___24t(V5__k)
=> ! [V6__v] :
( cV___24t(V6__v)
=> ! [V7__t] :
( cRedblack_2eTREES_2etree___24t(V7__t)
=> ( p(happ(V0__P,V7__t))
=> p(happ(V0__P,cRedblack_2eTREES_2eT___24a5(V2__c,V3__t,V5__k,V6__v,V7__t))) ) ) ) ) ) ) )
=> ! [V3__t] :
( cRedblack_2eTREES_2etree___24t(V3__t)
=> p(happ(V0__P,V3__t)) ) ) ) ) ).
fof('Redblack.color_ind',axiom,
! [V0__P] :
( c_24__type__3218___24t(V0__P)
=> ( p(happ(V0__P,cRedblack_2eRed))
=> ( p(happ(V0__P,cRedblack_2eBlack))
=> ! [V3__c] :
( cRedblack_2ecolor___24t(V3__c)
=> p(happ(V0__P,V3__c)) ) ) ) ) ).
fof('$adef_$_prop_59774_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__59774,V_24X1),V_24X2) = c_24__prop__59774___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.Ndigits.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eNdigits_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eNdigits_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Structures.OrderedTypeEx.String_as_OT.eq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq__dec,V_24X1),V_24X2) = cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.clearbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eclearbit,V_24X1),V_24X2) = cCoq_2eArith_2ePeanoNat_2eNat_2eclearbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_$_lam_43943_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__43943,V_24X1),V_24X2))
<=> c_24__lam__43943___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$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('$adef_$_prop_61469_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__61469,V_24X1),V_24X2) = c_24__prop__61469___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_3382_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__3382,V_24X1),V_24X2),V_24X3) = c_24__prop__3382___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.ZMicromega.Zeval_op1_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eZeval__op1,V_24X1) = cCoq_2emicromega_2eZMicromega_2eZeval__op1___24a1(V_24X1) ).
fof('$adef_$_prop_60422_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__60422,V_24X1),V_24X2),V_24X3) = c_24__prop__60422___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.bool_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2ebool__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2ebool__rect___24a1(V_24X1) ).
fof('$adef_$_prop_43922_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43922,V_24X1),V_24X2) = c_24__prop__43922___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_58793_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__58793,V_24X1),V_24X2) = c_24__prop__58793___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_64765_$a1',axiom,
! [V_24X1] : happ(c_24__lam__64765,V_24X1) = c_24__lam__64765___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.Exists_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eExists,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eExists___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_57152_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__57152,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__lam__57152___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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.Reals.Rfunctions.powerRZ_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2epowerRZ,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.count_occ_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2ecount__occ,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2ecount__occ___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.ZCoeff.gen_order_phi_Z_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_$_lam_59756_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__59756,V_24X1),V_24X2))
<=> c_24__lam__59756___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.ZArith.BinIntDef.Z.sgn_$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('$adef_$_prop_60387_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__60387,V_24X1),V_24X2) = c_24__prop__60387___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.nth_error_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2enth__error,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2enth__error___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_61392_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__61392,V_24X1),V_24X2) = c_24__prop__61392___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('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_prop_4093_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4093,V_24X1),V_24X2) = c_24__prop__4093___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_51924_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__51924,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__51924___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.Init.Nat.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_4091_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4091,V_24X1),V_24X2) = c_24__prop__4091___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_60418_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__60418,V_24X1),V_24X2),V_24X3) = c_24__prop__60418___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.BinList.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Coq.Strings.String.string_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eString_2estring__rec,V_24X1) = cCoq_2eStrings_2eString_2estring__rec___24a1(V_24X1) ).
fof('$adef_VFA.SearchTree.tree_$a1',axiom,
! [V_24X1] : happ(cVFA_2eSearchTree_2etree,V_24X1) = cVFA_2eSearchTree_2etree___24a1(V_24X1) ).
fof('$adef_$_prop_6677_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__6677,V_24X1),V_24X2) = c_24__prop__6677___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_49929_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__49929,V_24X1),V_24X2),V_24X3) = c_24__lam__49929___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).
fof('$adef_$_lam_49953_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__49953,V_24X1),V_24X2),V_24X3) = c_24__lam__49953___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_rect_eq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq,V_24X1))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V_24X1) ) ).
fof('$adef_$_lam_4337_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__4337,V_24X1),V_24X2) = c_24__lam__4337___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.eval_f_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__f,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.singleton_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esingleton,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esingleton___24a1(V_24X1) ).
fof('$adef_$_prop_59665_$a1',axiom,
! [V_24X1] : happ(c_24__prop__59665,V_24X1) = c_24__prop__59665___24a1(V_24X1) ).
fof('$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_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.FinFun.EqDec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLogic_2eFinFun_2eEqDec,V_24X1) = cCoq_2eLogic_2eFinFun_2eEqDec___24a1(V_24X1) ).
fof('$adef_$_lam_63652_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__63652,V_24X1),V_24X2) = c_24__lam__63652___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_4233_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4233,V_24X1),V_24X2) = c_24__prop__4233___24a2(V_24X1,V_24X2) ).
fof('$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_$_prop_3931_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__3931,V_24X1),V_24X2) = c_24__prop__3931___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_49945_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__49945,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__49945___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_$_lam_49945_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__49945,V_24X1),V_24X2),V_24X3) = c_24__lam__49945___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_4117_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4117,V_24X1),V_24X2) = c_24__prop__4117___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_60917_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__60917,V_24X1),V_24X2) = c_24__prop__60917___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_prop_4234_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4234,V_24X1),V_24X2) = c_24__prop__4234___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_116_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__116,V_24X1),V_24X2),V_24X3) = c_24__prop__116___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_63291_$a1',axiom,
! [V_24X1] : happ(c_24__lam__63291,V_24X1) = c_24__lam__63291___24a1(V_24X1) ).
fof('$adef_$_lam_63660_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__63660,V_24X1),V_24X2) = c_24__lam__63660___24a2(V_24X1,V_24X2) ).
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('$adef_$_prop_118_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__118,V_24X1),V_24X2),V_24X3) = c_24__prop__118___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Raxioms.INR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRaxioms_2eINR,V_24X1) = cCoq_2eReals_2eRaxioms_2eINR___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).
fof('$adef_$_let_11_subst_l_51852_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__51852,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__51852___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Init.Datatypes.option_$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('$adef_$_prop_60918_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__60918,V_24X1),V_24X2) = c_24__prop__60918___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.Ascii.ascii_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2eascii__rect,V_24X1) = cCoq_2eStrings_2eAscii_2eascii__rect___24a1(V_24X1) ).
fof('$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_$_prop_43929_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43929,V_24X1),V_24X2) = c_24__prop__43929___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_41620_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__41620,V_24X1),V_24X2),V_24X3) = c_24__prop__41620___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_VFA.Maps.t_update_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cVFA_2eMaps_2et__update,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cVFA_2eMaps_2et__update___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.Arith.Between.exists_between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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_$_prop_3932_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__3932,V_24X1),V_24X2) = c_24__prop__3932___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_63660_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__63660,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__63660___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.N_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eN__rec,V_24X1) = cCoq_2eNumbers_2eBinNums_2eN__rec___24a1(V_24X1) ).
fof('$adef_$_prop_4470_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4470,V_24X1),V_24X2) = c_24__prop__4470___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1),V_24X2),V_24X3) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_61470_$a1',axiom,
! [V_24X1] : happ(c_24__prop__61470,V_24X1) = c_24__prop__61470___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Zerob.zerob_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eZerob_2ezerob,V_24X1) = cCoq_2eBool_2eZerob_2ezerob___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.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.QArith.QArith_base.Qle_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQle,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Between.in_int_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ein__int,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ein__int___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_$_prop_4112_$a1',axiom,
! [V_24X1] : happ(c_24__prop__4112,V_24X1) = c_24__prop__4112___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.shiftl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eshiftl,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eshiftl___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('$adef_Redblack.TREES.makeBlack_$a1',axiom,
! [V_24X1] : happ(cRedblack_2eTREES_2emakeBlack,V_24X1) = cRedblack_2eTREES_2emakeBlack___24a1(V_24X1) ).
fof('$adef_Redblack.TREES.tree_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cRedblack_2eTREES_2etree__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cRedblack_2eTREES_2etree__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_59788_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__59788,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__59788___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Strings.String.length_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eString_2elength,V_24X1) = cCoq_2eStrings_2eString_2elength___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V_24X1) ).
fof('$adef_Coq.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_Redblack.TREES.lookup_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cRedblack_2eTREES_2elookup,V_24X1),V_24X2) = cRedblack_2eTREES_2elookup___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_$_prop_60419_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__60419,V_24X1),V_24X2),V_24X3) = c_24__prop__60419___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$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('$adef_Coq.Init.Datatypes.list_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rec,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.node_$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('$adef_$_let_var_6_p_52254_52256_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__52254__52256,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__52254__52256___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Env.jump_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnv_2ejump,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnv_2ejump___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.ltb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_prop_3381_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__3381,V_24X1),V_24X2),V_24X3) = c_24__prop__3381___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etestbit,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorEq.eqb_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorEq_2eeqb,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Redblack.TREES.tree_rec_$a1',axiom,
! [V_24X1] : happ(cRedblack_2eTREES_2etree__rec,V_24X1) = cRedblack_2eTREES_2etree__rec___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRminus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2egt,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.ltb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eltb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eltb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Init.Logic.eq_refl_$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('$adef_$_prop_60389_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__60389,V_24X1),V_24X2) = c_24__prop__60389___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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.Numbers.BinNums.N_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eN__rect,V_24X1) = cCoq_2eNumbers_2eBinNums_2eN__rect___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Add_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.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.ZArith.BinIntDef.Z.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Sumbool.sumbool_not_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eSumbool_2esumbool__not,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eSumbool_2esumbool__not___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec,V_24X1),V_24X2) = cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sorting.Permutation.Permutation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Sumbool.bool_of_sumbool_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eSumbool_2ebool__of__sumbool,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eSumbool_2ebool__of__sumbool___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.ZArith_dec.Z_zerop_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZArith__dec_2eZ__zerop,V_24X1) = cCoq_2eZArith_2eZArith__dec_2eZ__zerop___24a1(V_24X1) ).
fof('$adef_$_prop_60386_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__60386,V_24X1),V_24X2) = c_24__prop__60386___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emodulo,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Nat.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2epow,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zdiv.Remainder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZdiv_2eRemainder,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_$_lam_49929_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__49929,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__49929___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$63597_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2463597,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2463597___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ege,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2ege___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.QArith.QArith_base.Qeq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sumbool_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$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('$adef_$_prop_4113_$a1',axiom,
! [V_24X1] : happ(c_24__prop__4113,V_24X1) = c_24__prop__4113___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_prop_60420_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__60420,V_24X1),V_24X2),V_24X3) = c_24__prop__60420___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_VFA.SearchTree.T_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cVFA_2eSearchTree_2eT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cVFA_2eSearchTree_2eT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.bool_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2ebool__rec,V_24X1) = cCoq_2eInit_2eDatatypes_2ebool__rec___24a1(V_24X1) ).
fof('$adef_$_let_var_var_7_n_3336_3340_3349_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__var__7__n__3336__3340__3349,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__var__7__n__3336__3340__3349___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_VFA.Extract.ltb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cVFA_2eExtract_2eltb,V_24X1),V_24X2) = cVFA_2eExtract_2eltb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$63602_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2463602,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2463602___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Empty_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty,V_24X1))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V_24X1) ) ).
fof('$adef_Redblack.TREES.ins_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cRedblack_2eTREES_2eins,V_24X1),V_24X2),V_24X3) = cRedblack_2eTREES_2eins___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('$adef_$_prop_4235_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4235,V_24X1),V_24X2) = c_24__prop__4235___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_58818_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__58818,V_24X1),V_24X2) = c_24__prop__58818___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('$adef_Coq.Numbers.BinNums.Z_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZ__rec,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZ__rec___24a1(V_24X1) ).
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('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivide,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_59664_$a1',axiom,
! [V_24X1] : happ(c_24__prop__59664,V_24X1) = c_24__prop__59664___24a1(V_24X1) ).
fof('$adef_$_prop_4090_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4090,V_24X1),V_24X2) = c_24__prop__4090___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.Zbool.Z_noteq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZ__noteq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZ__noteq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zbool.Z_eq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZ__eq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZ__eq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$59791_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459791,V_24X1),V_24X2))
<=> c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459791___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq__bool,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$63580_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2463580,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2463580___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_58792_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__58792,V_24X1),V_24X2) = c_24__prop__58792___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).
fof('$adef_$_prop_41619_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__41619,V_24X1),V_24X2),V_24X3) = c_24__prop__41619___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
<=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).
fof('$adef_$_lam_4337_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__4337,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__4337___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_60423_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__60423,V_24X1),V_24X2) = c_24__prop__60423___24a2(V_24X1,V_24X2) ).
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('$adef_Redblack.TREES.tree_rect_$a1',axiom,
! [V_24X1] : happ(cRedblack_2eTREES_2etree__rect,V_24X1) = cRedblack_2eTREES_2etree__rect___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.Zeval_op2_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eZeval__op2,V_24X1) = cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V_24X1) ).
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('$adef_$_prop_3380_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__3380,V_24X1),V_24X2),V_24X3) = c_24__prop__3380___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).
fof('$adef_$_prop_59773_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__59773,V_24X1),V_24X2) = c_24__prop__59773___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_4092_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4092,V_24X1),V_24X2) = c_24__prop__4092___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.remove_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2eremove,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2eremove___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_VFA.SearchTree.E_$a1',axiom,
! [V_24X1] : happ(cVFA_2eSearchTree_2eE,V_24X1) = cVFA_2eSearchTree_2eE___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.positive_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2epositive__rect,V_24X1) = cCoq_2eNumbers_2eBinNums_2epositive__rect___24a1(V_24X1) ).
fof('$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_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Strings.String.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eeqb,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.Fin.eqb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eFin_2eeqb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eFin_2eeqb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Redblack.color_rect_$a1',axiom,
! [V_24X1] : happ(cRedblack_2ecolor__rect,V_24X1) = cRedblack_2ecolor__rect___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_3379_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__3379,V_24X1),V_24X2),V_24X3) = c_24__prop__3379___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.eq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_60919_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__60919,V_24X1),V_24X2) = c_24__prop__60919___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_49937_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__49937,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__49937___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.QArith.Qreals.Q2R_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQreals_2eQ2R,V_24X1) = cCoq_2eQArith_2eQreals_2eQ2R___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.shiftl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Strings.Ascii.ascii_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2eascii__rec,V_24X1) = cCoq_2eStrings_2eAscii_2eascii__rec___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).
fof('$adef_$_lam_59762_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__59762,V_24X1))
<=> c_24__lam__59762___24a1(V_24X1) ) ).
fof('$adef_$_prop_4656_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4656,V_24X1),V_24X2) = c_24__prop__4656___24a2(V_24X1,V_24X2) ).
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_63676_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__63676,V_24X1),V_24X2) = c_24__lam__63676___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_4655_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4655,V_24X1),V_24X2) = c_24__prop__4655___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$36878_$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_2ebool_2436878,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436878___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.Tauto.eval_tt_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__tt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Z_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZ__rect,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZ__rect___24a1(V_24X1) ).
fof('$adef_$_prop_60417_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__60417,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__60417___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.R_Ifp.frac_part_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eR__Ifp_2efrac__part,V_24X1) = cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V_24X1) ).
fof('$adef_$_lam_64761_$a1',axiom,
! [V_24X1] : happ(c_24__lam__64761,V_24X1) = c_24__lam__64761___24a1(V_24X1) ).
fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2egcd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rcase_abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRbasic__fun_2eRcase__abs,V_24X1) = cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$36840_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436840,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436840___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_63290_$a1',axiom,
! [V_24X1] : happ(c_24__lam__63290,V_24X1) = c_24__lam__63290___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_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_Coq.micromega.ZMicromega.isZ0_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eisZ0,V_24X1) = cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qcompare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQcompare,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQcompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.String.prefix_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eprefix,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eprefix___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_VFA.Maps.t_empty_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cVFA_2eMaps_2et__empty,V_24X1),V_24X2),V_24X3) = cVFA_2eMaps_2et__empty___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Redblack.color_rec_$a1',axiom,
! [V_24X1] : happ(cRedblack_2ecolor__rec,V_24X1) = cRedblack_2ecolor__rec___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_lam_63676_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__63676,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__63676___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).
fof('$adef_VFA.Maps.total_map_$a1',axiom,
! [V_24X1] : happ(cVFA_2eMaps_2etotal__map,V_24X1) = cVFA_2eMaps_2etotal__map___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('$adef_Coq.NArith.BinNatDef.N.pow_$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('$adef_$_case_Coq.Init.Datatypes.bool$36799_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436799,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436799___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Strings.Byte.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eByte_2eeqb,V_24X1),V_24X2) = cCoq_2eStrings_2eByte_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eleb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.Even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eEven,V_24X1))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2eEven___24a1(V_24X1) ) ).
fof('$adef_$_lam_4670_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__4670,V_24X1),V_24X2) = c_24__lam__4670___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.nat_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rec,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rec___24a1(V_24X1) ).
fof('$adef_$_prop_37114_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__37114,V_24X1),V_24X2) = c_24__prop__37114___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Strings.Ascii.ascii_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eAscii_2eascii__dec,V_24X1),V_24X2) = cCoq_2eStrings_2eAscii_2eascii__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_63668_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__63668,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__63668___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_$_prop_64699_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__64699,V_24X1),V_24X2) = c_24__prop__64699___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.in_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2ein__dec,V_24X1),V_24X2) = cCoq_2eLists_2eList_2ein__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_60421_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__60421,V_24X1),V_24X2),V_24X3) = c_24__prop__60421___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Logic.eq_ind_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__ind,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eLogic_2eeq__ind___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.Ascii.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eAscii_2eeqb,V_24X1),V_24X2) = cCoq_2eStrings_2eAscii_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_63652_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__63652,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__63652___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.cneqb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecneqb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.Zdiv.Remainder_alt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZdiv_2eRemainder__alt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZdiv_2eRemainder__alt___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('$adef_$_let_var_6_p_52252_52255_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__52252__52255,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__52252__52255___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.ListDec.In_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eListDec_2eIn__dec,V_24X1),V_24X2) = cCoq_2eLists_2eListDec_2eIn__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_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.Init.Specif.sumbool_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.R_Ifp.Int_part_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eR__Ifp_2eInt__part,V_24X1) = cCoq_2eReals_2eR__Ifp_2eInt__part___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_Redblack.TREES.insert_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cRedblack_2eTREES_2einsert,V_24X1),V_24X2),V_24X3) = cRedblack_2eTREES_2einsert___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eodd,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eleb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.Reals.RIneq.nonzero_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2enonzero,V_24X1) = cCoq_2eReals_2eRIneq_2enonzero___24a1(V_24X1) ).
fof('$adef_$_fix_60952_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__60952__1__add__carry,V_24X1),V_24X2) = c_24__fix__60952__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.clearbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eclearbit,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2eclearbit___24a2(V_24X1,V_24X2) ).
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_59788_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__59788,V_24X1),V_24X2) = c_24__lam__59788___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_57152_$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__57152,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__57152___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.list_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2elist__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_63668_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__63668,V_24X1),V_24X2) = c_24__lam__63668___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.eval_op1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Strings.String.string_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eString_2estring__rect,V_24X1) = cCoq_2eStrings_2eString_2estring__rect___24a1(V_24X1) ).
fof('$adef_$_lam_49953_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__49953,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__49953___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Numbers.BinNums.positive_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2epositive__rec,V_24X1) = cCoq_2eNumbers_2eBinNums_2epositive__rec___24a1(V_24X1) ).
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('$adef_VFA.Extract.IntMaps.total_map_$a1',axiom,
! [V_24X1] : happ(cVFA_2eExtract_2eIntMaps_2etotal__map,V_24X1) = cVFA_2eExtract_2eIntMaps_2etotal__map___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eleb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_64754_$a1',axiom,
! [V_24X1] : happ(c_24__lam__64754,V_24X1) = c_24__lam__64754___24a1(V_24X1) ).
fof('$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.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_Redblack.TREES.T_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cRedblack_2eTREES_2eT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cRedblack_2eTREES_2eT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.Odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eOdd,V_24X1))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2eOdd___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.ldiff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eldiff,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eldiff___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_43928_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43928,V_24X1),V_24X2) = c_24__prop__43928___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('$adef_Coq.Reals.Rpow_def.pow_$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('$adef_Coq.NArith.BinNatDef.N.ldiff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eldiff,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V_24X1,V_24X2) ).
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('$adef_$_prop_4118_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4118,V_24X1),V_24X2) = c_24__prop__4118___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quot_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equot,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2elog2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Strings.String.string_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2estring__dec,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2estring__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.Reval_op2_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eReval__op2,V_24X1) = cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V_24X1) ).
fof('$adef_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.ZArith.BinIntDef.Z.shiftl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.union_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ege,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$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_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.clause_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2eclause,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$36865_$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_2ebool_2436865,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436865___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_$_lam_59763_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__59763,V_24X1))
<=> c_24__lam__59763___24a1(V_24X1) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$36883_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436883,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436883___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.NArith.BinNat.N.clearbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eclearbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNat_2eN_2eclearbit___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_57115_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__57115,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__57115___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.hd_error_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2ehd__error,V_24X1),V_24X2) = cCoq_2eLists_2eList_2ehd__error___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rabs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRbasic__fun_2eRabs,V_24X1) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V_24X1) ).
fof('$adef_$_prop_60388_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__60388,V_24X1),V_24X2) = c_24__prop__60388___24a2(V_24X1,V_24X2) ).
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('$adef_Redblack.color_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cRedblack_2ecolor__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cRedblack_2ecolor__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_49937_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__49937,V_24X1),V_24X2),V_24X3) = c_24__lam__49937___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_41621_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__41621,V_24X1),V_24X2),V_24X3) = c_24__prop__41621___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Strings.String.substring_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eStrings_2eString_2esubstring,V_24X1),V_24X2),V_24X3) = cCoq_2eStrings_2eString_2esubstring___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_41618_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__41618,V_24X1),V_24X2),V_24X3) = c_24__prop__41618___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.SetoidList.equivlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eequivlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_64754_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__64754,V_24X1),V_24X2) = c_24__lam__64754___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Logic.eq_ind_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__ind,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eLogic_2eeq__ind___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.remove_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epow,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
<=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).
fof('$adef_Redblack.TREES.balance_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cRedblack_2eTREES_2ebalance,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cRedblack_2eTREES_2ebalance___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_4670_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__4670,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__4670___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_lam_64761_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__64761,V_24X1),V_24X2) = c_24__lam__64761___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).
fof('$adef_$_prop_6678_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__6678,V_24X1),V_24X2) = c_24__prop__6678___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.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_$_case_Coq.Init.Datatypes.bool$36738_$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(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436738,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2436738___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
<=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_$_lam_57115_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__57115,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__57115___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_117_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__117,V_24X1),V_24X2),V_24X3) = c_24__prop__117___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_59765_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__59765,V_24X1))
<=> c_24__lam__59765___24a1(V_24X1) ) ).
fof('$adef_Coq.Arith.Factorial.fact_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2eFactorial_2efact,V_24X1) = cCoq_2eArith_2eFactorial_2efact___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Specif.sumbool$3367_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esumbool_243367,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_243367___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.ldiff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eldiff,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eldiff___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$56717_$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_2456717,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_2456717___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_51924_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__51924,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__51924___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.setoid_ring.Field_theory.denum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2edenum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_Coq.Lists.List.incl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eincl,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eincl___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.ZArith_dec.Z_noteq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZArith__dec_2eZ__noteq__dec,V_24X1),V_24X2) = cCoq_2eZArith_2eZArith__dec_2eZ__noteq__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_59764_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__59764,V_24X1))
<=> c_24__lam__59764___24a1(V_24X1) ) ).
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('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_VFA.SearchTree.Abs_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cVFA_2eSearchTree_2eAbs,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cVFA_2eSearchTree_2eAbs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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_39770',axiom,
! [V_24Y] :
( c_24__type__39770___24t(V_24Y)
<=> t(V_24Y,c_24__type__39770) ) ).
fof('$tdef_$_type_49297',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__49297___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__49297___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_4316',axiom,
! [V_24Y] :
( c_24__type__4316___24t(V_24Y)
<=> t(V_24Y,c_24__type__4316) ) ).
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_$_type_56730',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__56730___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__56730___24a2(V_24X1,V_24X2)) ) ).
fof('$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_59708',axiom,
! [V_24Y] :
( c_24__type__59708___24t(V_24Y)
<=> t(V_24Y,c_24__type__59708) ) ).
fof('$tdef_$_type_62984',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__62984___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__62984___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4241',axiom,
! [V_24Y] :
( c_24__type__4241___24t(V_24Y)
<=> t(V_24Y,c_24__type__4241) ) ).
fof('$tdef_$_type_37239',axiom,
! [V_24Y] :
( c_24__type__37239___24t(V_24Y)
<=> t(V_24Y,c_24__type__37239) ) ).
fof('$tdef_$_type_61901',axiom,
! [V_24Y] :
( c_24__type__61901___24t(V_24Y)
<=> t(V_24Y,c_24__type__61901) ) ).
fof('$tdef_$_type_61243',axiom,
! [V_24Y] :
( c_24__type__61243___24t(V_24Y)
<=> t(V_24Y,c_24__type__61243) ) ).
fof('$tdef_$_type_41592',axiom,
! [V_24Y] :
( c_24__type__41592___24t(V_24Y)
<=> t(V_24Y,c_24__type__41592) ) ).
fof('$tdef_$_type_134',axiom,
! [V_24Y] :
( c_24__type__134___24t(V_24Y)
<=> t(V_24Y,c_24__type__134) ) ).
fof('$tdef_$_type_47613',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__47613___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__47613___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_43940',axiom,
! [V_24Y] :
( c_24__type__43940___24t(V_24Y)
<=> t(V_24Y,c_24__type__43940) ) ).
fof('$tdef_$_type_42626',axiom,
! [V_24Y] :
( c_24__type__42626___24t(V_24Y)
<=> t(V_24Y,c_24__type__42626) ) ).
fof('$tdef_$_type_54086',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__54086___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__54086___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_64711',axiom,
! [V_24Y] :
( c_24__type__64711___24t(V_24Y)
<=> t(V_24Y,c_24__type__64711) ) ).
fof('$tdef_$_type_4291',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4291___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4291___24a1(V_24X1)) ) ).
fof('$tdef_$_type_53636',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__53636___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__53636___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_39227',axiom,
! [V_24X1,V_24Y] :
( c_24__type__39227___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__39227___24a1(V_24X1)) ) ).
fof('$tdef_$_type_63038',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__63038___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__63038___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4460',axiom,
! [V_24Y] :
( c_24__type__4460___24t(V_24Y)
<=> t(V_24Y,c_24__type__4460) ) ).
fof('$tdef_$_type_3990',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3990___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3990___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3427',axiom,
! [V_24Y] :
( c_24__type__3427___24t(V_24Y)
<=> t(V_24Y,c_24__type__3427) ) ).
fof('$tdef_$_type_56604',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__56604___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__56604___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_53223',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__53223___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__53223___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_44891',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__44891___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__44891___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_51597',axiom,
! [V_24Y] :
( c_24__type__51597___24t(V_24Y)
<=> t(V_24Y,c_24__type__51597) ) ).
fof('$tdef_$_type_53277',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__53277___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__53277___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_38469',axiom,
! [V_24Y] :
( c_24__type__38469___24t(V_24Y)
<=> t(V_24Y,c_24__type__38469) ) ).
fof('$tdef_$_type_129',axiom,
! [V_24Y] :
( c_24__type__129___24t(V_24Y)
<=> t(V_24Y,c_24__type__129) ) ).
fof('$tdef_$_type_47290',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__47290___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__47290___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_6158',axiom,
! [V_24Y] :
( c_24__type__6158___24t(V_24Y)
<=> t(V_24Y,c_24__type__6158) ) ).
fof('$tdef_$_type_4489',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4489___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4489___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_61096',axiom,
! [V_24Y] :
( c_24__type__61096___24t(V_24Y)
<=> t(V_24Y,c_24__type__61096) ) ).
fof('$tdef_Redblack.key',axiom,
! [V_24Y] :
( cRedblack_2ekey___24t(V_24Y)
<=> t(V_24Y,cRedblack_2ekey) ) ).
fof('$tdef_$_type_6842',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6842___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6842___24a1(V_24X1)) ) ).
fof('$tdef_$_type_45560',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__45560___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__45560___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_61508',axiom,
! [V_24Y] :
( c_24__type__61508___24t(V_24Y)
<=> t(V_24Y,c_24__type__61508) ) ).
fof('$tdef_$_type_3326',axiom,
! [V_24Y] :
( c_24__type__3326___24t(V_24Y)
<=> t(V_24Y,c_24__type__3326) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ) ).
fof('$tdef_$_type_3299',axiom,
! [V_24Y] :
( c_24__type__3299___24t(V_24Y)
<=> t(V_24Y,c_24__type__3299) ) ).
fof('$tdef_$_type_62687',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__62687___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__62687___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_47959',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__47959___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__47959___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_4108',axiom,
! [V_24Y] :
( c_24__type__4108___24t(V_24Y)
<=> t(V_24Y,c_24__type__4108) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_53340',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__53340___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__53340___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_62244',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__62244___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__62244___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_61432',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__61432___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__61432___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_42614',axiom,
! [V_24Y] :
( c_24__type__42614___24t(V_24Y)
<=> t(V_24Y,c_24__type__42614) ) ).
fof('$tdef_$_type_38131',axiom,
! [V_24Y] :
( c_24__type__38131___24t(V_24Y)
<=> t(V_24Y,c_24__type__38131) ) ).
fof('$tdef_$_type_64056',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__64056___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__64056___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4055',axiom,
! [V_24Y] :
( c_24__type__4055___24t(V_24Y)
<=> t(V_24Y,c_24__type__4055) ) ).
fof('$tdef_$_type_53549',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__53549___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__53549___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_59442',axiom,
! [V_24X1,V_24Y] :
( c_24__type__59442___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__59442___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6802',axiom,
! [V_24Y] :
( c_24__type__6802___24t(V_24Y)
<=> t(V_24Y,c_24__type__6802) ) ).
fof('$tdef_$_type_56982',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__56982___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__56982___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4493',axiom,
! [V_24Y] :
( c_24__type__4493___24t(V_24Y)
<=> t(V_24Y,c_24__type__4493) ) ).
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_$_type_6728',axiom,
! [V_24Y] :
( c_24__type__6728___24t(V_24Y)
<=> t(V_24Y,c_24__type__6728) ) ).
fof('$tdef_$_type_63208',axiom,
! [V_24Y] :
( c_24__type__63208___24t(V_24Y)
<=> t(V_24Y,c_24__type__63208) ) ).
fof('$tdef_$_type_4297',axiom,
! [V_24Y] :
( c_24__type__4297___24t(V_24Y)
<=> t(V_24Y,c_24__type__4297) ) ).
fof('$tdef_$_type_3031',axiom,
! [V_24Y] :
( c_24__type__3031___24t(V_24Y)
<=> t(V_24Y,c_24__type__3031) ) ).
fof('$tdef_$_type_64161',axiom,
! [V_24Y] :
( c_24__type__64161___24t(V_24Y)
<=> t(V_24Y,c_24__type__64161) ) ).
fof('$tdef_$_type_39494',axiom,
! [V_24X1,V_24Y] :
( c_24__type__39494___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__39494___24a1(V_24X1)) ) ).
fof('$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_56654',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__56654___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__56654___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_57277',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__57277___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__57277___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_54920',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__54920___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__54920___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_64727',axiom,
! [V_24Y] :
( c_24__type__64727___24t(V_24Y)
<=> t(V_24Y,c_24__type__64727) ) ).
fof('$tdef_$_type_9',axiom,
! [V_24Y] :
( c_24__type__9___24t(V_24Y)
<=> t(V_24Y,c_24__type__9) ) ).
fof('$tdef_$_type_38162',axiom,
! [V_24Y] :
( c_24__type__38162___24t(V_24Y)
<=> t(V_24Y,c_24__type__38162) ) ).
fof('$tdef_$_type_64701',axiom,
! [V_24X1,V_24Y] :
( c_24__type__64701___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__64701___24a1(V_24X1)) ) ).
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_64046',axiom,
! [V_24Y] :
( c_24__type__64046___24t(V_24Y)
<=> t(V_24Y,c_24__type__64046) ) ).
fof('$tdef_$_type_4303',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4303___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4303___24a1(V_24X1)) ) ).
fof('$tdef_$_type_62594',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__62594___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__62594___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_58889',axiom,
! [V_24Y] :
( c_24__type__58889___24t(V_24Y)
<=> t(V_24Y,c_24__type__58889) ) ).
fof('$tdef_$_type_42456',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__42456___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__42456___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_VFA.Maps.total_map',axiom,
! [V_24X1,V_24Y] :
( cVFA_2eMaps_2etotal__map___24t(V_24X1,V_24Y)
<=> t(V_24Y,cVFA_2eMaps_2etotal__map___24a1(V_24X1)) ) ).
fof('$tdef_$_type_109',axiom,
! [V_24Y] :
( c_24__type__109___24t(V_24Y)
<=> t(V_24Y,c_24__type__109) ) ).
fof('$tdef_$_type_4318',axiom,
! [V_24Y] :
( c_24__type__4318___24t(V_24Y)
<=> t(V_24Y,c_24__type__4318) ) ).
fof('$tdef_$_type_4288',axiom,
! [V_24Y] :
( c_24__type__4288___24t(V_24Y)
<=> t(V_24Y,c_24__type__4288) ) ).
fof('$tdef_$_type_38941',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__38941___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__38941___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_48628',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__48628___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__48628___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_$_type_3074',axiom,
! [V_24Y] :
( c_24__type__3074___24t(V_24Y)
<=> t(V_24Y,c_24__type__3074) ) ).
fof('$tdef_$_type_6692',axiom,
! [V_24Y] :
( c_24__type__6692___24t(V_24Y)
<=> t(V_24Y,c_24__type__6692) ) ).
fof('$tdef_$_type_38464',axiom,
! [V_24Y] :
( c_24__type__38464___24t(V_24Y)
<=> t(V_24Y,c_24__type__38464) ) ).
fof('$tdef_$_type_43576',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__43576___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__43576___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Specif.sumbool',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_58153',axiom,
! [V_24Y] :
( c_24__type__58153___24t(V_24Y)
<=> t(V_24Y,c_24__type__58153) ) ).
fof('$tdef_$_type_53160',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__53160___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__53160___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_59781',axiom,
! [V_24Y] :
( c_24__type__59781___24t(V_24Y)
<=> t(V_24Y,c_24__type__59781) ) ).
fof('$tdef_$_type_63248',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__63248___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__63248___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_126',axiom,
! [V_24Y] :
( c_24__type__126___24t(V_24Y)
<=> t(V_24Y,c_24__type__126) ) ).
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_$_type_64065',axiom,
! [V_24Y] :
( c_24__type__64065___24t(V_24Y)
<=> t(V_24Y,c_24__type__64065) ) ).
fof('$tdef_$_type_59771',axiom,
! [V_24Y] :
( c_24__type__59771___24t(V_24Y)
<=> t(V_24Y,c_24__type__59771) ) ).
fof('$tdef_$_type_42480',axiom,
! [V_24Y] :
( c_24__type__42480___24t(V_24Y)
<=> t(V_24Y,c_24__type__42480) ) ).
fof('$tdef_$_type_61506',axiom,
! [V_24X1,V_24Y] :
( c_24__type__61506___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__61506___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4426',axiom,
! [V_24Y] :
( c_24__type__4426___24t(V_24Y)
<=> t(V_24Y,c_24__type__4426) ) ).
fof('$tdef_$_type_40140',axiom,
! [V_24X1,V_24Y] :
( c_24__type__40140___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__40140___24a1(V_24X1)) ) ).
fof('$tdef_$_type_63101',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__63101___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__63101___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_54512',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__54512___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__54512___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_52056',axiom,
! [V_24Y] :
( c_24__type__52056___24t(V_24Y)
<=> t(V_24Y,c_24__type__52056) ) ).
fof('$tdef_$_type_56963',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__56963___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__56963___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_39034',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__39034___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__39034___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_64104',axiom,
! [V_24Y] :
( c_24__type__64104___24t(V_24Y)
<=> t(V_24Y,c_24__type__64104) ) ).
fof('$tdef_$_type_41272',axiom,
! [V_24Y] :
( c_24__type__41272___24t(V_24Y)
<=> t(V_24Y,c_24__type__41272) ) ).
fof('$tdef_$_type_3970',axiom,
! [V_24Y] :
( c_24__type__3970___24t(V_24Y)
<=> t(V_24Y,c_24__type__3970) ) ).
fof('$tdef_$_type_190',axiom,
! [V_24Y] :
( c_24__type__190___24t(V_24Y)
<=> t(V_24Y,c_24__type__190) ) ).
fof('$tdef_$_type_59434',axiom,
! [V_24Y] :
( c_24__type__59434___24t(V_24Y)
<=> t(V_24Y,c_24__type__59434) ) ).
fof('$tdef_$_type_58816',axiom,
! [V_24Y] :
( c_24__type__58816___24t(V_24Y)
<=> t(V_24Y,c_24__type__58816) ) ).
fof('$tdef_$_type_4536',axiom,
! [V_24Y] :
( c_24__type__4536___24t(V_24Y)
<=> t(V_24Y,c_24__type__4536) ) ).
fof('$tdef_$_type_4043',axiom,
! [V_24Y] :
( c_24__type__4043___24t(V_24Y)
<=> t(V_24Y,c_24__type__4043) ) ).
fof('$tdef_$_type_114',axiom,
! [V_24X1,V_24Y] :
( c_24__type__114___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__114___24a1(V_24X1)) ) ).
fof('$tdef_$_type_44009',axiom,
! [V_24Y] :
( c_24__type__44009___24t(V_24Y)
<=> t(V_24Y,c_24__type__44009) ) ).
fof('$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_4554',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__4554___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__4554___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_54299',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__54299___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__54299___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_$_type_61892',axiom,
! [V_24Y] :
( c_24__type__61892___24t(V_24Y)
<=> t(V_24Y,c_24__type__61892) ) ).
fof('$tdef_$_type_3505',axiom,
! [V_24Y] :
( c_24__type__3505___24t(V_24Y)
<=> t(V_24Y,c_24__type__3505) ) ).
fof('$tdef_$_type_64768',axiom,
! [V_24Y] :
( c_24__type__64768___24t(V_24Y)
<=> t(V_24Y,c_24__type__64768) ) ).
fof('$tdef_$_type_59662',axiom,
! [V_24Y] :
( c_24__type__59662___24t(V_24Y)
<=> t(V_24Y,c_24__type__59662) ) ).
fof('$tdef_$_type_53579',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__53579___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__53579___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3407',axiom,
! [V_24Y] :
( c_24__type__3407___24t(V_24Y)
<=> t(V_24Y,c_24__type__3407) ) ).
fof('$tdef_$_type_44545',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__44545___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__44545___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_62419',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__62419___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__62419___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_6804',axiom,
! [V_24Y] :
( c_24__type__6804___24t(V_24Y)
<=> t(V_24Y,c_24__type__6804) ) ).
fof('$tdef_$_type_4016',axiom,
! [V_24Y] :
( c_24__type__4016___24t(V_24Y)
<=> t(V_24Y,c_24__type__4016) ) ).
fof('$tdef_$_type_39863',axiom,
! [V_24Y] :
( c_24__type__39863___24t(V_24Y)
<=> t(V_24Y,c_24__type__39863) ) ).
fof('$tdef_$_type_43475',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__43475___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__43475___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3216',axiom,
! [V_24Y] :
( c_24__type__3216___24t(V_24Y)
<=> t(V_24Y,c_24__type__3216) ) ).
fof('$tdef_$_type_41577',axiom,
! [V_24Y] :
( c_24__type__41577___24t(V_24Y)
<=> t(V_24Y,c_24__type__41577) ) ).
fof('$tdef_$_type_38136',axiom,
! [V_24Y] :
( c_24__type__38136___24t(V_24Y)
<=> t(V_24Y,c_24__type__38136) ) ).
fof('$tdef_$_type_43183',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__43183___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__43183___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_62512',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__62512___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__62512___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_63643',axiom,
! [V_24Y] :
( c_24__type__63643___24t(V_24Y)
<=> t(V_24Y,c_24__type__63643) ) ).
fof('$tdef_$_type_42452',axiom,
! [V_24Y] :
( c_24__type__42452___24t(V_24Y)
<=> t(V_24Y,c_24__type__42452) ) ).
fof('$tdef_$_type_4269',axiom,
! [V_24Y] :
( c_24__type__4269___24t(V_24Y)
<=> t(V_24Y,c_24__type__4269) ) ).
fof('$tdef_$_type_37142',axiom,
! [V_24Y] :
( c_24__type__37142___24t(V_24Y)
<=> t(V_24Y,c_24__type__37142) ) ).
fof('$tdef_$_type_3456',axiom,
! [V_24Y] :
( c_24__type__3456___24t(V_24Y)
<=> t(V_24Y,c_24__type__3456) ) ).
fof('$tdef_$_type_3929',axiom,
! [V_24Y] :
( c_24__type__3929___24t(V_24Y)
<=> t(V_24Y,c_24__type__3929) ) ).
fof('$tdef_$_type_53495',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__53495___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__53495___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_56512',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__56512___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__56512___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_59760',axiom,
! [V_24Y] :
( c_24__type__59760___24t(V_24Y)
<=> t(V_24Y,c_24__type__59760) ) ).
fof('$tdef_$_type_53519',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__53519___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__53519___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_Coq.Relations.Relation_Definitions.relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43967',axiom,
! [V_24Y] :
( c_24__type__43967___24t(V_24Y)
<=> t(V_24Y,c_24__type__43967) ) ).
fof('$tdef_$_type_56162',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__56162___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__56162___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_4231',axiom,
! [V_24Y] :
( c_24__type__4231___24t(V_24Y)
<=> t(V_24Y,c_24__type__4231) ) ).
fof('$tdef_$_type_3134',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3134___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3134___24a1(V_24X1)) ) ).
fof('$tdef_$_type_51592',axiom,
! [V_24Y] :
( c_24__type__51592___24t(V_24Y)
<=> t(V_24Y,c_24__type__51592) ) ).
fof('$tdef_$_type_4095',axiom,
! [V_24Y] :
( c_24__type__4095___24t(V_24Y)
<=> t(V_24Y,c_24__type__4095) ) ).
fof('$tdef_$_type_37221',axiom,
! [V_24Y] :
( c_24__type__37221___24t(V_24Y)
<=> t(V_24Y,c_24__type__37221) ) ).
fof('$tdef_$_type_39116',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__39116___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__39116___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_43374',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__43374___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__43374___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_61124',axiom,
! [V_24Y] :
( c_24__type__61124___24t(V_24Y)
<=> t(V_24Y,c_24__type__61124) ) ).
fof('$tdef_$_type_43284',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__43284___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__43284___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_61924',axiom,
! [V_24Y] :
( c_24__type__61924___24t(V_24Y)
<=> t(V_24Y,c_24__type__61924) ) ).
fof('$tdef_$_type_6165',axiom,
! [V_24Y] :
( c_24__type__6165___24t(V_24Y)
<=> t(V_24Y,c_24__type__6165) ) ).
fof('$tdef_$_type_51826',axiom,
! [V_24Y] :
( c_24__type__51826___24t(V_24Y)
<=> t(V_24Y,c_24__type__51826) ) ).
fof('$tdef_$_type_56919',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__56919___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__56919___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_3221',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3221___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3221___24a1(V_24X1)) ) ).
fof('$tdef_$_type_63713',axiom,
! [V_24Y] :
( c_24__type__63713___24t(V_24Y)
<=> t(V_24Y,c_24__type__63713) ) ).
fof('$tdef_$_type_52541',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__52541___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__52541___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_3983',axiom,
! [V_24Y] :
( c_24__type__3983___24t(V_24Y)
<=> t(V_24Y,c_24__type__3983) ) ).
fof('$tdef_$_type_38673',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__38673___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__38673___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.linear',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3002',axiom,
! [V_24Y] :
( c_24__type__3002___24t(V_24Y)
<=> t(V_24Y,c_24__type__3002) ) ).
fof('$tdef_$_type_60742',axiom,
! [V_24Y] :
( c_24__type__60742___24t(V_24Y)
<=> t(V_24Y,c_24__type__60742) ) ).
fof('$tdef_$_type_4435',axiom,
! [V_24Y] :
( c_24__type__4435___24t(V_24Y)
<=> t(V_24Y,c_24__type__4435) ) ).
fof('$tdef_$_type_56462',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__56462___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__56462___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_6196',axiom,
! [V_24Y] :
( c_24__type__6196___24t(V_24Y)
<=> t(V_24Y,c_24__type__6196) ) ).
fof('$tdef_$_type_43947',axiom,
! [V_24Y] :
( c_24__type__43947___24t(V_24Y)
<=> t(V_24Y,c_24__type__43947) ) ).
fof('$tdef_$_type_4463',axiom,
! [V_24Y] :
( c_24__type__4463___24t(V_24Y)
<=> t(V_24Y,c_24__type__4463) ) ).
fof('$tdef_$_type_37166',axiom,
! [V_24Y] :
( c_24__type__37166___24t(V_24Y)
<=> t(V_24Y,c_24__type__37166) ) ).
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_$_type_3985',axiom,
! [V_24Y] :
( c_24__type__3985___24t(V_24Y)
<=> t(V_24Y,c_24__type__3985) ) ).
fof('$tdef_$_type_3255',axiom,
! [V_24Y] :
( c_24__type__3255___24t(V_24Y)
<=> t(V_24Y,c_24__type__3255) ) ).
fof('$tdef_$_type_4453',axiom,
! [V_24Y] :
( c_24__type__4453___24t(V_24Y)
<=> t(V_24Y,c_24__type__4453) ) ).
fof('$tdef_$_type_37109',axiom,
! [V_24Y] :
( c_24__type__37109___24t(V_24Y)
<=> t(V_24Y,c_24__type__37109) ) ).
fof('$tdef_$_type_60915',axiom,
! [V_24Y] :
( c_24__type__60915___24t(V_24Y)
<=> t(V_24Y,c_24__type__60915) ) ).
fof('$tdef_$_type_37147',axiom,
! [V_24X1,V_24Y] :
( c_24__type__37147___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__37147___24a1(V_24X1)) ) ).
fof('$tdef_$_type_53097',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__53097___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__53097___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_58790',axiom,
! [V_24Y] :
( c_24__type__58790___24t(V_24Y)
<=> t(V_24Y,c_24__type__58790) ) ).
fof('$tdef_Redblack.TREES.tree',axiom,
! [V_24Y] :
( cRedblack_2eTREES_2etree___24t(V_24Y)
<=> t(V_24Y,cRedblack_2eTREES_2etree) ) ).
fof('$tdef_$_type_64648',axiom,
! [V_24Y] :
( c_24__type__64648___24t(V_24Y)
<=> t(V_24Y,c_24__type__64648) ) ).
fof('$tdef_$_type_61437',axiom,
! [V_24Y] :
( c_24__type__61437___24t(V_24Y)
<=> t(V_24Y,c_24__type__61437) ) ).
fof('$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_6675',axiom,
! [V_24Y] :
( c_24__type__6675___24t(V_24Y)
<=> t(V_24Y,c_24__type__6675) ) ).
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_$_type_55967',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__55967___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__55967___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_6761',axiom,
! [V_24Y] :
( c_24__type__6761___24t(V_24Y)
<=> t(V_24Y,c_24__type__6761) ) ).
fof('$tdef_$_type_53465',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__53465___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__53465___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_48305',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__48305___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__48305___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_53603',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__53603___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__53603___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_62151',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__62151___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__62151___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4011',axiom,
! [V_24Y] :
( c_24__type__4011___24t(V_24Y)
<=> t(V_24Y,c_24__type__4011) ) ).
fof('$tdef_$_type_3076',axiom,
! [V_24Y] :
( c_24__type__3076___24t(V_24Y)
<=> t(V_24Y,c_24__type__3076) ) ).
fof('$tdef_$_type_57230',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__57230___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__57230___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_4566',axiom,
! [V_24Y] :
( c_24__type__4566___24t(V_24Y)
<=> t(V_24Y,c_24__type__4566) ) ).
fof('$tdef_$_type_61439',axiom,
! [V_24Y] :
( c_24__type__61439___24t(V_24Y)
<=> t(V_24Y,c_24__type__61439) ) ).
fof('$tdef_$_type_51606',axiom,
! [V_24Y] :
( c_24__type__51606___24t(V_24Y)
<=> t(V_24Y,c_24__type__51606) ) ).
fof('$tdef_$_type_4472',axiom,
! [V_24Y] :
( c_24__type__4472___24t(V_24Y)
<=> t(V_24Y,c_24__type__4472) ) ).
fof('$tdef_$_type_63272',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__63272___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__63272___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_41631',axiom,
! [V_24Y] :
( c_24__type__41631___24t(V_24Y)
<=> t(V_24Y,c_24__type__41631) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_Coq.Init.Specif.sigT',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_58970',axiom,
! [V_24Y] :
( c_24__type__58970___24t(V_24Y)
<=> t(V_24Y,c_24__type__58970) ) ).
fof('$tdef_$_type_38174',axiom,
! [V_24Y] :
( c_24__type__38174___24t(V_24Y)
<=> t(V_24Y,c_24__type__38174) ) ).
fof('$tdef_$_type_4540',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4540___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4540___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_43969',axiom,
! [V_24Y] :
( c_24__type__43969___24t(V_24Y)
<=> t(V_24Y,c_24__type__43969) ) ).
fof('$tdef_$_type_38859',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__38859___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__38859___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_39518',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__39518___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__39518___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_39209',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__39209___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__39209___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4508',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4508___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4508___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_38242',axiom,
! [V_24Y] :
( c_24__type__38242___24t(V_24Y)
<=> t(V_24Y,c_24__type__38242) ) ).
fof('$tdef_$_type_62858',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__62858___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__62858___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_63546',axiom,
! [V_24Y] :
( c_24__type__63546___24t(V_24Y)
<=> t(V_24Y,c_24__type__63546) ) ).
fof('$tdef_$_type_63892',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__63892___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__63892___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_64023',axiom,
! [V_24Y] :
( c_24__type__64023___24t(V_24Y)
<=> t(V_24Y,c_24__type__64023) ) ).
fof('$tdef_$_type_4236',axiom,
! [V_24Y] :
( c_24__type__4236___24t(V_24Y)
<=> t(V_24Y,c_24__type__4236) ) ).
fof('$tdef_$_type_6193',axiom,
! [V_24Y] :
( c_24__type__6193___24t(V_24Y)
<=> t(V_24Y,c_24__type__6193) ) ).
fof('$tdef_$_type_38766',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__38766___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__38766___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_46252',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__46252___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__46252___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.EnvRing.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_56975',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__56975___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__56975___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_59767',axiom,
! [V_24Y] :
( c_24__type__59767___24t(V_24Y)
<=> t(V_24Y,c_24__type__59767) ) ).
fof('$tdef_$_type_51589',axiom,
! [V_24Y] :
( c_24__type__51589___24t(V_24Y)
<=> t(V_24Y,c_24__type__51589) ) ).
fof('$tdef_$_type_63295',axiom,
! [V_24Y] :
( c_24__type__63295___24t(V_24Y)
<=> t(V_24Y,c_24__type__63295) ) ).
fof('$tdef_$_type_3269',axiom,
! [V_24Y] :
( c_24__type__3269___24t(V_24Y)
<=> t(V_24Y,c_24__type__3269) ) ).
fof('$tdef_$_type_60391',axiom,
! [V_24Y] :
( c_24__type__60391___24t(V_24Y)
<=> t(V_24Y,c_24__type__60391) ) ).
fof('$tdef_$_type_4033',axiom,
! [V_24Y] :
( c_24__type__4033___24t(V_24Y)
<=> t(V_24Y,c_24__type__4033) ) ).
fof('$tdef_$_type_4007',axiom,
! [V_24Y] :
( c_24__type__4007___24t(V_24Y)
<=> t(V_24Y,c_24__type__4007) ) ).
fof('$tdef_$_type_3108',axiom,
! [V_24Y] :
( c_24__type__3108___24t(V_24Y)
<=> t(V_24Y,c_24__type__3108) ) ).
fof('$tdef_$_type_37112',axiom,
! [V_24Y] :
( c_24__type__37112___24t(V_24Y)
<=> t(V_24Y,c_24__type__37112) ) ).
fof('$tdef_$_type_52287',axiom,
! [V_24Y] :
( c_24__type__52287___24t(V_24Y)
<=> t(V_24Y,c_24__type__52287) ) ).
fof('$tdef_$_type_38186',axiom,
! [V_24Y] :
( c_24__type__38186___24t(V_24Y)
<=> t(V_24Y,c_24__type__38186) ) ).
fof('$tdef_$_type_61503',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__61503___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__61503___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_61030',axiom,
! [V_24Y] :
( c_24__type__61030___24t(V_24Y)
<=> t(V_24Y,c_24__type__61030) ) ).
fof('$tdef_$_type_43920',axiom,
! [V_24Y] :
( c_24__type__43920___24t(V_24Y)
<=> t(V_24Y,c_24__type__43920) ) ).
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_$_type_4264',axiom,
! [V_24Y] :
( c_24__type__4264___24t(V_24Y)
<=> t(V_24Y,c_24__type__4264) ) ).
fof('$tdef_$_type_43926',axiom,
! [V_24Y] :
( c_24__type__43926___24t(V_24Y)
<=> t(V_24Y,c_24__type__43926) ) ).
fof('$tdef_$_type_42487',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__42487___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__42487___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_64086',axiom,
! [V_24Y] :
( c_24__type__64086___24t(V_24Y)
<=> t(V_24Y,c_24__type__64086) ) ).
fof('$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_56839',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__56839___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__56839___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_4448',axiom,
! [V_24Y] :
( c_24__type__4448___24t(V_24Y)
<=> t(V_24Y,c_24__type__4448) ) ).
fof('$tdef_$_type_61411',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__61411___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__61411___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_60982',axiom,
! [V_24Y] :
( c_24__type__60982___24t(V_24Y)
<=> t(V_24Y,c_24__type__60982) ) ).
fof('$tdef_$_type_3218',axiom,
! [V_24Y] :
( c_24__type__3218___24t(V_24Y)
<=> t(V_24Y,c_24__type__3218) ) ).
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_$_type_52266',axiom,
! [V_24Y] :
( c_24__type__52266___24t(V_24Y)
<=> t(V_24Y,c_24__type__52266) ) ).
fof('$tdef_$_type_38477',axiom,
! [V_24Y] :
( c_24__type__38477___24t(V_24Y)
<=> t(V_24Y,c_24__type__38477) ) ).
fof('$tdef_$_type_52721',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__52721___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__52721___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_43677',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__43677___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__43677___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_64642',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__64642___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__64642___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4120',axiom,
! [V_24Y] :
( c_24__type__4120___24t(V_24Y)
<=> t(V_24Y,c_24__type__4120) ) ).
fof('$tdef_$_type_39539',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__39539___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__39539___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_64775',axiom,
! [V_24Y] :
( c_24__type__64775___24t(V_24Y)
<=> t(V_24Y,c_24__type__64775) ) ).
fof('$tdef_$_type_39236',axiom,
! [V_24X1,V_24Y] :
( c_24__type__39236___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__39236___24a1(V_24X1)) ) ).
fof('$tdef_$_type_56883',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__56883___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__56883___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_52667',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__52667___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__52667___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_62337',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__62337___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__62337___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3214',axiom,
! [V_24Y] :
( c_24__type__3214___24t(V_24Y)
<=> t(V_24Y,c_24__type__3214) ) ).
fof('$tdef_$_type_55346',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__55346___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__55346___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('$tdef_VFA.SearchTree.key',axiom,
! [V_24Y] :
( cVFA_2eSearchTree_2ekey___24t(V_24Y)
<=> t(V_24Y,cVFA_2eSearchTree_2ekey) ) ).
fof('$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_61887',axiom,
! [V_24Y] :
( c_24__type__61887___24t(V_24Y)
<=> t(V_24Y,c_24__type__61887) ) ).
fof('$tdef_$_type_57188',axiom,
! [V_24Y] :
( c_24__type__57188___24t(V_24Y)
<=> t(V_24Y,c_24__type__57188) ) ).
fof('$tdef_$_type_64082',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__64082___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__64082___24a2(V_24X1,V_24X2)) ) ).
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_$_type_37152',axiom,
! [V_24X1,V_24Y] :
( c_24__type__37152___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__37152___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_54707',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__54707___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__54707___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_42511',axiom,
! [V_24Y] :
( c_24__type__42511___24t(V_24Y)
<=> t(V_24Y,c_24__type__42511) ) ).
fof('$tdef_$_type_51611',axiom,
! [V_24Y] :
( c_24__type__51611___24t(V_24Y)
<=> t(V_24Y,c_24__type__51611) ) ).
fof('$tdef_$_type_51586',axiom,
! [V_24Y] :
( c_24__type__51586___24t(V_24Y)
<=> t(V_24Y,c_24__type__51586) ) ).
fof('$tdef_$_type_4496',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4496___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4496___24a1(V_24X1)) ) ).
fof('$tdef_$_type_63609',axiom,
! [V_24Y] :
( c_24__type__63609___24t(V_24Y)
<=> t(V_24Y,c_24__type__63609) ) ).
fof('$tdef_$_type_53660',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__53660___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__53660___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_39358',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__39358___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__39358___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Init.Datatypes.prod',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_61514',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__61514___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__61514___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_58134',axiom,
! [V_24Y] :
( c_24__type__58134___24t(V_24Y)
<=> t(V_24Y,c_24__type__58134) ) ).
fof('$tdef_$_type_37140',axiom,
! [V_24Y] :
( c_24__type__37140___24t(V_24Y)
<=> t(V_24Y,c_24__type__37140) ) ).
fof('$tdef_$_type_4022',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4022___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4022___24a1(V_24X1)) ) ).
fof('$tdef_$_type_63931',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__63931___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__63931___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
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_$_type_49996',axiom,
! [V_24Y] :
( c_24__type__49996___24t(V_24Y)
<=> t(V_24Y,c_24__type__49996) ) ).
fof('$tdef_$_type_57049',axiom,
! [V_24Y] :
( c_24__type__57049___24t(V_24Y)
<=> t(V_24Y,c_24__type__57049) ) ).
fof('$tdef_$_type_64809',axiom,
! [V_24Y] :
( c_24__type__64809___24t(V_24Y)
<=> t(V_24Y,c_24__type__64809) ) ).
fof('$tdef_$_type_3247',axiom,
! [V_24Y] :
( c_24__type__3247___24t(V_24Y)
<=> t(V_24Y,c_24__type__3247) ) ).
fof('$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_6169',axiom,
! [V_24Y] :
( c_24__type__6169___24t(V_24Y)
<=> t(V_24Y,c_24__type__6169) ) ).
fof('$tdef_$_type_3106',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3106___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3106___24a1(V_24X1)) ) ).
fof('$tdef_$_type_58151',axiom,
! [V_24Y] :
( c_24__type__58151___24t(V_24Y)
<=> t(V_24Y,c_24__type__58151) ) ).
fof('$tdef_$_type_4547',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__4547___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__4547___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_4468',axiom,
! [V_24Y] :
( c_24__type__4468___24t(V_24Y)
<=> t(V_24Y,c_24__type__4468) ) ).
fof('$tdef_$_type_144',axiom,
! [V_24Y] :
( c_24__type__144___24t(V_24Y)
<=> t(V_24Y,c_24__type__144) ) ).
fof('$tdef_$_type_61935',axiom,
! [V_24Y] :
( c_24__type__61935___24t(V_24Y)
<=> t(V_24Y,c_24__type__61935) ) ).
fof('$tdef_$_type_46944',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__46944___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__46944___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_4663',axiom,
! [V_24Y] :
( c_24__type__4663___24t(V_24Y)
<=> t(V_24Y,c_24__type__4663) ) ).
fof('$tdef_$_type_38198',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38198___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38198___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_57037',axiom,
! [V_24Y] :
( c_24__type__57037___24t(V_24Y)
<=> t(V_24Y,c_24__type__57037) ) ).
fof('$tdef_$_type_4267',axiom,
! [V_24Y] :
( c_24__type__4267___24t(V_24Y)
<=> t(V_24Y,c_24__type__4267) ) ).
fof('$tdef_$_type_38233',axiom,
! [V_24Y] :
( c_24__type__38233___24t(V_24Y)
<=> t(V_24Y,c_24__type__38233) ) ).
fof('$tdef_$_type_48951',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__48951___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__48951___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_51338',axiom,
! [V_24Y] :
( c_24__type__51338___24t(V_24Y)
<=> t(V_24Y,c_24__type__51338) ) ).
fof('$tdef_$_type_52604',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__52604___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__52604___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_64812',axiom,
! [V_24Y] :
( c_24__type__64812___24t(V_24Y)
<=> t(V_24Y,c_24__type__64812) ) ).
fof('$tdef_$_type_64779',axiom,
! [V_24Y] :
( c_24__type__64779___24t(V_24Y)
<=> t(V_24Y,c_24__type__64779) ) ).
fof('$tdef_$_type_64637',axiom,
! [V_24Y] :
( c_24__type__64637___24t(V_24Y)
<=> t(V_24Y,c_24__type__64637) ) ).
fof('$tdef_$_type_3274',axiom,
! [V_24Y] :
( c_24__type__3274___24t(V_24Y)
<=> t(V_24Y,c_24__type__3274) ) ).
fof('$tdef_$_type_55754',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__55754___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__55754___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('$tdef_Coq.Vectors.VectorDef.t',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_61884',axiom,
! [V_24Y] :
( c_24__type__61884___24t(V_24Y)
<=> t(V_24Y,c_24__type__61884) ) ).
fof('$tdef_$_type_4286',axiom,
! [V_24Y] :
( c_24__type__4286___24t(V_24Y)
<=> t(V_24Y,c_24__type__4286) ) ).
fof('$tdef_Redblack.color',axiom,
! [V_24Y] :
( cRedblack_2ecolor___24t(V_24Y)
<=> t(V_24Y,cRedblack_2ecolor) ) ).
fof('$tdef_$_type_39532',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__39532___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__39532___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_39367',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__39367___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__39367___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_3302',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3302___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3302___24a1(V_24X1)) ) ).
fof('$tdef_$_type_58129',axiom,
! [V_24Y] :
( c_24__type__58129___24t(V_24Y)
<=> t(V_24Y,c_24__type__58129) ) ).
fof('$tdef_$_type_53687',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__53687___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__53687___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_4115',axiom,
! [V_24Y] :
( c_24__type__4115___24t(V_24Y)
<=> t(V_24Y,c_24__type__4115) ) ).
fof('$tdef_$_type_39353',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__39353___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__39353___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_55133',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__55133___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__55133___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_45906',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__45906___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__45906___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_64806',axiom,
! [V_24Y] :
( c_24__type__64806___24t(V_24Y)
<=> t(V_24Y,c_24__type__64806) ) ).
fof('$tdef_$_type_37116',axiom,
! [V_24Y] :
( c_24__type__37116___24t(V_24Y)
<=> t(V_24Y,c_24__type__37116) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_60992',axiom,
! [V_24Y] :
( c_24__type__60992___24t(V_24Y)
<=> t(V_24Y,c_24__type__60992) ) ).
fof('$tdef_$_type_43082',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__43082___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__43082___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_VFA.Extract.int',axiom,
! [V_24Y] :
( cVFA_2eExtract_2eint___24t(V_24Y)
<=> t(V_24Y,cVFA_2eExtract_2eint) ) ).
fof('$tdef_$_type_3507',axiom,
! [V_24Y] :
( c_24__type__3507___24t(V_24Y)
<=> t(V_24Y,c_24__type__3507) ) ).
fof('$tdef_$_type_45237',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__45237___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__45237___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_6709',axiom,
! [V_24Y] :
( c_24__type__6709___24t(V_24Y)
<=> t(V_24Y,c_24__type__6709) ) ).
fof('$tdef_$_type_61362',axiom,
! [V_24Y] :
( c_24__type__61362___24t(V_24Y)
<=> t(V_24Y,c_24__type__61362) ) ).
fof('$tdef_$_type_43923',axiom,
! [V_24Y] :
( c_24__type__43923___24t(V_24Y)
<=> t(V_24Y,c_24__type__43923) ) ).
fof('$tdef_$_type_37164',axiom,
! [V_24Y] :
( c_24__type__37164___24t(V_24Y)
<=> t(V_24Y,c_24__type__37164) ) ).
fof('$tdef_$_type_63548',axiom,
! [V_24Y] :
( c_24__type__63548___24t(V_24Y)
<=> t(V_24Y,c_24__type__63548) ) ).
fof('$tdef_$_type_3502',axiom,
! [V_24Y] :
( c_24__type__3502___24t(V_24Y)
<=> t(V_24Y,c_24__type__3502) ) ).
fof('$tdef_$_type_46598',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__46598___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__46598___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_59794',axiom,
! [V_24Y] :
( c_24__type__59794___24t(V_24Y)
<=> t(V_24Y,c_24__type__59794) ) ).
fof('$tdef_$_type_61058',axiom,
! [V_24Y] :
( c_24__type__61058___24t(V_24Y)
<=> t(V_24Y,c_24__type__61058) ) ).
fof('$tdef_$_type_3436',axiom,
! [V_24Y] :
( c_24__type__3436___24t(V_24Y)
<=> t(V_24Y,c_24__type__3436) ) ).
fof('$tdef_$_type_3314',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3314___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3314___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_52784',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__52784___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__52784___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_V',axiom,
! [V_24Y] :
( cV___24t(V_24Y)
<=> t(V_24Y,cV) ) ).
fof('$tdef_$_type_139',axiom,
! [V_24Y] :
( c_24__type__139___24t(V_24Y)
<=> t(V_24Y,c_24__type__139) ) ).
fof('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).
fof('$tdef_$_type_61955',axiom,
! [V_24Y] :
( c_24__type__61955___24t(V_24Y)
<=> t(V_24Y,c_24__type__61955) ) ).
fof('$tdef_$_type_58842',axiom,
! [V_24Y] :
( c_24__type__58842___24t(V_24Y)
<=> t(V_24Y,c_24__type__58842) ) ).
fof('$tdef_$_type_42648',axiom,
! [V_24Y] :
( c_24__type__42648___24t(V_24Y)
<=> t(V_24Y,c_24__type__42648) ) ).
fof('$tdef_$_type_37236',axiom,
! [V_24Y] :
( c_24__type__37236___24t(V_24Y)
<=> t(V_24Y,c_24__type__37236) ) ).
fof('$tdef_$_type_64787',axiom,
! [V_24Y] :
( c_24__type__64787___24t(V_24Y)
<=> t(V_24Y,c_24__type__64787) ) ).
fof('$tdef_$_type_49679',axiom,
! [V_24Y] :
( c_24__type__49679___24t(V_24Y)
<=> t(V_24Y,c_24__type__49679) ) ).
fof('$tdef_VFA.SearchTree.tree',axiom,
! [V_24X1,V_24Y] :
( cVFA_2eSearchTree_2etree___24t(V_24X1,V_24Y)
<=> t(V_24Y,cVFA_2eSearchTree_2etree___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43954',axiom,
! [V_24Y] :
( c_24__type__43954___24t(V_24Y)
<=> t(V_24Y,c_24__type__43954) ) ).
fof('$tdef_$_type_56562',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__56562___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__56562___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_4110',axiom,
! [V_24Y] :
( c_24__type__4110___24t(V_24Y)
<=> t(V_24Y,c_24__type__4110) ) ).
fof('$tdef_$_type_4009',axiom,
! [V_24Y] :
( c_24__type__4009___24t(V_24Y)
<=> t(V_24Y,c_24__type__4009) ) ).
fof('$tdef_$_type_38133',axiom,
! [V_24Y] :
( c_24__type__38133___24t(V_24Y)
<=> t(V_24Y,c_24__type__38133) ) ).
fof('$tdef_$_type_58161',axiom,
! [V_24X1,V_24Y] :
( c_24__type__58161___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__58161___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4294',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4294___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4294___24a1(V_24X1)) ) ).
fof('$tdef_$_type_39218',axiom,
! [V_24X1,V_24Y] :
( c_24__type__39218___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__39218___24a1(V_24X1)) ) ).
fof('$tdef_$_type_62921',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__62921___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__62921___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_58849',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__58849___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__58849___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_63970',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__63970___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__63970___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_38146',axiom,
! [V_24Y] :
( c_24__type__38146___24t(V_24Y)
<=> t(V_24Y,c_24__type__38146) ) ).
fof('$tdef_$_type_37154',axiom,
! [V_24Y] :
( c_24__type__37154___24t(V_24Y)
<=> t(V_24Y,c_24__type__37154) ) ).
fof('$tdef_$_type_55559',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__55559___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__55559___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_61245',axiom,
! [V_24Y] :
( c_24__type__61245___24t(V_24Y)
<=> t(V_24Y,c_24__type__61245) ) ).
fof('$tdef_$_type_4038',axiom,
! [V_24Y] :
( c_24__type__4038___24t(V_24Y)
<=> t(V_24Y,c_24__type__4038) ) ).
fof('$tdef_$_type_3392',axiom,
! [V_24Y] :
( c_24__type__3392___24t(V_24Y)
<=> t(V_24Y,c_24__type__3392) ) ).
fof('$tdef_$_type_4456',axiom,
! [V_24Y] :
( c_24__type__4456___24t(V_24Y)
<=> t(V_24Y,c_24__type__4456) ) ).
fof('$tdef_$_type_39868',axiom,
! [V_24X1,V_24Y] :
( c_24__type__39868___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__39868___24a1(V_24X1)) ) ).
fof('$tdef_$_type_37169',axiom,
! [V_24X1,V_24Y] :
( c_24__type__37169___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__37169___24a1(V_24X1)) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__c] :
( cRedblack_2ecolor___24t(V0__c)
=> ! [V1__l] :
( cRedblack_2eTREES_2etree___24t(V1__l)
=> ! [V2__k] :
( cRedblack_2ekey___24t(V2__k)
=> ! [V3__v] :
( cV___24t(V3__v)
=> ! [V4__r] :
( cRedblack_2eTREES_2etree___24t(V4__r)
=> cRedblack_2eTREES_2eT___24a5(V0__c,V1__l,V2__k,V3__v,V4__r) != cRedblack_2eTREES_2eE ) ) ) ) ) ).
%------------------------------------------------------------------------------