TPTP Problem File: SEV656+1.p
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%------------------------------------------------------------------------------
% File : SEV656+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - Maplists ad list stutters app conv l
% 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 : Maplists.ad.list.stutters.app.conv.l.p [Kal26]
% Status : Theorem
% Rating : 0.61 v9.3.0
% Syntax : Number of formulae : 3042 (1169 unt; 0 def)
% Number of atoms : 11256 (3733 equ)
% Maximal formula atoms : 268 ( 3 avg)
% Number of connectives : 8359 ( 145 ~; 874 |;1966 &)
% (1057 <=>;4317 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 7 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 503 ( 502 usr; 0 prp; 1-23 aty)
% Number of functors : 1888 (1888 usr;1163 con; 0-22 aty)
% Number of variables : 10134 (9300 !; 834 ?)
% 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$4687',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_244687___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
| ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_244687___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$4692',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_244692___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_244692___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$53998',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,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_2454059___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_2453998___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_2454059___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_2453998___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$54059',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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_2454100___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_2454059___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_2454100___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_2454059___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$54100',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__8)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454125___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454100___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9) = cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__4,Vv__CANONICAL__9) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454125___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454100___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$54125',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454138___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454125___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__3,Vv__CANONICAL__7) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454138___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454125___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$54138',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454143___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454138___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__5) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454143___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454138___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$54143',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( ( cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454143___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) )
| ( cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454143___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$54376',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454376___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 )
| ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454376___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$55257',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455257___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(Vv__CANONICAL__0) )
| ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455257___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$55350',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( ( cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455350___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) )
| ( cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455350___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$55409',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455412___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455409___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esubset___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455412___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455409___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$55412',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ( ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455412___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455412___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$55627',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455627___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = c_24__lam__55651___24a1(Vv__CANONICAL__0) )
| ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455627___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = c_24__lam__55690___24a1(Vv__CANONICAL__0) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$56382',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__type__337___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eodd___24a1(Vv__CANONICAL__1)),cCoq_2eInit_2eNat_2eodd___24a1(Vv__CANONICAL__2)) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2456382___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ( happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eodd___24a1(Vv__CANONICAL__1)),cCoq_2eInit_2eNat_2eodd___24a1(Vv__CANONICAL__2)) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2456382___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$59771',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__type__55427___24t(Vv__CANONICAL__0)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459775___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459771___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459775___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459771___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exexists___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eNumbers_2eBinNums_2exI___24a1(Vv__CANONICAL__1)) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$59775',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459775___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__0,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev___24a1(Vv__CANONICAL__1)) )
| ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459775___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$9505',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249505___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3)) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249505___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3)) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$9553',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249553___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249553___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$9625',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249625___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4)) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249625___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$9641',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249641___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4)) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249641___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$975',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24975___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0),c_24__let__var__8__m__965__968___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24975___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,c_24__let__var__8__m__965__968___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5),cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$28937',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2429024___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2428937___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__28941] :
( t(Vvar__1___24Anonymous__28941,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__28942] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__28942)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2429024___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__28941,Vvar__2___24Anonymous__28942)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2428937___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__28941,c_24__fix__29069__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__28942,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$29024',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2429024___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__29028] :
( t(Vvar__1___24Anonymous__29028,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__29029] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__29029)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__29028,Vvar__2___24Anonymous__29029)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2429024___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__29028,c_24__fix__29069__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__29029,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$21717',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__13844___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__21722] :
( t(Vvar__2___24Anonymous__21722,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__21723] :
( t(Vvar__3___24Anonymous__21723,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__21722,Vvar__3___24Anonymous__21723)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2421717___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__21722)),Vvar__3___24Anonymous__21723)))) ) ) ) ) ) ) ) ) ).
fof('$_def_$_cast_322',axiom,
! [V1__b2] : c_24__cast__322___24a1(V1__b2) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__323,c_24__prop__324___24a1(V1__b2)) ).
fof('$_def_$_cast_325',axiom,
! [V1__b2] : c_24__cast__325___24a1(V1__b2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__326___24a1(V1__b2),c_24__prop__327___24a1(V1__b2)) ).
fof('$_def_$_cast_55541',axiom,
! [V1__b2] : c_24__cast__55541___24a1(V1__b2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__55542___24a1(V1__b2),c_24__prop__55543___24a1(V1__b2)) ).
fof('$_def_$_cast_55544',axiom,
! [V1__b2] : c_24__cast__55544___24a1(V1__b2) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__55545,c_24__prop__55546___24a1(V1__b2)) ).
fof('$_def_$_cast_55652',axiom,
! [Vv__CANONICAL__0] : c_24__cast__55652___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eLogic_2eand__rec___24a4(c_24__prop__55653___24a1(Vv__CANONICAL__0),c_24__prop__55654___24a1(Vv__CANONICAL__0),cCoq_2eBool_2eBool_2ereflect___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2etrue),c_24__lam__55667___24a1(Vv__CANONICAL__0)) ).
fof('$_def_$_cast_55691',axiom,
! [Vv__CANONICAL__0] : c_24__cast__55691___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eLogic_2eand__rec___24a4(c_24__prop__55692___24a1(Vv__CANONICAL__0),c_24__prop__55693___24a1(Vv__CANONICAL__0),cCoq_2eBool_2eBool_2ereflect___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2efalse),c_24__lam__55703___24a1(Vv__CANONICAL__0)) ).
fof('$_def_$_cast_55706',axiom,
! [Vv__CANONICAL__0] : c_24__cast__55706___24a1(Vv__CANONICAL__0) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vv__CANONICAL__0) ).
fof('$_def_$_cast_56861',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__cast__56861___24a2(V0__x,V1__y) = c_24__lam__56864___24a2(V0__x,V1__y) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__cast__56861___24a2(V0__x,V1__y) = c_24__lam__56985___24a2(V0__x,V1__y) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_14528',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__14528___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_17045',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__17048] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17048)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17048)
& c_24__let__16__mkpow__17045___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__17049] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17049)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17049)
& c_24__let__16__mkpow__17045___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__17045___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_mkopp_pow_17046',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__17046___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__17045___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_17047',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__17047___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__17045___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_var_6_p_17619_17622',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__17618] : c_24__let__var__6__p__17619__17622___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__17618) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__17618) ).
fof('$_def_$_let_var_6_p_17621_17623',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__17620] : c_24__let__var__6__p__17621__17623___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__17620) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__17620) ).
fof('$_def_$_let_var_8_m_965_968',axiom,
! [V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__963] : c_24__let__var__8__m__965__968___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__963) = cIntMap_2eMap_2eMapPut1___24a6(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27,Vvar__0___24Anonymous__963) ).
fof('$_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('$_def_Coq.Arith.PeanoNat.Nat.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.Bool.Bool.andb_false_elim',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eandb__false__elim___24a1(V0__b1) = c_24__cast__55541 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eandb__false__elim___24a1(V0__b1) = c_24__cast__55544 ) ) ) ).
fof('$_def_Coq.Bool.Bool.eqb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.eqb_spec',axiom,
! [V0__b,V1__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
=> ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b_27 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb__spec___24a2(V0__b,V1__b_27) = cCoq_2eBool_2eBool_2eReflectT___24a2(c_24__prop__55719,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2etrue)) )
| ( V1__b_27 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb__spec___24a2(V0__b,V1__b_27) = cCoq_2eBool_2eBool_2eReflectF___24a1(c_24__prop__55720) ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
=> ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b_27 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb__spec___24a2(V0__b,V1__b_27) = cCoq_2eBool_2eBool_2eReflectF___24a1(c_24__prop__55722) )
| ( V1__b_27 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb__spec___24a2(V0__b,V1__b_27) = cCoq_2eBool_2eBool_2eReflectT___24a2(c_24__prop__55724,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2efalse)) ) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.iff_reflect',axiom,
! [V0__P,V1__b] : cCoq_2eBool_2eBool_2eiff__reflect___24a2(V0__P,V1__b) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455627___24a2(V0__P,V1__b) ).
fof('$_def_Coq.Bool.Bool.orb_true_elim',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eorb__true__elim___24a1(V0__b1) = c_24__cast__322 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eorb__true__elim___24a1(V0__b1) = c_24__cast__325 ) ) ) ).
fof('$_def_Coq.Bool.Sumbool.bool_eq_rec',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eSumbool_2ebool__eq__rec___24a1(V0__b) = c_24__lam__56745 )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eSumbool_2ebool__eq__rec___24a1(V0__b) = c_24__lam__56752 ) ) ) ).
fof('$_def_Coq.Bool.Sumbool.sumbool_of_bool',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eSumbool_2esumbool__of__bool___24a1(V0__b) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24__prop__710,c_24__prop__711,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2etrue)) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eSumbool_2esumbool__of__bool___24a1(V0__b) = cCoq_2eInit_2eSpecif_2eright___24a3(c_24__prop__712,c_24__prop__713,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2efalse)) ) ) ) ).
fof('$_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__55038] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__55038)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__55038)
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V0__s)
<=> ! [V1__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__a)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__a,V0__s) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__i,V1__t)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__i,V1__t) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.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__45575] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45575)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45575)
& 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__45575,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf)) )
| ? [Vvar__0___24Anonymous__45576] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45576)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45576)
& 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__45576,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__45577] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__45577)
& ? [Vvar__1___24Anonymous__45578] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__45578)
& ? [Vvar__2___24Anonymous__45579] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__45579)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__45577,Vvar__1___24Anonymous__45578,Vvar__2___24Anonymous__45579)
& ( ? [Vvar__0___24Anonymous__45592] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45592)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45592)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__45577,Vvar__1___24Anonymous__45578,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__45592,Vvar__2___24Anonymous__45579)) )
| ? [Vvar__0___24Anonymous__45593] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45593)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45593)
& 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__45593,Vvar__0___24Anonymous__45577),Vvar__1___24Anonymous__45578,Vvar__2___24Anonymous__45579) )
| ( 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__45577,cCoq_2eInit_2eDatatypes_2etrue,Vvar__2___24Anonymous__45579) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.cardinal',axiom,
! [V1__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__m)
=> ( ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V1__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__55430] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55430)
& ? [Vvar__1___24Anonymous__55431] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55431)
& ? [Vvar__2___24Anonymous__55432] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__55432)
& ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55431)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__55430,Vvar__1___24Anonymous__55431,Vvar__2___24Anonymous__55432)
& ( ( Vvar__1___24Anonymous__55431 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V1__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__0___24Anonymous__55430),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__2___24Anonymous__55432))) )
| ( Vvar__1___24Anonymous__55431 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__0___24Anonymous__55430),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__2___24Anonymous__55432)) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.choose',axiom,
! [V1__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__m)
=> ( ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(V1__m) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) )
| ? [Vvar__0___24Anonymous__57112] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__57112)
& ? [Vvar__1___24Anonymous__57113] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__57113)
& ? [Vvar__2___24Anonymous__57114] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__57114)
& ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__57113)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__57112,Vvar__1___24Anonymous__57113,Vvar__2___24Anonymous__57114)
& ( ( Vvar__1___24Anonymous__57113 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(V1__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2exH) )
| ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__57112)
=> ( Vvar__1___24Anonymous__57113 = cCoq_2eInit_2eDatatypes_2efalse
& ( ? [Vvar__1___24Anonymous__57129] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1___24Anonymous__57129)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(Vvar__0___24Anonymous__57112) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,Vvar__1___24Anonymous__57129)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(V1__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__1___24Anonymous__57129)) )
| ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(Vvar__0___24Anonymous__57112) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(V1__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eomap___24a2(cCoq_2eNumbers_2eBinNums_2exI,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(Vvar__2___24Anonymous__57114)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__23776] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__23776)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__23776) ) ).
fof('$_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.equal',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_2eequal___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(V2__m_27) )
| ? [Vvar__0___24Anonymous__55310] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55310)
& ? [Vvar__1___24Anonymous__55311] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55311)
& ? [Vvar__2___24Anonymous__55312] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__55312)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m_27)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__55310,Vvar__1___24Anonymous__55311,Vvar__2___24Anonymous__55312)
& ( ( V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(V1__m) )
| ? [Vvar__0___24Anonymous__55334] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55334)
& ? [Vvar__1___24Anonymous__55335] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55335)
& ? [Vvar__2___24Anonymous__55336] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__55336)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55310)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55311)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55334)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55335)
=> ( V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__55334,Vvar__1___24Anonymous__55335,Vvar__2___24Anonymous__55336)
& ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455350___24a4(Vvar__0___24Anonymous__55310,Vvar__1___24Anonymous__55311,Vvar__0___24Anonymous__55334,Vvar__1___24Anonymous__55335) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(Vvar__2___24Anonymous__55312,Vvar__2___24Anonymous__55336) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455350___24a4(Vvar__0___24Anonymous__55310,Vvar__1___24Anonymous__55311,Vvar__0___24Anonymous__55334,Vvar__1___24Anonymous__55335) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(V1__m,V2__m_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.exists_',axiom,
! [V0__f,V1__m] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eexists_____24a2(V0__f,V1__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exexists___24a3(V0__f,V1__m,cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.filter',axiom,
! [V0__f,V1__m] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter___24a2(V0__f,V1__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfilter___24a3(V0__f,V1__m,cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.fold',axiom,
! [V0__B,V1__f,V2__m,V3__i] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold___24a4(V0__B,V1__f,V2__m,V3__i) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold___24a5(V0__B,V1__f,V2__m,V3__i,cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.for_all',axiom,
! [V0__f,V1__m] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efor__all___24a2(V0__f,V1__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exforall___24a3(V0__f,V1__m,cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.inter',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_2einter___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf )
| ? [Vvar__0___24Anonymous__55284] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55284)
& ? [Vvar__1___24Anonymous__55285] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55285)
& ? [Vvar__2___24Anonymous__55286] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__55286)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m_27)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__55284,Vvar__1___24Anonymous__55285,Vvar__2___24Anonymous__55286)
& ( ( V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf )
| ? [Vvar__0___24Anonymous__55302] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55302)
& ? [Vvar__1___24Anonymous__55303] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55303)
& ? [Vvar__2___24Anonymous__55304] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__55304)
& V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__55302,Vvar__1___24Anonymous__55303,Vvar__2___24Anonymous__55304)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(Vvar__0___24Anonymous__55284,Vvar__0___24Anonymous__55302),cCoq_2eInit_2eDatatypes_2eandb___24a2(Vvar__1___24Anonymous__55285,Vvar__1___24Anonymous__55303),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(Vvar__2___24Anonymous__55286,Vvar__2___24Anonymous__55304)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.is_empty',axiom,
! [V1__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__m)
=> ( ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(V1__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__55243] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55243)
& ? [Vvar__1___24Anonymous__55244] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55244)
& ? [Vvar__2___24Anonymous__55245] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__55245)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55243)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55244)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__55243,Vvar__1___24Anonymous__55244,Vvar__2___24Anonymous__55245)
& ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455257___24a2(Vvar__0___24Anonymous__55243,Vvar__1___24Anonymous__55244) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(V1__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(Vvar__2___24Anonymous__55245) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455257___24a2(Vvar__0___24Anonymous__55243,Vvar__1___24Anonymous__55244) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__23779] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__23779)
& ? [Vvar__1___24Anonymous__23780] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__23780)
& ? [Vvar__2___24Anonymous__23781] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__23781)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__23779,Vvar__1___24Anonymous__23780,Vvar__2___24Anonymous__23781)
& ( ? [Vvar__0___24Anonymous__23794] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23794)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23794)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__23794,Vvar__2___24Anonymous__23781) )
| ? [Vvar__0___24Anonymous__23795] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23795)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23795)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__23795,Vvar__0___24Anonymous__23779) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__23780 ) ) ) ) ) ) ) ) ) ).
fof('$_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__55265] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55265)
& ? [Vvar__1___24Anonymous__55266] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55266)
& ? [Vvar__2___24Anonymous__55267] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__55267)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__55265,Vvar__1___24Anonymous__55266,Vvar__2___24Anonymous__55267)
& ( ? [Vvar__0___24Anonymous__55280] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55280)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55280)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(Vvar__0___24Anonymous__55265,Vvar__1___24Anonymous__55266,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(Vvar__0___24Anonymous__55280,Vvar__2___24Anonymous__55267)) )
| ? [Vvar__0___24Anonymous__55281] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55281)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55281)
& 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__55281,Vvar__0___24Anonymous__55265),Vvar__1___24Anonymous__55266,Vvar__2___24Anonymous__55267) )
| ( 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__55265,cCoq_2eInit_2eDatatypes_2efalse,Vvar__2___24Anonymous__55267) ) ) ) ) ) ) ) ) ) ).
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.subset',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_2esubset___24a2(V1__m,V2__m_27) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__55359] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55359)
& ? [Vvar__1___24Anonymous__55360] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55360)
& ? [Vvar__2___24Anonymous__55361] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__55361)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m_27)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__55359,Vvar__1___24Anonymous__55360,Vvar__2___24Anonymous__55361)
& ( ( V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esubset___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(V1__m) )
| ? [Vvar__0___24Anonymous__55386] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55386)
& ? [Vvar__1___24Anonymous__55387] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55387)
& ? [Vvar__2___24Anonymous__55388] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__55388)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55359)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55360)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__55386)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__55387)
=> ( V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__55386,Vvar__1___24Anonymous__55387,Vvar__2___24Anonymous__55388)
& ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455409___24a4(Vvar__0___24Anonymous__55359,Vvar__1___24Anonymous__55360,Vvar__0___24Anonymous__55386,Vvar__1___24Anonymous__55387) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esubset___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esubset___24a2(Vvar__2___24Anonymous__55361,Vvar__2___24Anonymous__55388) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455409___24a4(Vvar__0___24Anonymous__55359,Vvar__1___24Anonymous__55360,Vvar__0___24Anonymous__55386,Vvar__1___24Anonymous__55387) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esubset___24a2(V1__m,V2__m_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__23777] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__23777)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__23777) ) ).
fof('$_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__23800] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__23800)
& ? [Vvar__1___24Anonymous__23801] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__23801)
& ? [Vvar__2___24Anonymous__23802] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__23802)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m_27)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__23800,Vvar__1___24Anonymous__23801,Vvar__2___24Anonymous__23802)
& ( ( V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V1__m,V2__m_27) = V1__m )
| ? [Vvar__0___24Anonymous__23818] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__23818)
& ? [Vvar__1___24Anonymous__23819] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__23819)
& ? [Vvar__2___24Anonymous__23820] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__23820)
& V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__23818,Vvar__1___24Anonymous__23819,Vvar__2___24Anonymous__23820)
& 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__23800,Vvar__0___24Anonymous__23818),cCoq_2eInit_2eDatatypes_2eorb___24a2(Vvar__1___24Anonymous__23801,Vvar__1___24Anonymous__23819),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(Vvar__2___24Anonymous__23802,Vvar__2___24Anonymous__23820)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.xexists',axiom,
! [V0__f,V2__m,V3__i] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exexists___24a3(V0__f,V2__m,V3__i) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__59748] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__59748)
& ? [Vvar__1___24Anonymous__59749] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__59749)
& ? [Vvar__2___24Anonymous__59750] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__59750)
& ( c_24__type__55427___24t(V0__f)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__i)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__59749)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__59750)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__59748,Vvar__1___24Anonymous__59749,Vvar__2___24Anonymous__59750)
& ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459771___24a4(V0__f,V3__i,Vvar__1___24Anonymous__59749,Vvar__2___24Anonymous__59750) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exexists___24a3(V0__f,V2__m,V3__i) = cCoq_2eInit_2eDatatypes_2etrue )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459771___24a4(V0__f,V3__i,Vvar__1___24Anonymous__59749,Vvar__2___24Anonymous__59750) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exexists___24a3(V0__f,V2__m,V3__i) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exexists___24a3(V0__f,Vvar__0___24Anonymous__59748,cCoq_2eNumbers_2eBinNums_2exO___24a1(V3__i)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__343] :
( t(Vvar__1___24Anonymous__343,V0__A)
& ? [Vvar__2___24Anonymous__344] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__344)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__343,Vvar__2___24Anonymous__344)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__343,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__344,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.bool_rect',axiom,
! [V0__P,V1__f,V2__f,V3__b] :
( c_24__type__62238___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(V3__b)
=> ( ( V3__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2ebool__rect___24a4(V0__P,V1__f,V2__f,V3__b) = V1__f )
| ( V3__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2ebool__rect___24a4(V0__P,V1__f,V2__f,V3__b) = V2__f ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__1567] :
( t(Vvar__2___24Anonymous__1567,V0__A)
& ? [Vvar__3___24Anonymous__1568] :
( t(Vvar__3___24Anonymous__1568,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__1567,Vvar__3___24Anonymous__1568)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__1567 ) ) ) ) ) ).
fof('$_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__4888] :
( t(Vvar__1___24Anonymous__4888,V0__A)
& ? [Vvar__2___24Anonymous__4889] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4889)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4888,Vvar__2___24Anonymous__4889)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__4889)) ) ) ) ) ) ).
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__4855___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__4849] :
( t(Vvar__1___24Anonymous__4849,V0__A)
& ? [Vvar__2___24Anonymous__4850] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4850)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4849,Vvar__2___24Anonymous__4850)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = happ(happ(happ(V3__f,Vvar__1___24Anonymous__4849),Vvar__2___24Anonymous__4850),cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,Vvar__2___24Anonymous__4850)) ) ) ) ) ) ) ).
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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__4837] :
( t(Vvar__2___24Anonymous__4837,V0__A)
& ? [Vvar__3___24Anonymous__4838] :
( t(Vvar__3___24Anonymous__4838,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__4837,Vvar__3___24Anonymous__4838)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__4838 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.xorb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__1473] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1473)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1473)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__1473,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.bitwise',axiom,
! [V1__op,V2__n,V3__a,V4__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ebitwise___24a4(V1__op,V2__n,V3__a,V4__b) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__56377] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__56377)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__56377)
& cCoq_2eInit_2eNat_2ebitwise___24a4(V1__op,V2__n,V3__a,V4__b) = cCoq_2eInit_2eNat_2eadd___24a2(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2456382___24a3(V1__op,V3__a,V4__b),cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cCoq_2eInit_2eNat_2ebitwise___24a4(V1__op,Vvar__0___24Anonymous__56377,cCoq_2eInit_2eNat_2ediv2___24a1(V3__a),cCoq_2eInit_2eNat_2ediv2___24a1(V4__b)))) ) ) ) ).
fof('$_def_Coq.Init.Nat.compare',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__54420] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54420)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54420)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__54421] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54421)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54421)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__54424] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54424)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54424)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__54421,Vvar__0___24Anonymous__54424) ) ) ) ) ) ) ) ).
fof('$_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__54431] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54431)
& V1__y = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54431)
& 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__54431,cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__54431)) ) ) ) ).
fof('$_def_Coq.Init.Nat.div2',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__54434] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54434)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54434)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54434)
& ( ( Vvar__0___24Anonymous__54434 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__54437] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54437)
& Vvar__0___24Anonymous__54434 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54437)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__54437)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.double',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2edouble___24a1(V0__n) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V0__n) ).
fof('$_def_Coq.Init.Nat.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__54406] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54406)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54406)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__54407] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54407)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54407)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__54410] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54410)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54410)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__54407,Vvar__0___24Anonymous__54410) ) ) ) ) ) ) ) ).
fof('$_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__45599] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45599)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45599)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__45599)
& ( ( Vvar__0___24Anonymous__45599 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__45602] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45602)
& Vvar__0___24Anonymous__45599 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__45602)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__45602) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.land',axiom,
! [V0__a,V1__b] : cCoq_2eInit_2eNat_2eland___24a2(V0__a,V1__b) = cCoq_2eInit_2eNat_2ebitwise___24a4(cCoq_2eInit_2eDatatypes_2eandb,V0__a,V0__a,V1__b) ).
fof('$_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__54413] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54413)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54413)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__54416] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54416)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54416)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__54413,Vvar__0___24Anonymous__54416) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.log2',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2elog2___24a1(V0__n) = cCoq_2eInit_2eNat_2elog2__iter___24a4(cCoq_2eInit_2eNat_2epred___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_Coq.Init.Nat.lor',axiom,
! [V0__a,V1__b] : cCoq_2eInit_2eNat_2elor___24a2(V0__a,V1__b) = cCoq_2eInit_2eNat_2ebitwise___24a4(cCoq_2eInit_2eDatatypes_2eorb,cCoq_2eInit_2eNat_2emax___24a2(V0__a,V1__b),V0__a,V1__b) ).
fof('$_def_Coq.Init.Nat.ltb',axiom,
! [V0__n,V1__m] : cCoq_2eInit_2eNat_2eltb___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eleb___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__11698] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11698)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11698)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__11701] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11701)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11701)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__11698,Vvar__0___24Anonymous__11701)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.modulo',axiom,
! [V0__x,V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ( V1__y = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emodulo___24a2(V0__x,V1__y) = V1__y )
| ? [Vvar__0___24Anonymous__57217] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__57217)
& V1__y = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__57217)
& cCoq_2eInit_2eNat_2emodulo___24a2(V0__x,V1__y) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__57217,cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2edivmod___24a4(V0__x,Vvar__0___24Anonymous__57217,cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__57217))) ) ) ) ).
fof('$_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__27153] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27153)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27153)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__27153,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__54429] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54429)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54429)
& 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__54429)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__27151] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27151)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27151)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__27151 ) ) ) ).
fof('$_def_Coq.Init.Nat.shiftl',axiom,
! [V0__a] : cCoq_2eInit_2eNat_2eshiftl___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__54441,V0__a,c_24__lam__54442) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__11692] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11692)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11692)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__11695] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11695)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11695)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__11692,Vvar__0___24Anonymous__11695) ) ) ) ) ) ) ) ).
fof('$_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__54439] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54439)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54439)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__54439) ) ) ) ).
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.sigT_rec',axiom,
! [V0__A,V1__P,V2__P] : cCoq_2eInit_2eSpecif_2esigT__rec___24a3(V0__A,V1__P,V2__P) = cCoq_2eInit_2eSpecif_2esigT__rect___24a3(V0__A,V1__P,V2__P) ).
fof('$_def_Coq.Init.Specif.sig_rec',axiom,
! [V0__A,V1__P,V2__P] : cCoq_2eInit_2eSpecif_2esig__rec___24a3(V0__A,V1__P,V2__P) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V0__A,V1__P,V2__P) ).
fof('$_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('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__8505] :
( t(Vvar__1___24Anonymous__8505,V0__A)
& ? [Vvar__2___24Anonymous__8506] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8506)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8505,Vvar__2___24Anonymous__8506)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__8505 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__8506) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.existsb',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8866] :
( t(Vvar__1___24Anonymous__8866,V0__A)
& ? [Vvar__2___24Anonymous__8867] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8867)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8866,Vvar__2___24Anonymous__8867)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(happ(V1__f,Vvar__1___24Anonymous__8866),cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__8867)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.filter',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__26879] :
( t(Vvar__1___24Anonymous__26879,V0__A)
& ? [Vvar__2___24Anonymous__26880] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__26880)
& ( cType___24t(V0__A)
=> ( c_24__type__3546___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__26879,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__26879,Vvar__2___24Anonymous__26880)
& ( ( happ(V1__f,Vvar__1___24Anonymous__26879) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__26879,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__26880)) )
| ( happ(V1__f,Vvar__1___24Anonymous__26879) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__26880) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.find',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__8880] :
( t(Vvar__1___24Anonymous__8880,V0__A)
& ? [Vvar__2___24Anonymous__8881] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8881)
& ( cType___24t(V0__A)
=> ( c_24__type__3546___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__8880,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8880,Vvar__2___24Anonymous__8881)
& ( ( happ(V1__f,Vvar__1___24Anonymous__8880) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__8880) )
| ( happ(V1__f,Vvar__1___24Anonymous__8880) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,Vvar__2___24Anonymous__8881) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
| ? [Vvar__1___24Anonymous__8800] :
( t(Vvar__1___24Anonymous__8800,V1__B)
& ? [Vvar__2___24Anonymous__8801] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__8801)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__8800,Vvar__2___24Anonymous__8801)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__8801,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__8800)) ) ) ) ) ) ) ).
fof('$_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__8835] :
( t(Vvar__1___24Anonymous__8835,V1__B)
& ? [Vvar__2___24Anonymous__8836] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__8836)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__8835,Vvar__2___24Anonymous__8836)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__8835),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__8836)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.forallb',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1___24Anonymous__26868] :
( t(Vvar__1___24Anonymous__26868,V0__A)
& ? [Vvar__2___24Anonymous__26869] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__26869)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__26868,Vvar__2___24Anonymous__26869)
& cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(V1__f,Vvar__1___24Anonymous__26868),cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__26869)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd',axiom,
! [V0__A,V1__default,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = V1__default )
| ? [Vvar__1___24Anonymous__8484] :
( t(Vvar__1___24Anonymous__8484,V0__A)
& ? [Vvar__2___24Anonymous__8485] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8485)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8484,Vvar__2___24Anonymous__8485)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__8484 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__1729] :
( t(Vvar__1___24Anonymous__1729,V0__A)
& ? [Vvar__2___24Anonymous__1730] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1730)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1729,Vvar__2___24Anonymous__1730)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__1729),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__1730)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__8625] :
( t(Vvar__1___24Anonymous__8625,V0__A)
& ? [Vvar__2___24Anonymous__8626] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8626)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8625,Vvar__2___24Anonymous__8626)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__8625 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__8628] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8628)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8628)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__8635] :
( t(Vvar__1___24Anonymous__8635,V0__A)
& ? [Vvar__2___24Anonymous__8636] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8636)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8635,Vvar__2___24Anonymous__8636)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__8628,Vvar__2___24Anonymous__8636,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.partition',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) )
| ? [Vvar__1___24Anonymous__8897] :
( t(Vvar__1___24Anonymous__8897,V0__A)
& ? [Vvar__2___24Anonymous__8898] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8898)
& ( cType___24t(V0__A)
=> ( c_24__type__3546___24t(V0__A,V1__f)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8898)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8897,Vvar__2___24Anonymous__8898)
& ? [Vvar__2___24Anonymous__8912] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8912)
& ? [Vvar__3___24Anonymous__8913] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__3___24Anonymous__8913)
& ( cType___24t(V0__A)
=> ( c_24__type__3546___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__8897,V0__A)
=> ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,Vvar__2___24Anonymous__8898) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__8912,Vvar__3___24Anonymous__8913)
& ( ( happ(V1__f,Vvar__1___24Anonymous__8897) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8897,Vvar__2___24Anonymous__8912),Vvar__3___24Anonymous__8913) )
| ( happ(V1__f,Vvar__1___24Anonymous__8897) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__8912,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8897,Vvar__3___24Anonymous__8913)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.rev',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__8772] :
( t(Vvar__1___24Anonymous__8772,V0__A)
& ? [Vvar__2___24Anonymous__8773] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8773)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8772,Vvar__2___24Anonymous__8773)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,Vvar__2___24Anonymous__8773),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8772,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.tl',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__8495] :
( t(Vvar__1___24Anonymous__8495,V0__A)
& ? [Vvar__2___24Anonymous__8496] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8496)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8495,Vvar__2___24Anonymous__8496)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__8496 ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.compat_bool',axiom,
! [V0__A,V1__eqA,V2__f] :
( cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(V0__A,V1__eqA,V2__f)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3546___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cCoq_2eInit_2eDatatypes_2ebool,V1__eqA,c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V2__f) ) ).
fof('$_def_Coq.Lists.SetoidList.compat_op',axiom,
! [V0__A,V1__B,V2__eqA,V3__eqB,V4__f] :
( cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V0__A,V1__B,V2__eqA,V3__eqB,V4__f)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__22267___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__2442___24a2(V0__A,V1__B),V2__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V1__B,V1__B,V3__eqB,V3__eqB)),V4__f) ) ).
fof('$_def_Coq.Lists.SetoidList.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.Lists.SetoidList.transpose_restr',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V7__z)))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr2',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ! [V8__z_27] :
( t(V8__z_27,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> ( p(happ(happ(V2__eqB,V7__z),V8__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V8__z_27)))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.discr',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNat_2eN_2ediscr___24a1(V0__n) = cCoq_2eInit_2eSpecif_2einright___24a3(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_24__lam__23714),c_24__prop__23715,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0)) )
| ? [Vvar__0___24Anonymous__23711] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23711)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23711)
& cCoq_2eNArith_2eBinNat_2eN_2ediscr___24a1(V0__n) = cCoq_2eInit_2eSpecif_2einleft___24a3(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_24__lam__23717___24a1(Vvar__0___24Anonymous__23711)),c_24__prop__23718___24a1(Vvar__0___24Anonymous__23711),cCoq_2eInit_2eSpecif_2eexist___24a4(cCoq_2eNumbers_2eBinNums_2epositive,c_24__lam__23717___24a1(Vvar__0___24Anonymous__23711),Vvar__0___24Anonymous__23711,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23711)))) ) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__23694] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23694)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23694)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__23697] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23697)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23697)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__23694,Vvar__0___24Anonymous__23697)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.compare',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__55059] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55059)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55059)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__55060] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55060)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55060)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__55063] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55063)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55063)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__55060,Vvar__0___24Anonymous__55063) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.NArith.BinNatDef.N.div2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__1481] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1481)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1481)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1481)
& ( ? [Vvar__0___24Anonymous__1485] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1485)
& Vvar__0___24Anonymous__1481 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1485)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1485) )
| ? [Vvar__0___24Anonymous__1486] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1486)
& Vvar__0___24Anonymous__1481 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1486)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1486) )
| ( Vvar__0___24Anonymous__1481 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__38599] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38599)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__38599)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
| ? [Vvar__0___24Anonymous__38602] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38602)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__38602)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__38599,V1__b) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__1480] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1480)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1480)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1480)) ) ) ) ).
fof('$_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__719] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__719)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__719)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__720] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__720)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__720)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__723] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__723)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__723)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__720,Vvar__0___24Anonymous__723) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__55071] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55071)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55071)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55071)
& ( ? [Vvar__0___24Anonymous__55075] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55075)
& Vvar__0___24Anonymous__55071 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55075)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55076] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55076)
& Vvar__0___24Anonymous__55071 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55076)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__55071 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.land',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__55096] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55096)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55096)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__55099] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55099)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55099)
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(Vvar__0___24Anonymous__55096,Vvar__0___24Anonymous__55099) ) ) ) ) ) ) ) ).
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__55082] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55082)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55082)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55082)
& ( ? [Vvar__0___24Anonymous__55086] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55086)
& Vvar__0___24Anonymous__55082 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55086)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__55086)) )
| ? [Vvar__0___24Anonymous__55087] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55087)
& Vvar__0___24Anonymous__55082 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55087)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__55087)) )
| ( Vvar__0___24Anonymous__55082 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.lor',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__55091] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55091)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55091)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__55094] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55094)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55094)
& cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(Vvar__0___24Anonymous__55091,Vvar__0___24Anonymous__55094)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.ltb',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_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2eltb___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_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.lxor',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__1489] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1489)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1489)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__1492] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1492)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1492)
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__1489,Vvar__0___24Anonymous__1492) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.min',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V1__n_27 ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.modulo',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__23699] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23699)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23699)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__23702] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23702)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23702)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__23699,Vvar__0___24Anonymous__23702)) ) ) ) ) ) ) ) ).
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__55077] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55077)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55077)
& ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__55080] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55080)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55080)
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(Vvar__0___24Anonymous__55080,Vvar__0___24Anonymous__55077)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__55045] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55045)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55045)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__55045) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.shiftl',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl___24a2(V0__a,V1__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__55107] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55107)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55107)
& cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl___24a2(V0__a,V1__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eshiftl___24a2(Vvar__0___24Anonymous__55107,V1__n)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.sub',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__55049] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55049)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55049)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__55054] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55054)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55049)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55054)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55054)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__55049,Vvar__0___24Anonymous__55054) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__55057] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55057)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__55049,Vvar__0___24Anonymous__55054) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__55057)
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55057) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__55049,Vvar__0___24Anonymous__55054) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__55044] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55044)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55044)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__55044)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ_double',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__1477] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1477)
& V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1477)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1477)) ) ) ) ).
fof('$_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__55114] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55114)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55114)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__55114,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat___24a1(V0__a) = c_24__lam__55110 )
| ? [Vvar__0___24Anonymous__55109] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55109)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55109)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(Vvar__0___24Anonymous__55109) ) ) ) ).
fof('$_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__23704] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23704)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23704)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__23704) ) ) ) ).
fof('$_def_Coq.NArith.Ndec.Nleb',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eNat_2eleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V1__b)) ).
fof('$_def_Coq.NArith.Ndigits.Neven',axiom,
! [V0__n] :
( cCoq_2eNArith_2eNdigits_2eNeven___24a1(V0__n)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_def_Coq.NArith.Ndigits.Nless',axiom,
! [V0__a,V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__11717] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11717)
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11717)
& cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V1__a_27) = cCoq_2eNArith_2eNdigits_2eNless__aux___24a3(V0__a,V1__a_27,Vvar__0___24Anonymous__11717) ) ) ) ) ).
fof('$_def_Coq.NArith.Ndigits.Nless_aux',axiom,
! [V1__a,V2__a_27,V3__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__56396] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__56396)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__56396)
& cCoq_2eNArith_2eNdigits_2eNless__aux___24a3(V1__a,V2__a_27,V3__p) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a)),cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a_27)) )
| ? [Vvar__0___24Anonymous__56397] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__56397)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__56397)
& cCoq_2eNArith_2eNdigits_2eNless__aux___24a3(V1__a,V2__a_27,V3__p) = cCoq_2eNArith_2eNdigits_2eNless__aux___24a3(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a),cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a_27),Vvar__0___24Anonymous__56397) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eNdigits_2eNless__aux___24a3(V1__a,V2__a_27,V3__p) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a)),cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a_27)) ) ) ) ).
fof('$_def_Coq.NArith.Ndigits.Nodd',axiom,
! [V0__n] :
( cCoq_2eNArith_2eNdigits_2eNodd___24a1(V0__n)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_Coq.NArith.Ndigits.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eNdigits_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.le',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_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__23738] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23738)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23738)
& ( ? [Vvar__0___24Anonymous__23742] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23742)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23742)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__23737__1__add__carry___24a2(Vvar__0___24Anonymous__23738,Vvar__0___24Anonymous__23742)) )
| ? [Vvar__0___24Anonymous__23743] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23743)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23743)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__23738,Vvar__0___24Anonymous__23743)) )
| ( 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__23738)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23744] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23744)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23744)
& ( ? [Vvar__0___24Anonymous__23748] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23748)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23748)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__23744,Vvar__0___24Anonymous__23748)) )
| ? [Vvar__0___24Anonymous__23749] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23749)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23749)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__23744,Vvar__0___24Anonymous__23749)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23744) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__23750] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23750)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23750)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__23750)) )
| ? [Vvar__0___24Anonymous__23751] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23751)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23751)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23751) )
| ( 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.eqb',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__55146] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55146)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55146)
& ( ? [Vvar__0___24Anonymous__55150] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55150)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55150)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__55146,Vvar__0___24Anonymous__55150) )
| ? [Vvar__0___24Anonymous__55151] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55151)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55151)
& 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__55152] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55152)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55152)
& ( ? [Vvar__0___24Anonymous__55156] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55156)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55156)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55157] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55157)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55157)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__55152,Vvar__0___24Anonymous__55157) )
| ( 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__55158] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55158)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55158)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55159] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55159)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55159)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__38622] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38622)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__38622)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__38622),Vvar__0___24Anonymous__38622)) )
| ? [Vvar__0___24Anonymous__38623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38623)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__38623)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__38623),Vvar__0___24Anonymous__38623) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.ltb',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_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2eltb___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_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( ? [Vvar__0___24Anonymous__55131] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55131)
& V0__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55131)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55131) )
| ? [Vvar__0___24Anonymous__55132] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55132)
& V0__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55132)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__55132) )
| ( V0__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_N',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( ? [Vvar__0___24Anonymous__55133] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55133)
& V0__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55133)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55133)) )
| ? [Vvar__0___24Anonymous__55134] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55134)
& V0__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55134)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__55134)) )
| ( V0__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__55138] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55138)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55138)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__55138)) )
| ? [Vvar__0___24Anonymous__55139] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55139)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55139)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__55139)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__23735] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23735)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23735)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__23735)) )
| ? [Vvar__0___24Anonymous__23736] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23736)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23736)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23736) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__55183] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55183)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55183)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__55196___24a1(Vvar__0___24Anonymous__55183) )
| ? [Vvar__0___24Anonymous__55187] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55187)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55187)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__55203___24a1(Vvar__0___24Anonymous__55187) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__55207 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qdiv',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQdiv___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V0__x,cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V1__y)) ).
fof('$_def_Coq.QArith.QArith_base.Qeq',axiom,
! [V0__p,V1__q] :
( cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__p,V1__q)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__p),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__q))) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__q),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__p))) ) ).
fof('$_def_Coq.QArith.QArith_base.Qeq_bool',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)))) ).
fof('$_def_Coq.QArith.QArith_base.Qminus',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQminus___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQplus___24a2(V0__x,cCoq_2eQArith_2eQArith__base_2eQopp___24a1(V1__y)) ).
fof('$_def_Coq.QArith.QArith_base.Qmult',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y)),cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))) ).
fof('$_def_Coq.QArith.QArith_base.Qopp',axiom,
! [V0__x] : cCoq_2eQArith_2eQArith__base_2eQopp___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x)),cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)) ).
fof('$_def_Coq.QArith.QArith_base.Qplus',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQplus___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)))),cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))) ).
fof('$_def_Coq.QArith.Qreals.Q2R',axiom,
! [V0__x] : cCoq_2eQArith_2eQreals_2eQ2R___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x)),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x))))) ).
fof('$_def_Coq.Reals.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__11854] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11854)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11854)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__11854) )
| ? [Vvar__0___24Anonymous__11855] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11855)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11855)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__11855)) ) ) ) ).
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.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__22101] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22101)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22101)
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r,cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,Vvar__0___24Anonymous__22101)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__2260___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.eqb',axiom,
! [V0__a,V1__b] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V0__a)
=> ? [Vvar__0___24Anonymous__53658] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__53658)
& ? [Vvar__1___24Anonymous__53659] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__53659)
& ? [Vvar__2___24Anonymous__53660] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__53660)
& ? [Vvar__3___24Anonymous__53661] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__53661)
& ? [Vvar__4___24Anonymous__53662] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__53662)
& ? [Vvar__5___24Anonymous__53663] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__53663)
& ? [Vvar__6___24Anonymous__53664] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__53664)
& ? [Vvar__7___24Anonymous__53665] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__53665)
& ( cCoq_2eStrings_2eAscii_2eascii___24t(V1__b)
=> ( V0__a = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__53658,Vvar__1___24Anonymous__53659,Vvar__2___24Anonymous__53660,Vvar__3___24Anonymous__53661,Vvar__4___24Anonymous__53662,Vvar__5___24Anonymous__53663,Vvar__6___24Anonymous__53664,Vvar__7___24Anonymous__53665)
& ? [Vvar__0___24Anonymous__53822] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__53822)
& ? [Vvar__1___24Anonymous__53823] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__53823)
& ? [Vvar__2___24Anonymous__53824] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__53824)
& ? [Vvar__3___24Anonymous__53825] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__53825)
& ? [Vvar__4___24Anonymous__53826] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__53826)
& ? [Vvar__5___24Anonymous__53827] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__53827)
& ? [Vvar__6___24Anonymous__53828] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__53828)
& ? [Vvar__7___24Anonymous__53829] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__53829)
& ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__53658)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__53659)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__53660)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__53661)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__53662)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__53663)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__53664)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__53822)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__53823)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__53824)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__53825)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__53826)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__53827)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__53828)
=> ( V1__b = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__53822,Vvar__1___24Anonymous__53823,Vvar__2___24Anonymous__53824,Vvar__3___24Anonymous__53825,Vvar__4___24Anonymous__53826,Vvar__5___24Anonymous__53827,Vvar__6___24Anonymous__53828,Vvar__7___24Anonymous__53829)
& ( ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2453998___24a14(Vvar__0___24Anonymous__53658,Vvar__1___24Anonymous__53659,Vvar__2___24Anonymous__53660,Vvar__3___24Anonymous__53661,Vvar__4___24Anonymous__53662,Vvar__5___24Anonymous__53663,Vvar__6___24Anonymous__53664,Vvar__0___24Anonymous__53822,Vvar__1___24Anonymous__53823,Vvar__2___24Anonymous__53824,Vvar__3___24Anonymous__53825,Vvar__4___24Anonymous__53826,Vvar__5___24Anonymous__53827,Vvar__6___24Anonymous__53828) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eStrings_2eAscii_2eeqb___24a2(V0__a,V1__b) = cCoq_2eBool_2eBool_2eeqb___24a2(Vvar__7___24Anonymous__53665,Vvar__7___24Anonymous__53829) )
| ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2453998___24a14(Vvar__0___24Anonymous__53658,Vvar__1___24Anonymous__53659,Vvar__2___24Anonymous__53660,Vvar__3___24Anonymous__53661,Vvar__4___24Anonymous__53662,Vvar__5___24Anonymous__53663,Vvar__6___24Anonymous__53664,Vvar__0___24Anonymous__53822,Vvar__1___24Anonymous__53823,Vvar__2___24Anonymous__53824,Vvar__3___24Anonymous__53825,Vvar__4___24Anonymous__53826,Vvar__5___24Anonymous__53827,Vvar__6___24Anonymous__53828) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eStrings_2eAscii_2eeqb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Strings.Byte.eqb',axiom,
! [V0__a,V1__b] :
( cCoq_2eInit_2eByte_2ebyte___24t(V0__a)
=> ? [Vvar__2___24Anonymous__55733] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__55733)
& ? [Vvar__3___24Anonymous__55734] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))))),Vvar__3___24Anonymous__55734)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))))),Vvar__3___24Anonymous__55734)
=> ( cCoq_2eInit_2eByte_2eto__bits___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)))))),Vvar__2___24Anonymous__55733,Vvar__3___24Anonymous__55734)
& ? [Vvar__2___24Anonymous__55818] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__55818)
& ? [Vvar__3___24Anonymous__55819] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)))),Vvar__3___24Anonymous__55819)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)))),Vvar__3___24Anonymous__55819)
=> ( Vvar__3___24Anonymous__55734 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))))),Vvar__2___24Anonymous__55818,Vvar__3___24Anonymous__55819)
& ? [Vvar__2___24Anonymous__55897] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__55897)
& ? [Vvar__3___24Anonymous__55898] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))),Vvar__3___24Anonymous__55898)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))),Vvar__3___24Anonymous__55898)
=> ( Vvar__3___24Anonymous__55819 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)))),Vvar__2___24Anonymous__55897,Vvar__3___24Anonymous__55898)
& ? [Vvar__2___24Anonymous__55970] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__55970)
& ? [Vvar__3___24Anonymous__55971] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)),Vvar__3___24Anonymous__55971)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)),Vvar__3___24Anonymous__55971)
=> ( Vvar__3___24Anonymous__55898 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))),Vvar__2___24Anonymous__55970,Vvar__3___24Anonymous__55971)
& ? [Vvar__2___24Anonymous__56037] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__56037)
& ? [Vvar__3___24Anonymous__56038] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool),Vvar__3___24Anonymous__56038)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool),Vvar__3___24Anonymous__56038)
=> ( Vvar__3___24Anonymous__55971 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)),Vvar__2___24Anonymous__56037,Vvar__3___24Anonymous__56038)
& ? [Vvar__2___24Anonymous__56098] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__56098)
& ? [Vvar__3___24Anonymous__56099] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,Vvar__3___24Anonymous__56099)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,Vvar__3___24Anonymous__56099)
=> ( Vvar__3___24Anonymous__56038 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool),Vvar__2___24Anonymous__56098,Vvar__3___24Anonymous__56099)
& ? [Vvar__2___24Anonymous__56153] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__56153)
& ? [Vvar__3___24Anonymous__56154] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__56154)
& ( cCoq_2eInit_2eByte_2ebyte___24t(V1__b)
=> ( Vvar__3___24Anonymous__56099 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,Vvar__2___24Anonymous__56153,Vvar__3___24Anonymous__56154)
& ? [Vvar__2___24Anonymous__56202] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__56202)
& ? [Vvar__3___24Anonymous__56203] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))))),Vvar__3___24Anonymous__56203)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))))),Vvar__3___24Anonymous__56203)
=> ( cCoq_2eInit_2eByte_2eto__bits___24a1(V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)))))),Vvar__2___24Anonymous__56202,Vvar__3___24Anonymous__56203)
& ? [Vvar__2___24Anonymous__56245] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__56245)
& ? [Vvar__3___24Anonymous__56246] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)))),Vvar__3___24Anonymous__56246)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)))),Vvar__3___24Anonymous__56246)
=> ( Vvar__3___24Anonymous__56203 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))))),Vvar__2___24Anonymous__56245,Vvar__3___24Anonymous__56246)
& ? [Vvar__2___24Anonymous__56282] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__56282)
& ? [Vvar__3___24Anonymous__56283] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))),Vvar__3___24Anonymous__56283)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))),Vvar__3___24Anonymous__56283)
=> ( Vvar__3___24Anonymous__56246 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)))),Vvar__2___24Anonymous__56282,Vvar__3___24Anonymous__56283)
& ? [Vvar__2___24Anonymous__56313] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__56313)
& ? [Vvar__3___24Anonymous__56314] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)),Vvar__3___24Anonymous__56314)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)),Vvar__3___24Anonymous__56314)
=> ( Vvar__3___24Anonymous__56283 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))),Vvar__2___24Anonymous__56313,Vvar__3___24Anonymous__56314)
& ? [Vvar__2___24Anonymous__56338] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__56338)
& ? [Vvar__3___24Anonymous__56339] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool),Vvar__3___24Anonymous__56339)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool),Vvar__3___24Anonymous__56339)
=> ( Vvar__3___24Anonymous__56314 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)),Vvar__2___24Anonymous__56338,Vvar__3___24Anonymous__56339)
& ? [Vvar__2___24Anonymous__56357] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__56357)
& ? [Vvar__3___24Anonymous__56358] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,Vvar__3___24Anonymous__56358)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,Vvar__3___24Anonymous__56358)
=> ( Vvar__3___24Anonymous__56339 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool),Vvar__2___24Anonymous__56357,Vvar__3___24Anonymous__56358)
& ? [Vvar__2___24Anonymous__56370] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__56370)
& ? [Vvar__3___24Anonymous__56371] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__56371)
& Vvar__3___24Anonymous__56358 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,Vvar__2___24Anonymous__56370,Vvar__3___24Anonymous__56371)
& cCoq_2eStrings_2eByte_2eeqb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eBool_2eBool_2eeqb___24a2(Vvar__2___24Anonymous__55733,Vvar__2___24Anonymous__56202),cCoq_2eBool_2eBool_2eeqb___24a2(Vvar__2___24Anonymous__55818,Vvar__2___24Anonymous__56245)),cCoq_2eBool_2eBool_2eeqb___24a2(Vvar__2___24Anonymous__55897,Vvar__2___24Anonymous__56282)),cCoq_2eBool_2eBool_2eeqb___24a2(Vvar__2___24Anonymous__55970,Vvar__2___24Anonymous__56313)),cCoq_2eBool_2eBool_2eeqb___24a2(Vvar__2___24Anonymous__56037,Vvar__2___24Anonymous__56338)),cCoq_2eBool_2eBool_2eeqb___24a2(Vvar__2___24Anonymous__56098,Vvar__2___24Anonymous__56357)),cCoq_2eBool_2eBool_2eeqb___24a2(Vvar__2___24Anonymous__56153,Vvar__2___24Anonymous__56370)),cCoq_2eBool_2eBool_2eeqb___24a2(Vvar__3___24Anonymous__56154,Vvar__3___24Anonymous__56371)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__55012] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__55012)
& ? [Vvar__1___24Anonymous__55013] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__55013)
& V2__s2 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__55012,Vvar__1___24Anonymous__55013)
& cCoq_2eStrings_2eString_2eeqb___24a2(V1__s1,V2__s2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__55015] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__55015)
& ? [Vvar__1___24Anonymous__55016] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__55016)
& ( cCoq_2eStrings_2eString_2estring___24t(V2__s2)
=> ( V1__s1 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__55015,Vvar__1___24Anonymous__55016)
& ( ( V2__s2 = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2eeqb___24a2(V1__s1,V2__s2) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55026] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__55026)
& ? [Vvar__1___24Anonymous__55027] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__55027)
& ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__55015)
=> ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__55026)
=> ( V2__s2 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__55026,Vvar__1___24Anonymous__55027)
& ( ( cCoq_2eStrings_2eAscii_2eeqb___24a2(Vvar__0___24Anonymous__55015,Vvar__0___24Anonymous__55026) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eStrings_2eString_2eeqb___24a2(V1__s1,V2__s2) = cCoq_2eStrings_2eString_2eeqb___24a2(Vvar__1___24Anonymous__55016,Vvar__1___24Anonymous__55027) )
| ( cCoq_2eStrings_2eAscii_2eeqb___24a2(Vvar__0___24Anonymous__55015,Vvar__0___24Anonymous__55026) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eStrings_2eString_2eeqb___24a2(V1__s1,V2__s2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_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__57180] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__57180)
& ( 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__57180)
& ( ? [Vvar__0__n__57187] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__57187)
& V4__q = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__57187)
& cCoq_2eVectors_2eFin_2eeqb___24a4(V1__m,V2__n,V3__p,V4__q) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0__n__57180,Vvar__0__n__57187) )
| ? [Vvar__0__n__57188] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__57188)
& ? [Vvar__1___24Anonymous__57189] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__57188,Vvar__1___24Anonymous__57189)
& V4__q = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__57188,Vvar__1___24Anonymous__57189)
& cCoq_2eVectors_2eFin_2eeqb___24a4(V1__m,V2__n,V3__p,V4__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__0__n__57191] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__57191)
& ? [Vvar__1___24Anonymous__57192] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__57191,Vvar__1___24Anonymous__57192)
& ( 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__57191)
=> ( V3__p = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__57191,Vvar__1___24Anonymous__57192)
& ( ? [Vvar__0__n__57205] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__57205)
& V4__q = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__57205)
& cCoq_2eVectors_2eFin_2eeqb___24a4(V1__m,V2__n,V3__p,V4__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0__n__57206] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__57206)
& ? [Vvar__1___24Anonymous__57207] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__57206,Vvar__1___24Anonymous__57207)
& V4__q = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__57206,Vvar__1___24Anonymous__57207)
& cCoq_2eVectors_2eFin_2eeqb___24a4(V1__m,V2__n,V3__p,V4__q) = cCoq_2eVectors_2eFin_2eeqb___24a4(Vvar__0__n__57191,Vvar__0__n__57206,Vvar__1___24Anonymous__57192,Vvar__1___24Anonymous__57207) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__57227] :
( t(Vvar__1__h__57227,V0__A)
& ? [Vvar__2__n__57228] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__57228)
& ? [Vvar__3___24Anonymous__57229] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__57228,Vvar__3___24Anonymous__57229)
& V6__v2 = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__57227,Vvar__2__n__57228,Vvar__3___24Anonymous__57229)
& 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__57234] :
( t(Vvar__1__h__57234,V0__A)
& ? [Vvar__2__n__57235] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__57235)
& ? [Vvar__3___24Anonymous__57236] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__57235,Vvar__3___24Anonymous__57236)
& ( 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__57235)
=> ( V5__v1 = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__57234,Vvar__2__n__57235,Vvar__3___24Anonymous__57236)
& ( ( 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__57259] :
( t(Vvar__1__h__57259,V0__A)
& ? [Vvar__2__n__57260] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__57260)
& ? [Vvar__3___24Anonymous__57261] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__57260,Vvar__3___24Anonymous__57261)
& V6__v2 = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__57259,Vvar__2__n__57260,Vvar__3___24Anonymous__57261)
& 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__57234),Vvar__1__h__57259),cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,Vvar__2__n__57235,Vvar__2__n__57260,Vvar__3___24Anonymous__57236,Vvar__3___24Anonymous__57261)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.b2z',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.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__45607] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45607)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45607)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45607) )
| ? [Vvar__0___24Anonymous__45608] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45608)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45608)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45608) ) ) ) ).
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__4624] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4624)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4624)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__4628] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4628)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4628)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__4624,Vvar__0___24Anonymous__4628)) )
| ? [Vvar__0___24Anonymous__4629] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4629)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4629)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__4624,Vvar__0___24Anonymous__4629) ) ) ) ) )
| ? [Vvar__0___24Anonymous__4630] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4630)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4630)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__4634] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4634)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4634)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__4634,Vvar__0___24Anonymous__4630) )
| ? [Vvar__0___24Anonymous__4635] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4635)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4635)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__4630,Vvar__0___24Anonymous__4635)) ) ) ) ) ) ) ) ).
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__23876] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23876)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23876)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__23877] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23877)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23877)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__23878] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23878)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23878)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__23882] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23882)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23882)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__23878,Vvar__0___24Anonymous__23882) )
| ? [Vvar__0___24Anonymous__23883] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23883)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23883)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__23884] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23884)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23884)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__23888] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23888)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23888)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__23889] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23889)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23889)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__23884,Vvar__0___24Anonymous__23889)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__55482] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__55482)
& ? [Vvar__3___24Anonymous__55483] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__55483)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__55482,Vvar__3___24Anonymous__55483)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__55482 ) ) ) ) ).
fof('$_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__55459] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55459)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__55459)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55460] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55460)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__55460)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__55461] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55461)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__55461)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55465] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55465)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__55465)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__55461,Vvar__0___24Anonymous__55465) )
| ? [Vvar__0___24Anonymous__55466] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55466)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__55466)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__55467] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55467)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__55467)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55471] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55471)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__55471)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55472] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55472)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__55472)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__55467,Vvar__0___24Anonymous__55472) ) ) ) ) ) ) ) ).
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__55486] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55486)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55486)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__55486)
& ( ? [Vvar__0___24Anonymous__55490] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55490)
& Vvar__0___24Anonymous__55486 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55490)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55491] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55491)
& Vvar__0___24Anonymous__55486 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55491)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__55486 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__55492] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55492)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55492)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__55492)
& ( ? [Vvar__0___24Anonymous__55496] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55496)
& Vvar__0___24Anonymous__55492 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55496)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55497] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55497)
& Vvar__0___24Anonymous__55492 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55497)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__55492 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.gtb',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_2egtb___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_2egtb___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_2eBinIntDef_2eZ_2egtb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
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__55510] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55510)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55510)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__55510)
& ( ? [Vvar__0___24Anonymous__55514] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55514)
& Vvar__0___24Anonymous__55510 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55514)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__55514)) )
| ? [Vvar__0___24Anonymous__55515] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55515)
& Vvar__0___24Anonymous__55510 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55515)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__55515)) )
| ( Vvar__0___24Anonymous__55510 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
| ? [Vvar__0___24Anonymous__55516] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55516)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__55516)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.ltb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__23903] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__23903)
& ? [Vvar__3___24Anonymous__23904] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__23904)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__23903,Vvar__3___24Anonymous__23904)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__23904 ) ) ) ) ).
fof('$_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__4644] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4644)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4644)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__4648] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4648)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4648)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__4644,Vvar__0___24Anonymous__4648)) )
| ? [Vvar__0___24Anonymous__4649] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4649)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4649)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__4644,Vvar__0___24Anonymous__4649)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__4650] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4650)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4650)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__4654] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4654)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4654)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__4650,Vvar__0___24Anonymous__4654)) )
| ? [Vvar__0___24Anonymous__4655] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4655)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4655)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__4650,Vvar__0___24Anonymous__4655)) ) ) ) ) ) ) ) ).
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__55498] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55498)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55498)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__55498)
& ( ? [Vvar__0___24Anonymous__55502] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55502)
& Vvar__0___24Anonymous__55498 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55502)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__55503] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55503)
& Vvar__0___24Anonymous__55498 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55503)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__55498 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__55504] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55504)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55504)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__55504)
& ( ? [Vvar__0___24Anonymous__55508] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55508)
& Vvar__0___24Anonymous__55504 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55508)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__55509] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55509)
& Vvar__0___24Anonymous__55504 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55509)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__55504 = 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__23896] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23896)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23896)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23896) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__23893] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23893)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23893)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__23893)) ) ) ) ).
fof('$_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__4639] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4639)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4639)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4639) )
| ? [Vvar__0___24Anonymous__4640] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4640)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4640)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4640) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__38782] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38782)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__38782)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__38782) )
| ? [Vvar__0___24Anonymous__38783] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38783)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__38783)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_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.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__23907] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23907)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23907)
& ( ( 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__23917] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23917)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23907)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23917)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23917)
& ? [Vvar__2___24Anonymous__23925] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__23925)
& ? [Vvar__3___24Anonymous__23926] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__23926)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__23907,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23917)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__23925,Vvar__3___24Anonymous__23926)
& 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__23925),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__23926)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23928] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23928)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23907)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23928)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23928)
& ? [Vvar__2___24Anonymous__23936] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__23936)
& ? [Vvar__3___24Anonymous__23937] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__23937)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__23907,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23928)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__23936,Vvar__3___24Anonymous__23937)
& 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__23936)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__23937)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23939] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23939)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23939)
& ( ( 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__23949] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23949)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23939)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23949)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23949)
& ? [Vvar__2___24Anonymous__23957] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__23957)
& ? [Vvar__3___24Anonymous__23958] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__23958)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__23939,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23949)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__23957,Vvar__3___24Anonymous__23958)
& 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__23957)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__23958))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23960] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23960)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23939)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23960)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23960)
& ? [Vvar__2___24Anonymous__23968] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__23968)
& ? [Vvar__3___24Anonymous__23969] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__23969)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__23939,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23960)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__23968,Vvar__3___24Anonymous__23969)
& 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__23968),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__23969))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__55517] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55517)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__55517)
& ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55521] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55521)
& V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__55521)
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__55521,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55517)) )
| ? [Vvar__0___24Anonymous__55522] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55522)
& V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__55522)
& 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__55522),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55517))) ) ) ) ) )
| ? [Vvar__0___24Anonymous__55523] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55523)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__55523)
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__55474] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55474)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__55474)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__55474) )
| ? [Vvar__0___24Anonymous__55475] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55475)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__55475)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_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('$_def_Coq.ZArith.Zbool.Zle_bool_total',axiom,
! [V0__x,V1__y] : cCoq_2eZArith_2eZbool_2eZle__bool__total___24a2(V0__x,V1__y) = c_24__cast__56861___24a3(V0__x,V1__y,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y))) ).
fof('$_def_Coq.micromega.EnvRing.Peq',axiom,
! [V0__C,V1__ceqb,V3__P,V4__P_27] :
( cType___24t(V0__C)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V3__P)
=> ( ? [Vvar__1___24Anonymous__58005] :
( t(Vvar__1___24Anonymous__58005,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V0__C,Vvar__1___24Anonymous__58005)
& ( ? [Vvar__1___24Anonymous__58015] :
( t(Vvar__1___24Anonymous__58015,V0__C)
& V4__P_27 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V0__C,Vvar__1___24Anonymous__58015)
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__58005),Vvar__1___24Anonymous__58015) )
| ? [Vvar__1___24Anonymous__58017] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__58017)
& ? [Vvar__2___24Anonymous__58018] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__2___24Anonymous__58018)
& V4__P_27 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__58017,Vvar__2___24Anonymous__58018)
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__58021] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__1___24Anonymous__58021)
& ? [Vvar__2___24Anonymous__58022] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__58022)
& ? [Vvar__3___24Anonymous__58023] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__3___24Anonymous__58023)
& V4__P_27 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V0__C,Vvar__1___24Anonymous__58021,Vvar__2___24Anonymous__58022,Vvar__3___24Anonymous__58023)
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__58028] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__58028)
& ? [Vvar__2___24Anonymous__58029] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__2___24Anonymous__58029)
& ( cType___24t(V0__C)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__58028,Vvar__2___24Anonymous__58029)
& ( ? [Vvar__1___24Anonymous__58049] :
( t(Vvar__1___24Anonymous__58049,V0__C)
& V4__P_27 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V0__C,Vvar__1___24Anonymous__58049)
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__58051] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__58051)
& ? [Vvar__2___24Anonymous__58052] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__2___24Anonymous__58052)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__58028)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__58051)
=> ( V4__P_27 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__58051,Vvar__2___24Anonymous__58052)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__58028,Vvar__1___24Anonymous__58051) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__58029,Vvar__2___24Anonymous__58052) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__58028,Vvar__1___24Anonymous__58051) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__58028,Vvar__1___24Anonymous__58051) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__58057] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__1___24Anonymous__58057)
& ? [Vvar__2___24Anonymous__58058] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__58058)
& ? [Vvar__3___24Anonymous__58059] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__3___24Anonymous__58059)
& V4__P_27 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V0__C,Vvar__1___24Anonymous__58057,Vvar__2___24Anonymous__58058,Vvar__3___24Anonymous__58059)
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__58064] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__1___24Anonymous__58064)
& ? [Vvar__2___24Anonymous__58065] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__58065)
& ? [Vvar__3___24Anonymous__58066] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__3___24Anonymous__58066)
& ( cType___24t(V0__C)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V0__C,Vvar__1___24Anonymous__58064,Vvar__2___24Anonymous__58065,Vvar__3___24Anonymous__58066)
& ( ? [Vvar__1___24Anonymous__58099] :
( t(Vvar__1___24Anonymous__58099,V0__C)
& V4__P_27 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V0__C,Vvar__1___24Anonymous__58099)
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__58101] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__58101)
& ? [Vvar__2___24Anonymous__58102] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__2___24Anonymous__58102)
& V4__P_27 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__58101,Vvar__2___24Anonymous__58102)
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__58105] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__1___24Anonymous__58105)
& ? [Vvar__2___24Anonymous__58106] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__58106)
& ? [Vvar__3___24Anonymous__58107] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__3___24Anonymous__58107)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__58065)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__58106)
=> ( V4__P_27 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V0__C,Vvar__1___24Anonymous__58105,Vvar__2___24Anonymous__58106,Vvar__3___24Anonymous__58107)
& ( ( cType___24t(V0__C)
=> ( c_24__type__6978___24t(V0__C,V1__ceqb)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__1___24Anonymous__58064)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__1___24Anonymous__58105)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__58065,Vvar__2___24Anonymous__58106) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__58064,Vvar__1___24Anonymous__58105) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,Vvar__3___24Anonymous__58066,Vvar__3___24Anonymous__58107) )
| ( cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__58064,Vvar__1___24Anonymous__58105) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__58065,Vvar__2___24Anonymous__58106) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__58065,Vvar__2___24Anonymous__58106) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RMicromega.is_neg',axiom,
! [V0__z] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,V0__z)
=> ( ? [Vvar__2___24Anonymous__56455] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__56455)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__56455)
=> ( V0__z = cCoq_2eInit_2eDatatypes_2einl___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__2___24Anonymous__56455)
& ( ( Vvar__2___24Anonymous__56455 = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2emicromega_2eRMicromega_2eis__neg___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__56459] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__56459)
& Vvar__2___24Anonymous__56455 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__56459)
& cCoq_2emicromega_2eRMicromega_2eis__neg___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__56460] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__56460)
& Vvar__2___24Anonymous__56455 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__56460)
& cCoq_2emicromega_2eRMicromega_2eis__neg___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__2___24Anonymous__56463] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__56463)
& V0__z = cCoq_2eInit_2eDatatypes_2einr___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__2___24Anonymous__56463)
& cCoq_2emicromega_2eRMicromega_2eis__neg___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_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__11862] :
( t(Vvar__1___24Anonymous__11862,V1__A)
& ? [Vvar__2___24Anonymous__11863] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__11863)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__11863)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__11862,Vvar__2___24Anonymous__11863)
& ( ( Vvar__2___24Anonymous__11863 = 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__11862)) ) )
| ? [Vvar__1___24Anonymous__11874] :
( t(Vvar__1___24Anonymous__11874,V1__A)
& ? [Vvar__2___24Anonymous__11875] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__11875)
& Vvar__2___24Anonymous__11863 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__11874,Vvar__2___24Anonymous__11875)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__11862))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__11863) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__2116] :
( t(Vvar__1___24Anonymous__2116,V1__A)
& ? [Vvar__2___24Anonymous__2117] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__2117)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__2116,Vvar__2___24Anonymous__2117)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__2116))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__2117,V4__goal) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.NFormula',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C) = cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_def_Coq.micromega.RingMicromega.PolC',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).
fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).
fof('$_def_Coq.micromega.RingMicromega.cltb',axiom,
! [V0__C,V1__ceqb,V2__cleb,V3__x,V4__y] : cCoq_2emicromega_2eRingMicromega_2ecltb___24a5(V0__C,V1__ceqb,V2__cleb,V3__x,V4__y) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(happ(V2__cleb,V3__x),V4__y),cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V0__C,V1__ceqb,V3__x,V4__y)) ).
fof('$_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('$_def_Coq.micromega.Tauto.clause',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.cnf',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.cnf_checker',axiom,
! [V0__Term_27,V1__Annot,V2__Witness,V3__checker,V5__f,V6__l] :
( cType___24t(V0__Term_27)
=> ( cType___24t(V1__Annot)
=> ( cType___24t(V2__Witness)
=> ( cCoq_2emicromega_2eTauto_2ecnf___24t(V0__Term_27,V1__Annot,V5__f)
=> ( ( V5__f = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot))
& cCoq_2emicromega_2eTauto_2ecnf__checker___24a6(V0__Term_27,V1__Annot,V2__Witness,V3__checker,V5__f,V6__l) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1___24Anonymous__3706] :
( cCoq_2emicromega_2eTauto_2eclause___24t(V0__Term_27,V1__Annot,Vvar__1___24Anonymous__3706)
& ? [Vvar__2___24Anonymous__3707] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot),Vvar__2___24Anonymous__3707)
& ( cType___24t(V0__Term_27)
=> ( cType___24t(V1__Annot)
=> ( cType___24t(V2__Witness)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V2__Witness,V6__l)
=> ( V5__f = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot),Vvar__1___24Anonymous__3706,Vvar__2___24Anonymous__3707)
& ( ( V6__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__Witness)
& cCoq_2emicromega_2eTauto_2ecnf__checker___24a6(V0__Term_27,V1__Annot,V2__Witness,V3__checker,V5__f,V6__l) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__3720] :
( t(Vvar__1___24Anonymous__3720,V2__Witness)
& ? [Vvar__2___24Anonymous__3721] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V2__Witness,Vvar__2___24Anonymous__3721)
& ( cType___24t(V0__Term_27)
=> ( cType___24t(V1__Annot)
=> ( cType___24t(V2__Witness)
=> ( c_24__type__3732___24t(V0__Term_27,V1__Annot,V2__Witness,V3__checker)
=> ( cCoq_2emicromega_2eTauto_2eclause___24t(V0__Term_27,V1__Annot,Vvar__1___24Anonymous__3706)
=> ( t(Vvar__1___24Anonymous__3720,V2__Witness)
=> ( V6__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__Witness,Vvar__1___24Anonymous__3720,Vvar__2___24Anonymous__3721)
& ( ( happ(happ(V3__checker,Vvar__1___24Anonymous__3706),Vvar__1___24Anonymous__3720) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2emicromega_2eTauto_2ecnf__checker___24a6(V0__Term_27,V1__Annot,V2__Witness,V3__checker,V5__f,V6__l) = cCoq_2emicromega_2eTauto_2ecnf__checker___24a6(V0__Term_27,V1__Annot,V2__Witness,V3__checker,Vvar__2___24Anonymous__3707,Vvar__2___24Anonymous__3721) )
| ( happ(happ(V3__checker,Vvar__1___24Anonymous__3706),Vvar__1___24Anonymous__3720) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2emicromega_2eTauto_2ecnf__checker___24a6(V0__Term_27,V1__Annot,V2__Witness,V3__checker,V5__f,V6__l) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.eval_clause',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__cl] :
( cCoq_2emicromega_2eTauto_2eeval__clause___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__cl)
<=> ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V1__Term_27,V2__Annot),cCoq_2emicromega_2eTauto_2eeval__tt___24a5(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env),V5__cl) ) ).
fof('$_def_Coq.micromega.Tauto.eval_cnf',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__f] :
( cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__f)
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V1__Term_27,V2__Annot),cCoq_2emicromega_2eTauto_2eeval__clause___24a5(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env),V5__f) ) ).
fof('$_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.Add',axiom,
cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd = cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eAdd ).
fof('$_def_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.eqb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( V0__x = V1__y
& cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__59706___24a2(V0__x,V1__y),c_24__prop__59707___24a2(V0__x,V1__y))
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__x != V1__y
& cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__59708___24a2(V0__x,V1__y),c_24__prop__59709___24a2(V0__x,V1__y))
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
! [Vvar__4027] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__4027)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__4027) ) ).
fof('$_def_Coq.micromega.ZMicromega.isZ0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__55034] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55034)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__55034)
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55035] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55035)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__55035)
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.is_pol_Z0',axiom,
! [V0__p] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,V0__p)
=> ( ? [Vvar__1___24Anonymous__53606] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__53606)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__53606)
=> ( V0__p = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__53606)
& ( ( Vvar__1___24Anonymous__53606 = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__53610] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__53610)
& Vvar__1___24Anonymous__53606 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__53610)
& cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__53611] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__53611)
& Vvar__1___24Anonymous__53606 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__53611)
& cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__1___24Anonymous__53613] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__53613)
& ? [Vvar__2___24Anonymous__53614] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__53614)
& V0__p = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__53613,Vvar__2___24Anonymous__53614)
& cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__53617] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__53617)
& ? [Vvar__2___24Anonymous__53618] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__53618)
& ? [Vvar__3___24Anonymous__53619] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3___24Anonymous__53619)
& V0__p = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__53617,Vvar__2___24Anonymous__53618,Vvar__3___24Anonymous__53619)
& cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.valid_cut_sign',axiom,
! [V0__op] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V0__op)
=> ( ( V0__op = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__op = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__op = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__op = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.FEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V9__C)
=> ( cType___24t(V11__Cpow)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,V16__pe)
=> ( ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V1__rO )
| ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__6271] :
( t(Vvar__1___24Anonymous__6271,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__6271)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V10__phi,Vvar__1___24Anonymous__6271) )
| ? [Vvar__1___24Anonymous__6273] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6273)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__6273)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__6273,V15__l) )
| ? [Vvar__1___24Anonymous__6275] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__6275)
& ? [Vvar__2___24Anonymous__6276] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__6276)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__6275,Vvar__2___24Anonymous__6276)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__6275)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__6276)) ) )
| ? [Vvar__1___24Anonymous__6279] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__6279)
& ? [Vvar__2___24Anonymous__6280] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__6280)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__6279,Vvar__2___24Anonymous__6280)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__6279)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__6280)) ) )
| ? [Vvar__1___24Anonymous__6283] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__6283)
& ? [Vvar__2___24Anonymous__6284] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__6284)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__6283,Vvar__2___24Anonymous__6284)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__6283)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__6284)) ) )
| ? [Vvar__1___24Anonymous__6287] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__6287)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__6287)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__6287)) )
| ? [Vvar__1___24Anonymous__6289] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__6289)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__6289)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V8__rinv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__6289)) )
| ? [Vvar__1___24Anonymous__6291] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__6291)
& ? [Vvar__2___24Anonymous__6292] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__6292)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__6291,Vvar__2___24Anonymous__6292)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V7__rdiv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__6291)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__6292)) ) )
| ? [Vvar__1___24Anonymous__6295] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__6295)
& ? [Vvar__2___24Anonymous__6296] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6296)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__6295,Vvar__2___24Anonymous__6296)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V13__rpow,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__6295)),happ(V12__Cp__phi,Vvar__2___24Anonymous__6296)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__25323] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__25323)
& ? [Vvar__2___24Anonymous__25324] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__25324)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__25323,Vvar__2___24Anonymous__25324)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__25323),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__25324,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEequiv',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,V13__e,V14__e_27] :
( cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___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,V13__e,V14__e_27)
<=> ! [V15__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V15__l)
=> 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,V15__l,V13__e)),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,V15__l,V14__e_27))) ) ) ).
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__6600] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__6600)
& ? [Vvar__2___24Anonymous__6601] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__6601)
& ( 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__6601)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__6600,Vvar__2___24Anonymous__6601)
& ( ( Vvar__2___24Anonymous__6601 = 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__6600)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__6612] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__6612)
& ? [Vvar__2___24Anonymous__6613] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__6613)
& Vvar__2___24Anonymous__6601 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__6612,Vvar__2___24Anonymous__6613)
& ( 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__6600)),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__6601) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.PExpr_eq',axiom,
! [V0__C,V1__ceqb,V3__e,V4__e_27] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V3__e)
=> ( ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47094] :
( t(Vvar__1___24Anonymous__47094,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__47094)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47111] :
( t(Vvar__1___24Anonymous__47111,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__47111)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__47094),Vvar__1___24Anonymous__47111) )
| ? [Vvar__1___24Anonymous__47113] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__47113)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__47113)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47115] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47115)
& ? [Vvar__2___24Anonymous__47116] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47116)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__47115,Vvar__2___24Anonymous__47116)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47119] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47119)
& ? [Vvar__2___24Anonymous__47120] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47120)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__47119,Vvar__2___24Anonymous__47120)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47123] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47123)
& ? [Vvar__2___24Anonymous__47124] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47124)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__47123,Vvar__2___24Anonymous__47124)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47127] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47127)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__47127)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47129] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47129)
& ? [Vvar__2___24Anonymous__47130] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__47130)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__47129,Vvar__2___24Anonymous__47130)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__47133] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__47133)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__47133)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47150] :
( t(Vvar__1___24Anonymous__47150,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__47150)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47152] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__47152)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__47152)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__1___24Anonymous__47133,Vvar__1___24Anonymous__47152) )
| ? [Vvar__1___24Anonymous__47154] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47154)
& ? [Vvar__2___24Anonymous__47155] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47155)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__47154,Vvar__2___24Anonymous__47155)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47158] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47158)
& ? [Vvar__2___24Anonymous__47159] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47159)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__47158,Vvar__2___24Anonymous__47159)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47162] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47162)
& ? [Vvar__2___24Anonymous__47163] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47163)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__47162,Vvar__2___24Anonymous__47163)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47166] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47166)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__47166)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47168] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47168)
& ? [Vvar__2___24Anonymous__47169] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__47169)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__47168,Vvar__2___24Anonymous__47169)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__47172] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47172)
& ? [Vvar__2___24Anonymous__47173] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47173)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__47172,Vvar__2___24Anonymous__47173)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47205] :
( t(Vvar__1___24Anonymous__47205,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__47205)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47207] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__47207)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__47207)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47209] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47209)
& ? [Vvar__2___24Anonymous__47210] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47210)
& ( cType___24t(V0__C)
=> ( c_24__type__6978___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47172)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47209)
=> ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__47209,Vvar__2___24Anonymous__47210)
& ( ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__47172,Vvar__1___24Anonymous__47209) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__47173,Vvar__2___24Anonymous__47210) )
| ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__47172,Vvar__1___24Anonymous__47209) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__47215] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47215)
& ? [Vvar__2___24Anonymous__47216] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47216)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__47215,Vvar__2___24Anonymous__47216)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47219] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47219)
& ? [Vvar__2___24Anonymous__47220] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47220)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__47219,Vvar__2___24Anonymous__47220)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47223] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47223)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__47223)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47225] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47225)
& ? [Vvar__2___24Anonymous__47226] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__47226)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__47225,Vvar__2___24Anonymous__47226)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__47229] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47229)
& ? [Vvar__2___24Anonymous__47230] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47230)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__47229,Vvar__2___24Anonymous__47230)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47262] :
( t(Vvar__1___24Anonymous__47262,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__47262)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47264] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__47264)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__47264)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47266] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47266)
& ? [Vvar__2___24Anonymous__47267] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47267)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__47266,Vvar__2___24Anonymous__47267)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47270] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47270)
& ? [Vvar__2___24Anonymous__47271] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47271)
& ( cType___24t(V0__C)
=> ( c_24__type__6978___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47229)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47270)
=> ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__47270,Vvar__2___24Anonymous__47271)
& ( ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__47229,Vvar__1___24Anonymous__47270) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__47230,Vvar__2___24Anonymous__47271) )
| ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__47229,Vvar__1___24Anonymous__47270) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__47276] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47276)
& ? [Vvar__2___24Anonymous__47277] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47277)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__47276,Vvar__2___24Anonymous__47277)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47280] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47280)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__47280)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47282] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47282)
& ? [Vvar__2___24Anonymous__47283] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__47283)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__47282,Vvar__2___24Anonymous__47283)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__47286] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47286)
& ? [Vvar__2___24Anonymous__47287] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47287)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__47286,Vvar__2___24Anonymous__47287)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47319] :
( t(Vvar__1___24Anonymous__47319,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__47319)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47321] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__47321)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__47321)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47323] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47323)
& ? [Vvar__2___24Anonymous__47324] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47324)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__47323,Vvar__2___24Anonymous__47324)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47327] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47327)
& ? [Vvar__2___24Anonymous__47328] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47328)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__47327,Vvar__2___24Anonymous__47328)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47331] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47331)
& ? [Vvar__2___24Anonymous__47332] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47332)
& ( cType___24t(V0__C)
=> ( c_24__type__6978___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47286)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47331)
=> ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__47331,Vvar__2___24Anonymous__47332)
& ( ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__47286,Vvar__1___24Anonymous__47331) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__47287,Vvar__2___24Anonymous__47332) )
| ( cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__47286,Vvar__1___24Anonymous__47331) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__47337] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47337)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__47337)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47339] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47339)
& ? [Vvar__2___24Anonymous__47340] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__47340)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__47339,Vvar__2___24Anonymous__47340)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__47343] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47343)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__47343)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47360] :
( t(Vvar__1___24Anonymous__47360,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__47360)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47362] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__47362)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__47362)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47364] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47364)
& ? [Vvar__2___24Anonymous__47365] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47365)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__47364,Vvar__2___24Anonymous__47365)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47368] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47368)
& ? [Vvar__2___24Anonymous__47369] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47369)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__47368,Vvar__2___24Anonymous__47369)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47372] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47372)
& ? [Vvar__2___24Anonymous__47373] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47373)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__47372,Vvar__2___24Anonymous__47373)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47376] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47376)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__47376)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__47343,Vvar__1___24Anonymous__47376) )
| ? [Vvar__1___24Anonymous__47378] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47378)
& ? [Vvar__2___24Anonymous__47379] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__47379)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__47378,Vvar__2___24Anonymous__47379)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__47382] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47382)
& ? [Vvar__2___24Anonymous__47383] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__47383)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e_27)
=> ( V3__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__47382,Vvar__2___24Anonymous__47383)
& ( ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47415] :
( t(Vvar__1___24Anonymous__47415,V0__C)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__47415)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47417] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__47417)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__47417)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47419] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47419)
& ? [Vvar__2___24Anonymous__47420] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47420)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__47419,Vvar__2___24Anonymous__47420)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47423] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47423)
& ? [Vvar__2___24Anonymous__47424] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47424)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__47423,Vvar__2___24Anonymous__47424)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47427] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47427)
& ? [Vvar__2___24Anonymous__47428] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__47428)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__47427,Vvar__2___24Anonymous__47428)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__47431] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47431)
& V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__47431)
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__47433] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__47433)
& ? [Vvar__2___24Anonymous__47434] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__47434)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__47383)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__47434)
=> ( V4__e_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__47433,Vvar__2___24Anonymous__47434)
& ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vvar__2___24Anonymous__47383,Vvar__2___24Anonymous__47434) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__47382,Vvar__1___24Anonymous__47433) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vvar__2___24Anonymous__47383,Vvar__2___24Anonymous__47434) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V0__C,V1__ceqb,V3__e,V4__e_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__6587] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__6587)
& ? [Vvar__2__denum__6588] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__6588)
& ? [Vvar__3__condition__6589] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__6589)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__6587,Vvar__2__denum__6588,Vvar__3__condition__6589)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__6589 ) ) ) ) ) ).
fof('$_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__6578] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__6578)
& ? [Vvar__2__denum__6579] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__6579)
& ? [Vvar__3__condition__6580] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__6580)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__6578,Vvar__2__denum__6579,Vvar__3__condition__6580)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__6579 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__6567] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__6567)
& ? [Vvar__2__denum__6568] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__6568)
& ? [Vvar__3__condition__6569] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__6569)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__6567,Vvar__2__denum__6568,Vvar__3__condition__6569)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__6567 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__6906] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__6906)
& ? [Vvar__2__rsplit__common__6907] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__6907)
& ? [Vvar__3__rsplit__right__6908] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__6908)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__6906,Vvar__2__rsplit__common__6907,Vvar__3__rsplit__right__6908)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__6906 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__6926] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__6926)
& ? [Vvar__2__rsplit__common__6927] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__6927)
& ? [Vvar__3__rsplit__right__6928] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__6928)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__6926,Vvar__2__rsplit__common__6927,Vvar__3__rsplit__right__6928)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__6928 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.split',axiom,
! [V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,V6__e2] : cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,V6__e2) = cCoq_2esetoid__ring_2eField__theory_2esplit__aux___24a8(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,cCoq_2eNumbers_2eBinNums_2exH,V6__e2) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nsub',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNsub = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nw_is0',axiom,
! [V1__w] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V1__w)
=> ( ( V1__w = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2eNw__is0___24a1(V1__w) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1___24Anonymous__54395] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__54395)
& ? [Vvar__2___24Anonymous__54396] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__54396)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__54395)
=> ( V1__w = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__54395,Vvar__2___24Anonymous__54396)
& ( ( Vvar__1___24Anonymous__54395 = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2eNw__is0___24a1(V1__w) = cCoq_2esetoid__ring_2eInitialRing_2eNw__is0___24a1(Vvar__2___24Anonymous__54396) )
| ? [Vvar__0___24Anonymous__54402] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54402)
& Vvar__1___24Anonymous__54395 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__54402)
& cCoq_2esetoid__ring_2eInitialRing_2eNw__is0___24a1(V1__w) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__26598] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__26598)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__26598) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__8338] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8338)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__8338)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__8338) )
| ? [Vvar__0___24Anonymous__8339] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8339)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__8339)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__8339)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.triv_div',axiom,
! [V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y] :
( cType___24t(V0__C)
=> ( c_24__type__6978___24t(V0__C,V3__ceqb)
=> ( t(V4__x,V0__C)
=> ( t(V5__y,V0__C)
=> ( ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V2__cI,V1__cO) )
| ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V1__cO,V4__x) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring.bool_eq',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V1__b2) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V7__C)
=> ( cType___24t(V9__Cpow)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,V14__pe)
=> ( ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V1__rO )
| ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__14316] :
( t(Vvar__1___24Anonymous__14316,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__14316)
& 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__14316) )
| ? [Vvar__1___24Anonymous__14318] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14318)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__14318)
& 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__14318,V13__l) )
| ? [Vvar__1___24Anonymous__14320] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__14320)
& ? [Vvar__2___24Anonymous__14321] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__14321)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__14320,Vvar__2___24Anonymous__14321)
& 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__14320)),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__14321)) ) )
| ? [Vvar__1___24Anonymous__14324] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__14324)
& ? [Vvar__2___24Anonymous__14325] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__14325)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__14324,Vvar__2___24Anonymous__14325)
& 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__14324)),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__14325)) ) )
| ? [Vvar__1___24Anonymous__14328] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__14328)
& ? [Vvar__2___24Anonymous__14329] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__14329)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__14328,Vvar__2___24Anonymous__14329)
& 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__14328)),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__14329)) ) )
| ? [Vvar__1___24Anonymous__14332] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__14332)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__14332)
& 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__14332)) )
| ? [Vvar__1___24Anonymous__14334] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__14334)
& ? [Vvar__2___24Anonymous__14335] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14335)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__14334,Vvar__2___24Anonymous__14335)
& 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__14334)),happ(V10__Cp__phi,Vvar__2___24Anonymous__14335)) ) ) ) ) ) ) ) ).
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__12270] :
( t(Vvar__1___24Anonymous__12270,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__12270)
& ( ? [Vvar__1___24Anonymous__12280] :
( t(Vvar__1___24Anonymous__12280,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__12280)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__12270),Vvar__1___24Anonymous__12280) )
| ? [Vvar__1___24Anonymous__12282] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12282)
& ? [Vvar__2___24Anonymous__12283] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__12283)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__12282,Vvar__2___24Anonymous__12283)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__12286] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12286)
& ? [Vvar__2___24Anonymous__12287] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12287)
& ? [Vvar__3___24Anonymous__12288] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__12288)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__12286,Vvar__2___24Anonymous__12287,Vvar__3___24Anonymous__12288)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__12293] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12293)
& ? [Vvar__2___24Anonymous__12294] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__12294)
& ( 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__12293,Vvar__2___24Anonymous__12294)
& ( ? [Vvar__1___24Anonymous__12314] :
( t(Vvar__1___24Anonymous__12314,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__12314)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__12316] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12316)
& ? [Vvar__2___24Anonymous__12317] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__12317)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12293)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12316)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__12316,Vvar__2___24Anonymous__12317)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__12293,Vvar__1___24Anonymous__12316) = 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__12294,Vvar__2___24Anonymous__12317) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__12293,Vvar__1___24Anonymous__12316) = 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__12293,Vvar__1___24Anonymous__12316) = 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__12322] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12322)
& ? [Vvar__2___24Anonymous__12323] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12323)
& ? [Vvar__3___24Anonymous__12324] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__12324)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__12322,Vvar__2___24Anonymous__12323,Vvar__3___24Anonymous__12324)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__12329] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12329)
& ? [Vvar__2___24Anonymous__12330] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12330)
& ? [Vvar__3___24Anonymous__12331] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__12331)
& ( 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__12329,Vvar__2___24Anonymous__12330,Vvar__3___24Anonymous__12331)
& ( ? [Vvar__1___24Anonymous__12364] :
( t(Vvar__1___24Anonymous__12364,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__12364)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__12366] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12366)
& ? [Vvar__2___24Anonymous__12367] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__12367)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__12366,Vvar__2___24Anonymous__12367)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__12370] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12370)
& ? [Vvar__2___24Anonymous__12371] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12371)
& ? [Vvar__3___24Anonymous__12372] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__12372)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12330)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12371)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__12370,Vvar__2___24Anonymous__12371,Vvar__3___24Anonymous__12372)
& ( ( cType___24t(V0__C)
=> ( c_24__type__6978___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12329)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12370)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__12330,Vvar__2___24Anonymous__12371) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__12329,Vvar__1___24Anonymous__12370) = 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__12331,Vvar__3___24Anonymous__12372) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__12329,Vvar__1___24Anonymous__12370) = 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__12330,Vvar__2___24Anonymous__12371) = 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__12330,Vvar__2___24Anonymous__12371) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi',axiom,
! [V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,V7__l,V8__P] :
( cType___24t(V0__R)
=> ( cType___24t(V4__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,V8__P)
=> ( ? [Vvar__1___24Anonymous__13310] :
( t(Vvar__1___24Anonymous__13310,V4__C)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V4__C,Vvar__1___24Anonymous__13310)
& cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,V7__l,V8__P) = happ(V5__phi,Vvar__1___24Anonymous__13310) )
| ? [Vvar__1___24Anonymous__13312] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13312)
& ? [Vvar__2___24Anonymous__13313] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__2___24Anonymous__13313)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V4__C,Vvar__1___24Anonymous__13312,Vvar__2___24Anonymous__13313)
& cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,V7__l,V8__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__R,Vvar__1___24Anonymous__13312,V7__l),Vvar__2___24Anonymous__13313) ) )
| ? [Vvar__1___24Anonymous__13316] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__1___24Anonymous__13316)
& ? [Vvar__2___24Anonymous__13317] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__13317)
& ? [Vvar__3___24Anonymous__13318] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__3___24Anonymous__13318)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V4__C,Vvar__1___24Anonymous__13316,Vvar__2___24Anonymous__13317,Vvar__3___24Anonymous__13318)
& cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,V7__l,V8__P) = happ(happ(V2__radd,happ(happ(V3__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,V7__l,Vvar__1___24Anonymous__13316)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V3__rmul,cCoq_2eLists_2eList_2ehd___24a3(V0__R,V1__rO,V7__l),Vvar__2___24Anonymous__13317))),cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V4__C,V5__phi,cCoq_2eLists_2eList_2etl___24a2(V0__R,V7__l),Vvar__3___24Anonymous__13318)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi_dev',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a13(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__get__sign,cCoq_2esetoid__ring_2eRing__polynom_2emkpow___24a2(V0__R,V4__rmul),cCoq_2esetoid__ring_2eRing__polynom_2emkopp__pow___24a3(V0__R,V4__rmul,V6__ropp),cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a2(V0__R,V4__rmul)) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__17045___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__17046___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__17047___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),V15__lpe)
=> ( ( V15__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__14754] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__14754)
& ? [Vvar__2___24Anonymous__14755] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__14755)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__14754)
=> ( V15__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__14754,Vvar__2___24Anonymous__14755)
& ? [Vvar__2___24Anonymous__14773] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__2___24Anonymous__14773)
& ? [Vvar__3___24Anonymous__14774] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__3___24Anonymous__14774)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__14755)
=> ( Vvar__1___24Anonymous__14754 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__14773,Vvar__3___24Anonymous__14774)
& ( ( Vvar__2___24Anonymous__14755 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__14773)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__14774))) ) )
| ? [Vvar__1___24Anonymous__14785] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__14785)
& ? [Vvar__2___24Anonymous__14786] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__14786)
& Vvar__2___24Anonymous__14755 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__14785,Vvar__2___24Anonymous__14786)
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> ( p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__14773)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__14774)))
& cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__14755) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),V10__lpe)
=> ( ( V10__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__15117] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__15117)
& ? [Vvar__2___24Anonymous__15118] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__2___24Anonymous__15118)
& ( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__15117)
=> ( V10__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__1___24Anonymous__15117,Vvar__2___24Anonymous__15118)
& ? [Vvar__2___24Anonymous__15134] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__15134)
& ? [Vvar__3___24Anonymous__15135] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__15135)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__1405___24t(V0__C,V3__cadd)
=> ( c_24__type__1405___24t(V0__C,V4__cmul)
=> ( c_24__type__1405___24t(V0__C,V5__csub)
=> ( c_24__type__2412___24t(V0__C,V6__copp)
=> ( c_24__type__6978___24t(V0__C,V7__ceqb)
=> ( c_24__type__12806___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__15134)
=> ( Vvar__1___24Anonymous__15117 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__15134,Vvar__3___24Anonymous__15135)
& ( ? [Vvar__1___24Anonymous__15143] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__15143)
& cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__15134)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__15143)
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C)),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C),Vvar__1___24Anonymous__15143,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__3___24Anonymous__15135)),cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__15118)) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__15134)) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__15118) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__14600___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.IDphi',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).
fof('$_def_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
! [V0__C,V1__c] : cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V0__C,V1__c) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__C) ).
fof('$_def_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__2564] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2564)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2564)
& 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__2564) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__17618] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17618)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17618)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__17619__17622___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__17618)),c_24__let__var__6__p__17619__17622___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__17618))) )
| ? [Vvar__0___24Anonymous__17620] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17620)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17620)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__17621__17623___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__17620)),c_24__let__var__6__p__17621__17623___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__17620)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_IntMap.Fset.FSet',axiom,
! [Vvar__76] :
( cIntMap_2eFset_2eFSet___24t(Vvar__76)
<=> cIntMap_2eMap_2eMap___24t(cCoq_2eInit_2eDatatypes_2eunit,Vvar__76) ) ).
fof('$_def_IntMap.Fset.FSetUnion',axiom,
! [V0__s,V1__s_27] : cIntMap_2eFset_2eFSetUnion___24a2(V0__s,V1__s_27) = cIntMap_2eMap_2eMapMerge___24a3(cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27) ).
fof('$_def_IntMap.Fset.MapDom',axiom,
! [V0__A,V2__m] :
( cType___24t(V0__A)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
& cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM0___24a1(cCoq_2eInit_2eDatatypes_2eunit) )
| ? [Vvar__1___24Anonymous__81] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__81)
& ? [Vvar__2___24Anonymous__82] :
( t(Vvar__2___24Anonymous__82,V0__A)
& V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__81,Vvar__2___24Anonymous__82)
& cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM1___24a3(cCoq_2eInit_2eDatatypes_2eunit,Vvar__1___24Anonymous__81,cCoq_2eInit_2eDatatypes_2ett) ) )
| ? [Vvar__1___24Anonymous__85] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__85)
& ? [Vvar__2___24Anonymous__86] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__86)
& V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__85,Vvar__2___24Anonymous__86)
& cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM2___24a3(cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eMapDom___24a2(V0__A,Vvar__1___24Anonymous__85),cIntMap_2eFset_2eMapDom___24a2(V0__A,Vvar__2___24Anonymous__86)) ) ) ) ) ) ).
fof('$_def_IntMap.Fset.in_FSet',axiom,
cIntMap_2eFset_2ein__FSet = cIntMap_2eFset_2ein__dom___24a1(cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_def_IntMap.Fset.in_dom',axiom,
! [V0__A,V1__a,V2__m] :
( cType___24t(V0__A)
=> ( cIntMap_2eMap_2ead___24t(V1__a)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ( ? [Vvar__1___24Anonymous__1687] :
( t(Vvar__1___24Anonymous__1687,V0__A)
& cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m,V1__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__1687)
& cIntMap_2eFset_2ein__dom___24a3(V0__A,V1__a,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m,V1__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cIntMap_2eFset_2ein__dom___24a3(V0__A,V1__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
fof('$_def_IntMap.Lsort.ad_monotonic',axiom,
! [V0__pf] :
( cIntMap_2eLsort_2ead__monotonic___24a1(V0__pf)
<=> ! [V1__a] :
( cIntMap_2eMap_2ead___24t(V1__a)
=> ! [V2__a_27] :
( cIntMap_2eMap_2ead___24t(V2__a_27)
=> ( cCoq_2eNArith_2eNdigits_2eNless___24a2(V1__a,V2__a_27) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eNArith_2eNdigits_2eNless___24a2(happ(V0__pf,V1__a),happ(V0__pf,V2__a_27)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('$_def_IntMap.Lsort.alist_nth_ad',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cIntMap_2eMapiter_2ealist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
& cIntMap_2eLsort_2ealist__nth__ad___24a3(V0__A,V2__n,V3__l) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__1___24Anonymous__9151] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__9151)
& ? [Vvar__2___24Anonymous__9152] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__2___24Anonymous__9152)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__9151)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__9151,Vvar__2___24Anonymous__9152)
& ? [Vvar__2___24Anonymous__9168] :
( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__9168)
& ? [Vvar__3___24Anonymous__9169] :
( t(Vvar__3___24Anonymous__9169,V0__A)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( Vvar__1___24Anonymous__9151 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,Vvar__2___24Anonymous__9168,Vvar__3___24Anonymous__9169)
& ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cIntMap_2eLsort_2ealist__nth__ad___24a3(V0__A,V2__n,V3__l) = Vvar__2___24Anonymous__9168 )
| ? [Vvar__0___24Anonymous__9175] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9175)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9175)
& cIntMap_2eLsort_2ealist__nth__ad___24a3(V0__A,V2__n,V3__l) = cIntMap_2eLsort_2ealist__nth__ad___24a3(V0__A,Vvar__0___24Anonymous__9175,Vvar__2___24Anonymous__9152) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_IntMap.Map.MapCard',axiom,
! [V0__A,V2__m] :
( cType___24t(V0__A)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
& cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__256] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__256)
& ? [Vvar__2___24Anonymous__257] :
( t(Vvar__2___24Anonymous__257,V0__A)
& V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__256,Vvar__2___24Anonymous__257)
& cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) )
| ? [Vvar__1___24Anonymous__260] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__260)
& ? [Vvar__2___24Anonymous__261] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__261)
& V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__260,Vvar__2___24Anonymous__261)
& cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,Vvar__1___24Anonymous__260),cIntMap_2eMap_2eMapCard___24a2(V0__A,Vvar__2___24Anonymous__261)) ) ) ) ) ) ).
fof('$_def_IntMap.Map.MapEmptyp',axiom,
! [V0__A,V1__m] :
( cType___24t(V0__A)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ( ( V1__m = cIntMap_2eMap_2eM0___24a1(V0__A)
& cIntMap_2eMap_2eMapEmptyp___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1___24Anonymous__9750] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__9750)
& ? [Vvar__2___24Anonymous__9751] :
( t(Vvar__2___24Anonymous__9751,V0__A)
& V1__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__9750,Vvar__2___24Anonymous__9751)
& cIntMap_2eMap_2eMapEmptyp___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__9754] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__9754)
& ? [Vvar__2___24Anonymous__9755] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__9755)
& V1__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__9754,Vvar__2___24Anonymous__9755)
& cIntMap_2eMap_2eMapEmptyp___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
fof('$_def_IntMap.Map.MapGet',axiom,
! [V0__A,V2__m] :
( cType___24t(V0__A)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
& cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__1783___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__1759] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1759)
& ? [Vvar__2___24Anonymous__1760] :
( t(Vvar__2___24Anonymous__1760,V0__A)
& V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1759,Vvar__2___24Anonymous__1760)
& cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__1791___24a3(V0__A,Vvar__1___24Anonymous__1759,Vvar__2___24Anonymous__1760) ) )
| ? [Vvar__1___24Anonymous__1767] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1767)
& ? [Vvar__2___24Anonymous__1768] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1768)
& V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1767,Vvar__2___24Anonymous__1768)
& cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__1818___24a3(V0__A,Vvar__1___24Anonymous__1767,Vvar__2___24Anonymous__1768) ) ) ) ) ) ).
fof('$_def_IntMap.Map.MapMerge',axiom,
! [V0__A,V2__m] :
( cType___24t(V0__A)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
& cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__388___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__1186] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1186)
& ? [Vvar__2___24Anonymous__1187] :
( t(Vvar__2___24Anonymous__1187,V0__A)
& V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1186,Vvar__2___24Anonymous__1187)
& cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__1211___24a3(V0__A,Vvar__1___24Anonymous__1186,Vvar__2___24Anonymous__1187) ) )
| ? [Vvar__1___24Anonymous__1192] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1192)
& ? [Vvar__2___24Anonymous__1193] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1193)
& V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1192,Vvar__2___24Anonymous__1193)
& cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__1243___24a4(V0__A,V2__m,Vvar__1___24Anonymous__1192,Vvar__2___24Anonymous__1193) ) ) ) ) ) ).
fof('$_def_IntMap.Map.MapPut',axiom,
! [V0__A,V2__m] :
( cType___24t(V0__A)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
& cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM1___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__154] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__154)
& ? [Vvar__2___24Anonymous__155] :
( t(Vvar__2___24Anonymous__155,V0__A)
& V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__154,Vvar__2___24Anonymous__155)
& cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = c_24__lam__200___24a3(V0__A,Vvar__1___24Anonymous__154,Vvar__2___24Anonymous__155) ) )
| ? [Vvar__1___24Anonymous__166] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__166)
& ? [Vvar__2___24Anonymous__167] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__167)
& V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__166,Vvar__2___24Anonymous__167)
& cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = c_24__lam__237___24a3(V0__A,Vvar__1___24Anonymous__166,Vvar__2___24Anonymous__167) ) ) ) ) ) ).
fof('$_def_IntMap.Map.MapPut1',axiom,
! [V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
=> ( ? [Vvar__0___24Anonymous__961] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__961)
& ( cType___24t(V0__A)
=> ( cIntMap_2eMap_2ead___24t(V2__a)
=> ( V6__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__961)
& ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2etrue
& cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y)) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2efalse
& cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__963] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__963)
& V6__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__963)
& cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24975___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__963) )
| ( cType___24t(V0__A)
=> ( cIntMap_2eMap_2ead___24t(V2__a)
=> ( V6__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2etrue
& cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y)) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2efalse
& cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27)) ) ) ) ) ) ) ) ) ).
fof('$_def_IntMap.Map.MapPut_behind',axiom,
! [V0__A,V2__m] :
( cType___24t(V0__A)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
& cIntMap_2eMap_2eMapPut__behind___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM1___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__997] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__997)
& ? [Vvar__2___24Anonymous__998] :
( t(Vvar__2___24Anonymous__998,V0__A)
& V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__997,Vvar__2___24Anonymous__998)
& cIntMap_2eMap_2eMapPut__behind___24a2(V0__A,V2__m) = c_24__lam__1047___24a4(V0__A,V2__m,Vvar__1___24Anonymous__997,Vvar__2___24Anonymous__998) ) )
| ? [Vvar__1___24Anonymous__1009] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1009)
& ? [Vvar__2___24Anonymous__1010] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1010)
& V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1009,Vvar__2___24Anonymous__1010)
& cIntMap_2eMap_2eMapPut__behind___24a2(V0__A,V2__m) = c_24__lam__1084___24a3(V0__A,Vvar__1___24Anonymous__1009,Vvar__2___24Anonymous__1010) ) ) ) ) ) ).
fof('$_def_IntMap.Map.ad',axiom,
! [Vvar__91] :
( cIntMap_2eMap_2ead___24t(Vvar__91)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__91) ) ).
fof('$_def_IntMap.Mapaxioms.eqmap',axiom,
! [V0__A,V1__m,V2__m_27] :
( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
<=> cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,V1__m),cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m_27)) ) ).
fof('$_def_IntMap.Mapiter.MapFold',axiom,
! [V0__A,V1__M,V2__neutral,V3__op,V4__f,V5__m] : cIntMap_2eMapiter_2eMapFold___24a6(V0__A,V1__M,V2__neutral,V3__op,V4__f,V5__m) = cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V4__f,c_24__lam__1312___24a2(V0__A,V1__M),V5__m) ).
fof('$_def_IntMap.Mapiter.MapFold1',axiom,
! [V0__A,V1__M,V2__neutral,V3__op,V5__f,V6__pf,V7__m] :
( cType___24t(V0__A)
=> ( cType___24t(V1__M)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,V7__m)
=> ( ( V7__m = cIntMap_2eMap_2eM0___24a1(V0__A)
& cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V5__f,V6__pf,V7__m) = V2__neutral )
| ? [Vvar__1___24Anonymous__1335] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1335)
& ? [Vvar__2___24Anonymous__1336] :
( t(Vvar__2___24Anonymous__1336,V0__A)
& V7__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__1335,Vvar__2___24Anonymous__1336)
& cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V5__f,V6__pf,V7__m) = happ(happ(V5__f,happ(V6__pf,Vvar__1___24Anonymous__1335)),Vvar__2___24Anonymous__1336) ) )
| ? [Vvar__1___24Anonymous__1339] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__1339)
& ? [Vvar__2___24Anonymous__1340] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__1340)
& V7__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__1339,Vvar__2___24Anonymous__1340)
& cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V5__f,V6__pf,V7__m) = happ(happ(V3__op,cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V5__f,c_24__lam__1351___24a3(V0__A,V1__M,V6__pf),Vvar__1___24Anonymous__1339)),cIntMap_2eMapiter_2eMapFold1___24a7(V0__A,V1__M,V2__neutral,V3__op,V5__f,c_24__lam__1357___24a3(V0__A,V1__M,V6__pf),Vvar__2___24Anonymous__1340)) ) ) ) ) ) ) ).
fof('$_def_IntMap.Mapiter.MapSweep',axiom,
! [V0__A,V1__f,V2__m] : cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,V1__f,V2__m) = cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,c_24__lam__10627___24a1(V0__A),V2__m) ).
fof('$_def_IntMap.Mapiter.MapSweep1',axiom,
! [V0__A,V1__f,V3__pf,V4__m] :
( cType___24t(V0__A)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m)
=> ( ( V4__m = cIntMap_2eMap_2eM0___24a1(V0__A)
& cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,V3__pf,V4__m) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A)) )
| ? [Vvar__1___24Anonymous__10574] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__10574)
& ? [Vvar__2___24Anonymous__10575] :
( t(Vvar__2___24Anonymous__10575,V0__A)
& V4__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__10574,Vvar__2___24Anonymous__10575)
& cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,V3__pf,V4__m) = cIntMap_2eMapiter_2eMapSweep2___24a4(V0__A,V1__f,happ(V3__pf,Vvar__1___24Anonymous__10574),Vvar__2___24Anonymous__10575) ) )
| ? [Vvar__1___24Anonymous__10578] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__10578)
& ? [Vvar__2___24Anonymous__10579] :
( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__10579)
& ( cType___24t(V0__A)
=> ( c_24__type__10443___24t(V0__A,V1__f)
=> ( c_24__type__9263___24t(V0__A,V3__pf)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__10578)
=> ( V4__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__10578,Vvar__2___24Anonymous__10579)
& ( ? [Vvar__1___24Anonymous__10591] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__10591)
& cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,c_24__lam__10600___24a2(V0__A,V3__pf),Vvar__1___24Anonymous__10578) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__10591)
& cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,V3__pf,V4__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__10591) )
| ( cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,c_24__lam__10604___24a2(V0__A,V3__pf),Vvar__1___24Anonymous__10578) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
& cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,V3__pf,V4__m) = cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,c_24__lam__10608___24a2(V0__A,V3__pf),Vvar__2___24Anonymous__10579) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_IntMap.Mapiter.MapSweep2',axiom,
! [V0__A,V1__f,V2__a0,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__10443___24t(V0__A,V1__f)
=> ( cIntMap_2eMap_2ead___24t(V2__a0)
=> ( t(V3__y,V0__A)
=> ( ( happ(happ(V1__f,V2__a0),V3__y) = cCoq_2eInit_2eDatatypes_2etrue
& cIntMap_2eMapiter_2eMapSweep2___24a4(V0__A,V1__f,V2__a0,V3__y) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,V2__a0,V3__y)) )
| ( happ(happ(V1__f,V2__a0),V3__y) = cCoq_2eInit_2eDatatypes_2efalse
& cIntMap_2eMapiter_2eMapSweep2___24a4(V0__A,V1__f,V2__a0,V3__y) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A)) ) ) ) ) ) ) ).
fof('$_def_IntMap.Mapiter.aapp',axiom,
! [V0__A] : cIntMap_2eMapiter_2eaapp___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2eapp___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A)) ).
fof('$_def_IntMap.Mapiter.alist',axiom,
! [V0__A] : cIntMap_2eMapiter_2ealist___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A)) ).
fof('$_def_IntMap.Mapiter.alist_semantics',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cIntMap_2eMapiter_2ealist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
& cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,V2__l) = c_24__lam__1783___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__11275] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__11275)
& ? [Vvar__2___24Anonymous__11276] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__2___24Anonymous__11276)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__11275)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__11275,Vvar__2___24Anonymous__11276)
& ? [Vvar__2___24Anonymous__11294] :
( cIntMap_2eMap_2ead___24t(Vvar__2___24Anonymous__11294)
& ? [Vvar__3___24Anonymous__11295] :
( t(Vvar__3___24Anonymous__11295,V0__A)
& Vvar__1___24Anonymous__11275 = cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,V0__A,Vvar__2___24Anonymous__11294,Vvar__3___24Anonymous__11295)
& cIntMap_2eMapiter_2ealist__semantics___24a2(V0__A,V2__l) = c_24__lam__11311___24a4(V0__A,Vvar__2___24Anonymous__11276,Vvar__2___24Anonymous__11294,Vvar__3___24Anonymous__11295) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_IntMap.Mapsubset.MapDisjoint',axiom,
! [V0__A,V1__B,V2__m,V3__m_27] :
( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,V3__m_27)
<=> ! [V4__a] :
( cIntMap_2eMap_2ead___24t(V4__a)
=> ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V2__m) = cCoq_2eInit_2eDatatypes_2etrue
=> ( cIntMap_2eFset_2ein__dom___24a3(V1__B,V4__a,V3__m_27) = cCoq_2eInit_2eDatatypes_2etrue
=> p(c_24False) ) ) ) ) ).
fof('$_def_IntMap.Mapsubset.MapDisjoint_1',axiom,
! [V0__A,V1__B,V2__m,V3__m_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
=> ( ? [Vvar__1___24Anonymous__11668] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,V0__A,Vvar__1___24Anonymous__11668)
& cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,c_24__lam__11677___24a3(V0__A,V1__B,V3__m_27),V2__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A),Vvar__1___24Anonymous__11668)
& cIntMap_2eMapsubset_2eMapDisjoint__1___24a4(V0__A,V1__B,V2__m,V3__m_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,c_24__lam__11677___24a3(V0__A,V1__B,V3__m_27),V2__m) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
& cIntMap_2eMapsubset_2eMapDisjoint__1___24a4(V0__A,V1__B,V2__m,V3__m_27) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_IntMap.Mapsubset.MapSubset',axiom,
! [V0__A,V1__B,V2__m,V3__m_27] :
( cIntMap_2eMapsubset_2eMapSubset___24a4(V0__A,V1__B,V2__m,V3__m_27)
<=> ! [V4__a] :
( cIntMap_2eMap_2ead___24t(V4__a)
=> ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V2__m) = cCoq_2eInit_2eDatatypes_2etrue
=> cIntMap_2eFset_2ein__dom___24a3(V1__B,V4__a,V3__m_27) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_def_Maplists.MapLists.Elems',axiom,
! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)
& cMaplists_2eMapLists_2eElems___24a1(V1__l) = cIntMap_2eMap_2eM0___24a1(cCoq_2eInit_2eDatatypes_2eunit) )
| ? [Vvar__1___24Anonymous__290] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__290)
& ? [Vvar__2___24Anonymous__291] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,Vvar__2___24Anonymous__291)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead,Vvar__1___24Anonymous__290,Vvar__2___24Anonymous__291)
& cMaplists_2eMapLists_2eElems___24a1(V1__l) = cIntMap_2eMap_2eMapPut___24a4(cCoq_2eInit_2eDatatypes_2eunit,cMaplists_2eMapLists_2eElems___24a1(Vvar__2___24Anonymous__291),Vvar__1___24Anonymous__290,cCoq_2eInit_2eDatatypes_2ett) ) ) ) ) ).
fof('$_def_Maplists.MapLists.ad_in_list',axiom,
! [V1__a,V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)
& cMaplists_2eMapLists_2ead__in__list___24a2(V1__a,V2__l) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__791] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__791)
& ? [Vvar__2___24Anonymous__792] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,Vvar__2___24Anonymous__792)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead,Vvar__1___24Anonymous__791,Vvar__2___24Anonymous__792)
& cMaplists_2eMapLists_2ead__in__list___24a2(V1__a,V2__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__a,Vvar__1___24Anonymous__791),cMaplists_2eMapLists_2ead__in__list___24a2(V1__a,Vvar__2___24Anonymous__792)) ) ) ) ) ).
fof('$_def_Maplists.MapLists.ad_list_stutters',axiom,
! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)
& cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__782] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782)
& ? [Vvar__2___24Anonymous__783] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,Vvar__2___24Anonymous__783)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead,Vvar__1___24Anonymous__782,Vvar__2___24Anonymous__783)
& cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782,Vvar__2___24Anonymous__783),cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783)) ) ) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__24545,Vvar__1___24Anonymous__24546,Vvar__0__P__24547,Vvar__1___24Anonymous__24548] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__24545) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__24547) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__38722,Vvar__1___24Anonymous__38723,Vvar__2___24Anonymous__38724] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__38722,Vvar__1___24Anonymous__38723,Vvar__2___24Anonymous__38724) ).
fof('$_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$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__1517,Vvar__1___24Anonymous__1518,Vvar__0__A__1519] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1517,Vvar__1___24Anonymous__1518) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1519) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__4760,Vvar__1__B__4761,Vvar__2___24Anonymous__4762,Vvar__0__A__4763,Vvar__1__B__4764,Vvar__2___24Anonymous__4765] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4760,Vvar__1__B__4761,Vvar__2___24Anonymous__4762) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4763,Vvar__1__B__4764,Vvar__2___24Anonymous__4765) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__17,Vvar__0__A__18,Vvar__1___24Anonymous__19,Vvar__2___24Anonymous__20] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__17) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18,Vvar__1___24Anonymous__19,Vvar__2___24Anonymous__20) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__2611,Vvar__1__B__2612,Vvar__2___24Anonymous__2613,Vvar__0__A__2614,Vvar__1__B__2615,Vvar__2___24Anonymous__2616] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2611,Vvar__1__B__2612,Vvar__2___24Anonymous__2613) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2614,Vvar__1__B__2615) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__648,Vvar__1__B__649,Vvar__2___24Anonymous__650,Vvar__0__A__651,Vvar__1__B__652,Vvar__2___24Anonymous__653] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__648,Vvar__1__B__649) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__651,Vvar__1__B__652) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__319] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__319) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1502] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1502) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__802,Vvar__0___24Anonymous__803] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__802) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__803) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__38139,Vvar__1___24Anonymous__38140] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__38139,Vvar__1___24Anonymous__38140) ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__26480,Vvar__0__n__26481,Vvar__1___24Anonymous__26482] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__26480) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__26481,Vvar__1___24Anonymous__26482) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__38228,Vvar__0__A__38229,Vvar__1__h__38230,Vvar__2__n__38231,Vvar__3___24Anonymous__38232] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__38228) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__38229,Vvar__1__h__38230,Vvar__2__n__38231,Vvar__3___24Anonymous__38232) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__5085,Vvar__1___24Anonymous__5086,Vvar__0__C__5087,Vvar__1___24Anonymous__5088,Vvar__2___24Anonymous__5089] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5085,Vvar__1___24Anonymous__5086) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5087,Vvar__1___24Anonymous__5088,Vvar__2___24Anonymous__5089) ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__11997,Vvar__1___24Anonymous__11998,Vvar__0__C__11999,Vvar__1___24Anonymous__12000] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__11997,Vvar__1___24Anonymous__11998) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__11999,Vvar__1___24Anonymous__12000) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__2984,Vvar__1__TX__2985,Vvar__2__AA__2986,Vvar__3__AF__2987,Vvar__0__TA__2988,Vvar__1__TX__2989,Vvar__2__AA__2990,Vvar__3__AF__2991] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__2984,Vvar__1__TX__2985,Vvar__2__AA__2986,Vvar__3__AF__2987) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__2988,Vvar__1__TX__2989,Vvar__2__AA__2990,Vvar__3__AF__2991) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__4080,Vvar__1___24Anonymous__4081] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__4080,Vvar__1___24Anonymous__4081) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__6214,Vvar__0__C__6215] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__6214) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__6215) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__14264,Vvar__0__C__14265] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14264) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14265) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__12215,Vvar__1___24Anonymous__12216,Vvar__0__C__12217,Vvar__1___24Anonymous__12218,Vvar__2___24Anonymous__12219] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12215,Vvar__1___24Anonymous__12216) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12217,Vvar__1___24Anonymous__12218,Vvar__2___24Anonymous__12219) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__12759,Vvar__1___24Anonymous__12760] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__12759,Vvar__1___24Anonymous__12760) ).
fof('$_discrim_IntMap.Map.M0$IntMap.Map.M1',axiom,
! [Vvar__0__A__111,Vvar__0__A__112,Vvar__1___24Anonymous__113,Vvar__2___24Anonymous__114] : cIntMap_2eMap_2eM0___24a1(Vvar__0__A__111) != cIntMap_2eMap_2eM1___24a3(Vvar__0__A__112,Vvar__1___24Anonymous__113,Vvar__2___24Anonymous__114) ).
fof('$_fix_23737_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__23752] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23752)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23752)
& ( ? [Vvar__0___24Anonymous__23756] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23756)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23756)
& c_24__fix__23737__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__23737__1__add__carry___24a2(Vvar__0___24Anonymous__23752,Vvar__0___24Anonymous__23756)) )
| ? [Vvar__0___24Anonymous__23757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23757)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23757)
& c_24__fix__23737__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__23737__1__add__carry___24a2(Vvar__0___24Anonymous__23752,Vvar__0___24Anonymous__23757)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__23737__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__23752)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23758] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23758)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23758)
& ( ? [Vvar__0___24Anonymous__23762] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23762)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23762)
& c_24__fix__23737__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__23737__1__add__carry___24a2(Vvar__0___24Anonymous__23758,Vvar__0___24Anonymous__23762)) )
| ? [Vvar__0___24Anonymous__23763] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23763)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23763)
& c_24__fix__23737__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__23758,Vvar__0___24Anonymous__23763)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__23737__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__23758)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__23764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23764)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23764)
& c_24__fix__23737__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__23764)) )
| ? [Vvar__0___24Anonymous__23765] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23765)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23765)
& c_24__fix__23737__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__23765)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__23737__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_fix_29069_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__29069__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__29073] :
( t(Vvar__1___24Anonymous__29073,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__29074] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__29074)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__29073,Vvar__2___24Anonymous__29074)
& c_24__fix__29069__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__29073,c_24__fix__29069__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__29074,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__24553,Vvar__0__P__24554,Vvar__1___24Anonymous__24555,Vvar__1___24Anonymous__24556] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__24553) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__24554)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__24553 = Vvar__0__P__24554 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__24549,Vvar__0__P__24550,Vvar__1___24Anonymous__24551,Vvar__1___24Anonymous__24552] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__24549) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__24550)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__24549 = Vvar__0__P__24550 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__38725,Vvar__0___24Anonymous__38726,Vvar__1___24Anonymous__38727,Vvar__1___24Anonymous__38728,Vvar__2___24Anonymous__38729,Vvar__2___24Anonymous__38730] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__38725,Vvar__1___24Anonymous__38727,Vvar__2___24Anonymous__38729) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__38726,Vvar__1___24Anonymous__38728,Vvar__2___24Anonymous__38730)
=> ( Vvar__2___24Anonymous__38729 = Vvar__2___24Anonymous__38730
& Vvar__1___24Anonymous__38727 = Vvar__1___24Anonymous__38728
& Vvar__0___24Anonymous__38725 = Vvar__0___24Anonymous__38726 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__1524,Vvar__0__A__1525] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1524) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1525)
=> Vvar__0__A__1524 = Vvar__0__A__1525 ) ).
fof('$_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('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__1520,Vvar__0__A__1521,Vvar__1___24Anonymous__1522,Vvar__1___24Anonymous__1523] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1520,Vvar__1___24Anonymous__1522) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1521,Vvar__1___24Anonymous__1523)
=> ( Vvar__1___24Anonymous__1522 = Vvar__1___24Anonymous__1523
& Vvar__0__A__1520 = Vvar__0__A__1521 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__23,Vvar__0__A__24,Vvar__1___24Anonymous__25,Vvar__1___24Anonymous__26,Vvar__2___24Anonymous__27,Vvar__2___24Anonymous__28] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23,Vvar__1___24Anonymous__25,Vvar__2___24Anonymous__27) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24,Vvar__1___24Anonymous__26,Vvar__2___24Anonymous__28)
=> ( Vvar__2___24Anonymous__27 = Vvar__2___24Anonymous__28
& Vvar__1___24Anonymous__25 = Vvar__1___24Anonymous__26
& Vvar__0__A__23 = Vvar__0__A__24 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__4766,Vvar__0__A__4767,Vvar__1__B__4768,Vvar__1__B__4769,Vvar__2___24Anonymous__4770,Vvar__2___24Anonymous__4771] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4766,Vvar__1__B__4768,Vvar__2___24Anonymous__4770) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4767,Vvar__1__B__4769,Vvar__2___24Anonymous__4771)
=> ( Vvar__2___24Anonymous__4770 = Vvar__2___24Anonymous__4771
& Vvar__1__B__4768 = Vvar__1__B__4769
& Vvar__0__A__4766 = Vvar__0__A__4767 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__4772,Vvar__0__A__4773,Vvar__1__B__4774,Vvar__1__B__4775,Vvar__2___24Anonymous__4776,Vvar__2___24Anonymous__4777] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4772,Vvar__1__B__4774,Vvar__2___24Anonymous__4776) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4773,Vvar__1__B__4775,Vvar__2___24Anonymous__4777)
=> ( Vvar__2___24Anonymous__4776 = Vvar__2___24Anonymous__4777
& Vvar__1__B__4774 = Vvar__1__B__4775
& Vvar__0__A__4772 = Vvar__0__A__4773 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__21,Vvar__0__A__22] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__21) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22)
=> Vvar__0__A__21 = Vvar__0__A__22 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__1541,Vvar__0__A__1542,Vvar__1__B__1543,Vvar__1__B__1544,Vvar__2___24Anonymous__1545,Vvar__2___24Anonymous__1546,Vvar__3___24Anonymous__1547,Vvar__3___24Anonymous__1548] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1541,Vvar__1__B__1543,Vvar__2___24Anonymous__1545,Vvar__3___24Anonymous__1547) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1542,Vvar__1__B__1544,Vvar__2___24Anonymous__1546,Vvar__3___24Anonymous__1548)
=> ( Vvar__3___24Anonymous__1547 = Vvar__3___24Anonymous__1548
& Vvar__2___24Anonymous__1545 = Vvar__2___24Anonymous__1546
& Vvar__1__B__1543 = Vvar__1__B__1544
& Vvar__0__A__1541 = Vvar__0__A__1542 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__497,Vvar__0__A__498,Vvar__1__P__499,Vvar__1__P__500,Vvar__2__x__501,Vvar__2__x__502,Vvar__3___24Anonymous__503,Vvar__3___24Anonymous__504] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__497,Vvar__1__P__499,Vvar__2__x__501) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__498,Vvar__1__P__500,Vvar__2__x__502)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__501 = Vvar__2__x__502
& Vvar__1__P__499 = Vvar__1__P__500
& Vvar__0__A__497 = Vvar__0__A__498 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__578,Vvar__0__A__579,Vvar__1__P__580,Vvar__1__P__581,Vvar__2__x__582,Vvar__2__x__583,Vvar__3___24Anonymous__584,Vvar__3___24Anonymous__585] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__578,Vvar__1__P__580,Vvar__2__x__582,Vvar__3___24Anonymous__584) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__579,Vvar__1__P__581,Vvar__2__x__583,Vvar__3___24Anonymous__585)
=> ( Vvar__3___24Anonymous__584 = Vvar__3___24Anonymous__585
& Vvar__2__x__582 = Vvar__2__x__583
& Vvar__1__P__580 = Vvar__1__P__581
& Vvar__0__A__578 = Vvar__0__A__579 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__2617,Vvar__0__A__2618,Vvar__1__B__2619,Vvar__1__B__2620,Vvar__2___24Anonymous__2621,Vvar__2___24Anonymous__2622] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2617,Vvar__1__B__2619,Vvar__2___24Anonymous__2621) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2618,Vvar__1__B__2620,Vvar__2___24Anonymous__2622)
=> ( Vvar__2___24Anonymous__2621 = Vvar__2___24Anonymous__2622
& Vvar__1__B__2619 = Vvar__1__B__2620
& Vvar__0__A__2617 = Vvar__0__A__2618 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__2623,Vvar__0__A__2624,Vvar__1__B__2625,Vvar__1__B__2626,Vvar__2___24Anonymous__2627,Vvar__2___24Anonymous__2628] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2623,Vvar__1__B__2625) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2624,Vvar__1__B__2626)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2625 = Vvar__1__B__2626
& Vvar__0__A__2623 = Vvar__0__A__2624 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__654,Vvar__0__A__655,Vvar__1__B__656,Vvar__1__B__657,Vvar__2___24Anonymous__658,Vvar__2___24Anonymous__659] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__654,Vvar__1__B__656) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__655,Vvar__1__B__657)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__656 = Vvar__1__B__657
& Vvar__0__A__654 = Vvar__0__A__655 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__660,Vvar__0__A__661,Vvar__1__B__662,Vvar__1__B__663,Vvar__2___24Anonymous__664,Vvar__2___24Anonymous__665] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__660,Vvar__1__B__662) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__661,Vvar__1__B__663)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__662 = Vvar__1__B__663
& Vvar__0__A__660 = Vvar__0__A__661 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__320,Vvar__0___24Anonymous__321] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__320) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__321)
=> Vvar__0___24Anonymous__320 = Vvar__0___24Anonymous__321 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__1505,Vvar__0___24Anonymous__1506] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1505) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1506)
=> Vvar__0___24Anonymous__1505 = Vvar__0___24Anonymous__1506 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1503,Vvar__0___24Anonymous__1504] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1503) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1504)
=> Vvar__0___24Anonymous__1503 = Vvar__0___24Anonymous__1504 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__804,Vvar__0___24Anonymous__805] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__804) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__805)
=> Vvar__0___24Anonymous__804 = Vvar__0___24Anonymous__805 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__806,Vvar__0___24Anonymous__807] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__806) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__807)
=> Vvar__0___24Anonymous__806 = Vvar__0___24Anonymous__807 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__1910,Vvar__0__Qnum__1911,Vvar__1__Qden__1912,Vvar__1__Qden__1913] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__1910,Vvar__1__Qden__1912) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__1911,Vvar__1__Qden__1913)
=> ( Vvar__1__Qden__1912 = Vvar__1__Qden__1913
& Vvar__0__Qnum__1910 = Vvar__0__Qnum__1911 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__24419,Vvar__0___24Anonymous__24420,Vvar__1___24Anonymous__24421,Vvar__1___24Anonymous__24422,Vvar__2___24Anonymous__24423,Vvar__2___24Anonymous__24424,Vvar__3___24Anonymous__24425,Vvar__3___24Anonymous__24426,Vvar__4___24Anonymous__24427,Vvar__4___24Anonymous__24428,Vvar__5___24Anonymous__24429,Vvar__5___24Anonymous__24430,Vvar__6___24Anonymous__24431,Vvar__6___24Anonymous__24432,Vvar__7___24Anonymous__24433,Vvar__7___24Anonymous__24434] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__24419,Vvar__1___24Anonymous__24421,Vvar__2___24Anonymous__24423,Vvar__3___24Anonymous__24425,Vvar__4___24Anonymous__24427,Vvar__5___24Anonymous__24429,Vvar__6___24Anonymous__24431,Vvar__7___24Anonymous__24433) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__24420,Vvar__1___24Anonymous__24422,Vvar__2___24Anonymous__24424,Vvar__3___24Anonymous__24426,Vvar__4___24Anonymous__24428,Vvar__5___24Anonymous__24430,Vvar__6___24Anonymous__24432,Vvar__7___24Anonymous__24434)
=> ( Vvar__7___24Anonymous__24433 = Vvar__7___24Anonymous__24434
& Vvar__6___24Anonymous__24431 = Vvar__6___24Anonymous__24432
& Vvar__5___24Anonymous__24429 = Vvar__5___24Anonymous__24430
& Vvar__4___24Anonymous__24427 = Vvar__4___24Anonymous__24428
& Vvar__3___24Anonymous__24425 = Vvar__3___24Anonymous__24426
& Vvar__2___24Anonymous__24423 = Vvar__2___24Anonymous__24424
& Vvar__1___24Anonymous__24421 = Vvar__1___24Anonymous__24422
& Vvar__0___24Anonymous__24419 = Vvar__0___24Anonymous__24420 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__38141,Vvar__0___24Anonymous__38142,Vvar__1___24Anonymous__38143,Vvar__1___24Anonymous__38144] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__38141,Vvar__1___24Anonymous__38143) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__38142,Vvar__1___24Anonymous__38144)
=> ( Vvar__1___24Anonymous__38143 = Vvar__1___24Anonymous__38144
& Vvar__0___24Anonymous__38141 = Vvar__0___24Anonymous__38142 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__26483,Vvar__0__n__26484] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__26483) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__26484)
=> Vvar__0__n__26483 = Vvar__0__n__26484 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__26485,Vvar__0__n__26486,Vvar__1___24Anonymous__26487,Vvar__1___24Anonymous__26488] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__26485,Vvar__1___24Anonymous__26487) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__26486,Vvar__1___24Anonymous__26488)
=> ( Vvar__1___24Anonymous__26487 = Vvar__1___24Anonymous__26488
& Vvar__0__n__26485 = Vvar__0__n__26486 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__38235,Vvar__0__A__38236,Vvar__1__h__38237,Vvar__1__h__38238,Vvar__2__n__38239,Vvar__2__n__38240,Vvar__3___24Anonymous__38241,Vvar__3___24Anonymous__38242] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__38235,Vvar__1__h__38237,Vvar__2__n__38239,Vvar__3___24Anonymous__38241) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__38236,Vvar__1__h__38238,Vvar__2__n__38240,Vvar__3___24Anonymous__38242)
=> ( Vvar__3___24Anonymous__38241 = Vvar__3___24Anonymous__38242
& Vvar__2__n__38239 = Vvar__2__n__38240
& Vvar__1__h__38237 = Vvar__1__h__38238
& Vvar__0__A__38235 = Vvar__0__A__38236 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__38233,Vvar__0__A__38234] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__38233) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__38234)
=> Vvar__0__A__38233 = Vvar__0__A__38234 ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__5100,Vvar__0__C__5101,Vvar__1___24Anonymous__5102,Vvar__1___24Anonymous__5103,Vvar__2___24Anonymous__5104,Vvar__2___24Anonymous__5105,Vvar__3___24Anonymous__5106,Vvar__3___24Anonymous__5107] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__5100,Vvar__1___24Anonymous__5102,Vvar__2___24Anonymous__5104,Vvar__3___24Anonymous__5106) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__5101,Vvar__1___24Anonymous__5103,Vvar__2___24Anonymous__5105,Vvar__3___24Anonymous__5107)
=> ( Vvar__3___24Anonymous__5106 = Vvar__3___24Anonymous__5107
& Vvar__2___24Anonymous__5104 = Vvar__2___24Anonymous__5105
& Vvar__1___24Anonymous__5102 = Vvar__1___24Anonymous__5103
& Vvar__0__C__5100 = Vvar__0__C__5101 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__5090,Vvar__0__C__5091,Vvar__1___24Anonymous__5092,Vvar__1___24Anonymous__5093] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5090,Vvar__1___24Anonymous__5092) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5091,Vvar__1___24Anonymous__5093)
=> ( Vvar__1___24Anonymous__5092 = Vvar__1___24Anonymous__5093
& Vvar__0__C__5090 = Vvar__0__C__5091 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__5094,Vvar__0__C__5095,Vvar__1___24Anonymous__5096,Vvar__1___24Anonymous__5097,Vvar__2___24Anonymous__5098,Vvar__2___24Anonymous__5099] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5094,Vvar__1___24Anonymous__5096,Vvar__2___24Anonymous__5098) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5095,Vvar__1___24Anonymous__5097,Vvar__2___24Anonymous__5099)
=> ( Vvar__2___24Anonymous__5098 = Vvar__2___24Anonymous__5099
& Vvar__1___24Anonymous__5096 = Vvar__1___24Anonymous__5097
& Vvar__0__C__5094 = Vvar__0__C__5095 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__2536,Vvar__0__T__2537,Vvar__1__Flhs__2538,Vvar__1__Flhs__2539,Vvar__2__Fop__2540,Vvar__2__Fop__2541,Vvar__3__Frhs__2542,Vvar__3__Frhs__2543] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__2536,Vvar__1__Flhs__2538,Vvar__2__Fop__2540,Vvar__3__Frhs__2542) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__2537,Vvar__1__Flhs__2539,Vvar__2__Fop__2541,Vvar__3__Frhs__2543)
=> ( Vvar__3__Frhs__2542 = Vvar__3__Frhs__2543
& Vvar__2__Fop__2540 = Vvar__2__Fop__2541
& Vvar__1__Flhs__2538 = Vvar__1__Flhs__2539
& Vvar__0__T__2536 = Vvar__0__T__2537 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__12021,Vvar__0__C__12022,Vvar__1___24Anonymous__12023,Vvar__1___24Anonymous__12024,Vvar__2___24Anonymous__12025,Vvar__2___24Anonymous__12026] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__12021,Vvar__1___24Anonymous__12023,Vvar__2___24Anonymous__12025) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__12022,Vvar__1___24Anonymous__12024,Vvar__2___24Anonymous__12026)
=> ( Vvar__2___24Anonymous__12025 = Vvar__2___24Anonymous__12026
& Vvar__1___24Anonymous__12023 = Vvar__1___24Anonymous__12024
& Vvar__0__C__12021 = Vvar__0__C__12022 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__12027,Vvar__0__C__12028,Vvar__1___24Anonymous__12029,Vvar__1___24Anonymous__12030] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__12027,Vvar__1___24Anonymous__12029) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__12028,Vvar__1___24Anonymous__12030)
=> ( Vvar__1___24Anonymous__12029 = Vvar__1___24Anonymous__12030
& Vvar__0__C__12027 = Vvar__0__C__12028 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__12001,Vvar__0__C__12002,Vvar__1___24Anonymous__12003,Vvar__1___24Anonymous__12004] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__12001,Vvar__1___24Anonymous__12003) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__12002,Vvar__1___24Anonymous__12004)
=> ( Vvar__1___24Anonymous__12003 = Vvar__1___24Anonymous__12004
& Vvar__0__C__12001 = Vvar__0__C__12002 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__12009,Vvar__0__C__12010,Vvar__1___24Anonymous__12011,Vvar__1___24Anonymous__12012,Vvar__2___24Anonymous__12013,Vvar__2___24Anonymous__12014] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__12009,Vvar__1___24Anonymous__12011,Vvar__2___24Anonymous__12013) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__12010,Vvar__1___24Anonymous__12012,Vvar__2___24Anonymous__12014)
=> ( Vvar__2___24Anonymous__12013 = Vvar__2___24Anonymous__12014
& Vvar__1___24Anonymous__12011 = Vvar__1___24Anonymous__12012
& Vvar__0__C__12009 = Vvar__0__C__12010 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__12015,Vvar__0__C__12016,Vvar__1___24Anonymous__12017,Vvar__1___24Anonymous__12018,Vvar__2___24Anonymous__12019,Vvar__2___24Anonymous__12020] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__12015,Vvar__1___24Anonymous__12017,Vvar__2___24Anonymous__12019) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__12016,Vvar__1___24Anonymous__12018,Vvar__2___24Anonymous__12020)
=> ( Vvar__2___24Anonymous__12019 = Vvar__2___24Anonymous__12020
& Vvar__1___24Anonymous__12017 = Vvar__1___24Anonymous__12018
& Vvar__0__C__12015 = Vvar__0__C__12016 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__12005,Vvar__0__C__12006,Vvar__1___24Anonymous__12007,Vvar__1___24Anonymous__12008] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__12005,Vvar__1___24Anonymous__12007) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__12006,Vvar__1___24Anonymous__12008)
=> ( Vvar__1___24Anonymous__12007 = Vvar__1___24Anonymous__12008
& Vvar__0__C__12005 = Vvar__0__C__12006 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__12031,Vvar__0__C__12032] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__12031) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__12032)
=> Vvar__0__C__12031 = Vvar__0__C__12032 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__3018,Vvar__0__TA__3019,Vvar__1__TX__3020,Vvar__1__TX__3021,Vvar__2__AA__3022,Vvar__2__AA__3023,Vvar__3__AF__3024,Vvar__3__AF__3025,Vvar__4___24Anonymous__3026,Vvar__4___24Anonymous__3027,Vvar__5___24Anonymous__3028,Vvar__5___24Anonymous__3029] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__3018,Vvar__1__TX__3020,Vvar__2__AA__3022,Vvar__3__AF__3024,Vvar__4___24Anonymous__3026,Vvar__5___24Anonymous__3028) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__3019,Vvar__1__TX__3021,Vvar__2__AA__3023,Vvar__3__AF__3025,Vvar__4___24Anonymous__3027,Vvar__5___24Anonymous__3029)
=> ( Vvar__5___24Anonymous__3028 = Vvar__5___24Anonymous__3029
& Vvar__4___24Anonymous__3026 = Vvar__4___24Anonymous__3027
& Vvar__3__AF__3024 = Vvar__3__AF__3025
& Vvar__2__AA__3022 = Vvar__2__AA__3023
& Vvar__1__TX__3020 = Vvar__1__TX__3021
& Vvar__0__TA__3018 = Vvar__0__TA__3019 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__3030,Vvar__0__TA__3031,Vvar__1__TX__3032,Vvar__1__TX__3033,Vvar__2__AA__3034,Vvar__2__AA__3035,Vvar__3__AF__3036,Vvar__3__AF__3037,Vvar__4___24Anonymous__3038,Vvar__4___24Anonymous__3039,Vvar__5___24Anonymous__3040,Vvar__5___24Anonymous__3041] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__3030,Vvar__1__TX__3032,Vvar__2__AA__3034,Vvar__3__AF__3036,Vvar__4___24Anonymous__3038,Vvar__5___24Anonymous__3040) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__3031,Vvar__1__TX__3033,Vvar__2__AA__3035,Vvar__3__AF__3037,Vvar__4___24Anonymous__3039,Vvar__5___24Anonymous__3041)
=> ( Vvar__5___24Anonymous__3040 = Vvar__5___24Anonymous__3041
& Vvar__4___24Anonymous__3038 = Vvar__4___24Anonymous__3039
& Vvar__3__AF__3036 = Vvar__3__AF__3037
& Vvar__2__AA__3034 = Vvar__2__AA__3035
& Vvar__1__TX__3032 = Vvar__1__TX__3033
& Vvar__0__TA__3030 = Vvar__0__TA__3031 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__3042,Vvar__0__TA__3043,Vvar__1__TX__3044,Vvar__1__TX__3045,Vvar__2__AA__3046,Vvar__2__AA__3047,Vvar__3__AF__3048,Vvar__3__AF__3049,Vvar__4___24Anonymous__3050,Vvar__4___24Anonymous__3051,Vvar__5___24Anonymous__3052,Vvar__5___24Anonymous__3053] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__3042,Vvar__1__TX__3044,Vvar__2__AA__3046,Vvar__3__AF__3048,Vvar__4___24Anonymous__3050,Vvar__5___24Anonymous__3052) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__3043,Vvar__1__TX__3045,Vvar__2__AA__3047,Vvar__3__AF__3049,Vvar__4___24Anonymous__3051,Vvar__5___24Anonymous__3053)
=> ( Vvar__5___24Anonymous__3052 = Vvar__5___24Anonymous__3053
& Vvar__4___24Anonymous__3050 = Vvar__4___24Anonymous__3051
& Vvar__3__AF__3048 = Vvar__3__AF__3049
& Vvar__2__AA__3046 = Vvar__2__AA__3047
& Vvar__1__TX__3044 = Vvar__1__TX__3045
& Vvar__0__TA__3042 = Vvar__0__TA__3043 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__3000,Vvar__0__TA__3001,Vvar__1__TX__3002,Vvar__1__TX__3003,Vvar__2__AA__3004,Vvar__2__AA__3005,Vvar__3__AF__3006,Vvar__3__AF__3007] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__3000,Vvar__1__TX__3002,Vvar__2__AA__3004,Vvar__3__AF__3006) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__3001,Vvar__1__TX__3003,Vvar__2__AA__3005,Vvar__3__AF__3007)
=> ( Vvar__3__AF__3006 = Vvar__3__AF__3007
& Vvar__2__AA__3004 = Vvar__2__AA__3005
& Vvar__1__TX__3002 = Vvar__1__TX__3003
& Vvar__0__TA__3000 = Vvar__0__TA__3001 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__3064,Vvar__0__TA__3065,Vvar__1__TX__3066,Vvar__1__TX__3067,Vvar__2__AA__3068,Vvar__2__AA__3069,Vvar__3__AF__3070,Vvar__3__AF__3071,Vvar__4___24Anonymous__3072,Vvar__4___24Anonymous__3073,Vvar__5___24Anonymous__3074,Vvar__5___24Anonymous__3075,Vvar__6___24Anonymous__3076,Vvar__6___24Anonymous__3077] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__3064,Vvar__1__TX__3066,Vvar__2__AA__3068,Vvar__3__AF__3070,Vvar__4___24Anonymous__3072,Vvar__5___24Anonymous__3074,Vvar__6___24Anonymous__3076) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__3065,Vvar__1__TX__3067,Vvar__2__AA__3069,Vvar__3__AF__3071,Vvar__4___24Anonymous__3073,Vvar__5___24Anonymous__3075,Vvar__6___24Anonymous__3077)
=> ( Vvar__6___24Anonymous__3076 = Vvar__6___24Anonymous__3077
& Vvar__5___24Anonymous__3074 = Vvar__5___24Anonymous__3075
& Vvar__4___24Anonymous__3072 = Vvar__4___24Anonymous__3073
& Vvar__3__AF__3070 = Vvar__3__AF__3071
& Vvar__2__AA__3068 = Vvar__2__AA__3069
& Vvar__1__TX__3066 = Vvar__1__TX__3067
& Vvar__0__TA__3064 = Vvar__0__TA__3065 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__3054,Vvar__0__TA__3055,Vvar__1__TX__3056,Vvar__1__TX__3057,Vvar__2__AA__3058,Vvar__2__AA__3059,Vvar__3__AF__3060,Vvar__3__AF__3061,Vvar__4___24Anonymous__3062,Vvar__4___24Anonymous__3063] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__3054,Vvar__1__TX__3056,Vvar__2__AA__3058,Vvar__3__AF__3060,Vvar__4___24Anonymous__3062) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__3055,Vvar__1__TX__3057,Vvar__2__AA__3059,Vvar__3__AF__3061,Vvar__4___24Anonymous__3063)
=> ( Vvar__4___24Anonymous__3062 = Vvar__4___24Anonymous__3063
& Vvar__3__AF__3060 = Vvar__3__AF__3061
& Vvar__2__AA__3058 = Vvar__2__AA__3059
& Vvar__1__TX__3056 = Vvar__1__TX__3057
& Vvar__0__TA__3054 = Vvar__0__TA__3055 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__2992,Vvar__0__TA__2993,Vvar__1__TX__2994,Vvar__1__TX__2995,Vvar__2__AA__2996,Vvar__2__AA__2997,Vvar__3__AF__2998,Vvar__3__AF__2999] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__2992,Vvar__1__TX__2994,Vvar__2__AA__2996,Vvar__3__AF__2998) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__2993,Vvar__1__TX__2995,Vvar__2__AA__2997,Vvar__3__AF__2999)
=> ( Vvar__3__AF__2998 = Vvar__3__AF__2999
& Vvar__2__AA__2996 = Vvar__2__AA__2997
& Vvar__1__TX__2994 = Vvar__1__TX__2995
& Vvar__0__TA__2992 = Vvar__0__TA__2993 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__3008,Vvar__0__TA__3009,Vvar__1__TX__3010,Vvar__1__TX__3011,Vvar__2__AA__3012,Vvar__2__AA__3013,Vvar__3__AF__3014,Vvar__3__AF__3015,Vvar__4___24Anonymous__3016,Vvar__4___24Anonymous__3017] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__3008,Vvar__1__TX__3010,Vvar__2__AA__3012,Vvar__3__AF__3014,Vvar__4___24Anonymous__3016) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__3009,Vvar__1__TX__3011,Vvar__2__AA__3013,Vvar__3__AF__3015,Vvar__4___24Anonymous__3017)
=> ( Vvar__4___24Anonymous__3016 = Vvar__4___24Anonymous__3017
& Vvar__3__AF__3014 = Vvar__3__AF__3015
& Vvar__2__AA__3012 = Vvar__2__AA__3013
& Vvar__1__TX__3010 = Vvar__1__TX__3011
& Vvar__0__TA__3008 = Vvar__0__TA__3009 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__4086,Vvar__0___24Anonymous__4087,Vvar__1___24Anonymous__4088,Vvar__1___24Anonymous__4089] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__4086,Vvar__1___24Anonymous__4088) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__4087,Vvar__1___24Anonymous__4089)
=> ( Vvar__1___24Anonymous__4088 = Vvar__1___24Anonymous__4089
& Vvar__0___24Anonymous__4086 = Vvar__0___24Anonymous__4087 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__4090,Vvar__0___24Anonymous__4091,Vvar__1___24Anonymous__4092,Vvar__1___24Anonymous__4093,Vvar__2___24Anonymous__4094,Vvar__2___24Anonymous__4095] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__4090,Vvar__1___24Anonymous__4092,Vvar__2___24Anonymous__4094) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__4091,Vvar__1___24Anonymous__4093,Vvar__2___24Anonymous__4095)
=> ( Vvar__2___24Anonymous__4094 = Vvar__2___24Anonymous__4095
& Vvar__1___24Anonymous__4092 = Vvar__1___24Anonymous__4093
& Vvar__0___24Anonymous__4090 = Vvar__0___24Anonymous__4091 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__4082,Vvar__0___24Anonymous__4083,Vvar__1___24Anonymous__4084,Vvar__1___24Anonymous__4085] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__4082,Vvar__1___24Anonymous__4084) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__4083,Vvar__1___24Anonymous__4085)
=> ( Vvar__1___24Anonymous__4084 = Vvar__1___24Anonymous__4085
& Vvar__0___24Anonymous__4082 = Vvar__0___24Anonymous__4083 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__6218,Vvar__0__C__6219] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__6218) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__6219)
=> Vvar__0__C__6218 = Vvar__0__C__6219 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__6216,Vvar__0__C__6217] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__6216) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__6217)
=> Vvar__0__C__6216 = Vvar__0__C__6217 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__6224,Vvar__0__C__6225,Vvar__1___24Anonymous__6226,Vvar__1___24Anonymous__6227] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__6224,Vvar__1___24Anonymous__6226) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__6225,Vvar__1___24Anonymous__6227)
=> ( Vvar__1___24Anonymous__6226 = Vvar__1___24Anonymous__6227
& Vvar__0__C__6224 = Vvar__0__C__6225 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__6228,Vvar__0__C__6229,Vvar__1___24Anonymous__6230,Vvar__1___24Anonymous__6231,Vvar__2___24Anonymous__6232,Vvar__2___24Anonymous__6233] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__6228,Vvar__1___24Anonymous__6230,Vvar__2___24Anonymous__6232) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__6229,Vvar__1___24Anonymous__6231,Vvar__2___24Anonymous__6233)
=> ( Vvar__2___24Anonymous__6232 = Vvar__2___24Anonymous__6233
& Vvar__1___24Anonymous__6230 = Vvar__1___24Anonymous__6231
& Vvar__0__C__6228 = Vvar__0__C__6229 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__6220,Vvar__0__C__6221,Vvar__1___24Anonymous__6222,Vvar__1___24Anonymous__6223] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__6220,Vvar__1___24Anonymous__6222) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__6221,Vvar__1___24Anonymous__6223)
=> ( Vvar__1___24Anonymous__6222 = Vvar__1___24Anonymous__6223
& Vvar__0__C__6220 = Vvar__0__C__6221 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__6254,Vvar__0__C__6255,Vvar__1___24Anonymous__6256,Vvar__1___24Anonymous__6257,Vvar__2___24Anonymous__6258,Vvar__2___24Anonymous__6259] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__6254,Vvar__1___24Anonymous__6256,Vvar__2___24Anonymous__6258) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__6255,Vvar__1___24Anonymous__6257,Vvar__2___24Anonymous__6259)
=> ( Vvar__2___24Anonymous__6258 = Vvar__2___24Anonymous__6259
& Vvar__1___24Anonymous__6256 = Vvar__1___24Anonymous__6257
& Vvar__0__C__6254 = Vvar__0__C__6255 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__6250,Vvar__0__C__6251,Vvar__1___24Anonymous__6252,Vvar__1___24Anonymous__6253] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__6250,Vvar__1___24Anonymous__6252) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__6251,Vvar__1___24Anonymous__6253)
=> ( Vvar__1___24Anonymous__6252 = Vvar__1___24Anonymous__6253
& Vvar__0__C__6250 = Vvar__0__C__6251 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__6240,Vvar__0__C__6241,Vvar__1___24Anonymous__6242,Vvar__1___24Anonymous__6243,Vvar__2___24Anonymous__6244,Vvar__2___24Anonymous__6245] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__6240,Vvar__1___24Anonymous__6242,Vvar__2___24Anonymous__6244) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__6241,Vvar__1___24Anonymous__6243,Vvar__2___24Anonymous__6245)
=> ( Vvar__2___24Anonymous__6244 = Vvar__2___24Anonymous__6245
& Vvar__1___24Anonymous__6242 = Vvar__1___24Anonymous__6243
& Vvar__0__C__6240 = Vvar__0__C__6241 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__6246,Vvar__0__C__6247,Vvar__1___24Anonymous__6248,Vvar__1___24Anonymous__6249] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__6246,Vvar__1___24Anonymous__6248) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__6247,Vvar__1___24Anonymous__6249)
=> ( Vvar__1___24Anonymous__6248 = Vvar__1___24Anonymous__6249
& Vvar__0__C__6246 = Vvar__0__C__6247 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__6260,Vvar__0__C__6261,Vvar__1___24Anonymous__6262,Vvar__1___24Anonymous__6263,Vvar__2___24Anonymous__6264,Vvar__2___24Anonymous__6265] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__6260,Vvar__1___24Anonymous__6262,Vvar__2___24Anonymous__6264) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__6261,Vvar__1___24Anonymous__6263,Vvar__2___24Anonymous__6265)
=> ( Vvar__2___24Anonymous__6264 = Vvar__2___24Anonymous__6265
& Vvar__1___24Anonymous__6262 = Vvar__1___24Anonymous__6263
& Vvar__0__C__6260 = Vvar__0__C__6261 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__6234,Vvar__0__C__6235,Vvar__1___24Anonymous__6236,Vvar__1___24Anonymous__6237,Vvar__2___24Anonymous__6238,Vvar__2___24Anonymous__6239] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__6234,Vvar__1___24Anonymous__6236,Vvar__2___24Anonymous__6238) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__6235,Vvar__1___24Anonymous__6237,Vvar__2___24Anonymous__6239)
=> ( Vvar__2___24Anonymous__6238 = Vvar__2___24Anonymous__6239
& Vvar__1___24Anonymous__6236 = Vvar__1___24Anonymous__6237
& Vvar__0__C__6234 = Vvar__0__C__6235 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__6557,Vvar__0__C__6558,Vvar__1__num__6559,Vvar__1__num__6560,Vvar__2__denum__6561,Vvar__2__denum__6562,Vvar__3__condition__6563,Vvar__3__condition__6564] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__6557,Vvar__1__num__6559,Vvar__2__denum__6561,Vvar__3__condition__6563) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__6558,Vvar__1__num__6560,Vvar__2__denum__6562,Vvar__3__condition__6564)
=> ( Vvar__3__condition__6563 = Vvar__3__condition__6564
& Vvar__2__denum__6561 = Vvar__2__denum__6562
& Vvar__1__num__6559 = Vvar__1__num__6560
& Vvar__0__C__6557 = Vvar__0__C__6558 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__6896,Vvar__0__C__6897,Vvar__1__rsplit__left__6898,Vvar__1__rsplit__left__6899,Vvar__2__rsplit__common__6900,Vvar__2__rsplit__common__6901,Vvar__3__rsplit__right__6902,Vvar__3__rsplit__right__6903] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__6896,Vvar__1__rsplit__left__6898,Vvar__2__rsplit__common__6900,Vvar__3__rsplit__right__6902) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__6897,Vvar__1__rsplit__left__6899,Vvar__2__rsplit__common__6901,Vvar__3__rsplit__right__6903)
=> ( Vvar__3__rsplit__right__6902 = Vvar__3__rsplit__right__6903
& Vvar__2__rsplit__common__6900 = Vvar__2__rsplit__common__6901
& Vvar__1__rsplit__left__6898 = Vvar__1__rsplit__left__6899
& Vvar__0__C__6896 = Vvar__0__C__6897 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__14268,Vvar__0__C__14269] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14268) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14269)
=> Vvar__0__C__14268 = Vvar__0__C__14269 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__14266,Vvar__0__C__14267] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14266) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14267)
=> Vvar__0__C__14266 = Vvar__0__C__14267 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__14274,Vvar__0__C__14275,Vvar__1___24Anonymous__14276,Vvar__1___24Anonymous__14277] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__14274,Vvar__1___24Anonymous__14276) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__14275,Vvar__1___24Anonymous__14277)
=> ( Vvar__1___24Anonymous__14276 = Vvar__1___24Anonymous__14277
& Vvar__0__C__14274 = Vvar__0__C__14275 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__14278,Vvar__0__C__14279,Vvar__1___24Anonymous__14280,Vvar__1___24Anonymous__14281,Vvar__2___24Anonymous__14282,Vvar__2___24Anonymous__14283] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__14278,Vvar__1___24Anonymous__14280,Vvar__2___24Anonymous__14282) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__14279,Vvar__1___24Anonymous__14281,Vvar__2___24Anonymous__14283)
=> ( Vvar__2___24Anonymous__14282 = Vvar__2___24Anonymous__14283
& Vvar__1___24Anonymous__14280 = Vvar__1___24Anonymous__14281
& Vvar__0__C__14278 = Vvar__0__C__14279 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__14270,Vvar__0__C__14271,Vvar__1___24Anonymous__14272,Vvar__1___24Anonymous__14273] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__14270,Vvar__1___24Anonymous__14272) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__14271,Vvar__1___24Anonymous__14273)
=> ( Vvar__1___24Anonymous__14272 = Vvar__1___24Anonymous__14273
& Vvar__0__C__14270 = Vvar__0__C__14271 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__14290,Vvar__0__C__14291,Vvar__1___24Anonymous__14292,Vvar__1___24Anonymous__14293,Vvar__2___24Anonymous__14294,Vvar__2___24Anonymous__14295] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__14290,Vvar__1___24Anonymous__14292,Vvar__2___24Anonymous__14294) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__14291,Vvar__1___24Anonymous__14293,Vvar__2___24Anonymous__14295)
=> ( Vvar__2___24Anonymous__14294 = Vvar__2___24Anonymous__14295
& Vvar__1___24Anonymous__14292 = Vvar__1___24Anonymous__14293
& Vvar__0__C__14290 = Vvar__0__C__14291 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__14296,Vvar__0__C__14297,Vvar__1___24Anonymous__14298,Vvar__1___24Anonymous__14299] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__14296,Vvar__1___24Anonymous__14298) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__14297,Vvar__1___24Anonymous__14299)
=> ( Vvar__1___24Anonymous__14298 = Vvar__1___24Anonymous__14299
& Vvar__0__C__14296 = Vvar__0__C__14297 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__14300,Vvar__0__C__14301,Vvar__1___24Anonymous__14302,Vvar__1___24Anonymous__14303,Vvar__2___24Anonymous__14304,Vvar__2___24Anonymous__14305] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__14300,Vvar__1___24Anonymous__14302,Vvar__2___24Anonymous__14304) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__14301,Vvar__1___24Anonymous__14303,Vvar__2___24Anonymous__14305)
=> ( Vvar__2___24Anonymous__14304 = Vvar__2___24Anonymous__14305
& Vvar__1___24Anonymous__14302 = Vvar__1___24Anonymous__14303
& Vvar__0__C__14300 = Vvar__0__C__14301 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__14284,Vvar__0__C__14285,Vvar__1___24Anonymous__14286,Vvar__1___24Anonymous__14287,Vvar__2___24Anonymous__14288,Vvar__2___24Anonymous__14289] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__14284,Vvar__1___24Anonymous__14286,Vvar__2___24Anonymous__14288) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__14285,Vvar__1___24Anonymous__14287,Vvar__2___24Anonymous__14289)
=> ( Vvar__2___24Anonymous__14288 = Vvar__2___24Anonymous__14289
& Vvar__1___24Anonymous__14286 = Vvar__1___24Anonymous__14287
& Vvar__0__C__14284 = Vvar__0__C__14285 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__12230,Vvar__0__C__12231,Vvar__1___24Anonymous__12232,Vvar__1___24Anonymous__12233,Vvar__2___24Anonymous__12234,Vvar__2___24Anonymous__12235,Vvar__3___24Anonymous__12236,Vvar__3___24Anonymous__12237] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__12230,Vvar__1___24Anonymous__12232,Vvar__2___24Anonymous__12234,Vvar__3___24Anonymous__12236) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__12231,Vvar__1___24Anonymous__12233,Vvar__2___24Anonymous__12235,Vvar__3___24Anonymous__12237)
=> ( Vvar__3___24Anonymous__12236 = Vvar__3___24Anonymous__12237
& Vvar__2___24Anonymous__12234 = Vvar__2___24Anonymous__12235
& Vvar__1___24Anonymous__12232 = Vvar__1___24Anonymous__12233
& Vvar__0__C__12230 = Vvar__0__C__12231 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__12220,Vvar__0__C__12221,Vvar__1___24Anonymous__12222,Vvar__1___24Anonymous__12223] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12220,Vvar__1___24Anonymous__12222) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12221,Vvar__1___24Anonymous__12223)
=> ( Vvar__1___24Anonymous__12222 = Vvar__1___24Anonymous__12223
& Vvar__0__C__12220 = Vvar__0__C__12221 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__12224,Vvar__0__C__12225,Vvar__1___24Anonymous__12226,Vvar__1___24Anonymous__12227,Vvar__2___24Anonymous__12228,Vvar__2___24Anonymous__12229] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12224,Vvar__1___24Anonymous__12226,Vvar__2___24Anonymous__12228) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12225,Vvar__1___24Anonymous__12227,Vvar__2___24Anonymous__12229)
=> ( Vvar__2___24Anonymous__12228 = Vvar__2___24Anonymous__12229
& Vvar__1___24Anonymous__12226 = Vvar__1___24Anonymous__12227
& Vvar__0__C__12224 = Vvar__0__C__12225 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__12765,Vvar__0___24Anonymous__12766,Vvar__1___24Anonymous__12767,Vvar__1___24Anonymous__12768] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__12765,Vvar__1___24Anonymous__12767) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__12766,Vvar__1___24Anonymous__12768)
=> ( Vvar__1___24Anonymous__12767 = Vvar__1___24Anonymous__12768
& Vvar__0___24Anonymous__12765 = Vvar__0___24Anonymous__12766 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__12761,Vvar__0___24Anonymous__12762,Vvar__1___24Anonymous__12763,Vvar__1___24Anonymous__12764] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__12761,Vvar__1___24Anonymous__12763) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__12762,Vvar__1___24Anonymous__12764)
=> ( Vvar__1___24Anonymous__12763 = Vvar__1___24Anonymous__12764
& Vvar__0___24Anonymous__12761 = Vvar__0___24Anonymous__12762 ) ) ).
fof('$_inj_IntMap.Map.M0',axiom,
! [Vvar__0__A__115,Vvar__0__A__116] :
( cIntMap_2eMap_2eM0___24a1(Vvar__0__A__115) = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__116)
=> Vvar__0__A__115 = Vvar__0__A__116 ) ).
fof('$_inj_IntMap.Map.M1',axiom,
! [Vvar__0__A__117,Vvar__0__A__118,Vvar__1___24Anonymous__119,Vvar__1___24Anonymous__120,Vvar__2___24Anonymous__121,Vvar__2___24Anonymous__122] :
( cIntMap_2eMap_2eM1___24a3(Vvar__0__A__117,Vvar__1___24Anonymous__119,Vvar__2___24Anonymous__121) = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__118,Vvar__1___24Anonymous__120,Vvar__2___24Anonymous__122)
=> ( Vvar__2___24Anonymous__121 = Vvar__2___24Anonymous__122
& Vvar__1___24Anonymous__119 = Vvar__1___24Anonymous__120
& Vvar__0__A__117 = Vvar__0__A__118 ) ) ).
fof('$_inj_IntMap.Map.M2',axiom,
! [Vvar__0__A__123,Vvar__0__A__124,Vvar__1___24Anonymous__125,Vvar__1___24Anonymous__126,Vvar__2___24Anonymous__127,Vvar__2___24Anonymous__128] :
( cIntMap_2eMap_2eM2___24a3(Vvar__0__A__123,Vvar__1___24Anonymous__125,Vvar__2___24Anonymous__127) = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__124,Vvar__1___24Anonymous__126,Vvar__2___24Anonymous__128)
=> ( Vvar__2___24Anonymous__127 = Vvar__2___24Anonymous__128
& Vvar__1___24Anonymous__125 = Vvar__1___24Anonymous__126
& Vvar__0__A__123 = Vvar__0__A__124 ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__24535,Vvar__1___24Anonymous__24536,VX24537] :
( cProp___24t(Vvar__0__P__24535)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__24536)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__24535,Vvar__1___24Anonymous__24536,VX24537)
=> ( ( p(Vvar__0__P__24535)
& Vvar__1___24Anonymous__24536 = cCoq_2eInit_2eDatatypes_2etrue
& VX24537 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__24535) )
| ( ~ p(Vvar__0__P__24535)
& Vvar__1___24Anonymous__24536 = cCoq_2eInit_2eDatatypes_2efalse
& VX24537 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__24535) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX38718] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX38718)
=> ( VX38718 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__38719] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__38719)
& ? [Vvar__1___24Anonymous__38720] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__38720)
& ? [Vvar__2___24Anonymous__38721] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__38721)
& VX38718 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__38719,Vvar__1___24Anonymous__38720,Vvar__2___24Anonymous__38721) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX24557] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX24557)
=> ( VX24557 = cCoq_2eInit_2eByte_2ex00
| VX24557 = cCoq_2eInit_2eByte_2ex01
| VX24557 = cCoq_2eInit_2eByte_2ex02
| VX24557 = cCoq_2eInit_2eByte_2ex03
| VX24557 = cCoq_2eInit_2eByte_2ex04
| VX24557 = cCoq_2eInit_2eByte_2ex05
| VX24557 = cCoq_2eInit_2eByte_2ex06
| VX24557 = cCoq_2eInit_2eByte_2ex07
| VX24557 = cCoq_2eInit_2eByte_2ex08
| VX24557 = cCoq_2eInit_2eByte_2ex09
| VX24557 = cCoq_2eInit_2eByte_2ex0a
| VX24557 = cCoq_2eInit_2eByte_2ex0b
| VX24557 = cCoq_2eInit_2eByte_2ex0c
| VX24557 = cCoq_2eInit_2eByte_2ex0d
| VX24557 = cCoq_2eInit_2eByte_2ex0e
| VX24557 = cCoq_2eInit_2eByte_2ex0f
| VX24557 = cCoq_2eInit_2eByte_2ex10
| VX24557 = cCoq_2eInit_2eByte_2ex11
| VX24557 = cCoq_2eInit_2eByte_2ex12
| VX24557 = cCoq_2eInit_2eByte_2ex13
| VX24557 = cCoq_2eInit_2eByte_2ex14
| VX24557 = cCoq_2eInit_2eByte_2ex15
| VX24557 = cCoq_2eInit_2eByte_2ex16
| VX24557 = cCoq_2eInit_2eByte_2ex17
| VX24557 = cCoq_2eInit_2eByte_2ex18
| VX24557 = cCoq_2eInit_2eByte_2ex19
| VX24557 = cCoq_2eInit_2eByte_2ex1a
| VX24557 = cCoq_2eInit_2eByte_2ex1b
| VX24557 = cCoq_2eInit_2eByte_2ex1c
| VX24557 = cCoq_2eInit_2eByte_2ex1d
| VX24557 = cCoq_2eInit_2eByte_2ex1e
| VX24557 = cCoq_2eInit_2eByte_2ex1f
| VX24557 = cCoq_2eInit_2eByte_2ex20
| VX24557 = cCoq_2eInit_2eByte_2ex21
| VX24557 = cCoq_2eInit_2eByte_2ex22
| VX24557 = cCoq_2eInit_2eByte_2ex23
| VX24557 = cCoq_2eInit_2eByte_2ex24
| VX24557 = cCoq_2eInit_2eByte_2ex25
| VX24557 = cCoq_2eInit_2eByte_2ex26
| VX24557 = cCoq_2eInit_2eByte_2ex27
| VX24557 = cCoq_2eInit_2eByte_2ex28
| VX24557 = cCoq_2eInit_2eByte_2ex29
| VX24557 = cCoq_2eInit_2eByte_2ex2a
| VX24557 = cCoq_2eInit_2eByte_2ex2b
| VX24557 = cCoq_2eInit_2eByte_2ex2c
| VX24557 = cCoq_2eInit_2eByte_2ex2d
| VX24557 = cCoq_2eInit_2eByte_2ex2e
| VX24557 = cCoq_2eInit_2eByte_2ex2f
| VX24557 = cCoq_2eInit_2eByte_2ex30
| VX24557 = cCoq_2eInit_2eByte_2ex31
| VX24557 = cCoq_2eInit_2eByte_2ex32
| VX24557 = cCoq_2eInit_2eByte_2ex33
| VX24557 = cCoq_2eInit_2eByte_2ex34
| VX24557 = cCoq_2eInit_2eByte_2ex35
| VX24557 = cCoq_2eInit_2eByte_2ex36
| VX24557 = cCoq_2eInit_2eByte_2ex37
| VX24557 = cCoq_2eInit_2eByte_2ex38
| VX24557 = cCoq_2eInit_2eByte_2ex39
| VX24557 = cCoq_2eInit_2eByte_2ex3a
| VX24557 = cCoq_2eInit_2eByte_2ex3b
| VX24557 = cCoq_2eInit_2eByte_2ex3c
| VX24557 = cCoq_2eInit_2eByte_2ex3d
| VX24557 = cCoq_2eInit_2eByte_2ex3e
| VX24557 = cCoq_2eInit_2eByte_2ex3f
| VX24557 = cCoq_2eInit_2eByte_2ex40
| VX24557 = cCoq_2eInit_2eByte_2ex41
| VX24557 = cCoq_2eInit_2eByte_2ex42
| VX24557 = cCoq_2eInit_2eByte_2ex43
| VX24557 = cCoq_2eInit_2eByte_2ex44
| VX24557 = cCoq_2eInit_2eByte_2ex45
| VX24557 = cCoq_2eInit_2eByte_2ex46
| VX24557 = cCoq_2eInit_2eByte_2ex47
| VX24557 = cCoq_2eInit_2eByte_2ex48
| VX24557 = cCoq_2eInit_2eByte_2ex49
| VX24557 = cCoq_2eInit_2eByte_2ex4a
| VX24557 = cCoq_2eInit_2eByte_2ex4b
| VX24557 = cCoq_2eInit_2eByte_2ex4c
| VX24557 = cCoq_2eInit_2eByte_2ex4d
| VX24557 = cCoq_2eInit_2eByte_2ex4e
| VX24557 = cCoq_2eInit_2eByte_2ex4f
| VX24557 = cCoq_2eInit_2eByte_2ex50
| VX24557 = cCoq_2eInit_2eByte_2ex51
| VX24557 = cCoq_2eInit_2eByte_2ex52
| VX24557 = cCoq_2eInit_2eByte_2ex53
| VX24557 = cCoq_2eInit_2eByte_2ex54
| VX24557 = cCoq_2eInit_2eByte_2ex55
| VX24557 = cCoq_2eInit_2eByte_2ex56
| VX24557 = cCoq_2eInit_2eByte_2ex57
| VX24557 = cCoq_2eInit_2eByte_2ex58
| VX24557 = cCoq_2eInit_2eByte_2ex59
| VX24557 = cCoq_2eInit_2eByte_2ex5a
| VX24557 = cCoq_2eInit_2eByte_2ex5b
| VX24557 = cCoq_2eInit_2eByte_2ex5c
| VX24557 = cCoq_2eInit_2eByte_2ex5d
| VX24557 = cCoq_2eInit_2eByte_2ex5e
| VX24557 = cCoq_2eInit_2eByte_2ex5f
| VX24557 = cCoq_2eInit_2eByte_2ex60
| VX24557 = cCoq_2eInit_2eByte_2ex61
| VX24557 = cCoq_2eInit_2eByte_2ex62
| VX24557 = cCoq_2eInit_2eByte_2ex63
| VX24557 = cCoq_2eInit_2eByte_2ex64
| VX24557 = cCoq_2eInit_2eByte_2ex65
| VX24557 = cCoq_2eInit_2eByte_2ex66
| VX24557 = cCoq_2eInit_2eByte_2ex67
| VX24557 = cCoq_2eInit_2eByte_2ex68
| VX24557 = cCoq_2eInit_2eByte_2ex69
| VX24557 = cCoq_2eInit_2eByte_2ex6a
| VX24557 = cCoq_2eInit_2eByte_2ex6b
| VX24557 = cCoq_2eInit_2eByte_2ex6c
| VX24557 = cCoq_2eInit_2eByte_2ex6d
| VX24557 = cCoq_2eInit_2eByte_2ex6e
| VX24557 = cCoq_2eInit_2eByte_2ex6f
| VX24557 = cCoq_2eInit_2eByte_2ex70
| VX24557 = cCoq_2eInit_2eByte_2ex71
| VX24557 = cCoq_2eInit_2eByte_2ex72
| VX24557 = cCoq_2eInit_2eByte_2ex73
| VX24557 = cCoq_2eInit_2eByte_2ex74
| VX24557 = cCoq_2eInit_2eByte_2ex75
| VX24557 = cCoq_2eInit_2eByte_2ex76
| VX24557 = cCoq_2eInit_2eByte_2ex77
| VX24557 = cCoq_2eInit_2eByte_2ex78
| VX24557 = cCoq_2eInit_2eByte_2ex79
| VX24557 = cCoq_2eInit_2eByte_2ex7a
| VX24557 = cCoq_2eInit_2eByte_2ex7b
| VX24557 = cCoq_2eInit_2eByte_2ex7c
| VX24557 = cCoq_2eInit_2eByte_2ex7d
| VX24557 = cCoq_2eInit_2eByte_2ex7e
| VX24557 = cCoq_2eInit_2eByte_2ex7f
| VX24557 = cCoq_2eInit_2eByte_2ex80
| VX24557 = cCoq_2eInit_2eByte_2ex81
| VX24557 = cCoq_2eInit_2eByte_2ex82
| VX24557 = cCoq_2eInit_2eByte_2ex83
| VX24557 = cCoq_2eInit_2eByte_2ex84
| VX24557 = cCoq_2eInit_2eByte_2ex85
| VX24557 = cCoq_2eInit_2eByte_2ex86
| VX24557 = cCoq_2eInit_2eByte_2ex87
| VX24557 = cCoq_2eInit_2eByte_2ex88
| VX24557 = cCoq_2eInit_2eByte_2ex89
| VX24557 = cCoq_2eInit_2eByte_2ex8a
| VX24557 = cCoq_2eInit_2eByte_2ex8b
| VX24557 = cCoq_2eInit_2eByte_2ex8c
| VX24557 = cCoq_2eInit_2eByte_2ex8d
| VX24557 = cCoq_2eInit_2eByte_2ex8e
| VX24557 = cCoq_2eInit_2eByte_2ex8f
| VX24557 = cCoq_2eInit_2eByte_2ex90
| VX24557 = cCoq_2eInit_2eByte_2ex91
| VX24557 = cCoq_2eInit_2eByte_2ex92
| VX24557 = cCoq_2eInit_2eByte_2ex93
| VX24557 = cCoq_2eInit_2eByte_2ex94
| VX24557 = cCoq_2eInit_2eByte_2ex95
| VX24557 = cCoq_2eInit_2eByte_2ex96
| VX24557 = cCoq_2eInit_2eByte_2ex97
| VX24557 = cCoq_2eInit_2eByte_2ex98
| VX24557 = cCoq_2eInit_2eByte_2ex99
| VX24557 = cCoq_2eInit_2eByte_2ex9a
| VX24557 = cCoq_2eInit_2eByte_2ex9b
| VX24557 = cCoq_2eInit_2eByte_2ex9c
| VX24557 = cCoq_2eInit_2eByte_2ex9d
| VX24557 = cCoq_2eInit_2eByte_2ex9e
| VX24557 = cCoq_2eInit_2eByte_2ex9f
| VX24557 = cCoq_2eInit_2eByte_2exa0
| VX24557 = cCoq_2eInit_2eByte_2exa1
| VX24557 = cCoq_2eInit_2eByte_2exa2
| VX24557 = cCoq_2eInit_2eByte_2exa3
| VX24557 = cCoq_2eInit_2eByte_2exa4
| VX24557 = cCoq_2eInit_2eByte_2exa5
| VX24557 = cCoq_2eInit_2eByte_2exa6
| VX24557 = cCoq_2eInit_2eByte_2exa7
| VX24557 = cCoq_2eInit_2eByte_2exa8
| VX24557 = cCoq_2eInit_2eByte_2exa9
| VX24557 = cCoq_2eInit_2eByte_2exaa
| VX24557 = cCoq_2eInit_2eByte_2exab
| VX24557 = cCoq_2eInit_2eByte_2exac
| VX24557 = cCoq_2eInit_2eByte_2exad
| VX24557 = cCoq_2eInit_2eByte_2exae
| VX24557 = cCoq_2eInit_2eByte_2exaf
| VX24557 = cCoq_2eInit_2eByte_2exb0
| VX24557 = cCoq_2eInit_2eByte_2exb1
| VX24557 = cCoq_2eInit_2eByte_2exb2
| VX24557 = cCoq_2eInit_2eByte_2exb3
| VX24557 = cCoq_2eInit_2eByte_2exb4
| VX24557 = cCoq_2eInit_2eByte_2exb5
| VX24557 = cCoq_2eInit_2eByte_2exb6
| VX24557 = cCoq_2eInit_2eByte_2exb7
| VX24557 = cCoq_2eInit_2eByte_2exb8
| VX24557 = cCoq_2eInit_2eByte_2exb9
| VX24557 = cCoq_2eInit_2eByte_2exba
| VX24557 = cCoq_2eInit_2eByte_2exbb
| VX24557 = cCoq_2eInit_2eByte_2exbc
| VX24557 = cCoq_2eInit_2eByte_2exbd
| VX24557 = cCoq_2eInit_2eByte_2exbe
| VX24557 = cCoq_2eInit_2eByte_2exbf
| VX24557 = cCoq_2eInit_2eByte_2exc0
| VX24557 = cCoq_2eInit_2eByte_2exc1
| VX24557 = cCoq_2eInit_2eByte_2exc2
| VX24557 = cCoq_2eInit_2eByte_2exc3
| VX24557 = cCoq_2eInit_2eByte_2exc4
| VX24557 = cCoq_2eInit_2eByte_2exc5
| VX24557 = cCoq_2eInit_2eByte_2exc6
| VX24557 = cCoq_2eInit_2eByte_2exc7
| VX24557 = cCoq_2eInit_2eByte_2exc8
| VX24557 = cCoq_2eInit_2eByte_2exc9
| VX24557 = cCoq_2eInit_2eByte_2exca
| VX24557 = cCoq_2eInit_2eByte_2excb
| VX24557 = cCoq_2eInit_2eByte_2excc
| VX24557 = cCoq_2eInit_2eByte_2excd
| VX24557 = cCoq_2eInit_2eByte_2exce
| VX24557 = cCoq_2eInit_2eByte_2excf
| VX24557 = cCoq_2eInit_2eByte_2exd0
| VX24557 = cCoq_2eInit_2eByte_2exd1
| VX24557 = cCoq_2eInit_2eByte_2exd2
| VX24557 = cCoq_2eInit_2eByte_2exd3
| VX24557 = cCoq_2eInit_2eByte_2exd4
| VX24557 = cCoq_2eInit_2eByte_2exd5
| VX24557 = cCoq_2eInit_2eByte_2exd6
| VX24557 = cCoq_2eInit_2eByte_2exd7
| VX24557 = cCoq_2eInit_2eByte_2exd8
| VX24557 = cCoq_2eInit_2eByte_2exd9
| VX24557 = cCoq_2eInit_2eByte_2exda
| VX24557 = cCoq_2eInit_2eByte_2exdb
| VX24557 = cCoq_2eInit_2eByte_2exdc
| VX24557 = cCoq_2eInit_2eByte_2exdd
| VX24557 = cCoq_2eInit_2eByte_2exde
| VX24557 = cCoq_2eInit_2eByte_2exdf
| VX24557 = cCoq_2eInit_2eByte_2exe0
| VX24557 = cCoq_2eInit_2eByte_2exe1
| VX24557 = cCoq_2eInit_2eByte_2exe2
| VX24557 = cCoq_2eInit_2eByte_2exe3
| VX24557 = cCoq_2eInit_2eByte_2exe4
| VX24557 = cCoq_2eInit_2eByte_2exe5
| VX24557 = cCoq_2eInit_2eByte_2exe6
| VX24557 = cCoq_2eInit_2eByte_2exe7
| VX24557 = cCoq_2eInit_2eByte_2exe8
| VX24557 = cCoq_2eInit_2eByte_2exe9
| VX24557 = cCoq_2eInit_2eByte_2exea
| VX24557 = cCoq_2eInit_2eByte_2exeb
| VX24557 = cCoq_2eInit_2eByte_2exec
| VX24557 = cCoq_2eInit_2eByte_2exed
| VX24557 = cCoq_2eInit_2eByte_2exee
| VX24557 = cCoq_2eInit_2eByte_2exef
| VX24557 = cCoq_2eInit_2eByte_2exf0
| VX24557 = cCoq_2eInit_2eByte_2exf1
| VX24557 = cCoq_2eInit_2eByte_2exf2
| VX24557 = cCoq_2eInit_2eByte_2exf3
| VX24557 = cCoq_2eInit_2eByte_2exf4
| VX24557 = cCoq_2eInit_2eByte_2exf5
| VX24557 = cCoq_2eInit_2eByte_2exf6
| VX24557 = cCoq_2eInit_2eByte_2exf7
| VX24557 = cCoq_2eInit_2eByte_2exf8
| VX24557 = cCoq_2eInit_2eByte_2exf9
| VX24557 = cCoq_2eInit_2eByte_2exfa
| VX24557 = cCoq_2eInit_2eByte_2exfb
| VX24557 = cCoq_2eInit_2eByte_2exfc
| VX24557 = cCoq_2eInit_2eByte_2exfd
| VX24557 = cCoq_2eInit_2eByte_2exfe
| VX24557 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__4711,Vvar__1__Q__4712,Vvar__2___24Anonymous__4713] :
( cProp___24t(Vvar__0__P__4711)
=> ( cProp___24t(Vvar__1__Q__4712)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__4713)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__4711,Vvar__1__Q__4712,Vvar__2___24Anonymous__4713)
=> ( ( p(Vvar__0__P__4711)
& Vvar__2___24Anonymous__4713 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__4712)
& Vvar__2___24Anonymous__4713 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__24571,Vvar__1__Plt__24572,Vvar__2__Pgt__24573,Vvar__3___24Anonymous__24574] :
( cProp___24t(Vvar__0__Peq__24571)
=> ( cProp___24t(Vvar__1__Plt__24572)
=> ( cProp___24t(Vvar__2__Pgt__24573)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__24574)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__24571,Vvar__1__Plt__24572,Vvar__2__Pgt__24573,Vvar__3___24Anonymous__24574)
=> ( ( p(Vvar__0__Peq__24571)
& Vvar__3___24Anonymous__24574 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__24572)
& Vvar__3___24Anonymous__24574 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__24573)
& Vvar__3___24Anonymous__24574 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX335] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX335)
=> ( VX335 = cCoq_2eInit_2eDatatypes_2etrue
| VX335 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX4894] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX4894)
=> ( VX4894 = cCoq_2eInit_2eDatatypes_2eEq
| VX4894 = cCoq_2eInit_2eDatatypes_2eLt
| VX4894 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__9,VX10] :
( cType___24t(Vvar__0__A__9)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9,VX10)
=> ( VX10 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__9)
| ? [Vvar__1___24Anonymous__13] :
( t(Vvar__1___24Anonymous__13,Vvar__0__A__9)
& ? [Vvar__2___24Anonymous__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9,Vvar__2___24Anonymous__14)
& VX10 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9,Vvar__1___24Anonymous__13,Vvar__2___24Anonymous__14) ) ) ) ) ) ).
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__1512,VX1513] :
( cType___24t(Vvar__0__A__1512)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__1512,VX1513)
=> ( ? [Vvar__1___24Anonymous__1515] :
( t(Vvar__1___24Anonymous__1515,Vvar__0__A__1512)
& VX1513 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1512,Vvar__1___24Anonymous__1515) )
| VX1513 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1512) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__1531,Vvar__1__B__1532,VX1533] :
( cType___24t(Vvar__0__A__1531)
=> ( cType___24t(Vvar__1__B__1532)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__1531,Vvar__1__B__1532,VX1533)
=> ? [Vvar__2___24Anonymous__1536] :
( t(Vvar__2___24Anonymous__1536,Vvar__0__A__1531)
& ? [Vvar__3___24Anonymous__1537] :
( t(Vvar__3___24Anonymous__1537,Vvar__1__B__1532)
& VX1533 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1531,Vvar__1__B__1532,Vvar__2___24Anonymous__1536,Vvar__3___24Anonymous__1537) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__4750,Vvar__1__B__4751,VX4752] :
( cType___24t(Vvar__0__A__4750)
=> ( cType___24t(Vvar__1__B__4751)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__4750,Vvar__1__B__4751,VX4752)
=> ( ? [Vvar__2___24Anonymous__4755] :
( t(Vvar__2___24Anonymous__4755,Vvar__0__A__4750)
& VX4752 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4750,Vvar__1__B__4751,Vvar__2___24Anonymous__4755) )
| ? [Vvar__2___24Anonymous__4758] :
( t(Vvar__2___24Anonymous__4758,Vvar__1__B__4751)
& VX4752 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4750,Vvar__1__B__4751,Vvar__2___24Anonymous__4758) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX1] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX1)
=> VX1 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__279,Vvar__1___24Anonymous__280] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__279)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__280)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__279,Vvar__1___24Anonymous__280)
=> ( Vvar__1___24Anonymous__280 = Vvar__0__n__279
| ? [Vvar__1__m__284] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__284)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__279,Vvar__1__m__284)
& Vvar__1___24Anonymous__280 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__284) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__474,Vvar__1__P__475,VX478] :
( cType___24t(Vvar__0__A__474)
=> ( c_24__type__488___24t(Vvar__0__A__474,Vvar__1__P__475,Vvar__1__P__475)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__474,Vvar__1__P__475,VX478)
=> ? [Vvar__2__x__483] :
( t(Vvar__2__x__483,Vvar__0__A__474)
& p(happ(Vvar__1__P__475,Vvar__2__x__483))
& VX478 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__474,Vvar__1__P__475,Vvar__2__x__483) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__555,Vvar__1__P__556,VX559] :
( cType___24t(Vvar__0__A__555)
=> ( c_24__type__569___24t(Vvar__0__A__555,Vvar__1__P__556,Vvar__1__P__556)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__555,Vvar__1__P__556,VX559)
=> ? [Vvar__2__x__564] :
( t(Vvar__2__x__564,Vvar__0__A__555)
& ? [Vvar__3___24Anonymous__565] :
( t(Vvar__3___24Anonymous__565,happ(Vvar__1__P__556,Vvar__2__x__564))
& VX559 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__555,Vvar__1__P__556,Vvar__2__x__564,Vvar__3___24Anonymous__565) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__636,Vvar__1__B__637,VX638] :
( cProp___24t(Vvar__0__A__636)
=> ( cProp___24t(Vvar__1__B__637)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__636,Vvar__1__B__637,VX638)
=> ( ( p(Vvar__0__A__636)
& VX638 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__636,Vvar__1__B__637) )
| ( p(Vvar__1__B__637)
& VX638 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__636,Vvar__1__B__637) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__2599,Vvar__1__B__2600,VX2601] :
( cType___24t(Vvar__0__A__2599)
=> ( cProp___24t(Vvar__1__B__2600)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__2599,Vvar__1__B__2600,VX2601)
=> ( ? [Vvar__2___24Anonymous__2604] :
( t(Vvar__2___24Anonymous__2604,Vvar__0__A__2599)
& VX2601 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2599,Vvar__1__B__2600,Vvar__2___24Anonymous__2604) )
| ( p(Vvar__1__B__2600)
& VX2601 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2599,Vvar__1__B__2600) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__8965,Vvar__1__a__8966,Vvar__2___24Anonymous__8967,Vvar__3___24Anonymous__8968] :
( cType___24t(Vvar__0__A__8965)
=> ( t(Vvar__1__a__8966,Vvar__0__A__8965)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8965,Vvar__2___24Anonymous__8967)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8965,Vvar__3___24Anonymous__8968)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__8965,Vvar__1__a__8966,Vvar__2___24Anonymous__8967,Vvar__3___24Anonymous__8968)
=> ( ? [Vvar__2__l__8972] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8965,Vvar__2__l__8972)
& Vvar__3___24Anonymous__8968 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8965,Vvar__1__a__8966,Vvar__2__l__8972)
& Vvar__2___24Anonymous__8967 = Vvar__2__l__8972 )
| ? [Vvar__2__x__8975] :
( t(Vvar__2__x__8975,Vvar__0__A__8965)
& ? [Vvar__3__l__8976] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8965,Vvar__3__l__8976)
& ? [Vvar__4__l_27__8977] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8965,Vvar__4__l_27__8977)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__8965,Vvar__1__a__8966,Vvar__3__l__8976,Vvar__4__l_27__8977)
& Vvar__3___24Anonymous__8968 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8965,Vvar__2__x__8975,Vvar__4__l_27__8977)
& Vvar__2___24Anonymous__8967 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8965,Vvar__2__x__8975,Vvar__3__l__8976) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__9041,Vvar__1__P__9042,Vvar__2___24Anonymous__9045] :
( cType___24t(Vvar__0__A__9041)
=> ( c_24__type__9063___24t(Vvar__0__A__9041,Vvar__1__P__9042,Vvar__2___24Anonymous__9045,Vvar__1__P__9042)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9041,Vvar__2___24Anonymous__9045)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__9041,Vvar__1__P__9042,Vvar__2___24Anonymous__9045)
=> ( Vvar__2___24Anonymous__9045 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__9041)
| ? [Vvar__2__x__9055] :
( t(Vvar__2__x__9055,Vvar__0__A__9041)
& ? [Vvar__3__l__9056] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9041,Vvar__3__l__9056)
& p(happ(Vvar__1__P__9042,Vvar__2__x__9055))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__9041,Vvar__1__P__9042,Vvar__3__l__9056)
& Vvar__2___24Anonymous__9045 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9041,Vvar__2__x__9055,Vvar__3__l__9056) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__27031,Vvar__1__B__27032,Vvar__2__R__27033,Vvar__3___24Anonymous__27038,Vvar__4___24Anonymous__27039] :
( cType___24t(Vvar__0__A__27031)
=> ( cType___24t(Vvar__1__B__27032)
=> ( c_24__type__27076___24t(Vvar__0__A__27031,Vvar__1__B__27032,Vvar__2__R__27033,Vvar__3___24Anonymous__27038,Vvar__4___24Anonymous__27039,Vvar__2__R__27033)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27031,Vvar__3___24Anonymous__27038)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__27032,Vvar__4___24Anonymous__27039)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__27031,Vvar__1__B__27032,Vvar__2__R__27033,Vvar__3___24Anonymous__27038,Vvar__4___24Anonymous__27039)
=> ( ( Vvar__4___24Anonymous__27039 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__27032)
& Vvar__3___24Anonymous__27038 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__27031) )
| ? [Vvar__3__x__27055] :
( t(Vvar__3__x__27055,Vvar__0__A__27031)
& ? [Vvar__4__y__27056] :
( t(Vvar__4__y__27056,Vvar__1__B__27032)
& ? [Vvar__5__l__27057] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27031,Vvar__5__l__27057)
& ? [Vvar__6__l_27__27058] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__27032,Vvar__6__l_27__27058)
& p(happ(happ(Vvar__2__R__27033,Vvar__3__x__27055),Vvar__4__y__27056))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__27031,Vvar__1__B__27032,Vvar__2__R__27033,Vvar__5__l__27057,Vvar__6__l_27__27058)
& Vvar__4___24Anonymous__27039 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__27032,Vvar__4__y__27056,Vvar__6__l_27__27058)
& Vvar__3___24Anonymous__27038 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27031,Vvar__3__x__27055,Vvar__5__l__27057) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__27093,Vvar__1__R__27094,Vvar__2___24Anonymous__27099] :
( cType___24t(Vvar__0__A__27093)
=> ( c_24__type__27126___24t(Vvar__0__A__27093,Vvar__1__R__27094,Vvar__2___24Anonymous__27099,Vvar__1__R__27094)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27093,Vvar__2___24Anonymous__27099)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__27093,Vvar__1__R__27094,Vvar__2___24Anonymous__27099)
=> ( Vvar__2___24Anonymous__27099 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__27093)
| ? [Vvar__2__a__27113] :
( t(Vvar__2__a__27113,Vvar__0__A__27093)
& ? [Vvar__3__l__27114] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27093,Vvar__3__l__27114)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__27093,happ(Vvar__1__R__27094,Vvar__2__a__27113),Vvar__3__l__27114)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__27093,Vvar__1__R__27094,Vvar__3__l__27114)
& Vvar__2___24Anonymous__27099 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27093,Vvar__2__a__27113,Vvar__3__l__27114) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__8979,Vvar__1___24Anonymous__8980] :
( cType___24t(Vvar__0__A__8979)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8979,Vvar__1___24Anonymous__8980)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__8979,Vvar__1___24Anonymous__8980)
=> ( Vvar__1___24Anonymous__8980 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__8979)
| ? [Vvar__1__x__8984] :
( t(Vvar__1__x__8984,Vvar__0__A__8979)
& ? [Vvar__2__l__8985] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8979,Vvar__2__l__8985)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__8979,Vvar__1__x__8984,Vvar__2__l__8985)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__8979,Vvar__2__l__8985)
& Vvar__1___24Anonymous__8980 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8979,Vvar__1__x__8984,Vvar__2__l__8985) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__22105,Vvar__1__eqA__22106,Vvar__2__x__22111,Vvar__3___24Anonymous__22112] :
( cType___24t(Vvar__0__A__22105)
=> ( c_24__type__22145___24t(Vvar__0__A__22105,Vvar__1__eqA__22106,Vvar__2__x__22111,Vvar__3___24Anonymous__22112,Vvar__1__eqA__22106)
=> ( t(Vvar__2__x__22111,Vvar__0__A__22105)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22105,Vvar__3___24Anonymous__22112)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__22105,Vvar__1__eqA__22106,Vvar__2__x__22111,Vvar__3___24Anonymous__22112)
=> ( ? [Vvar__3__y__22121] :
( t(Vvar__3__y__22121,Vvar__0__A__22105)
& ? [Vvar__4__l__22122] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22105,Vvar__4__l__22122)
& p(happ(happ(Vvar__1__eqA__22106,Vvar__2__x__22111),Vvar__3__y__22121))
& Vvar__3___24Anonymous__22112 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22105,Vvar__3__y__22121,Vvar__4__l__22122) ) )
| ? [Vvar__3__y__22131] :
( t(Vvar__3__y__22131,Vvar__0__A__22105)
& ? [Vvar__4__l__22132] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22105,Vvar__4__l__22132)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__22105,Vvar__1__eqA__22106,Vvar__2__x__22111,Vvar__4__l__22132)
& Vvar__3___24Anonymous__22112 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22105,Vvar__3__y__22131,Vvar__4__l__22132) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__22147,Vvar__1__eqA__22148,Vvar__2___24Anonymous__22153] :
( cType___24t(Vvar__0__A__22147)
=> ( c_24__type__22180___24t(Vvar__0__A__22147,Vvar__1__eqA__22148,Vvar__2___24Anonymous__22153,Vvar__1__eqA__22148)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22147,Vvar__2___24Anonymous__22153)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__22147,Vvar__1__eqA__22148,Vvar__2___24Anonymous__22153)
=> ( Vvar__2___24Anonymous__22153 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22147)
| ? [Vvar__2__x__22167] :
( t(Vvar__2__x__22167,Vvar__0__A__22147)
& ? [Vvar__3__l__22168] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22147,Vvar__3__l__22168)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__22147,Vvar__1__eqA__22148,Vvar__2__x__22167,Vvar__3__l__22168)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__22147,Vvar__1__eqA__22148,Vvar__3__l__22168)
& Vvar__2___24Anonymous__22153 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22147,Vvar__2__x__22167,Vvar__3__l__22168) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__22199,Vvar__1__eqA__22200,Vvar__2___24Anonymous__22205,Vvar__3___24Anonymous__22206] :
( cType___24t(Vvar__0__A__22199)
=> ( c_24__type__22237___24t(Vvar__0__A__22199,Vvar__1__eqA__22200,Vvar__2___24Anonymous__22205,Vvar__3___24Anonymous__22206,Vvar__1__eqA__22200)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22199,Vvar__2___24Anonymous__22205)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22199,Vvar__3___24Anonymous__22206)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__22199,Vvar__1__eqA__22200,Vvar__2___24Anonymous__22205,Vvar__3___24Anonymous__22206)
=> ( ( Vvar__3___24Anonymous__22206 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22199)
& Vvar__2___24Anonymous__22205 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22199) )
| ? [Vvar__2__x__22220] :
( t(Vvar__2__x__22220,Vvar__0__A__22199)
& ? [Vvar__3__x_27__22221] :
( t(Vvar__3__x_27__22221,Vvar__0__A__22199)
& ? [Vvar__4__l__22222] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22199,Vvar__4__l__22222)
& ? [Vvar__5__l_27__22223] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22199,Vvar__5__l_27__22223)
& p(happ(happ(Vvar__1__eqA__22200,Vvar__2__x__22220),Vvar__3__x_27__22221))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__22199,Vvar__1__eqA__22200,Vvar__4__l__22222,Vvar__5__l_27__22223)
& Vvar__3___24Anonymous__22206 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22199,Vvar__3__x_27__22221,Vvar__5__l_27__22223)
& Vvar__2___24Anonymous__22205 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22199,Vvar__2__x__22220,Vvar__4__l__22222) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX317] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX317)
=> ( VX317 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__318] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__318)
& VX317 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__318) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX1496] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX1496)
=> ( VX1496 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__1497] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1497)
& VX1496 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1497) )
| ? [Vvar__0___24Anonymous__1498] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1498)
& VX1496 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1498) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX797] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX797)
=> ( ? [Vvar__0___24Anonymous__798] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__798)
& VX797 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__798) )
| ? [Vvar__0___24Anonymous__799] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__799)
& VX797 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__799) )
| VX797 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX1907] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX1907)
=> ? [Vvar__0__Qnum__1908] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__1908)
& ? [Vvar__1__Qden__1909] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__1909)
& VX1907 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__1908,Vvar__1__Qden__1909) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__28643,Vvar__1__leA__28644,Vvar__2___24Anonymous__28649] :
( cType___24t(Vvar__0__A__28643)
=> ( c_24__type__28739___24t(Vvar__0__A__28643,Vvar__1__leA__28644,Vvar__2___24Anonymous__28649,Vvar__1__leA__28644)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28643,Vvar__2___24Anonymous__28649)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__28643,Vvar__1__leA__28644,Vvar__2___24Anonymous__28649)
=> ( Vvar__2___24Anonymous__28649 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28643)
| ? [Vvar__2__x__28663] :
( t(Vvar__2__x__28663,Vvar__0__A__28643)
& Vvar__2___24Anonymous__28649 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28643,Vvar__2__x__28663,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28643)) )
| ? [Vvar__2__x__28670] :
( t(Vvar__2__x__28670,Vvar__0__A__28643)
& ? [Vvar__3__y__28671] :
( t(Vvar__3__y__28671,Vvar__0__A__28643)
& ? [Vvar__4__l__28672] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28643,Vvar__4__l__28672)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__28643,Vvar__1__leA__28644,Vvar__2__x__28670,Vvar__3__y__28671)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__28643,Vvar__1__leA__28644,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__28643,Vvar__4__l__28672,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28643,Vvar__3__y__28671,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28643))))
& Vvar__2___24Anonymous__28649 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2428937___24a6(Vvar__0__A__28643,Vvar__1__leA__28644,Vvar__2___24Anonymous__28649,Vvar__2__x__28670,Vvar__3__y__28671,Vvar__4__l__28672) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__28573,Vvar__1__R__28574,Vvar__2__x__28575,Vvar__3___24Anonymous__28576] :
( cType___24t(Vvar__0__A__28573)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28573,Vvar__1__R__28574)
=> ( t(Vvar__2__x__28575,Vvar__0__A__28573)
=> ( t(Vvar__3___24Anonymous__28576,Vvar__0__A__28573)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__28573,Vvar__1__R__28574,Vvar__2__x__28575,Vvar__3___24Anonymous__28576)
=> ( ? [Vvar__3__y__28581] :
( t(Vvar__3__y__28581,Vvar__0__A__28573)
& p(happ(happ(Vvar__1__R__28574,Vvar__2__x__28575),Vvar__3__y__28581))
& Vvar__3___24Anonymous__28576 = Vvar__3__y__28581 )
| Vvar__3___24Anonymous__28576 = Vvar__2__x__28575 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__37890,Vvar__1__R__37891,Vvar__2__a__37896,Vvar__3___24Anonymous__37897] :
( cType___24t(Vvar__0__A__37890)
=> ( c_24__type__37927___24t(Vvar__0__A__37890,Vvar__1__R__37891,Vvar__2__a__37896,Vvar__3___24Anonymous__37897,Vvar__1__R__37891)
=> ( t(Vvar__2__a__37896,Vvar__0__A__37890)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__37890,Vvar__3___24Anonymous__37897)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__37890,Vvar__1__R__37891,Vvar__2__a__37896,Vvar__3___24Anonymous__37897)
=> ( Vvar__3___24Anonymous__37897 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__37890)
| ? [Vvar__3__b__37913] :
( t(Vvar__3__b__37913,Vvar__0__A__37890)
& ? [Vvar__4__l__37914] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__37890,Vvar__4__l__37914)
& p(happ(happ(Vvar__1__R__37891,Vvar__2__a__37896),Vvar__3__b__37913))
& Vvar__3___24Anonymous__37897 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__37890,Vvar__3__b__37913,Vvar__4__l__37914) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__22403,Vvar__1__R__22404,Vvar__2___24Anonymous__22409] :
( cType___24t(Vvar__0__A__22403)
=> ( c_24__type__22436___24t(Vvar__0__A__22403,Vvar__1__R__22404,Vvar__2___24Anonymous__22409,Vvar__1__R__22404)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22403,Vvar__2___24Anonymous__22409)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__22403,Vvar__1__R__22404,Vvar__2___24Anonymous__22409)
=> ( Vvar__2___24Anonymous__22409 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22403)
| ? [Vvar__2__a__22423] :
( t(Vvar__2__a__22423,Vvar__0__A__22403)
& ? [Vvar__3__l__22424] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22403,Vvar__3__l__22424)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__22403,Vvar__1__R__22404,Vvar__3__l__22424)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__22403,Vvar__1__R__22404,Vvar__2__a__22423,Vvar__3__l__22424)
& Vvar__2___24Anonymous__22409 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22403,Vvar__2__a__22423,Vvar__3__l__22424) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX24410] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX24410)
=> ? [Vvar__0___24Anonymous__24411] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__24411)
& ? [Vvar__1___24Anonymous__24412] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__24412)
& ? [Vvar__2___24Anonymous__24413] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__24413)
& ? [Vvar__3___24Anonymous__24414] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__24414)
& ? [Vvar__4___24Anonymous__24415] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__24415)
& ? [Vvar__5___24Anonymous__24416] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__24416)
& ? [Vvar__6___24Anonymous__24417] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__24417)
& ? [Vvar__7___24Anonymous__24418] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__24418)
& VX24410 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__24411,Vvar__1___24Anonymous__24412,Vvar__2___24Anonymous__24413,Vvar__3___24Anonymous__24414,Vvar__4___24Anonymous__24415,Vvar__5___24Anonymous__24416,Vvar__6___24Anonymous__24417,Vvar__7___24Anonymous__24418) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX38136] :
( cCoq_2eStrings_2eString_2estring___24t(VX38136)
=> ( VX38136 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__38137] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__38137)
& ? [Vvar__1___24Anonymous__38138] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__38138)
& VX38136 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__38137,Vvar__1___24Anonymous__38138) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__26475,VX26476] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26475)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__26475,VX26476)
=> ( ? [Vvar__0__n__26477] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__26477)
& Vvar__0___24Anonymous__26475 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__26477)
& VX26476 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__26477) )
| ? [Vvar__0__n__26478] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__26478)
& ? [Vvar__1___24Anonymous__26479] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__26478,Vvar__1___24Anonymous__26479)
& Vvar__0___24Anonymous__26475 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__26478)
& VX26476 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__26478,Vvar__1___24Anonymous__26479) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__38217,Vvar__1___24Anonymous__38218,VX38219] :
( cType___24t(Vvar__0__A__38217)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__38218)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__38217,Vvar__1___24Anonymous__38218,VX38219)
=> ( ( Vvar__1___24Anonymous__38218 = cCoq_2eInit_2eDatatypes_2eO
& VX38219 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__38217) )
| ? [Vvar__1__h__38222] :
( t(Vvar__1__h__38222,Vvar__0__A__38217)
& ? [Vvar__2__n__38223] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__38223)
& ? [Vvar__3___24Anonymous__38224] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__38217,Vvar__2__n__38223,Vvar__3___24Anonymous__38224)
& Vvar__1___24Anonymous__38218 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__38223)
& VX38219 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__38217,Vvar__1__h__38222,Vvar__2__n__38223,Vvar__3___24Anonymous__38224) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__5061,VX5062] :
( cType___24t(Vvar__0__C__5061)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5061,VX5062)
=> ( ? [Vvar__1___24Anonymous__5064] :
( t(Vvar__1___24Anonymous__5064,Vvar__0__C__5061)
& VX5062 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5061,Vvar__1___24Anonymous__5064) )
| ? [Vvar__1___24Anonymous__5066] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5066)
& ? [Vvar__2___24Anonymous__5067] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5061,Vvar__2___24Anonymous__5067)
& VX5062 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5061,Vvar__1___24Anonymous__5066,Vvar__2___24Anonymous__5067) ) )
| ? [Vvar__1___24Anonymous__5069] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5061,Vvar__1___24Anonymous__5069)
& ? [Vvar__2___24Anonymous__5070] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5070)
& ? [Vvar__3___24Anonymous__5071] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5061,Vvar__3___24Anonymous__5071)
& VX5062 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__5061,Vvar__1___24Anonymous__5069,Vvar__2___24Anonymous__5070,Vvar__3___24Anonymous__5071) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__27155,Vvar__1__rO__27156,Vvar__2__rI__27157,Vvar__3__rplus__27158,Vvar__4__rtimes__27163,Vvar__5__rminus__27168,Vvar__6__ropp__27173,Vvar__7__req__27176,Vvar__8__rle__27181,Vvar__9__rlt__27186] :
( cType___24t(Vvar__0__R__27155)
=> ( t(Vvar__1__rO__27156,Vvar__0__R__27155)
=> ( t(Vvar__2__rI__27157,Vvar__0__R__27155)
=> ( c_24__type__27587___24t(Vvar__0__R__27155,Vvar__1__rO__27156,Vvar__2__rI__27157,Vvar__3__rplus__27158,Vvar__4__rtimes__27163,Vvar__5__rminus__27168,Vvar__6__ropp__27173,Vvar__7__req__27176,Vvar__8__rle__27181,Vvar__9__rlt__27186,Vvar__3__rplus__27158)
=> ( c_24__type__27688___24t(Vvar__0__R__27155,Vvar__1__rO__27156,Vvar__2__rI__27157,Vvar__3__rplus__27158,Vvar__4__rtimes__27163,Vvar__5__rminus__27168,Vvar__6__ropp__27173,Vvar__7__req__27176,Vvar__8__rle__27181,Vvar__9__rlt__27186,Vvar__4__rtimes__27163)
=> ( c_24__type__27789___24t(Vvar__0__R__27155,Vvar__1__rO__27156,Vvar__2__rI__27157,Vvar__3__rplus__27158,Vvar__4__rtimes__27163,Vvar__5__rminus__27168,Vvar__6__ropp__27173,Vvar__7__req__27176,Vvar__8__rle__27181,Vvar__9__rlt__27186,Vvar__5__rminus__27168)
=> ( c_24__type__27879___24t(Vvar__0__R__27155,Vvar__1__rO__27156,Vvar__2__rI__27157,Vvar__3__rplus__27158,Vvar__4__rtimes__27163,Vvar__5__rminus__27168,Vvar__6__ropp__27173,Vvar__7__req__27176,Vvar__8__rle__27181,Vvar__9__rlt__27186,Vvar__6__ropp__27173)
=> ( c_24__type__27980___24t(Vvar__0__R__27155,Vvar__1__rO__27156,Vvar__2__rI__27157,Vvar__3__rplus__27158,Vvar__4__rtimes__27163,Vvar__5__rminus__27168,Vvar__6__ropp__27173,Vvar__7__req__27176,Vvar__8__rle__27181,Vvar__9__rlt__27186,Vvar__7__req__27176)
=> ( c_24__type__28081___24t(Vvar__0__R__27155,Vvar__1__rO__27156,Vvar__2__rI__27157,Vvar__3__rplus__27158,Vvar__4__rtimes__27163,Vvar__5__rminus__27168,Vvar__6__ropp__27173,Vvar__7__req__27176,Vvar__8__rle__27181,Vvar__9__rlt__27186,Vvar__8__rle__27181)
=> ( c_24__type__28182___24t(Vvar__0__R__27155,Vvar__1__rO__27156,Vvar__2__rI__27157,Vvar__3__rplus__27158,Vvar__4__rtimes__27163,Vvar__5__rminus__27168,Vvar__6__ropp__27173,Vvar__7__req__27176,Vvar__8__rle__27181,Vvar__9__rlt__27186,Vvar__9__rlt__27186)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__27155,Vvar__1__rO__27156,Vvar__2__rI__27157,Vvar__3__rplus__27158,Vvar__4__rtimes__27163,Vvar__5__rminus__27168,Vvar__6__ropp__27173,Vvar__7__req__27176,Vvar__8__rle__27181,Vvar__9__rlt__27186)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__27155,Vvar__7__req__27176)
& ! [Vvar__var__var__var__var__11__x1__27230__27236__27341__27347__27353] :
( t(Vvar__var__var__var__var__11__x1__27230__27236__27341__27347__27353,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__12__x2__27231__27237__27342__27348__27354] :
( t(Vvar__var__var__var__var__12__x2__27231__27237__27342__27348__27354,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__11__x1__27230__27236__27341__27347__27353),Vvar__var__var__var__var__12__x2__27231__27237__27342__27348__27354))
=> ! [Vvar__var__var__var__var__14__y1__27232__27238__27343__27349__27355] :
( t(Vvar__var__var__var__var__14__y1__27232__27238__27343__27349__27355,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__15__y2__27233__27239__27344__27350__27356] :
( t(Vvar__var__var__var__var__15__y2__27233__27239__27344__27350__27356,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__14__y1__27232__27238__27343__27349__27355),Vvar__var__var__var__var__15__y2__27233__27239__27344__27350__27356))
=> p(happ(happ(Vvar__7__req__27176,happ(happ(Vvar__3__rplus__27158,Vvar__var__var__var__var__11__x1__27230__27236__27341__27347__27353),Vvar__var__var__var__var__14__y1__27232__27238__27343__27349__27355)),happ(happ(Vvar__3__rplus__27158,Vvar__var__var__var__var__12__x2__27231__27237__27342__27348__27354),Vvar__var__var__var__var__15__y2__27233__27239__27344__27350__27356))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__27243__27249__27359__27365__27371] :
( t(Vvar__var__var__var__var__12__x1__27243__27249__27359__27365__27371,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__13__x2__27244__27250__27360__27366__27372] :
( t(Vvar__var__var__var__var__13__x2__27244__27250__27360__27366__27372,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__12__x1__27243__27249__27359__27365__27371),Vvar__var__var__var__var__13__x2__27244__27250__27360__27366__27372))
=> ! [Vvar__var__var__var__var__15__y1__27245__27251__27361__27367__27373] :
( t(Vvar__var__var__var__var__15__y1__27245__27251__27361__27367__27373,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__16__y2__27246__27252__27362__27368__27374] :
( t(Vvar__var__var__var__var__16__y2__27246__27252__27362__27368__27374,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__15__y1__27245__27251__27361__27367__27373),Vvar__var__var__var__var__16__y2__27246__27252__27362__27368__27374))
=> p(happ(happ(Vvar__7__req__27176,happ(happ(Vvar__4__rtimes__27163,Vvar__var__var__var__var__12__x1__27243__27249__27359__27365__27371),Vvar__var__var__var__var__15__y1__27245__27251__27361__27367__27373)),happ(happ(Vvar__4__rtimes__27163,Vvar__var__var__var__var__13__x2__27244__27250__27360__27366__27372),Vvar__var__var__var__var__16__y2__27246__27252__27362__27368__27374))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__27256__27259__27377__27380__27383] :
( t(Vvar__var__var__var__var__13__x1__27256__27259__27377__27380__27383,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__14__x2__27257__27260__27378__27381__27384] :
( t(Vvar__var__var__var__var__14__x2__27257__27260__27378__27381__27384,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__13__x1__27256__27259__27377__27380__27383),Vvar__var__var__var__var__14__x2__27257__27260__27378__27381__27384))
=> p(happ(happ(Vvar__7__req__27176,happ(Vvar__6__ropp__27173,Vvar__var__var__var__var__13__x1__27256__27259__27377__27380__27383)),happ(Vvar__6__ropp__27173,Vvar__var__var__var__var__14__x2__27257__27260__27378__27381__27384))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__27263__27269__27386__27392__27398] :
( t(Vvar__var__var__var__var__14__x1__27263__27269__27386__27392__27398,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__15__x2__27264__27270__27387__27393__27399] :
( t(Vvar__var__var__var__var__15__x2__27264__27270__27387__27393__27399,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__14__x1__27263__27269__27386__27392__27398),Vvar__var__var__var__var__15__x2__27264__27270__27387__27393__27399))
=> ! [Vvar__var__var__var__var__17__y1__27265__27271__27388__27394__27400] :
( t(Vvar__var__var__var__var__17__y1__27265__27271__27388__27394__27400,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__18__y2__27266__27272__27389__27395__27401] :
( t(Vvar__var__var__var__var__18__y2__27266__27272__27389__27395__27401,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__17__y1__27265__27271__27388__27394__27400),Vvar__var__var__var__var__18__y2__27266__27272__27389__27395__27401))
=> ( p(happ(happ(Vvar__8__rle__27181,Vvar__var__var__var__var__14__x1__27263__27269__27386__27392__27398),Vvar__var__var__var__var__17__y1__27265__27271__27388__27394__27400))
<=> p(happ(happ(Vvar__8__rle__27181,Vvar__var__var__var__var__15__x2__27264__27270__27387__27393__27399),Vvar__var__var__var__var__18__y2__27266__27272__27389__27395__27401)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__27276__27282__27404__27410__27416] :
( t(Vvar__var__var__var__var__15__x1__27276__27282__27404__27410__27416,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__16__x2__27277__27283__27405__27411__27417] :
( t(Vvar__var__var__var__var__16__x2__27277__27283__27405__27411__27417,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__15__x1__27276__27282__27404__27410__27416),Vvar__var__var__var__var__16__x2__27277__27283__27405__27411__27417))
=> ! [Vvar__var__var__var__var__18__y1__27278__27284__27406__27412__27418] :
( t(Vvar__var__var__var__var__18__y1__27278__27284__27406__27412__27418,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__19__y2__27279__27285__27407__27413__27419] :
( t(Vvar__var__var__var__var__19__y2__27279__27285__27407__27413__27419,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__18__y1__27278__27284__27406__27412__27418),Vvar__var__var__var__var__19__y2__27279__27285__27407__27413__27419))
=> ( p(happ(happ(Vvar__9__rlt__27186,Vvar__var__var__var__var__15__x1__27276__27282__27404__27410__27416),Vvar__var__var__var__var__18__y1__27278__27284__27406__27412__27418))
<=> p(happ(happ(Vvar__9__rlt__27186,Vvar__var__var__var__var__16__x2__27277__27283__27405__27411__27417),Vvar__var__var__var__var__19__y2__27279__27285__27407__27413__27419)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__27155,Vvar__1__rO__27156,Vvar__2__rI__27157,Vvar__3__rplus__27158,Vvar__4__rtimes__27163,Vvar__5__rminus__27168,Vvar__6__ropp__27173,Vvar__7__req__27176)
& ! [Vvar__var__var__var__17__n__27290__27291__27422__27423] :
( t(Vvar__var__var__var__17__n__27290__27291__27422__27423,Vvar__0__R__27155)
=> p(happ(happ(Vvar__8__rle__27181,Vvar__var__var__var__17__n__27290__27291__27422__27423),Vvar__var__var__var__17__n__27290__27291__27422__27423)) )
& ! [Vvar__var__var__var__var__18__n__27293__27297__27424__27428__27432] :
( t(Vvar__var__var__var__var__18__n__27293__27297__27424__27428__27432,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__19__m__27294__27298__27425__27429__27433] :
( t(Vvar__var__var__var__var__19__m__27294__27298__27425__27429__27433,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__8__rle__27181,Vvar__var__var__var__var__18__n__27293__27297__27424__27428__27432),Vvar__var__var__var__var__19__m__27294__27298__27425__27429__27433))
=> ( p(happ(happ(Vvar__8__rle__27181,Vvar__var__var__var__var__19__m__27294__27298__27425__27429__27433),Vvar__var__var__var__var__18__n__27293__27297__27424__27428__27432))
=> p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__18__n__27293__27297__27424__27428__27432),Vvar__var__var__var__var__19__m__27294__27298__27425__27429__27433)) ) ) ) )
& ! [Vvar__var__var__var__19__n__27302__27307__27436__27441] :
( t(Vvar__var__var__var__19__n__27302__27307__27436__27441,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__20__m__27303__27308__27437__27442] :
( t(Vvar__var__var__var__20__m__27303__27308__27437__27442,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__21__p__27304__27309__27438__27443] :
( t(Vvar__var__var__var__21__p__27304__27309__27438__27443,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__8__rle__27181,Vvar__var__var__var__19__n__27302__27307__27436__27441),Vvar__var__var__var__20__m__27303__27308__27437__27442))
=> ( p(happ(happ(Vvar__8__rle__27181,Vvar__var__var__var__20__m__27303__27308__27437__27442),Vvar__var__var__var__21__p__27304__27309__27438__27443))
=> p(happ(happ(Vvar__8__rle__27181,Vvar__var__var__var__19__n__27302__27307__27436__27441),Vvar__var__var__var__21__p__27304__27309__27438__27443)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__27313__27315__27446__27448__27450__27452] :
( t(Vvar__var__var__var__var__var__20__n__27313__27315__27446__27448__27450__27452,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__var__21__m__27314__27316__27447__27449__27451__27453] :
( t(Vvar__var__var__var__var__var__21__m__27314__27316__27447__27449__27451__27453,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__9__rlt__27186,Vvar__var__var__var__var__var__20__n__27313__27315__27446__27448__27450__27452),Vvar__var__var__var__var__var__21__m__27314__27316__27447__27449__27451__27453))
<=> ( p(happ(happ(Vvar__8__rle__27181,Vvar__var__var__var__var__var__20__n__27313__27315__27446__27448__27450__27452),Vvar__var__var__var__var__var__21__m__27314__27316__27447__27449__27451__27453))
& ~ p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__var__20__n__27313__27315__27446__27448__27450__27452),Vvar__var__var__var__var__var__21__m__27314__27316__27447__27449__27451__27453)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__27318__27320__27454__27456__27458] :
( t(Vvar__var__var__var__var__21__n__27318__27320__27454__27456__27458,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__22__m__27319__27321__27455__27457__27459] :
( t(Vvar__var__var__var__var__22__m__27319__27321__27455__27457__27459,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__9__rlt__27186,Vvar__var__var__var__var__21__n__27318__27320__27454__27456__27458),Vvar__var__var__var__var__22__m__27319__27321__27455__27457__27459))
| p(happ(happ(Vvar__7__req__27176,Vvar__var__var__var__var__21__n__27318__27320__27454__27456__27458),Vvar__var__var__var__var__22__m__27319__27321__27455__27457__27459))
| p(happ(happ(Vvar__9__rlt__27186,Vvar__var__var__var__var__22__m__27319__27321__27455__27457__27459),Vvar__var__var__var__var__21__n__27318__27320__27454__27456__27458)) ) ) )
& ! [Vvar__var__var__var__var__22__n__27323__27327__27460__27464__27468] :
( t(Vvar__var__var__var__var__22__n__27323__27327__27460__27464__27468,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__23__m__27324__27328__27461__27465__27469] :
( t(Vvar__var__var__var__var__23__m__27324__27328__27461__27465__27469,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__24__p__27325__27329__27462__27466__27470] :
( t(Vvar__var__var__var__var__24__p__27325__27329__27462__27466__27470,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__8__rle__27181,Vvar__var__var__var__var__22__n__27323__27327__27460__27464__27468),Vvar__var__var__var__var__23__m__27324__27328__27461__27465__27469))
=> p(happ(happ(Vvar__8__rle__27181,happ(happ(Vvar__3__rplus__27158,Vvar__var__var__var__var__24__p__27325__27329__27462__27466__27470),Vvar__var__var__var__var__22__n__27323__27327__27460__27464__27468)),happ(happ(Vvar__3__rplus__27158,Vvar__var__var__var__var__24__p__27325__27329__27462__27466__27470),Vvar__var__var__var__var__23__m__27324__27328__27461__27465__27469))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__27332__27336__27472__27476__27480__27484] :
( t(Vvar__var__var__var__var__var__23__n__27332__27336__27472__27476__27480__27484,Vvar__0__R__27155)
=> ! [Vvar__var__var__var__var__var__24__m__27333__27337__27473__27477__27481__27485] :
( t(Vvar__var__var__var__var__var__24__m__27333__27337__27473__27477__27481__27485,Vvar__0__R__27155)
=> ( p(happ(happ(Vvar__9__rlt__27186,Vvar__1__rO__27156),Vvar__var__var__var__var__var__23__n__27332__27336__27472__27476__27480__27484))
=> ( p(happ(happ(Vvar__9__rlt__27186,Vvar__1__rO__27156),Vvar__var__var__var__var__var__24__m__27333__27337__27473__27477__27481__27485))
=> p(happ(happ(Vvar__9__rlt__27186,Vvar__1__rO__27156),happ(happ(Vvar__4__rtimes__27163,Vvar__var__var__var__var__var__23__n__27332__27336__27472__27476__27480__27484),Vvar__var__var__var__var__var__24__m__27333__27337__27473__27477__27481__27485))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__27176,Vvar__1__rO__27156),Vvar__2__rI__27157))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__2530,VX2531] :
( cType___24t(Vvar__0__T__2530)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__2530,VX2531)
=> ? [Vvar__1__Flhs__2533] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__2530,Vvar__1__Flhs__2533)
& ? [Vvar__2__Fop__2534] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__2534)
& ? [Vvar__3__Frhs__2535] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__2530,Vvar__3__Frhs__2535)
& VX2531 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__2530,Vvar__1__Flhs__2533,Vvar__2__Fop__2534,Vvar__3__Frhs__2535) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX2180] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX2180)
=> ( VX2180 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX2180 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX2180 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX2180 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__11887,VX11888] :
( cType___24t(Vvar__0__C__11887)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__11887,VX11888)
=> ( ? [Vvar__1___24Anonymous__11890] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__11890)
& VX11888 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__11887,Vvar__1___24Anonymous__11890) )
| ? [Vvar__1___24Anonymous__11892] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__11887,Vvar__1___24Anonymous__11892)
& VX11888 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__11887,Vvar__1___24Anonymous__11892) )
| ? [Vvar__1___24Anonymous__11894] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__11887,Vvar__1___24Anonymous__11894)
& ? [Vvar__2___24Anonymous__11895] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__11887,Vvar__2___24Anonymous__11895)
& VX11888 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__11887,Vvar__1___24Anonymous__11894,Vvar__2___24Anonymous__11895) ) )
| ? [Vvar__1___24Anonymous__11897] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__11887,Vvar__1___24Anonymous__11897)
& ? [Vvar__2___24Anonymous__11898] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__11887,Vvar__2___24Anonymous__11898)
& VX11888 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__11887,Vvar__1___24Anonymous__11897,Vvar__2___24Anonymous__11898) ) )
| ? [Vvar__1___24Anonymous__11900] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__11887,Vvar__1___24Anonymous__11900)
& ? [Vvar__2___24Anonymous__11901] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__11887,Vvar__2___24Anonymous__11901)
& VX11888 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__11887,Vvar__1___24Anonymous__11900,Vvar__2___24Anonymous__11901) ) )
| ? [Vvar__1___24Anonymous__11903] :
( t(Vvar__1___24Anonymous__11903,Vvar__0__C__11887)
& VX11888 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__11887,Vvar__1___24Anonymous__11903) )
| VX11888 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__11887) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327] :
( cType___24t(Vvar__0__R__29258)
=> ( t(Vvar__1__rO__29259,Vvar__0__R__29258)
=> ( t(Vvar__2__rI__29260,Vvar__0__R__29258)
=> ( c_24__type__29791___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__3__rplus__29261)
=> ( c_24__type__30137___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__4__rtimes__29266)
=> ( c_24__type__30483___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__5__rminus__29271)
=> ( c_24__type__30806___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__6__ropp__29276)
=> ( c_24__type__31152___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__7__req__29279)
=> ( c_24__type__31498___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__8__rle__29284)
=> ( cType___24t(Vvar__9__C__29289)
=> ( t(Vvar__10__cO__29290,Vvar__9__C__29289)
=> ( t(Vvar__11__cI__29291,Vvar__9__C__29289)
=> ( c_24__type__31844___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__12__cplus__29292)
=> ( c_24__type__32190___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__13__ctimes__29297)
=> ( c_24__type__32536___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__14__cminus__29302)
=> ( c_24__type__32859___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__15__copp__29307)
=> ( c_24__type__33205___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__16__ceqb__29310)
=> ( c_24__type__33551___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__17__cleb__29315)
=> ( c_24__type__33874___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__18__phi__29320)
=> ( cType___24t(Vvar__19__E__29323)
=> ( c_24__type__34197___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__20__pow__phi__29324)
=> ( c_24__type__34543___24t(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327,Vvar__21__rpow__29327)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__8__rle__29284,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__17__cleb__29315,Vvar__18__phi__29320,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__29258,Vvar__1__rO__29259,Vvar__2__rI__29260,Vvar__3__rplus__29261,Vvar__4__rtimes__29266,Vvar__5__rminus__29271,Vvar__6__ropp__29276,Vvar__7__req__29279,Vvar__9__C__29289,Vvar__10__cO__29290,Vvar__11__cI__29291,Vvar__12__cplus__29292,Vvar__13__ctimes__29297,Vvar__14__cminus__29302,Vvar__15__copp__29307,Vvar__16__ceqb__29310,Vvar__18__phi__29320)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__29258,Vvar__2__rI__29260,Vvar__4__rtimes__29266,Vvar__7__req__29279,Vvar__19__E__29323,Vvar__20__pow__phi__29324,Vvar__21__rpow__29327)
& ! [Vvar__var__var__var__var__var__24__x__29410__29413__29423__29426__29429__29432] :
( t(Vvar__var__var__var__var__var__24__x__29410__29413__29423__29426__29429__29432,Vvar__9__C__29289)
=> ! [Vvar__var__var__var__var__var__25__y__29411__29414__29424__29427__29430__29433] :
( t(Vvar__var__var__var__var__var__25__y__29411__29414__29424__29427__29430__29433,Vvar__9__C__29289)
=> ( happ(happ(Vvar__16__ceqb__29310,Vvar__var__var__var__var__var__24__x__29410__29413__29423__29426__29429__29432),Vvar__var__var__var__var__var__25__y__29411__29414__29424__29427__29430__29433) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__29279,happ(Vvar__18__phi__29320,Vvar__var__var__var__var__var__24__x__29410__29413__29423__29426__29429__29432)),happ(Vvar__18__phi__29320,Vvar__var__var__var__var__var__25__y__29411__29414__29424__29427__29430__29433))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__29417__29420__29435__29438__29441__29444] :
( t(Vvar__var__var__var__var__var__25__x__29417__29420__29435__29438__29441__29444,Vvar__9__C__29289)
=> ! [Vvar__var__var__var__var__var__26__y__29418__29421__29436__29439__29442__29445] :
( t(Vvar__var__var__var__var__var__26__y__29418__29421__29436__29439__29442__29445,Vvar__9__C__29289)
=> ( happ(happ(Vvar__17__cleb__29315,Vvar__var__var__var__var__var__25__x__29417__29420__29435__29438__29441__29444),Vvar__var__var__var__var__var__26__y__29418__29421__29436__29439__29442__29445) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__29284,happ(Vvar__18__phi__29320,Vvar__var__var__var__var__var__25__x__29417__29420__29435__29438__29441__29444)),happ(Vvar__18__phi__29320,Vvar__var__var__var__var__var__26__y__29418__29421__29436__29439__29442__29445))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,VX2639] :
( cType___24t(Vvar__0__TA__2635)
=> ( cType___24t(Vvar__1__TX__2636)
=> ( cType___24t(Vvar__2__AA__2637)
=> ( cType___24t(Vvar__3__AF__2638)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,VX2639)
=> ( VX2639 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638)
| VX2639 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638)
| ? [Vvar__4___24Anonymous__2652] :
( t(Vvar__4___24Anonymous__2652,Vvar__1__TX__2636)
& VX2639 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__4___24Anonymous__2652) )
| ? [Vvar__4___24Anonymous__2657] :
( t(Vvar__4___24Anonymous__2657,Vvar__0__TA__2635)
& ? [Vvar__5___24Anonymous__2658] :
( t(Vvar__5___24Anonymous__2658,Vvar__2__AA__2637)
& VX2639 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__4___24Anonymous__2657,Vvar__5___24Anonymous__2658) ) )
| ? [Vvar__4___24Anonymous__2663] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__4___24Anonymous__2663)
& ? [Vvar__5___24Anonymous__2664] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__5___24Anonymous__2664)
& VX2639 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__4___24Anonymous__2663,Vvar__5___24Anonymous__2664) ) )
| ? [Vvar__4___24Anonymous__2669] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__4___24Anonymous__2669)
& ? [Vvar__5___24Anonymous__2670] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__5___24Anonymous__2670)
& VX2639 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__4___24Anonymous__2669,Vvar__5___24Anonymous__2670) ) )
| ? [Vvar__4___24Anonymous__2675] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__4___24Anonymous__2675)
& VX2639 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__4___24Anonymous__2675) )
| ? [Vvar__4___24Anonymous__2680] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__4___24Anonymous__2680)
& ? [Vvar__5___24Anonymous__2681] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__2638,Vvar__5___24Anonymous__2681)
& ? [Vvar__6___24Anonymous__2682] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__6___24Anonymous__2682)
& VX2639 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__2635,Vvar__1__TX__2636,Vvar__2__AA__2637,Vvar__3__AF__2638,Vvar__4___24Anonymous__2680,Vvar__5___24Anonymous__2681,Vvar__6___24Anonymous__2682) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX4053] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX4053)
=> ( VX4053 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__4054] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__4054)
& ? [Vvar__1___24Anonymous__4055] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__4055)
& VX4053 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__4054,Vvar__1___24Anonymous__4055) ) )
| ? [Vvar__0___24Anonymous__4056] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__4056)
& ? [Vvar__1___24Anonymous__4057] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__4057)
& VX4053 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__4056,Vvar__1___24Anonymous__4057) ) )
| ? [Vvar__0___24Anonymous__4058] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__4058)
& ? [Vvar__1___24Anonymous__4059] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__4059)
& ? [Vvar__2___24Anonymous__4060] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__4060)
& VX4053 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__4058,Vvar__1___24Anonymous__4059,Vvar__2___24Anonymous__4060) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__5939,VX5940] :
( cType___24t(Vvar__0__C__5939)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,VX5940)
=> ( VX5940 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__5939)
| VX5940 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__5939)
| ? [Vvar__1___24Anonymous__5944] :
( t(Vvar__1___24Anonymous__5944,Vvar__0__C__5939)
& VX5940 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__5939,Vvar__1___24Anonymous__5944) )
| ? [Vvar__1___24Anonymous__5946] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5946)
& VX5940 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__5939,Vvar__1___24Anonymous__5946) )
| ? [Vvar__1___24Anonymous__5948] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,Vvar__1___24Anonymous__5948)
& ? [Vvar__2___24Anonymous__5949] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,Vvar__2___24Anonymous__5949)
& VX5940 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__5939,Vvar__1___24Anonymous__5948,Vvar__2___24Anonymous__5949) ) )
| ? [Vvar__1___24Anonymous__5951] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,Vvar__1___24Anonymous__5951)
& ? [Vvar__2___24Anonymous__5952] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,Vvar__2___24Anonymous__5952)
& VX5940 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__5939,Vvar__1___24Anonymous__5951,Vvar__2___24Anonymous__5952) ) )
| ? [Vvar__1___24Anonymous__5954] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,Vvar__1___24Anonymous__5954)
& ? [Vvar__2___24Anonymous__5955] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,Vvar__2___24Anonymous__5955)
& VX5940 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__5939,Vvar__1___24Anonymous__5954,Vvar__2___24Anonymous__5955) ) )
| ? [Vvar__1___24Anonymous__5957] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,Vvar__1___24Anonymous__5957)
& VX5940 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__5939,Vvar__1___24Anonymous__5957) )
| ? [Vvar__1___24Anonymous__5959] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,Vvar__1___24Anonymous__5959)
& VX5940 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__5939,Vvar__1___24Anonymous__5959) )
| ? [Vvar__1___24Anonymous__5961] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,Vvar__1___24Anonymous__5961)
& ? [Vvar__2___24Anonymous__5962] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,Vvar__2___24Anonymous__5962)
& VX5940 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__5939,Vvar__1___24Anonymous__5961,Vvar__2___24Anonymous__5962) ) )
| ? [Vvar__1___24Anonymous__5964] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__5939,Vvar__1___24Anonymous__5964)
& ? [Vvar__2___24Anonymous__5965] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__5965)
& VX5940 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__5939,Vvar__1___24Anonymous__5964,Vvar__2___24Anonymous__5965) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__5111,Vvar__1__rO__5112,Vvar__2__rI__5113,Vvar__3__radd__5114,Vvar__4__rmul__5119,Vvar__5__rsub__5124,Vvar__6__ropp__5129,Vvar__7__rdiv__5132,Vvar__8__rinv__5137,Vvar__9__req__5140] :
( cType___24t(Vvar__0__R__5111)
=> ( t(Vvar__1__rO__5112,Vvar__0__R__5111)
=> ( t(Vvar__2__rI__5113,Vvar__0__R__5111)
=> ( c_24__type__5305___24t(Vvar__0__R__5111,Vvar__1__rO__5112,Vvar__2__rI__5113,Vvar__3__radd__5114,Vvar__4__rmul__5119,Vvar__5__rsub__5124,Vvar__6__ropp__5129,Vvar__7__rdiv__5132,Vvar__8__rinv__5137,Vvar__9__req__5140,Vvar__3__radd__5114)
=> ( c_24__type__5398___24t(Vvar__0__R__5111,Vvar__1__rO__5112,Vvar__2__rI__5113,Vvar__3__radd__5114,Vvar__4__rmul__5119,Vvar__5__rsub__5124,Vvar__6__ropp__5129,Vvar__7__rdiv__5132,Vvar__8__rinv__5137,Vvar__9__req__5140,Vvar__4__rmul__5119)
=> ( c_24__type__5491___24t(Vvar__0__R__5111,Vvar__1__rO__5112,Vvar__2__rI__5113,Vvar__3__radd__5114,Vvar__4__rmul__5119,Vvar__5__rsub__5124,Vvar__6__ropp__5129,Vvar__7__rdiv__5132,Vvar__8__rinv__5137,Vvar__9__req__5140,Vvar__5__rsub__5124)
=> ( c_24__type__5573___24t(Vvar__0__R__5111,Vvar__1__rO__5112,Vvar__2__rI__5113,Vvar__3__radd__5114,Vvar__4__rmul__5119,Vvar__5__rsub__5124,Vvar__6__ropp__5129,Vvar__7__rdiv__5132,Vvar__8__rinv__5137,Vvar__9__req__5140,Vvar__6__ropp__5129)
=> ( c_24__type__5666___24t(Vvar__0__R__5111,Vvar__1__rO__5112,Vvar__2__rI__5113,Vvar__3__radd__5114,Vvar__4__rmul__5119,Vvar__5__rsub__5124,Vvar__6__ropp__5129,Vvar__7__rdiv__5132,Vvar__8__rinv__5137,Vvar__9__req__5140,Vvar__7__rdiv__5132)
=> ( c_24__type__5748___24t(Vvar__0__R__5111,Vvar__1__rO__5112,Vvar__2__rI__5113,Vvar__3__radd__5114,Vvar__4__rmul__5119,Vvar__5__rsub__5124,Vvar__6__ropp__5129,Vvar__7__rdiv__5132,Vvar__8__rinv__5137,Vvar__9__req__5140,Vvar__8__rinv__5137)
=> ( c_24__type__5841___24t(Vvar__0__R__5111,Vvar__1__rO__5112,Vvar__2__rI__5113,Vvar__3__radd__5114,Vvar__4__rmul__5119,Vvar__5__rsub__5124,Vvar__6__ropp__5129,Vvar__7__rdiv__5132,Vvar__8__rinv__5137,Vvar__9__req__5140,Vvar__9__req__5140)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__5111,Vvar__1__rO__5112,Vvar__2__rI__5113,Vvar__3__radd__5114,Vvar__4__rmul__5119,Vvar__5__rsub__5124,Vvar__6__ropp__5129,Vvar__7__rdiv__5132,Vvar__8__rinv__5137,Vvar__9__req__5140)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__5111,Vvar__1__rO__5112,Vvar__2__rI__5113,Vvar__3__radd__5114,Vvar__4__rmul__5119,Vvar__5__rsub__5124,Vvar__6__ropp__5129,Vvar__9__req__5140)
& ~ p(happ(happ(Vvar__9__req__5140,Vvar__2__rI__5113),Vvar__1__rO__5112))
& ! [Vvar__var__var__var__var__var__var__12__p__5183__5185__5192__5194__5196__5198__5200] :
( t(Vvar__var__var__var__var__var__var__12__p__5183__5185__5192__5194__5196__5198__5200,Vvar__0__R__5111)
=> ! [Vvar__var__var__var__var__var__var__13__q__5184__5186__5193__5195__5197__5199__5201] :
( t(Vvar__var__var__var__var__var__var__13__q__5184__5186__5193__5195__5197__5199__5201,Vvar__0__R__5111)
=> p(happ(happ(Vvar__9__req__5140,happ(happ(Vvar__7__rdiv__5132,Vvar__var__var__var__var__var__var__12__p__5183__5185__5192__5194__5196__5198__5200),Vvar__var__var__var__var__var__var__13__q__5184__5186__5193__5195__5197__5199__5201)),happ(happ(Vvar__4__rmul__5119,Vvar__var__var__var__var__var__var__12__p__5183__5185__5192__5194__5196__5198__5200),happ(Vvar__8__rinv__5137,Vvar__var__var__var__var__var__var__13__q__5184__5186__5193__5195__5197__5199__5201)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__5188__5190__5202__5204__5206__5208__5210__5212] :
( t(Vvar__var__var__var__var__var__var__var__13__p__5188__5190__5202__5204__5206__5208__5210__5212,Vvar__0__R__5111)
=> ( ~ p(happ(happ(Vvar__9__req__5140,Vvar__var__var__var__var__var__var__var__13__p__5188__5190__5202__5204__5206__5208__5210__5212),Vvar__1__rO__5112))
=> p(happ(happ(Vvar__9__req__5140,happ(happ(Vvar__4__rmul__5119,happ(Vvar__8__rinv__5137,Vvar__var__var__var__var__var__var__var__13__p__5188__5190__5202__5204__5206__5208__5210__5212)),Vvar__var__var__var__var__var__var__var__13__p__5188__5190__5202__5204__5206__5208__5210__5212)),Vvar__2__rI__5113)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__6551,VX6552] :
( cType___24t(Vvar__0__C__6551)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__6551,VX6552)
=> ? [Vvar__1__num__6554] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6551,Vvar__1__num__6554)
& ? [Vvar__2__denum__6555] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6551,Vvar__2__denum__6555)
& ? [Vvar__3__condition__6556] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__6551),Vvar__3__condition__6556)
& VX6552 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__6551,Vvar__1__num__6554,Vvar__2__denum__6555,Vvar__3__condition__6556) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__6890,VX6891] :
( cType___24t(Vvar__0__C__6890)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__6890,VX6891)
=> ? [Vvar__1__rsplit__left__6893] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6890,Vvar__1__rsplit__left__6893)
& ? [Vvar__2__rsplit__common__6894] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6890,Vvar__2__rsplit__common__6894)
& ? [Vvar__3__rsplit__right__6895] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6890,Vvar__3__rsplit__right__6895)
& VX6891 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__6890,Vvar__1__rsplit__left__6893,Vvar__2__rsplit__common__6894,Vvar__3__rsplit__right__6895) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX12748] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX12748)
=> ( VX12748 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__12749] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12749)
& ? [Vvar__1___24Anonymous__12750] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__12750)
& VX12748 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__12749,Vvar__1___24Anonymous__12750) ) )
| ? [Vvar__0___24Anonymous__12751] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12751)
& ? [Vvar__1___24Anonymous__12752] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__12752)
& VX12748 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__12751,Vvar__1___24Anonymous__12752) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__14084,VX14085] :
( cType___24t(Vvar__0__C__14084)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14084,VX14085)
=> ( VX14085 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14084)
| VX14085 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14084)
| ? [Vvar__1___24Anonymous__14089] :
( t(Vvar__1___24Anonymous__14089,Vvar__0__C__14084)
& VX14085 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__14084,Vvar__1___24Anonymous__14089) )
| ? [Vvar__1___24Anonymous__14091] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14091)
& VX14085 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__14084,Vvar__1___24Anonymous__14091) )
| ? [Vvar__1___24Anonymous__14093] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14084,Vvar__1___24Anonymous__14093)
& ? [Vvar__2___24Anonymous__14094] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14084,Vvar__2___24Anonymous__14094)
& VX14085 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__14084,Vvar__1___24Anonymous__14093,Vvar__2___24Anonymous__14094) ) )
| ? [Vvar__1___24Anonymous__14096] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14084,Vvar__1___24Anonymous__14096)
& ? [Vvar__2___24Anonymous__14097] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14084,Vvar__2___24Anonymous__14097)
& VX14085 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__14084,Vvar__1___24Anonymous__14096,Vvar__2___24Anonymous__14097) ) )
| ? [Vvar__1___24Anonymous__14099] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14084,Vvar__1___24Anonymous__14099)
& ? [Vvar__2___24Anonymous__14100] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14084,Vvar__2___24Anonymous__14100)
& VX14085 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__14084,Vvar__1___24Anonymous__14099,Vvar__2___24Anonymous__14100) ) )
| ? [Vvar__1___24Anonymous__14102] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14084,Vvar__1___24Anonymous__14102)
& VX14085 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__14084,Vvar__1___24Anonymous__14102) )
| ? [Vvar__1___24Anonymous__14104] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14084,Vvar__1___24Anonymous__14104)
& ? [Vvar__2___24Anonymous__14105] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14105)
& VX14085 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__14084,Vvar__1___24Anonymous__14104,Vvar__2___24Anonymous__14105) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__12191,VX12192] :
( cType___24t(Vvar__0__C__12191)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12191,VX12192)
=> ( ? [Vvar__1___24Anonymous__12194] :
( t(Vvar__1___24Anonymous__12194,Vvar__0__C__12191)
& VX12192 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12191,Vvar__1___24Anonymous__12194) )
| ? [Vvar__1___24Anonymous__12196] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12196)
& ? [Vvar__2___24Anonymous__12197] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12191,Vvar__2___24Anonymous__12197)
& VX12192 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12191,Vvar__1___24Anonymous__12196,Vvar__2___24Anonymous__12197) ) )
| ? [Vvar__1___24Anonymous__12199] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12191,Vvar__1___24Anonymous__12199)
& ? [Vvar__2___24Anonymous__12200] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12200)
& ? [Vvar__3___24Anonymous__12201] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12191,Vvar__3___24Anonymous__12201)
& VX12192 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__12191,Vvar__1___24Anonymous__12199,Vvar__2___24Anonymous__12200,Vvar__3___24Anonymous__12201) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__17638,Vvar__1__rO__17639,Vvar__2__rI__17640,Vvar__3__radd__17641,Vvar__4__rmul__17646,Vvar__5__rsub__17651,Vvar__6__ropp__17656,Vvar__7__req__17659] :
( cType___24t(Vvar__0__R__17638)
=> ( t(Vvar__1__rO__17639,Vvar__0__R__17638)
=> ( t(Vvar__2__rI__17640,Vvar__0__R__17638)
=> ( c_24__type__17887___24t(Vvar__0__R__17638,Vvar__1__rO__17639,Vvar__2__rI__17640,Vvar__3__radd__17641,Vvar__4__rmul__17646,Vvar__5__rsub__17651,Vvar__6__ropp__17656,Vvar__7__req__17659,Vvar__3__radd__17641)
=> ( c_24__type__17950___24t(Vvar__0__R__17638,Vvar__1__rO__17639,Vvar__2__rI__17640,Vvar__3__radd__17641,Vvar__4__rmul__17646,Vvar__5__rsub__17651,Vvar__6__ropp__17656,Vvar__7__req__17659,Vvar__4__rmul__17646)
=> ( c_24__type__18013___24t(Vvar__0__R__17638,Vvar__1__rO__17639,Vvar__2__rI__17640,Vvar__3__radd__17641,Vvar__4__rmul__17646,Vvar__5__rsub__17651,Vvar__6__ropp__17656,Vvar__7__req__17659,Vvar__5__rsub__17651)
=> ( c_24__type__18067___24t(Vvar__0__R__17638,Vvar__1__rO__17639,Vvar__2__rI__17640,Vvar__3__radd__17641,Vvar__4__rmul__17646,Vvar__5__rsub__17651,Vvar__6__ropp__17656,Vvar__7__req__17659,Vvar__6__ropp__17656)
=> ( c_24__type__18130___24t(Vvar__0__R__17638,Vvar__1__rO__17639,Vvar__2__rI__17640,Vvar__3__radd__17641,Vvar__4__rmul__17646,Vvar__5__rsub__17651,Vvar__6__ropp__17656,Vvar__7__req__17659,Vvar__7__req__17659)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__17638,Vvar__1__rO__17639,Vvar__2__rI__17640,Vvar__3__radd__17641,Vvar__4__rmul__17646,Vvar__5__rsub__17651,Vvar__6__ropp__17656,Vvar__7__req__17659)
=> ( ! [Vvar__var__var__var__var__var__8__x__17692__17693__17746__17747__17748__17749] :
( t(Vvar__var__var__var__var__var__8__x__17692__17693__17746__17747__17748__17749,Vvar__0__R__17638)
=> p(happ(happ(Vvar__7__req__17659,happ(happ(Vvar__3__radd__17641,Vvar__1__rO__17639),Vvar__var__var__var__var__var__8__x__17692__17693__17746__17747__17748__17749)),Vvar__var__var__var__var__var__8__x__17692__17693__17746__17747__17748__17749)) )
& ! [Vvar__var__var__var__var__9__x__17695__17697__17750__17752__17754] :
( t(Vvar__var__var__var__var__9__x__17695__17697__17750__17752__17754,Vvar__0__R__17638)
=> ! [Vvar__var__var__var__var__10__y__17696__17698__17751__17753__17755] :
( t(Vvar__var__var__var__var__10__y__17696__17698__17751__17753__17755,Vvar__0__R__17638)
=> p(happ(happ(Vvar__7__req__17659,happ(happ(Vvar__3__radd__17641,Vvar__var__var__var__var__9__x__17695__17697__17750__17752__17754),Vvar__var__var__var__var__10__y__17696__17698__17751__17753__17755)),happ(happ(Vvar__3__radd__17641,Vvar__var__var__var__var__10__y__17696__17698__17751__17753__17755),Vvar__var__var__var__var__9__x__17695__17697__17750__17752__17754))) ) )
& ! [Vvar__var__var__var__var__10__x__17700__17703__17756__17759__17762] :
( t(Vvar__var__var__var__var__10__x__17700__17703__17756__17759__17762,Vvar__0__R__17638)
=> ! [Vvar__var__var__var__var__11__y__17701__17704__17757__17760__17763] :
( t(Vvar__var__var__var__var__11__y__17701__17704__17757__17760__17763,Vvar__0__R__17638)
=> ! [Vvar__var__var__var__var__12__z__17702__17705__17758__17761__17764] :
( t(Vvar__var__var__var__var__12__z__17702__17705__17758__17761__17764,Vvar__0__R__17638)
=> p(happ(happ(Vvar__7__req__17659,happ(happ(Vvar__3__radd__17641,Vvar__var__var__var__var__10__x__17700__17703__17756__17759__17762),happ(happ(Vvar__3__radd__17641,Vvar__var__var__var__var__11__y__17701__17704__17757__17760__17763),Vvar__var__var__var__var__12__z__17702__17705__17758__17761__17764))),happ(happ(Vvar__3__radd__17641,happ(happ(Vvar__3__radd__17641,Vvar__var__var__var__var__10__x__17700__17703__17756__17759__17762),Vvar__var__var__var__var__11__y__17701__17704__17757__17760__17763)),Vvar__var__var__var__var__12__z__17702__17705__17758__17761__17764))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__17707__17708__17765__17766__17767__17768] :
( t(Vvar__var__var__var__var__var__11__x__17707__17708__17765__17766__17767__17768,Vvar__0__R__17638)
=> p(happ(happ(Vvar__7__req__17659,happ(happ(Vvar__4__rmul__17646,Vvar__2__rI__17640),Vvar__var__var__var__var__var__11__x__17707__17708__17765__17766__17767__17768)),Vvar__var__var__var__var__var__11__x__17707__17708__17765__17766__17767__17768)) )
& ! [Vvar__var__var__var__var__var__12__x__17710__17711__17769__17770__17771__17772] :
( t(Vvar__var__var__var__var__var__12__x__17710__17711__17769__17770__17771__17772,Vvar__0__R__17638)
=> p(happ(happ(Vvar__7__req__17659,happ(happ(Vvar__4__rmul__17646,Vvar__1__rO__17639),Vvar__var__var__var__var__var__12__x__17710__17711__17769__17770__17771__17772)),Vvar__1__rO__17639)) )
& ! [Vvar__var__var__var__var__13__x__17713__17715__17773__17775__17777] :
( t(Vvar__var__var__var__var__13__x__17713__17715__17773__17775__17777,Vvar__0__R__17638)
=> ! [Vvar__var__var__var__var__14__y__17714__17716__17774__17776__17778] :
( t(Vvar__var__var__var__var__14__y__17714__17716__17774__17776__17778,Vvar__0__R__17638)
=> p(happ(happ(Vvar__7__req__17659,happ(happ(Vvar__4__rmul__17646,Vvar__var__var__var__var__13__x__17713__17715__17773__17775__17777),Vvar__var__var__var__var__14__y__17714__17716__17774__17776__17778)),happ(happ(Vvar__4__rmul__17646,Vvar__var__var__var__var__14__y__17714__17716__17774__17776__17778),Vvar__var__var__var__var__13__x__17713__17715__17773__17775__17777))) ) )
& ! [Vvar__var__var__var__var__14__x__17718__17721__17779__17782__17785] :
( t(Vvar__var__var__var__var__14__x__17718__17721__17779__17782__17785,Vvar__0__R__17638)
=> ! [Vvar__var__var__var__var__15__y__17719__17722__17780__17783__17786] :
( t(Vvar__var__var__var__var__15__y__17719__17722__17780__17783__17786,Vvar__0__R__17638)
=> ! [Vvar__var__var__var__var__16__z__17720__17723__17781__17784__17787] :
( t(Vvar__var__var__var__var__16__z__17720__17723__17781__17784__17787,Vvar__0__R__17638)
=> p(happ(happ(Vvar__7__req__17659,happ(happ(Vvar__4__rmul__17646,Vvar__var__var__var__var__14__x__17718__17721__17779__17782__17785),happ(happ(Vvar__4__rmul__17646,Vvar__var__var__var__var__15__y__17719__17722__17780__17783__17786),Vvar__var__var__var__var__16__z__17720__17723__17781__17784__17787))),happ(happ(Vvar__4__rmul__17646,happ(happ(Vvar__4__rmul__17646,Vvar__var__var__var__var__14__x__17718__17721__17779__17782__17785),Vvar__var__var__var__var__15__y__17719__17722__17780__17783__17786)),Vvar__var__var__var__var__16__z__17720__17723__17781__17784__17787))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__17725__17728__17788__17791__17794__17797] :
( t(Vvar__var__var__var__var__var__15__x__17725__17728__17788__17791__17794__17797,Vvar__0__R__17638)
=> ! [Vvar__var__var__var__var__var__16__y__17726__17729__17789__17792__17795__17798] :
( t(Vvar__var__var__var__var__var__16__y__17726__17729__17789__17792__17795__17798,Vvar__0__R__17638)
=> ! [Vvar__var__var__var__var__var__17__z__17727__17730__17790__17793__17796__17799] :
( t(Vvar__var__var__var__var__var__17__z__17727__17730__17790__17793__17796__17799,Vvar__0__R__17638)
=> p(happ(happ(Vvar__7__req__17659,happ(happ(Vvar__4__rmul__17646,happ(happ(Vvar__3__radd__17641,Vvar__var__var__var__var__var__15__x__17725__17728__17788__17791__17794__17797),Vvar__var__var__var__var__var__16__y__17726__17729__17789__17792__17795__17798)),Vvar__var__var__var__var__var__17__z__17727__17730__17790__17793__17796__17799)),happ(happ(Vvar__3__radd__17641,happ(happ(Vvar__4__rmul__17646,Vvar__var__var__var__var__var__15__x__17725__17728__17788__17791__17794__17797),Vvar__var__var__var__var__var__17__z__17727__17730__17790__17793__17796__17799)),happ(happ(Vvar__4__rmul__17646,Vvar__var__var__var__var__var__16__y__17726__17729__17789__17792__17795__17798),Vvar__var__var__var__var__var__17__z__17727__17730__17790__17793__17796__17799)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__17732__17734__17800__17802__17804__17806] :
( t(Vvar__var__var__var__var__var__16__x__17732__17734__17800__17802__17804__17806,Vvar__0__R__17638)
=> ! [Vvar__var__var__var__var__var__17__y__17733__17735__17801__17803__17805__17807] :
( t(Vvar__var__var__var__var__var__17__y__17733__17735__17801__17803__17805__17807,Vvar__0__R__17638)
=> p(happ(happ(Vvar__7__req__17659,happ(Vvar__6__ropp__17656,happ(happ(Vvar__4__rmul__17646,Vvar__var__var__var__var__var__16__x__17732__17734__17800__17802__17804__17806),Vvar__var__var__var__var__var__17__y__17733__17735__17801__17803__17805__17807))),happ(happ(Vvar__4__rmul__17646,happ(Vvar__6__ropp__17656,Vvar__var__var__var__var__var__16__x__17732__17734__17800__17802__17804__17806)),Vvar__var__var__var__var__var__17__y__17733__17735__17801__17803__17805__17807))) ) )
& ! [Vvar__var__var__var__var__var__17__x__17737__17739__17808__17810__17812__17814] :
( t(Vvar__var__var__var__var__var__17__x__17737__17739__17808__17810__17812__17814,Vvar__0__R__17638)
=> ! [Vvar__var__var__var__var__var__18__y__17738__17740__17809__17811__17813__17815] :
( t(Vvar__var__var__var__var__var__18__y__17738__17740__17809__17811__17813__17815,Vvar__0__R__17638)
=> p(happ(happ(Vvar__7__req__17659,happ(Vvar__6__ropp__17656,happ(happ(Vvar__3__radd__17641,Vvar__var__var__var__var__var__17__x__17737__17739__17808__17810__17812__17814),Vvar__var__var__var__var__var__18__y__17738__17740__17809__17811__17813__17815))),happ(happ(Vvar__3__radd__17641,happ(Vvar__6__ropp__17656,Vvar__var__var__var__var__var__17__x__17737__17739__17808__17810__17812__17814)),happ(Vvar__6__ropp__17656,Vvar__var__var__var__var__var__18__y__17738__17740__17809__17811__17813__17815)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__17742__17744__17816__17818__17820__17822__17824] :
( t(Vvar__var__var__var__var__var__var__18__x__17742__17744__17816__17818__17820__17822__17824,Vvar__0__R__17638)
=> ! [Vvar__var__var__var__var__var__var__19__y__17743__17745__17817__17819__17821__17823__17825] :
( t(Vvar__var__var__var__var__var__var__19__y__17743__17745__17817__17819__17821__17823__17825,Vvar__0__R__17638)
=> p(happ(happ(Vvar__7__req__17659,happ(happ(Vvar__5__rsub__17651,Vvar__var__var__var__var__var__var__18__x__17742__17744__17816__17818__17820__17822__17824),Vvar__var__var__var__var__var__var__19__y__17743__17745__17817__17819__17821__17823__17825)),happ(happ(Vvar__3__radd__17641,Vvar__var__var__var__var__var__var__18__x__17742__17744__17816__17818__17820__17822__17824),happ(Vvar__6__ropp__17656,Vvar__var__var__var__var__var__var__19__y__17743__17745__17817__17819__17821__17823__17825)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__21322,Vvar__1__req__21323,Vvar__2__C__21328,Vvar__3__cadd__21329,Vvar__4__cmul__21334,Vvar__5__phi__21339,Vvar__6__cdiv__21342] :
( cType___24t(Vvar__0__R__21322)
=> ( c_24__type__21462___24t(Vvar__0__R__21322,Vvar__1__req__21323,Vvar__2__C__21328,Vvar__3__cadd__21329,Vvar__4__cmul__21334,Vvar__5__phi__21339,Vvar__6__cdiv__21342,Vvar__1__req__21323)
=> ( cType___24t(Vvar__2__C__21328)
=> ( c_24__type__21512___24t(Vvar__0__R__21322,Vvar__1__req__21323,Vvar__2__C__21328,Vvar__3__cadd__21329,Vvar__4__cmul__21334,Vvar__5__phi__21339,Vvar__6__cdiv__21342,Vvar__3__cadd__21329)
=> ( c_24__type__21562___24t(Vvar__0__R__21322,Vvar__1__req__21323,Vvar__2__C__21328,Vvar__3__cadd__21329,Vvar__4__cmul__21334,Vvar__5__phi__21339,Vvar__6__cdiv__21342,Vvar__4__cmul__21334)
=> ( c_24__type__21604___24t(Vvar__0__R__21322,Vvar__1__req__21323,Vvar__2__C__21328,Vvar__3__cadd__21329,Vvar__4__cmul__21334,Vvar__5__phi__21339,Vvar__6__cdiv__21342,Vvar__5__phi__21339)
=> ( c_24__type__21654___24t(Vvar__0__R__21322,Vvar__1__req__21323,Vvar__2__C__21328,Vvar__3__cadd__21329,Vvar__4__cmul__21334,Vvar__5__phi__21339,Vvar__6__cdiv__21342,Vvar__6__cdiv__21342)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__21322,Vvar__1__req__21323,Vvar__2__C__21328,Vvar__3__cadd__21329,Vvar__4__cmul__21334,Vvar__5__phi__21339,Vvar__6__cdiv__21342)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__21374__21379__21384__21389__21394__21399__21404__21409] :
( t(Vvar__var__var__var__var__var__var__var__7__a__21374__21379__21384__21389__21394__21399__21404__21409,Vvar__2__C__21328)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__21375__21380__21385__21390__21395__21400__21405__21410] :
( t(Vvar__var__var__var__var__var__var__var__8__b__21375__21380__21385__21390__21395__21400__21405__21410,Vvar__2__C__21328)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2421717___24a9(Vvar__0__R__21322,Vvar__1__req__21323,Vvar__2__C__21328,Vvar__3__cadd__21329,Vvar__4__cmul__21334,Vvar__5__phi__21339,Vvar__6__cdiv__21342,Vvar__var__var__var__var__var__var__var__7__a__21374__21379__21384__21389__21394__21399__21404__21409,Vvar__var__var__var__var__var__var__var__8__b__21375__21380__21385__21390__21395__21400__21405__21410) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__21757,Vvar__1__rI__21758,Vvar__2__rmul__21759,Vvar__3__req__21764,Vvar__4__Cpow__21769,Vvar__5__Cp__phi__21770,Vvar__6__rpow__21773] :
( cType___24t(Vvar__0__R__21757)
=> ( t(Vvar__1__rI__21758,Vvar__0__R__21757)
=> ( c_24__type__21859___24t(Vvar__0__R__21757,Vvar__1__rI__21758,Vvar__2__rmul__21759,Vvar__3__req__21764,Vvar__4__Cpow__21769,Vvar__5__Cp__phi__21770,Vvar__6__rpow__21773,Vvar__2__rmul__21759)
=> ( c_24__type__21903___24t(Vvar__0__R__21757,Vvar__1__rI__21758,Vvar__2__rmul__21759,Vvar__3__req__21764,Vvar__4__Cpow__21769,Vvar__5__Cp__phi__21770,Vvar__6__rpow__21773,Vvar__3__req__21764)
=> ( cType___24t(Vvar__4__Cpow__21769)
=> ( c_24__type__21939___24t(Vvar__0__R__21757,Vvar__1__rI__21758,Vvar__2__rmul__21759,Vvar__3__req__21764,Vvar__4__Cpow__21769,Vvar__5__Cp__phi__21770,Vvar__6__rpow__21773,Vvar__5__Cp__phi__21770)
=> ( c_24__type__21983___24t(Vvar__0__R__21757,Vvar__1__rI__21758,Vvar__2__rmul__21759,Vvar__3__req__21764,Vvar__4__Cpow__21769,Vvar__5__Cp__phi__21770,Vvar__6__rpow__21773,Vvar__6__rpow__21773)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__21757,Vvar__1__rI__21758,Vvar__2__rmul__21759,Vvar__3__req__21764,Vvar__4__Cpow__21769,Vvar__5__Cp__phi__21770,Vvar__6__rpow__21773)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__21801__21803__21805__21807__21809__21811__21813__21815] :
( t(Vvar__var__var__var__var__var__var__var__7__r__21801__21803__21805__21807__21809__21811__21813__21815,Vvar__0__R__21757)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__21802__21804__21806__21808__21810__21812__21814__21816] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__21802__21804__21806__21808__21810__21812__21814__21816)
=> p(happ(happ(Vvar__3__req__21764,happ(happ(Vvar__6__rpow__21773,Vvar__var__var__var__var__var__var__var__7__r__21801__21803__21805__21807__21809__21811__21813__21815),happ(Vvar__5__Cp__phi__21770,Vvar__var__var__var__var__var__var__var__8__n__21802__21804__21806__21808__21810__21812__21814__21816))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__21757,Vvar__1__rI__21758,Vvar__2__rmul__21759,Vvar__var__var__var__var__var__var__var__7__r__21801__21803__21805__21807__21809__21811__21813__21815,Vvar__var__var__var__var__var__var__var__8__n__21802__21804__21806__21808__21810__21812__21814__21816))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__18258,Vvar__1__radd__18259,Vvar__2__rmul__18264,Vvar__3__ropp__18269,Vvar__4__req__18272] :
( cType___24t(Vvar__0__R__18258)
=> ( c_24__type__18363___24t(Vvar__0__R__18258,Vvar__1__radd__18259,Vvar__2__rmul__18264,Vvar__3__ropp__18269,Vvar__4__req__18272,Vvar__1__radd__18259)
=> ( c_24__type__18393___24t(Vvar__0__R__18258,Vvar__1__radd__18259,Vvar__2__rmul__18264,Vvar__3__ropp__18269,Vvar__4__req__18272,Vvar__2__rmul__18264)
=> ( c_24__type__18417___24t(Vvar__0__R__18258,Vvar__1__radd__18259,Vvar__2__rmul__18264,Vvar__3__ropp__18269,Vvar__4__req__18272,Vvar__3__ropp__18269)
=> ( c_24__type__18447___24t(Vvar__0__R__18258,Vvar__1__radd__18259,Vvar__2__rmul__18264,Vvar__3__ropp__18269,Vvar__4__req__18272,Vvar__4__req__18272)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__18258,Vvar__1__radd__18259,Vvar__2__rmul__18264,Vvar__3__ropp__18269,Vvar__4__req__18272)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__18477___24a5(Vvar__0__R__18258,Vvar__1__radd__18259,Vvar__2__rmul__18264,Vvar__3__ropp__18269,Vvar__4__req__18272),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__18258,c_24__type__18501___24a5(Vvar__0__R__18258,Vvar__1__radd__18259,Vvar__2__rmul__18264,Vvar__3__ropp__18269,Vvar__4__req__18272),Vvar__4__req__18272,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__18258,Vvar__0__R__18258,Vvar__4__req__18272,Vvar__4__req__18272)),Vvar__1__radd__18259)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__18534___24a5(Vvar__0__R__18258,Vvar__1__radd__18259,Vvar__2__rmul__18264,Vvar__3__ropp__18269,Vvar__4__req__18272),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__18258,c_24__type__18558___24a5(Vvar__0__R__18258,Vvar__1__radd__18259,Vvar__2__rmul__18264,Vvar__3__ropp__18269,Vvar__4__req__18272),Vvar__4__req__18272,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__18258,Vvar__0__R__18258,Vvar__4__req__18272,Vvar__4__req__18272)),Vvar__2__rmul__18264)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__18585___24a5(Vvar__0__R__18258,Vvar__1__radd__18259,Vvar__2__rmul__18264,Vvar__3__ropp__18269,Vvar__4__req__18272),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__18258,Vvar__0__R__18258,Vvar__4__req__18272,Vvar__4__req__18272),Vvar__3__ropp__18269)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680] :
( cType___24t(Vvar__0__R__18628)
=> ( t(Vvar__1__rO__18629,Vvar__0__R__18628)
=> ( t(Vvar__2__rI__18630,Vvar__0__R__18628)
=> ( c_24__type__19024___24t(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680,Vvar__3__radd__18631)
=> ( c_24__type__19237___24t(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680,Vvar__4__rmul__18636)
=> ( c_24__type__19450___24t(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680,Vvar__5__rsub__18641)
=> ( c_24__type__19645___24t(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680,Vvar__6__ropp__18646)
=> ( c_24__type__19858___24t(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680,Vvar__7__req__18649)
=> ( cType___24t(Vvar__8__C__18654)
=> ( t(Vvar__9__cO__18655,Vvar__8__C__18654)
=> ( t(Vvar__10__cI__18656,Vvar__8__C__18654)
=> ( c_24__type__20071___24t(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680,Vvar__11__cadd__18657)
=> ( c_24__type__20284___24t(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680,Vvar__12__cmul__18662)
=> ( c_24__type__20497___24t(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680,Vvar__13__csub__18667)
=> ( c_24__type__20692___24t(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680,Vvar__14__copp__18672)
=> ( c_24__type__20905___24t(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680,Vvar__15__ceqb__18675)
=> ( c_24__type__21100___24t(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680,Vvar__16__phi__18680)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__18628,Vvar__1__rO__18629,Vvar__2__rI__18630,Vvar__3__radd__18631,Vvar__4__rmul__18636,Vvar__5__rsub__18641,Vvar__6__ropp__18646,Vvar__7__req__18649,Vvar__8__C__18654,Vvar__9__cO__18655,Vvar__10__cI__18656,Vvar__11__cadd__18657,Vvar__12__cmul__18662,Vvar__13__csub__18667,Vvar__14__copp__18672,Vvar__15__ceqb__18675,Vvar__16__phi__18680)
=> ( p(happ(happ(Vvar__7__req__18649,happ(Vvar__16__phi__18680,Vvar__9__cO__18655)),Vvar__1__rO__18629))
& p(happ(happ(Vvar__7__req__18649,happ(Vvar__16__phi__18680,Vvar__10__cI__18656)),Vvar__2__rI__18630))
& ! [Vvar__var__var__var__var__var__var__19__x__18742__18744__18766__18768__18770__18772__18774] :
( t(Vvar__var__var__var__var__var__var__19__x__18742__18744__18766__18768__18770__18772__18774,Vvar__8__C__18654)
=> ! [Vvar__var__var__var__var__var__var__20__y__18743__18745__18767__18769__18771__18773__18775] :
( t(Vvar__var__var__var__var__var__var__20__y__18743__18745__18767__18769__18771__18773__18775,Vvar__8__C__18654)
=> p(happ(happ(Vvar__7__req__18649,happ(Vvar__16__phi__18680,happ(happ(Vvar__11__cadd__18657,Vvar__var__var__var__var__var__var__19__x__18742__18744__18766__18768__18770__18772__18774),Vvar__var__var__var__var__var__var__20__y__18743__18745__18767__18769__18771__18773__18775))),happ(happ(Vvar__3__radd__18631,happ(Vvar__16__phi__18680,Vvar__var__var__var__var__var__var__19__x__18742__18744__18766__18768__18770__18772__18774)),happ(Vvar__16__phi__18680,Vvar__var__var__var__var__var__var__20__y__18743__18745__18767__18769__18771__18773__18775)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__18747__18749__18776__18778__18780__18782__18784] :
( t(Vvar__var__var__var__var__var__var__20__x__18747__18749__18776__18778__18780__18782__18784,Vvar__8__C__18654)
=> ! [Vvar__var__var__var__var__var__var__21__y__18748__18750__18777__18779__18781__18783__18785] :
( t(Vvar__var__var__var__var__var__var__21__y__18748__18750__18777__18779__18781__18783__18785,Vvar__8__C__18654)
=> p(happ(happ(Vvar__7__req__18649,happ(Vvar__16__phi__18680,happ(happ(Vvar__13__csub__18667,Vvar__var__var__var__var__var__var__20__x__18747__18749__18776__18778__18780__18782__18784),Vvar__var__var__var__var__var__var__21__y__18748__18750__18777__18779__18781__18783__18785))),happ(happ(Vvar__5__rsub__18641,happ(Vvar__16__phi__18680,Vvar__var__var__var__var__var__var__20__x__18747__18749__18776__18778__18780__18782__18784)),happ(Vvar__16__phi__18680,Vvar__var__var__var__var__var__var__21__y__18748__18750__18777__18779__18781__18783__18785)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__18752__18754__18786__18788__18790__18792__18794] :
( t(Vvar__var__var__var__var__var__var__21__x__18752__18754__18786__18788__18790__18792__18794,Vvar__8__C__18654)
=> ! [Vvar__var__var__var__var__var__var__22__y__18753__18755__18787__18789__18791__18793__18795] :
( t(Vvar__var__var__var__var__var__var__22__y__18753__18755__18787__18789__18791__18793__18795,Vvar__8__C__18654)
=> p(happ(happ(Vvar__7__req__18649,happ(Vvar__16__phi__18680,happ(happ(Vvar__12__cmul__18662,Vvar__var__var__var__var__var__var__21__x__18752__18754__18786__18788__18790__18792__18794),Vvar__var__var__var__var__var__var__22__y__18753__18755__18787__18789__18791__18793__18795))),happ(happ(Vvar__4__rmul__18636,happ(Vvar__16__phi__18680,Vvar__var__var__var__var__var__var__21__x__18752__18754__18786__18788__18790__18792__18794)),happ(Vvar__16__phi__18680,Vvar__var__var__var__var__var__var__22__y__18753__18755__18787__18789__18791__18793__18795)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__18757__18758__18796__18797__18798__18799__18800] :
( t(Vvar__var__var__var__var__var__var__22__x__18757__18758__18796__18797__18798__18799__18800,Vvar__8__C__18654)
=> p(happ(happ(Vvar__7__req__18649,happ(Vvar__16__phi__18680,happ(Vvar__14__copp__18672,Vvar__var__var__var__var__var__var__22__x__18757__18758__18796__18797__18798__18799__18800))),happ(Vvar__6__ropp__18646,happ(Vvar__16__phi__18680,Vvar__var__var__var__var__var__var__22__x__18757__18758__18796__18797__18798__18799__18800)))) )
& ! [Vvar__var__var__var__var__var__23__x__18760__18763__18801__18804__18807__18810] :
( t(Vvar__var__var__var__var__var__23__x__18760__18763__18801__18804__18807__18810,Vvar__8__C__18654)
=> ! [Vvar__var__var__var__var__var__24__y__18761__18764__18802__18805__18808__18811] :
( t(Vvar__var__var__var__var__var__24__y__18761__18764__18802__18805__18808__18811,Vvar__8__C__18654)
=> ( happ(happ(Vvar__15__ceqb__18675,Vvar__var__var__var__var__var__23__x__18760__18763__18801__18804__18807__18810),Vvar__var__var__var__var__var__24__y__18761__18764__18802__18805__18808__18811) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__18649,happ(Vvar__16__phi__18680,Vvar__var__var__var__var__var__23__x__18760__18763__18801__18804__18807__18810)),happ(Vvar__16__phi__18680,Vvar__var__var__var__var__var__24__y__18761__18764__18802__18805__18808__18811))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__21223,Vvar__1__copp__21224,Vvar__2__ceqb__21227,Vvar__3__get__sign__21232] :
( cType___24t(Vvar__0__C__21223)
=> ( c_24__type__21279___24t(Vvar__0__C__21223,Vvar__1__copp__21224,Vvar__2__ceqb__21227,Vvar__3__get__sign__21232,Vvar__1__copp__21224)
=> ( c_24__type__21298___24t(Vvar__0__C__21223,Vvar__1__copp__21224,Vvar__2__ceqb__21227,Vvar__3__get__sign__21232,Vvar__2__ceqb__21227)
=> ( c_24__type__21312___24t(Vvar__0__C__21223,Vvar__1__copp__21224,Vvar__2__ceqb__21227,Vvar__3__get__sign__21232,Vvar__3__get__sign__21232)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__21223,Vvar__1__copp__21224,Vvar__2__ceqb__21227,Vvar__3__get__sign__21232)
=> ( ! [Vvar__var__var__var__var__var__4__c__21249__21252__21255__21258__21261__21264] :
( t(Vvar__var__var__var__var__var__4__c__21249__21252__21255__21258__21261__21264,Vvar__0__C__21223)
=> ! [Vvar__var__var__var__var__var__5__c_27__21250__21253__21256__21259__21262__21265] :
( t(Vvar__var__var__var__var__var__5__c_27__21250__21253__21256__21259__21262__21265,Vvar__0__C__21223)
=> ( happ(Vvar__3__get__sign__21232,Vvar__var__var__var__var__var__4__c__21249__21252__21255__21258__21261__21264) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__21223,Vvar__var__var__var__var__var__5__c_27__21250__21253__21256__21259__21262__21265)
=> happ(happ(Vvar__2__ceqb__21227,Vvar__var__var__var__var__var__4__c__21249__21252__21255__21258__21261__21264),happ(Vvar__1__copp__21224,Vvar__var__var__var__var__var__5__c_27__21250__21253__21256__21259__21262__21265)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_IntMap.Map.Map',axiom,
! [Vvar__0__A__92,VX93] :
( cType___24t(Vvar__0__A__92)
=> ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__92,VX93)
=> ( VX93 = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__92)
| ? [Vvar__1___24Anonymous__96] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__96)
& ? [Vvar__2___24Anonymous__97] :
( t(Vvar__2___24Anonymous__97,Vvar__0__A__92)
& VX93 = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__92,Vvar__1___24Anonymous__96,Vvar__2___24Anonymous__97) ) )
| ? [Vvar__1___24Anonymous__99] :
( cIntMap_2eMap_2eMap___24t(Vvar__0__A__92,Vvar__1___24Anonymous__99)
& ? [Vvar__2___24Anonymous__100] :
( cIntMap_2eMap_2eMap___24t(Vvar__0__A__92,Vvar__2___24Anonymous__100)
& VX93 = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__92,Vvar__1___24Anonymous__99,Vvar__2___24Anonymous__100) ) ) ) ) ) ).
fof('$_inversion_IntMap.Mapcanon.mapcanon',axiom,
! [Vvar__0__A__266,Vvar__1___24Anonymous__267] :
( cType___24t(Vvar__0__A__266)
=> ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__266,Vvar__1___24Anonymous__267)
=> ( cIntMap_2eMapcanon_2emapcanon___24a2(Vvar__0__A__266,Vvar__1___24Anonymous__267)
=> ( Vvar__1___24Anonymous__267 = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__266)
| ? [Vvar__1__a__271] :
( cIntMap_2eMap_2ead___24t(Vvar__1__a__271)
& ? [Vvar__2__y__272] :
( t(Vvar__2__y__272,Vvar__0__A__266)
& Vvar__1___24Anonymous__267 = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__266,Vvar__1__a__271,Vvar__2__y__272) ) )
| ? [Vvar__1__m1__274] :
( cIntMap_2eMap_2eMap___24t(Vvar__0__A__266,Vvar__1__m1__274)
& ? [Vvar__2__m2__275] :
( cIntMap_2eMap_2eMap___24t(Vvar__0__A__266,Vvar__2__m2__275)
& cIntMap_2eMapcanon_2emapcanon___24a2(Vvar__0__A__266,Vvar__1__m1__274)
& cIntMap_2eMapcanon_2emapcanon___24a2(Vvar__0__A__266,Vvar__2__m2__275)
& cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cIntMap_2eMap_2eMapCard___24a2(Vvar__0__A__266,cIntMap_2eMap_2eM2___24a3(Vvar__0__A__266,Vvar__1__m1__274,Vvar__2__m2__275)))
& Vvar__1___24Anonymous__267 = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__266,Vvar__1__m1__274,Vvar__2__m2__275) ) ) ) ) ) ) ).
fof('$_lam_10439',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] : c_24__lam__10439___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(happ(Vv__CANONICAL__4,Vv__CANONICAL__6),happ(happ(Vv__CANONICAL__5,Vv__CANONICAL__7),Vv__CANONICAL__8)) ).
fof('$_lam_1047',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eNumbers_2eBinNums_2eN0
& c_24__lam__1047___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__1 )
| ? [Vvar__0___24Anonymous__1048] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1048)
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1048)
& c_24__lam__1047___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eMapPut1___24a6(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__0___24Anonymous__1048) ) ) ) ) ) ).
fof('$_lam_10600',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__10600___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__2)) ).
fof('$_lam_10604',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__10604___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__2)) ).
fof('$_lam_10608',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__10608___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__2)) ).
fof('$_lam_10627',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__10627___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_1084',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
& c_24__lam__1084___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4),Vv__CANONICAL__2) )
| ? [Vvar__0___24Anonymous__1085] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1085)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1085)
=> ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1085)
& ( ? [Vvar__0___24Anonymous__1089] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1089)
& Vvar__0___24Anonymous__1085 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1089)
& c_24__lam__1084___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1089),Vv__CANONICAL__4)) )
| ? [Vvar__0___24Anonymous__1090] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1090)
& Vvar__0___24Anonymous__1085 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1090)
& c_24__lam__1084___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1090),Vv__CANONICAL__4),Vv__CANONICAL__2) )
| ( Vvar__0___24Anonymous__1085 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__lam__1084___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4)) ) ) ) ) ) ) ) ) ) ).
fof('$_lam_11311',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__lam__11311___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__lam__11311___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMapiter_2ealist__semantics___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4) ) ) ) ) ) ).
fof('$_lam_11677',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__11677___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eFset_2ein__dom___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__2) ).
fof('$_lam_1211',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1211___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_1243',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( ( Vv__CANONICAL__4 = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0)
& c_24__lam__1243___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
| ? [Vvar__1___24Anonymous__1247] :
( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__1247)
& ? [Vvar__2___24Anonymous__1248] :
( t(Vvar__2___24Anonymous__1248,Vv__CANONICAL__0)
& Vv__CANONICAL__4 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__1247,Vvar__2___24Anonymous__1248)
& c_24__lam__1243___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__1247,Vvar__2___24Anonymous__1248) ) )
| ? [Vvar__1___24Anonymous__1251] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__1251)
& ? [Vvar__2___24Anonymous__1252] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__1252)
& Vv__CANONICAL__4 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__1251,Vvar__2___24Anonymous__1252)
& c_24__lam__1243___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapMerge___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__1251),cIntMap_2eMap_2eMapMerge___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vvar__2___24Anonymous__1252)) ) ) ) ) ) ).
fof('$_lam_1312',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1312___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_1351',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1351___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__3)) ).
fof('$_lam_1357',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1357___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__3)) ).
fof('$_lam_14600',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__14600___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__14528___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('$_lam_1709',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__1709___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) ) ).
fof('$_lam_1753',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__1753___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) ) ).
fof('$_lam_1783',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__1783___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ).
fof('$_lam_1791',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__lam__1791___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__lam__1791___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_lam_1818',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
& c_24__lam__1818___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__1819] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1819)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1819)
=> ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1819)
& ( ? [Vvar__0___24Anonymous__1823] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1823)
& Vvar__0___24Anonymous__1819 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1823)
& c_24__lam__1818___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1823)) )
| ? [Vvar__0___24Anonymous__1824] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1824)
& Vvar__0___24Anonymous__1819 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1824)
& c_24__lam__1818___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1824)) )
| ( Vvar__0___24Anonymous__1819 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__lam__1818___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0) ) ) ) ) ) ) ) ) ) ).
fof('$_lam_200',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eNumbers_2eBinNums_2eN0
& c_24__lam__200___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4) )
| ? [Vvar__0___24Anonymous__201] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__201)
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__201)
& c_24__lam__200___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapPut1___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__0___24Anonymous__201) ) ) ) ) ) ).
fof('$_lam_237',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
& c_24__lam__237___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4),Vv__CANONICAL__2) )
| ? [Vvar__0___24Anonymous__238] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__238)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__238)
=> ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__238)
& ( ? [Vvar__0___24Anonymous__242] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__242)
& Vvar__0___24Anonymous__238 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__242)
& c_24__lam__237___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__242),Vv__CANONICAL__4)) )
| ? [Vvar__0___24Anonymous__243] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__243)
& Vvar__0___24Anonymous__238 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__243)
& c_24__lam__237___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__243),Vv__CANONICAL__4),Vv__CANONICAL__2) )
| ( Vvar__0___24Anonymous__238 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__lam__237___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4)) ) ) ) ) ) ) ) ) ) ).
fof('$_lam_23714',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__23714___24a1(Vv__CANONICAL__0)
<=> cCoq_2eNumbers_2eBinNums_2eN0 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__0) ) ).
fof('$_lam_23717',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__23717___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__1) ) ).
fof('$_lam_23724',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__23724___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__1) ) ).
fof('$_lam_312',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__312___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(cIntMap_2eMap_2ead),c_24__lam__316___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_316',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__316___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead,Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ).
fof('$_lam_388',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__388___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_38932',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__38932___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2enegb___24a1(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_42454',axiom,
! [Vv__CANONICAL__0] : c_24__lam__42454___24a1(Vv__CANONICAL__0) = Vv__CANONICAL__0 ).
fof('$_lam_54441',axiom,
! [Vv__CANONICAL__0] : c_24__lam__54441___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enat ).
fof('$_lam_54442',axiom,
! [Vv__CANONICAL__0] : c_24__lam__54442___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eNat_2edouble ).
fof('$_lam_55110',axiom,
! [Vv__CANONICAL__0] : c_24__lam__55110___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_lam_55196',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__55196___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__55197] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__55197)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__55197)
& c_24__lam__55196___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__55197) ) ) ) ).
fof('$_lam_55203',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__55203___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__55204] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__55204)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__55204)
& c_24__lam__55203___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__55204) ) ) ) ).
fof('$_lam_55207',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__55207___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__55208] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__55208)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__55208)
& c_24__lam__55207___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_lam_55651',axiom,
! [Vv__CANONICAL__0] : c_24__lam__55651___24a1(Vv__CANONICAL__0) = c_24__cast__55652___24a1(Vv__CANONICAL__0) ).
fof('$_lam_55667',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__lam__55667___24a1(Vv__CANONICAL__0))
<=> p(Vv__CANONICAL__0) ) ).
fof('$_lam_55690',axiom,
! [Vv__CANONICAL__0] : c_24__lam__55690___24a1(Vv__CANONICAL__0) = c_24__cast__55691___24a1(Vv__CANONICAL__0) ).
fof('$_lam_55703',axiom,
! [Vv__CANONICAL__0] : c_24__lam__55703___24a1(Vv__CANONICAL__0) = c_24__cast__55706___24a1(Vv__CANONICAL__0) ).
fof('$_lam_56745',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__56745___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__1,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2etrue)) ).
fof('$_lam_56752',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__56752___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__2,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2efalse)) ).
fof('$_lam_56864',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__56864___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24__prop__56865___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__56866___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2etrue)) ).
fof('$_lam_56985',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__56985___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eright___24a3(c_24__prop__56986___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__56987___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__56991___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_57009',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__57009___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,Vv__CANONICAL__1)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_lam_57034',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__57034___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_57058',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__57058___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
& happ(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_lam_754',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__754___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2esigT___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(cIntMap_2eMap_2ead),c_24__lam__764___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_764',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__764___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esigT___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(cIntMap_2eMap_2ead),c_24__lam__772___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_772',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__772___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(cIntMap_2eMap_2ead),c_24__lam__777___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_777',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__777___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead,Vv__CANONICAL__1,Vv__CANONICAL__4)))) ) ).
fof('$_prop_1754',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1754___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ).
fof('$_prop_23715',axiom,
( p(c_24__prop__23715)
<=> cCoq_2eNumbers_2eBinNums_2eN0 = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('$_prop_23718',axiom,
! [Vvar__0___24Anonymous__23711] :
( p(c_24__prop__23718___24a1(Vvar__0___24Anonymous__23711))
<=> cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23711) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('$_prop_23725',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__23725___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('$_prop_323',axiom,
( p(c_24__prop__323)
<=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_324',axiom,
! [V1__b2] :
( p(c_24__prop__324___24a1(V1__b2))
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_326',axiom,
! [V1__b2] :
( p(c_24__prop__326___24a1(V1__b2))
<=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_327',axiom,
! [V1__b2] :
( p(c_24__prop__327___24a1(V1__b2))
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_333',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__333___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_334',axiom,
! [Vv__CANONICAL__1] :
( p(c_24__prop__334___24a1(Vv__CANONICAL__1))
<=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_55042',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__55042___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_55043',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__55043___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_55120',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__55120___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_55128',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__55128___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_55542',axiom,
! [V1__b2] :
( p(c_24__prop__55542___24a1(V1__b2))
<=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_prop_55543',axiom,
! [V1__b2] :
( p(c_24__prop__55543___24a1(V1__b2))
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_prop_55545',axiom,
( p(c_24__prop__55545)
<=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_prop_55546',axiom,
! [V1__b2] :
( p(c_24__prop__55546___24a1(V1__b2))
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_prop_55552',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__55552___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_prop_55553',axiom,
! [Vv__CANONICAL__1] :
( p(c_24__prop__55553___24a1(Vv__CANONICAL__1))
<=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_prop_55653',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__55653___24a1(Vv__CANONICAL__0))
<=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_prop_55654',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__55654___24a1(Vv__CANONICAL__0))
<=> ( cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2etrue
=> p(Vv__CANONICAL__0) ) ) ).
fof('$_prop_55692',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__55692___24a1(Vv__CANONICAL__0))
<=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_prop_55693',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__55693___24a1(Vv__CANONICAL__0))
<=> ( cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue
=> p(Vv__CANONICAL__0) ) ) ).
fof('$_prop_55719',axiom,
( p(c_24__prop__55719)
<=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_55720',axiom,
( p(c_24__prop__55720)
<=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_prop_55722',axiom,
( p(c_24__prop__55722)
<=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_55724',axiom,
( p(c_24__prop__55724)
<=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_prop_55728',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__55728___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_56865',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__56865___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_56866',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__56866___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_56986',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__56986___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_56987',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__56987___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_56991',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__56991___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__5)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__5,Vv__CANONICAL__4) ) ) ) ) ).
fof('$_prop_56996',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__56996___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_56997',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__56997___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_59706',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__59706___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_59707',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__59707___24a2(V0__x,V1__y))
<=> V0__x != V1__y ) ).
fof('$_prop_59708',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__59708___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_59709',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__59709___24a2(V0__x,V1__y))
<=> V0__x != V1__y ) ).
fof('$_prop_710',axiom,
( p(c_24__prop__710)
<=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_711',axiom,
( p(c_24__prop__711)
<=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_prop_712',axiom,
( p(c_24__prop__712)
<=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_713',axiom,
( p(c_24__prop__713)
<=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_prop_716',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__716___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_717',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__717___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('$_type_10272',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10273] :
( c_24__type__10272___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10273)
<=> ! [Vv__CANONICAL__4] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10273,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_10391',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10392] :
( c_24__type__10391___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10392)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10392,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_10443',axiom,
! [Vv__CANONICAL__0,Vvar__10444] :
( c_24__type__10443___24t(Vv__CANONICAL__0,Vvar__10444)
<=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__10444,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_10565',axiom,
! [Vvar__10566] :
( c_24__type__10565___24t(Vvar__10566)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10443___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__10566,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_10620',axiom,
! [Vvar__10621] :
( c_24__type__10620___24t(Vvar__10621)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10443___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__9263___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__10621,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_10634',axiom,
! [Vvar__10635] :
( c_24__type__10634___24t(Vvar__10635)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10443___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),happ(happ(happ(Vvar__10635,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_11263',axiom,
! [Vvar__11264] :
( c_24__type__11263___24t(Vvar__11264)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,Vv__CANONICAL__0),happ(happ(happ(Vvar__11264,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_11315',axiom,
! [Vvar__11316] :
( c_24__type__11315___24t(Vvar__11316)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMapiter_2ealist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__11316,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_11719',axiom,
! [Vvar__11720] :
( c_24__type__11719___24t(Vvar__11720)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__11720,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11722',axiom,
! [Vv__CANONICAL__0,Vvar__11723] :
( c_24__type__11722___24t(Vv__CANONICAL__0,Vvar__11723)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__11723,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_11725',axiom,
! [Vvar__11726] :
( c_24__type__11725___24t(Vvar__11726)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__11726,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11820',axiom,
! [Vvar__11821] :
( c_24__type__11820___24t(Vvar__11821)
<=> ! [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__11821,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11823',axiom,
! [Vvar__11824] :
( c_24__type__11823___24t(Vvar__11824)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__11824,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11826',axiom,
! [Vvar__11827] :
( c_24__type__11826___24t(Vvar__11827)
<=> ! [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__11827,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11830',axiom,
! [Vvar__11831] :
( c_24__type__11830___24t(Vvar__11831)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__11831,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11833',axiom,
! [Vvar__11834] :
( c_24__type__11833___24t(Vvar__11834)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(Vvar__11834,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11847',axiom,
! [Vvar__11848] :
( c_24__type__11847___24t(Vvar__11848)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__11848,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11850',axiom,
! [Vvar__11851] :
( c_24__type__11850___24t(Vvar__11851)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__11851,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11856',axiom,
! [Vvar__11857] :
( c_24__type__11856___24t(Vvar__11857)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__11857,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11881',axiom,
! [Vvar__11882] :
( c_24__type__11881___24t(Vvar__11882)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__495___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__11882,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12394',axiom,
! [Vvar__12395] :
( c_24__type__12394___24t(Vvar__12395)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6978___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__12395,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_12806',axiom,
! [Vv__CANONICAL__0,Vvar__12807] :
( c_24__type__12806___24t(Vv__CANONICAL__0,Vvar__12807)
<=> ! [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__12807,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1287',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1288] :
( c_24__type__1287___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1288)
<=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
=> cIntMap_2eMap_2ead___24t(happ(Vvar__1288,Vv__CANONICAL__2)) ) ) ).
fof('$_type_129',axiom,
! [Vvar__130] :
( c_24__type__129___24t(Vvar__130)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(Vvar__130,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13367',axiom,
! [Vvar__13368] :
( c_24__type__13367___24t(Vvar__13368)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2178___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__4,Vv__CANONICAL__7)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__13368,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ).
fof('$_type_134',axiom,
! [Vvar__135] :
( c_24__type__134___24t(Vvar__135)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__135,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_13844',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13845] :
( c_24__type__13844___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13845)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__13845,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_139',axiom,
! [Vvar__140] :
( c_24__type__139___24t(Vvar__140)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__140,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1400',axiom,
! [Vvar__1401] :
( c_24__type__1400___24t(Vvar__1401)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1405___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1287___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__1401,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__1) ) ) ) ) ) ) ) ) ).
fof('$_type_1405',axiom,
! [Vv__CANONICAL__0,Vvar__1406] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vvar__1406)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1406,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1412',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1413] :
( c_24__type__1412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1413)
<=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1413,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_142',axiom,
! [Vv__CANONICAL__0,Vvar__143] :
( c_24__type__142___24t(Vv__CANONICAL__0,Vvar__143)
<=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__143,Vv__CANONICAL__1)) ) ) ).
fof('$_type_14309',axiom,
! [Vvar__14310] :
( c_24__type__14309___24t(Vvar__14310)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__14310,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1449',axiom,
! [Vvar__1450] :
( c_24__type__1449___24t(Vvar__1450)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1405___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__1450,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__1) ) ) ) ) ) ) ) ).
fof('$_type_14502',axiom,
! [Vvar__14503] :
( c_24__type__14502___24t(Vvar__14503)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__2178___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__2461___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__2470___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__14503,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1470',axiom,
! [Vvar__1471] :
( c_24__type__1470___24t(Vvar__1471)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__1471,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_14732',axiom,
! [Vvar__14733] :
( c_24__type__14732___24t(Vvar__14733)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__6978___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__12806___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__14733,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1475',axiom,
! [Vvar__1476] :
( c_24__type__1475___24t(Vvar__1476)
<=> ! [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__1476,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1478',axiom,
! [Vvar__1479] :
( c_24__type__1478___24t(Vvar__1479)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__1479,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1487',axiom,
! [Vvar__1488] :
( c_24__type__1487___24t(Vvar__1488)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__1488,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1494',axiom,
! [Vvar__1495] :
( c_24__type__1494___24t(Vvar__1495)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__1495,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14986',axiom,
! [Vvar__14987] :
( c_24__type__14986___24t(Vvar__14987)
<=> ! [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__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__2260___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__2178___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__2461___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__2470___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8)),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__14987,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),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('$_type_15',axiom,
! [Vvar__16] :
( c_24__type__15___24t(Vvar__16)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__16,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1507',axiom,
! [Vvar__1508] :
( c_24__type__1507___24t(Vvar__1508)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__1508,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1527',axiom,
! [Vvar__1528] :
( c_24__type__1527___24t(Vvar__1528)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__1528,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15271',axiom,
! [Vvar__15272] :
( c_24__type__15271___24t(Vvar__15272)
<=> ! [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__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__6978___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__12806___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__15272,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1529',axiom,
! [Vvar__1530] :
( c_24__type__1529___24t(Vvar__1530)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__1530,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15332',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15333] :
( c_24__type__15332___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15333)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__15333,Vv__CANONICAL__2)) ) ) ).
fof('$_type_1539',axiom,
! [Vvar__1540] :
( c_24__type__1539___24t(Vvar__1540)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__1540,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1555',axiom,
! [Vvar__1556] :
( c_24__type__1555___24t(Vvar__1556)
<=> ! [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__1556,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1559',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1560] :
( c_24__type__1559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1560)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__1560,Vv__CANONICAL__2)) ) ) ).
fof('$_type_1573',axiom,
! [Vvar__1574] :
( c_24__type__1573___24t(Vvar__1574)
<=> ! [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__1574,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_1576',axiom,
! [Vv__CANONICAL__0,Vvar__1577] :
( c_24__type__1576___24t(Vv__CANONICAL__0,Vvar__1577)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__1577,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1692',axiom,
! [Vvar__1693] :
( c_24__type__1692___24t(Vvar__1693)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__1693,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1704',axiom,
! [Vvar__1705] :
( c_24__type__1704___24t(Vvar__1705)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
=> ( cIntMap_2eFset_2ein__dom___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__1709___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__1705,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_1720',axiom,
! [Vvar__1721] :
( c_24__type__1720___24t(Vvar__1721)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
=> ( cIntMap_2eFset_2ein__FSet___24a2(Vv__CANONICAL__2,cIntMap_2eFset_2eMapDom___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__1709___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__1721,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_17325',axiom,
! [Vvar__17326] :
( c_24__type__17325___24t(Vvar__17326)
<=> ! [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__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__10] :
( c_24__type__2449___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__2178___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__2461___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__2470___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__8068___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__16)
=> ! [Vv__CANONICAL__17] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__7,Vv__CANONICAL__17)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__17326,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__16),Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1740',axiom,
! [Vvar__1741] :
( c_24__type__1740___24t(Vvar__1741)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1744___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__1741,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1744',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1745] :
( c_24__type__1744___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1745)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__1745,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_1749',axiom,
! [Vvar__1750] :
( c_24__type__1749___24t(Vvar__1750)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esig___24a2(Vv__CANONICAL__0,c_24__lam__1753___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),c_24__prop__1754___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__1750,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17539',axiom,
! [Vvar__17540] :
( c_24__type__17539___24t(Vvar__17540)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__10] :
( c_24__type__2449___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__2178___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__15332___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__7,Vv__CANONICAL__14)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__17540,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_17633',axiom,
! [Vvar__17634] :
( c_24__type__17633___24t(Vvar__17634)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1405___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__17634,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_17887',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__17888] :
( c_24__type__17887___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__17888)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17888,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17950',axiom,
! [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__17951] :
( c_24__type__17950___24t(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__17951)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17951,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18013',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__18014] :
( c_24__type__18013___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__18014)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18014,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18067',axiom,
! [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__18068] :
( c_24__type__18067___24t(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__18068)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__18068,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_18130',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__18131] :
( c_24__type__18130___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__18131)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__18131,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_1828',axiom,
! [Vvar__1829] :
( c_24__type__1828___24t(Vvar__1829)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1829,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1833',axiom,
! [Vvar__1834] :
( c_24__type__1833___24t(Vvar__1834)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__1834,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_18363',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18364] :
( c_24__type__18363___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18364)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18364,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18393',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18394] :
( c_24__type__18393___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18394)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18394,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18417',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18418] :
( c_24__type__18417___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18418)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__18418,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_18447',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18448] :
( c_24__type__18447___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18448)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__18448,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_18477',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18478] :
( c_24__type__18477___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18478)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18478,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18501',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18502] :
( c_24__type__18501___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18502)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__18502,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_18534',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18535] :
( c_24__type__18534___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18535)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18535,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18558',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18559] :
( c_24__type__18558___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18559)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__18559,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_18585',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18586] :
( c_24__type__18585___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18586)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__18586,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_19024',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19025] :
( c_24__type__19024___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19025)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19025,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1905',axiom,
! [Vvar__1906] :
( c_24__type__1905___24t(Vvar__1906)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__1906,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_19237',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19238] :
( c_24__type__19237___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19238)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19238,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19450',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__19451] :
( c_24__type__19450___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__19451)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19451,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19645',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19646] :
( c_24__type__19645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19646)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__19646,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_19858',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__19859] :
( c_24__type__19858___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__19859)
<=> ! [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__19859,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_20071',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20072] :
( c_24__type__20071___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20072)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20072,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_20284',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20285] :
( c_24__type__20284___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20285)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20285,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_20497',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20498] :
( c_24__type__20497___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20498)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20498,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_20692',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20693] :
( c_24__type__20692___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20693)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__20693,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_20905',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20906] :
( c_24__type__20905___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20906)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__20906,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_21100',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__21101] :
( c_24__type__21100___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__21101)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__21101,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_21279',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__21280] :
( c_24__type__21279___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__21280)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__21280,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_2128',axiom,
! [Vvar__2129] :
( c_24__type__2128___24t(Vvar__2129)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__495___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__2129,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_21298',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__21299] :
( c_24__type__21298___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__21299)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__21299,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_21312',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__21313] :
( c_24__type__21312___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__21313)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__21313,Vv__CANONICAL__4)) ) ) ).
fof('$_type_21462',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21463] :
( c_24__type__21462___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21463)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21463,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_21512',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21513] :
( c_24__type__21512___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21513)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__21513,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_21562',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21563] :
( c_24__type__21562___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21563)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__21563,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_21604',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21605] :
( c_24__type__21604___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21605)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__21605,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_21654',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21655] :
( c_24__type__21654___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21655)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__21655,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_21736',axiom,
! [Vvar__21737] :
( c_24__type__21736___24t(Vvar__21737)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21737,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2178',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2179] :
( c_24__type__2178___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2179)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__2179,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_21859',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21860] :
( c_24__type__21859___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21860)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21860,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21903',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21904] :
( c_24__type__21903___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21904)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21904,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_21939',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21940] :
( c_24__type__21939___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21940)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__21940,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_21983',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21984] :
( c_24__type__21983___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21984)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__21984,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21995',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21996] :
( c_24__type__21995___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21996)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__21996,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_22103',axiom,
! [Vvar__22104] :
( c_24__type__22103___24t(Vvar__22104)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__22104,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22145',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22146] :
( c_24__type__22145___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22146)
<=> ! [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__22146,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_22180',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22181] :
( c_24__type__22180___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22181)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22181,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_22194',axiom,
! [Vvar__22195] :
( c_24__type__22194___24t(Vvar__22195)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2260___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__22195,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_22237',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22238] :
( c_24__type__22237___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22238)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22238,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_22257',axiom,
! [Vvar__22258] :
( c_24__type__22257___24t(Vvar__22258)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2260___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__22267___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__22258,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_22267',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22268] :
( c_24__type__22267___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22268)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__22268,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_22300',axiom,
! [Vvar__22301] :
( c_24__type__22300___24t(Vvar__22301)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2260___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__22310___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__22267___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__22301,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_22310',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22311] :
( c_24__type__22310___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22311)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22311,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_22325',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22326] :
( c_24__type__22325___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22326)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__22326,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_22436',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22437] :
( c_24__type__22436___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22437)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22437,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_22541',axiom,
! [Vvar__22542] :
( c_24__type__22541___24t(Vvar__22542)
<=> ! [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__22542,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_22546',axiom,
! [Vvar__22547] :
( c_24__type__22546___24t(Vvar__22547)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__22547,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_2260',axiom,
! [Vv__CANONICAL__0,Vvar__2261] :
( c_24__type__2260___24t(Vv__CANONICAL__0,Vvar__2261)
<=> ! [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__2261,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_22876',axiom,
! [Vvar__22877] :
( c_24__type__22876___24t(Vvar__22877)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3598___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2eclause___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__22877,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_23705',axiom,
! [Vvar__23706] :
( c_24__type__23705___24t(Vvar__23706)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__23706,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23708',axiom,
! [Vvar__23709] :
( c_24__type__23708___24t(Vvar__23709)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__23709,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23721',axiom,
! [Vvar__23722] :
( c_24__type__23721___24t(Vvar__23722)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_24__lam__23724___24a1(Vv__CANONICAL__0)),c_24__prop__23725___24a1(Vv__CANONICAL__0),happ(Vvar__23722,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23767',axiom,
! [Vvar__23768] :
( c_24__type__23767___24t(Vvar__23768)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__23768,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23773',axiom,
! [Vvar__23774] :
( c_24__type__23773___24t(Vvar__23774)
<=> ! [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__23774,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23797',axiom,
! [Vvar__23798] :
( c_24__type__23797___24t(Vvar__23798)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__23798,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23825',axiom,
! [Vvar__23826] :
( c_24__type__23825___24t(Vvar__23826)
<=> ! [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__23826,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23836',axiom,
! [Vvar__23837] :
( c_24__type__23836___24t(Vvar__23837)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__23841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__23837,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_23841',axiom,
! [Vv__CANONICAL__0,Vvar__23842] :
( c_24__type__23841___24t(Vv__CANONICAL__0,Vvar__23842)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23842,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23891',axiom,
! [Vvar__23892] :
( c_24__type__23891___24t(Vvar__23892)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__23892,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23894',axiom,
! [Vvar__23895] :
( c_24__type__23894___24t(Vvar__23895)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__23895,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23897',axiom,
! [Vvar__23898] :
( c_24__type__23897___24t(Vvar__23898)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__23898,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23972',axiom,
! [Vvar__23973] :
( c_24__type__23972___24t(Vvar__23973)
<=> ! [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__23973,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2412',axiom,
! [Vv__CANONICAL__0,Vvar__2413] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vvar__2413)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__2413,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_2428',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2429] :
( c_24__type__2428___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2429)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__2429,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_2442',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2443] :
( c_24__type__2442___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2443)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__2443,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_2449',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2450] :
( c_24__type__2449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2450)
<=> ! [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__2450,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_24543',axiom,
! [Vvar__24544] :
( c_24__type__24543___24t(Vvar__24544)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__24544,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24564',axiom,
! [Vvar__24565] :
( c_24__type__24564___24t(Vvar__24565)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__24565,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_24569',axiom,
! [Vvar__24570] :
( c_24__type__24569___24t(Vvar__24570)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__24570,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2461',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2462] :
( c_24__type__2461___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2462)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__2462,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_24668',axiom,
! [Vvar__24669] :
( c_24__type__24668___24t(Vvar__24669)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__24669,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2470',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2471] :
( c_24__type__2470___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2471)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__2471,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_250',axiom,
! [Vvar__251] :
( c_24__type__250___24t(Vvar__251)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__251,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_25202',axiom,
! [Vvar__25203] :
( c_24__type__25202___24t(Vvar__25203)
<=> ! [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__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__2260___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__2178___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__2461___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__2470___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__25203,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),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('$_type_25335',axiom,
! [Vvar__25336] :
( c_24__type__25335___24t(Vvar__25336)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__25340___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__25336,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_25340',axiom,
! [Vv__CANONICAL__0,Vvar__25341] :
( c_24__type__25340___24t(Vv__CANONICAL__0,Vvar__25341)
<=> ! [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__25341,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_2580',axiom,
! [Vvar__2581] :
( c_24__type__2580___24t(Vvar__2581)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__2581,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_2589',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2590] :
( c_24__type__2589___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2590)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__2590,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2595',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2596] :
( c_24__type__2595___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2596)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__2596,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2609',axiom,
! [Vvar__2610] :
( c_24__type__2609___24t(Vvar__2610)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2610,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2631',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2632] :
( c_24__type__2631___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2632)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__2632,Vv__CANONICAL__2)) ) ) ).
fof('$_type_264',axiom,
! [Vvar__265] :
( c_24__type__264___24t(Vvar__265)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__265,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26889',axiom,
! [Vvar__26890] :
( c_24__type__26889___24t(Vvar__26890)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3546___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__26890,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2689',axiom,
! [Vvar__2690] :
( c_24__type__2689___24t(Vvar__2690)
<=> ! [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__2690,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_27076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__27077] :
( c_24__type__27076___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__27077)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__27077,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_27126',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__27127] :
( c_24__type__27126___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__27127)
<=> ! [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__27127,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_27587',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27588] :
( c_24__type__27587___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27588)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27588,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27688',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__27689] :
( c_24__type__27688___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__27689)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27689,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27789',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27790] :
( c_24__type__27789___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27790)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27790,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27879',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__27880] :
( c_24__type__27879___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__27880)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__27880,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_27980',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27981] :
( c_24__type__27980___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27981)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27981,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_28081',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__28082] :
( c_24__type__28081___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__28082)
<=> ! [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__28082,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_28182',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__28183] :
( c_24__type__28182___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__28183)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28183,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_28739',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28740] :
( c_24__type__28739___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28740)
<=> ! [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__28740,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_29',axiom,
! [Vvar__30] :
( c_24__type__29___24t(Vvar__30)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__30,Vv__CANONICAL__0)) ) ) ).
fof('$_type_293',axiom,
! [Vvar__294] :
( c_24__type__293___24t(Vvar__294)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,Vv__CANONICAL__0)
=> cIntMap_2eFset_2eFSet___24t(happ(Vvar__294,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29791',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29792] :
( c_24__type__29791___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29792)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29792,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30137',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30138] :
( c_24__type__30137___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30138)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30138,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30483',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__30484] :
( c_24__type__30483___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__30484)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30484,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_305',axiom,
! [Vvar__306] :
( c_24__type__305___24t(Vvar__306)
<=> ! [Vv__CANONICAL__0] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,Vv__CANONICAL__1)
=> ( cMaplists_2eMapLists_2ead__in__list___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eInit_2eSpecif_2esigT___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(cIntMap_2eMap_2ead),c_24__lam__312___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__306,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_30806',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__30807] :
( c_24__type__30806___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__30807)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__30807,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_31152',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31153] :
( c_24__type__31152___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31153)
<=> ! [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__31153,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_31498',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__31499] :
( c_24__type__31498___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__31499)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31499,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_31844',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31845] :
( c_24__type__31844___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31845)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__31845,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_32190',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__32191] :
( c_24__type__32190___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__32191)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__32191,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_32536',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__32537] :
( c_24__type__32536___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__32537)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__32537,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_32859',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__32860] :
( c_24__type__32859___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__32860)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__32860,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_331',axiom,
! [Vvar__332] :
( c_24__type__331___24t(Vvar__332)
<=> ! [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_2eorb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__333___24a1(Vv__CANONICAL__0),c_24__prop__334___24a1(Vv__CANONICAL__1),happ(happ(Vvar__332,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_33205',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__33206] :
( c_24__type__33205___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__33206)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__33206,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_33551',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__33552] :
( c_24__type__33551___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__33552)
<=> ! [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__33552,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_337',axiom,
! [Vvar__338] :
( c_24__type__337___24t(Vvar__338)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__338,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33874',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__33875] :
( c_24__type__33874___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__33875)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__33875,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_34',axiom,
! [Vvar__35] :
( c_24__type__34___24t(Vvar__35)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__35,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34197',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__34198] :
( c_24__type__34197___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__34198)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__34198,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_34543',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__34544] :
( c_24__type__34543___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__34544)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__34544,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34681',axiom,
! [Vvar__34682] :
( c_24__type__34681___24t(Vvar__34682)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6978___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6978___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(happ(Vvar__34682,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_34781',axiom,
! [Vvar__34782] :
( c_24__type__34781___24t(Vvar__34782)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__34782,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34827',axiom,
! [Vvar__34828] :
( c_24__type__34827___24t(Vvar__34828)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__34828,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34830',axiom,
! [Vvar__34831] :
( c_24__type__34830___24t(Vvar__34831)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__34831,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34833',axiom,
! [Vvar__34834] :
( c_24__type__34833___24t(Vvar__34834)
<=> ! [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__34834,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_349',axiom,
! [Vvar__350] :
( c_24__type__349___24t(Vvar__350)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__350,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_352',axiom,
! [Vvar__353] :
( c_24__type__352___24t(Vvar__353)
<=> ! [Vv__CANONICAL__0] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eFset_2eFSet___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__353,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3546',axiom,
! [Vv__CANONICAL__0,Vvar__3547] :
( c_24__type__3546___24t(Vv__CANONICAL__0,Vvar__3547)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__3547,Vv__CANONICAL__1)) ) ) ).
fof('$_type_3591',axiom,
! [Vvar__3592] :
( c_24__type__3591___24t(Vvar__3592)
<=> ! [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__3598___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__3592,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_3598',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3599] :
( c_24__type__3598___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3599)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__3599,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_3622',axiom,
! [Vvar__3623] :
( c_24__type__3622___24t(Vvar__3623)
<=> ! [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__3598___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__3623,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_3732',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3733] :
( c_24__type__3732___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3733)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__3733,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_37382',axiom,
! [Vvar__37383] :
( c_24__type__37382___24t(Vvar__37383)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__37383,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_3756',axiom,
! [Vvar__3757] :
( c_24__type__3756___24t(Vvar__3757)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__3732___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(happ(happ(Vvar__3757,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_37658',axiom,
! [Vvar__37659] :
( c_24__type__37658___24t(Vvar__37659)
<=> ! [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__37659,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37927',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__37928] :
( c_24__type__37927___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__37928)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__37928,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_38226',axiom,
! [Vvar__38227] :
( c_24__type__38226___24t(Vvar__38227)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__38227,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38243',axiom,
! [Vvar__38244] :
( c_24__type__38243___24t(Vvar__38244)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__38244,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38251',axiom,
! [Vvar__38252] :
( c_24__type__38251___24t(Vvar__38252)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__38252,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_38365',axiom,
! [Vvar__38366] :
( c_24__type__38365___24t(Vvar__38366)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__38366,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38604',axiom,
! [Vvar__38605] :
( c_24__type__38604___24t(Vvar__38605)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,happ(happ(Vvar__38605,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38631',axiom,
! [Vvar__38632] :
( c_24__type__38631___24t(Vvar__38632)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__38632,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_38734',axiom,
! [Vvar__38735] :
( c_24__type__38734___24t(Vvar__38735)
<=> ! [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__38735,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38752',axiom,
! [Vvar__38753] :
( c_24__type__38752___24t(Vvar__38753)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__38753,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38754',axiom,
! [Vvar__38755] :
( c_24__type__38754___24t(Vvar__38755)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__38755,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43813',axiom,
! [Vvar__43814] :
( c_24__type__43813___24t(Vvar__43814)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1487___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1487___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__43814,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43819',axiom,
! [Vvar__43820] :
( c_24__type__43819___24t(Vvar__43820)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__43821___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__43821___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__43820,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43821',axiom,
! [Vvar__43822] :
( c_24__type__43821___24t(Vvar__43822)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__43822,Vv__CANONICAL__0)) ) ) ).
fof('$_type_45595',axiom,
! [Vvar__45596] :
( c_24__type__45595___24t(Vvar__45596)
<=> ! [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__45596,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4622',axiom,
! [Vvar__4623] :
( c_24__type__4622___24t(Vvar__4623)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__4623,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4637',axiom,
! [Vvar__4638] :
( c_24__type__4637___24t(Vvar__4638)
<=> ! [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__4638,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4641',axiom,
! [Vvar__4642] :
( c_24__type__4641___24t(Vvar__4642)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__4642,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4659',axiom,
! [Vvar__4660] :
( c_24__type__4659___24t(Vvar__4660)
<=> ! [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__4660,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4706',axiom,
! [Vvar__4707] :
( c_24__type__4706___24t(Vvar__4707)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4707,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4709',axiom,
! [Vvar__4710] :
( c_24__type__4709___24t(Vvar__4710)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__4710,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4739',axiom,
! [Vvar__4740] :
( c_24__type__4739___24t(Vvar__4740)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__4740,Vv__CANONICAL__0)) ) ) ).
fof('$_type_47456',axiom,
! [Vvar__47457] :
( c_24__type__47456___24t(Vvar__47457)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6978___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_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__47457,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4746',axiom,
! [Vvar__4747] :
( c_24__type__4746___24t(Vvar__4747)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4747,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4843',axiom,
! [Vvar__4844] :
( c_24__type__4843___24t(Vvar__4844)
<=> ! [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__4844,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_4855',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4856] :
( c_24__type__4855___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4856)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__4856,Vv__CANONICAL__2)) ) ) ).
fof('$_type_488',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__489] :
( c_24__type__488___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__489)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__489,Vv__CANONICAL__2)) ) ) ).
fof('$_type_4892',axiom,
! [Vvar__4893] :
( c_24__type__4892___24t(Vvar__4893)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__4893,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_492',axiom,
! [Vvar__493] :
( c_24__type__492___24t(Vvar__493)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__495___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__493,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_49337',axiom,
! [Vvar__49338] :
( c_24__type__49337___24t(Vvar__49338)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__49338,Vv__CANONICAL__0)) ) ) ).
fof('$_type_495',axiom,
! [Vv__CANONICAL__0,Vvar__496] :
( c_24__type__495___24t(Vv__CANONICAL__0,Vvar__496)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__496,Vv__CANONICAL__1)) ) ) ).
fof('$_type_5109',axiom,
! [Vvar__5110] :
( c_24__type__5109___24t(Vvar__5110)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__5110,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_512',axiom,
! [Vvar__513] :
( c_24__type__512___24t(Vvar__513)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__495___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__513,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_5305',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5306] :
( c_24__type__5305___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5306)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5306,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_535',axiom,
! [Vvar__536] :
( c_24__type__535___24t(Vvar__536)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__495___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__541___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__553___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__536,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_53623',axiom,
! [Vvar__53624] :
( c_24__type__53623___24t(Vvar__53624)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__53624,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5398',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__5399] :
( c_24__type__5398___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__5399)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5399,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_541',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__542] :
( c_24__type__541___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__542)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__542,Vv__CANONICAL__2)) ) ) ).
fof('$_type_54369',axiom,
! [Vvar__54370] :
( c_24__type__54369___24t(Vvar__54370)
<=> ! [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__54370,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_54381',axiom,
! [Vvar__54382] :
( c_24__type__54381___24t(Vvar__54382)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2etrue,happ(Vvar__54382,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_54384',axiom,
! [Vvar__54385] :
( c_24__type__54384___24t(Vvar__54385)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__54385,Vv__CANONICAL__0)) ) ) ).
fof('$_type_54403',axiom,
! [Vvar__54404] :
( c_24__type__54403___24t(Vvar__54404)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__54404,Vv__CANONICAL__0)) ) ) ).
fof('$_type_54426',axiom,
! [Vvar__54427] :
( c_24__type__54426___24t(Vvar__54427)
<=> ! [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__54427,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_54460',axiom,
! [Vvar__54461] :
( c_24__type__54460___24t(Vvar__54461)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6978___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__54461,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_5491',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__5492] :
( c_24__type__5491___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__5492)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5492,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_55005',axiom,
! [Vvar__55006] :
( c_24__type__55005___24t(Vvar__55006)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2260___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3546___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__55006,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_55032',axiom,
! [Vvar__55033] :
( c_24__type__55032___24t(Vvar__55033)
<=> ! [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__55033,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55036',axiom,
! [Vvar__55037] :
( c_24__type__55036___24t(Vvar__55037)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__55037,Vv__CANONICAL__0)) ) ) ).
fof('$_type_55040',axiom,
! [Vvar__55041] :
( c_24__type__55040___24t(Vvar__55041)
<=> ! [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__55042___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__55043___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__55041,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55065',axiom,
! [Vvar__55066] :
( c_24__type__55065___24t(Vvar__55066)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__55066,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55112',axiom,
! [Vvar__55113] :
( c_24__type__55112___24t(Vvar__55113)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__55113,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55121',axiom,
! [Vvar__55122] :
( c_24__type__55121___24t(Vvar__55122)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__55122,Vv__CANONICAL__0)) ) ) ).
fof('$_type_55129',axiom,
! [Vvar__55130] :
( c_24__type__55129___24t(Vvar__55130)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__55130,Vv__CANONICAL__0)) ) ) ).
fof('$_type_55140',axiom,
! [Vvar__55141] :
( c_24__type__55140___24t(Vvar__55141)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__55141,Vv__CANONICAL__0)) ) ) ).
fof('$_type_55143',axiom,
! [Vvar__55144] :
( c_24__type__55143___24t(Vvar__55144)
<=> ! [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__55144,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55161',axiom,
! [Vvar__55162] :
( c_24__type__55161___24t(Vvar__55162)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__55162,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55210',axiom,
! [Vvar__55211] :
( c_24__type__55210___24t(Vvar__55211)
<=> ! [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__55211,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55233',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55234] :
( c_24__type__55233___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__55234)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__55234,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_55260',axiom,
! [Vvar__55261] :
( c_24__type__55260___24t(Vvar__55261)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__55261,Vv__CANONICAL__0)) ) ) ).
fof('$_type_55262',axiom,
! [Vvar__55263] :
( c_24__type__55262___24t(Vvar__55263)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(Vvar__55263,Vv__CANONICAL__0)) ) ) ).
fof('$_type_553',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__554] :
( c_24__type__553___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__554)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(Vvar__554,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexist___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ).
fof('$_type_55356',axiom,
! [Vvar__55357] :
( c_24__type__55356___24t(Vvar__55357)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__55357,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55425',axiom,
! [Vvar__55426] :
( c_24__type__55425___24t(Vvar__55426)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__55427___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__55426,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55427',axiom,
! [Vvar__55428] :
( c_24__type__55427___24t(Vvar__55428)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__55428,Vv__CANONICAL__0)) ) ) ).
fof('$_type_55439',axiom,
! [Vvar__55440] :
( c_24__type__55439___24t(Vvar__55440)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__55440,Vv__CANONICAL__0)) ) ) ).
fof('$_type_55445',axiom,
! [Vvar__55446] :
( c_24__type__55445___24t(Vvar__55446)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__55446,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55476',axiom,
! [Vvar__55477] :
( c_24__type__55476___24t(Vvar__55477)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__55477,Vv__CANONICAL__0)) ) ) ).
fof('$_type_55527',axiom,
! [Vvar__55528] :
( c_24__type__55527___24t(Vvar__55528)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__55528,Vv__CANONICAL__0)) ) ) ).
fof('$_type_55531',axiom,
! [Vvar__55532] :
( c_24__type__55531___24t(Vvar__55532)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__55036___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__55036___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__55532,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_55550',axiom,
! [Vvar__55551] :
( c_24__type__55550___24t(Vvar__55551)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2eandb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__55552___24a1(Vv__CANONICAL__0),c_24__prop__55553___24a1(Vv__CANONICAL__1),happ(happ(Vvar__55551,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_55555',axiom,
! [Vvar__55556] :
( c_24__type__55555___24t(Vvar__55556)
<=> ! [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__55556,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_55711',axiom,
! [Vvar__55712] :
( c_24__type__55711___24t(Vvar__55712)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( ( p(Vv__CANONICAL__0)
<=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue )
=> cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__55712,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_55726',axiom,
! [Vvar__55727] :
( c_24__type__55726___24t(Vvar__55727)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eBool_2eBool_2ereflect___24t(c_24__prop__55728___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eBool_2eBool_2eeqb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__55727,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5573',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5574] :
( c_24__type__5573___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5574)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__5574,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_56374',axiom,
! [Vvar__56375] :
( c_24__type__56374___24t(Vvar__56375)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__56375,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_56391',axiom,
! [Vvar__56392] :
( c_24__type__56391___24t(Vvar__56392)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__337___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__56392,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_56401',axiom,
! [Vvar__56402] :
( c_24__type__56401___24t(Vvar__56402)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__56402,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_56464',axiom,
! [Vvar__56465] :
( c_24__type__56464___24t(Vvar__56465)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__56465,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5666',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__5667] :
( c_24__type__5666___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__5667)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5667,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_56724',axiom,
! [Vvar__56725] :
( c_24__type__56724___24t(Vvar__56725)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2260___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__22325___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__22267___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__56725,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_56765',axiom,
! [Vvar__56766] :
( c_24__type__56765___24t(Vvar__56766)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__56767___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__56772___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__56777___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__56766,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__1,Vv__CANONICAL__0)) ) ) ) ) ) ).
fof('$_type_56767',axiom,
! [Vvar__56768] :
( c_24__type__56767___24t(Vvar__56768)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__56768,Vv__CANONICAL__0)) ) ) ).
fof('$_type_56772',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56773] :
( c_24__type__56772___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56773)
<=> ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2etrue
=> t(Vvar__56773,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2etrue)) ) ) ).
fof('$_type_56777',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56778] :
( c_24__type__56777___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56778)
<=> ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2efalse
=> t(Vvar__56778,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2efalse)) ) ) ).
fof('$_type_569',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__570] :
( c_24__type__569___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__570)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__570,Vv__CANONICAL__2)) ) ) ).
fof('$_type_56994',axiom,
! [Vvar__56995] :
( c_24__type__56994___24t(Vvar__56995)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__56996___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__56997___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__56995,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_57001',axiom,
! [Vvar__57002] :
( c_24__type__57001___24t(Vvar__57002)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__57002,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_57006',axiom,
! [Vvar__57007] :
( c_24__type__57006___24t(Vvar__57007)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,c_24__lam__57009___24a1(Vv__CANONICAL__0),happ(Vvar__57007,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_57030',axiom,
! [Vvar__57031] :
( c_24__type__57030___24t(Vvar__57031)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__57031,Vv__CANONICAL__0)) ) ) ).
fof('$_type_57053',axiom,
! [Vvar__57054] :
( c_24__type__57053___24t(Vvar__57054)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__55427___24t(Vv__CANONICAL__0)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__57030,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efor__all___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,c_24__lam__57058___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),happ(happ(Vvar__57054,Vv__CANONICAL__0),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_57108',axiom,
! [Vvar__57109] :
( c_24__type__57108___24t(Vvar__57109)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__55427___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__57109,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_57131',axiom,
! [Vvar__57132] :
( c_24__type__57131___24t(Vvar__57132)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,happ(Vvar__57132,Vv__CANONICAL__0)) ) ) ).
fof('$_type_57176',axiom,
! [Vvar__57177] :
( c_24__type__57176___24t(Vvar__57177)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__56767___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__57177,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_57215',axiom,
! [Vvar__57216] :
( c_24__type__57215___24t(Vvar__57216)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__57216,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_57283',axiom,
! [Vvar__57284] :
( c_24__type__57283___24t(Vvar__57284)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6978___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__57284,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_573',axiom,
! [Vvar__574] :
( c_24__type__573___24t(Vvar__574)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__576___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__574,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_57325',axiom,
! [Vvar__57326] :
( c_24__type__57325___24t(Vvar__57326)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__57327___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__57339___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__57351___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty))
=> ! [Vv__CANONICAL__4] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__57326,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_57327',axiom,
! [Vvar__57328] :
( c_24__type__57327___24t(Vvar__57328)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__57328,Vv__CANONICAL__0)) ) ) ).
fof('$_type_57339',axiom,
! [Vv__CANONICAL__0,Vvar__57340] :
( c_24__type__57339___24t(Vv__CANONICAL__0,Vvar__57340)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(happ(Vvar__57340,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_57351',axiom,
! [Vv__CANONICAL__0,Vvar__57352] :
( c_24__type__57351___24t(Vv__CANONICAL__0,Vvar__57352)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__2)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(happ(Vvar__57352,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1))) ) ) ) ) ) ).
fof('$_type_5748',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__5749] :
( c_24__type__5748___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__5749)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__5749,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_576',axiom,
! [Vv__CANONICAL__0,Vvar__577] :
( c_24__type__576___24t(Vv__CANONICAL__0,Vvar__577)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__577,Vv__CANONICAL__1)) ) ) ).
fof('$_type_58129',axiom,
! [Vvar__58130] :
( c_24__type__58129___24t(Vvar__58130)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6978___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__58130,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_5841',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5842] :
( c_24__type__5841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5842)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__5842,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_59',axiom,
! [Vvar__60] :
( c_24__type__59___24t(Vvar__60)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__62___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__74___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__60,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_593',axiom,
! [Vvar__594] :
( c_24__type__593___24t(Vvar__594)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__576___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__594,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_59790',axiom,
! [Vvar__59791] :
( c_24__type__59790___24t(Vvar__59791)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__55427___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__59791,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_616',axiom,
! [Vvar__617] :
( c_24__type__616___24t(Vvar__617)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__576___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__622___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__634___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__617,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_62',axiom,
! [Vv__CANONICAL__0,Vvar__63] :
( c_24__type__62___24t(Vv__CANONICAL__0,Vvar__63)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__63,Vv__CANONICAL__1)) ) ) ).
fof('$_type_622',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__623] :
( c_24__type__622___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__623)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__623,Vv__CANONICAL__2)) ) ) ).
fof('$_type_62238',axiom,
! [Vv__CANONICAL__0,Vvar__62239] :
( c_24__type__62238___24t(Vv__CANONICAL__0,Vvar__62239)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__62239,Vv__CANONICAL__1)) ) ) ).
fof('$_type_634',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__635] :
( c_24__type__634___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__635)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(Vvar__635,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexistT___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ).
fof('$_type_646',axiom,
! [Vvar__647] :
( c_24__type__646___24t(Vvar__647)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__647,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6523',axiom,
! [Vvar__6524] :
( c_24__type__6523___24t(Vvar__6524)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__2178___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__2461___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__2470___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__9,Vv__CANONICAL__15)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__6524,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_6574',axiom,
! [Vvar__6575] :
( c_24__type__6574___24t(Vvar__6575)
<=> ! [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__6575,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6594',axiom,
! [Vvar__6595] :
( c_24__type__6594___24t(Vvar__6595)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__6595,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6813',axiom,
! [Vvar__6814] :
( c_24__type__6813___24t(Vvar__6814)
<=> ! [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__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2412___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__2260___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__2178___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__2461___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__2470___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__6814,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),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('$_type_690',axiom,
! [Vvar__691] :
( c_24__type__690___24t(Vvar__691)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__694___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__701___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__691,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_6913',axiom,
! [Vvar__6914] :
( c_24__type__6913___24t(Vvar__6914)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__6914,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_694',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__695] :
( c_24__type__694___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__695)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__695,Vv__CANONICAL__2)) ) ) ).
fof('$_type_6970',axiom,
! [Vvar__6971] :
( c_24__type__6970___24t(Vvar__6971)
<=> ! [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__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__6978___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(Vvar__6971,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_6978',axiom,
! [Vv__CANONICAL__0,Vvar__6979] :
( c_24__type__6978___24t(Vv__CANONICAL__0,Vvar__6979)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__6979,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_7',axiom,
! [Vvar__8] :
( c_24__type__7___24t(Vvar__8)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__8,Vv__CANONICAL__0)) ) ) ).
fof('$_type_701',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__702] :
( c_24__type__701___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__702)
<=> ( p(Vv__CANONICAL__0)
=> t(Vvar__702,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_708',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__709] :
( c_24__type__708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__709)
<=> ( p(Vv__CANONICAL__1)
=> t(Vvar__709,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_714',axiom,
! [Vvar__715] :
( c_24__type__714___24t(Vvar__715)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__716___24a1(Vv__CANONICAL__0),c_24__prop__717___24a1(Vv__CANONICAL__0),happ(Vvar__715,Vv__CANONICAL__0)) ) ) ).
fof('$_type_725',axiom,
! [Vvar__726] :
( c_24__type__725___24t(Vvar__726)
<=> ! [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__726,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_74',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75] :
( c_24__type__74___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(happ(Vvar__75,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))) ) ) ) ) ).
fof('$_type_742',axiom,
! [Vvar__743] :
( c_24__type__742___24t(Vvar__743)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,Vv__CANONICAL__0)
=> ( cMaplists_2eMapLists_2ead__list__stutters___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eInit_2eSpecif_2esigT___24t(cIntMap_2eMap_2ead,c_24__lam__754___24a1(Vv__CANONICAL__0),happ(Vvar__743,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_785',axiom,
! [Vvar__786] :
( c_24__type__785___24t(Vvar__786)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786,Vv__CANONICAL__0)) ) ) ).
fof('$_type_795',axiom,
! [Vvar__796] :
( c_24__type__795___24t(Vvar__796)
<=> ! [Vv__CANONICAL__0] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__796,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8068',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8069] :
( c_24__type__8068___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8069)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__8069,Vv__CANONICAL__3)) ) ) ).
fof('$_type_808',axiom,
! [Vvar__809] :
( c_24__type__808___24t(Vvar__809)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__809,Vv__CANONICAL__0)) ) ) ).
fof('$_type_810',axiom,
! [Vvar__811] :
( c_24__type__810___24t(Vvar__811)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__811,Vv__CANONICAL__0)) ) ) ).
fof('$_type_816',axiom,
! [Vvar__817] :
( c_24__type__816___24t(Vvar__817)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__817,Vv__CANONICAL__0)) ) ) ).
fof('$_type_818',axiom,
! [Vvar__819] :
( c_24__type__818___24t(Vvar__819)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__819,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8382',axiom,
! [Vvar__8383] :
( c_24__type__8382___24t(Vvar__8383)
<=> ! [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__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1405___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2412___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__8383,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('$_type_8433',axiom,
! [Vvar__8434] :
( c_24__type__8433___24t(Vvar__8434)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__6978___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__8434,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_8479',axiom,
! [Vv__CANONICAL__0,Vvar__8480] :
( c_24__type__8479___24t(Vv__CANONICAL__0,Vvar__8480)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__8480,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_8490',axiom,
! [Vvar__8491] :
( c_24__type__8490___24t(Vvar__8491)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__8491,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_8499',axiom,
! [Vvar__8500] :
( c_24__type__8499___24t(Vvar__8500)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__8500,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8511',axiom,
! [Vvar__8512] :
( c_24__type__8511___24t(Vvar__8512)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__8512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8644',axiom,
! [Vvar__8645] :
( c_24__type__8644___24t(Vvar__8645)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__8645,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_8818',axiom,
! [Vvar__8819] :
( c_24__type__8818___24t(Vvar__8819)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8825___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(Vvar__8819,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_8825',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8826] :
( c_24__type__8825___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8826)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__8826,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8853',axiom,
! [Vvar__8854] :
( c_24__type__8853___24t(Vvar__8854)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8860___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__8854,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_8860',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8861] :
( c_24__type__8860___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8861)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8861,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8873',axiom,
! [Vvar__8874] :
( c_24__type__8873___24t(Vvar__8874)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3546___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__8874,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8890',axiom,
! [Vvar__8891] :
( c_24__type__8890___24t(Vvar__8891)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3546___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__8891,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_89',axiom,
! [Vvar__90] :
( c_24__type__89___24t(Vvar__90)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cIntMap_2eFset_2eFSet___24t(happ(happ(Vvar__90,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8923',axiom,
! [Vvar__8924] :
( c_24__type__8923___24t(Vvar__8924)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3546___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(happ(happ(Vvar__8924,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9063',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9064] :
( c_24__type__9063___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9064)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__9064,Vv__CANONICAL__3)) ) ) ).
fof('$_type_9179',axiom,
! [Vvar__9180] :
( c_24__type__9179___24t(Vvar__9180)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cIntMap_2eMapiter_2ealist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cIntMap_2eMap_2ead___24t(happ(happ(happ(Vvar__9180,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9263',axiom,
! [Vv__CANONICAL__0,Vvar__9264] :
( c_24__type__9263___24t(Vv__CANONICAL__0,Vvar__9264)
<=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
=> cIntMap_2eMap_2ead___24t(happ(Vvar__9264,Vv__CANONICAL__1)) ) ) ).
fof('$_type_9277',axiom,
! [Vvar__9278] :
( c_24__type__9277___24t(Vvar__9278)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__9279___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__9278,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9279',axiom,
! [Vvar__9280] :
( c_24__type__9279___24t(Vvar__9280)
<=> ! [Vv__CANONICAL__0] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
=> cIntMap_2eMap_2ead___24t(happ(Vvar__9280,Vv__CANONICAL__0)) ) ) ).
fof('$_type_957',axiom,
! [Vvar__958] :
( c_24__type__957___24t(Vvar__958)
<=> ! [Vv__CANONICAL__0] :
( cIntMap_2eFset_2eFSet___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eFset_2eFSet___24t(Vv__CANONICAL__1)
=> cIntMap_2eFset_2eFSet___24t(happ(happ(Vvar__958,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9758',axiom,
! [Vvar__9759] :
( c_24__type__9758___24t(Vvar__9759)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__9759,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_991',axiom,
! [Vvar__992] :
( c_24__type__991___24t(Vvar__992)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__5)
=> cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__992,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.Even',axiom,
c_24__type__4746___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eEven) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
c_24__type__55129___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__43819___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Bool.Bool.ReflectF',axiom,
c_24__type__55555___24t(cCoq_2eBool_2eBool_2eReflectF) ).
fof('$_typeof_Coq.Bool.Bool.ReflectT',axiom,
c_24__type__54381___24t(cCoq_2eBool_2eBool_2eReflectT) ).
fof('$_typeof_Coq.Bool.Bool.andb_false_elim',axiom,
c_24__type__55550___24t(cCoq_2eBool_2eBool_2eandb__false__elim) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__337___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.eqb_spec',axiom,
c_24__type__55726___24t(cCoq_2eBool_2eBool_2eeqb__spec) ).
fof('$_typeof_Coq.Bool.Bool.iff_reflect',axiom,
c_24__type__55711___24t(cCoq_2eBool_2eBool_2eiff__reflect) ).
fof('$_typeof_Coq.Bool.Bool.orb_true_elim',axiom,
c_24__type__331___24t(cCoq_2eBool_2eBool_2eorb__true__elim) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__24543___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Sumbool.bool_eq_rec',axiom,
c_24__type__56765___24t(cCoq_2eBool_2eSumbool_2ebool__eq__rec) ).
fof('$_typeof_Coq.Bool.Sumbool.sumbool_of_bool',axiom,
c_24__type__714___24t(cCoq_2eBool_2eSumbool_2esumbool__of__bool) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__43821___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
c_24__type__38754___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
c_24__type__55445___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__38752___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
c_24__type__38734___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.add',axiom,
c_24__type__45595___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.cardinal',axiom,
c_24__type__55439___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.choose',axiom,
c_24__type__57131___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose) ).
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('$_typeof_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
c_24__type__55445___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.equal',axiom,
c_24__type__55356___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.exists_',axiom,
c_24__type__57108___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eexists__) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.filter',axiom,
c_24__type__55425___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.fold',axiom,
c_24__type__23836___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.for_all',axiom,
c_24__type__57108___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efor__all) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.inter',axiom,
c_24__type__23825___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.is_empty',axiom,
c_24__type__55260___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__23797___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.remove',axiom,
c_24__type__45595___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.singleton',axiom,
c_24__type__55262___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esingleton) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.subset',axiom,
c_24__type__55356___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esubset) ).
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('$_typeof_Coq.FSets.FSetPositive.PositiveSet.union',axiom,
c_24__type__23825___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.xexists',axiom,
c_24__type__59790___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exexists) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__54384___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__1529___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__7___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__1527___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__337___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__349___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_typeof_Coq.Init.Datatypes.bool',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_typeof_Coq.Init.Datatypes.bool_rec',axiom,
c_24__type__57176___24t(cCoq_2eInit_2eDatatypes_2ebool__rec) ).
fof('$_typeof_Coq.Init.Datatypes.bool_rect',axiom,
c_24__type__57176___24t(cCoq_2eInit_2eDatatypes_2ebool__rect) ).
fof('$_typeof_Coq.Init.Datatypes.comparison',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2ecomparison) ).
fof('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__34___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__1573___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__24564___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__24569___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__4892___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__15___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.list_rec',axiom,
c_24__type__59___24t(cCoq_2eInit_2eDatatypes_2elist__rec) ).
fof('$_typeof_Coq.Init.Datatypes.list_rect',axiom,
c_24__type__59___24t(cCoq_2eInit_2eDatatypes_2elist__rect) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__4709___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__29___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__15___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__337___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__1555___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__1539___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__4843___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__1539___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_typeof_Coq.Init.Datatypes.true',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2etrue) ).
fof('$_typeof_Coq.Init.Datatypes.tt',axiom,
cCoq_2eInit_2eDatatypes_2eunit___24t(cCoq_2eInit_2eDatatypes_2ett) ).
fof('$_typeof_Coq.Init.Datatypes.unit',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__337___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__1475___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.bitwise',axiom,
c_24__type__56391___24t(cCoq_2eInit_2eNat_2ebitwise) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__54426___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div',axiom,
c_24__type__1475___24t(cCoq_2eInit_2eNat_2ediv) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__7___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__7___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__34781___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__43821___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.land',axiom,
c_24__type__1475___24t(cCoq_2eInit_2eNat_2eland) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__34781___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.log2',axiom,
c_24__type__7___24t(cCoq_2eInit_2eNat_2elog2) ).
fof('$_typeof_Coq.Init.Nat.lor',axiom,
c_24__type__1475___24t(cCoq_2eInit_2eNat_2elor) ).
fof('$_typeof_Coq.Init.Nat.ltb',axiom,
c_24__type__34781___24t(cCoq_2eInit_2eNat_2eltb) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__1475___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.modulo',axiom,
c_24__type__1475___24t(cCoq_2eInit_2eNat_2emodulo) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__1475___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.odd',axiom,
c_24__type__43821___24t(cCoq_2eInit_2eNat_2eodd) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__1475___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__7___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.shiftl',axiom,
c_24__type__1475___24t(cCoq_2eInit_2eNat_2eshiftl) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__1475___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__34781___24t(cCoq_2eInit_2eNat_2etestbit) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__11725___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__11725___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__11725___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__512___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__593___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__22541___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__22546___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__492___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__573___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT_rec',axiom,
c_24__type__616___24t(cCoq_2eInit_2eSpecif_2esigT__rec) ).
fof('$_typeof_Coq.Init.Specif.sig_rec',axiom,
c_24__type__535___24t(cCoq_2eInit_2eSpecif_2esig__rec) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__646___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
c_24__type__690___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__2609___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__8511___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.existsb',axiom,
c_24__type__8873___24t(cCoq_2eLists_2eList_2eexistsb) ).
fof('$_typeof_Coq.Lists.List.filter',axiom,
c_24__type__26889___24t(cCoq_2eLists_2eList_2efilter) ).
fof('$_typeof_Coq.Lists.List.find',axiom,
c_24__type__8890___24t(cCoq_2eLists_2eList_2efind) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__8818___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__8853___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.forallb',axiom,
c_24__type__8873___24t(cCoq_2eLists_2eList_2eforallb) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__8490___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__1740___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__8644___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.partition',axiom,
c_24__type__8923___24t(cCoq_2eLists_2eList_2epartition) ).
fof('$_typeof_Coq.Lists.List.rev',axiom,
c_24__type__8499___24t(cCoq_2eLists_2eList_2erev) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__8499___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Lists.SetoidList.compat_bool',axiom,
c_24__type__55005___24t(cCoq_2eLists_2eSetoidList_2ecompat__bool) ).
fof('$_typeof_Coq.Lists.SetoidList.compat_op',axiom,
c_24__type__56724___24t(cCoq_2eLists_2eSetoidList_2ecompat__op) ).
fof('$_typeof_Coq.Lists.SetoidList.equivlistA',axiom,
c_24__type__22194___24t(cCoq_2eLists_2eSetoidList_2eequivlistA) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__22257___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__22300___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__22300___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__24668___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.NArith.BinNat.N.b2n',axiom,
c_24__type__55121___24t(cCoq_2eNArith_2eBinNat_2eN_2eb2n) ).
fof('$_typeof_Coq.NArith.BinNat.N.discr',axiom,
c_24__type__23721___24t(cCoq_2eNArith_2eBinNat_2eN_2ediscr) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__43813___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__23708___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__23708___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__1494___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
c_24__type__55065___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div',axiom,
c_24__type__1494___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
c_24__type__1478___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__38604___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__1478___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__725___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__1487___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.land',axiom,
c_24__type__1494___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eland) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.leb',axiom,
c_24__type__725___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eleb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.log2',axiom,
c_24__type__1478___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elog2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.lor',axiom,
c_24__type__1494___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elor) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.ltb',axiom,
c_24__type__725___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eltb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
c_24__type__1494___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__1494___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.modulo',axiom,
c_24__type__1494___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__1494___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.odd',axiom,
c_24__type__1487___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eodd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pow',axiom,
c_24__type__1494___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epow) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__1478___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.shiftl',axiom,
c_24__type__1494___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sub',axiom,
c_24__type__1494___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esub) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__1478___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
c_24__type__1478___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__725___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit_nat',axiom,
c_24__type__55112___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__23705___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.Ndec.Nleb',axiom,
c_24__type__725___24t(cCoq_2eNArith_2eNdec_2eNleb) ).
fof('$_typeof_Coq.NArith.Ndigits.Neven',axiom,
c_24__type__818___24t(cCoq_2eNArith_2eNdigits_2eNeven) ).
fof('$_typeof_Coq.NArith.Ndigits.Nless',axiom,
c_24__type__725___24t(cCoq_2eNArith_2eNdigits_2eNless) ).
fof('$_typeof_Coq.NArith.Ndigits.Nless_aux',axiom,
c_24__type__56401___24t(cCoq_2eNArith_2eNdigits_2eNless__aux) ).
fof('$_typeof_Coq.NArith.Ndigits.Nodd',axiom,
c_24__type__818___24t(cCoq_2eNArith_2eNdigits_2eNodd) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__43819___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__816___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_typeof_Coq.Numbers.BinNums.Z',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_typeof_Coq.Numbers.BinNums.Z0',axiom,
cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__1507___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__1507___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_typeof_Coq.Numbers.BinNums.positive',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_typeof_Coq.Numbers.BinNums.xH',axiom,
cCoq_2eNumbers_2eBinNums_2epositive___24t(cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__808___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__808___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__23773___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__23773___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__23767___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__55143___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__55161___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__38631___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.leb',axiom,
c_24__type__55161___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eleb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.ltb',axiom,
c_24__type__55161___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eltb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred',axiom,
c_24__type__808___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_N',axiom,
c_24__type__816___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
c_24__type__55140___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__808___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
c_24__type__55210___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qdiv',axiom,
c_24__type__11830___24t(cCoq_2eQArith_2eQArith__base_2eQdiv) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq',axiom,
c_24__type__11823___24t(cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq_bool',axiom,
c_24__type__11826___24t(cCoq_2eQArith_2eQArith__base_2eQeq__bool) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__11820___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qminus',axiom,
c_24__type__11830___24t(cCoq_2eQArith_2eQArith__base_2eQminus) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmult',axiom,
c_24__type__11830___24t(cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('$_typeof_Coq.QArith.QArith_base.Qopp',axiom,
c_24__type__11833___24t(cCoq_2eQArith_2eQArith__base_2eQopp) ).
fof('$_typeof_Coq.QArith.QArith_base.Qplus',axiom,
c_24__type__11830___24t(cCoq_2eQArith_2eQArith__base_2eQplus) ).
fof('$_typeof_Coq.QArith.Qreals.Q2R',axiom,
c_24__type__49337___24t(cCoq_2eQArith_2eQreals_2eQ2R) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__11856___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__11847___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__11850___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__11847___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__11847___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__11850___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__11847___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__22103___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__15___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__37658___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.Ascii.eqb',axiom,
c_24__type__54369___24t(cCoq_2eStrings_2eAscii_2eeqb) ).
fof('$_typeof_Coq.Strings.Byte.eqb',axiom,
c_24__type__56374___24t(cCoq_2eStrings_2eByte_2eeqb) ).
fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).
fof('$_typeof_Coq.Strings.String.eqb',axiom,
c_24__type__55032___24t(cCoq_2eStrings_2eString_2eeqb) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__23773___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec',axiom,
c_24__type__55040___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec) ).
fof('$_typeof_Coq.Vectors.Fin.eqb',axiom,
c_24__type__57215___24t(cCoq_2eVectors_2eFin_2eeqb) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__4739___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__38251___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__38243___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__38226___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.Vectors.VectorEq.eqb',axiom,
c_24__type__57283___24t(cCoq_2eVectors_2eVectorEq_2eeqb) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
c_24__type__55527___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__55531___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__4659___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__4659___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__4659___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__4659___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__4641___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__4637___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__23891___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__4637___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.eqb',axiom,
c_24__type__4622___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__55036___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gtb',axiom,
c_24__type__4622___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egtb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__4622___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.log2',axiom,
c_24__type__4641___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.ltb',axiom,
c_24__type__4622___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__4637___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__4637___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__4637___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__55036___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__23897___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__23894___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__4641___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__4637___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__4641___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__23972___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__4637___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__4641___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.testbit',axiom,
c_24__type__4622___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_N',axiom,
c_24__type__55476___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__4622___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zbool.Zle_bool_total',axiom,
c_24__type__56994___24t(cCoq_2eZArith_2eZbool_2eZle__bool__total) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__5109___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Peq',axiom,
c_24__type__58129___24t(cCoq_2emicromega_2eEnvRing_2ePeq) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__15___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.RMicromega.is_neg',axiom,
c_24__type__56464___24t(cCoq_2emicromega_2eRMicromega_2eis__neg) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__11881___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__2128___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__15___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__15___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__15___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__15___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__15___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.cltb',axiom,
c_24__type__34681___24t(cCoq_2emicromega_2eRingMicromega_2ecltb) ).
fof('$_typeof_Coq.micromega.RingMicromega.cneqb',axiom,
c_24__type__54460___24t(cCoq_2emicromega_2eRingMicromega_2ecneqb) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__2689___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__1539___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.Tauto.cnf',axiom,
c_24__type__1539___24t(cCoq_2emicromega_2eTauto_2ecnf) ).
fof('$_typeof_Coq.micromega.Tauto.cnf_checker',axiom,
c_24__type__3756___24t(cCoq_2emicromega_2eTauto_2ecnf__checker) ).
fof('$_typeof_Coq.micromega.Tauto.eval_clause',axiom,
c_24__type__22876___24t(cCoq_2emicromega_2eTauto_2eeval__clause) ).
fof('$_typeof_Coq.micromega.Tauto.eval_cnf',axiom,
c_24__type__3622___24t(cCoq_2emicromega_2eTauto_2eeval__cnf) ).
fof('$_typeof_Coq.micromega.Tauto.eval_tt',axiom,
c_24__type__3591___24t(cCoq_2emicromega_2eTauto_2eeval__tt) ).
fof('$_typeof_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
c_24__type__8382___24t(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
c_24__type__57001___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.eqb',axiom,
c_24__type__55161___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.choose_mem_3',axiom,
c_24__type__57006___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2echoose__mem__3) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.for_all_mem_4',axiom,
c_24__type__57053___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2efor__all__mem__4) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.set_rec',axiom,
c_24__type__57325___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eset__rec) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZWitness',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZWitness) ).
fof('$_typeof_Coq.micromega.ZMicromega.isZ0',axiom,
c_24__type__55036___24t(cCoq_2emicromega_2eZMicromega_2eisZ0) ).
fof('$_typeof_Coq.micromega.ZMicromega.is_pol_Z0',axiom,
c_24__type__53623___24t(cCoq_2emicromega_2eZMicromega_2eis__pol__Z0) ).
fof('$_typeof_Coq.micromega.ZMicromega.valid_cut_sign',axiom,
c_24__type__38365___24t(cCoq_2emicromega_2eZMicromega_2evalid__cut__sign) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__6523___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__15___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__25335___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
c_24__type__25202___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__6813___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PExpr_eq',axiom,
c_24__type__47456___24t(cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__6594___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__6574___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__15___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__6574___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__15___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__6913___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__6913___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.split',axiom,
c_24__type__6970___24t(cCoq_2esetoid__ring_2eField__theory_2esplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__1478___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nsub',axiom,
c_24__type__1494___24t(cCoq_2esetoid__ring_2eInitialRing_2eNsub) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nw_is0',axiom,
c_24__type__54403___24t(cCoq_2esetoid__ring_2eInitialRing_2eNw__is0) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__8382___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
c_24__type__8433___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__337___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__34827___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__34833___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__34830___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__14502___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__14309___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__15___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__12394___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__15___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi',axiom,
c_24__type__13367___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_dev',axiom,
c_24__type__17539___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__17325___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
c_24__type__14986___24t(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__15271___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__14732___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__21736___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__21736___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__37382___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
c_24__type__1527___24t(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__1478___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__2580___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__17633___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_IntMap.Fset.FSet',axiom,
cType___24t(cIntMap_2eFset_2eFSet) ).
fof('$_typeof_IntMap.Fset.FSetUnion',axiom,
c_24__type__957___24t(cIntMap_2eFset_2eFSetUnion) ).
fof('$_typeof_IntMap.Fset.MapDom',axiom,
c_24__type__89___24t(cIntMap_2eFset_2eMapDom) ).
fof('$_typeof_IntMap.Fset.MapDom_semantics_2',axiom,
c_24__type__1720___24t(cIntMap_2eFset_2eMapDom__semantics__2) ).
fof('$_typeof_IntMap.Fset.in_FSet',axiom,
c_24__type__352___24t(cIntMap_2eFset_2ein__FSet) ).
fof('$_typeof_IntMap.Fset.in_dom',axiom,
c_24__type__1692___24t(cIntMap_2eFset_2ein__dom) ).
fof('$_typeof_IntMap.Fset.in_dom_some',axiom,
c_24__type__1704___24t(cIntMap_2eFset_2ein__dom__some) ).
fof('$_typeof_IntMap.Lsort.ad_monotonic',axiom,
c_24__type__9277___24t(cIntMap_2eLsort_2ead__monotonic) ).
fof('$_typeof_IntMap.Lsort.alist_nth_ad',axiom,
c_24__type__9179___24t(cIntMap_2eLsort_2ealist__nth__ad) ).
fof('$_typeof_IntMap.Map.M0',axiom,
c_24__type__129___24t(cIntMap_2eMap_2eM0) ).
fof('$_typeof_IntMap.Map.M1',axiom,
c_24__type__134___24t(cIntMap_2eMap_2eM1) ).
fof('$_typeof_IntMap.Map.M2',axiom,
c_24__type__139___24t(cIntMap_2eMap_2eM2) ).
fof('$_typeof_IntMap.Map.Map',axiom,
c_24__type__15___24t(cIntMap_2eMap_2eMap) ).
fof('$_typeof_IntMap.Map.MapCard',axiom,
c_24__type__264___24t(cIntMap_2eMap_2eMapCard) ).
fof('$_typeof_IntMap.Map.MapEmptyp',axiom,
c_24__type__9758___24t(cIntMap_2eMap_2eMapEmptyp) ).
fof('$_typeof_IntMap.Map.MapGet',axiom,
c_24__type__1828___24t(cIntMap_2eMap_2eMapGet) ).
fof('$_typeof_IntMap.Map.MapMerge',axiom,
c_24__type__139___24t(cIntMap_2eMap_2eMapMerge) ).
fof('$_typeof_IntMap.Map.MapPut',axiom,
c_24__type__250___24t(cIntMap_2eMap_2eMapPut) ).
fof('$_typeof_IntMap.Map.MapPut1',axiom,
c_24__type__991___24t(cIntMap_2eMap_2eMapPut1) ).
fof('$_typeof_IntMap.Map.MapPut_behind',axiom,
c_24__type__250___24t(cIntMap_2eMap_2eMapPut__behind) ).
fof('$_typeof_IntMap.Map.ad',axiom,
cType___24t(cIntMap_2eMap_2ead) ).
fof('$_typeof_IntMap.Map.option_sum',axiom,
c_24__type__1749___24t(cIntMap_2eMap_2eoption__sum) ).
fof('$_typeof_IntMap.Mapaxioms.eqmap',axiom,
c_24__type__1833___24t(cIntMap_2eMapaxioms_2eeqmap) ).
fof('$_typeof_IntMap.Mapiter.MapFold',axiom,
c_24__type__1449___24t(cIntMap_2eMapiter_2eMapFold) ).
fof('$_typeof_IntMap.Mapiter.MapFold1',axiom,
c_24__type__1400___24t(cIntMap_2eMapiter_2eMapFold1) ).
fof('$_typeof_IntMap.Mapiter.MapSweep',axiom,
c_24__type__10634___24t(cIntMap_2eMapiter_2eMapSweep) ).
fof('$_typeof_IntMap.Mapiter.MapSweep1',axiom,
c_24__type__10620___24t(cIntMap_2eMapiter_2eMapSweep1) ).
fof('$_typeof_IntMap.Mapiter.MapSweep2',axiom,
c_24__type__10565___24t(cIntMap_2eMapiter_2eMapSweep2) ).
fof('$_typeof_IntMap.Mapiter.aapp',axiom,
c_24__type__11263___24t(cIntMap_2eMapiter_2eaapp) ).
fof('$_typeof_IntMap.Mapiter.alist',axiom,
c_24__type__15___24t(cIntMap_2eMapiter_2ealist) ).
fof('$_typeof_IntMap.Mapiter.alist_semantics',axiom,
c_24__type__11315___24t(cIntMap_2eMapiter_2ealist__semantics) ).
fof('$_typeof_IntMap.Mapsubset.MapDisjoint',axiom,
c_24__type__1470___24t(cIntMap_2eMapsubset_2eMapDisjoint) ).
fof('$_typeof_IntMap.Mapsubset.MapDisjoint_1',axiom,
c_24__type__1905___24t(cIntMap_2eMapsubset_2eMapDisjoint__1) ).
fof('$_typeof_IntMap.Mapsubset.MapSubset',axiom,
c_24__type__1470___24t(cIntMap_2eMapsubset_2eMapSubset) ).
fof('$_typeof_Maplists.MapLists.Elems',axiom,
c_24__type__293___24t(cMaplists_2eMapLists_2eElems) ).
fof('$_typeof_Maplists.MapLists.ad_in_list',axiom,
c_24__type__795___24t(cMaplists_2eMapLists_2ead__in__list) ).
fof('$_typeof_Maplists.MapLists.ad_in_list_forms_circuit',axiom,
c_24__type__305___24t(cMaplists_2eMapLists_2ead__in__list__forms__circuit) ).
fof('$_typeof_Maplists.MapLists.ad_list_stutters',axiom,
c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters) ).
fof('$_typeof_Maplists.MapLists.ad_list_stutters_has_circuit',axiom,
c_24__type__742___24t(cMaplists_2eMapLists_2ead__list__stutters__has__circuit) ).
fof('Coq.Arith.Compare_dec.leb_complete',axiom,
! [V0__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__m)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2eNat_2eleb___24a2(V0__m,V1__n) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__m,V1__n) ) ) ) ).
fof('Coq.Arith.Compare_dec.leb_complete_conv',axiom,
! [V0__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__m)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V0__m) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__m,V1__n) ) ) ) ).
fof('Coq.Arith.Compare_dec.leb_correct',axiom,
! [V0__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__m)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__m,V1__n)
=> cCoq_2eInit_2eNat_2eleb___24a2(V0__m,V1__n) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.Arith.Compare_dec.leb_correct_conv',axiom,
! [V0__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__m)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__m,V1__n)
=> cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V0__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.Arith.Compare_dec.leb_iff_conv',axiom,
! [V0__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__m)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V0__m) = cCoq_2eInit_2eDatatypes_2efalse
<=> cCoq_2eInit_2ePeano_2elt___24a2(V0__m,V1__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.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_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.Le.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.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_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.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.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.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.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.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_b2n_double_bit0',axiom,
! [V0__a0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a0)
=> ! [V1__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__a)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__a0),cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__a)),cCoq_2eInit_2eDatatypes_2eO) = V0__a0 ) ) ).
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_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1475,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__7,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.are_bits',axiom,
! [V0__f] :
( c_24__type__43821___24t(V0__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__43821,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V0__f)
=> ( ? [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
& cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,cCoq_2eInit_2eNat_2etestbit___24a1(V2__n)) )
<=> ? [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
& ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V2__k,V3__m)
=> happ(V0__f,V3__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.b2n_div2',axiom,
! [V0__a0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a0)
=> cCoq_2eInit_2eNat_2ediv___24a2(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__a0),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.bit_log2',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ( V0__a != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eNat_2etestbit___24a2(V0__a,cCoq_2eInit_2eNat_2elog2___24a1(V0__a)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.Arith.PeanoNat.Nat.bits_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Arith.PeanoNat.Nat.bits_above_log2',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eNat_2elog2___24a1(V0__a),V1__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.bits_inj_0',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
=> V0__a = cCoq_2eInit_2eDatatypes_2eO ) ) ).
fof('Coq.Arith.PeanoNat.Nat.clearbit_eq',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eArith_2ePeanoNat_2eNat_2eclearbit___24a2(V0__a,V1__n),V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.Arith.PeanoNat.Nat.div2_bits',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv___24a2(V0__a,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))),V1__n) = cCoq_2eInit_2eNat_2etestbit___24a2(V0__a,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.div2_bitwise',axiom,
! [V0__op] :
( c_24__type__337___24t(V0__op)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__a)
=> ! [V3__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__b)
=> cCoq_2eInit_2eNat_2ediv2___24a1(cCoq_2eInit_2eNat_2ebitwise___24a4(V0__op,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__a,V3__b)) = cCoq_2eInit_2eNat_2ebitwise___24a4(V0__op,V1__n,cCoq_2eInit_2eNat_2ediv2___24a1(V2__a),cCoq_2eInit_2eNat_2ediv2___24a1(V3__b)) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.div2_decr',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__a,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n))
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V0__a),V1__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.div_0_l',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ( V0__a != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eNat_2ediv___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__a) = cCoq_2eInit_2eDatatypes_2eO ) ) ).
fof('Coq.Arith.PeanoNat.Nat.div_small',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__a,V1__b)
=> cCoq_2eInit_2eNat_2ediv___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.div_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1475,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__7,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_2ediv) ).
fof('Coq.Arith.PeanoNat.Nat.eq_0_gt_0_cases',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.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__55128___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.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.even_0',axiom,
cCoq_2eInit_2eNat_2eeven___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.Arith.PeanoNat.Nat.even_1',axiom,
cCoq_2eInit_2eNat_2eeven___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = cCoq_2eInit_2eDatatypes_2efalse ).
fof('Coq.Arith.PeanoNat.Nat.even_spec',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eInit_2eNat_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue
<=> cCoq_2eArith_2ePeanoNat_2eNat_2eEven___24a1(V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.induction',axiom,
! [V0__A] :
( c_24__type__4746___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4746,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.land_spec',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2eland___24a2(V0__a,V1__b),V2__n) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eNat_2etestbit___24a2(V0__a,V2__n),cCoq_2eInit_2eNat_2etestbit___24a2(V1__b,V2__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.land_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1475,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__7,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_2eland) ).
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_lt_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
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_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_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_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11725,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__4746,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_gt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2eNat_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x) ) ) ) ).
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.leb_nle',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2eNat_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> ~ cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.log2_bits_unique',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2eNat_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2etrue
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__n,V3__m)
=> cCoq_2eInit_2eNat_2etestbit___24a2(V0__a,V3__m) = cCoq_2eInit_2eDatatypes_2efalse ) )
=> cCoq_2eInit_2eNat_2elog2___24a1(V0__a) = V1__n ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lor_0_l',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> cCoq_2eInit_2eNat_2elor___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__a) = V0__a ) ).
fof('Coq.Arith.PeanoNat.Nat.lor_eq_0_l',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( cCoq_2eInit_2eNat_2elor___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2eO
=> V0__a = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lor_spec',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2elor___24a2(V0__a,V1__b),V2__n) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eInit_2eNat_2etestbit___24a2(V0__a,V2__n),cCoq_2eInit_2eNat_2etestbit___24a2(V1__b,V2__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lor_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1475,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__7,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_2elor) ).
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_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_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_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_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_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_2elt___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11725,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__4746,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.ltb_ge',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2eNat_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.ltb_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> cCoq_2eInit_2eNat_2eltb___24a2(V0__x,V0__x) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Arith.PeanoNat.Nat.ltb_nlt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2eNat_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mod_pow2_bits_high',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_2ePeano_2ele___24a2(V1__n,V2__m)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V0__a,cCoq_2eInit_2eNat_2epow___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__n)),V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mod_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1475,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__7,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_2emodulo) ).
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_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_pow2_bits_low',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_2ePeano_2elt___24a2(V2__m,V1__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2emul___24a2(V0__a,cCoq_2eInit_2eNat_2epow___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__n)),V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1475,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__7,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.negb_even',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eNat_2eeven___24a1(V0__n)) = cCoq_2eInit_2eNat_2eodd___24a1(V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.odd_0',axiom,
cCoq_2eInit_2eNat_2eodd___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2efalse ).
fof('Coq.Arith.PeanoNat.Nat.odd_1',axiom,
cCoq_2eInit_2eNat_2eodd___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.Arith.PeanoNat.Nat.odd_2',axiom,
cCoq_2eInit_2eNat_2eodd___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) = cCoq_2eInit_2eDatatypes_2efalse ).
fof('Coq.Arith.PeanoNat.Nat.odd_bitwise',axiom,
! [V0__op] :
( c_24__type__337___24t(V0__op)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__a)
=> ! [V3__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__b)
=> cCoq_2eInit_2eNat_2eodd___24a1(cCoq_2eInit_2eNat_2ebitwise___24a4(V0__op,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__a,V3__b)) = happ(happ(V0__op,cCoq_2eInit_2eNat_2eodd___24a1(V2__a)),cCoq_2eInit_2eNat_2eodd___24a1(V3__b)) ) ) ) ) ).
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.ones_spec_high',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_2etestbit___24a2(cCoq_2eArith_2ePeanoNat_2eNat_2eones___24a1(V0__n),V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.pow2_bits_false',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_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2epow___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V0__n),V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.pow_0_r',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> cCoq_2eInit_2eNat_2epow___24a2(V0__a,cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.PeanoNat.Nat.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( V0__a != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eNat_2epow___24a2(V0__a,V1__b) != cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.pow_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1475,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__7,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_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.shiftl_spec_low',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_2ePeano_2elt___24a2(V2__m,V1__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2eshiftl___24a2(V0__a,V1__n),V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2esub___24a2(V1__m,V0__n),V0__n) = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_le_mono',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.Arith.PeanoNat.Nat.succ_pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2epred___24a1(V0__n)) = V0__n ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7,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.testbit_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Arith.PeanoNat.Nat.testbit_bitwise_1',axiom,
! [V0__op] :
( c_24__type__337___24t(V0__op)
=> ( ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> happ(happ(V0__op,cCoq_2eInit_2eDatatypes_2efalse),V1__b) = cCoq_2eInit_2eDatatypes_2efalse )
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ! [V4__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__a)
=> ! [V5__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__b)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V4__a,V2__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ebitwise___24a4(V0__op,V2__n,V4__a,V5__b),V3__m) = happ(happ(V0__op,cCoq_2eInit_2eNat_2etestbit___24a2(V4__a,V3__m)),cCoq_2eInit_2eNat_2etestbit___24a2(V5__b,V3__m)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.testbit_bitwise_2',axiom,
! [V0__op] :
( c_24__type__337___24t(V0__op)
=> ( happ(happ(V0__op,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2efalse
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ! [V4__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__a)
=> ! [V5__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__b)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V4__a,V2__n)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V5__b,V2__n)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ebitwise___24a4(V0__op,V2__n,V4__a,V5__b),V3__m) = happ(happ(V0__op,cCoq_2eInit_2eNat_2etestbit___24a2(V4__a,V3__m)),cCoq_2eInit_2eNat_2etestbit___24a2(V5__b,V3__m)) ) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.testbit_even_0',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V0__a),cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Arith.PeanoNat.Nat.testbit_neg_r',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2eO)
=> cCoq_2eInit_2eNat_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.testbit_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__34781,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__43821,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool))),cCoq_2eInit_2eNat_2etestbit) ).
fof('Coq.Arith.PeanoNat.Nat.zero_or_succ',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.Plus.le_plus_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(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Plus.le_plus_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
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_false_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_2efalse
<=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
| V1__b2 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.Bool.Bool.andb_false_intro1',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.Bool.Bool.andb_false_intro2',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.Bool.Bool.andb_false_l',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2efalse,V0__b) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Bool.Bool.andb_false_r',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Bool.Bool.andb_lazy_alt',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__a,V1__b) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454376___24a2(V0__a,V1__b) ) ) ).
fof('Coq.Bool.Bool.andb_negb_r',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b)) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Bool.Bool.andb_true_eq',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__a,V1__b)
=> ( cCoq_2eInit_2eDatatypes_2etrue = V0__a
& cCoq_2eInit_2eDatatypes_2etrue = V1__b ) ) ) ) ).
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.eq_true_false_abs',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
=> p(c_24False) ) ) ) ).
fof('Coq.Bool.Bool.eq_true_iff_eq',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
=> V0__b1 = V1__b2 ) ) ) ).
fof('Coq.Bool.Bool.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.eqb_negb1',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eBool_2eBool_2eeqb___24a2(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b),V0__b) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Bool.Bool.eqb_negb2',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eBool_2eBool_2eeqb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b)) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Bool.Bool.if_negb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> c_24__case__Coq_2eInit_2eDatatypes_2ebool_244687___24a4(V0__A,V1__b,V2__x,V3__y) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_244692___24a4(V0__A,V1__b,V2__x,V3__y) ) ) ) ) ).
fof('Coq.Bool.Bool.negb_false_iff',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse
<=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.Bool.Bool.negb_involutive',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b)) = V0__b ) ).
fof('Coq.Bool.Bool.negb_involutive_reverse',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> V0__b = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__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.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.Bool.orb_false_elim',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& V1__b2 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.Bool.Bool.orb_false_iff',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse
<=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& V1__b2 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.Bool.Bool.orb_false_intro',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
=> ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.Bool.Bool.orb_false_l',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eInit_2eDatatypes_2efalse,V0__b) = V0__b ) ).
fof('Coq.Bool.Bool.orb_false_r',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2efalse) = V0__b ) ).
fof('Coq.Bool.Bool.orb_prop',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__a = cCoq_2eInit_2eDatatypes_2etrue
| V1__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Bool.Bool.orb_true_intro',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
| V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.Bool.Bool.orb_true_r',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2etrue) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('Coq.Bool.Bool.trans_eq_bool',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Bool.Bool.xorb_eq',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ! [V1__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
=> ( cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b,V1__b_27) = cCoq_2eInit_2eDatatypes_2efalse
=> V0__b = V1__b_27 ) ) ) ).
fof('Coq.Bool.Bool.xorb_false_l',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2exorb___24a2(cCoq_2eInit_2eDatatypes_2efalse,V0__b) = V0__b ) ).
fof('Coq.Bool.Bool.xorb_false_r',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2efalse) = V0__b ) ).
fof('Coq.Bool.Bool.xorb_nilpotent',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b,V0__b) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Bool.Sumbool.bool_eq_ind',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ! [V1__P] :
( c_24__type__4706___24t(V1__P)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2etrue)) )
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2efalse)) )
=> p(happ(V1__P,V0__b)) ) ) ) ) ).
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.Bool.Zerob.zerob_false_intro',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_2efalse ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.choose_1',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(V0__s) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V1__x)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s) ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.empty_1',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('Coq.FSets.FSetPositive.PositiveSet.eq_dec_subproof',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(V0__s,V1__s_27) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27) ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.equal_1',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(V0__s,V1__s_27) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.equal_2',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(V0__s,V1__s_27) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27) ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.is_empty_1',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(V0__s) = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.mem_1',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,V0__s) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.mem_Leaf',axiom,
! [V0__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V0__x)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.Init.Datatypes.andb_prop',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__a = cCoq_2eInit_2eDatatypes_2etrue
& V1__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Init.Datatypes.bool_ind',axiom,
! [V0__P] :
( c_24__type__4706___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2etrue))
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2efalse))
=> ! [V3__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V3__b)
=> p(happ(V0__P,V3__b)) ) ) ) ) ).
fof('Coq.Init.Datatypes.bool_sind',axiom,
! [V0__P] :
( c_24__type__4706___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2etrue))
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2efalse))
=> ! [V3__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V3__b)
=> p(happ(V0__P,V3__b)) ) ) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1576___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__4746___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Datatypes.prod_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__1559___24t(V0__A,V1__B,V2__P)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V3__a,V4__b))) ) )
=> ! [V4__p] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
=> p(happ(V2__P,V4__p)) ) ) ) ) ) ).
fof('Coq.Init.Peano.O_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Init.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__11722___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_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.Init.Peano.plus_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Init.Specif.sig_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__495___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__2589___24t(V0__A,V1__P,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,V3__x))) ) )
=> ! [V4__s] :
( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V4__s)
=> p(happ(V2__P,V4__s)) ) ) ) ) ) ).
fof('Coq.Init.Specif.sumbool_ind',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__2595___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Init.Specif.sumor_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__2631___24t(V0__A,V1__B,V2__P)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2einleft___24a3(V0__A,V1__B,V3__a))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2einright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumor___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l2))) ) ) ) ) ).
fof('Coq.Lists.List.Forall2_app_inv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__3598___24t(V0__A,V1__B,V2__R)
=> ! [V3__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1)
=> ! [V4__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l2)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l_27)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l1,V4__l2),V5__l_27)
=> ? [V7__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V7__l1_27)
& ? [V8__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V8__l2_27)
& cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V3__l1,V7__l1_27)
& cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V4__l2,V8__l2_27)
& V5__l_27 = cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,V7__l1_27,V8__l2_27) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall2_app_inv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__3598___24t(V0__A,V1__B,V2__R)
=> ! [V3__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l1_27)
=> ! [V4__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l2_27)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V5__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,V3__l1_27,V4__l2_27))
=> ? [V7__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l1)
& ? [V8__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V8__l2)
& cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V7__l1,V3__l1_27)
& cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V8__l2,V4__l2_27)
& V5__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l1,V8__l2) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall2_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__3598___24t(V0__A,V1__B,V2__R)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V6__l_27)
=> ( p(happ(happ(V2__R,V3__x),V4__y))
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V5__l,V6__l_27)
=> cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V5__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,V4__y,V6__l_27)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_forall',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__495___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l)
=> p(happ(V1__P,V3__x)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_remove_1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__l_27)))
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_remove_2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__l_27)))
=> ~ cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) ) ) ) ) ) ).
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.app_eq_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
=> ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& V2__l_27 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ) ) ).
fof('Coq.Lists.List.app_eq_unit',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_2eapp___24a3(V0__A,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))
=> ( ( V1__x = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& V2__y = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) )
| ( V1__x = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))
& V2__y = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.app_inj_tail',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)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__b,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( V1__x = V2__y
& V3__a = V4__b ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.app_inv_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l1) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V3__l2)
=> V2__l1 = V3__l2 ) ) ) ) ) ).
fof('Coq.Lists.List.app_inv_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V1__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l2,V1__l)
=> V2__l1 = V3__l2 ) ) ) ) ) ).
fof('Coq.Lists.List.app_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27)) ) ) ) ).
fof('Coq.Lists.List.app_nil_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) = V1__l ) ) ).
fof('Coq.Lists.List.existsb_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__3546___24t(V0__A,V1__f)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V2__l1),cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.existsb_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__3546___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__d] :
( t(V4__d,V0__A)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l))
=> ( cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2efalse
=> happ(V1__f,cCoq_2eLists_2eList_2enth___24a4(V0__A,V3__n,V2__l,V4__d)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.find_none',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__3546___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V2__l)
=> happ(V1__f,V4__x) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('Coq.Lists.List.forallb_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__3546___24t(V0__A,V1__f)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V2__l1),cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.in_app_or',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m))
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_or_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m) )
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m)) ) ) ) ) ) ).
fof('Coq.Lists.List.partition_cons2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__3546___24t(V0__A,V1__f)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V4__l1,V5__l2)
=> ( happ(V1__f,V2__a) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V5__l2)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.rev_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1576___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.rev_involutive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) = V1__l ) ) ).
fof('Coq.Lists.SetoidList.InA_alt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V3__l)
<=> ? [V4__y] :
( t(V4__y,V0__A)
& p(happ(happ(V1__eqA,V2__x),V4__y))
& cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__y,V3__l) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2))
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l1)
| cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l2) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_app_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2))
<=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l1)
| cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l2) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l))
<=> ( p(happ(happ(V1__eqA,V2__x),V3__y))
| cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V4__l) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(happ(V1__eqA,V2__x),V3__y))
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V4__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.In_InA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V3__l_27)))
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x,V4__l_27)))
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27))) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.SortA_InfA_InA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__ltA] :
( c_24__type__2260___24t(V0__A,V3__ltA)
=> ( cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(V0__A,V3__ltA)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2260___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__495___24a1(V0__A),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cProp,V1__eqA,c_3c_3d_3e)),V3__ltA)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__x] :
( t(V7__x,V0__A)
=> ! [V8__a] :
( t(V8__a,V0__A)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,V6__l)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V3__ltA,V8__a,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V7__x,V6__l)
=> p(happ(happ(V3__ltA,V8__a),V7__x)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqarefl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__A,V1__eqA) ) ) ) ).
fof('Coq.Lists.SetoidList.filter_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__ltA] :
( c_24__type__2260___24t(V0__A,V3__ltA)
=> ( cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(V0__A,V3__ltA)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2260___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__495___24a1(V0__A),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cProp,V1__eqA,c_3c_3d_3e)),V3__ltA)
=> ! [V6__f] :
( c_24__type__3546___24t(V0__A,V6__f)
=> ( ! [V7__x] :
( t(V7__x,V0__A)
=> ! [V8__y] :
( t(V8__y,V0__A)
=> ( happ(V6__f,V7__x) = cCoq_2eInit_2eDatatypes_2etrue
=> ( happ(V6__f,V8__y) = cCoq_2eInit_2eDatatypes_2efalse
=> p(happ(happ(V3__ltA,V7__x),V8__y)) ) ) ) )
=> ! [V8__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V8__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,V8__l)
=> V8__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V6__f,V8__l),cCoq_2eLists_2eList_2efilter___24a3(V0__A,c_24__lam__38932___24a2(V0__A,V6__f),V8__l)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.UIP_refl_bool',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b = V0__b
=> c_24Proof = cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,V0__b) ) ) ).
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.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.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.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.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_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1494,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__1478,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.are_bits',axiom,
! [V0__f] :
( c_24__type__1487___24t(V0__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1487,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V0__f)
=> ( ? [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
& cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a1(V2__n)) )
<=> ? [V2__k] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__k)
& ! [V3__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__k,V3__m)
=> happ(V0__f,V3__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.bit_log2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eN0
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__a)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.NArith.BinNat.N.bits_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.NArith.BinNat.N.bits_above_log2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__a),V1__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.BinNat.N.bits_inj_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
=> V0__a = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ).
fof('Coq.NArith.BinNat.N.clearbit_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNArith_2eBinNat_2eN_2eclearbit___24a2(V0__a,V1__n),V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.NArith.BinNat.N.div2_bits',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V1__n) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__n)) ) ) ).
fof('Coq.NArith.BinNat.N.div2_double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n)) = V0__n ) ).
fof('Coq.NArith.BinNat.N.div2_succ_double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__n)) = V0__n ) ).
fof('Coq.NArith.BinNat.N.div_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eN0
=> cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__a) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ).
fof('Coq.NArith.BinNat.N.div_small',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__a,V1__b)
=> cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.div_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1494,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__1478,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_2ediv) ).
fof('Coq.NArith.BinNat.N.eq_0_gt_0_cases',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.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__55120___24a2(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.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.eqb_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__x,V0__x) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('Coq.NArith.BinNat.N.eqb_sym',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_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__y,V0__x) ) ) ).
fof('Coq.NArith.BinNat.N.even_0',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.NArith.BinNat.N.even_1',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eInit_2eDatatypes_2efalse ).
fof('Coq.NArith.BinNat.N.induction',axiom,
! [V0__A] :
( c_24__type__818___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__818,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.land_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__a,V1__a_27),V2__n) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V2__n),cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V1__a_27,V2__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.land_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1494,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__1478,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN))),cCoq_2eNArith_2eBinNatDef_2eN_2eland) ).
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_antisymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ).
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_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_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__23708,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__818,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.leb_gt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.NArith.BinNat.N.leb_nle',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> ~ cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.log2_bits_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2etrue
=> ( ! [V3__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__n,V3__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V3__m) = cCoq_2eInit_2eDatatypes_2efalse ) )
=> cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__a) = V1__n ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lor_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__a) = V0__a ) ).
fof('Coq.NArith.BinNat.N.lor_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V0__a,V1__a_27),V2__n) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V2__n),cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V1__a_27,V2__n)) ) ) ) ).
fof('Coq.NArith.BinNat.N.lor_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1494,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__1478,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN))),cCoq_2eNArith_2eBinNatDef_2eN_2elor) ).
fof('Coq.NArith.BinNat.N.lt_0_1',axiom,
cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.NArith.BinNat.N.lt_1_2',axiom,
cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.NArith.BinNat.N.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
<=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.ltb_ge',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.NArith.BinNat.N.ltb_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eltb___24a2(V0__x,V0__x) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.NArith.BinNat.N.ltb_nlt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.lxor_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eN0
=> V0__a = V1__a_27 ) ) ) ).
fof('Coq.NArith.BinNat.N.lxor_nilpotent',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V0__a) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.min_le_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m),V2__p)
<=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V2__p)
| cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mod_pow2_bits_high',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_2eBinNat_2eN_2ele___24a2(V1__n,V2__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V0__a,cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n)),V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
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_pow2_bits_low',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_2eBinNat_2eN_2elt___24a2(V2__m,V1__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__a,cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n)),V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.NArith.BinNat.N.negb_even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n)) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) ) ).
fof('Coq.NArith.BinNat.N.odd_0',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eInit_2eDatatypes_2efalse ).
fof('Coq.NArith.BinNat.N.odd_1',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.NArith.BinNat.N.odd_2',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eInit_2eDatatypes_2efalse ).
fof('Coq.NArith.BinNat.N.one_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('Coq.NArith.BinNat.N.ones_spec_high',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_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNArith_2eBinNat_2eN_2eones___24a1(V0__n),V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.BinNat.N.pow2_bits_false',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_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n),V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.BinNat.N.pow_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ).
fof('Coq.NArith.BinNat.N.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eN0
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.pred_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) = V0__n ) ).
fof('Coq.NArith.BinNat.N.shiftl_spec_low',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_2eBinNat_2eN_2elt___24a2(V2__m,V1__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl___24a2(V0__a,V1__n),V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.NArith.BinNat.N.succ_le_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m)) ) ) ) ).
fof('Coq.NArith.BinNat.N.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1478,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.NArith.BinNat.N.testbit_even_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__a),cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.NArith.BinNat.N.testbit_neg_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__n,cCoq_2eNumbers_2eBinNums_2eN0)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.BinNat.N.testbit_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__725,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__1487,cCoq_2eNArith_2eBinNat_2eN_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eNArith_2eBinNat_2eN_2eeq,c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool))),cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('Coq.NArith.BinNat.N.zero_or_succ',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.Ndec.Nbit0_neq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2efalse
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.NArith.Ndec.Ncompare_Gt_Nltb',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2eGt
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndec.Ncompare_Lt_Nltb',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2eLt
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V1__b,V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndec.Ndiv2_bit_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__a) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a_27)
=> V0__a = V1__a_27 ) ) ) ) ).
fof('Coq.NArith.Ndec.Ndiv2_bit_neq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a_27)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.NArith.Ndec.Ndiv2_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a_27)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.NArith.Ndec.Ndiv2_neq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a_27)) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndec.Neqb_complete',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2etrue
=> V0__n = V1__n_27 ) ) ) ).
fof('Coq.NArith.Ndec.Neven_not_double_plus_one',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( cCoq_2eNArith_2eNdigits_2eNeven___24a1(V0__a)
=> ! [V2__a0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__a0)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V2__a0),V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndec.Nleb_Nle',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__a,V1__b) ) ) ) ).
fof('Coq.NArith.Ndec.Nleb_double_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V1__b)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.NArith.Ndec.Nleb_double_mono_conv',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V1__b)) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.NArith.Ndec.Nleb_double_plus_one_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V1__b)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.NArith.Ndec.Nleb_double_plus_one_mono_conv',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V1__b)) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.NArith.Ndec.Nleb_ltb_trans',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__c)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V2__c,V1__b) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V2__c,V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
fof('Coq.NArith.Ndec.Nltb_Ncompare',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efalse
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).
fof('Coq.NArith.Ndec.Nltb_double_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V1__b)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndec.Nltb_double_mono_conv',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V1__b)) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndec.Nltb_double_plus_one_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V1__b)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndec.Nltb_double_plus_one_mono_conv',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V1__b)) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndec.Nltb_leb_trans',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__c)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V1__b,V0__a) = cCoq_2eInit_2eDatatypes_2efalse
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V1__b,V2__c) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V2__c,V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
fof('Coq.NArith.Ndec.Nltb_leb_weak',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V1__b,V0__a) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.NArith.Ndec.Nltb_trans',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__c)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V1__b,V0__a) = cCoq_2eInit_2eDatatypes_2efalse
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(V2__c,V1__b) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V2__c,V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
fof('Coq.NArith.Ndec.Nmin_lt_3',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__c)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V1__b,V2__c),V0__a) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V1__b,V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.NArith.Ndec.Nmin_lt_4',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__c)
=> ( cCoq_2eNArith_2eNdec_2eNleb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V1__b,V2__c),V0__a) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eNdec_2eNleb___24a2(V2__c,V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.NArith.Ndec.Nneq_elim',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27))
| cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a_27)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.NArith.Ndec.Nnot_div2_not_double',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a0)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__a),V1__a0) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__a,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V1__a0)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndec.Nnot_div2_not_double_plus_one',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a0)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__a),V1__a0) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V1__a0),V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndec.Nodd_not_double',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( cCoq_2eNArith_2eNdigits_2eNodd___24a1(V0__a)
=> ! [V2__a0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__a0)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V2__a0),V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndec.Nxor_eq_false',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__n_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.NArith.Ndigits.N0_less_2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( cCoq_2eNArith_2eNdigits_2eNless___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__a) = cCoq_2eInit_2eDatatypes_2efalse
=> V0__a = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ).
fof('Coq.NArith.Ndigits.Nbit0_gt',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2etrue
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.NArith.Ndigits.Nbit0_less',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2efalse
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.NArith.Ndigits.Nbit_Nsize',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__p)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esize__nat___24a1(V0__n),V1__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat___24a2(V0__n,V1__p) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.NArith.Ndigits.Ndiv2_double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNArith_2eNdigits_2eNeven___24a1(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n)) = V0__n ) ) ).
fof('Coq.NArith.Ndigits.Ndiv2_double_plus_one',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNArith_2eNdigits_2eNodd___24a1(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n)) = V0__n ) ) ).
fof('Coq.NArith.Ndigits.Ndouble_bit0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n)) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.NArith.Ndigits.Ndouble_plus_one_bit0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__n)) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('Coq.NArith.Ndigits.Nless_def_4',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> cCoq_2eNArith_2eNdigits_2eNless___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V1__a_27)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.NArith.Ndigits.Nless_not_refl',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V0__a) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.NArith.Ndigits.Nless_trans',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ! [V2__a_27_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__a_27_27)
=> ( cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2etrue
=> ( cCoq_2eNArith_2eNdigits_2eNless___24a2(V1__a_27,V2__a_27_27) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,V2__a_27_27) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ).
fof('Coq.NArith.Ndigits.Nless_z',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> cCoq_2eNArith_2eNdigits_2eNless___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eN0) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.NArith.Ndigits.Nneg_bit0_1',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27)) ) ) ) ).
fof('Coq.NArith.Ndigits.Nneg_bit0_2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__p))
=> cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27)) ) ) ) ) ).
fof('Coq.NArith.Ndigits.Nsame_bit0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))
=> cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27) ) ) ) ) ).
fof('Coq.NArith.Ndigits.Nshiftl_nat_spec_low',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__m,V1__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl__nat___24a2(V0__a,V1__n),V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.NArith.Ndigits.Nxor_bit0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27)) = cCoq_2eInit_2eDatatypes_2exorb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27)) ) ) ).
fof('Coq.NArith.Ndigits.Nxor_div2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__a_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
=> cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27)) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a_27)) ) ) ).
fof('Coq.Numbers.BinNums.N_ind',axiom,
! [V0__P] :
( c_24__type__818___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V2__p))) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__810___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.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive)) ).
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.iter_invariant',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__f] :
( c_24__type__2412___24t(V1__A,V2__f)
=> ! [V3__Inv] :
( c_24__type__495___24t(V1__A,V3__Inv)
=> ( ! [V4__x] :
( t(V4__x,V1__A)
=> ( p(happ(V3__Inv,V4__x))
=> p(happ(V3__Inv,happ(V2__f,V4__x))) ) )
=> ! [V5__x] :
( t(V5__x,V1__A)
=> ( p(happ(V3__Inv,V5__x))
=> p(happ(V3__Inv,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__A,V2__f,V5__x,V0__p))) ) ) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.iter_swap_gen',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__1744___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__55233___24t(V0__A,V1__B,V3__g)
=> ! [V4__h] :
( c_24__type__2442___24t(V0__A,V1__B,V4__h)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> happ(V2__f,happ(V3__g,V5__a)) = happ(V4__h,happ(V2__f,V5__a)) )
=> ! [V6__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> happ(V2__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V3__g,V7__a,V6__p)) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__B,V4__h,happ(V2__f,V7__a),V6__p) ) ) ) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.le_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_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__m,V2__p)
=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.leb_gt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.leb_nle',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> ~ cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.lt_le_incl',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)
=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__p,V1__q) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.lt_succ_diag_r',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V0__p)) ) ).
fof('Coq.PArith.BinPos.Pos.ltb_ge',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.ltb_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eltb___24a2(V0__x,V0__x) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.PArith.BinPos.Pos.ltb_nlt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.QArith.QArith_base.Q_Setoid',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('Coq.QArith.QArith_base.Qeq_bool_eq',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.QArith.QArith_base.Qeq_bool_iff',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
<=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.QArith.QArith_base.Qeq_bool_neq',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.QArith.QArith_base.Qmult_comp',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11830,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,c_24__type__11833,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eQArith_2eQArith__base_2eQeq)),cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('Coq.QArith.QArith_base.Qopp_comp',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11833,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eQArith_2eQArith__base_2eQeq),cCoq_2eQArith_2eQArith__base_2eQopp) ).
fof('Coq.QArith.QArith_base.Qplus_comp',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11830,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,c_24__type__11833,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eQArith_2eQArith__base_2eQeq)),cCoq_2eQArith_2eQArith__base_2eQplus) ).
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.Setoids.Setoid.Seq_sym',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)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> p(happ(happ(V1__Aeq,V4__y),V3__x)) ) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_trans',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)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ! [V5__z] :
( t(V5__z,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> ( p(happ(happ(V1__Aeq,V4__y),V5__z))
=> p(happ(happ(V1__Aeq,V3__x),V5__z)) ) ) ) ) ) ) ) ) ).
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.byte_dec_bl',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_2etrue
=> 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.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_refl',axiom,
! [V0__x] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Vectors.Fin.eqb_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__p] :
( cCoq_2eVectors_2eFin_2et___24t(V0__n,V1__p)
=> ! [V2__q] :
( cCoq_2eVectors_2eFin_2et___24t(V0__n,V2__q)
=> ( cCoq_2eVectors_2eFin_2eeqb___24a4(V0__n,V0__n,V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2etrue
<=> V1__p = V2__q ) ) ) ) ).
fof('Coq.Vectors.VectorEq.eqb_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__A__beq] :
( c_24__type__6978___24t(V0__A,V1__A__beq)
=> ( ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( happ(happ(V1__A__beq,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2etrue
<=> V2__x = V3__y ) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V4__v1)
=> ! [V5__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V5__v2)
=> ( cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,V3__n,V3__n,V4__v1,V5__v2) = cCoq_2eInit_2eDatatypes_2etrue
<=> V4__v1 = V5__v2 ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V2__z) ) ) ) ) ) ).
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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.abs_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( 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.bit_log2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.ZArith.BinInt.Z.bits_above_log2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),V1__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_above_log2_neg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__a))),V1__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_iff_neg_ex',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0)
<=> ? [V1__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__k)
& ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__k,V2__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__m) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_iff_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a)),V1__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_iff_nonneg_ex',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a)
<=> ? [V1__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__k)
& ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__k,V2__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_inj\'',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V1__b,V2__n) ) )
=> V0__a = V1__b ) ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_inj_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
=> V0__a = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.clearbit_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinInt_2eZ_2eclearbit___24a2(V0__a,V1__n),V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.ZArith.BinInt.Z.div2_bits',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.div_small',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a)
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4637,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__4641,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_2ediv) ).
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.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.even_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.ZArith.BinInt.Z.even_1',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eInit_2eDatatypes_2efalse ).
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)
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.land_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V0__a,V1__b),V2__n) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__n),cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V1__b,V2__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.land_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4637,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__4641,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),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_2eland) ).
fof('Coq.ZArith.BinInt.Z.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ).
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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ind',axiom,
! [V0__A] :
( c_24__type__11719___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11719,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e),V0__A)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( p(happ(V0__A,V2__n))
=> ( ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,V4__m)
=> ( p(happ(V0__A,V4__m))
=> p(happ(V0__A,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V4__m))) ) ) )
=> ! [V5__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,V5__m)
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ngt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
<=> ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m)
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4659,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__11719,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.leb_gt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.leb_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.leb_nle',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> ~ cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_bits_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2etrue
=> ( ! [V3__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V3__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V3__m) = cCoq_2eInit_2eDatatypes_2efalse ) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a) = V1__n ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a)) ) ).
fof('Coq.ZArith.BinInt.Z.lor_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = V0__a ) ).
fof('Coq.ZArith.BinInt.Z.lor_eq_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__a = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lor_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V0__a,V1__b),V2__n) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__n),cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V1__b,V2__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lor_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4637,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__4641,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),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_2elor) ).
fof('Coq.ZArith.BinInt.Z.lt_0_1',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.ZArith.BinInt.Z.lt_1_2',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.ZArith.BinInt.Z.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
<=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> 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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4659,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__11719,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.ltb_ge',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ltb_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V0__x) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.ZArith.BinInt.Z.ltb_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ltb_nlt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
<=> ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_pow2_bits_high',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_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n)
& cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__n,V2__m) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n)),V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
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_pow2_bits_low',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_2eBinInt_2eZ_2elt___24a2(V2__m,V1__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n)),V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4637,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__4641,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.negb_even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.odd_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eInit_2eDatatypes_2efalse ).
fof('Coq.ZArith.BinInt.Z.odd_1',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.ZArith.BinInt.Z.odd_2',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eInit_2eDatatypes_2efalse ).
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.ones_spec_high',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)
& cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinInt_2eZ_2eones___24a1(V0__n),V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
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.pow2_bits_false',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_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n),V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ).
fof('Coq.ZArith.BinInt.Z.pow_neg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pred_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.shiftl_spec_low',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_2eBinInt_2eZ_2elt___24a2(V2__m,V1__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,V1__n),V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.succ_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.testbit_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.ZArith.BinInt.Z.testbit_even_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__a),cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.ZArith.BinInt.Z.testbit_neg_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.ZArith.BinInt.Z.testbit_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4622,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__55036,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eZArith_2eBinInt_2eZ_2eeq,c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool))),cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit) ).
fof('Coq.ZArith.Zbool.Zeq_bool_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> V0__x != V1__y ) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_is_eq_bool',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
<=> cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.ZArith.Zbool.Zone_min_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.ZArith.Zbool.Zone_pos',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eInit_2eDatatypes_2efalse ).
fof('Coq.ZArith.Zorder.Znot_ge_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.Zorder.dec_Zge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.auxiliary.Zle_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> 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.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__1405___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1405___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1405___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__2260___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__2260___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.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__1405___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1405___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1405___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__2260___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__2260___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.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.RMicromega.is_neg_false',axiom,
! [V0__z] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,V0__z)
=> ( cCoq_2emicromega_2eRMicromega_2eis__neg___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2emicromega_2eRMicromega_2ez__of__exp___24a1(V0__z),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.micromega.Refl.make_conj_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__495___24t(V0__A,V1__eval)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2))
<=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V2__l1)
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V3__l2) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__495___24t(V0__A,V1__eval)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l))
<=> ( p(happ(V1__eval,V2__a))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V3__l) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.not_make_conj_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__t)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__a)
=> ! [V3__eval] :
( c_24__type__495___24t(V0__A,V3__eval)
=> ( ! [V4__d] :
( t(V4__d,V0__A)
=> ( p(happ(V3__eval,V4__d))
| ~ p(happ(V3__eval,V4__d)) ) )
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__t,V2__a))
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V1__t)
| ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V2__a) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.not_make_conj_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__t] :
( t(V1__t,V0__A)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__a)
=> ! [V3__eval] :
( c_24__type__495___24t(V0__A,V3__eval)
=> ( ( p(happ(V3__eval,V1__t))
| ~ p(happ(V3__eval,V1__t)) )
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__t,V2__a))
=> ( ~ p(happ(V3__eval,V1__t))
| ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V2__a) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.SORcleb_morph',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__1405___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1405___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1405___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__2260___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__2428___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__2428___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__2428___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__2442___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__2449___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__2449___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__2178___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__2461___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__2470___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
=> ! [V23__x] :
( t(V23__x,V9__C)
=> ! [V24__y] :
( t(V24__y,V9__C)
=> ( happ(happ(V17__cleb,V23__x),V24__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V8__rle,happ(V18__phi,V23__x)),happ(V18__phi,V24__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.SORcneqb_morph',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__1405___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1405___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1405___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__2260___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__2428___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__2428___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__2428___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__2442___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__2449___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__2449___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__2178___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__2461___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__2470___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
=> ! [V23__x] :
( t(V23__x,V9__C)
=> ! [V24__y] :
( t(V24__y,V9__C)
=> ( happ(happ(V16__ceqb,V23__x),V24__y) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(V7__req,happ(V18__phi,V23__x)),happ(V18__phi,V24__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.SORpower',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__1405___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1405___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1405___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__2260___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__2428___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__2428___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__2428___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__2442___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__2449___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__2449___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__2178___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__2461___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__2470___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V2__rI,V4__rtimes,V7__req,V19__E,V20__pow__phi,V21__rpow) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.SORrm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1405___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1405___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1405___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__2260___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__2428___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__2428___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__2428___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__2442___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__2449___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__2449___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__2178___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__2461___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__2470___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V18__phi) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.mk_SOR_addon',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__1405___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1405___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1405___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__2260___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__2428___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__2428___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__2428___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__2442___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__2449___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__2449___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__2178___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__2461___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__2470___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V18__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V2__rI,V4__rtimes,V7__req,V19__E,V20__pow__phi,V21__rpow)
=> ( ! [V24__x] :
( t(V24__x,V9__C)
=> ! [V25__y] :
( t(V25__y,V9__C)
=> ( happ(happ(V16__ceqb,V24__x),V25__y) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(V7__req,happ(V18__phi,V24__x)),happ(V18__phi,V25__y))) ) ) )
=> ( ! [V25__x] :
( t(V25__x,V9__C)
=> ! [V26__y] :
( t(V26__y,V9__C)
=> ( happ(happ(V17__cleb,V25__x),V26__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V8__rle,happ(V18__phi,V25__x)),happ(V18__phi,V26__y))) ) ) )
=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Tauto.eval_cnf_app',axiom,
! [V0__Env] :
( cType___24t(V0__Env)
=> ! [V1__Term_27] :
( cType___24t(V1__Term_27)
=> ! [V2__Annot] :
( cType___24t(V2__Annot)
=> ! [V3__eval_27] :
( c_24__type__3598___24t(V0__Env,V1__Term_27,V3__eval_27)
=> ! [V4__env] :
( t(V4__env,V0__Env)
=> ! [V5__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eTauto_2eclause___24a2(V1__Term_27,V2__Annot),V5__x)
=> ! [V6__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eTauto_2eclause___24a2(V1__Term_27,V2__Annot),V6__y)
=> ( cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V1__Term_27,V2__Annot),V5__x,V6__y))
=> ( cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__x)
& cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V6__y) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZCoeff.Zcneqb_morph',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__1405___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1405___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1405___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__2260___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__2260___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V11__x)
=> ! [V12__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V12__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V11__x,V12__y) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(V7__req,cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a7(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V6__ropp,V11__x)),cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a7(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V6__ropp,V12__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZCoeff.clt_morph',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__1405___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1405___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1405___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__2260___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__2260___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V11__x)
=> ! [V12__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V12__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V11__x,V12__y)
=> p(happ(happ(V9__rlt,cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a7(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V6__ropp,V11__x)),cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a7(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V6__ropp,V12__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__x,V0__s))
<=> ( V1__x = V2__y
| cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,V0__s) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.empty_b',axiom,
! [V0__y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V0__y)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.empty_iff',axiom,
! [V0__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V0__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty)
<=> p(c_24False) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.filter_b',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ! [V2__f] :
( c_24__type__55427___24t(V2__f)
=> ( cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),V2__f)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter___24a2(V2__f,V0__s)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,V0__s),happ(V2__f,V1__x)) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.filter_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ! [V2__f] :
( c_24__type__55427___24t(V2__f)
=> ( cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),V2__f)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter___24a2(V2__f,V0__s))
<=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s)
& happ(V2__f,V1__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.mem_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,V0__s) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.not_mem_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,V0__s) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Equal_cardinal',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V0__s) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V1__s_27) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.remove_equal',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__x,V0__s),V0__s) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.subset_antisym',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V0__s,V1__s_27)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V1__s_27,V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.subset_equal',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V0__s,V1__s_27) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.add_cardinal_2',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,V0__s) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__x,V0__s)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V0__s)) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.add_filter_2',axiom,
! [V0__f] :
( c_24__type__55427___24t(V0__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__57030,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V0__f)
=> ! [V2__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__s)
=> ! [V3__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V3__s_27)
=> ! [V4__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V4__x)
=> ( happ(V0__f,V4__x) = cCoq_2eInit_2eDatatypes_2efalse
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd___24a3(V4__x,V2__s,V3__s_27)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter___24a2(V0__f,V2__s),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter___24a2(V0__f,V3__s_27)) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.empty_mem',axiom,
! [V0__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V0__x)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.equal_mem_2',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(V0__s,V1__s_27) = cCoq_2eInit_2eDatatypes_2etrue
=> ! [V3__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__a)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V3__a,V0__s) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V3__a,V1__s_27) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.exclusive_set',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)
=> ( ~ ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V0__s)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V1__s_27) )
<=> cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V2__x,V0__s),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V2__x,V1__s_27)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.exists_mem_1',axiom,
! [V0__f] :
( c_24__type__55427___24t(V0__f)
=> ( cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),V0__f)
=> ! [V2__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__s)
=> ( ! [V3__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V3__x,V2__s) = cCoq_2eInit_2eDatatypes_2etrue
=> happ(V0__f,V3__x) = cCoq_2eInit_2eDatatypes_2efalse ) )
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eexists_____24a2(V0__f,V2__s) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.exists_mem_2',axiom,
! [V0__f] :
( c_24__type__55427___24t(V0__f)
=> ( cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),V0__f)
=> ! [V2__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__s)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eexists_____24a2(V0__f,V2__s) = cCoq_2eInit_2eDatatypes_2efalse
=> ! [V4__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V4__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V4__x,V2__s) = cCoq_2eInit_2eDatatypes_2etrue
=> happ(V0__f,V4__x) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.filter_add_2',axiom,
! [V0__f] :
( c_24__type__55427___24t(V0__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__57030,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V0__f)
=> ! [V2__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__s)
=> ! [V3__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__x)
=> ( happ(V0__f,V3__x) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter___24a2(V0__f,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V3__x,V2__s)),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter___24a2(V0__f,V2__s)) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.fold_add',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__2260___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__f] :
( c_24__type__23841___24t(V0__A,V3__f)
=> ( cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(cCoq_2eNumbers_2eBinNums_2epositive,V0__A,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),V1__eqA,V3__f)
=> ( cCoq_2eLists_2eSetoidList_2etranspose___24a4(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V0__A,V1__eqA,V3__f)
=> ! [V6__i] :
( t(V6__i,V0__A)
=> ! [V7__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V7__s)
=> ! [V8__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V8__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V8__x,V7__s) = cCoq_2eInit_2eDatatypes_2efalse
=> p(happ(happ(V1__eqA,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold___24a4(V0__A,V3__f,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V8__x,V7__s),V6__i)),happ(happ(V3__f,V8__x),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold___24a4(V0__A,V3__f,V7__s,V6__i)))) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.for_all_exists',axiom,
! [V0__f] :
( c_24__type__55427___24t(V0__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__57030,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V0__f)
=> ! [V2__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eexists_____24a2(V0__f,V2__s) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efor__all___24a2(c_24__lam__57034___24a1(V0__f),V2__s)) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.for_all_filter',axiom,
! [V0__f] :
( c_24__type__55427___24t(V0__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__57030,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V0__f)
=> ! [V2__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efor__all___24a2(V0__f,V2__s) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter___24a2(c_24__lam__57034___24a1(V0__f),V2__s)) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.for_all_mem_1',axiom,
! [V0__f] :
( c_24__type__55427___24t(V0__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__57030,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V0__f)
=> ! [V2__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__s)
=> ( ! [V3__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V3__x,V2__s) = cCoq_2eInit_2eDatatypes_2etrue
=> happ(V0__f,V3__x) = cCoq_2eInit_2eDatatypes_2etrue ) )
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efor__all___24a2(V0__f,V2__s) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.for_all_mem_2',axiom,
! [V0__f] :
( c_24__type__55427___24t(V0__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__57030,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V0__f)
=> ! [V2__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__s)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efor__all___24a2(V0__f,V2__s) = cCoq_2eInit_2eDatatypes_2etrue
=> ! [V4__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V4__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V4__x,V2__s) = cCoq_2eInit_2eDatatypes_2etrue
=> happ(V0__f,V4__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.for_all_mem_3',axiom,
! [V0__f] :
( c_24__type__55427___24t(V0__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__57030,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V0__f)
=> ! [V2__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__s)
=> ! [V3__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V3__x,V2__s) = cCoq_2eInit_2eDatatypes_2etrue
=> ( happ(V0__f,V3__x) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efor__all___24a2(V0__f,V2__s) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.inter_add_2',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)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V2__x,V1__s_27) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V2__x,V0__s),V1__s_27),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(V0__s,V1__s_27)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.is_empty_equal_empty',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(V0__s) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(V0__s,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.mem_3',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,V0__s) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.mem_4',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,V0__s) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.remove_add',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,V0__s) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__x,V0__s)),V0__s) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.remove_cardinal_2',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,V0__s) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__x,V0__s)) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V0__s) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.remove_equal',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,V0__s) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__x,V0__s),V0__s) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.remove_mem_1',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__x,V0__s)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.singleton_mem_2',axiom,
! [V0__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__y)
=> ( V0__x != V1__y
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esingleton___24a1(V0__x)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.union_cardinal',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)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V2__x,V0__s),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V2__x,V1__s_27)) = cCoq_2eInit_2eDatatypes_2efalse )
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V0__s,V1__s_27)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V0__s),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V1__s_27)) ) ) ) ).
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.micromega.ZMicromega.le_xO',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2exO___24a1(V0__x)) ) ).
fof('Coq.micromega.ZMicromega.leb_xI_false',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(cCoq_2eNumbers_2eBinNums_2exI___24a1(V0__x),V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.micromega.ZMicromega.leb_xO_false',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(cCoq_2eNumbers_2eBinNums_2exO___24a1(V0__x),V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y)) ) ) ) ) ).
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__11719___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__11719___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_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__11719___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__11719___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.intro_Z',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = V1__y
& cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1405___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2412___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__2260___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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1405___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2412___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__2260___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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1405___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2412___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__2260___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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1405___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2412___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__2260___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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1405___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__2412___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__2260___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.if_true',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454376___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__a = cCoq_2eInit_2eDatatypes_2etrue
& V1__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1405___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1405___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2412___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__2260___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__1405___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2412___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.Ztriv_div_th',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__2260___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> ! [V3__zphi] :
( c_24__type__8479___24t(V0__R,V3__zphi)
=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V0__R,V1__req,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V3__zphi,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.triv_div_th',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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__2428___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__2428___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__2428___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__2442___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__2449___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2178___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_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)
=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V0__R,V7__req,V8__C,V11__cadd,V12__cmul,V16__phi,cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a4(V8__C,V9__cO,V10__cI,V15__ceqb)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring.BoolTheory',axiom,
cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2exorb,cCoq_2eInit_2eDatatypes_2eandb,cCoq_2eInit_2eDatatypes_2exorb,c_24__lam__42454,c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)) ).
fof('Coq.setoid_ring.Ring.bool_eq_ok',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue
=> V0__b1 = V1__b2 ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARdistr_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ! [V13__z] :
( t(V13__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__z),happ(happ(V3__radd,V11__x),V12__y))),happ(happ(V3__radd,happ(happ(V4__rmul,V13__z),V11__x)),happ(happ(V4__rmul,V13__z),V12__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V9__x),V10__y))),happ(happ(V4__rmul,happ(V6__ropp,V9__x)),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_zero',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> p(happ(happ(V7__req,happ(V6__ropp,V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARsub_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1405___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1405___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2412___24t(V0__R,V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).
fof('Coq.setoid_ring.Ring_theory.IDmorph',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__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ! [V9__reqb] :
( c_24__type__6978___24t(V0__R,V9__reqb)
=> ( ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ( happ(happ(V9__reqb,V10__x),V11__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V7__req,V10__x),V11__y)) ) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__reqb,cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(V0__R)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Rth_ARth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.get_sign_None_th',axiom,
! [V0__C] :
( cType___24t(V0__C)
=> ! [V1__copp] :
( c_24__type__2412___24t(V0__C,V1__copp)
=> ! [V2__ceqb] :
( c_24__type__6978___24t(V0__C,V2__ceqb)
=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V0__C,V1__copp,V2__ceqb,cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a1(V0__C)) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_reqe',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1405___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1405___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__2412___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__2260___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1405___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2412___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1405___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__2412___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2412___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__2428___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__2428___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__2428___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__2442___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__2449___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2178___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V9__cO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__2428___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__2428___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__2428___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__2442___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__2449___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2178___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_add',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__2428___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__2428___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__2428___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__2442___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__2449___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2178___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V11__cadd,V18__x),V19__y))),happ(happ(V3__radd,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_eq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__2428___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__2428___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__2428___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__2442___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__2449___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2178___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> ( happ(happ(V15__ceqb,V18__x),V19__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V7__req,happ(V16__phi,V18__x)),happ(V16__phi,V19__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_mul',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__2428___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__2428___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__2428___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__2442___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__2449___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2178___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V12__cmul,V18__x),V19__y))),happ(happ(V4__rmul,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_opp',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__2428___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__2428___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__2428___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__2442___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__2449___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2178___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(V14__copp,V18__x))),happ(V6__ropp,happ(V16__phi,V18__x)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_sub',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1405___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1405___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1405___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__2412___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__2260___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__2428___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__2428___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__2428___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__2442___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__2449___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__2178___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V13__csub,V18__x),V19__y))),happ(happ(V5__rsub,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('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__1405___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__2260___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__21995___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__8825___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('IntMap.Fset.MapDom_semantics_1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__y)
=> cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eMapDom___24a2(V0__A,V1__m)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ).
fof('IntMap.Fset.MapDom_semantics_3',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
=> cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eMapDom___24a2(V0__A,V1__m)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('IntMap.Fset.MapDom_semantics_4',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> ( cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eMapDom___24a2(V0__A,V1__m)) = cCoq_2eInit_2eDatatypes_2efalse
=> cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ).
fof('IntMap.Fset.in_dom_M0',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( cIntMap_2eMap_2ead___24t(V1__a)
=> cIntMap_2eFset_2ein__dom___24a3(V0__A,V1__a,cIntMap_2eMap_2eM0___24a1(V0__A)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('IntMap.Fset.in_dom_M1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( cIntMap_2eMap_2ead___24t(V1__a)
=> ! [V2__a0] :
( cIntMap_2eMap_2ead___24t(V2__a0)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> cIntMap_2eFset_2ein__dom___24a3(V0__A,V2__a0,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V3__y)) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__a,V2__a0) ) ) ) ) ).
fof('IntMap.Fset.in_dom_M1_1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( cIntMap_2eMap_2ead___24t(V1__a)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> cIntMap_2eFset_2ein__dom___24a3(V0__A,V1__a,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('IntMap.Fset.in_dom_M1_2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( cIntMap_2eMap_2ead___24t(V1__a)
=> ! [V2__a0] :
( cIntMap_2eMap_2ead___24t(V2__a0)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V2__a0,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V3__y)) = cCoq_2eInit_2eDatatypes_2etrue
=> V1__a = V2__a0 ) ) ) ) ) ).
fof('IntMap.Fset.in_dom_merge',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__m_27] :
( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
=> ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V1__m),cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V2__m_27)) ) ) ) ) ).
fof('IntMap.Fset.in_dom_none',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V2__a,V1__m) = cCoq_2eInit_2eDatatypes_2efalse
=> cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ).
fof('IntMap.Fset.in_dom_put',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__a0] :
( cIntMap_2eMap_2ead___24t(V2__a0)
=> ! [V3__y0] :
( t(V3__y0,V0__A)
=> ! [V4__a] :
( cIntMap_2eMap_2ead___24t(V4__a)
=> cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a0,V3__y0)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V4__a,V2__a0),cIntMap_2eFset_2ein__dom___24a3(V0__A,V4__a,V1__m)) ) ) ) ) ) ).
fof('IntMap.Map.M1_semantics_2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( cIntMap_2eMap_2ead___24t(V1__a)
=> ! [V2__a_27] :
( cIntMap_2eMap_2ead___24t(V2__a_27)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__a,V2__a_27) = cCoq_2eInit_2eDatatypes_2efalse
=> cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V3__y),V2__a_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ) ).
fof('IntMap.Map.MapGet_M2_bit_0_0',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( cIntMap_2eMap_2ead___24t(V1__a)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a) = cCoq_2eInit_2eDatatypes_2efalse
=> ! [V3__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
=> ! [V4__m_27] :
( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_27)
=> cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V3__m,V4__m_27),V1__a) = cIntMap_2eMap_2eMapGet___24a3(V0__A,V3__m,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a)) ) ) ) ) ) ).
fof('IntMap.Map.MapGet_M2_bit_0_1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( cIntMap_2eMap_2ead___24t(V1__a)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a) = cCoq_2eInit_2eDatatypes_2etrue
=> ! [V3__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
=> ! [V4__m_27] :
( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_27)
=> cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V3__m,V4__m_27),V1__a) = cIntMap_2eMap_2eMapGet___24a3(V0__A,V4__m_27,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a)) ) ) ) ) ) ).
fof('IntMap.Map.MapGet_M2_bit_0_2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__m_27] :
( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
=> ! [V3__m_27_27] :
( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27_27)
=> ! [V4__a] :
( cIntMap_2eMap_2ead___24t(V4__a)
=> cIntMap_2eMap_2eMapGet___24a3(V0__A,c_24__case__Coq_2eInit_2eDatatypes_2ebool_249553___24a5(V0__A,V1__m,V2__m_27,V3__m_27_27,V4__a),V4__a) = cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m_27,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a)) ) ) ) ) ) ).
fof('IntMap.Map.MapGet_M2_bit_0_if',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__m_27] :
( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
=> ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27),V3__a) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249505___24a4(V0__A,V1__m,V2__m_27,V3__a) ) ) ) ) ).
fof('IntMap.Map.MapPut1_semantics_3',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> ! [V3__a_27] :
( cIntMap_2eMap_2ead___24t(V3__a_27)
=> ! [V4__a0] :
( cIntMap_2eMap_2ead___24t(V4__a0)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__y_27] :
( t(V6__y_27,V0__A)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V2__a,V3__a_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V1__p)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V2__a,V4__a0) = cCoq_2eInit_2eDatatypes_2efalse
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V3__a_27,V4__a0) = cCoq_2eInit_2eDatatypes_2efalse
=> cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V5__y,V3__a_27,V6__y_27,V1__p),V4__a0) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ) ) ) ) ) ) ).
fof('IntMap.Map.MapPut_behind_as_before',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__a0] :
( cIntMap_2eMap_2ead___24t(V4__a0)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V2__a,V4__a0) = cCoq_2eInit_2eDatatypes_2efalse
=> cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y),V4__a0) = cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a,V3__y),V4__a0) ) ) ) ) ) ) ).
fof('IntMap.Map.MapPut_behind_as_before_1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( cIntMap_2eMap_2ead___24t(V1__a)
=> ! [V2__a_27] :
( cIntMap_2eMap_2ead___24t(V2__a_27)
=> ! [V3__a0] :
( cIntMap_2eMap_2ead___24t(V3__a0)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V2__a_27,V3__a0) = cCoq_2eInit_2eDatatypes_2efalse
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__y_27] :
( t(V6__y_27,V0__A)
=> cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V5__y),V2__a_27,V6__y_27),V3__a0) = cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V5__y),V2__a_27,V6__y_27),V3__a0) ) ) ) ) ) ) ) ).
fof('IntMap.Map.MapPut_behind_semantics_3_1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__m_27] :
( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
=> ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27),V3__a,V4__y) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249641___24a5(V0__A,V1__m,V2__m_27,V3__a,V4__y) ) ) ) ) ) ).
fof('IntMap.Map.MapPut_semantics_3_1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__m_27] :
( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
=> ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> cIntMap_2eMap_2eMapPut___24a4(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27),V3__a,V4__y) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249625___24a5(V0__A,V1__m,V2__m_27,V3__a,V4__y) ) ) ) ) ) ).
fof('IntMap.Map.Map_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__142___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cIntMap_2eMap_2eM0___24a1(V0__A)))
=> ( ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> p(happ(V1__P,cIntMap_2eMap_2eM1___24a3(V0__A,V3__a,V4__a))) ) )
=> ( ! [V4__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V4__m)
=> ( p(happ(V1__P,V4__m))
=> ! [V6__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V6__m)
=> ( p(happ(V1__P,V6__m))
=> p(happ(V1__P,cIntMap_2eMap_2eM2___24a3(V0__A,V4__m,V6__m))) ) ) ) )
=> ! [V5__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V5__m)
=> p(happ(V1__P,V5__m)) ) ) ) ) ) ) ).
fof('IntMap.Mapc.FSetUnion_assoc_c',axiom,
! [V0__s] :
( cIntMap_2eFset_2eFSet___24t(V0__s)
=> ! [V1__s_27] :
( cIntMap_2eFset_2eFSet___24t(V1__s_27)
=> ! [V2__s_27_27] :
( cIntMap_2eFset_2eFSet___24t(V2__s_27_27)
=> ( cIntMap_2eMapcanon_2emapcanon___24a2(cCoq_2eInit_2eDatatypes_2eunit,V0__s)
=> ( cIntMap_2eMapcanon_2emapcanon___24a2(cCoq_2eInit_2eDatatypes_2eunit,V1__s_27)
=> ( cIntMap_2eMapcanon_2emapcanon___24a2(cCoq_2eInit_2eDatatypes_2eunit,V2__s_27_27)
=> cIntMap_2eFset_2eFSetUnion___24a2(cIntMap_2eFset_2eFSetUnion___24a2(V0__s,V1__s_27),V2__s_27_27) = cIntMap_2eFset_2eFSetUnion___24a2(V0__s,cIntMap_2eFset_2eFSetUnion___24a2(V1__s_27,V2__s_27_27)) ) ) ) ) ) ) ).
fof('IntMap.Mapc.FSetUnion_comm_c',axiom,
! [V0__s] :
( cIntMap_2eFset_2eFSet___24t(V0__s)
=> ! [V1__s_27] :
( cIntMap_2eFset_2eFSet___24t(V1__s_27)
=> ( cIntMap_2eMapcanon_2emapcanon___24a2(cCoq_2eInit_2eDatatypes_2eunit,V0__s)
=> ( cIntMap_2eMapcanon_2emapcanon___24a2(cCoq_2eInit_2eDatatypes_2eunit,V1__s_27)
=> cIntMap_2eFset_2eFSetUnion___24a2(V0__s,V1__s_27) = cIntMap_2eFset_2eFSetUnion___24a2(V1__s_27,V0__s) ) ) ) ) ).
fof('IntMap.Mapc.MapPut_as_Merge_c',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m)
=> ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V3__a,V4__y) = cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,cIntMap_2eMap_2eM1___24a3(V0__A,V3__a,V4__y)) ) ) ) ) ) ).
fof('IntMap.Mapcanon.M0_canon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eM0___24a1(V0__A)) ) ).
fof('IntMap.Mapcanon.M1_canon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( cIntMap_2eMap_2ead___24t(V1__a)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y)) ) ) ) ).
fof('IntMap.Mapcanon.MapPut_canon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ( cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,V1__m)
=> ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> cIntMap_2eMapcanon_2emapcanon___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V3__a,V4__y)) ) ) ) ) ) ).
fof('IntMap.Mapcard.MapCard_Put_1_conv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__y_27] :
( t(V4__y_27,V0__A)
=> ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__y)
=> cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V4__y_27)) = cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m) ) ) ) ) ) ) ).
fof('IntMap.Mapcard.MapCard_Put_2_conv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
=> cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m)) ) ) ) ) ) ).
fof('IntMap.Mapcard.MapCard_Put_ub',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> cCoq_2eInit_2ePeano_2ele___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y)),cCoq_2eInit_2eDatatypes_2eS___24a1(cIntMap_2eMap_2eMapCard___24a2(V0__A,V1__m))) ) ) ) ) ).
fof('IntMap.Mapfold.MapFold_distr_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__M] :
( cType___24t(V1__M)
=> ! [V2__neutral] :
( t(V2__neutral,V1__M)
=> ! [V3__op] :
( c_24__type__1405___24t(V1__M,V3__op)
=> ! [V4__M_27] :
( cType___24t(V4__M_27)
=> ! [V5__neutral_27] :
( t(V5__neutral_27,V4__M_27)
=> ! [V6__op_27] :
( c_24__type__2428___24t(V1__M,V4__M_27,V6__op_27)
=> ! [V7__N] :
( cType___24t(V7__N)
=> ! [V8__times] :
( c_24__type__10391___24t(V1__M,V4__M_27,V7__N,V8__times)
=> ( ! [V9__c] :
( t(V9__c,V7__N)
=> happ(happ(V8__times,V9__c),V2__neutral) = V5__neutral_27 )
=> ( ! [V10__a] :
( t(V10__a,V1__M)
=> ! [V11__b] :
( t(V11__b,V1__M)
=> ! [V12__c] :
( t(V12__c,V7__N)
=> happ(happ(V8__times,V12__c),happ(happ(V3__op,V10__a),V11__b)) = happ(happ(V6__op_27,happ(happ(V8__times,V12__c),V10__a)),happ(happ(V8__times,V12__c),V11__b)) ) ) )
=> ! [V11__f] :
( c_24__type__10272___24t(V0__A,V1__M,V4__M_27,V7__N,V11__f)
=> ! [V12__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V12__m)
=> ! [V13__c] :
( t(V13__c,V7__N)
=> happ(happ(V8__times,V13__c),cIntMap_2eMapiter_2eMapFold___24a6(V0__A,V1__M,V2__neutral,V3__op,V11__f,V12__m)) = cIntMap_2eMapiter_2eMapFold___24a6(V0__A,V4__M_27,V5__neutral_27,V6__op_27,c_24__lam__10439___24a7(V0__A,V1__M,V4__M_27,V7__N,V8__times,V11__f,V13__c),V12__m) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('IntMap.Mapiter.MapSweep_semantics_3',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__10443___24t(V0__A,V1__f)
=> ! [V2__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ( cIntMap_2eMapiter_2eMapSweep___24a3(V0__A,V1__f,V2__m) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
=> ! [V4__a] :
( cIntMap_2eMap_2ead___24t(V4__a)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m,V4__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V5__y)
=> happ(happ(V1__f,V4__a),V5__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('IntMap.Mapiter.MapSweep_semantics_3_1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__10443___24t(V0__A,V1__f)
=> ! [V2__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ! [V3__pf] :
( c_24__type__9263___24t(V0__A,V3__pf)
=> ( cIntMap_2eMapiter_2eMapSweep1___24a4(V0__A,V1__f,V3__pf,V2__m) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,V0__A))
=> ! [V5__a] :
( cIntMap_2eMap_2ead___24t(V5__a)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m,V5__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V6__y)
=> happ(happ(V1__f,happ(V3__pf,V5__a)),V6__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ).
fof('IntMap.Mapsubset.MapDisjoint_M1_conv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse
=> cIntMap_2eMapsubset_2eMapDisjoint___24a4(V1__B,V0__A,cIntMap_2eMap_2eM1___24a3(V1__B,V3__a,V4__y),V2__m) ) ) ) ) ) ) ).
fof('IntMap.Mapsubset.MapDisjoint_M1_conv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse
=> cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM1___24a3(V1__B,V3__a,V4__y)) ) ) ) ) ) ) ).
fof('IntMap.Mapsubset.MapDisjoint_M1_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V1__B,V0__A,cIntMap_2eMap_2eM1___24a3(V1__B,V3__a,V4__y),V2__m)
=> cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('IntMap.Mapsubset.MapDisjoint_M1_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
=> ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ( cIntMap_2eMapsubset_2eMapDisjoint___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM1___24a3(V1__B,V3__a,V4__y))
=> cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('IntMap.Mapsubset.map_dom_empty_1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A))
=> ! [V3__a] :
( cIntMap_2eMap_2ead___24t(V3__a)
=> cIntMap_2eFset_2ein__dom___24a3(V0__A,V3__a,V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('IntMap.Mapsubset.map_dom_empty_2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
=> ( ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> cIntMap_2eFset_2ein__dom___24a3(V0__A,V2__a,V1__m) = cCoq_2eInit_2eDatatypes_2efalse )
=> cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,cIntMap_2eMap_2eM0___24a1(V0__A)) ) ) ) ).
fof('Maplists.MapLists.Elems_app',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> ! [V1__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V1__l_27)
=> cMaplists_2eMapLists_2eElems___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead,V0__l,V1__l_27)) = cIntMap_2eFset_2eFSetUnion___24a2(cMaplists_2eMapLists_2eElems___24a1(V0__l),cMaplists_2eMapLists_2eElems___24a1(V1__l_27)) ) ) ).
fof('Maplists.MapLists.Elems_canon',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> cIntMap_2eMapcanon_2emapcanon___24a2(cCoq_2eInit_2eDatatypes_2eunit,cMaplists_2eMapLists_2eElems___24a1(V0__l)) ) ).
fof('Maplists.MapLists.Elems_rev',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> cMaplists_2eMapLists_2eElems___24a1(cCoq_2eLists_2eList_2erev___24a2(cIntMap_2eMap_2ead,V0__l)) = cMaplists_2eMapLists_2eElems___24a1(V0__l) ) ).
fof('Maplists.MapLists.ad_in_elems_in_list',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> ! [V1__a] :
( cIntMap_2eMap_2ead___24t(V1__a)
=> cIntMap_2eFset_2ein__FSet___24a2(V1__a,cMaplists_2eMapLists_2eElems___24a1(V0__l)) = cMaplists_2eMapLists_2ead__in__list___24a2(V1__a,V0__l) ) ) ).
fof('Maplists.MapLists.ad_in_list_l',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> ! [V1__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V1__l_27)
=> ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> ( cMaplists_2eMapLists_2ead__in__list___24a2(V2__a,V0__l) = cCoq_2eInit_2eDatatypes_2etrue
=> cMaplists_2eMapLists_2ead__in__list___24a2(V2__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead,V0__l,V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Maplists.MapLists.ad_in_list_r',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> ! [V1__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V1__l_27)
=> ! [V2__a] :
( cIntMap_2eMap_2ead___24t(V2__a)
=> ( cMaplists_2eMapLists_2ead__in__list___24a2(V2__a,V1__l_27) = cCoq_2eInit_2eDatatypes_2etrue
=> cMaplists_2eMapLists_2ead__in__list___24a2(V2__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead,V0__l,V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Maplists.MapLists.ad_list_card',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> cCoq_2eInit_2ePeano_2ele___24a2(cIntMap_2eMap_2eMapCard___24a2(cCoq_2eInit_2eDatatypes_2eunit,cMaplists_2eMapLists_2eElems___24a1(V0__l)),cCoq_2eInit_2eDatatypes_2elength___24a2(cIntMap_2eMap_2ead,V0__l)) ) ).
fof('Maplists.MapLists.ad_list_not_stutters_card',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> ( cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cIntMap_2eMap_2ead,V0__l) = cIntMap_2eMap_2eMapCard___24a2(cCoq_2eInit_2eDatatypes_2eunit,cMaplists_2eMapLists_2eElems___24a1(V0__l)) ) ) ).
fof('Maplists.MapLists.ad_list_not_stutters_card_conv',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(cIntMap_2eMap_2ead,V0__l) = cIntMap_2eMap_2eMapCard___24a2(cCoq_2eInit_2eDatatypes_2eunit,cMaplists_2eMapLists_2eElems___24a1(V0__l))
=> cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Maplists.MapLists.ad_list_stutters_app_l',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> ! [V1__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V1__l_27)
=> ( cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue
=> cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead,V0__l,V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Maplists.MapLists.ad_list_stutters_app_r',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> ! [V1__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V1__l_27)
=> ( cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l_27) = cCoq_2eInit_2eDatatypes_2etrue
=> cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead,V0__l,V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Maplists.MapLists.ad_list_stutters_card',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> ( cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eInit_2ePeano_2elt___24a2(cIntMap_2eMap_2eMapCard___24a2(cCoq_2eInit_2eDatatypes_2eunit,cMaplists_2eMapLists_2eElems___24a1(V0__l)),cCoq_2eInit_2eDatatypes_2elength___24a2(cIntMap_2eMap_2ead,V0__l)) ) ) ).
fof('Maplists.MapLists.ad_list_stutters_card_conv',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(cIntMap_2eMap_2eMapCard___24a2(cCoq_2eInit_2eDatatypes_2eunit,cMaplists_2eMapLists_2eElems___24a1(V0__l)),cCoq_2eInit_2eDatatypes_2elength___24a2(cIntMap_2eMap_2ead,V0__l))
=> cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$adef_IntMap.Map.M0_$a1',axiom,
! [V_24X1] : happ(cIntMap_2eMap_2eM0,V_24X1) = cIntMap_2eMap_2eM0___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.xfold_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_237_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__237,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__237___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.FSets.FSetPositive.PositiveSet.omap_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eomap,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eomap___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.orb_true_elim_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eorb__true__elim,V_24X1) = cCoq_2eBool_2eBool_2eorb__true__elim___24a1(V_24X1) ).
fof('$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_$_lam_316_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__316,V_24X1),V_24X2),V_24X3) = c_24__lam__316___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_$_prop_717_$a1',axiom,
! [V_24X1] : happ(c_24__prop__717,V_24X1) = c_24__prop__717___24a1(V_24X1) ).
fof('$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_$_prop_55692_$a1',axiom,
! [V_24X1] : happ(c_24__prop__55692,V_24X1) = c_24__prop__55692___24a1(V_24X1) ).
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('$adef_Coq.FSets.FSetPositive.PositiveSet.filter_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_14600_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__14600,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__14600___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1243_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1243,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1243___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.rev_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.bool_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2ebool__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2ebool__rect___24a1(V_24X1) ).
fof('$adef_$_lam_56864_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__56864,V_24X1),V_24X2) = c_24__lam__56864___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mk_monpol_list_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Init.Specif.sig_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEequiv_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_55196_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__55196,V_24X1),V_24X2) = c_24__lam__55196___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_55693_$a1',axiom,
! [V_24X1] : happ(c_24__prop__55693,V_24X1) = c_24__prop__55693___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.get_sign_None_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_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_Coq.FSets.FSetPositive.PositiveSet.inter_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.eval_tt_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__tt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eeval__tt___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_1709_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__1709,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__1709___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.List.partition_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2epartition,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2epartition___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$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('$adef_Maplists.MapLists.ad_list_stutters_$a1',axiom,
! [V_24X1] : happ(cMaplists_2eMapLists_2ead__list__stutters,V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1) ).
fof('$adef_$_lam_55110_$a1',axiom,
! [V_24X1] : happ(c_24__lam__55110,V_24X1) = c_24__lam__55110___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.log2_iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2elog2__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2elog2__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.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_$_lam_57034_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__57034,V_24X1),V_24X2) = c_24__lam__57034___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_18_mkmult_pow_17047_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__17047,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__17047___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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_$_lam_10604_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__10604,V_24X1),V_24X2),V_24X3) = c_24__lam__10604___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_IntMap.Mapsubset.MapSubset_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cIntMap_2eMapsubset_2eMapSubset,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cIntMap_2eMapsubset_2eMapSubset___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_$_lam_55651_$a1',axiom,
! [V_24X1] : happ(c_24__lam__55651,V_24X1) = c_24__lam__55651___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.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.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_$_lam_1243_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1243,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1243___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_cast_55652_$a1',axiom,
! [V_24X1] : happ(c_24__cast__55652,V_24X1) = c_24__cast__55652___24a1(V_24X1) ).
fof('$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.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_IntMap.Map.MapPut_behind_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapPut__behind,V_24X1),V_24X2) = cIntMap_2eMap_2eMapPut__behind___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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_$_let_17_mkopp_pow_17046_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__17046,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__17046___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
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_55667_$a1',axiom,
! [V_24X1] : happ(c_24__lam__55667,V_24X1) = c_24__lam__55667___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.StrictOrder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eStrictOrder,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_57058_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__57058,V_24X1),V_24X2) = c_24__lam__57058___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkpow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkpow,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2emkpow___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Map.MapPut_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapPut,V_24X1),V_24X2) = cIntMap_2eMap_2eMapPut___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.subset_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esubset,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esubset___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_16_mkpow_17045_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__17045,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__17045___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.xfilter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfilter,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfilter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_IntMap.Mapiter.MapSweep2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMapiter_2eMapSweep2,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMapiter_2eMapSweep2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.existsb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eexistsb,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eexistsb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.Ndigits.Nless_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eNdigits_2eNless,V_24X1),V_24X2) = cCoq_2eNArith_2eNdigits_2eNless___24a2(V_24X1,V_24X2) ).
fof('$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_$_cast_55541_$a1',axiom,
! [V_24X1] : happ(c_24__cast__55541,V_24X1) = c_24__cast__55541___24a1(V_24X1) ).
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('$adef_Coq.Lists.List.hd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2ehd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.cardinal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_57058_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__57058,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__57058___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_let_var_8_m_965_968_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__var__8__m__965__968,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__var__8__m__965__968___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_$_let_17_mkopp_pow_17046_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__17046,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__17046___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.forallb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eforallb,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eforallb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_316_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__316,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__316___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$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('$adef_Coq.FSets.FSetPositive.PositiveSet.xforall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exforall,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exforall___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1351_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1351,V_24X1),V_24X2),V_24X3) = c_24__lam__1351___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_$_lam_55207_$a1',axiom,
! [V_24X1] : happ(c_24__lam__55207,V_24X1) = c_24__lam__55207___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_$_prop_56997_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__56997,V_24X1),V_24X2) = c_24__prop__56997___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2eb2n,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.bool_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2ebool__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2ebool__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_1753_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__1753,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__1753___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_11311_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__11311,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__11311___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_10627_$a1',axiom,
! [V_24X1] : happ(c_24__lam__10627,V_24X1) = c_24__lam__10627___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.split_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esplit,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.xexists_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exexists,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exexists___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNat.N.ones_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2eones,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2eones___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a1(V_24X1) ).
fof('$adef_$_lam_764_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__764,V_24X1),V_24X2) = c_24__lam__764___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.eval_cnf_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__cnf,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.interp_PElist_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.Init.Specif.sigT_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Maplists.MapLists.Elems_$a1',axiom,
! [V_24X1] : happ(cMaplists_2eMapLists_2eElems,V_24X1) = cMaplists_2eMapLists_2eElems___24a1(V_24X1) ).
fof('$adef_$_cast_55706_$a1',axiom,
! [V_24X1] : happ(c_24__cast__55706,V_24X1) = c_24__cast__55706___24a1(V_24X1) ).
fof('$adef_$_let_18_mkmult_pow_17047_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__17047,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__17047___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Bool.Zerob.zerob_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eZerob_2ezerob,V_24X1) = cCoq_2eBool_2eZerob_2ezerob___24a1(V_24X1) ).
fof('$adef_$_lam_56752_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__56752,V_24X1),V_24X2),V_24X3) = c_24__lam__56752___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_IntMap.Map.M1_$a1',axiom,
! [V_24X1] : happ(cIntMap_2eMap_2eM1,V_24X1) = cIntMap_2eMap_2eM1___24a1(V_24X1) ).
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('$adef_$_case_Coq.Init.Datatypes.bool$59771_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459771,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459771___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Nat.shiftl_$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('$adef_$_case_Coq.Init.Datatypes.bool$59775_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459775,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2459775___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_754_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__754,V_24X1),V_24X2) = c_24__lam__754___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$9553_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_249553,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249553___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_59706_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__59706,V_24X1),V_24X2) = c_24__prop__59706___24a2(V_24X1,V_24X2) ).
fof('$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.Init.Logic.and_rec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eand__rec,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eLogic_2eand__rec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.RingMicromega.cltb_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecltb,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2ecltb___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_IntMap.Mapiter.aapp_$a1',axiom,
! [V_24X1] : happ(cIntMap_2eMapiter_2eaapp,V_24X1) = cIntMap_2eMapiter_2eaapp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring.bool_eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing_2ebool__eq,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.b2z_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2eb2z,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.Forall2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eList_2eForall2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Map.M1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eM1,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eM1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$9505_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_249505,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249505___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__left,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_6_p_17619_17622_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__17619__17622,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__17619__17622___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RMicromega.z_of_exp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2ez__of__exp,V_24X1) = cCoq_2emicromega_2eRMicromega_2ez__of__exp___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.list_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rec,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_23725_$a1',axiom,
! [V_24X1] : happ(c_24__prop__23725,V_24X1) = c_24__prop__23725___24a1(V_24X1) ).
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('$adef_Coq.micromega.Tauto.cnf_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf___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('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$53998_$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_2453998,V_24X1),V_24X2),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_2453998___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('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_200_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__200,V_24X1),V_24X2),V_24X3) = c_24__lam__200___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_IntMap.Map.MapPut1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cIntMap_2eMap_2eMapPut1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cIntMap_2eMap_2eMapPut1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Bool.Sumbool.bool_eq_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eSumbool_2ebool__eq__rec,V_24X1) = cCoq_2eBool_2eSumbool_2ebool__eq__rec___24a1(V_24X1) ).
fof('$adef_$_cast_325_$a1',axiom,
! [V_24X1] : happ(c_24__cast__325,V_24X1) = c_24__cast__325___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_777_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__777,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__777___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_$_lam_56745_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__56745,V_24X1),V_24X2),V_24X3) = c_24__lam__56745___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_54441_$a1',axiom,
! [V_24X1] : happ(c_24__lam__54441,V_24X1) = c_24__lam__54441___24a1(V_24X1) ).
fof('$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_Coq.FSets.FSetPositive.PositiveSet.for_all_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efor__all,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efor__all___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_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.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2elog2,V_24X1) = cCoq_2eInit_2eNat_2elog2___24a1(V_24X1) ).
fof('$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.NArith.Ndec.Nleb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eNdec_2eNleb,V_24X1),V_24X2) = cCoq_2eNArith_2eNdec_2eNleb___24a2(V_24X1,V_24X2) ).
fof('$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_$_case_Coq.Init.Datatypes.list$29024_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2429024,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2429024___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_$_cast_55691_$a1',axiom,
! [V_24X1] : happ(c_24__cast__55691,V_24X1) = c_24__cast__55691___24a1(V_24X1) ).
fof('$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_$_case_Coq.Init.Datatypes.bool$975_$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_24975,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24975___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_10604_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__10604,V_24X1),V_24X2) = c_24__lam__10604___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.ForallOrdPairs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallOrdPairs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.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_$_prop_333_$a1',axiom,
! [V_24X1] : happ(c_24__prop__333,V_24X1) = c_24__prop__333___24a1(V_24X1) ).
fof('$adef_$_prop_55553_$a1',axiom,
! [V_24X1] : happ(c_24__prop__55553,V_24X1) = c_24__prop__55553___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_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.NArith.BinNatDef.N.shiftl_nat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl__nat,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eshiftl__nat___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_772_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__772,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__772___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_11311_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__11311,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__11311___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.NArith.BinNatDef.N.size_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esize__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esize__nat___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Logic.eq_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eeq__refl,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.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.Lists.List.rev_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2erev,V_24X1),V_24X2) = cCoq_2eLists_2eList_2erev___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sig_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_55728_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__55728,V_24X1),V_24X2) = c_24__prop__55728___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$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('$adef_$_case_Coq.Init.Datatypes.bool$54376_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454376,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454376___24a2(V_24X1,V_24X2) ).
fof('$adef_$_cast_55544_$a1',axiom,
! [V_24X1] : happ(c_24__cast__55544,V_24X1) = c_24__cast__55544___24a1(V_24X1) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.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_$_lam_1709_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1709,V_24X1),V_24X2),V_24X3) = c_24__lam__1709___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_1211_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1211,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1211___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_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.micromega.ZMicromega.RatProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_IntMap.Mapiter.MapFold_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cIntMap_2eMapiter_2eMapFold,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cIntMap_2eMapiter_2eMapFold___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Nat.lor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2elor,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2elor___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_388_$a1',axiom,
! [V_24X1] : happ(c_24__lam__388,V_24X1) = c_24__lam__388___24a1(V_24X1) ).
fof('$adef_$_prop_55120_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__55120,V_24X1),V_24X2) = c_24__prop__55120___24a2(V_24X1,V_24X2) ).
fof('$adef_Maplists.MapLists.ad_in_list_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cMaplists_2eMapLists_2ead__in__list,V_24X1),V_24X2) = cMaplists_2eMapLists_2ead__in__list___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Map.M2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eM2,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eM2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_$_lam_1783_$a1',axiom,
! [V_24X1] : happ(c_24__lam__1783,V_24X1) = c_24__lam__1783___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$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('$adef_$_fix_23737_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__23737__1__add__carry,V_24X1),V_24X2) = c_24__fix__23737__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_avoid_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_Coq.Init.Nat.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emodulo,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_23724_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__23724,V_24X1),V_24X2))
<=> c_24__lam__23724___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('$adef_$_case_Coq.Init.Datatypes.bool$54125_$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_2454125,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454125___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
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('$adef_Coq.Bool.Sumbool.sumbool_of_bool_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eSumbool_2esumbool__of__bool,V_24X1) = cCoq_2eBool_2eSumbool_2esumbool__of__bool___24a1(V_24X1) ).
fof('$adef_IntMap.Mapiter.alist_semantics_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMapiter_2ealist__semantics,V_24X1),V_24X2) = cIntMap_2eMapiter_2ealist__semantics___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.land_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eland,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_$_prop_55546_$a1',axiom,
! [V_24X1] : happ(c_24__prop__55546,V_24X1) = c_24__prop__55546___24a1(V_24X1) ).
fof('$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_$_lam_1753_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1753,V_24X1),V_24X2) = c_24__lam__1753___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_57034_$a1',axiom,
! [V_24X1] : happ(c_24__lam__57034,V_24X1) = c_24__lam__57034___24a1(V_24X1) ).
fof('$adef_$_lam_10439_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__10439,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__10439___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.QArith.QArith_base.Qdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQdiv,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$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('$adef_$_prop_326_$a1',axiom,
! [V_24X1] : happ(c_24__prop__326,V_24X1) = c_24__prop__326___24a1(V_24X1) ).
fof('$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.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.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.Init.Datatypes.sum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEeval_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.InitialRing.triv_div_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2etriv__div,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
fof('$adef_IntMap.Mapiter.alist_semantics_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMapiter_2ealist__semantics,V_24X1),V_24X2),V_24X3) = cIntMap_2eMapiter_2ealist__semantics___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_57009_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__57009,V_24X1),V_24X2))
<=> c_24__lam__57009___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_388_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__388,V_24X1),V_24X2) = c_24__lam__388___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Map.MapPut_behind_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMap_2eMapPut__behind,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMap_2eMapPut__behind___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_10608_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__10608,V_24X1),V_24X2) = c_24__lam__10608___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.land_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eland,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.eval_clause_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__clause,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eeval__clause___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$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('$adef_$_lam_10608_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__10608,V_24X1),V_24X2),V_24X3) = c_24__lam__10608___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.exist_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_754_$a1',axiom,
! [V_24X1] : happ(c_24__lam__754,V_24X1) = c_24__lam__754___24a1(V_24X1) ).
fof('$adef_$_prop_59709_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__59709,V_24X1),V_24X2) = c_24__prop__59709___24a2(V_24X1,V_24X2) ).
fof('$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.micromega.ZMicromega.is_pol_Z0_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eis__pol__Z0,V_24X1) = cCoq_2emicromega_2eZMicromega_2eis__pol__Z0___24a1(V_24X1) ).
fof('$adef_$_lam_1047_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__1047,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__1047___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_$_lam_200_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__200,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__200___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_IntMap.Mapaxioms.eqmap_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cIntMap_2eMapaxioms_2eeqmap,V_24X1),V_24X2),V_24X3))
<=> cIntMap_2eMapaxioms_2eeqmap___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_IntMap.Fset.in_dom_$a1',axiom,
! [V_24X1] : happ(cIntMap_2eFset_2ein__dom,V_24X1) = cIntMap_2eFset_2ein__dom___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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.Arith.PeanoNat.Nat.ones_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eones,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eones___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmult,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_IntMap.Map.MapMerge_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eMapMerge,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eMapMerge___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_lam_23724_$a1',axiom,
! [V_24X1] : happ(c_24__lam__23724,V_24X1) = c_24__lam__23724___24a1(V_24X1) ).
fof('$adef_IntMap.Lsort.ad_monotonic_$a1',axiom,
! [V_24X1] :
( p(happ(cIntMap_2eLsort_2ead__monotonic,V_24X1))
<=> cIntMap_2eLsort_2ead__monotonic___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Byte.to_bits_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eByte_2eto__bits,V_24X1) = cCoq_2eInit_2eByte_2eto__bits___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.choose_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zbool.Zle_bool_total_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZle__bool__total,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZle__bool__total___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_57009_$a1',axiom,
! [V_24X1] : happ(c_24__lam__57009,V_24X1) = c_24__lam__57009___24a1(V_24X1) ).
fof('$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.NArith.BinNat.N.discr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2ediscr,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2ediscr___24a1(V_24X1) ).
fof('$adef_$_lam_1312_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1312,V_24X1),V_24X2),V_24X3) = c_24__lam__1312___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_14600_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__14600,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__14600___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_lam_1084_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1084,V_24X1),V_24X2),V_24X3) = c_24__lam__1084___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_56991_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__56991,V_24X1),V_24X2) = c_24__prop__56991___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$4687_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_244687,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_244687___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).
fof('$adef_$_lam_55203_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__55203,V_24X1),V_24X2) = c_24__lam__55203___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_10627_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__10627,V_24X1),V_24X2) = c_24__lam__10627___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_312_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__312,V_24X1),V_24X2),V_24X3) = c_24__lam__312___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.land_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eland,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_55128_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__55128,V_24X1),V_24X2) = c_24__prop__55128___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Fset.in_FSet_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2ein__FSet,V_24X1),V_24X2) = cIntMap_2eFset_2ein__FSet___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Mapiter.MapFold1_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cIntMap_2eMapiter_2eMapFold1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cIntMap_2eMapiter_2eMapFold1___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.Desc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eDesc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.Add_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.lor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_1211_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1211,V_24X1),V_24X2),V_24X3) = c_24__lam__1211___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_fix_29069_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__29069__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__29069__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.shiftl_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eshiftl,V_24X1) = cCoq_2eInit_2eNat_2eshiftl___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.BinNatDef.N.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.eval_tt_$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('$adef_Coq.micromega.ZMicromega.valid_cut_sign_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2evalid__cut__sign,V_24X1) = cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V_24X1) ).
fof('$adef_$_cast_56861_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__cast__56861,V_24X1),V_24X2) = c_24__cast__56861___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1818_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1818,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1818___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$54138_$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_2454138,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454138___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Lists.SetoidList.compat_op_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2ecompat__op,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_$_lam_1312_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1312,V_24X1),V_24X2) = c_24__lam__1312___24a2(V_24X1,V_24X2) ).
fof('$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.Arith.PeanoNat.Nat.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.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_$_prop_56866_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__56866,V_24X1),V_24X2) = c_24__prop__56866___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_dev_$a13',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$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('$adef_$_let_var_6_p_17621_17623_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__17621__17623,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__17621__17623___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$4692_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_244692,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_244692___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQminus,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQminus___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1783_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1783,V_24X1),V_24X2) = c_24__lam__1783___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Map.MapCard_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapCard,V_24X1),V_24X2) = cIntMap_2eMap_2eMapCard___24a2(V_24X1,V_24X2) ).
fof('$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_$_case_Coq.Init.Datatypes.bool$9625_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_249625,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249625___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_IntMap.Map.MapEmptyp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapEmptyp,V_24X1),V_24X2) = cIntMap_2eMap_2eMapEmptyp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_56985_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__56985,V_24X1),V_24X2) = c_24__lam__56985___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_55042_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__55042,V_24X1),V_24X2) = c_24__prop__55042___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_59708_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__59708,V_24X1),V_24X2) = c_24__prop__59708___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_59707_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__59707,V_24X1),V_24X2) = c_24__prop__59707___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1351_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1351,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1351___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_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_$_prop_716_$a1',axiom,
! [V_24X1] : happ(c_24__prop__716,V_24X1) = c_24__prop__716___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$56382_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2456382,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2456382___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_772_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__772,V_24X1),V_24X2),V_24X3) = c_24__lam__772___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_IntMap.Mapsubset.MapDisjoint_1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMapsubset_2eMapDisjoint__1,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMapsubset_2eMapDisjoint__1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$9641_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_249641,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249641___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.ones_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2eones,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2eones___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.gtb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2egtb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.exists__$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eexists__,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eexists_____24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.Ndigits.Neven_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eNArith_2eNdigits_2eNeven,V_24X1))
<=> cCoq_2eNArith_2eNdigits_2eNeven___24a1(V_24X1) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.lor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.testbit_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2etestbit,V_24X1) = cCoq_2eInit_2eNat_2etestbit___24a1(V_24X1) ).
fof('$adef_$_prop_55654_$a1',axiom,
! [V_24X1] : happ(c_24__prop__55654,V_24X1) = c_24__prop__55654___24a1(V_24X1) ).
fof('$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.Bool.Bool.eqb_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb__spec,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.Ndigits.Nless_aux_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eNArith_2eNdigits_2eNless__aux,V_24X1),V_24X2),V_24X3) = cCoq_2eNArith_2eNdigits_2eNless__aux___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_theory.get_sign_None_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a1(V_24X1) ).
fof('$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_$_lam_1791_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1791,V_24X1),V_24X2),V_24X3) = c_24__lam__1791___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.cnf_checker_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2ecnf__checker,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2ecnf__checker___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.eqlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.cneqb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecneqb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Map.MapGet_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapGet,V_24X1),V_24X2) = cIntMap_2eMap_2eMapGet___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('$adef_Coq.setoid_ring.Field_theory.split_aux_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esplit__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eField__theory_2esplit__aux___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Init.Datatypes.app_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1) = cCoq_2eInit_2eDatatypes_2eapp___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Classes.Morphisms.respectful_$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('$adef_$_prop_56987_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__56987,V_24X1),V_24X2) = c_24__prop__56987___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.inright_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einright___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_1357_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1357,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1357___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$28937_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2428937,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2428937___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_$_lam_55196_$a1',axiom,
! [V_24X1] : happ(c_24__lam__55196,V_24X1) = c_24__lam__55196___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_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_$_case_Coq.Init.Datatypes.bool$54100_$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_2454100,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_2454100___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Init.Nat.leb_$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('$adef_IntMap.Map.MapPut_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMap_2eMapPut,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMap_2eMapPut___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_324_$a1',axiom,
! [V_24X1] : happ(c_24__prop__324,V_24X1) = c_24__prop__324___24a1(V_24X1) ).
fof('$adef_$_lam_764_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__764,V_24X1),V_24X2),V_24X3) = c_24__lam__764___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_55043_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__55043,V_24X1),V_24X2) = c_24__prop__55043___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.Init.Nat.land_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eland,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eland___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.triv_div_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2etriv__div,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_1047_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1047,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1047___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_IntMap.Mapiter.alist_$a1',axiom,
! [V_24X1] : happ(cIntMap_2eMapiter_2ealist,V_24X1) = cIntMap_2eMapiter_2ealist___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Map.MapMerge_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapMerge,V_24X1),V_24X2) = cIntMap_2eMap_2eMapMerge___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1818_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1818,V_24X1),V_24X2),V_24X3) = c_24__lam__1818___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_55543_$a1',axiom,
! [V_24X1] : happ(c_24__prop__55543,V_24X1) = c_24__prop__55543___24a1(V_24X1) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.BinList.jump_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2ejump,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.is_empty_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eis__empty___24a1(V_24X1) ).
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_1791_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1791,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1791___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Subset_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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.Classes.RelationClasses.Reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eReflexive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$54059_$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_2454059,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_2454059___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('$adef_$_lam_11677_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__11677,V_24X1),V_24X2),V_24X3) = c_24__lam__11677___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_IntMap.Fset.FSetUnion_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eFSetUnion,V_24X1),V_24X2) = cIntMap_2eFset_2eFSetUnion___24a2(V_24X1,V_24X2) ).
fof('$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_$_case_Coq.Init.Datatypes.bool$55627_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455627,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455627___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sorting.Sorted.Sorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eSorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkopp_pow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkopp__pow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2emkopp__pow___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.NArith.BinNatDef.N.mul_$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('$adef_Coq.PArith.BinPosDef.Pos.ltb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eltb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eltb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_23714_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__23714,V_24X1))
<=> c_24__lam__23714___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_lam_10439_$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__10439,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__lam__10439___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_IntMap.Mapiter.MapSweep1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMapiter_2eMapSweep1,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMapiter_2eMapSweep1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Bool.Bool.ReflectT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eReflectT___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_23717_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__23717,V_24X1),V_24X2))
<=> c_24__lam__23717___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_55542_$a1',axiom,
! [V_24X1] : happ(c_24__prop__55542,V_24X1) = c_24__prop__55542___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).
fof('$adef_$_lam_23717_$a1',axiom,
! [V_24X1] : happ(c_24__lam__23717,V_24X1) = c_24__lam__23717___24a1(V_24X1) ).
fof('$adef_$_lam_55203_$a1',axiom,
! [V_24X1] : happ(c_24__lam__55203,V_24X1) = c_24__lam__55203___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_16_mkpow_17045_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__17045,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__17045___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_$_case_Coq.Init.Datatypes.bool$55350_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455350,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455350___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_237_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__237,V_24X1),V_24X2),V_24X3) = c_24__lam__237___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.NArith.Ndigits.Nodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eNArith_2eNdigits_2eNodd,V_24X1))
<=> cCoq_2eNArith_2eNdigits_2eNodd___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_IntMap.Mapiter.MapSweep_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMapiter_2eMapSweep,V_24X1),V_24X2),V_24X3) = cIntMap_2eMapiter_2eMapSweep___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_cast_56861_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__cast__56861,V_24X1),V_24X2),V_24X3) = c_24__cast__56861___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Nat.bitwise_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2ebitwise,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2ebitwise___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_10600_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__10600,V_24X1),V_24X2) = c_24__lam__10600___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Mapcanon.mapcanon_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cIntMap_2eMapcanon_2emapcanon,V_24X1),V_24X2))
<=> cIntMap_2eMapcanon_2emapcanon___24a2(V_24X1,V_24X2) ) ).
fof('$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.Lists.List.find_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efind,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efind___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_327_$a1',axiom,
! [V_24X1] : happ(c_24__prop__327,V_24X1) = c_24__prop__327___24a1(V_24X1) ).
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('$adef_Coq.Bool.Bool.andb_false_elim_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eandb__false__elim,V_24X1) = cCoq_2eBool_2eBool_2eandb__false__elim___24a1(V_24X1) ).
fof('$adef_$_lam_312_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__312,V_24X1),V_24X2) = c_24__lam__312___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.micromega.ZCoeff.gen_order_phi_Z_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_55703_$a1',axiom,
! [V_24X1] : happ(c_24__lam__55703,V_24X1) = c_24__lam__55703___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQinv,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$55409_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455409,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455409___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_$_prop_56865_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__56865,V_24X1),V_24X2) = c_24__prop__56865___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1357_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1357,V_24X1),V_24X2),V_24X3) = c_24__lam__1357___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_11677_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__11677,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__11677___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.QArith.QArith_base.Qplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQplus,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$54143_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454143,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2454143___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_56986_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__56986,V_24X1),V_24X2) = c_24__prop__56986___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_10600_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__10600,V_24X1),V_24X2),V_24X3) = c_24__lam__10600___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.PExpr_eq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2ePExpr__eq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_IntMap.Lsort.alist_nth_ad_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eLsort_2ealist__nth__ad,V_24X1),V_24X2),V_24X3) = cIntMap_2eLsort_2ealist__nth__ad___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Bool.Bool.iff_reflect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eiff__reflect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eiff__reflect___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_38932_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__38932,V_24X1),V_24X2) = c_24__lam__38932___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mon_of_pol_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$21717_$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_2421717,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_2421717___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RMicromega.is_neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eis__neg,V_24X1) = cCoq_2emicromega_2eRMicromega_2eis__neg___24a1(V_24X1) ).
fof('$adef_$_lam_38932_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38932,V_24X1),V_24X2),V_24X3) = c_24__lam__38932___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$55257_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455257,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455257___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_334_$a1',axiom,
! [V_24X1] : happ(c_24__prop__334,V_24X1) = c_24__prop__334___24a1(V_24X1) ).
fof('$adef_$_lam_1084_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1084,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1084___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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_42454_$a1',axiom,
! [V_24X1] : happ(c_24__lam__42454,V_24X1) = c_24__lam__42454___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.filter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efilter,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efilter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_55653_$a1',axiom,
! [V_24X1] : happ(c_24__prop__55653,V_24X1) = c_24__prop__55653___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.remove_$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('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
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('$adef_Coq.Init.Specif.left_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_IntMap.Map.MapGet_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eMapGet,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eMapGet___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_55690_$a1',axiom,
! [V_24X1] : happ(c_24__lam__55690,V_24X1) = c_24__lam__55690___24a1(V_24X1) ).
fof('$adef_$_lam_54442_$a1',axiom,
! [V_24X1] : happ(c_24__lam__54442,V_24X1) = c_24__lam__54442___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.eval_clause_$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__clause,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__clause___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Lists.List.fold_right_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.InitialRing.Nw_is0_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eInitialRing_2eNw__is0,V_24X1) = cCoq_2esetoid__ring_2eInitialRing_2eNw__is0___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.tl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2etl,V_24X1),V_24X2) = cCoq_2eLists_2eList_2etl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.equal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eequal___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_let_11_subst_l_14528_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__14528,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__14528___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).
fof('$adef_$_prop_56996_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__56996,V_24X1),V_24X2) = c_24__prop__56996___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Mapsubset.MapDisjoint_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cIntMap_2eMapsubset_2eMapDisjoint,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cIntMap_2eMapsubset_2eMapDisjoint___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_777_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__777,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__777___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
<=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_nat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit__nat___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.compat_bool_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2ecompat__bool,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.ltb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eltb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eltb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$55412_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455412,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2455412___24a2(V_24X1,V_24X2) ).
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('$adef_IntMap.Map.eqm_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cIntMap_2eMap_2eeqm,V_24X1),V_24X2),V_24X3))
<=> cIntMap_2eMap_2eeqm___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.FSets.FSetPositive.PositiveSet.fold_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_IntMap.Map.Map_$a1',axiom,
! [V_24X1] : happ(cIntMap_2eMap_2eMap,V_24X1) = cIntMap_2eMap_2eMap___24a1(V_24X1) ).
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('$adef_Coq.PArith.BinPosDef.Pos.shiftl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eshiftl,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eshiftl___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_55552_$a1',axiom,
! [V_24X1] : happ(c_24__prop__55552,V_24X1) = c_24__prop__55552___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_1754_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1754,V_24X1),V_24X2) = c_24__prop__1754___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Specif.right_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eright___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$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('$adef_Coq.ZArith.BinIntDef.Z.lor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2elor,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V_24X1,V_24X2) ).
fof('$adef_IntMap.Fset.MapDom_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eMapDom,V_24X1),V_24X2) = cIntMap_2eFset_2eMapDom___24a2(V_24X1,V_24X2) ).
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('$adef_$_prop_23718_$a1',axiom,
! [V_24X1] : happ(c_24__prop__23718,V_24X1) = c_24__prop__23718___24a1(V_24X1) ).
fof('$adef_$_cast_322_$a1',axiom,
! [V_24X1] : happ(c_24__cast__322,V_24X1) = c_24__cast__322___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQopp,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQopp___24a1(V_24X1) ).
fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_IntMap.Fset.in_dom_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eFset_2ein__dom,V_24X1),V_24X2),V_24X3) = cIntMap_2eFset_2ein__dom___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$tdef_$_type_957',axiom,
! [V_24Y] :
( c_24__type__957___24t(V_24Y)
<=> t(V_24Y,c_24__type__957) ) ).
fof('$tdef_$_type_9277',axiom,
! [V_24Y] :
( c_24__type__9277___24t(V_24Y)
<=> t(V_24Y,c_24__type__9277) ) ).
fof('$tdef_$_type_38631',axiom,
! [V_24Y] :
( c_24__type__38631___24t(V_24Y)
<=> t(V_24Y,c_24__type__38631) ) ).
fof('$tdef_$_type_29791',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__29791___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__29791___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_23894',axiom,
! [V_24Y] :
( c_24__type__23894___24t(V_24Y)
<=> t(V_24Y,c_24__type__23894) ) ).
fof('$tdef_$_type_9063',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9063___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9063___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_714',axiom,
! [V_24Y] :
( c_24__type__714___24t(V_24Y)
<=> t(V_24Y,c_24__type__714) ) ).
fof('$tdef_$_type_22310',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22310___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22310___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_134',axiom,
! [V_24Y] :
( c_24__type__134___24t(V_24Y)
<=> t(V_24Y,c_24__type__134) ) ).
fof('$tdef_$_type_55036',axiom,
! [V_24Y] :
( c_24__type__55036___24t(V_24Y)
<=> t(V_24Y,c_24__type__55036) ) ).
fof('$tdef_$_type_1478',axiom,
! [V_24Y] :
( c_24__type__1478___24t(V_24Y)
<=> t(V_24Y,c_24__type__1478) ) ).
fof('$tdef_$_type_535',axiom,
! [V_24Y] :
( c_24__type__535___24t(V_24Y)
<=> t(V_24Y,c_24__type__535) ) ).
fof('$tdef_$_type_1744',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1744___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1744___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34781',axiom,
! [V_24Y] :
( c_24__type__34781___24t(V_24Y)
<=> t(V_24Y,c_24__type__34781) ) ).
fof('$tdef_$_type_23836',axiom,
! [V_24Y] :
( c_24__type__23836___24t(V_24Y)
<=> t(V_24Y,c_24__type__23836) ) ).
fof('$tdef_$_type_1400',axiom,
! [V_24Y] :
( c_24__type__1400___24t(V_24Y)
<=> t(V_24Y,c_24__type__1400) ) ).
fof('$tdef_$_type_21939',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21939___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21939___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_6523',axiom,
! [V_24Y] :
( c_24__type__6523___24t(V_24Y)
<=> t(V_24Y,c_24__type__6523) ) ).
fof('$tdef_$_type_23767',axiom,
! [V_24Y] :
( c_24__type__23767___24t(V_24Y)
<=> t(V_24Y,c_24__type__23767) ) ).
fof('$tdef_$_type_22876',axiom,
! [V_24Y] :
( c_24__type__22876___24t(V_24Y)
<=> t(V_24Y,c_24__type__22876) ) ).
fof('$tdef_$_type_28182',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__28182___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__28182___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_991',axiom,
! [V_24Y] :
( c_24__type__991___24t(V_24Y)
<=> t(V_24Y,c_24__type__991) ) ).
fof('$tdef_$_type_11722',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11722___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11722___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23972',axiom,
! [V_24Y] :
( c_24__type__23972___24t(V_24Y)
<=> t(V_24Y,c_24__type__23972) ) ).
fof('$tdef_$_type_30806',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__30806___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__30806___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_1475',axiom,
! [V_24Y] :
( c_24__type__1475___24t(V_24Y)
<=> t(V_24Y,c_24__type__1475) ) ).
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_$_type_8860',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8860___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8860___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_818',axiom,
! [V_24Y] :
( c_24__type__818___24t(V_24Y)
<=> t(V_24Y,c_24__type__818) ) ).
fof('$tdef_$_type_59790',axiom,
! [V_24Y] :
( c_24__type__59790___24t(V_24Y)
<=> t(V_24Y,c_24__type__59790) ) ).
fof('$tdef_$_type_21654',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21654___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21654___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1449',axiom,
! [V_24Y] :
( c_24__type__1449___24t(V_24Y)
<=> t(V_24Y,c_24__type__1449) ) ).
fof('$tdef_$_type_55711',axiom,
! [V_24Y] :
( c_24__type__55711___24t(V_24Y)
<=> t(V_24Y,c_24__type__55711) ) ).
fof('$tdef_$_type_15332',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15332___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15332___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6970',axiom,
! [V_24Y] :
( c_24__type__6970___24t(V_24Y)
<=> t(V_24Y,c_24__type__6970) ) ).
fof('$tdef_$_type_701',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__701___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__701___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22541',axiom,
! [V_24Y] :
( c_24__type__22541___24t(V_24Y)
<=> t(V_24Y,c_24__type__22541) ) ).
fof('$tdef_$_type_30137',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__30137___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__30137___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_27688',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__27688___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__27688___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_54460',axiom,
! [V_24Y] :
( c_24__type__54460___24t(V_24Y)
<=> t(V_24Y,c_24__type__54460) ) ).
fof('$tdef_$_type_8923',axiom,
! [V_24Y] :
( c_24__type__8923___24t(V_24Y)
<=> t(V_24Y,c_24__type__8923) ) ).
fof('$tdef_$_type_5398',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__5398___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__5398___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_622',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__622___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__622___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_349',axiom,
! [V_24Y] :
( c_24__type__349___24t(V_24Y)
<=> t(V_24Y,c_24__type__349) ) ).
fof('$tdef_$_type_816',axiom,
! [V_24Y] :
( c_24__type__816___24t(V_24Y)
<=> t(V_24Y,c_24__type__816) ) ).
fof('$tdef_$_type_2442',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2442___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2442___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_56765',axiom,
! [V_24Y] :
( c_24__type__56765___24t(V_24Y)
<=> t(V_24Y,c_24__type__56765) ) ).
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_1487',axiom,
! [V_24Y] :
( c_24__type__1487___24t(V_24Y)
<=> t(V_24Y,c_24__type__1487) ) ).
fof('$tdef_$_type_54403',axiom,
! [V_24Y] :
( c_24__type__54403___24t(V_24Y)
<=> t(V_24Y,c_24__type__54403) ) ).
fof('$tdef_$_type_56777',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__56777___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__56777___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_53623',axiom,
! [V_24Y] :
( c_24__type__53623___24t(V_24Y)
<=> t(V_24Y,c_24__type__53623) ) ).
fof('$tdef_$_type_20692',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__20692___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__20692___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_55356',axiom,
! [V_24Y] :
( c_24__type__55356___24t(V_24Y)
<=> t(V_24Y,c_24__type__55356) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_28739',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__28739___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__28739___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_34',axiom,
! [V_24Y] :
( c_24__type__34___24t(V_24Y)
<=> t(V_24Y,c_24__type__34) ) ).
fof('$tdef_$_type_2449',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2449___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2449___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_21859',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21859___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21859___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_54426',axiom,
! [V_24Y] :
( c_24__type__54426___24t(V_24Y)
<=> t(V_24Y,c_24__type__54426) ) ).
fof('$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_8479',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8479___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8479___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26889',axiom,
! [V_24Y] :
( c_24__type__26889___24t(V_24Y)
<=> t(V_24Y,c_24__type__26889) ) ).
fof('$tdef_$_type_24569',axiom,
! [V_24Y] :
( c_24__type__24569___24t(V_24Y)
<=> t(V_24Y,c_24__type__24569) ) ).
fof('$tdef_$_type_1494',axiom,
! [V_24Y] :
( c_24__type__1494___24t(V_24Y)
<=> t(V_24Y,c_24__type__1494) ) ).
fof('$tdef_$_type_55476',axiom,
! [V_24Y] :
( c_24__type__55476___24t(V_24Y)
<=> t(V_24Y,c_24__type__55476) ) ).
fof('$tdef_$_type_57351',axiom,
! [V_24X1,V_24Y] :
( c_24__type__57351___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__57351___24a1(V_24X1)) ) ).
fof('$tdef_$_type_47456',axiom,
! [V_24Y] :
( c_24__type__47456___24t(V_24Y)
<=> t(V_24Y,c_24__type__47456) ) ).
fof('$tdef_$_type_34681',axiom,
! [V_24Y] :
( c_24__type__34681___24t(V_24Y)
<=> t(V_24Y,c_24__type__34681) ) ).
fof('$tdef_$_type_25202',axiom,
! [V_24Y] :
( c_24__type__25202___24t(V_24Y)
<=> t(V_24Y,c_24__type__25202) ) ).
fof('$tdef_$_type_56772',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__56772___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__56772___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6978',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6978___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6978___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1573',axiom,
! [V_24Y] :
( c_24__type__1573___24t(V_24Y)
<=> t(V_24Y,c_24__type__1573) ) ).
fof('$tdef_$_type_34543',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__34543___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__34543___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_4892',axiom,
! [V_24Y] :
( c_24__type__4892___24t(V_24Y)
<=> t(V_24Y,c_24__type__4892) ) ).
fof('$tdef_$_type_1828',axiom,
! [V_24Y] :
( c_24__type__1828___24t(V_24Y)
<=> t(V_24Y,c_24__type__1828) ) ).
fof('$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_21604',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21604___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21604___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_27126',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__27126___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__27126___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_15',axiom,
! [V_24Y] :
( c_24__type__15___24t(V_24Y)
<=> t(V_24Y,c_24__type__15) ) ).
fof('$tdef_$_type_21312',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__21312___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__21312___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_18501',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18501___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18501___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_10443',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10443___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10443___24a1(V_24X1)) ) ).
fof('$tdef_$_type_55129',axiom,
! [V_24Y] :
( c_24__type__55129___24t(V_24Y)
<=> t(V_24Y,c_24__type__55129) ) ).
fof('$tdef_$_type_28081',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__28081___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__28081___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_8873',axiom,
! [V_24Y] :
( c_24__type__8873___24t(V_24Y)
<=> t(V_24Y,c_24__type__8873) ) ).
fof('$tdef_$_type_725',axiom,
! [V_24Y] :
( c_24__type__725___24t(V_24Y)
<=> t(V_24Y,c_24__type__725) ) ).
fof('$tdef_$_type_2128',axiom,
! [V_24Y] :
( c_24__type__2128___24t(V_24Y)
<=> t(V_24Y,c_24__type__2128) ) ).
fof('$tdef_$_type_21298',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__21298___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__21298___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_27587',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__27587___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__27587___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_31844',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__31844___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__31844___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_12394',axiom,
! [V_24Y] :
( c_24__type__12394___24t(V_24Y)
<=> t(V_24Y,c_24__type__12394) ) ).
fof('$tdef_$_type_6574',axiom,
! [V_24Y] :
( c_24__type__6574___24t(V_24Y)
<=> t(V_24Y,c_24__type__6574) ) ).
fof('$tdef_$_type_37382',axiom,
! [V_24Y] :
( c_24__type__37382___24t(V_24Y)
<=> t(V_24Y,c_24__type__37382) ) ).
fof('$tdef_$_type_11856',axiom,
! [V_24Y] :
( c_24__type__11856___24t(V_24Y)
<=> t(V_24Y,c_24__type__11856) ) ).
fof('$tdef_$_type_22267',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22267___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22267___24a2(V_24X1,V_24X2)) ) ).
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_$_type_6913',axiom,
! [V_24Y] :
( c_24__type__6913___24t(V_24Y)
<=> t(V_24Y,c_24__type__6913) ) ).
fof('$tdef_$_type_11833',axiom,
! [V_24Y] :
( c_24__type__11833___24t(V_24Y)
<=> t(V_24Y,c_24__type__11833) ) ).
fof('$tdef_$_type_293',axiom,
! [V_24Y] :
( c_24__type__293___24t(V_24Y)
<=> t(V_24Y,c_24__type__293) ) ).
fof('$tdef_$_type_18534',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18534___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18534___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_22237',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__22237___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__22237___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_55121',axiom,
! [V_24Y] :
( c_24__type__55121___24t(V_24Y)
<=> t(V_24Y,c_24__type__55121) ) ).
fof('$tdef_$_type_43821',axiom,
! [V_24Y] :
( c_24__type__43821___24t(V_24Y)
<=> t(V_24Y,c_24__type__43821) ) ).
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_$_type_11725',axiom,
! [V_24Y] :
( c_24__type__11725___24t(V_24Y)
<=> t(V_24Y,c_24__type__11725) ) ).
fof('$tdef_$_type_32859',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__32859___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__32859___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_IntMap.Map.ad',axiom,
! [V_24Y] :
( cIntMap_2eMap_2ead___24t(V_24Y)
<=> t(V_24Y,cIntMap_2eMap_2ead) ) ).
fof('$tdef_$_type_8825',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8825___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8825___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_55032',axiom,
! [V_24Y] :
( c_24__type__55032___24t(V_24Y)
<=> t(V_24Y,c_24__type__55032) ) ).
fof('$tdef_$_type_21903',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21903___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21903___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_38226',axiom,
! [V_24Y] :
( c_24__type__38226___24t(V_24Y)
<=> t(V_24Y,c_24__type__38226) ) ).
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_$_type_3591',axiom,
! [V_24Y] :
( c_24__type__3591___24t(V_24Y)
<=> t(V_24Y,c_24__type__3591) ) ).
fof('$tdef_$_type_18477',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18477___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18477___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_495',axiom,
! [V_24X1,V_24Y] :
( c_24__type__495___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__495___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3622',axiom,
! [V_24Y] :
( c_24__type__3622___24t(V_24Y)
<=> t(V_24Y,c_24__type__3622) ) ).
fof('$tdef_$_type_17325',axiom,
! [V_24Y] :
( c_24__type__17325___24t(V_24Y)
<=> t(V_24Y,c_24__type__17325) ) ).
fof('$tdef_$_type_2580',axiom,
! [V_24Y] :
( c_24__type__2580___24t(V_24Y)
<=> t(V_24Y,c_24__type__2580) ) ).
fof('$tdef_$_type_21279',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__21279___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__21279___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_55210',axiom,
! [V_24Y] :
( c_24__type__55210___24t(V_24Y)
<=> t(V_24Y,c_24__type__55210) ) ).
fof('$tdef_$_type_23705',axiom,
! [V_24Y] :
( c_24__type__23705___24t(V_24Y)
<=> t(V_24Y,c_24__type__23705) ) ).
fof('$tdef_$_type_10391',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__10391___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__10391___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1405',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1405___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1405___24a1(V_24X1)) ) ).
fof('$tdef_$_type_56401',axiom,
! [V_24Y] :
( c_24__type__56401___24t(V_24Y)
<=> t(V_24Y,c_24__type__56401) ) ).
fof('$tdef_$_type_57176',axiom,
! [V_24Y] :
( c_24__type__57176___24t(V_24Y)
<=> t(V_24Y,c_24__type__57176) ) ).
fof('$tdef_$_type_553',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__553___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__553___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_55550',axiom,
! [V_24Y] :
( c_24__type__55550___24t(V_24Y)
<=> t(V_24Y,c_24__type__55550) ) ).
fof('$tdef_$_type_54384',axiom,
! [V_24Y] :
( c_24__type__54384___24t(V_24Y)
<=> t(V_24Y,c_24__type__54384) ) ).
fof('$tdef_$_type_12806',axiom,
! [V_24X1,V_24Y] :
( c_24__type__12806___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__12806___24a1(V_24X1)) ) ).
fof('$tdef_$_type_810',axiom,
! [V_24Y] :
( c_24__type__810___24t(V_24Y)
<=> t(V_24Y,c_24__type__810) ) ).
fof('$tdef_$_type_55439',axiom,
! [V_24Y] :
( c_24__type__55439___24t(V_24Y)
<=> t(V_24Y,c_24__type__55439) ) ).
fof('$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_569',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__569___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__569___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4843',axiom,
! [V_24Y] :
( c_24__type__4843___24t(V_24Y)
<=> t(V_24Y,c_24__type__4843) ) ).
fof('$tdef_$_type_56994',axiom,
! [V_24Y] :
( c_24__type__56994___24t(V_24Y)
<=> t(V_24Y,c_24__type__56994) ) ).
fof('$tdef_$_type_43813',axiom,
! [V_24Y] :
( c_24__type__43813___24t(V_24Y)
<=> t(V_24Y,c_24__type__43813) ) ).
fof('$tdef_$_type_21562',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21562___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21562___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_33874',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__33874___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__33874___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_22257',axiom,
! [V_24Y] :
( c_24__type__22257___24t(V_24Y)
<=> t(V_24Y,c_24__type__22257) ) ).
fof('$tdef_$_type_22145',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__22145___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__22145___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_11830',axiom,
! [V_24Y] :
( c_24__type__11830___24t(V_24Y)
<=> t(V_24Y,c_24__type__11830) ) ).
fof('$tdef_$_type_8499',axiom,
! [V_24Y] :
( c_24__type__8499___24t(V_24Y)
<=> t(V_24Y,c_24__type__8499) ) ).
fof('$tdef_$_type_4706',axiom,
! [V_24Y] :
( c_24__type__4706___24t(V_24Y)
<=> t(V_24Y,c_24__type__4706) ) ).
fof('$tdef_$_type_55161',axiom,
! [V_24Y] :
( c_24__type__55161___24t(V_24Y)
<=> t(V_24Y,c_24__type__55161) ) ).
fof('$tdef_$_type_22325',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22325___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22325___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.Tauto.cnf',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20905',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20905___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20905___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).
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_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_17633',axiom,
! [V_24Y] :
( c_24__type__17633___24t(V_24Y)
<=> t(V_24Y,c_24__type__17633) ) ).
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_$_type_21462',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21462___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21462___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_31498',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__31498___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__31498___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_23825',axiom,
! [V_24Y] :
( c_24__type__23825___24t(V_24Y)
<=> t(V_24Y,c_24__type__23825) ) ).
fof('$tdef_$_type_19024',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19024___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19024___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_56391',axiom,
! [V_24Y] :
( c_24__type__56391___24t(V_24Y)
<=> t(V_24Y,c_24__type__56391) ) ).
fof('$tdef_$_type_17950',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__17950___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__17950___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_25340',axiom,
! [V_24X1,V_24Y] :
( c_24__type__25340___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__25340___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27076',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__27076___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__27076___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_57215',axiom,
! [V_24Y] :
( c_24__type__57215___24t(V_24Y)
<=> t(V_24Y,c_24__type__57215) ) ).
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_$_type_23841',axiom,
! [V_24X1,V_24Y] :
( c_24__type__23841___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__23841___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3756',axiom,
! [V_24Y] :
( c_24__type__3756___24t(V_24Y)
<=> t(V_24Y,c_24__type__3756) ) ).
fof('$tdef_$_type_27980',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__27980___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__27980___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_33551',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__33551___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__33551___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_4855',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4855___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4855___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_55425',axiom,
! [V_24Y] :
( c_24__type__55425___24t(V_24Y)
<=> t(V_24Y,c_24__type__55425) ) ).
fof('$tdef_$_type_21736',axiom,
! [V_24Y] :
( c_24__type__21736___24t(V_24Y)
<=> t(V_24Y,c_24__type__21736) ) ).
fof('$tdef_$_type_1576',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1576___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1576___24a1(V_24X1)) ) ).
fof('$tdef_$_type_57001',axiom,
! [V_24Y] :
( c_24__type__57001___24t(V_24Y)
<=> t(V_24Y,c_24__type__57001) ) ).
fof('$tdef_$_type_6594',axiom,
! [V_24Y] :
( c_24__type__6594___24t(V_24Y)
<=> t(V_24Y,c_24__type__6594) ) ).
fof('$tdef_Coq.micromega.Tauto.clause',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2emicromega_2eTauto_2eclause___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_57053',axiom,
! [V_24Y] :
( c_24__type__57053___24t(V_24Y)
<=> t(V_24Y,c_24__type__57053) ) ).
fof('$tdef_$_type_57030',axiom,
! [V_24Y] :
( c_24__type__57030___24t(V_24Y)
<=> t(V_24Y,c_24__type__57030) ) ).
fof('$tdef_$_type_18013',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__18013___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__18013___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_8890',axiom,
! [V_24Y] :
( c_24__type__8890___24t(V_24Y)
<=> t(V_24Y,c_24__type__8890) ) ).
fof('$tdef_$_type_58129',axiom,
! [V_24Y] :
( c_24__type__58129___24t(V_24Y)
<=> t(V_24Y,c_24__type__58129) ) ).
fof('$tdef_$_type_55531',axiom,
! [V_24Y] :
( c_24__type__55531___24t(V_24Y)
<=> t(V_24Y,c_24__type__55531) ) ).
fof('$tdef_$_type_38604',axiom,
! [V_24Y] :
( c_24__type__38604___24t(V_24Y)
<=> t(V_24Y,c_24__type__38604) ) ).
fof('$tdef_$_type_55555',axiom,
! [V_24Y] :
( c_24__type__55555___24t(V_24Y)
<=> t(V_24Y,c_24__type__55555) ) ).
fof('$tdef_$_type_8644',axiom,
! [V_24Y] :
( c_24__type__8644___24t(V_24Y)
<=> t(V_24Y,c_24__type__8644) ) ).
fof('$tdef_$_type_646',axiom,
! [V_24Y] :
( c_24__type__646___24t(V_24Y)
<=> t(V_24Y,c_24__type__646) ) ).
fof('$tdef_$_type_18067',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__18067___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__18067___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_616',axiom,
! [V_24Y] :
( c_24__type__616___24t(V_24Y)
<=> t(V_24Y,c_24__type__616) ) ).
fof('$tdef_$_type_14732',axiom,
! [V_24Y] :
( c_24__type__14732___24t(V_24Y)
<=> t(V_24Y,c_24__type__14732) ) ).
fof('$tdef_$_type_24564',axiom,
! [V_24Y] :
( c_24__type__24564___24t(V_24Y)
<=> t(V_24Y,c_24__type__24564) ) ).
fof('$tdef_$_type_1740',axiom,
! [V_24Y] :
( c_24__type__1740___24t(V_24Y)
<=> t(V_24Y,c_24__type__1740) ) ).
fof('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$tdef_$_type_59',axiom,
! [V_24Y] :
( c_24__type__59___24t(V_24Y)
<=> t(V_24Y,c_24__type__59) ) ).
fof('$tdef_$_type_55065',axiom,
! [V_24Y] :
( c_24__type__55065___24t(V_24Y)
<=> t(V_24Y,c_24__type__55065) ) ).
fof('$tdef_$_type_593',axiom,
! [V_24Y] :
( c_24__type__593___24t(V_24Y)
<=> t(V_24Y,c_24__type__593) ) ).
fof('$tdef_$_type_21512',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21512___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21512___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_55040',axiom,
! [V_24Y] :
( c_24__type__55040___24t(V_24Y)
<=> t(V_24Y,c_24__type__55040) ) ).
fof('$tdef_$_type_1527',axiom,
! [V_24Y] :
( c_24__type__1527___24t(V_24Y)
<=> t(V_24Y,c_24__type__1527) ) ).
fof('$tdef_$_type_8382',axiom,
! [V_24Y] :
( c_24__type__8382___24t(V_24Y)
<=> t(V_24Y,c_24__type__8382) ) ).
fof('$tdef_$_type_14309',axiom,
! [V_24Y] :
( c_24__type__14309___24t(V_24Y)
<=> t(V_24Y,c_24__type__14309) ) ).
fof('$tdef_$_type_21995',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21995___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21995___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_13367',axiom,
! [V_24Y] :
( c_24__type__13367___24t(V_24Y)
<=> t(V_24Y,c_24__type__13367) ) ).
fof('$tdef_$_type_22436',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22436___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22436___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_17887',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__17887___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__17887___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_5748',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__5748___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__5748___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_$_type_62238',axiom,
! [V_24X1,V_24Y] :
( c_24__type__62238___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__62238___24a1(V_24X1)) ) ).
fof('$tdef_$_type_512',axiom,
! [V_24Y] :
( c_24__type__512___24t(V_24Y)
<=> t(V_24Y,c_24__type__512) ) ).
fof('$tdef_$_type_13844',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__13844___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__13844___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_18363',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18363___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18363___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_4746',axiom,
! [V_24Y] :
( c_24__type__4746___24t(V_24Y)
<=> t(V_24Y,c_24__type__4746) ) ).
fof('$tdef_$_type_4641',axiom,
! [V_24Y] :
( c_24__type__4641___24t(V_24Y)
<=> t(V_24Y,c_24__type__4641) ) ).
fof('$tdef_$_type_9279',axiom,
! [V_24Y] :
( c_24__type__9279___24t(V_24Y)
<=> t(V_24Y,c_24__type__9279) ) ).
fof('$tdef_$_type_2412',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2412___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2412___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23773',axiom,
! [V_24Y] :
( c_24__type__23773___24t(V_24Y)
<=> t(V_24Y,c_24__type__23773) ) ).
fof('$tdef_$_type_2470',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2470___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2470___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1692',axiom,
! [V_24Y] :
( c_24__type__1692___24t(V_24Y)
<=> t(V_24Y,c_24__type__1692) ) ).
fof('$tdef_$_type_1539',axiom,
! [V_24Y] :
( c_24__type__1539___24t(V_24Y)
<=> t(V_24Y,c_24__type__1539) ) ).
fof('$tdef_$_type_56374',axiom,
! [V_24Y] :
( c_24__type__56374___24t(V_24Y)
<=> t(V_24Y,c_24__type__56374) ) ).
fof('$tdef_IntMap.Map.Map',axiom,
! [V_24X1,V_24Y] :
( cIntMap_2eMap_2eMap___24t(V_24X1,V_24Y)
<=> t(V_24Y,cIntMap_2eMap_2eMap___24a1(V_24X1)) ) ).
fof('$tdef_$_type_129',axiom,
! [V_24Y] :
( c_24__type__129___24t(V_24Y)
<=> t(V_24Y,c_24__type__129) ) ).
fof('$tdef_$_type_38243',axiom,
! [V_24Y] :
( c_24__type__38243___24t(V_24Y)
<=> t(V_24Y,c_24__type__38243) ) ).
fof('$tdef_$_type_8433',axiom,
! [V_24Y] :
( c_24__type__8433___24t(V_24Y)
<=> t(V_24Y,c_24__type__8433) ) ).
fof('$tdef_$_type_23891',axiom,
! [V_24Y] :
( c_24__type__23891___24t(V_24Y)
<=> t(V_24Y,c_24__type__23891) ) ).
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_$_type_8490',axiom,
! [V_24Y] :
( c_24__type__8490___24t(V_24Y)
<=> t(V_24Y,c_24__type__8490) ) ).
fof('$tdef_$_type_8818',axiom,
! [V_24Y] :
( c_24__type__8818___24t(V_24Y)
<=> t(V_24Y,c_24__type__8818) ) ).
fof('$tdef_$_type_56724',axiom,
! [V_24Y] :
( c_24__type__56724___24t(V_24Y)
<=> t(V_24Y,c_24__type__56724) ) ).
fof('$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_264',axiom,
! [V_24Y] :
( c_24__type__264___24t(V_24Y)
<=> t(V_24Y,c_24__type__264) ) ).
fof('$tdef_$_type_56464',axiom,
! [V_24Y] :
( c_24__type__56464___24t(V_24Y)
<=> t(V_24Y,c_24__type__56464) ) ).
fof('$tdef_$_type_18417',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18417___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18417___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2609',axiom,
! [V_24Y] :
( c_24__type__2609___24t(V_24Y)
<=> t(V_24Y,c_24__type__2609) ) ).
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_$_type_3598',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3598___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3598___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11315',axiom,
! [V_24Y] :
( c_24__type__11315___24t(V_24Y)
<=> t(V_24Y,c_24__type__11315) ) ).
fof('$tdef_$_type_37927',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__37927___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__37927___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_785',axiom,
! [V_24Y] :
( c_24__type__785___24t(V_24Y)
<=> t(V_24Y,c_24__type__785) ) ).
fof('$tdef_$_type_10565',axiom,
! [V_24Y] :
( c_24__type__10565___24t(V_24Y)
<=> t(V_24Y,c_24__type__10565) ) ).
fof('$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_1507',axiom,
! [V_24Y] :
( c_24__type__1507___24t(V_24Y)
<=> t(V_24Y,c_24__type__1507) ) ).
fof('$tdef_$_type_20497',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__20497___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__20497___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_634',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__634___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__634___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1529',axiom,
! [V_24Y] :
( c_24__type__1529___24t(V_24Y)
<=> t(V_24Y,c_24__type__1529) ) ).
fof('$tdef_$_type_57339',axiom,
! [V_24X1,V_24Y] :
( c_24__type__57339___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__57339___24a1(V_24X1)) ) ).
fof('$tdef_$_type_55726',axiom,
! [V_24Y] :
( c_24__type__55726___24t(V_24Y)
<=> t(V_24Y,c_24__type__55726) ) ).
fof('$tdef_$_type_31152',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__31152___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__31152___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_24668',axiom,
! [V_24Y] :
( c_24__type__24668___24t(V_24Y)
<=> t(V_24Y,c_24__type__24668) ) ).
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_$_type_23721',axiom,
! [V_24Y] :
( c_24__type__23721___24t(V_24Y)
<=> t(V_24Y,c_24__type__23721) ) ).
fof('$tdef_$_type_11820',axiom,
! [V_24Y] :
( c_24__type__11820___24t(V_24Y)
<=> t(V_24Y,c_24__type__11820) ) ).
fof('$tdef_$_type_4637',axiom,
! [V_24Y] :
( c_24__type__4637___24t(V_24Y)
<=> t(V_24Y,c_24__type__4637) ) ).
fof('$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_5573',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__5573___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__5573___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_573',axiom,
! [V_24Y] :
( c_24__type__573___24t(V_24Y)
<=> t(V_24Y,c_24__type__573) ) ).
fof('$tdef_$_type_2461',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2461___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2461___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_19237',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__19237___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__19237___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('$tdef_Coq.micromega.ZMicromega.ZWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZWitness) ) ).
fof('$tdef_$_type_22546',axiom,
! [V_24Y] :
( c_24__type__22546___24t(V_24Y)
<=> t(V_24Y,c_24__type__22546) ) ).
fof('$tdef_$_type_57131',axiom,
! [V_24Y] :
( c_24__type__57131___24t(V_24Y)
<=> t(V_24Y,c_24__type__57131) ) ).
fof('$tdef_$_type_55260',axiom,
! [V_24Y] :
( c_24__type__55260___24t(V_24Y)
<=> t(V_24Y,c_24__type__55260) ) ).
fof('$tdef_$_type_2260',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2260___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2260___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1470',axiom,
! [V_24Y] :
( c_24__type__1470___24t(V_24Y)
<=> t(V_24Y,c_24__type__1470) ) ).
fof('$tdef_$_type_305',axiom,
! [V_24Y] :
( c_24__type__305___24t(V_24Y)
<=> t(V_24Y,c_24__type__305) ) ).
fof('$tdef_$_type_24543',axiom,
! [V_24Y] :
( c_24__type__24543___24t(V_24Y)
<=> t(V_24Y,c_24__type__24543) ) ).
fof('$tdef_$_type_23897',axiom,
! [V_24Y] :
( c_24__type__23897___24t(V_24Y)
<=> t(V_24Y,c_24__type__23897) ) ).
fof('$tdef_$_type_37658',axiom,
! [V_24Y] :
( c_24__type__37658___24t(V_24Y)
<=> t(V_24Y,c_24__type__37658) ) ).
fof('$tdef_$_type_2595',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2595___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2595___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_55262',axiom,
! [V_24Y] :
( c_24__type__55262___24t(V_24Y)
<=> t(V_24Y,c_24__type__55262) ) ).
fof('$tdef_$_type_34830',axiom,
! [V_24Y] :
( c_24__type__34830___24t(V_24Y)
<=> t(V_24Y,c_24__type__34830) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).
fof('$tdef_$_type_38734',axiom,
! [V_24Y] :
( c_24__type__38734___24t(V_24Y)
<=> t(V_24Y,c_24__type__38734) ) ).
fof('$tdef_$_type_2178',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2178___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2178___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_18393',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18393___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18393___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_56767',axiom,
! [V_24Y] :
( c_24__type__56767___24t(V_24Y)
<=> t(V_24Y,c_24__type__56767) ) ).
fof('$tdef_$_type_55427',axiom,
! [V_24Y] :
( c_24__type__55427___24t(V_24Y)
<=> t(V_24Y,c_24__type__55427) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_22300',axiom,
! [V_24Y] :
( c_24__type__22300___24t(V_24Y)
<=> t(V_24Y,c_24__type__22300) ) ).
fof('$tdef_$_type_30483',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__30483___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__30483___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_4622',axiom,
! [V_24Y] :
( c_24__type__4622___24t(V_24Y)
<=> t(V_24Y,c_24__type__4622) ) ).
fof('$tdef_$_type_9758',axiom,
! [V_24Y] :
( c_24__type__9758___24t(V_24Y)
<=> t(V_24Y,c_24__type__9758) ) ).
fof('$tdef_$_type_4739',axiom,
! [V_24Y] :
( c_24__type__4739___24t(V_24Y)
<=> t(V_24Y,c_24__type__4739) ) ).
fof('$tdef_$_type_18130',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__18130___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__18130___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_IntMap.Fset.FSet',axiom,
! [V_24Y] :
( cIntMap_2eFset_2eFSet___24t(V_24Y)
<=> t(V_24Y,cIntMap_2eFset_2eFSet) ) ).
fof('$tdef_Coq.Init.Datatypes.sum',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14502',axiom,
! [V_24Y] :
( c_24__type__14502___24t(V_24Y)
<=> t(V_24Y,c_24__type__14502) ) ).
fof('$tdef_$_type_5109',axiom,
! [V_24Y] :
( c_24__type__5109___24t(V_24Y)
<=> t(V_24Y,c_24__type__5109) ) ).
fof('$tdef_$_type_2689',axiom,
! [V_24Y] :
( c_24__type__2689___24t(V_24Y)
<=> t(V_24Y,c_24__type__2689) ) ).
fof('$tdef_$_type_18447',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18447___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18447___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_$_type_55140',axiom,
! [V_24Y] :
( c_24__type__55140___24t(V_24Y)
<=> t(V_24Y,c_24__type__55140) ) ).
fof('$tdef_$_type_54369',axiom,
! [V_24Y] :
( c_24__type__54369___24t(V_24Y)
<=> t(V_24Y,c_24__type__54369) ) ).
fof('$tdef_$_type_1905',axiom,
! [V_24Y] :
( c_24__type__1905___24t(V_24Y)
<=> t(V_24Y,c_24__type__1905) ) ).
fof('$tdef_$_type_10272',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__10272___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__10272___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_11263',axiom,
! [V_24Y] :
( c_24__type__11263___24t(V_24Y)
<=> t(V_24Y,c_24__type__11263) ) ).
fof('$tdef_$_type_74',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__74___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__74___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_55233',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__55233___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__55233___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34197',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__34197___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__34197___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_3546',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3546___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3546___24a1(V_24X1)) ) ).
fof('$tdef_$_type_89',axiom,
! [V_24Y] :
( c_24__type__89___24t(V_24Y)
<=> t(V_24Y,c_24__type__89) ) ).
fof('$tdef_$_type_38752',axiom,
! [V_24Y] :
( c_24__type__38752___24t(V_24Y)
<=> t(V_24Y,c_24__type__38752) ) ).
fof('$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('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_23797',axiom,
! [V_24Y] :
( c_24__type__23797___24t(V_24Y)
<=> t(V_24Y,c_24__type__23797) ) ).
fof('$tdef_$_type_5841',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5841___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5841___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_27879',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__27879___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__27879___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_1555',axiom,
! [V_24Y] :
( c_24__type__1555___24t(V_24Y)
<=> t(V_24Y,c_24__type__1555) ) ).
fof('$tdef_$_type_492',axiom,
! [V_24Y] :
( c_24__type__492___24t(V_24Y)
<=> t(V_24Y,c_24__type__492) ) ).
fof('$tdef_$_type_690',axiom,
! [V_24Y] :
( c_24__type__690___24t(V_24Y)
<=> t(V_24Y,c_24__type__690) ) ).
fof('$tdef_$_type_352',axiom,
! [V_24Y] :
( c_24__type__352___24t(V_24Y)
<=> t(V_24Y,c_24__type__352) ) ).
fof('$tdef_$_type_9179',axiom,
! [V_24Y] :
( c_24__type__9179___24t(V_24Y)
<=> t(V_24Y,c_24__type__9179) ) ).
fof('$tdef_$_type_1412',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1412___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1412___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29',axiom,
! [V_24Y] :
( c_24__type__29___24t(V_24Y)
<=> t(V_24Y,c_24__type__29) ) ).
fof('$tdef_$_type_38251',axiom,
! [V_24Y] :
( c_24__type__38251___24t(V_24Y)
<=> t(V_24Y,c_24__type__38251) ) ).
fof('$tdef_$_type_57327',axiom,
! [V_24Y] :
( c_24__type__57327___24t(V_24Y)
<=> t(V_24Y,c_24__type__57327) ) ).
fof('$tdef_$_type_34833',axiom,
! [V_24Y] :
( c_24__type__34833___24t(V_24Y)
<=> t(V_24Y,c_24__type__34833) ) ).
fof('$tdef_$_type_55445',axiom,
! [V_24Y] :
( c_24__type__55445___24t(V_24Y)
<=> t(V_24Y,c_24__type__55445) ) ).
fof('$tdef_$_type_11826',axiom,
! [V_24Y] :
( c_24__type__11826___24t(V_24Y)
<=> t(V_24Y,c_24__type__11826) ) ).
fof('$tdef_$_type_337',axiom,
! [V_24Y] :
( c_24__type__337___24t(V_24Y)
<=> t(V_24Y,c_24__type__337) ) ).
fof('$tdef_$_type_57006',axiom,
! [V_24Y] :
( c_24__type__57006___24t(V_24Y)
<=> t(V_24Y,c_24__type__57006) ) ).
fof('$tdef_$_type_11719',axiom,
! [V_24Y] :
( c_24__type__11719___24t(V_24Y)
<=> t(V_24Y,c_24__type__11719) ) ).
fof('$tdef_$_type_57108',axiom,
! [V_24Y] :
( c_24__type__57108___24t(V_24Y)
<=> t(V_24Y,c_24__type__57108) ) ).
fof('$tdef_$_type_55005',axiom,
! [V_24Y] :
( c_24__type__55005___24t(V_24Y)
<=> t(V_24Y,c_24__type__55005) ) ).
fof('$tdef_$_type_250',axiom,
! [V_24Y] :
( c_24__type__250___24t(V_24Y)
<=> t(V_24Y,c_24__type__250) ) ).
fof('$tdef_$_type_1559',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1559___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1559___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_$_type_694',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__694___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__694___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2428',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2428___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2428___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1704',axiom,
! [V_24Y] :
( c_24__type__1704___24t(V_24Y)
<=> t(V_24Y,c_24__type__1704) ) ).
fof('$tdef_$_type_1287',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1287___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1287___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20071',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__20071___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__20071___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_5491',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__5491___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__5491___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8511',axiom,
! [V_24Y] :
( c_24__type__8511___24t(V_24Y)
<=> t(V_24Y,c_24__type__8511) ) ).
fof('$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_11847',axiom,
! [V_24Y] :
( c_24__type__11847___24t(V_24Y)
<=> t(V_24Y,c_24__type__11847) ) ).
fof('$tdef_$_type_10620',axiom,
! [V_24Y] :
( c_24__type__10620___24t(V_24Y)
<=> t(V_24Y,c_24__type__10620) ) ).
fof('$tdef_$_type_38365',axiom,
! [V_24Y] :
( c_24__type__38365___24t(V_24Y)
<=> t(V_24Y,c_24__type__38365) ) ).
fof('$tdef_$_type_5666',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__5666___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__5666___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_21100',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__21100___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__21100___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_62',axiom,
! [V_24X1,V_24Y] :
( c_24__type__62___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__62___24a1(V_24X1)) ) ).
fof('$tdef_$_type_49337',axiom,
! [V_24Y] :
( c_24__type__49337___24t(V_24Y)
<=> t(V_24Y,c_24__type__49337) ) ).
fof('$tdef_$_type_142',axiom,
! [V_24X1,V_24Y] :
( c_24__type__142___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__142___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15271',axiom,
! [V_24Y] :
( c_24__type__15271___24t(V_24Y)
<=> t(V_24Y,c_24__type__15271) ) ).
fof('$tdef_IntMap.Mapiter.alist',axiom,
! [V_24X1,V_24Y] :
( cIntMap_2eMapiter_2ealist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cIntMap_2eMapiter_2ealist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_19858',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19858___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19858___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_9263',axiom,
! [V_24X1,V_24Y] :
( c_24__type__9263___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__9263___24a1(V_24X1)) ) ).
fof('$tdef_$_type_55527',axiom,
! [V_24Y] :
( c_24__type__55527___24t(V_24Y)
<=> t(V_24Y,c_24__type__55527) ) ).
fof('$tdef_$_type_18558',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18558___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18558___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_8068',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__8068___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__8068___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11823',axiom,
! [V_24Y] :
( c_24__type__11823___24t(V_24Y)
<=> t(V_24Y,c_24__type__11823) ) ).
fof('$tdef_$_type_8853',axiom,
! [V_24Y] :
( c_24__type__8853___24t(V_24Y)
<=> t(V_24Y,c_24__type__8853) ) ).
fof('$tdef_$_type_742',axiom,
! [V_24Y] :
( c_24__type__742___24t(V_24Y)
<=> t(V_24Y,c_24__type__742) ) ).
fof('$tdef_$_type_32190',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__32190___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__32190___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.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_10634',axiom,
! [V_24Y] :
( c_24__type__10634___24t(V_24Y)
<=> t(V_24Y,c_24__type__10634) ) ).
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_$_type_795',axiom,
! [V_24Y] :
( c_24__type__795___24t(V_24Y)
<=> t(V_24Y,c_24__type__795) ) ).
fof('$tdef_$_type_18585',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18585___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18585___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_27789',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__27789___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__27789___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_57283',axiom,
! [V_24Y] :
( c_24__type__57283___24t(V_24Y)
<=> t(V_24Y,c_24__type__57283) ) ).
fof('$tdef_$_type_19645',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19645___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19645___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_21983',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21983___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21983___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_32536',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__32536___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__32536___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_57325',axiom,
! [V_24Y] :
( c_24__type__57325___24t(V_24Y)
<=> t(V_24Y,c_24__type__57325) ) ).
fof('$tdef_$_type_43819',axiom,
! [V_24Y] :
( c_24__type__43819___24t(V_24Y)
<=> t(V_24Y,c_24__type__43819) ) ).
fof('$tdef_$_type_11881',axiom,
! [V_24Y] :
( c_24__type__11881___24t(V_24Y)
<=> t(V_24Y,c_24__type__11881) ) ).
fof('$tdef_$_type_2589',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2589___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2589___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_25335',axiom,
! [V_24Y] :
( c_24__type__25335___24t(V_24Y)
<=> t(V_24Y,c_24__type__25335) ) ).
fof('$tdef_$_type_20284',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20284___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20284___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_54381',axiom,
! [V_24Y] :
( c_24__type__54381___24t(V_24Y)
<=> t(V_24Y,c_24__type__54381) ) ).
fof('$tdef_$_type_34827',axiom,
! [V_24Y] :
( c_24__type__34827___24t(V_24Y)
<=> t(V_24Y,c_24__type__34827) ) ).
fof('$tdef_$_type_4659',axiom,
! [V_24Y] :
( c_24__type__4659___24t(V_24Y)
<=> t(V_24Y,c_24__type__4659) ) ).
fof('$tdef_$_type_45595',axiom,
! [V_24Y] :
( c_24__type__45595___24t(V_24Y)
<=> t(V_24Y,c_24__type__45595) ) ).
fof('$tdef_$_type_55143',axiom,
! [V_24Y] :
( c_24__type__55143___24t(V_24Y)
<=> t(V_24Y,c_24__type__55143) ) ).
fof('$tdef_$_type_2631',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2631___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2631___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_$_type_5305',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5305___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5305___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_38754',axiom,
! [V_24Y] :
( c_24__type__38754___24t(V_24Y)
<=> t(V_24Y,c_24__type__38754) ) ).
fof('$tdef_$_type_17539',axiom,
! [V_24Y] :
( c_24__type__17539___24t(V_24Y)
<=> t(V_24Y,c_24__type__17539) ) ).
fof('$tdef_$_type_19450',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19450___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19450___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_576',axiom,
! [V_24X1,V_24Y] :
( c_24__type__576___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__576___24a1(V_24X1)) ) ).
fof('$tdef_$_type_808',axiom,
! [V_24Y] :
( c_24__type__808___24t(V_24Y)
<=> t(V_24Y,c_24__type__808) ) ).
fof('$tdef_$_type_22180',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22180___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22180___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1749',axiom,
! [V_24Y] :
( c_24__type__1749___24t(V_24Y)
<=> t(V_24Y,c_24__type__1749) ) ).
fof('$tdef_$_type_708',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__708___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__708___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_55112',axiom,
! [V_24Y] :
( c_24__type__55112___24t(V_24Y)
<=> t(V_24Y,c_24__type__55112) ) ).
fof('$tdef_$_type_22194',axiom,
! [V_24Y] :
( c_24__type__22194___24t(V_24Y)
<=> t(V_24Y,c_24__type__22194) ) ).
fof('$tdef_$_type_23708',axiom,
! [V_24Y] :
( c_24__type__23708___24t(V_24Y)
<=> t(V_24Y,c_24__type__23708) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_7',axiom,
! [V_24Y] :
( c_24__type__7___24t(V_24Y)
<=> t(V_24Y,c_24__type__7) ) ).
fof('$tdef_$_type_1833',axiom,
! [V_24Y] :
( c_24__type__1833___24t(V_24Y)
<=> t(V_24Y,c_24__type__1833) ) ).
fof('$tdef_$_type_22103',axiom,
! [V_24Y] :
( c_24__type__22103___24t(V_24Y)
<=> t(V_24Y,c_24__type__22103) ) ).
fof('$tdef_$_type_11850',axiom,
! [V_24Y] :
( c_24__type__11850___24t(V_24Y)
<=> t(V_24Y,c_24__type__11850) ) ).
fof('$tdef_$_type_139',axiom,
! [V_24Y] :
( c_24__type__139___24t(V_24Y)
<=> t(V_24Y,c_24__type__139) ) ).
fof('$tdef_$_type_4709',axiom,
! [V_24Y] :
( c_24__type__4709___24t(V_24Y)
<=> t(V_24Y,c_24__type__4709) ) ).
fof('$tdef_$_type_331',axiom,
! [V_24Y] :
( c_24__type__331___24t(V_24Y)
<=> t(V_24Y,c_24__type__331) ) ).
fof('$tdef_$_type_1720',axiom,
! [V_24Y] :
( c_24__type__1720___24t(V_24Y)
<=> t(V_24Y,c_24__type__1720) ) ).
fof('$tdef_$_type_6813',axiom,
! [V_24Y] :
( c_24__type__6813___24t(V_24Y)
<=> t(V_24Y,c_24__type__6813) ) ).
fof('$tdef_$_type_14986',axiom,
! [V_24Y] :
( c_24__type__14986___24t(V_24Y)
<=> t(V_24Y,c_24__type__14986) ) ).
fof('$tdef_$_type_33205',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__33205___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__33205___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_541',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__541___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__541___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.Nword',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2eNword) ) ).
fof('$tdef_$_type_488',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__488___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__488___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3732',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__3732___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__3732___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V0__l)
=> ! [V1__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead,V1__l_27)
=> ( cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead,V0__l,V1__l_27)) = cCoq_2eInit_2eDatatypes_2efalse
=> cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
%------------------------------------------------------------------------------