TPTP Problem File: SEV611+1.p
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%------------------------------------------------------------------------------
% File : SEV611+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - Eta Eta red ctx
% 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 : Eta.Eta.red.ctx.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 3370 (1203 unt; 0 def)
% Number of atoms : 13450 (3508 equ)
% Maximal formula atoms : 413 ( 3 avg)
% Number of connectives : 10209 ( 129 ~; 947 |;2439 &)
% (1325 <=>;5369 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 7 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 681 ( 680 usr; 0 prp; 1-23 aty)
% Number of functors : 2041 (2041 usr;1289 con; 0-22 aty)
% Number of variables : 12745 (11665 !;1080 ?)
% SPC : FOF_UNK_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.bool$1207',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> ( ( cEta_2eis__eta__core___24a2(c_24__let__var__var__4__r_27__1198__1200__1204___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_241207___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cTait_2eTerm_2edown___24a2(cCoq_2eInit_2eDatatypes_2eO,cTait_2eApps_2eleft__app___24a1(c_24__let__var__var__4__r_27__1198__1200__1204___24a1(Vv__CANONICAL__1))) )
| ( cEta_2eis__eta__core___24a2(c_24__let__var__var__4__r_27__1198__1200__1204___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_241207___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cTait_2eTerm_2eAbs___24a2(Vv__CANONICAL__0,c_24__let__var__var__4__r_27__1198__1200__1204___24a1(Vv__CANONICAL__1)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$153299',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
& ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_24153299___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
& ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_24153299___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$100174',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_24101187___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)) )
| ? [Vvar__1___24Anonymous__100178] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__100178)
& ? [Vvar__2___24Anonymous__100179] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__2___24Anonymous__100179)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24101187___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__1___24Anonymous__100178,Vvar__2___24Anonymous__100179)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__1___24Anonymous__100178,c_24__fix__103877__v__CANONICAL__0___24a2(Vvar__2___24Anonymous__100179,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)))) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$101187',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_24101466___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24101187___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm) )
| ? [Vvar__1___24Anonymous__101191] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__101191)
& ? [Vvar__2___24Anonymous__101192] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__2___24Anonymous__101192)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24101466___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__1___24Anonymous__101191,Vvar__2___24Anonymous__101192)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24101187___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,c_24__case__Tait_2eTerm_2eterm_24101877___24a1(Vvar__1___24Anonymous__101191),c_24__fix__102516__v__CANONICAL__0___24a1(Vvar__2___24Anonymous__101192)) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$101466',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_24101511___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24101466___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm) )
| ? [Vvar__1___24Anonymous__101470] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__101470)
& ? [Vvar__2___24Anonymous__101471] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__2___24Anonymous__101471)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24101511___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1___24Anonymous__101470,Vvar__2___24Anonymous__101471)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24101466___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,cTait_2eTerm_2eVar___24a1(Vvar__1___24Anonymous__101470),c_24__fix__101566__v__CANONICAL__0___24a1(Vvar__2___24Anonymous__101471)) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$66700',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2466787___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2466700___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__66704] :
( t(Vvar__1___24Anonymous__66704,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__66705] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__66705)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2466787___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__66704,Vvar__2___24Anonymous__66705)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2466700___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__66704,c_24__fix__66832__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__66705,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$66787',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2466787___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__66791] :
( t(Vvar__1___24Anonymous__66791,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__66792] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__66792)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__66791,Vvar__2___24Anonymous__66792)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2466787___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__66791,c_24__fix__66832__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__66792,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$84376',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vv__CANONICAL__4)
=> ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2484376___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__5) )
| ? [Vvar__1___24Anonymous__84380] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__84380)
& ? [Vvar__2___24Anonymous__84381] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__2___24Anonymous__84381)
& Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__1___24Anonymous__84380,Vvar__2___24Anonymous__84381)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2484376___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = c_24__fix__84413__v__CANONICAL__0___24a2(Vvar__2___24Anonymous__84381,cTait_2eTerm_2eApp___24a2(cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__5),Vvar__1___24Anonymous__84380)) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$101511',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24101511___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__0___24Anonymous__101512] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__101512)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__101512)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24101511___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eO,c_24__fix__101530__v__CANONICAL__0___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),Vvar__0___24Anonymous__101512)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$82480',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2482480___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__82481] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82481)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82481)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2482480___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__82481)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$82502',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2482502___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__82503] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82503)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82503)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2482502___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__82503)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$150833',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__53311___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__150838] :
( t(Vvar__2___24Anonymous__150838,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__150839] :
( t(Vvar__3___24Anonymous__150839,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__150838,Vvar__3___24Anonymous__150839)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_24150833___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__150838)),Vvar__3___24Anonymous__150839)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$53298',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__53311___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__53303] :
( t(Vvar__2___24Anonymous__53303,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__53304] :
( t(Vvar__3___24Anonymous__53304,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__53303,Vvar__3___24Anonymous__53304)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2453298___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__53303)),Vvar__3___24Anonymous__53304)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Specif.sumbool$1214',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( cTait_2eApps_2eright__app___24a1(Vv__CANONICAL__0) = cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__1)
& cTait_2eTerm_2eterm__dec___24a2(cTait_2eApps_2eright__app___24a1(Vv__CANONICAL__0),cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__1)) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__1223___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__1224___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_241214___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cTait_2eApps_2eright__app___24a1(Vv__CANONICAL__0) != cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__1)
& cTait_2eTerm_2eterm__dec___24a2(cTait_2eApps_2eright__app___24a1(Vv__CANONICAL__0),cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__1)) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__1225___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__1226___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_241214___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$153578',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZ0
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24153578___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) )
| ? [Vvar__0___24Anonymous__153579] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153579)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__153579)
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24153578___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__153579) ) )
| ? [Vvar__0___24Anonymous__153580] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153580)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__153580)
& ( c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24153578___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__1 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__153580) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$82497',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2482502___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2482497___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__82498] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82498)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2482502___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__82498)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2482497___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__82498) )
| ? [Vvar__0___24Anonymous__82499] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82499)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2482502___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__82499)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2482497___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__82499) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$153533',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__153534] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153534)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__153534)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24153533___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__153549__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__153534)) )
| ? [Vvar__0___24Anonymous__153541] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153541)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__153541)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24153533___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__153541) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24153533___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_case_Tait.Term.term$101877',axiom,
! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ( ? [Vvar__0___24Anonymous__101878] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__101878)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__101878)
=> ( Vv__CANONICAL__0 = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__101878)
& ( ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__101878))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__101878) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__101878),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__101878,cCoq_2eInit_2eDatatypes_2eO))
& c_24__case__Tait_2eTerm_2eterm_24101877___24a1(Vv__CANONICAL__0) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__101878)) )
| ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__101878,cCoq_2eInit_2eDatatypes_2eO))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__101878) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__101878),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__101878,cCoq_2eInit_2eDatatypes_2eO))
& c_24__case__Tait_2eTerm_2eterm_24101877___24a1(Vv__CANONICAL__0) = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__101878) ) ) ) ) )
| ? [Vvar__0___24Anonymous__101890] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__101890)
& ? [Vvar__1___24Anonymous__101891] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__101891)
& Vv__CANONICAL__0 = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__101890,Vvar__1___24Anonymous__101891)
& c_24__case__Tait_2eTerm_2eterm_24101877___24a1(Vv__CANONICAL__0) = cTait_2eTerm_2eApp___24a2(c_24__fix__102016__v__CANONICAL__0___24a2(cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__101890),c_24__fix__102016__v__CANONICAL__0___24a2(cCoq_2eInit_2eDatatypes_2eO,Vvar__1___24Anonymous__101891)) ) )
| ? [Vvar__0___24Anonymous__101949] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__101949)
& ? [Vvar__1___24Anonymous__101950] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__101950)
& Vv__CANONICAL__0 = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__101949,Vvar__1___24Anonymous__101950)
& c_24__case__Tait_2eTerm_2eterm_24101877___24a1(Vv__CANONICAL__0) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__101949,c_24__fix__102016__v__CANONICAL__0___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),Vvar__1___24Anonymous__101950)) ) ) ) ) ).
fof('$_case_Tait.Term.term$134937',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__5)
=> ( ? [Vvar__0___24Anonymous__134938] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__134938)
& Vv__CANONICAL__5 = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__134938)
& c_24__case__Tait_2eTerm_2eterm_24134937___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eLists_2eList_2enth___24a4(cTait_2eTerm_2eterm,Vvar__0___24Anonymous__134938,cTait_2eSubst_2esupport___24a1(cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4)))),cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__134938,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2eterm,cTait_2eSubst_2esupport___24a1(cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4)))))),cTait_2eSubst_2eshift___24a1(cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4))))))) )
| ? [Vvar__0___24Anonymous__135665] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__135665)
& ? [Vvar__1___24Anonymous__135666] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__135666)
& Vv__CANONICAL__5 = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__135665,Vvar__1___24Anonymous__135666)
& c_24__case__Tait_2eTerm_2eterm_24134937___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cTait_2eTerm_2eApp___24a2(c_24__fix__105972__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__135665,cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4)))),c_24__fix__105972__v__CANONICAL__0___24a2(Vvar__1___24Anonymous__135666,cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4))))) ) )
| ? [Vvar__0___24Anonymous__136476] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__136476)
& ? [Vvar__1___24Anonymous__136477] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__136477)
& Vv__CANONICAL__5 = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__136476,Vvar__1___24Anonymous__136477)
& c_24__case__Tait_2eTerm_2eterm_24134937___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__136476,c_24__fix__105972__v__CANONICAL__0___24a2(Vvar__1___24Anonymous__136477,cTait_2eSubst_2esublift___24a1(cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4)))))) ) ) ) ) ).
fof('$_case_Tait.Term.term$97196',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__4)
=> ( ? [Vvar__0___24Anonymous__97197] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__97197)
& Vv__CANONICAL__4 = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__97197)
& c_24__case__Tait_2eTerm_2eterm_2497196___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eLists_2eList_2enth___24a4(cTait_2eTerm_2eterm,Vvar__0___24Anonymous__97197,cTait_2eSubst_2esupport___24a1(cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__5),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5)))),cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__97197,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2eterm,cTait_2eSubst_2esupport___24a1(cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__5),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5)))))),cTait_2eSubst_2eshift___24a1(cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__5),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5))))))) )
| ? [Vvar__0___24Anonymous__97924] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__97924)
& ? [Vvar__1___24Anonymous__97925] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__97925)
& Vv__CANONICAL__4 = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__97924,Vvar__1___24Anonymous__97925)
& c_24__case__Tait_2eTerm_2eterm_2497196___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cTait_2eTerm_2eApp___24a2(c_24__fix__105972__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__97924,cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__5),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5)))),c_24__fix__105972__v__CANONICAL__0___24a2(Vvar__1___24Anonymous__97925,cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__5),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5))))) ) )
| ? [Vvar__0___24Anonymous__98735] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__98735)
& ? [Vvar__1___24Anonymous__98736] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__98736)
& Vv__CANONICAL__4 = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__98735,Vvar__1___24Anonymous__98736)
& c_24__case__Tait_2eTerm_2eterm_2497196___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__98735,c_24__fix__105972__v__CANONICAL__0___24a2(Vvar__1___24Anonymous__98736,cTait_2eSubst_2esublift___24a1(cTait_2eSubst_2emk__sub___24a2(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(Vv__CANONICAL__5),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5)))))) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_33300',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__33300___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_75950',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__75953] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__75953)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__75953)
& c_24__let__16__mkpow__75950___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__75954] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__75954)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__75954)
& c_24__let__16__mkpow__75950___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__75950___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_mkopp_pow_75951',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__75951___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__75950___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_75952',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__75952___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__75950___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_var_6_p_50317_50320',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__50316] : c_24__let__var__6__p__50317__50320___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__50316) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__50316) ).
fof('$_def_$_let_var_6_p_50319_50321',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__50318] : c_24__let__var__6__p__50319__50321___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__50318) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__50318) ).
fof('$_def_$_let_var_v_CANONICAL_4_509_513',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__0___24Anonymous__508] : c_24__let__var__v__CANONICAL__4__509__513___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__0___24Anonymous__508) = happ(Vv__CANONICAL__1,Vvar__0___24Anonymous__508) ).
fof('$_def_$_let_var_var_4_r\'_1198_1200_1204',axiom,
! [Vvar__1___24Anonymous__1196] : c_24__let__var__var__4__r_27__1198__1200__1204___24a1(Vvar__1___24Anonymous__1196) = cEta_2eeta__red___24a1(Vvar__1___24Anonymous__1196) ).
fof('$_def_Coq.Arith.Compare_dec.le_gt_dec',axiom,
! [V0__n,V1__m] : cCoq_2eArith_2eCompare__dec_2ele__gt__dec___24a2(V0__n,V1__m) = cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V0__n,V1__m) ).
fof('$_def_Coq.Arith.Compare_dec.le_lt_dec',axiom,
! [V0__n,V1__m] : cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2enat__rec___24a5(c_24__lam__26,c_24__lam__30,c_24__lam__53,V0__n,V1__m) ).
fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__81185] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81185)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__81185)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__81186] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81186)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__81186)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__81189] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81189)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__81189)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__81186,Vvar__0___24Anonymous__81189) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eq_dec',axiom,
! [V0__n] : cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enat__rec___24a4(c_24__lam__414,c_24__lam__422,c_24__lam__507,V0__n) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.le',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2ele = cCoq_2eInit_2ePeano_2ele ).
fof('$_def_Coq.Arith.PeanoNat.Nat.lt',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2elt = cCoq_2eInit_2ePeano_2elt ).
fof('$_def_Coq.Arith.Wf_nat.ltof',axiom,
! [V0__A,V1__f,V2__a,V3__b] :
( cCoq_2eArith_2eWf__nat_2eltof___24a4(V0__A,V1__f,V2__a,V3__b)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(happ(V1__f,V2__a),happ(V1__f,V3__b))) ) ).
fof('$_def_Coq.Bool.Bool.Is_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24True) ) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24False) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.eqb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.ifb',axiom,
! [V0__b1,V1__b2,V2__b3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V2__b3 ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V0__s)
<=> ! [V1__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__a)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__a,V0__s) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__i,V1__t)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__i,V1__t) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__37557] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__37557)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__37557) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__37603] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__37603)
& ? [Vvar__1___24Anonymous__37604] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__37604)
& ? [Vvar__2___24Anonymous__37605] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__37605)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37603,Vvar__1___24Anonymous__37604,Vvar__2___24Anonymous__37605)
& ( ? [Vvar__0___24Anonymous__37618] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37618)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37618)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__37618,Vvar__2___24Anonymous__37605) )
| ? [Vvar__0___24Anonymous__37619] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37619)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37619)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__37619,Vvar__0___24Anonymous__37603) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__37604 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.rev',axiom,
! [V0__x] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev___24a1(V0__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
! [V1__y,V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__y)
=> ( ? [Vvar__0___24Anonymous__37807] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37807)
& V1__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37807)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__37807,cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__x)) )
| ? [Vvar__0___24Anonymous__37808] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37808)
& V1__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37808)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__37808,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__x)) )
| ( V1__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = V2__x ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__37583] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__37583)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__37583) ) ).
fof('$_def_Coq.Init.Datatypes.ID',axiom,
! [Vvar__152019] :
( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__152019)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> t(happ(happ(Vvar__152019,V0__A),V1___24Anonymous),V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.IDProp',axiom,
( p(cCoq_2eInit_2eDatatypes_2eIDProp)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> p(V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.andb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__743] :
( t(Vvar__1___24Anonymous__743,V0__A)
& ? [Vvar__2___24Anonymous__744] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__744)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__743,Vvar__2___24Anonymous__744)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__743,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__744,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__40865] :
( t(Vvar__2___24Anonymous__40865,V0__A)
& ? [Vvar__3___24Anonymous__40866] :
( t(Vvar__3___24Anonymous__40866,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__40865,Vvar__3___24Anonymous__40866)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__40865 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__733] :
( t(Vvar__1___24Anonymous__733,V0__A)
& ? [Vvar__2___24Anonymous__734] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__734)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__733,Vvar__2___24Anonymous__734)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__734)) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Datatypes.list_rect',axiom,
! [V0__A,V1__P,V2__f,V3__f,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__66210___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = V2__f )
| ? [Vvar__1___24Anonymous__66204] :
( t(Vvar__1___24Anonymous__66204,V0__A)
& ? [Vvar__2___24Anonymous__66205] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66205)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__66204,Vvar__2___24Anonymous__66205)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = happ(happ(happ(V3__f,Vvar__1___24Anonymous__66204),Vvar__2___24Anonymous__66205),cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,Vvar__2___24Anonymous__66205)) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__63243___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
| ? [Vvar__0___24Anonymous__63241] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63241)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__63241)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__63241),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__63241)) ) ) ) ) ).
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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__40877] :
( t(Vvar__2___24Anonymous__40877,V0__A)
& ? [Vvar__3___24Anonymous__40878] :
( t(Vvar__3___24Anonymous__40878,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__40877,Vvar__3___24Anonymous__40878)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__40878 ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Logic_Type.notT',axiom,
! [V0__A] :
( cCoq_2eInit_2eLogic__Type_2enotT___24a1(V0__A)
<=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> p(c_24False) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__297] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__297)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__297)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__297,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__32529] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32529)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32529)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__32532] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32532)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32532)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__32529,Vvar__0___24Anonymous__32532)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.min',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__66001] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66001)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66001)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__66004] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66004)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66004)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__66001,Vvar__0___24Anonymous__66004)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__32501] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32501)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32501)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__32501,V2__m)) ) ) ) ).
fof('$_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__85] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__85)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__85)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__85 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__87] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__87)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__87)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__90] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__90)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__90)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__87,Vvar__0___24Anonymous__90) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.t',axiom,
! [Vvar__152593] :
( cCoq_2eInit_2eNat_2et___24t(Vvar__152593)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__152593) ) ).
fof('$_def_Coq.Init.Nat.zero',axiom,
cCoq_2eInit_2eNat_2ezero = cCoq_2eInit_2eDatatypes_2eO ).
fof('$_def_Coq.Init.Peano.IsSucc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__82450] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82450)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82450)
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ).
fof('$_def_Coq.Init.Specif.except',axiom,
cCoq_2eInit_2eSpecif_2eexcept = cCoq_2eInit_2eLogic_2eFalse__rec ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__78288___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__78282] :
( t(Vvar__2__x__78282,V0__A)
& p(happ(V1__P,Vvar__2__x__78282))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__78282)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__78282 ) ) ) ) ).
fof('$_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('$_def_Coq.Lists.List.ForallPairs',axiom,
! [V0__A,V1__R,V2__l] :
( cCoq_2eLists_2eList_2eForallPairs___24a3(V0__A,V1__R,V2__l)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__b,V2__l)
=> p(happ(happ(V1__R,V3__a),V4__b)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__43486] :
( t(Vvar__1___24Anonymous__43486,V0__A)
& ? [Vvar__2___24Anonymous__43487] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__43487)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__43486,Vvar__2___24Anonymous__43487)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__43486 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__43487) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.concat',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A))
& cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__72035] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__1___24Anonymous__72035)
& ? [Vvar__2___24Anonymous__72036] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__72036)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__1___24Anonymous__72035,Vvar__2___24Anonymous__72036)
& cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__1___24Anonymous__72035,cCoq_2eLists_2eList_2econcat___24a2(V0__A,Vvar__2___24Anonymous__72036)) ) ) ) ) ) ).
fof('$_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__32487] :
( t(Vvar__1___24Anonymous__32487,V0__A)
& ? [Vvar__2___24Anonymous__32488] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__32488)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__32487,Vvar__2___24Anonymous__32488)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(happ(V1__f,Vvar__1___24Anonymous__32487),cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__32488)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.filter',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__43509] :
( t(Vvar__1___24Anonymous__43509,V0__A)
& ? [Vvar__2___24Anonymous__43510] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__43510)
& ( cType___24t(V0__A)
=> ( c_24__type__851___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__43509,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__43509,Vvar__2___24Anonymous__43510)
& ( ( happ(V1__f,Vvar__1___24Anonymous__43509) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__43509,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__43510)) )
| ( happ(V1__f,Vvar__1___24Anonymous__43509) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__43510) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__144785] :
( t(Vvar__1___24Anonymous__144785,V0__A)
& ? [Vvar__2___24Anonymous__144786] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__144786)
& ( cType___24t(V0__A)
=> ( c_24__type__851___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__144785,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__144785,Vvar__2___24Anonymous__144786)
& ( ( happ(V1__f,Vvar__1___24Anonymous__144785) = 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__144785) )
| ( happ(V1__f,Vvar__1___24Anonymous__144785) = 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__144786) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.firstn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__0___24Anonymous__72997] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__72997)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__72997)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__73004] :
( t(Vvar__1___24Anonymous__73004,V0__A)
& ? [Vvar__2___24Anonymous__73005] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__73005)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__73004,Vvar__2___24Anonymous__73005)
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__73004,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,Vvar__0___24Anonymous__72997,Vvar__2___24Anonymous__73005)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.flat_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_2eflat__map___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__72833] :
( t(Vvar__1___24Anonymous__72833,V0__A)
& ? [Vvar__2___24Anonymous__72834] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__72834)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__72833,Vvar__2___24Anonymous__72834)
& cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__72833),cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__72834)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
| ? [Vvar__1___24Anonymous__785] :
( t(Vvar__1___24Anonymous__785,V1__B)
& ? [Vvar__2___24Anonymous__786] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__786)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__785,Vvar__2___24Anonymous__786)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__786,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__785)) ) ) ) ) ) ) ).
fof('$_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__32456] :
( t(Vvar__1___24Anonymous__32456,V1__B)
& ? [Vvar__2___24Anonymous__32457] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__32457)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__32456,Vvar__2___24Anonymous__32457)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__32456),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__32457)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.forallb',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1___24Anonymous__43498] :
( t(Vvar__1___24Anonymous__43498,V0__A)
& ? [Vvar__2___24Anonymous__43499] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__43499)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__43498,Vvar__2___24Anonymous__43499)
& cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(V1__f,Vvar__1___24Anonymous__43498),cCoq_2eLists_2eList_2eforallb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__43499)) ) ) ) ) ) ).
fof('$_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__144729] :
( t(Vvar__1___24Anonymous__144729,V0__A)
& ? [Vvar__2___24Anonymous__144730] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__144730)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__144729,Vvar__2___24Anonymous__144730)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__144729 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd_error',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__71727] :
( t(Vvar__1___24Anonymous__71727,V0__A)
& ? [Vvar__2___24Anonymous__71728] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__71728)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__71727,Vvar__2___24Anonymous__71728)
& cCoq_2eLists_2eList_2ehd__error___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__71727) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.incl',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__66279] :
( t(Vvar__1___24Anonymous__66279,V0__A)
& ? [Vvar__2___24Anonymous__66280] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66280)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66280)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__66279,Vvar__2___24Anonymous__66280)
& ( ( Vvar__2___24Anonymous__66280 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__66279 )
| ? [Vvar__1___24Anonymous__66291] :
( t(Vvar__1___24Anonymous__66291,V0__A)
& ? [Vvar__2___24Anonymous__66292] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66292)
& Vvar__2___24Anonymous__66280 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__66291,Vvar__2___24Anonymous__66292)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__66280,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.lel',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V2__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__m))) ) ).
fof('$_def_Coq.Lists.List.list_prod',axiom,
! [V0__A,V1__B,V3__l,V4__l_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__72973] :
( t(Vvar__1___24Anonymous__72973,V0__A)
& ? [Vvar__2___24Anonymous__72974] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__72974)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__72973,Vvar__2___24Anonymous__72974)
& cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eLists_2eList_2emap___24a4(V1__B,cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),c_24__lam__72981___24a3(V0__A,V1__B,Vvar__1___24Anonymous__72973),V4__l_27),cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,Vvar__2___24Anonymous__72974,V4__l_27)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__766] :
( t(Vvar__1___24Anonymous__766,V0__A)
& ? [Vvar__2___24Anonymous__767] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__767)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__766,Vvar__2___24Anonymous__767)
& 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__766),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__767)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__259] :
( t(Vvar__1___24Anonymous__259,V0__A)
& ? [Vvar__2___24Anonymous__260] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__260)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__259,Vvar__2___24Anonymous__260)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__259 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__262] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__262)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__262)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__269] :
( t(Vvar__1___24Anonymous__269,V0__A)
& ? [Vvar__2___24Anonymous__270] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__270)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__269,Vvar__2___24Anonymous__270)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__262,Vvar__2___24Anonymous__270,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_default',axiom,
! [V0__A,V1__default,V2__l,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ? [Vvar__1___24Anonymous__144764] :
( t(Vvar__1___24Anonymous__144764,V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__144764)
& cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V1__default,V2__l,V3__n) = Vvar__1___24Anonymous__144764 )
| ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V1__default,V2__l,V3__n) = V1__default ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_error',axiom,
! [V0__A,V2__l,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__71871] :
( t(Vvar__1___24Anonymous__71871,V0__A)
& ? [Vvar__2___24Anonymous__71872] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__71872)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__71871,Vvar__2___24Anonymous__71872)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__71871) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__71874] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__71874)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__71874)
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__71881] :
( t(Vvar__1___24Anonymous__71881,V0__A)
& ? [Vvar__2___24Anonymous__71882] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__71882)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__71881,Vvar__2___24Anonymous__71882)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,Vvar__2___24Anonymous__71882,Vvar__0___24Anonymous__71874) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_ok',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__144741] :
( t(Vvar__1___24Anonymous__144741,V0__A)
& ? [Vvar__2___24Anonymous__144742] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__144742)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__144741,Vvar__2___24Anonymous__144742)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__144744] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__144744)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__144744)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__144751] :
( t(Vvar__1___24Anonymous__144751,V0__A)
& ? [Vvar__2___24Anonymous__144752] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__144752)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__144751,Vvar__2___24Anonymous__144752)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,Vvar__0___24Anonymous__144744,Vvar__2___24Anonymous__144752,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.removelast',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__66303] :
( t(Vvar__1___24Anonymous__66303,V0__A)
& ? [Vvar__2___24Anonymous__66304] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66304)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66304)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__66303,Vvar__2___24Anonymous__66304)
& ( ( Vvar__2___24Anonymous__66304 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__66315] :
( t(Vvar__1___24Anonymous__66315,V0__A)
& ? [Vvar__2___24Anonymous__66316] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66316)
& Vvar__2___24Anonymous__66304 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__66315,Vvar__2___24Anonymous__66316)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__66303,cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,Vvar__2___24Anonymous__66304)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.repeat',axiom,
! [V0__A,V2__x,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,V3__n) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__0___24Anonymous__73674] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__73674)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__73674)
& cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,V3__n) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,Vvar__0___24Anonymous__73674)) ) ) ) ) ).
fof('$_def_Coq.Lists.List.rev',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__756] :
( t(Vvar__1___24Anonymous__756,V0__A)
& ? [Vvar__2___24Anonymous__757] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__757)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__756,Vvar__2___24Anonymous__757)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,Vvar__2___24Anonymous__757),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__756,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.rev\'',axiom,
! [V0__A,V1__l] : cCoq_2eLists_2eList_2erev_27___24a2(V0__A,V1__l) = cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ).
fof('$_def_Coq.Lists.List.rev_append',axiom,
! [V0__A,V2__l,V3__l_27] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V2__l,V3__l_27) = V3__l_27 )
| ? [Vvar__1___24Anonymous__72016] :
( t(Vvar__1___24Anonymous__72016,V0__A)
& ? [Vvar__2___24Anonymous__72017] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__72017)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__72016,Vvar__2___24Anonymous__72017)
& cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V2__l,V3__l_27) = cCoq_2eLists_2eList_2erev__append___24a3(V0__A,Vvar__2___24Anonymous__72017,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__72016,V3__l_27)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.seq',axiom,
! [V1__start,V2__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__len)
=> ( ( V2__len = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__0___24Anonymous__281] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__281)
& V2__len = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__281)
& cCoq_2eLists_2eList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,V1__start,cCoq_2eLists_2eList_2eseq___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__start),Vvar__0___24Anonymous__281)) ) ) ) ).
fof('$_def_Coq.Lists.List.skipn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = V3__l )
| ? [Vvar__0___24Anonymous__73013] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__73013)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__73013)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__73020] :
( t(Vvar__1___24Anonymous__73020,V0__A)
& ? [Vvar__2___24Anonymous__73021] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__73021)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__73020,Vvar__2___24Anonymous__73021)
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = cCoq_2eLists_2eList_2eskipn___24a3(V0__A,Vvar__0___24Anonymous__73013,Vvar__2___24Anonymous__73021) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__71736] :
( t(Vvar__1___24Anonymous__71736,V0__A)
& ? [Vvar__2___24Anonymous__71737] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__71737)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__71736,Vvar__2___24Anonymous__71737)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__71737 ) ) ) ) ) ).
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.inclA',axiom,
! [V0__A,V1__eqA,V2__l,V3__l_27] :
( cCoq_2eLists_2eSetoidList_2einclA___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.transpose2',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> ! [V7__z_27] :
( t(V7__z_27,V1__B)
=> ( p(happ(happ(V2__eqB,V6__z),V7__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V7__z_27)))) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V7__z)))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr2',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ! [V8__z_27] :
( t(V8__z_27,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> ( p(happ(happ(V2__eqB,V7__z),V8__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V8__z_27)))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.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__37252] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37252)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37252)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__37255] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37255)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37255)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__37252,Vvar__0___24Anonymous__37255)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__65774] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65774)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__65774)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
| ? [Vvar__0___24Anonymous__65777] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65777)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__65777)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__65774,V1__b) ) ) ) ) ) ) ) ).
fof('$_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__37265] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37265)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37265)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__37266] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37266)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37266)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__37269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37269)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37269)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__37266,Vvar__0___24Anonymous__37269) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__37259] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37259)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37259)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__37262] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37262)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37262)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__37259,Vvar__0___24Anonymous__37262)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
! [Vvar__153490] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__153490)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__153490) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__54822] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54822)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__54822)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__54822) ) ) ) ).
fof('$_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__54828] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54828)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54828)
& ( ? [Vvar__0___24Anonymous__54832] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54832)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54832)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__54827__1__add__carry___24a2(Vvar__0___24Anonymous__54828,Vvar__0___24Anonymous__54832)) )
| ? [Vvar__0___24Anonymous__54833] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54833)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54833)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__54828,Vvar__0___24Anonymous__54833)) )
| ( 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__54828)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__54834] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54834)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54834)
& ( ? [Vvar__0___24Anonymous__54838] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54838)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54838)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__54834,Vvar__0___24Anonymous__54838)) )
| ? [Vvar__0___24Anonymous__54839] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54839)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54839)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__54834,Vvar__0___24Anonymous__54839)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54834) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__54840] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54840)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54840)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__54840)) )
| ? [Vvar__0___24Anonymous__54841] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54841)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54841)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54841) )
| ( 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.div2',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__159382] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__159382)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__159382)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__159382 )
| ? [Vvar__0___24Anonymous__159383] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__159383)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__159383)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__159383 )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__54873] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54873)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54873)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__54873),Vvar__0___24Anonymous__54873)) )
| ? [Vvar__0___24Anonymous__54874] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54874)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54874)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__54874),Vvar__0___24Anonymous__54874) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__82550] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82550)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__82550)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__82550,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__82551] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82551)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__82551)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__82551,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__54858] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54858)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54858)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54858)) )
| ? [Vvar__0___24Anonymous__54859] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54859)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54859)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__54859)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__54870] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54870)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__54870)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__54870 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__54825] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54825)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54825)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__54825)) )
| ? [Vvar__0___24Anonymous__54826] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54826)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54826)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54826) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
! [Vvar__153492] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__153492)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__153492) ) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__44609] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__44609)
& ? [Vvar__1__Qden__44610] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__44610)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__44609,Vvar__1__Qden__44610)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__44610 ) ) ) ).
fof('$_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('$_def_Coq.QArith.QArith_base.Qinv',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ( ( cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__73711] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__73711)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__73711)
& cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)),Vvar__0___24Anonymous__73711) )
| ? [Vvar__0___24Anonymous__73712] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__73712)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__73712)
& cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)),Vvar__0___24Anonymous__73712) ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qle',axiom,
! [V0__x,V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQle___24a2(V0__x,V1__y)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x))))) ) ).
fof('$_def_Coq.QArith.QArith_base.Qlt',axiom,
! [V0__x,V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQlt___24a2(V0__x,V1__y)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x))))) ) ).
fof('$_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.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__44604] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__44604)
& ? [Vvar__1__Qden__44605] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__44605)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__44604,Vvar__1__Qden__44605)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__44604 ) ) ) ).
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('$_def_Coq.QArith.QArith_base.Qpower',axiom,
! [V0__q,V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( ( V1__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V0__q,V1__z) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__73716] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__73716)
& V1__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__73716)
& cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V0__q,V1__z) = cCoq_2eQArith_2eQArith__base_2eQpower__positive___24a2(V0__q,Vvar__0___24Anonymous__73716) )
| ? [Vvar__0___24Anonymous__73717] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__73717)
& V1__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__73717)
& cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V0__q,V1__z) = cCoq_2eQArith_2eQArith__base_2eQinv___24a1(cCoq_2eQArith_2eQArith__base_2eQpower__positive___24a2(V0__q,Vvar__0___24Anonymous__73717)) ) ) ) ).
fof('$_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__44772] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44772)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__44772)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__44772) )
| ? [Vvar__0___24Anonymous__44773] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44773)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__44773)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__44773)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.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__53981] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__53981)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__53981)
& 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__53981)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__32418___24a1(V0__A) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__32418___24a1(V0__U) ).
fof('$_def_Coq.Sets.Relations_1.Transitive',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ! [V4__z] :
( t(V4__z,V0__U)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Strings.String.append',axiom,
! [V1__s1,V2__s2] :
( cCoq_2eStrings_2eString_2estring___24t(V1__s1)
=> ( ( V1__s1 = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2eappend___24a2(V1__s1,V2__s2) = V2__s2 )
| ? [Vvar__0___24Anonymous__153207] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__153207)
& ? [Vvar__1___24Anonymous__153208] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__153208)
& V1__s1 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__153207,Vvar__1___24Anonymous__153208)
& cCoq_2eStrings_2eString_2eappend___24a2(V1__s1,V2__s2) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__153207,cCoq_2eStrings_2eString_2eappend___24a2(Vvar__1___24Anonymous__153208,V2__s2)) ) ) ) ) ).
fof('$_def_Coq.Strings.String.string_of_list_ascii',axiom,
! [V1__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,V1__s)
=> ( ( V1__s = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eStrings_2eAscii_2eascii)
& cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(V1__s) = cCoq_2eStrings_2eString_2eEmptyString )
| ? [Vvar__1___24Anonymous__78584] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1___24Anonymous__78584)
& ? [Vvar__2___24Anonymous__78585] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,Vvar__2___24Anonymous__78585)
& V1__s = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eStrings_2eAscii_2eascii,Vvar__1___24Anonymous__78584,Vvar__2___24Anonymous__78585)
& cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(V1__s) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1___24Anonymous__78584,cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(Vvar__2___24Anonymous__78585)) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt = cCoq_2eNArith_2eBinNat_2eN_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__153491] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__153491)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__153491) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt = cCoq_2eInit_2ePeano_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__83749] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__83749)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__83749) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__153428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153428)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__153428)
& ( ? [Vvar__0___24Anonymous__153432] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153432)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__153432)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__153428,Vvar__0___24Anonymous__153432) ) )
| ? [Vvar__0___24Anonymous__153433] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153433)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__153433)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__153434] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153434)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__153434)
& ( ? [Vvar__0___24Anonymous__153438] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153438)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__153438)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__153439] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153439)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__153439)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__153434,Vvar__0___24Anonymous__153439) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__153440] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153440)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__153440)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__153441] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153441)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__153441)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__153426] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__153426)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__153426) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__153569] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__153569)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__153569) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__153570] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__153570)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__153570) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__153581] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__153581)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__153581) ) ).
fof('$_def_Coq.Vectors.VectorDef.to_list',axiom,
! [V0__A,V1__n,V2__v] : cCoq_2eVectors_2eVectorDef_2eto__list___24a3(V0__A,V1__n,V2__v) = c_24__fix__80294__v__CANONICAL__2___24a5(V0__A,V1__n,V1__n,V2__v,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ).
fof('$_def_Coq.ZArith.BinInt.Z.eq',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__54964] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54964)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__54964)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__54964) )
| ? [Vvar__0___24Anonymous__54965] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54965)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__54965)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__54965) ) ) ) ).
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__521] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__521)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__521)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__525] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__525)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__525)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__521,Vvar__0___24Anonymous__525)) )
| ? [Vvar__0___24Anonymous__526] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__526)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__526)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__521,Vvar__0___24Anonymous__526) ) ) ) ) )
| ? [Vvar__0___24Anonymous__527] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__527)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__527)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__531] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__531)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__531)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__531,Vvar__0___24Anonymous__527) )
| ? [Vvar__0___24Anonymous__532] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__532)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__532)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__527,Vvar__0___24Anonymous__532)) ) ) ) ) ) ) ) ).
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__554] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__554)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__554)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__555] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__555)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__555)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__556] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__556)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__556)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__560] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__560)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__560)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__556,Vvar__0___24Anonymous__560) )
| ? [Vvar__0___24Anonymous__561] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__561)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__561)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__562] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__562)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__562)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__566] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__566)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__566)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__567] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__567)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__567)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__562,Vvar__0___24Anonymous__567)) ) ) ) ) ) ) ) ).
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('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.mul',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__541] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__541)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__541)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__545] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__545)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__545)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__541,Vvar__0___24Anonymous__545)) )
| ? [Vvar__0___24Anonymous__546] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__546)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__546)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__541,Vvar__0___24Anonymous__546)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__547] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__547)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__547)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__551] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__551)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__551)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__547,Vvar__0___24Anonymous__551)) )
| ? [Vvar__0___24Anonymous__552] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__552)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__552)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__547,Vvar__0___24Anonymous__552)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__37901] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37901)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37901)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37901) ) ) ) ).
fof('$_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__571] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__571)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__571)
& 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__571)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__536] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__536)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__536)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__536) )
| ? [Vvar__0___24Anonymous__537] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__537)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__537)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__537) ) ) ) ).
fof('$_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__37879] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37879)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__37879)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__37879) )
| ? [Vvar__0___24Anonymous__37880] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37880)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37880)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__66133] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66133)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66133)
& ( ( 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__66143] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66143)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66133)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66143)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66143)
& ? [Vvar__2___24Anonymous__66151] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__66151)
& ? [Vvar__3___24Anonymous__66152] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__66152)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__66133,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__66143)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__66151,Vvar__3___24Anonymous__66152)
& 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__66151),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__66152)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__66154] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66154)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66133)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66154)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66154)
& ? [Vvar__2___24Anonymous__66162] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__66162)
& ? [Vvar__3___24Anonymous__66163] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__66163)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__66133,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__66154)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__66162,Vvar__3___24Anonymous__66163)
& 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__66162)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__66163)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__66165] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66165)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66165)
& ( ( 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__66175] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66175)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66165)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66175)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66175)
& ? [Vvar__2___24Anonymous__66183] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__66183)
& ? [Vvar__3___24Anonymous__66184] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__66184)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__66165,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__66175)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__66183,Vvar__3___24Anonymous__66184)
& 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__66183)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__66184))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__66186] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66186)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66165)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66186)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66186)
& ? [Vvar__2___24Anonymous__66194] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__66194)
& ? [Vvar__3___24Anonymous__66195] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__66195)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__66165,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__66186)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__66194,Vvar__3___24Anonymous__66195)
& 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__66194),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__66195))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.t',axiom,
! [Vvar__153571] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__153571)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__153571) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__54970] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54970)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__54970)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__54970 )
| ? [Vvar__0___24Anonymous__54971] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54971)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__54971)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.zero',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2ezero = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zcomplements.Zlength',axiom,
cCoq_2eZArith_2eZcomplements_2eZlength = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('$_def_Coq.ZArith.Zcomplements.Zlength_aux',axiom,
! [V1__acc,V2__A,V3__l] :
( cType___24t(V2__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V2__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__A)
& cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V1__acc,V2__A,V3__l) = V1__acc )
| ? [Vvar__1___24Anonymous__153304] :
( t(Vvar__1___24Anonymous__153304,V2__A)
& ? [Vvar__2___24Anonymous__153305] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V2__A,Vvar__2___24Anonymous__153305)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__A,Vvar__1___24Anonymous__153304,Vvar__2___24Anonymous__153305)
& cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V1__acc,V2__A,V3__l) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__acc),V2__A,Vvar__2___24Anonymous__153305) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zeven',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__54758] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54758)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54758)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__54758)
& ( ? [Vvar__0___24Anonymous__54762] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54762)
& Vvar__0___24Anonymous__54758 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54762)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__54763] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54763)
& Vvar__0___24Anonymous__54758 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54763)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__54758 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__54764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54764)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54764)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__54764)
& ( ? [Vvar__0___24Anonymous__54768] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54768)
& Vvar__0___24Anonymous__54764 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54768)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__54769] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54769)
& Vvar__0___24Anonymous__54764 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54769)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__54764 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zodd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__54770] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54770)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54770)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__54770)
& ( ? [Vvar__0___24Anonymous__54774] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54774)
& Vvar__0___24Anonymous__54770 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54774)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__54775] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54775)
& Vvar__0___24Anonymous__54770 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54775)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__54770 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__54776] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54776)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54776)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__54776)
& ( ? [Vvar__0___24Anonymous__54780] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54780)
& Vvar__0___24Anonymous__54776 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54780)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__54781] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54781)
& Vvar__0___24Anonymous__54776 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54781)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__54776 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.Is_power',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__83733] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83733)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__83733)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__83734] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83734)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__83734)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__83734) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__40888___24a1(V0__D) ).
fof('$_def_Coq.micromega.QMicromega.QWitness',axiom,
! [Vvar__152660] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(Vvar__152660)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__152660) ) ).
fof('$_def_Coq.micromega.RMicromega.RWitness',axiom,
! [Vvar__152696] :
( cCoq_2emicromega_2eRMicromega_2eRWitness___24t(Vvar__152696)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__152696) ) ).
fof('$_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__44799] :
( t(Vvar__1___24Anonymous__44799,V1__A)
& ? [Vvar__2___24Anonymous__44800] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__44800)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__44800)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__44799,Vvar__2___24Anonymous__44800)
& ( ( Vvar__2___24Anonymous__44800 = 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__44799)) ) )
| ? [Vvar__1___24Anonymous__44811] :
( t(Vvar__1___24Anonymous__44811,V1__A)
& ? [Vvar__2___24Anonymous__44812] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__44812)
& Vvar__2___24Anonymous__44800 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__44811,Vvar__2___24Anonymous__44812)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__44799))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__44800) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__44780] :
( t(Vvar__1___24Anonymous__44780,V1__A)
& ? [Vvar__2___24Anonymous__44781] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__44781)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__44780,Vvar__2___24Anonymous__44781)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__44780))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__44781,V4__goal) ) ) ) ) ) ) ) ).
fof('$_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.eval_op1',axiom,
! [V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V5__o)
=> ( ( V5__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__152780___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__152788___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__152796___24a3(V0__R,V1__rO,V4__rlt) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__152804___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_pol',axiom,
! [V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi] : cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a5(V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi) ).
fof('$_def_Coq.micromega.RingMicromega.ge_bool',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__50262] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__50262)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__50262)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__50263] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__50263)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__50263)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__50266] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__50266)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__50266)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__50263,Vvar__0___24Anonymous__50266) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.map_option',axiom,
! [V0__A,V1__B,V2__f,V3__o] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V3__o)
=> ( ? [Vvar__1___24Anonymous__145240] :
( t(Vvar__1___24Anonymous__145240,V0__A)
& V3__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__145240)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = happ(V2__f,Vvar__1___24Anonymous__145240) )
| ( V3__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.map_option2',axiom,
! [V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V4__o)
=> ( ? [Vvar__1___24Anonymous__145258] :
( t(Vvar__1___24Anonymous__145258,V0__A)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V1__B,V5__o_27)
=> ( V4__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__145258)
& ( ? [Vvar__1___24Anonymous__145263] :
( t(Vvar__1___24Anonymous__145263,V1__B)
& V5__o_27 = cCoq_2eInit_2eDatatypes_2eSome___24a2(V1__B,Vvar__1___24Anonymous__145263)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = happ(happ(V3__f,Vvar__1___24Anonymous__145258),Vvar__1___24Anonymous__145263) )
| ( V5__o_27 = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ) )
| ( V4__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.nhyps_of_psatz',axiom,
! [V0__C,V2__prf] :
( cType___24t(V0__C)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,V2__prf)
=> ( ? [Vvar__1___24Anonymous__73908] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__73908)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V0__C,Vvar__1___24Anonymous__73908)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1___24Anonymous__73908,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat)) )
| ? [Vvar__1___24Anonymous__73910] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V0__C,Vvar__1___24Anonymous__73910)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V0__C,Vvar__1___24Anonymous__73910)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__1___24Anonymous__73912] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V0__C,Vvar__1___24Anonymous__73912)
& ? [Vvar__2___24Anonymous__73913] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__2___24Anonymous__73913)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V0__C,Vvar__1___24Anonymous__73912,Vvar__2___24Anonymous__73913)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__2___24Anonymous__73913) ) )
| ? [Vvar__1___24Anonymous__73916] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__1___24Anonymous__73916)
& ? [Vvar__2___24Anonymous__73917] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__2___24Anonymous__73917)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V0__C,Vvar__1___24Anonymous__73916,Vvar__2___24Anonymous__73917)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__1___24Anonymous__73916),cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__2___24Anonymous__73917)) ) )
| ? [Vvar__1___24Anonymous__73920] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__1___24Anonymous__73920)
& ? [Vvar__2___24Anonymous__73921] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V0__C,Vvar__2___24Anonymous__73921)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V0__C,Vvar__1___24Anonymous__73920,Vvar__2___24Anonymous__73921)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__1___24Anonymous__73920),cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,Vvar__2___24Anonymous__73921)) ) )
| ? [Vvar__1___24Anonymous__73924] :
( t(Vvar__1___24Anonymous__73924,V0__C)
& V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V0__C,Vvar__1___24Anonymous__73924)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ( V2__prf = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V0__C)
& cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V0__C,V2__prf) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.psubC',axiom,
! [V0__C,V1__cminus] : cCoq_2emicromega_2eRingMicromega_2epsubC___24a2(V0__C,V1__cminus) = cCoq_2emicromega_2eEnvRing_2ePsubC___24a2(V0__C,V1__cminus) ).
fof('$_def_Coq.micromega.Tauto.BFormula',axiom,
! [V0__A] : cCoq_2emicromega_2eTauto_2eBFormula___24a1(V0__A) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__A,cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_def_Coq.micromega.Tauto.TFormula',axiom,
! [V0__Term,V1__Annot,V2__TX,V3__AF] : cCoq_2emicromega_2eTauto_2eTFormula___24a4(V0__Term,V1__Annot,V2__TX,V3__AF) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__Term,V2__TX,V1__Annot,V3__AF) ).
fof('$_def_Coq.micromega.Tauto.and_cnf',axiom,
! [V0__Term_27,V1__Annot,V2__f1,V3__f2] : cCoq_2emicromega_2eTauto_2eand__cnf___24a4(V0__Term_27,V1__Annot,V2__f1,V3__f2) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot),V2__f1,V3__f2) ).
fof('$_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_ff',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf__ff___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)))) ).
fof('$_def_Coq.micromega.Tauto.cnf_tt',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.collect_annot',axiom,
! [V0__TA,V1__TX,V2__AA,V3__AF,V5__f] :
( cType___24t(V0__TA)
=> ( cType___24t(V1__TX)
=> ( cType___24t(V2__AA)
=> ( cType___24t(V3__AF)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,V5__f)
=> ( ( V5__f = cCoq_2emicromega_2eTauto_2eTT___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__AA) )
| ( V5__f = cCoq_2emicromega_2eTauto_2eFF___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__AA) )
| ? [Vvar__4___24Anonymous__78687] :
( t(Vvar__4___24Anonymous__78687,V1__TX)
& V5__f = cCoq_2emicromega_2eTauto_2eX___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78687)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__AA) )
| ? [Vvar__4___24Anonymous__78692] :
( t(Vvar__4___24Anonymous__78692,V0__TA)
& ? [Vvar__5___24Anonymous__78693] :
( t(Vvar__5___24Anonymous__78693,V2__AA)
& V5__f = cCoq_2emicromega_2eTauto_2eA___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78692,Vvar__5___24Anonymous__78693)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__AA,Vvar__5___24Anonymous__78693,cCoq_2eInit_2eDatatypes_2enil___24a1(V2__AA)) ) )
| ? [Vvar__4___24Anonymous__78699] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78699)
& ? [Vvar__5___24Anonymous__78700] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__78700)
& V5__f = cCoq_2emicromega_2eTauto_2eCj___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78699,Vvar__5___24Anonymous__78700)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V2__AA,cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78699),cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__78700)) ) )
| ? [Vvar__4___24Anonymous__78706] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78706)
& ? [Vvar__5___24Anonymous__78707] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__78707)
& V5__f = cCoq_2emicromega_2eTauto_2eD___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78706,Vvar__5___24Anonymous__78707)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V2__AA,cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78706),cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__78707)) ) )
| ? [Vvar__4___24Anonymous__78713] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78713)
& V5__f = cCoq_2emicromega_2eTauto_2eN___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78713)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78713) )
| ? [Vvar__4___24Anonymous__78718] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78718)
& ? [Vvar__5___24Anonymous__78719] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V3__AF,Vvar__5___24Anonymous__78719)
& ? [Vvar__6___24Anonymous__78720] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__78720)
& V5__f = cCoq_2emicromega_2eTauto_2eI___24a7(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78718,Vvar__5___24Anonymous__78719,Vvar__6___24Anonymous__78720)
& cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,V5__f) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V2__AA,cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__78718),cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__78720)) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.cons_id',axiom,
! [V0__AF,V1__id,V2__l] :
( cType___24t(V0__AF)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__AF,V1__id)
=> ( ? [Vvar__1___24Anonymous__78597] :
( t(Vvar__1___24Anonymous__78597,V0__AF)
& V1__id = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__AF,Vvar__1___24Anonymous__78597)
& cCoq_2emicromega_2eTauto_2econs__id___24a3(V0__AF,V1__id,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__AF,Vvar__1___24Anonymous__78597,V2__l) )
| ( V1__id = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__AF)
& cCoq_2emicromega_2eTauto_2econs__id___24a3(V0__AF,V1__id,V2__l) = V2__l ) ) ) ) ).
fof('$_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_f',axiom,
! [V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f] :
( cType___24t(V0__TA)
=> ( cType___24t(V1__TX)
=> ( cType___24t(V2__AA)
=> ( cType___24t(V3__AF)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,V7__f)
=> ( ( V7__f = cCoq_2emicromega_2eTauto_2eTT___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24True) ) )
| ( V7__f = cCoq_2emicromega_2eTauto_2eFF___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24False) ) )
| ? [Vvar__4___24Anonymous__151136] :
( t(Vvar__4___24Anonymous__151136,V1__TX)
& V7__f = cCoq_2emicromega_2eTauto_2eX___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__151136)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(happ(V4__ex,Vvar__4___24Anonymous__151136)) ) )
| ? [Vvar__4___24Anonymous__151141] :
( t(Vvar__4___24Anonymous__151141,V0__TA)
& ? [Vvar__5___24Anonymous__151142] :
( t(Vvar__5___24Anonymous__151142,V2__AA)
& V7__f = cCoq_2emicromega_2eTauto_2eA___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__151141,Vvar__5___24Anonymous__151142)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(happ(V5__ea,Vvar__4___24Anonymous__151141)) ) ) )
| ? [Vvar__4___24Anonymous__151148] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__151148)
& ? [Vvar__5___24Anonymous__151149] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__151149)
& V7__f = cCoq_2emicromega_2eTauto_2eCj___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__151148,Vvar__5___24Anonymous__151149)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__151148)
& cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__151149) ) ) ) )
| ? [Vvar__4___24Anonymous__151155] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__151155)
& ? [Vvar__5___24Anonymous__151156] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__151156)
& V7__f = cCoq_2emicromega_2eTauto_2eD___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__151155,Vvar__5___24Anonymous__151156)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__151155)
| cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__151156) ) ) ) )
| ? [Vvar__4___24Anonymous__151162] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__151162)
& V7__f = cCoq_2emicromega_2eTauto_2eN___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__151162)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ~ cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__151162) ) )
| ? [Vvar__4___24Anonymous__151167] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__151167)
& ? [Vvar__5___24Anonymous__151168] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V3__AF,Vvar__5___24Anonymous__151168)
& ? [Vvar__6___24Anonymous__151169] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__151169)
& V7__f = cCoq_2emicromega_2eTauto_2eI___24a7(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__151167,Vvar__5___24Anonymous__151168,Vvar__6___24Anonymous__151169)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__151167)
=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__6___24Anonymous__151169) ) ) ) ) ) ) ) ) ) ) ) ).
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.ZMicromega.Vars.Facts.MP.to_list',axiom,
cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eto__list = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements ).
fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
! [Vvar__54712] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__54712)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__54712) ) ).
fof('$_def_Coq.micromega.ZMicromega.make_conj',axiom,
cCoq_2emicromega_2eZMicromega_2emake__conj = cCoq_2emicromega_2eRefl_2emake__conj ).
fof('$_def_Coq.micromega.ZMicromega.make_impl',axiom,
cCoq_2emicromega_2eZMicromega_2emake__impl = cCoq_2emicromega_2eRefl_2emake__impl ).
fof('$_def_Coq.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('$_def_Coq.omega.PreOmega.Z_of_nat\'',axiom,
cCoq_2eomega_2ePreOmega_2eZ__of__nat_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat ).
fof('$_def_Coq.setoid_ring.BinList.jump',axiom,
! [V0__A,V2__p,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( ? [Vvar__0___24Anonymous__143325] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143325)
& V2__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__143325)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__143325,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__143325,cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l))) )
| ? [Vvar__0___24Anonymous__143326] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143326)
& V2__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__143326)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__143326,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__143326,V3__l)) )
| ( V2__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.BinList.nth',axiom,
! [V0__A,V1__default,V3__p,V4__l] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__143333] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143333)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__143333)
& cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,V3__p,V4__l) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,Vvar__0___24Anonymous__143333,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__143333,cCoq_2eLists_2eList_2etl___24a2(V0__A,V4__l))) )
| ? [Vvar__0___24Anonymous__143334] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__143334)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__143334)
& cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,V3__p,V4__l) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,Vvar__0___24Anonymous__143334,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__143334,V4__l)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__A,V1__default,V3__p,V4__l) = cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V4__l) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.FEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V9__C)
=> ( cType___24t(V11__Cpow)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,V16__pe)
=> ( ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V1__rO )
| ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__69650] :
( t(Vvar__1___24Anonymous__69650,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__69650)
& 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__69650) )
| ? [Vvar__1___24Anonymous__69652] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__69652)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__69652)
& 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__69652,V15__l) )
| ? [Vvar__1___24Anonymous__69654] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__69654)
& ? [Vvar__2___24Anonymous__69655] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__69655)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__69654,Vvar__2___24Anonymous__69655)
& 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__69654)),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__69655)) ) )
| ? [Vvar__1___24Anonymous__69658] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__69658)
& ? [Vvar__2___24Anonymous__69659] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__69659)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__69658,Vvar__2___24Anonymous__69659)
& 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__69658)),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__69659)) ) )
| ? [Vvar__1___24Anonymous__69662] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__69662)
& ? [Vvar__2___24Anonymous__69663] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__69663)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__69662,Vvar__2___24Anonymous__69663)
& 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__69662)),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__69663)) ) )
| ? [Vvar__1___24Anonymous__69666] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__69666)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__69666)
& 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__69666)) )
| ? [Vvar__1___24Anonymous__69668] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__69668)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__69668)
& 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__69668)) )
| ? [Vvar__1___24Anonymous__69670] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__69670)
& ? [Vvar__2___24Anonymous__69671] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__69671)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__69670,Vvar__2___24Anonymous__69671)
& 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__69670)),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__69671)) ) )
| ? [Vvar__1___24Anonymous__69674] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__69674)
& ? [Vvar__2___24Anonymous__69675] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__69675)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__69674,Vvar__2___24Anonymous__69675)
& 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__69674)),happ(V12__Cp__phi,Vvar__2___24Anonymous__69675)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__42549] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__42549)
& ? [Vvar__2___24Anonymous__42550] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__42550)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__42549,Vvar__2___24Anonymous__42550)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__42549),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__42550,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEadd',axiom,
! [V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V4__e1)
=> ( ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__67931] :
( t(Vvar__1___24Anonymous__67931,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__67931,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__67931)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67931),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67931),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__67934] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__67934)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__67934)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__67936] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__67936)
& ? [Vvar__2___24Anonymous__67937] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__67937)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__67936,Vvar__2___24Anonymous__67937)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__67940] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__67940)
& ? [Vvar__2___24Anonymous__67941] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__67941)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__67940,Vvar__2___24Anonymous__67941)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__67944] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__67944)
& ? [Vvar__2___24Anonymous__67945] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__67945)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__67944,Vvar__2___24Anonymous__67945)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__67948] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__67948)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__67948)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__67950] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__67950)
& ? [Vvar__2___24Anonymous__67951] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__67951)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__67950,Vvar__2___24Anonymous__67951)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__67958] :
( t(Vvar__1___24Anonymous__67958,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__67958,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__67958)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67958),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67958),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__67961] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__67961)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__67961)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__67963] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__67963)
& ? [Vvar__2___24Anonymous__67964] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__67964)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__67963,Vvar__2___24Anonymous__67964)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__67967] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__67967)
& ? [Vvar__2___24Anonymous__67968] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__67968)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__67967,Vvar__2___24Anonymous__67968)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__67971] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__67971)
& ? [Vvar__2___24Anonymous__67972] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__67972)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__67971,Vvar__2___24Anonymous__67972)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__67975] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__67975)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__67975)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__67977] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__67977)
& ? [Vvar__2___24Anonymous__67978] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__67978)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__67977,Vvar__2___24Anonymous__67978)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__67981] :
( t(Vvar__1___24Anonymous__67981,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__67981)
& ( ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__67981,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__67981,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68006] :
( t(Vvar__1___24Anonymous__68006,V0__C)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__68006)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,happ(happ(V2__cadd,Vvar__1___24Anonymous__67981),Vvar__1___24Anonymous__68006)) )
| ? [Vvar__1___24Anonymous__68008] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__68008)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__67981,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__68008)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68011] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68011)
& ? [Vvar__2___24Anonymous__68012] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68012)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__67981,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__68011,Vvar__2___24Anonymous__68012)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68017] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68017)
& ? [Vvar__2___24Anonymous__68018] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68018)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__67981,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__68017,Vvar__2___24Anonymous__68018)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68023] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68023)
& ? [Vvar__2___24Anonymous__68024] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68024)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__67981,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__68023,Vvar__2___24Anonymous__68024)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68029] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68029)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__67981,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__68029)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68032] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68032)
& ? [Vvar__2___24Anonymous__68033] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__68033)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__67981,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__68032,Vvar__2___24Anonymous__68033)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V5__e2 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__67981),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68038] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__68038)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__68038)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68056] :
( t(Vvar__1___24Anonymous__68056,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__68056,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__68056)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68056),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68056),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68059] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__68059)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__68059)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68061] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68061)
& ? [Vvar__2___24Anonymous__68062] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68062)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__68061,Vvar__2___24Anonymous__68062)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68065] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68065)
& ? [Vvar__2___24Anonymous__68066] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68066)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__68065,Vvar__2___24Anonymous__68066)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68069] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68069)
& ? [Vvar__2___24Anonymous__68070] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68070)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__68069,Vvar__2___24Anonymous__68070)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68073] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68073)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__68073)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68075] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68075)
& ? [Vvar__2___24Anonymous__68076] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__68076)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__68075,Vvar__2___24Anonymous__68076)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68079] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68079)
& ? [Vvar__2___24Anonymous__68080] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68080)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__68079,Vvar__2___24Anonymous__68080)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68112] :
( t(Vvar__1___24Anonymous__68112,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__68112,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__68112)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68112),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68112),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68115] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__68115)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__68115)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68117] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68117)
& ? [Vvar__2___24Anonymous__68118] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68118)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__68117,Vvar__2___24Anonymous__68118)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68121] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68121)
& ? [Vvar__2___24Anonymous__68122] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68122)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__68121,Vvar__2___24Anonymous__68122)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68125] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68125)
& ? [Vvar__2___24Anonymous__68126] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68126)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__68125,Vvar__2___24Anonymous__68126)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68129] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68129)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__68129)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68131] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68131)
& ? [Vvar__2___24Anonymous__68132] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__68132)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__68131,Vvar__2___24Anonymous__68132)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68135] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68135)
& ? [Vvar__2___24Anonymous__68136] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68136)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__68135,Vvar__2___24Anonymous__68136)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68168] :
( t(Vvar__1___24Anonymous__68168,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__68168,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__68168)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68168),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68168),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68171] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__68171)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__68171)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68173] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68173)
& ? [Vvar__2___24Anonymous__68174] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68174)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__68173,Vvar__2___24Anonymous__68174)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68177] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68177)
& ? [Vvar__2___24Anonymous__68178] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68178)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__68177,Vvar__2___24Anonymous__68178)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68181] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68181)
& ? [Vvar__2___24Anonymous__68182] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68182)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__68181,Vvar__2___24Anonymous__68182)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68185] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68185)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__68185)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68187] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68187)
& ? [Vvar__2___24Anonymous__68188] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__68188)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__68187,Vvar__2___24Anonymous__68188)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68191] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68191)
& ? [Vvar__2___24Anonymous__68192] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68192)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__68191,Vvar__2___24Anonymous__68192)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68224] :
( t(Vvar__1___24Anonymous__68224,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__68224,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__68224)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68224),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68224),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68227] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__68227)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__68227)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68229] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68229)
& ? [Vvar__2___24Anonymous__68230] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68230)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__68229,Vvar__2___24Anonymous__68230)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68233] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68233)
& ? [Vvar__2___24Anonymous__68234] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68234)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__68233,Vvar__2___24Anonymous__68234)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68237] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68237)
& ? [Vvar__2___24Anonymous__68238] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68238)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__68237,Vvar__2___24Anonymous__68238)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68241] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68241)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__68241)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68243] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68243)
& ? [Vvar__2___24Anonymous__68244] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__68244)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__68243,Vvar__2___24Anonymous__68244)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68247] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68247)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__68247)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68265] :
( t(Vvar__1___24Anonymous__68265,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__68265,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__68265)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68265),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68265),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68268] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__68268)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__68268)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68270] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68270)
& ? [Vvar__2___24Anonymous__68271] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68271)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__68270,Vvar__2___24Anonymous__68271)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68274] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68274)
& ? [Vvar__2___24Anonymous__68275] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68275)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__68274,Vvar__2___24Anonymous__68275)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68278] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68278)
& ? [Vvar__2___24Anonymous__68279] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68279)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__68278,Vvar__2___24Anonymous__68279)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68282] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68282)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__68282)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68284] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68284)
& ? [Vvar__2___24Anonymous__68285] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__68285)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__68284,Vvar__2___24Anonymous__68285)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68288] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68288)
& ? [Vvar__2___24Anonymous__68289] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__68289)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V5__e2)
=> ( V4__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__68288,Vvar__2___24Anonymous__68289)
& ( ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68321] :
( t(Vvar__1___24Anonymous__68321,V0__C)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__32372___24t(V0__C,V3__ceqb)
=> ( t(Vvar__1___24Anonymous__68321,V0__C)
=> ( V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__68321)
& ( ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68321),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = V4__e1 )
| ( happ(happ(V3__ceqb,Vvar__1___24Anonymous__68321),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__68324] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__68324)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__68324)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68326] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68326)
& ? [Vvar__2___24Anonymous__68327] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68327)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__68326,Vvar__2___24Anonymous__68327)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68330] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68330)
& ? [Vvar__2___24Anonymous__68331] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68331)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__68330,Vvar__2___24Anonymous__68331)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68334] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68334)
& ? [Vvar__2___24Anonymous__68335] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68335)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__68334,Vvar__2___24Anonymous__68335)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) )
| ? [Vvar__1___24Anonymous__68338] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68338)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__68338)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) )
| ? [Vvar__1___24Anonymous__68340] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68340)
& ? [Vvar__2___24Anonymous__68341] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__68341)
& V5__e2 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__68340,Vvar__2___24Anonymous__68341)
& cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V2__cadd,V3__ceqb,V4__e1,V5__e2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,V4__e1,V5__e2) ) ) ) ) ) ) ) ) ) ) ) ).
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.NPEopp',axiom,
! [V0__C,V1__copp,V2__e1] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V2__e1)
=> ( ( V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) )
| ( V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) )
| ? [Vvar__1___24Anonymous__68923] :
( t(Vvar__1___24Anonymous__68923,V0__C)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__68923)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,happ(V1__copp,Vvar__1___24Anonymous__68923)) )
| ? [Vvar__1___24Anonymous__68925] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__68925)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__68925)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) )
| ? [Vvar__1___24Anonymous__68927] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68927)
& ? [Vvar__2___24Anonymous__68928] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68928)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__68927,Vvar__2___24Anonymous__68928)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) ) )
| ? [Vvar__1___24Anonymous__68931] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68931)
& ? [Vvar__2___24Anonymous__68932] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68932)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__68931,Vvar__2___24Anonymous__68932)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) ) )
| ? [Vvar__1___24Anonymous__68935] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68935)
& ? [Vvar__2___24Anonymous__68936] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__68936)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__68935,Vvar__2___24Anonymous__68936)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) ) )
| ? [Vvar__1___24Anonymous__68939] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68939)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__68939)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) )
| ? [Vvar__1___24Anonymous__68941] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68941)
& ? [Vvar__2___24Anonymous__68942] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__68942)
& V2__e1 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__68941,Vvar__2___24Anonymous__68942)
& cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V1__copp,V2__e1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,V2__e1) ) ) ) ) ) ).
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__42291] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__42291)
& ? [Vvar__2___24Anonymous__42292] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__42292)
& ( 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__42292)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__42291,Vvar__2___24Anonymous__42292)
& ( ( Vvar__2___24Anonymous__42292 = 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__42291)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__42303] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__42303)
& ? [Vvar__2___24Anonymous__42304] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__42304)
& Vvar__2___24Anonymous__42292 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__42303,Vvar__2___24Anonymous__42304)
& ( 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__42291)),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__42292) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__42278] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__42278)
& ? [Vvar__2__denum__42279] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__42279)
& ? [Vvar__3__condition__42280] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__42280)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__42278,Vvar__2__denum__42279,Vvar__3__condition__42280)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__42280 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__42269] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__42269)
& ? [Vvar__2__denum__42270] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__42270)
& ? [Vvar__3__condition__42271] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__42271)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__42269,Vvar__2__denum__42270,Vvar__3__condition__42271)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__42270 ) ) ) ) ) ).
fof('$_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__42258] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__42258)
& ? [Vvar__2__denum__42259] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__42259)
& ? [Vvar__3__condition__42260] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__42260)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__42258,Vvar__2__denum__42259,Vvar__3__condition__42260)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__42258 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__70004] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__70004)
& ? [Vvar__2__rsplit__common__70005] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__70005)
& ? [Vvar__3__rsplit__right__70006] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__70006)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__70004,Vvar__2__rsplit__common__70005,Vvar__3__rsplit__right__70006)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,V1__r) = Vvar__2__rsplit__common__70005 ) ) ) ) ) ).
fof('$_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__69993] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__69993)
& ? [Vvar__2__rsplit__common__69994] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__69994)
& ? [Vvar__3__rsplit__right__69995] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__69995)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__69993,Vvar__2__rsplit__common__69994,Vvar__3__rsplit__right__69995)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__69993 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__70013] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__70013)
& ? [Vvar__2__rsplit__common__70014] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__70014)
& ? [Vvar__3__rsplit__right__70015] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__70015)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__70013,Vvar__2__rsplit__common__70014,Vvar__3__rsplit__right__70015)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__70015 ) ) ) ) ) ).
fof('$_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('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__71516] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__71516)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__71516) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__43442] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43442)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__43442)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__43442) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiNword',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w] :
( cType___24t(V0__R)
=> ( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V8__w)
=> ( ( V8__w = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = V1__rO )
| ? [Vvar__1___24Anonymous__71597] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__71597)
& ? [Vvar__2___24Anonymous__71598] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__71598)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__71597)
=> ( V8__w = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__71597,Vvar__2___24Anonymous__71598)
& ( ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__71598)
=> ( Vvar__1___24Anonymous__71597 = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( Vvar__2___24Anonymous__71598 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,Vvar__1___24Anonymous__71597) )
| ? [Vvar__1___24Anonymous__71619] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__71619)
& ? [Vvar__2___24Anonymous__71620] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__71620)
& Vvar__2___24Anonymous__71598 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__71619,Vvar__2___24Anonymous__71620)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = happ(V6__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,Vvar__2___24Anonymous__71598)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__71622] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__71622)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__71598)
=> ( Vvar__1___24Anonymous__71597 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__71622)
& ( ( Vvar__2___24Anonymous__71598 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eNumbers_2eBinNums_2eN)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,Vvar__1___24Anonymous__71597) )
| ? [Vvar__1___24Anonymous__71629] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__1___24Anonymous__71629)
& ? [Vvar__2___24Anonymous__71630] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__71630)
& Vvar__2___24Anonymous__71598 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eNumbers_2eBinNums_2eN,Vvar__1___24Anonymous__71629,Vvar__2___24Anonymous__71630)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__w) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,Vvar__1___24Anonymous__71597)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,Vvar__2___24Anonymous__71598)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__43355] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43355)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43355)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43355)
& ( ? [Vvar__0___24Anonymous__43359] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43359)
& Vvar__0___24Anonymous__43355 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43359)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__43355))) )
| ? [Vvar__0___24Anonymous__43360] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43360)
& Vvar__0___24Anonymous__43355 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43360)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__43355))) )
| ( Vvar__0___24Anonymous__43355 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V2__radd,V1__rI),V1__rI)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__43361] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43361)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43361)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43361)
& ( ? [Vvar__0___24Anonymous__43365] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43365)
& Vvar__0___24Anonymous__43361 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43365)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__43361)) )
| ? [Vvar__0___24Anonymous__43366] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43366)
& Vvar__0___24Anonymous__43361 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43366)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__43361)) )
| ( Vvar__0___24Anonymous__43361 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),V1__rI) ) ) ) ) ) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__43322] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43322)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43322)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__43322))) )
| ? [Vvar__0___24Anonymous__43323] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43323)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43323)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__43323)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__43389] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43389)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__43389)
& 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__43389) )
| ? [Vvar__0___24Anonymous__43390] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43390)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__43390)
& 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__43390)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.get_signZ',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__71498] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__71498)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__71498)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__71499] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__71499)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__71499)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__71499)) ) ) ) ).
fof('$_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__32372___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.P0',axiom,
! [V0__C,V1__cO] : cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V0__C,V1__cO) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,V1__cO) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.P1',axiom,
! [V0__C,V1__cI] : cCoq_2esetoid__ring_2eRing__polynom_2eP1___24a2(V0__C,V1__cI) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,V1__cI) ).
fof('$_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__33084] :
( t(Vvar__1___24Anonymous__33084,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__33084)
& 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__33084) )
| ? [Vvar__1___24Anonymous__33086] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__33086)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__33086)
& 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__33086,V13__l) )
| ? [Vvar__1___24Anonymous__33088] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__33088)
& ? [Vvar__2___24Anonymous__33089] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__33089)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__33088,Vvar__2___24Anonymous__33089)
& 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__33088)),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__33089)) ) )
| ? [Vvar__1___24Anonymous__33092] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__33092)
& ? [Vvar__2___24Anonymous__33093] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__33093)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__33092,Vvar__2___24Anonymous__33093)
& 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__33092)),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__33093)) ) )
| ? [Vvar__1___24Anonymous__33096] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__33096)
& ? [Vvar__2___24Anonymous__33097] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__33097)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__33096,Vvar__2___24Anonymous__33097)
& 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__33096)),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__33097)) ) )
| ? [Vvar__1___24Anonymous__33100] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__33100)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__33100)
& 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__33100)) )
| ? [Vvar__1___24Anonymous__33102] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__33102)
& ? [Vvar__2___24Anonymous__33103] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__33103)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__33102,Vvar__2___24Anonymous__33103)
& 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__33102)),happ(V10__Cp__phi,Vvar__2___24Anonymous__33103)) ) ) ) ) ) ) ) ).
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__32707] :
( t(Vvar__1___24Anonymous__32707,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__32707)
& ( ? [Vvar__1___24Anonymous__32717] :
( t(Vvar__1___24Anonymous__32717,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__32717)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__32707),Vvar__1___24Anonymous__32717) )
| ? [Vvar__1___24Anonymous__32719] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32719)
& ? [Vvar__2___24Anonymous__32720] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__32720)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__32719,Vvar__2___24Anonymous__32720)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__32723] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__32723)
& ? [Vvar__2___24Anonymous__32724] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__32724)
& ? [Vvar__3___24Anonymous__32725] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__32725)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__32723,Vvar__2___24Anonymous__32724,Vvar__3___24Anonymous__32725)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__32730] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32730)
& ? [Vvar__2___24Anonymous__32731] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__32731)
& ( 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__32730,Vvar__2___24Anonymous__32731)
& ( ? [Vvar__1___24Anonymous__32751] :
( t(Vvar__1___24Anonymous__32751,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__32751)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__32753] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32753)
& ? [Vvar__2___24Anonymous__32754] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__32754)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32730)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32753)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__32753,Vvar__2___24Anonymous__32754)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__32730,Vvar__1___24Anonymous__32753) = 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__32731,Vvar__2___24Anonymous__32754) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__32730,Vvar__1___24Anonymous__32753) = 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__32730,Vvar__1___24Anonymous__32753) = 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__32759] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__32759)
& ? [Vvar__2___24Anonymous__32760] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__32760)
& ? [Vvar__3___24Anonymous__32761] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__32761)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__32759,Vvar__2___24Anonymous__32760,Vvar__3___24Anonymous__32761)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__32766] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__32766)
& ? [Vvar__2___24Anonymous__32767] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__32767)
& ? [Vvar__3___24Anonymous__32768] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__32768)
& ( 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__32766,Vvar__2___24Anonymous__32767,Vvar__3___24Anonymous__32768)
& ( ? [Vvar__1___24Anonymous__32801] :
( t(Vvar__1___24Anonymous__32801,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__32801)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__32803] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32803)
& ? [Vvar__2___24Anonymous__32804] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__32804)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__32803,Vvar__2___24Anonymous__32804)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__32807] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__32807)
& ? [Vvar__2___24Anonymous__32808] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__32808)
& ? [Vvar__3___24Anonymous__32809] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__32809)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__32767)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__32808)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__32807,Vvar__2___24Anonymous__32808,Vvar__3___24Anonymous__32809)
& ( ( cType___24t(V0__C)
=> ( c_24__type__32372___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__32766)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__32807)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__32767,Vvar__2___24Anonymous__32808) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__32766,Vvar__1___24Anonymous__32807) = 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__32768,Vvar__3___24Anonymous__32809) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__32766,Vvar__1___24Anonymous__32807) = 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__32767,Vvar__2___24Anonymous__32808) = 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__32767,Vvar__2___24Anonymous__32808) = 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.Pequiv',axiom,
! [V0__R,V1__rO,V2__radd,V3__rmul,V4__req,V5__C,V6__phi,V7__P,V8__Q] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePequiv___24a9(V0__R,V1__rO,V2__radd,V3__rmul,V4__req,V5__C,V6__phi,V7__P,V8__Q)
<=> ! [V9__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V9__l)
=> p(happ(happ(V4__req,cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V5__C,V6__phi,V9__l,V7__P)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi___24a8(V0__R,V1__rO,V2__radd,V3__rmul,V5__C,V6__phi,V9__l,V8__Q))) ) ) ).
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__74687] :
( t(Vvar__1___24Anonymous__74687,V4__C)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V4__C,Vvar__1___24Anonymous__74687)
& 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__74687) )
| ? [Vvar__1___24Anonymous__74689] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__74689)
& ? [Vvar__2___24Anonymous__74690] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__2___24Anonymous__74690)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V4__C,Vvar__1___24Anonymous__74689,Vvar__2___24Anonymous__74690)
& 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__74689,V7__l),Vvar__2___24Anonymous__74690) ) )
| ? [Vvar__1___24Anonymous__74693] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__1___24Anonymous__74693)
& ? [Vvar__2___24Anonymous__74694] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__74694)
& ? [Vvar__3___24Anonymous__74695] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V4__C,Vvar__3___24Anonymous__74695)
& V8__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V4__C,Vvar__1___24Anonymous__74693,Vvar__2___24Anonymous__74694,Vvar__3___24Anonymous__74695)
& 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__74693)),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__74694))),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__74695)) ) ) ) ) ) ) ) ).
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('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__75950___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__75951___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__75952___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_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__33528] :
( 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__33528)
& ? [Vvar__2___24Anonymous__33529] :
( 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__33529)
& ( 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__33528)
=> ( 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__33528,Vvar__2___24Anonymous__33529)
& ? [Vvar__2___24Anonymous__33547] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__2___24Anonymous__33547)
& ? [Vvar__3___24Anonymous__33548] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__3___24Anonymous__33548)
& ( 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__33529)
=> ( Vvar__1___24Anonymous__33528 = 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__33547,Vvar__3___24Anonymous__33548)
& ( ( Vvar__2___24Anonymous__33529 = 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__33547)),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__33548))) ) )
| ? [Vvar__1___24Anonymous__33559] :
( 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__33559)
& ? [Vvar__2___24Anonymous__33560] :
( 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__33560)
& Vvar__2___24Anonymous__33529 = 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__33559,Vvar__2___24Anonymous__33560)
& ( 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__33547)),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__33548)))
& 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__33529) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkPinj',axiom,
! [V0__C,V1__j,V2__P] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V2__P)
=> ( ? [Vvar__1___24Anonymous__146190] :
( t(Vvar__1___24Anonymous__146190,V0__C)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__146190)
& cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = V2__P )
| ? [Vvar__1___24Anonymous__146192] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__146192)
& ? [Vvar__2___24Anonymous__146193] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__146193)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__146192,Vvar__2___24Anonymous__146193)
& cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__j,Vvar__1___24Anonymous__146192),Vvar__2___24Anonymous__146193) ) )
| ? [Vvar__1___24Anonymous__146196] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__146196)
& ? [Vvar__2___24Anonymous__146197] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__146197)
& ? [Vvar__3___24Anonymous__146198] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__146198)
& V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__146196,Vvar__2___24Anonymous__146197,Vvar__3___24Anonymous__146198)
& cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,V1__j,V2__P) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkZmon',axiom,
! [V0__j,V1__M] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V1__M)
=> ( ( V1__M = cCoq_2esetoid__ring_2eRing__polynom_2emon0
& cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2emon0 )
| ? [Vvar__0___24Anonymous__146836] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__146836)
& ? [Vvar__1___24Anonymous__146837] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__146837)
& V1__M = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__146836,Vvar__1___24Anonymous__146837)
& cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V0__j,V1__M) ) )
| ? [Vvar__0___24Anonymous__146839] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__146839)
& ? [Vvar__1___24Anonymous__146840] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__146840)
& V1__M = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__146839,Vvar__1___24Anonymous__146840)
& cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V0__j,V1__M) ) ) ) ) ).
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__33791] :
( 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__33791)
& ? [Vvar__2___24Anonymous__33792] :
( 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__33792)
& ( 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__33791)
=> ( 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__33791,Vvar__2___24Anonymous__33792)
& ? [Vvar__2___24Anonymous__33808] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__33808)
& ? [Vvar__3___24Anonymous__33809] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__33809)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__32404___24t(V0__C,V3__cadd)
=> ( c_24__type__32404___24t(V0__C,V4__cmul)
=> ( c_24__type__32404___24t(V0__C,V5__csub)
=> ( c_24__type__32413___24t(V0__C,V6__copp)
=> ( c_24__type__32372___24t(V0__C,V7__ceqb)
=> ( c_24__type__33522___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__33808)
=> ( Vvar__1___24Anonymous__33791 = 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__33808,Vvar__3___24Anonymous__33809)
& ( ? [Vvar__1___24Anonymous__33817] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__33817)
& 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__33808)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__33817)
& 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__33817,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__33809)),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__33792)) )
| ( 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__33808)) = 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__33792) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__150507] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150507)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__150507)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(happ(V1__rmul,V3__r),V4__x),V4__x,Vvar__0___24Anonymous__150507),V4__x,Vvar__0___24Anonymous__150507) )
| ? [Vvar__0___24Anonymous__150508] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__150508)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__150508)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,Vvar__0___24Anonymous__150508),V4__x,Vvar__0___24Anonymous__150508) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkmult_rec',axiom,
! [V0__R,V1__mkmult__pow,V3__r,V4__lm] :
( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),V4__lm)
=> ( ( V4__lm = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive))
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V0__R,V1__mkmult__pow,V3__r,V4__lm) = V3__r )
| ? [Vvar__1___24Anonymous__150236] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__150236)
& ? [Vvar__2___24Anonymous__150237] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__150237)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__150236)
=> ( V4__lm = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__1___24Anonymous__150236,Vvar__2___24Anonymous__150237)
& ? [Vvar__2___24Anonymous__150249] :
( t(Vvar__2___24Anonymous__150249,V0__R)
& ? [Vvar__3___24Anonymous__150250] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__150250)
& Vvar__1___24Anonymous__150236 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__150249,Vvar__3___24Anonymous__150250)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V0__R,V1__mkmult__pow,V3__r,V4__lm) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V0__R,V1__mkmult__pow,happ(happ(happ(V1__mkmult__pow,V3__r),Vvar__2___24Anonymous__150249),Vvar__3___24Anonymous__150250),Vvar__2___24Anonymous__150237) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__33372___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.r_list_pow',axiom,
! [V0__R,V1__rI,V2__rmul,V4__l] :
( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive))
& cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,V4__l) = V1__rI )
| ? [Vvar__1___24Anonymous__150461] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__150461)
& ? [Vvar__2___24Anonymous__150462] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__150462)
& ( cType___24t(V0__R)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__1___24Anonymous__150461)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__1___24Anonymous__150461,Vvar__2___24Anonymous__150462)
& ? [Vvar__2___24Anonymous__150474] :
( t(Vvar__2___24Anonymous__150474,V0__R)
& ? [Vvar__3___24Anonymous__150475] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__150475)
& Vvar__1___24Anonymous__150461 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__150474,Vvar__3___24Anonymous__150475)
& cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,V4__l) = happ(happ(V2__rmul,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,Vvar__2___24Anonymous__150474,Vvar__3___24Anonymous__150475)),cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V0__R,V1__rI,V2__rmul,Vvar__2___24Anonymous__150462)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__34285] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34285)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34285)
& 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__34285) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__50316] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__50316)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__50316)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__50317__50320___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__50316)),c_24__let__var__6__p__50317__50320___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__50316))) )
| ? [Vvar__0___24Anonymous__50318] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__50318)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__50318)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__50319__50321___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__50318)),c_24__let__var__6__p__50319__50321___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__50318)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_Eta.eta_red',axiom,
! [V1__r] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ( ? [Vvar__0___24Anonymous__1191] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1191)
& V1__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__1191)
& cEta_2eeta__red___24a1(V1__r) = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__1191) )
| ? [Vvar__0___24Anonymous__1192] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__1192)
& ? [Vvar__1___24Anonymous__1193] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__1193)
& V1__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__1192,Vvar__1___24Anonymous__1193)
& cEta_2eeta__red___24a1(V1__r) = cTait_2eTerm_2eApp___24a2(cEta_2eeta__red___24a1(Vvar__0___24Anonymous__1192),cEta_2eeta__red___24a1(Vvar__1___24Anonymous__1193)) ) )
| ? [Vvar__0___24Anonymous__1195] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__1195)
& ? [Vvar__1___24Anonymous__1196] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__1196)
& V1__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__1195,Vvar__1___24Anonymous__1196)
& cEta_2eeta__red___24a1(V1__r) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241207___24a2(Vvar__0___24Anonymous__1195,Vvar__1___24Anonymous__1196) ) ) ) ) ).
fof('$_def_Eta.is_eta_core',axiom,
! [V0__r,V1__k] : cEta_2eis__eta__core___24a2(V0__r,V1__k) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eInit_2eDatatypes_2eandb___24a2(cTait_2eApps_2eis__app___24a1(V0__r),c_24__case__Coq_2eInit_2eSpecif_2esumbool_241214___24a2(V0__r,V1__k)),cCoq_2eInit_2eDatatypes_2enegb___24a1(cTait_2eTerm_2eoccurs___24a2(V1__k,cTait_2eApps_2eleft__app___24a1(V0__r)))) ).
fof('$_def_Hammer.Tactics.Reconstr.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eReconstr_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_Hammer.Tactics.Tactics.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eTactics_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_Tait.Apps.apps',axiom,
! [V0__r,V1__l] : cTait_2eApps_2eapps___24a2(V0__r,V1__l) = cCoq_2eLists_2eList_2efold__left___24a5(cTait_2eTerm_2eterm,cTait_2eTerm_2eterm,cTait_2eTerm_2eApp,V1__l,V0__r) ).
fof('$_def_Tait.Apps.arrows',axiom,
! [V0__rho,V1__l] : cTait_2eApps_2earrows___24a2(V0__rho,V1__l) = cCoq_2eLists_2eList_2efold__right___24a5(cTait_2eTerm_2etype,cTait_2eTerm_2etype,cTait_2eTerm_2eArrow,V0__rho,V1__l) ).
fof('$_def_Tait.Apps.get_apps',axiom,
! [V1__r] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ( ? [Vvar__0___24Anonymous__603] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__603)
& V1__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__603)
& cTait_2eApps_2eget__apps___24a1(V1__r) = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm) )
| ? [Vvar__0___24Anonymous__604] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__604)
& ? [Vvar__1___24Anonymous__605] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__605)
& V1__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__604,Vvar__1___24Anonymous__605)
& cTait_2eApps_2eget__apps___24a1(V1__r) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2eterm,cTait_2eApps_2eget__apps___24a1(Vvar__0___24Anonymous__604),cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__1___24Anonymous__605,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm))) ) )
| ? [Vvar__0___24Anonymous__607] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__607)
& ? [Vvar__1___24Anonymous__608] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__608)
& V1__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__607,Vvar__1___24Anonymous__608)
& cTait_2eApps_2eget__apps___24a1(V1__r) = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm) ) ) ) ) ).
fof('$_def_Tait.Apps.head_apps',axiom,
! [V1__r] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ( ? [Vvar__0___24Anonymous__613] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__613)
& V1__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__613)
& cTait_2eApps_2ehead__apps___24a1(V1__r) = V1__r )
| ? [Vvar__0___24Anonymous__614] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__614)
& ? [Vvar__1___24Anonymous__615] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__615)
& V1__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__614,Vvar__1___24Anonymous__615)
& cTait_2eApps_2ehead__apps___24a1(V1__r) = cTait_2eApps_2ehead__apps___24a1(Vvar__0___24Anonymous__614) ) )
| ? [Vvar__0___24Anonymous__617] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__617)
& ? [Vvar__1___24Anonymous__618] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__618)
& V1__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__617,Vvar__1___24Anonymous__618)
& cTait_2eApps_2ehead__apps___24a1(V1__r) = V1__r ) ) ) ) ).
fof('$_def_Tait.Apps.is_app',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ( ? [Vvar__0___24Anonymous__577] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__577)
& V0__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__577)
& cTait_2eApps_2eis__app___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__578] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__578)
& ? [Vvar__1___24Anonymous__579] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__579)
& V0__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__578,Vvar__1___24Anonymous__579)
& cTait_2eApps_2eis__app___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2etrue ) )
| ? [Vvar__0___24Anonymous__581] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__581)
& ? [Vvar__1___24Anonymous__582] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__582)
& V0__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__581,Vvar__1___24Anonymous__582)
& cTait_2eApps_2eis__app___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Tait.Apps.left_app',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ( ? [Vvar__0___24Anonymous__586] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__586)
& V0__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__586)
& cTait_2eApps_2eleft__app___24a1(V0__r) = cTait_2eTerm_2edterm )
| ? [Vvar__0___24Anonymous__587] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__587)
& ? [Vvar__1___24Anonymous__588] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__588)
& V0__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__587,Vvar__1___24Anonymous__588)
& cTait_2eApps_2eleft__app___24a1(V0__r) = Vvar__0___24Anonymous__587 ) )
| ? [Vvar__0___24Anonymous__590] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__590)
& ? [Vvar__1___24Anonymous__591] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__591)
& V0__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__590,Vvar__1___24Anonymous__591)
& cTait_2eApps_2eleft__app___24a1(V0__r) = cTait_2eTerm_2edterm ) ) ) ) ).
fof('$_def_Tait.Apps.right_app',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ( ? [Vvar__0___24Anonymous__595] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__595)
& V0__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__595)
& cTait_2eApps_2eright__app___24a1(V0__r) = cTait_2eTerm_2edterm )
| ? [Vvar__0___24Anonymous__596] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__596)
& ? [Vvar__1___24Anonymous__597] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__597)
& V0__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__596,Vvar__1___24Anonymous__597)
& cTait_2eApps_2eright__app___24a1(V0__r) = Vvar__1___24Anonymous__597 ) )
| ? [Vvar__0___24Anonymous__599] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__599)
& ? [Vvar__1___24Anonymous__600] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__600)
& V0__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__599,Vvar__1___24Anonymous__600)
& cTait_2eApps_2eright__app___24a1(V0__r) = cTait_2eTerm_2edterm ) ) ) ) ).
fof('$_def_Tait.MoreList.consn',axiom,
! [V0__A,V1__n,V2__a,V3__l] : cTait_2eMoreList_2econsn___24a4(V0__A,V1__n,V2__a,V3__l) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(c_24__lam__55008___24a1(V0__A),V3__l,c_24__lam__55011___24a2(V0__A,V2__a),V1__n) ).
fof('$_def_Tait.MoreList.existsb',axiom,
! [V0__A,V2__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)
& cTait_2eMoreList_2eexistsb___24a3(V0__A,V2__f,V3__l) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__841] :
( t(Vvar__1___24Anonymous__841,V0__A)
& ? [Vvar__2___24Anonymous__842] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__842)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__841,Vvar__2___24Anonymous__842)
& cTait_2eMoreList_2eexistsb___24a3(V0__A,V2__f,V3__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(happ(V2__f,Vvar__1___24Anonymous__841),cTait_2eMoreList_2eexistsb___24a3(V0__A,V2__f,Vvar__2___24Anonymous__842)) ) ) ) ) ) ).
fof('$_def_Tait.MoreList.firstn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cTait_2eMoreList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__0___24Anonymous__73691] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__73691)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__73691)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cTait_2eMoreList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__73698] :
( t(Vvar__1___24Anonymous__73698,V0__A)
& ? [Vvar__2___24Anonymous__73699] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__73699)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__73698,Vvar__2___24Anonymous__73699)
& cTait_2eMoreList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__73698,cTait_2eMoreList_2efirstn___24a3(V0__A,Vvar__0___24Anonymous__73691,Vvar__2___24Anonymous__73699)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Tait.MoreList.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cTait_2eMoreList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__66345] :
( t(Vvar__1___24Anonymous__66345,V0__A)
& ? [Vvar__2___24Anonymous__66346] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66346)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66346)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__66345,Vvar__2___24Anonymous__66346)
& ( ( Vvar__2___24Anonymous__66346 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cTait_2eMoreList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__66345 )
| ? [Vvar__1___24Anonymous__66357] :
( t(Vvar__1___24Anonymous__66357,V0__A)
& ? [Vvar__2___24Anonymous__66358] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66358)
& Vvar__2___24Anonymous__66346 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__66357,Vvar__2___24Anonymous__66358)
& cTait_2eMoreList_2elast___24a3(V0__A,V2__l,V3__d) = cTait_2eMoreList_2elast___24a3(V0__A,Vvar__2___24Anonymous__66346,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Tait.MoreList.removelast',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cTait_2eMoreList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__66367] :
( t(Vvar__1___24Anonymous__66367,V0__A)
& ? [Vvar__2___24Anonymous__66368] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66368)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66368)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__66367,Vvar__2___24Anonymous__66368)
& ( ( Vvar__2___24Anonymous__66368 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cTait_2eMoreList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__66379] :
( t(Vvar__1___24Anonymous__66379,V0__A)
& ? [Vvar__2___24Anonymous__66380] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__66380)
& Vvar__2___24Anonymous__66368 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__66379,Vvar__2___24Anonymous__66380)
& cTait_2eMoreList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__66367,cTait_2eMoreList_2eremovelast___24a2(V0__A,Vvar__2___24Anonymous__66368)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Tait.MoreList.rev_acc',axiom,
! [V0__A,V2__l,V3__l_27] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cTait_2eMoreList_2erev__acc___24a3(V0__A,V2__l,V3__l_27) = V3__l_27 )
| ? [Vvar__1___24Anonymous__73684] :
( t(Vvar__1___24Anonymous__73684,V0__A)
& ? [Vvar__2___24Anonymous__73685] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__73685)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__73684,Vvar__2___24Anonymous__73685)
& cTait_2eMoreList_2erev__acc___24a3(V0__A,V2__l,V3__l_27) = cTait_2eMoreList_2erev__acc___24a3(V0__A,Vvar__2___24Anonymous__73685,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__73684,V3__l_27)) ) ) ) ) ) ).
fof('$_def_Tait.MoreList.seq',axiom,
! [V1__start,V2__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__len)
=> ( ( V2__len = cCoq_2eInit_2eDatatypes_2eO
& cTait_2eMoreList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__0___24Anonymous__286] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__286)
& V2__len = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__286)
& cTait_2eMoreList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,V1__start,cTait_2eMoreList_2eseq___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__start),Vvar__0___24Anonymous__286)) ) ) ) ).
fof('$_def_Tait.Subst.id',axiom,
! [V0__k] : cTait_2eSubst_2eid___24a1(V0__k) = cTait_2eSubst_2emk__sub___24a2(cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2enat,cTait_2eTerm_2eterm,cTait_2eTerm_2eVar,cTait_2eMoreList_2eseq___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__k)),V0__k) ).
fof('$_def_Tait.Subst.shift',axiom,
! [V0__s] :
( cTait_2eSubst_2esubstitution___24t(V0__s)
=> ? [Vvar__0__support__855] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__0__support__855)
& ? [Vvar__1__shift__856] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__shift__856)
& V0__s = cTait_2eSubst_2emk__sub___24a2(Vvar__0__support__855,Vvar__1__shift__856)
& cTait_2eSubst_2eshift___24a1(V0__s) = Vvar__1__shift__856 ) ) ) ).
fof('$_def_Tait.Subst.sub',axiom,
! [V1__r,V2__rs] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ( ? [Vvar__0___24Anonymous__351] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__351)
& V1__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__351)
& cTait_2eSubst_2esub___24a2(V1__r,V2__rs) = cCoq_2eLists_2eList_2enth___24a4(cTait_2eTerm_2eterm,Vvar__0___24Anonymous__351,cTait_2eSubst_2esupport___24a1(V2__rs),cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__351,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2eterm,cTait_2eSubst_2esupport___24a1(V2__rs))),cTait_2eSubst_2eshift___24a1(V2__rs)))) )
| ? [Vvar__0___24Anonymous__352] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__352)
& ? [Vvar__1___24Anonymous__353] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__353)
& V1__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__352,Vvar__1___24Anonymous__353)
& cTait_2eSubst_2esub___24a2(V1__r,V2__rs) = cTait_2eTerm_2eApp___24a2(cTait_2eSubst_2esub___24a2(Vvar__0___24Anonymous__352,V2__rs),cTait_2eSubst_2esub___24a2(Vvar__1___24Anonymous__353,V2__rs)) ) )
| ? [Vvar__0___24Anonymous__355] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__355)
& ? [Vvar__1___24Anonymous__356] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__356)
& V1__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__355,Vvar__1___24Anonymous__356)
& cTait_2eSubst_2esub___24a2(V1__r,V2__rs) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__355,cTait_2eSubst_2esub___24a2(Vvar__1___24Anonymous__356,cTait_2eSubst_2esublift___24a1(V2__rs))) ) ) ) ) ).
fof('$_def_Tait.Subst.sub1',axiom,
! [V0__r] : cTait_2eSubst_2esub1___24a1(V0__r) = cTait_2eSubst_2emk__sub___24a2(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,V0__r,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)),cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_Tait.Subst.sub_swap0',axiom,
! [V0__r,V1__k] : cTait_2eSubst_2esub__swap0___24a2(V0__r,V1__k) = cTait_2eSubst_2esub___24a2(V0__r,cTait_2eSubst_2eswap0___24a1(V1__k)) ).
fof('$_def_Tait.Subst.sublift',axiom,
! [V0__rs] : cTait_2eSubst_2esublift___24a1(V0__rs) = cTait_2eSubst_2emk__sub___24a2(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eLists_2eList_2emap___24a4(cTait_2eTerm_2eterm,cTait_2eTerm_2eterm,cTait_2eTerm_2eup___24a1(cCoq_2eInit_2eDatatypes_2eO),cTait_2eSubst_2esupport___24a1(V0__rs))),cCoq_2eInit_2eDatatypes_2eS___24a1(cTait_2eSubst_2eshift___24a1(V0__rs))) ).
fof('$_def_Tait.Subst.support',axiom,
! [V0__s] :
( cTait_2eSubst_2esubstitution___24t(V0__s)
=> ? [Vvar__0__support__343] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__0__support__343)
& ? [Vvar__1__shift__344] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__shift__344)
& V0__s = cTait_2eSubst_2emk__sub___24a2(Vvar__0__support__343,Vvar__1__shift__344)
& cTait_2eSubst_2esupport___24a1(V0__s) = Vvar__0__support__343 ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.PushList',axiom,
! [V1__l,V2__theta] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)
& cTait_2eSubst2_2eJoachimski_2ePushList___24a2(V1__l,V2__theta) = V2__theta )
| ? [Vvar__1___24Anonymous__1160] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__1160)
& ? [Vvar__2___24Anonymous__1161] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__2___24Anonymous__1161)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__1___24Anonymous__1160,Vvar__2___24Anonymous__1161)
& cTait_2eSubst2_2eJoachimski_2ePushList___24a2(V1__l,V2__theta) = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__1___24Anonymous__1160,cTait_2eSubst2_2eJoachimski_2ePushList___24a2(Vvar__2___24Anonymous__1161,V2__theta)) ) ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.Spare',axiom,
! [V1__n,V2__theta] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cTait_2eSubst2_2eJoachimski_2eSpare___24a2(V1__n,V2__theta) = V2__theta )
| ? [Vvar__0___24Anonymous__1167] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1167)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1167)
& cTait_2eSubst2_2eJoachimski_2eSpare___24a2(V1__n,V2__theta) = cTait_2eSubst2_2eJoachimski_2eSpare___24a2(Vvar__0___24Anonymous__1167,cTait_2eSubst2_2eJoachimski_2eDot___24a2(cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__1167),V2__theta)) ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.comp',axiom,
! [V1__theta,V2__theta_27] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V1__theta)
=> ( ? [Vvar__0___24Anonymous__1149] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__1149)
& ? [Vvar__1___24Anonymous__1150] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vvar__1___24Anonymous__1150)
& V1__theta = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__1149,Vvar__1___24Anonymous__1150)
& cTait_2eSubst2_2eJoachimski_2ecomp___24a2(V1__theta,V2__theta_27) = cTait_2eSubst2_2eJoachimski_2eDot___24a2(cTait_2eSubst2_2eJoachimski_2esub___24a2(Vvar__0___24Anonymous__1149,V2__theta_27),cTait_2eSubst2_2eJoachimski_2ecomp___24a2(Vvar__1___24Anonymous__1150,V2__theta_27)) ) )
| ? [Vvar__0___24Anonymous__1152] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1152)
& V1__theta = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__1152)
& cTait_2eSubst2_2eJoachimski_2ecomp___24a2(V1__theta,V2__theta_27) = cTait_2eSubst2_2eJoachimski_2ecomp_27___24a2(Vvar__0___24Anonymous__1152,V2__theta_27) ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.comp\'',axiom,
! [V1__n,V2__theta] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cTait_2eSubst2_2eJoachimski_2ecomp_27___24a2(V1__n,V2__theta) = V2__theta )
| ? [Vvar__0___24Anonymous__37238] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__37238)
& ( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V2__theta)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__37238)
& ( ? [Vvar__0___24Anonymous__37243] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__37243)
& ? [Vvar__1___24Anonymous__37244] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vvar__1___24Anonymous__37244)
& V2__theta = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__37243,Vvar__1___24Anonymous__37244)
& cTait_2eSubst2_2eJoachimski_2ecomp_27___24a2(V1__n,V2__theta) = cTait_2eSubst2_2eJoachimski_2ecomp_27___24a2(Vvar__0___24Anonymous__37238,Vvar__1___24Anonymous__37244) ) )
| ? [Vvar__0___24Anonymous__37246] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__37246)
& V2__theta = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__37246)
& cTait_2eSubst2_2eJoachimski_2ecomp_27___24a2(V1__n,V2__theta) = cTait_2eSubst2_2eJoachimski_2eUp___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__37238),Vvar__0___24Anonymous__37246)) ) ) ) ) ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.sub',axiom,
! [V1__r,V2__theta] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ( ? [Vvar__0___24Anonymous__1138] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1138)
& V1__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__1138)
& cTait_2eSubst2_2eJoachimski_2esub___24a2(V1__r,V2__theta) = cTait_2eSubst2_2eJoachimski_2esub_27___24a2(Vvar__0___24Anonymous__1138,V2__theta) )
| ? [Vvar__0___24Anonymous__1139] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__1139)
& ? [Vvar__1___24Anonymous__1140] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__1140)
& V1__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__1139,Vvar__1___24Anonymous__1140)
& cTait_2eSubst2_2eJoachimski_2esub___24a2(V1__r,V2__theta) = cTait_2eTerm_2eApp___24a2(cTait_2eSubst2_2eJoachimski_2esub___24a2(Vvar__0___24Anonymous__1139,V2__theta),cTait_2eSubst2_2eJoachimski_2esub___24a2(Vvar__1___24Anonymous__1140,V2__theta)) ) )
| ? [Vvar__0___24Anonymous__1142] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__1142)
& ? [Vvar__1___24Anonymous__1143] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__1143)
& V1__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__1142,Vvar__1___24Anonymous__1143)
& cTait_2eSubst2_2eJoachimski_2esub___24a2(V1__r,V2__theta) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__1142,cTait_2eSubst2_2eJoachimski_2esub___24a2(Vvar__1___24Anonymous__1143,cTait_2eSubst2_2eJoachimski_2eDot___24a2(cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eDatatypes_2eO),cTait_2eSubst2_2eJoachimski_2esublift___24a2(V2__theta,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))) ) ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.sub\'',axiom,
! [V1__k,V2__theta] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V2__theta)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eO
& ( ? [Vvar__0___24Anonymous__1121] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__1121)
& ? [Vvar__1___24Anonymous__1122] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vvar__1___24Anonymous__1122)
& V2__theta = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__1121,Vvar__1___24Anonymous__1122)
& cTait_2eSubst2_2eJoachimski_2esub_27___24a2(V1__k,V2__theta) = Vvar__0___24Anonymous__1121 ) )
| ? [Vvar__0___24Anonymous__1124] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1124)
& V2__theta = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__1124)
& cTait_2eSubst2_2eJoachimski_2esub_27___24a2(V1__k,V2__theta) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__k,Vvar__0___24Anonymous__1124)) ) ) ) )
| ? [Vvar__0___24Anonymous__1125] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1125)
& ( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V2__theta)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1125)
& ( ? [Vvar__0___24Anonymous__1130] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__1130)
& ? [Vvar__1___24Anonymous__1131] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vvar__1___24Anonymous__1131)
& V2__theta = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__1130,Vvar__1___24Anonymous__1131)
& cTait_2eSubst2_2eJoachimski_2esub_27___24a2(V1__k,V2__theta) = cTait_2eSubst2_2eJoachimski_2esub_27___24a2(Vvar__0___24Anonymous__1125,Vvar__1___24Anonymous__1131) ) )
| ? [Vvar__0___24Anonymous__1133] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1133)
& V2__theta = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__1133)
& cTait_2eSubst2_2eJoachimski_2esub_27___24a2(V1__k,V2__theta) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__k,Vvar__0___24Anonymous__1133)) ) ) ) ) ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.sublift',axiom,
! [V1__theta,V2__n] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V1__theta)
=> ( ? [Vvar__0___24Anonymous__1113] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__1113)
& ? [Vvar__1___24Anonymous__1114] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vvar__1___24Anonymous__1114)
& V1__theta = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__1113,Vvar__1___24Anonymous__1114)
& cTait_2eSubst2_2eJoachimski_2esublift___24a2(V1__theta,V2__n) = cTait_2eSubst2_2eJoachimski_2eDot___24a2(cTait_2eTerm_2elift___24a3(cCoq_2eInit_2eDatatypes_2eO,V2__n,Vvar__0___24Anonymous__1113),cTait_2eSubst2_2eJoachimski_2esublift___24a2(Vvar__1___24Anonymous__1114,V2__n)) ) )
| ? [Vvar__0___24Anonymous__1116] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1116)
& V1__theta = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__1116)
& cTait_2eSubst2_2eJoachimski_2esublift___24a2(V1__theta,V2__n) = cTait_2eSubst2_2eJoachimski_2eUp___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__1116,V2__n)) ) ) ) ).
fof('$_def_Tait.Subst2.Joachimski.substitution_rect',axiom,
! [V0__P,V1__f,V2__f,V4__s] :
( c_24__type__1075___24t(V0__P,V0__P)
=> ( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V4__s)
=> ( ? [Vvar__0___24Anonymous__1070] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__1070)
& ? [Vvar__1___24Anonymous__1071] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vvar__1___24Anonymous__1071)
& V4__s = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__1070,Vvar__1___24Anonymous__1071)
& cTait_2eSubst2_2eJoachimski_2esubstitution__rect___24a4(V0__P,V1__f,V2__f,V4__s) = happ(happ(happ(V1__f,Vvar__0___24Anonymous__1070),Vvar__1___24Anonymous__1071),cTait_2eSubst2_2eJoachimski_2esubstitution__rect___24a4(V0__P,V1__f,V2__f,Vvar__1___24Anonymous__1071)) ) )
| ? [Vvar__0___24Anonymous__1073] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1073)
& V4__s = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__1073)
& cTait_2eSubst2_2eJoachimski_2esubstitution__rect___24a4(V0__P,V1__f,V2__f,V4__s) = happ(V2__f,Vvar__0___24Anonymous__1073) ) ) ) ) ).
fof('$_def_Tait.Subst2.above',axiom,
! [V0__k,V1__r] :
( cTait_2eSubst2_2eabove___24a2(V0__k,V1__r)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__k,V2__n))
=> cTait_2eTerm_2eoccurs___24a2(V2__n,V1__r) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Tait.Term.arrow_left',axiom,
! [V0__sigma] :
( cTait_2eTerm_2etype___24t(V0__sigma)
=> ( ( V0__sigma = cTait_2eTerm_2eIota
& cTait_2eTerm_2earrow__left___24a1(V0__sigma) = cTait_2eTerm_2edtype )
| ? [Vvar__0___24Anonymous__151959] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__151959)
& ? [Vvar__1___24Anonymous__151960] :
( cTait_2eTerm_2etype___24t(Vvar__1___24Anonymous__151960)
& V0__sigma = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__151959,Vvar__1___24Anonymous__151960)
& cTait_2eTerm_2earrow__left___24a1(V0__sigma) = Vvar__0___24Anonymous__151959 ) ) ) ) ).
fof('$_def_Tait.Term.arrow_right',axiom,
! [V0__sigma] :
( cTait_2eTerm_2etype___24t(V0__sigma)
=> ( ( V0__sigma = cTait_2eTerm_2eIota
& cTait_2eTerm_2earrow__right___24a1(V0__sigma) = cTait_2eTerm_2edtype )
| ? [Vvar__0___24Anonymous__979] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__979)
& ? [Vvar__1___24Anonymous__980] :
( cTait_2eTerm_2etype___24t(Vvar__1___24Anonymous__980)
& V0__sigma = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__979,Vvar__1___24Anonymous__980)
& cTait_2eTerm_2earrow__right___24a1(V0__sigma) = Vvar__1___24Anonymous__980 ) ) ) ) ).
fof('$_def_Tait.Term.down',axiom,
! [V1__l,V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> ( ? [Vvar__0___24Anonymous__234] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__234)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__234)
=> ( V2__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__234)
& ( ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__234))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__234) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__234),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__234,V1__l))
& cTait_2eTerm_2edown___24a2(V1__l,V2__r) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2epred___24a1(Vvar__0___24Anonymous__234)) )
| ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__234,V1__l))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__234) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__234),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__234,V1__l))
& cTait_2eTerm_2edown___24a2(V1__l,V2__r) = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__234) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__246] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__246)
& ? [Vvar__1___24Anonymous__247] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__247)
& V2__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__246,Vvar__1___24Anonymous__247)
& cTait_2eTerm_2edown___24a2(V1__l,V2__r) = cTait_2eTerm_2eApp___24a2(cTait_2eTerm_2edown___24a2(V1__l,Vvar__0___24Anonymous__246),cTait_2eTerm_2edown___24a2(V1__l,Vvar__1___24Anonymous__247)) ) )
| ? [Vvar__0___24Anonymous__249] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__249)
& ? [Vvar__1___24Anonymous__250] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__250)
& V2__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__249,Vvar__1___24Anonymous__250)
& cTait_2eTerm_2edown___24a2(V1__l,V2__r) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__249,cTait_2eTerm_2edown___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__l),Vvar__1___24Anonymous__250)) ) ) ) ) ).
fof('$_def_Tait.Term.lift',axiom,
! [V1__l,V2__k,V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ( ? [Vvar__0___24Anonymous__366] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__366)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__366)
=> ( V3__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__366)
& ( ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__366))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__366) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__366),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__366,V1__l))
& cTait_2eTerm_2elift___24a3(V1__l,V2__k,V3__r) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V2__k,Vvar__0___24Anonymous__366)) )
| ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__366,V1__l))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__366) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__366),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__366,V1__l))
& cTait_2eTerm_2elift___24a3(V1__l,V2__k,V3__r) = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__366) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__378] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__378)
& ? [Vvar__1___24Anonymous__379] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__379)
& V3__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__378,Vvar__1___24Anonymous__379)
& cTait_2eTerm_2elift___24a3(V1__l,V2__k,V3__r) = cTait_2eTerm_2eApp___24a2(cTait_2eTerm_2elift___24a3(V1__l,V2__k,Vvar__0___24Anonymous__378),cTait_2eTerm_2elift___24a3(V1__l,V2__k,Vvar__1___24Anonymous__379)) ) )
| ? [Vvar__0___24Anonymous__381] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__381)
& ? [Vvar__1___24Anonymous__382] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__382)
& V3__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__381,Vvar__1___24Anonymous__382)
& cTait_2eTerm_2elift___24a3(V1__l,V2__k,V3__r) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__381,cTait_2eTerm_2elift___24a3(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__l),V2__k,Vvar__1___24Anonymous__382)) ) ) ) ) ).
fof('$_def_Tait.Term.occurs',axiom,
! [V1__k,V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> ( ? [Vvar__0___24Anonymous__133] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__133)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__133)
=> ( V2__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__133)
& ( ( Vvar__0___24Anonymous__133 = V1__k
& cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a2(Vvar__0___24Anonymous__133,V1__k) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__151___24a2(V1__k,Vvar__0___24Anonymous__133),c_24__prop__152___24a2(V1__k,Vvar__0___24Anonymous__133))
& cTait_2eTerm_2eoccurs___24a2(V1__k,V2__r) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__133 != V1__k
& cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a2(Vvar__0___24Anonymous__133,V1__k) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__153___24a2(V1__k,Vvar__0___24Anonymous__133),c_24__prop__154___24a2(V1__k,Vvar__0___24Anonymous__133))
& cTait_2eTerm_2eoccurs___24a2(V1__k,V2__r) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__145] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__145)
& ? [Vvar__1___24Anonymous__146] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__146)
& V2__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__145,Vvar__1___24Anonymous__146)
& cTait_2eTerm_2eoccurs___24a2(V1__k,V2__r) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cTait_2eTerm_2eoccurs___24a2(V1__k,Vvar__0___24Anonymous__145),cTait_2eTerm_2eoccurs___24a2(V1__k,Vvar__1___24Anonymous__146)) ) )
| ? [Vvar__0___24Anonymous__148] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__148)
& ? [Vvar__1___24Anonymous__149] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__149)
& V2__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__148,Vvar__1___24Anonymous__149)
& cTait_2eTerm_2eoccurs___24a2(V1__k,V2__r) = cTait_2eTerm_2eoccurs___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__k),Vvar__1___24Anonymous__149) ) ) ) ) ).
fof('$_def_Tait.Term.term_rec',axiom,
! [V0__P] : cTait_2eTerm_2eterm__rec___24a1(V0__P) = cTait_2eTerm_2eterm__rect___24a1(V0__P) ).
fof('$_def_Tait.Term.term_rect',axiom,
! [V0__P,V1__f,V2__f,V3__f,V5__t] :
( c_24__type__876___24t(V0__P,V0__P)
=> ( cTait_2eTerm_2eterm___24t(V5__t)
=> ( ? [Vvar__0___24Anonymous__868] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__868)
& V5__t = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__868)
& cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__t) = happ(V1__f,Vvar__0___24Anonymous__868) )
| ? [Vvar__0___24Anonymous__869] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__869)
& ? [Vvar__1___24Anonymous__870] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__870)
& V5__t = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__869,Vvar__1___24Anonymous__870)
& cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__t) = happ(happ(happ(happ(V2__f,Vvar__0___24Anonymous__869),cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__0___24Anonymous__869)),Vvar__1___24Anonymous__870),cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__1___24Anonymous__870)) ) )
| ? [Vvar__0___24Anonymous__872] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__872)
& ? [Vvar__1___24Anonymous__873] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__873)
& V5__t = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__872,Vvar__1___24Anonymous__873)
& cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__t) = happ(happ(happ(V3__f,Vvar__0___24Anonymous__872),Vvar__1___24Anonymous__873),cTait_2eTerm_2eterm__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__1___24Anonymous__873)) ) ) ) ) ) ).
fof('$_def_Tait.Term.type_rec',axiom,
! [V0__P] : cTait_2eTerm_2etype__rec___24a1(V0__P) = cTait_2eTerm_2etype__rect___24a1(V0__P) ).
fof('$_def_Tait.Term.type_rect',axiom,
! [V0__P,V1__f,V2__f,V4__t] :
( c_24__type__151895___24t(V0__P,V0__P)
=> ( cTait_2eTerm_2etype___24t(V4__t)
=> ( ( V4__t = cTait_2eTerm_2eIota
& cTait_2eTerm_2etype__rect___24a4(V0__P,V1__f,V2__f,V4__t) = V1__f )
| ? [Vvar__0___24Anonymous__151891] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__151891)
& ? [Vvar__1___24Anonymous__151892] :
( cTait_2eTerm_2etype___24t(Vvar__1___24Anonymous__151892)
& V4__t = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__151891,Vvar__1___24Anonymous__151892)
& cTait_2eTerm_2etype__rect___24a4(V0__P,V1__f,V2__f,V4__t) = happ(happ(happ(happ(V2__f,Vvar__0___24Anonymous__151891),cTait_2eTerm_2etype__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__151891)),Vvar__1___24Anonymous__151892),cTait_2eTerm_2etype__rect___24a4(V0__P,V1__f,V2__f,Vvar__1___24Anonymous__151892)) ) ) ) ) ) ).
fof('$_def_Tait.Term.up',axiom,
! [V1__l,V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> ( ? [Vvar__0___24Anonymous__390] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__390)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__390)
=> ( V2__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__390)
& ( ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__390))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__390) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__390),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__390,V1__l))
& cTait_2eTerm_2eup___24a2(V1__l,V2__r) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__390)) )
| ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__390,V1__l))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V1__l,Vvar__0___24Anonymous__390) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__l,Vvar__0___24Anonymous__390),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__390,V1__l))
& cTait_2eTerm_2eup___24a2(V1__l,V2__r) = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__390) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__402] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__402)
& ? [Vvar__1___24Anonymous__403] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__403)
& V2__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__402,Vvar__1___24Anonymous__403)
& cTait_2eTerm_2eup___24a2(V1__l,V2__r) = cTait_2eTerm_2eApp___24a2(cTait_2eTerm_2eup___24a2(V1__l,Vvar__0___24Anonymous__402),cTait_2eTerm_2eup___24a2(V1__l,Vvar__1___24Anonymous__403)) ) )
| ? [Vvar__0___24Anonymous__405] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__405)
& ? [Vvar__1___24Anonymous__406] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__406)
& V2__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__405,Vvar__1___24Anonymous__406)
& cTait_2eTerm_2eup___24a2(V1__l,V2__r) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__405,cTait_2eTerm_2eup___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__l),Vvar__1___24Anonymous__406)) ) ) ) ) ).
fof('$_def_Tait.Typing.TypJ',axiom,
! [V0__rhos,V1__r,V2__rho] :
( cTait_2eTyping_2eTypJ___24a3(V0__rhos,V1__r,V2__rho)
<=> ( cTait_2eTyping_2eCorTyp___24a2(V0__rhos,V1__r)
& cTait_2eTyping_2etyp___24a2(V0__rhos,V1__r) = V2__rho ) ) ).
fof('$_def_Tait.Typing.context',axiom,
! [Vvar__989] :
( cTait_2eTyping_2econtext___24t(Vvar__989)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__989) ) ).
fof('$_def_Tait.Typing.ext_ctx',axiom,
! [V0__rhos,V1__k,V2__rho] : cTait_2eTyping_2eext__ctx___24a3(V0__rhos,V1__k,V2__rho) = cTait_2eMoreList_2econsn___24a4(cTait_2eTerm_2etype,cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__k),cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos)),V2__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)) ).
fof('$_def_Tait.Typing.typ',axiom,
! [V1__rhos,V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> ( ? [Vvar__0___24Anonymous__991] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__991)
& V2__r = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__991)
& cTait_2eTyping_2etyp___24a2(V1__rhos,V2__r) = cCoq_2eLists_2eList_2enth___24a4(cTait_2eTerm_2etype,Vvar__0___24Anonymous__991,V1__rhos,cTait_2eTerm_2edtype) )
| ? [Vvar__0___24Anonymous__992] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__992)
& ? [Vvar__1___24Anonymous__993] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__993)
& V2__r = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__992,Vvar__1___24Anonymous__993)
& cTait_2eTyping_2etyp___24a2(V1__rhos,V2__r) = cTait_2eTerm_2earrow__right___24a1(cTait_2eTyping_2etyp___24a2(V1__rhos,Vvar__0___24Anonymous__992)) ) )
| ? [Vvar__0___24Anonymous__995] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__995)
& ? [Vvar__1___24Anonymous__996] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__996)
& V2__r = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__995,Vvar__1___24Anonymous__996)
& cTait_2eTyping_2etyp___24a2(V1__rhos,V2__r) = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__995,cTait_2eTyping_2etyp___24a2(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,Vvar__0___24Anonymous__995,V1__rhos),Vvar__1___24Anonymous__996)) ) ) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__31555,Vvar__1___24Anonymous__31556,Vvar__0__P__31557,Vvar__1___24Anonymous__31558] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31555) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31557) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__37562,Vvar__1___24Anonymous__37563,Vvar__2___24Anonymous__37564] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37562,Vvar__1___24Anonymous__37563,Vvar__2___24Anonymous__37564) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__82225,Vvar__1__Plt__82226,Vvar__2__Pgt__82227,Vvar__3___24Anonymous__82228,Vvar__0__Peq__82229,Vvar__1__Plt__82230,Vvar__2__Pgt__82231,Vvar__3___24Anonymous__82232] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__82225,Vvar__1__Plt__82226,Vvar__2__Pgt__82227) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__82229,Vvar__1__Plt__82230,Vvar__2__Pgt__82231) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__79] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__79) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__31738,Vvar__1___24Anonymous__31739,Vvar__0__A__31740] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__31738,Vvar__1___24Anonymous__31739) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__31740) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__40825,Vvar__1__B__40826,Vvar__2___24Anonymous__40827,Vvar__0__A__40828,Vvar__1__B__40829,Vvar__2___24Anonymous__40830] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__40825,Vvar__1__B__40826,Vvar__2___24Anonymous__40827) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__40828,Vvar__1__B__40829,Vvar__2___24Anonymous__40830) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__704,Vvar__0__A__705,Vvar__1___24Anonymous__706,Vvar__2___24Anonymous__707] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__704) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__705,Vvar__1___24Anonymous__706,Vvar__2___24Anonymous__707) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Decimal$Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__152029,Vvar__1__f__152030,Vvar__0__i__152031,Vvar__1__f__152032,Vvar__2__e__152033] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__152029,Vvar__1__f__152030) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__152031,Vvar__1__f__152032,Vvar__2__e__152033) ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__81150] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__81150) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__83387,Vvar__0__d__83388] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__83387) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__83388) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__315,Vvar__1__B__316,Vvar__2___24Anonymous__317,Vvar__0__A__318,Vvar__1__B__319,Vvar__2___24Anonymous__320] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__315,Vvar__1__B__316,Vvar__2___24Anonymous__317) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__318,Vvar__1__B__319) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__182,Vvar__1__B__183,Vvar__2___24Anonymous__184,Vvar__0__A__185,Vvar__1__B__186,Vvar__2___24Anonymous__187] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__182,Vvar__1__B__183) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__185,Vvar__1__B__186) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__31534] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31534) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__18] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__18) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__6,Vvar__0___24Anonymous__7] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__6) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__153554,Vvar__1___24Anonymous__153555] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__153554,Vvar__1___24Anonymous__153555) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__54865] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__54865) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__82522,Vvar__1___24Anonymous__82523,Vvar__0__x__82524,Vvar__1__n__82525,Vvar__2___24Anonymous__82526] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__82522) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__82524,Vvar__1__n__82525) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__34720,Vvar__1___24Anonymous__34721] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__34720,Vvar__1___24Anonymous__34721) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__82401,Vvar__1__lt__82402,Vvar__2__eq__82403,Vvar__3__x__82404,Vvar__4__y__82405,Vvar__5___24Anonymous__82406,Vvar__0__X__82407,Vvar__1__lt__82408,Vvar__2__eq__82409,Vvar__3__x__82410,Vvar__4__y__82411,Vvar__5___24Anonymous__82412] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__82401,Vvar__1__lt__82402,Vvar__2__eq__82403,Vvar__3__x__82404,Vvar__4__y__82405) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__82407,Vvar__1__lt__82408,Vvar__2__eq__82409,Vvar__3__x__82410,Vvar__4__y__82411) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__31794,Vvar__0__n__31795,Vvar__1___24Anonymous__31796] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__31794) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__31795,Vvar__1___24Anonymous__31796) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__35509,Vvar__0__A__35510,Vvar__1__h__35511,Vvar__2__n__35512,Vvar__3___24Anonymous__35513] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__35509) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__35510,Vvar__1__h__35511,Vvar__2__n__35512,Vvar__3___24Anonymous__35513) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__41014,Vvar__1___24Anonymous__41015,Vvar__0__C__41016,Vvar__1___24Anonymous__41017] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__41014,Vvar__1___24Anonymous__41015) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__41016,Vvar__1___24Anonymous__41017) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__41078,Vvar__1___24Anonymous__41079,Vvar__0__C__41080,Vvar__1___24Anonymous__41081,Vvar__2___24Anonymous__41082] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__41078,Vvar__1___24Anonymous__41079) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__41080,Vvar__1___24Anonymous__41081,Vvar__2___24Anonymous__41082) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__41115,Vvar__1___24Anonymous__41116] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__41115,Vvar__1___24Anonymous__41116) ).
fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__50225,Vvar__1___24Anonymous__50226,Vvar__0__C__50227,Vvar__1___24Anonymous__50228] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__50225,Vvar__1___24Anonymous__50226) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__50227,Vvar__1___24Anonymous__50228) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__54548,Vvar__1__TX__54549,Vvar__2__AA__54550,Vvar__3__AF__54551,Vvar__0__TA__54552,Vvar__1__TX__54553,Vvar__2__AA__54554,Vvar__3__AF__54555] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__54548,Vvar__1__TX__54549,Vvar__2__AA__54550,Vvar__3__AF__54551) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__54552,Vvar__1__TX__54553,Vvar__2__AA__54554,Vvar__3__AF__54555) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__153234,Vvar__0__A__153235,Vvar__1___24Anonymous__153236] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__153234) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__153235,Vvar__1___24Anonymous__153236) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__54740,Vvar__1___24Anonymous__54741] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__54740,Vvar__1___24Anonymous__54741) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__42190,Vvar__0__C__42191] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__42190) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__42191) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__33037,Vvar__0__C__33038] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__33037) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__33038) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__32681,Vvar__1___24Anonymous__32682,Vvar__0__C__32683,Vvar__1___24Anonymous__32684,Vvar__2___24Anonymous__32685] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__32681,Vvar__1___24Anonymous__32682) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__32683,Vvar__1___24Anonymous__32684,Vvar__2___24Anonymous__32685) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__32847,Vvar__1___24Anonymous__32848] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__32847,Vvar__1___24Anonymous__32848) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__34522,Vvar__1__req__34523,Vvar__2__reqb__34524,Vvar__3___24Anonymous__34525] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34522,Vvar__1__req__34523,Vvar__2__reqb__34524) ).
fof('$_discrim_Hammer.Tactics.Reconstr.Empty$Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eEmpty != cHammer_2eTactics_2eReconstr_2eAllHyps ).
fof('$_discrim_Tait.Subst2.Joachimski.Dot$Tait.Subst2.Joachimski.Up',axiom,
! [Vvar__0___24Anonymous__1055,Vvar__1___24Anonymous__1056,Vvar__0___24Anonymous__1057] : cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__1055,Vvar__1___24Anonymous__1056) != cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__1057) ).
fof('$_discrim_Tait.Term.Iota$Tait.Term.Arrow',axiom,
! [Vvar__0___24Anonymous__209,Vvar__1___24Anonymous__210] : cTait_2eTerm_2eIota != cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__209,Vvar__1___24Anonymous__210) ).
fof('$_discrim_Tait.Term.Var$Tait.Term.App',axiom,
! [Vvar__0___24Anonymous__119,Vvar__0___24Anonymous__120,Vvar__1___24Anonymous__121] : cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__119) != cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__120,Vvar__1___24Anonymous__121) ).
fof('$_fix_101530_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__fix__101530__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__0___24Anonymous__101531] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__101531)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__101531)
& c_24__fix__101530__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__1,c_24__fix__101530__v__CANONICAL__0___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vvar__0___24Anonymous__101531)) ) ) ) ).
fof('$_fix_101566_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat)
& c_24__fix__101566__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm) )
| ? [Vvar__1___24Anonymous__101570] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__101570)
& ? [Vvar__2___24Anonymous__101571] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__2___24Anonymous__101571)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1___24Anonymous__101570,Vvar__2___24Anonymous__101571)
& c_24__fix__101566__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,cTait_2eTerm_2eVar___24a1(Vvar__1___24Anonymous__101570),c_24__fix__101566__v__CANONICAL__0___24a1(Vvar__2___24Anonymous__101571)) ) ) ) ) ).
fof('$_fix_102016_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__2)
=> ( ? [Vvar__0___24Anonymous__102017] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__102017)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__102017)
=> ( Vv__CANONICAL__2 = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__102017)
& ( ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__102017))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__102017) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__102017),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__102017,Vv__CANONICAL__1))
& c_24__fix__102016__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__102017)) )
| ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__102017,Vv__CANONICAL__1))
& cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__102017) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__102017),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__102017,Vv__CANONICAL__1))
& c_24__fix__102016__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__102017) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__102029] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__102029)
& ? [Vvar__1___24Anonymous__102030] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__102030)
& Vv__CANONICAL__2 = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__102029,Vvar__1___24Anonymous__102030)
& c_24__fix__102016__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cTait_2eTerm_2eApp___24a2(c_24__fix__102016__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__102029),c_24__fix__102016__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vvar__1___24Anonymous__102030)) ) )
| ? [Vvar__0___24Anonymous__102032] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__102032)
& ? [Vvar__1___24Anonymous__102033] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__102033)
& Vv__CANONICAL__2 = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__102032,Vvar__1___24Anonymous__102033)
& c_24__fix__102016__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__102032,c_24__fix__102016__v__CANONICAL__0___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vvar__1___24Anonymous__102033)) ) ) ) ) ).
fof('$_fix_102516_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)
& c_24__fix__102516__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm) )
| ? [Vvar__1___24Anonymous__102520] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__102520)
& ? [Vvar__2___24Anonymous__102521] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__2___24Anonymous__102521)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__1___24Anonymous__102520,Vvar__2___24Anonymous__102521)
& c_24__fix__102516__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,c_24__case__Tait_2eTerm_2eterm_24101877___24a1(Vvar__1___24Anonymous__102520),c_24__fix__102516__v__CANONICAL__0___24a1(Vvar__2___24Anonymous__102521)) ) ) ) ) ).
fof('$_fix_103877_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)
& c_24__fix__103877__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
| ? [Vvar__1___24Anonymous__103881] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__103881)
& ? [Vvar__2___24Anonymous__103882] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__2___24Anonymous__103882)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__1___24Anonymous__103881,Vvar__2___24Anonymous__103882)
& c_24__fix__103877__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__1___24Anonymous__103881,c_24__fix__103877__v__CANONICAL__0___24a2(Vvar__2___24Anonymous__103882,Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_fix_105972_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__105973] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__105973)
& Vv__CANONICAL__1 = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__105973)
& c_24__fix__105972__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eLists_2eList_2enth___24a4(cTait_2eTerm_2eterm,Vvar__0___24Anonymous__105973,cTait_2eSubst_2esupport___24a1(Vv__CANONICAL__2),cTait_2eTerm_2eVar___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__105973,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2eterm,cTait_2eSubst_2esupport___24a1(Vv__CANONICAL__2))),cTait_2eSubst_2eshift___24a1(Vv__CANONICAL__2)))) )
| ? [Vvar__0___24Anonymous__105974] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__105974)
& ? [Vvar__1___24Anonymous__105975] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__105975)
& Vv__CANONICAL__1 = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__105974,Vvar__1___24Anonymous__105975)
& c_24__fix__105972__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cTait_2eTerm_2eApp___24a2(c_24__fix__105972__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__105974,Vv__CANONICAL__2),c_24__fix__105972__v__CANONICAL__0___24a2(Vvar__1___24Anonymous__105975,Vv__CANONICAL__2)) ) )
| ? [Vvar__0___24Anonymous__105977] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__105977)
& ? [Vvar__1___24Anonymous__105978] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__105978)
& Vv__CANONICAL__1 = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__105977,Vvar__1___24Anonymous__105978)
& c_24__fix__105972__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__105977,c_24__fix__105972__v__CANONICAL__0___24a2(Vvar__1___24Anonymous__105978,cTait_2eSubst_2esublift___24a1(Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_fix_153549_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__153550] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153550)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__153550)
& c_24__fix__153549__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__153549__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__153550)) )
| ? [Vvar__0___24Anonymous__153551] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153551)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__153551)
& c_24__fix__153549__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__153551) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__153549__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_fix_54827_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__54842] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54842)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54842)
& ( ? [Vvar__0___24Anonymous__54846] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54846)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54846)
& c_24__fix__54827__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__54827__1__add__carry___24a2(Vvar__0___24Anonymous__54842,Vvar__0___24Anonymous__54846)) )
| ? [Vvar__0___24Anonymous__54847] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54847)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54847)
& c_24__fix__54827__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__54827__1__add__carry___24a2(Vvar__0___24Anonymous__54842,Vvar__0___24Anonymous__54847)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__54827__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__54842)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__54848] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54848)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54848)
& ( ? [Vvar__0___24Anonymous__54852] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54852)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54852)
& c_24__fix__54827__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__54827__1__add__carry___24a2(Vvar__0___24Anonymous__54848,Vvar__0___24Anonymous__54852)) )
| ? [Vvar__0___24Anonymous__54853] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54853)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54853)
& c_24__fix__54827__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__54848,Vvar__0___24Anonymous__54853)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__54827__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__54848)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__54854] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54854)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__54854)
& c_24__fix__54827__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__54854)) )
| ? [Vvar__0___24Anonymous__54855] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54855)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__54855)
& c_24__fix__54827__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__54855)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__54827__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_fix_66832_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__66832__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__66836] :
( t(Vvar__1___24Anonymous__66836,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__66837] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__66837)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__66836,Vvar__2___24Anonymous__66837)
& c_24__fix__66832__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__66836,c_24__fix__66832__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__66837,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_80294_v_CANONICAL_2',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ( ( Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__80294__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__5 )
| ? [Vvar__1__h__80299] :
( t(Vvar__1__h__80299,Vv__CANONICAL__0)
& ? [Vvar__2__n__80300] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__80300)
& ? [Vvar__3___24Anonymous__80301] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vvar__2__n__80300,Vvar__3___24Anonymous__80301)
& Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vvar__1__h__80299,Vvar__2__n__80300,Vvar__3___24Anonymous__80301)
& c_24__fix__80294__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1__h__80299,c_24__fix__80294__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2__n__80300,Vvar__3___24Anonymous__80301,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_fix_84413_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)
& c_24__fix__84413__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
| ? [Vvar__1___24Anonymous__84417] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__84417)
& ? [Vvar__2___24Anonymous__84418] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__2___24Anonymous__84418)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__1___24Anonymous__84417,Vvar__2___24Anonymous__84418)
& c_24__fix__84413__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__fix__84413__v__CANONICAL__0___24a2(Vvar__2___24Anonymous__84418,cTait_2eTerm_2eApp___24a2(Vv__CANONICAL__2,Vvar__1___24Anonymous__84417)) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__31563,Vvar__0__P__31564,Vvar__1___24Anonymous__31565,Vvar__1___24Anonymous__31566] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31563) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31564)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__31563 = Vvar__0__P__31564 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__31559,Vvar__0__P__31560,Vvar__1___24Anonymous__31561,Vvar__1___24Anonymous__31562] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31559) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31560)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__31559 = Vvar__0__P__31560 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__37565,Vvar__0___24Anonymous__37566,Vvar__1___24Anonymous__37567,Vvar__1___24Anonymous__37568,Vvar__2___24Anonymous__37569,Vvar__2___24Anonymous__37570] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37565,Vvar__1___24Anonymous__37567,Vvar__2___24Anonymous__37569) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37566,Vvar__1___24Anonymous__37568,Vvar__2___24Anonymous__37570)
=> ( Vvar__2___24Anonymous__37569 = Vvar__2___24Anonymous__37570
& Vvar__1___24Anonymous__37567 = Vvar__1___24Anonymous__37568
& Vvar__0___24Anonymous__37565 = Vvar__0___24Anonymous__37566 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__82233,Vvar__0__Peq__82234,Vvar__1__Plt__82235,Vvar__1__Plt__82236,Vvar__2__Pgt__82237,Vvar__2__Pgt__82238,Vvar__3___24Anonymous__82239,Vvar__3___24Anonymous__82240] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__82233,Vvar__1__Plt__82235,Vvar__2__Pgt__82237) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__82234,Vvar__1__Plt__82236,Vvar__2__Pgt__82238)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__82237 = Vvar__2__Pgt__82238
& Vvar__1__Plt__82235 = Vvar__1__Plt__82236
& Vvar__0__Peq__82233 = Vvar__0__Peq__82234 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__82249,Vvar__0__Peq__82250,Vvar__1__Plt__82251,Vvar__1__Plt__82252,Vvar__2__Pgt__82253,Vvar__2__Pgt__82254,Vvar__3___24Anonymous__82255,Vvar__3___24Anonymous__82256] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__82249,Vvar__1__Plt__82251,Vvar__2__Pgt__82253) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__82250,Vvar__1__Plt__82252,Vvar__2__Pgt__82254)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__82253 = Vvar__2__Pgt__82254
& Vvar__1__Plt__82251 = Vvar__1__Plt__82252
& Vvar__0__Peq__82249 = Vvar__0__Peq__82250 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__82241,Vvar__0__Peq__82242,Vvar__1__Plt__82243,Vvar__1__Plt__82244,Vvar__2__Pgt__82245,Vvar__2__Pgt__82246,Vvar__3___24Anonymous__82247,Vvar__3___24Anonymous__82248] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__82241,Vvar__1__Plt__82243,Vvar__2__Pgt__82245) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__82242,Vvar__1__Plt__82244,Vvar__2__Pgt__82246)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__82245 = Vvar__2__Pgt__82246
& Vvar__1__Plt__82243 = Vvar__1__Plt__82244
& Vvar__0__Peq__82241 = Vvar__0__Peq__82242 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__31745,Vvar__0__A__31746] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__31745) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__31746)
=> Vvar__0__A__31745 = Vvar__0__A__31746 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__80,Vvar__0___24Anonymous__81] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__80) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__81)
=> Vvar__0___24Anonymous__80 = Vvar__0___24Anonymous__81 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__31741,Vvar__0__A__31742,Vvar__1___24Anonymous__31743,Vvar__1___24Anonymous__31744] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__31741,Vvar__1___24Anonymous__31743) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__31742,Vvar__1___24Anonymous__31744)
=> ( Vvar__1___24Anonymous__31743 = Vvar__1___24Anonymous__31744
& Vvar__0__A__31741 = Vvar__0__A__31742 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__710,Vvar__0__A__711,Vvar__1___24Anonymous__712,Vvar__1___24Anonymous__713,Vvar__2___24Anonymous__714,Vvar__2___24Anonymous__715] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__710,Vvar__1___24Anonymous__712,Vvar__2___24Anonymous__714) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__711,Vvar__1___24Anonymous__713,Vvar__2___24Anonymous__715)
=> ( Vvar__2___24Anonymous__714 = Vvar__2___24Anonymous__715
& Vvar__1___24Anonymous__712 = Vvar__1___24Anonymous__713
& Vvar__0__A__710 = Vvar__0__A__711 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__40831,Vvar__0__A__40832,Vvar__1__B__40833,Vvar__1__B__40834,Vvar__2___24Anonymous__40835,Vvar__2___24Anonymous__40836] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__40831,Vvar__1__B__40833,Vvar__2___24Anonymous__40835) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__40832,Vvar__1__B__40834,Vvar__2___24Anonymous__40836)
=> ( Vvar__2___24Anonymous__40835 = Vvar__2___24Anonymous__40836
& Vvar__1__B__40833 = Vvar__1__B__40834
& Vvar__0__A__40831 = Vvar__0__A__40832 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__40837,Vvar__0__A__40838,Vvar__1__B__40839,Vvar__1__B__40840,Vvar__2___24Anonymous__40841,Vvar__2___24Anonymous__40842] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__40837,Vvar__1__B__40839,Vvar__2___24Anonymous__40841) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__40838,Vvar__1__B__40840,Vvar__2___24Anonymous__40842)
=> ( Vvar__2___24Anonymous__40841 = Vvar__2___24Anonymous__40842
& Vvar__1__B__40839 = Vvar__1__B__40840
& Vvar__0__A__40837 = Vvar__0__A__40838 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__708,Vvar__0__A__709] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__708) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__709)
=> Vvar__0__A__708 = Vvar__0__A__709 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__31762,Vvar__0__A__31763,Vvar__1__B__31764,Vvar__1__B__31765,Vvar__2___24Anonymous__31766,Vvar__2___24Anonymous__31767,Vvar__3___24Anonymous__31768,Vvar__3___24Anonymous__31769] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31762,Vvar__1__B__31764,Vvar__2___24Anonymous__31766,Vvar__3___24Anonymous__31768) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31763,Vvar__1__B__31765,Vvar__2___24Anonymous__31767,Vvar__3___24Anonymous__31769)
=> ( Vvar__3___24Anonymous__31768 = Vvar__3___24Anonymous__31769
& Vvar__2___24Anonymous__31766 = Vvar__2___24Anonymous__31767
& Vvar__1__B__31764 = Vvar__1__B__31765
& Vvar__0__A__31762 = Vvar__0__A__31763 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__81151,Vvar__0___24Anonymous__81152] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__81151) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__81152)
=> Vvar__0___24Anonymous__81151 = Vvar__0___24Anonymous__81152 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__81153,Vvar__0___24Anonymous__81154] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__81153) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__81154)
=> Vvar__0___24Anonymous__81153 = Vvar__0___24Anonymous__81154 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__81155,Vvar__0___24Anonymous__81156] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__81155) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__81156)
=> Vvar__0___24Anonymous__81155 = Vvar__0___24Anonymous__81156 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__81157,Vvar__0___24Anonymous__81158] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__81157) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__81158)
=> Vvar__0___24Anonymous__81157 = Vvar__0___24Anonymous__81158 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__81159,Vvar__0___24Anonymous__81160] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__81159) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__81160)
=> Vvar__0___24Anonymous__81159 = Vvar__0___24Anonymous__81160 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__81161,Vvar__0___24Anonymous__81162] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__81161) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__81162)
=> Vvar__0___24Anonymous__81161 = Vvar__0___24Anonymous__81162 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__81163,Vvar__0___24Anonymous__81164] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__81163) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__81164)
=> Vvar__0___24Anonymous__81163 = Vvar__0___24Anonymous__81164 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__81165,Vvar__0___24Anonymous__81166] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__81165) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__81166)
=> Vvar__0___24Anonymous__81165 = Vvar__0___24Anonymous__81166 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__81167,Vvar__0___24Anonymous__81168] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__81167) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__81168)
=> Vvar__0___24Anonymous__81167 = Vvar__0___24Anonymous__81168 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__81169,Vvar__0___24Anonymous__81170] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__81169) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__81170)
=> Vvar__0___24Anonymous__81169 = Vvar__0___24Anonymous__81170 ) ).
fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
! [Vvar__0__i__152034,Vvar__0__i__152035,Vvar__1__f__152036,Vvar__1__f__152037] :
( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__152034,Vvar__1__f__152036) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__152035,Vvar__1__f__152037)
=> ( Vvar__1__f__152036 = Vvar__1__f__152037
& Vvar__0__i__152034 = Vvar__0__i__152035 ) ) ).
fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__152038,Vvar__0__i__152039,Vvar__1__f__152040,Vvar__1__f__152041,Vvar__2__e__152042,Vvar__2__e__152043] :
( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__152038,Vvar__1__f__152040,Vvar__2__e__152042) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__152039,Vvar__1__f__152041,Vvar__2__e__152043)
=> ( Vvar__2__e__152042 = Vvar__2__e__152043
& Vvar__1__f__152040 = Vvar__1__f__152041
& Vvar__0__i__152038 = Vvar__0__i__152039 ) ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__83391,Vvar__0__d__83392] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__83391) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__83392)
=> Vvar__0__d__83391 = Vvar__0__d__83392 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__83389,Vvar__0__d__83390] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__83389) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__83390)
=> Vvar__0__d__83389 = Vvar__0__d__83390 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__34645,Vvar__0__A__34646,Vvar__1__P__34647,Vvar__1__P__34648,Vvar__2__x__34649,Vvar__2__x__34650,Vvar__3___24Anonymous__34651,Vvar__3___24Anonymous__34652] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__34645,Vvar__1__P__34647,Vvar__2__x__34649) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__34646,Vvar__1__P__34648,Vvar__2__x__34650)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__34649 = Vvar__2__x__34650
& Vvar__1__P__34647 = Vvar__1__P__34648
& Vvar__0__A__34645 = Vvar__0__A__34646 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__153135,Vvar__0__A__153136,Vvar__1__P__153137,Vvar__1__P__153138,Vvar__2__Q__153139,Vvar__2__Q__153140,Vvar__3__x__153141,Vvar__3__x__153142,Vvar__4___24Anonymous__153143,Vvar__4___24Anonymous__153144,Vvar__5___24Anonymous__153145,Vvar__5___24Anonymous__153146] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__153135,Vvar__1__P__153137,Vvar__2__Q__153139,Vvar__3__x__153141) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__153136,Vvar__1__P__153138,Vvar__2__Q__153140,Vvar__3__x__153142)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__153141 = Vvar__3__x__153142
& Vvar__2__Q__153139 = Vvar__2__Q__153140
& Vvar__1__P__153137 = Vvar__1__P__153138
& Vvar__0__A__153135 = Vvar__0__A__153136 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__66973,Vvar__0__A__66974,Vvar__1__P__66975,Vvar__1__P__66976,Vvar__2__x__66977,Vvar__2__x__66978,Vvar__3___24Anonymous__66979,Vvar__3___24Anonymous__66980] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__66973,Vvar__1__P__66975,Vvar__2__x__66977,Vvar__3___24Anonymous__66979) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__66974,Vvar__1__P__66976,Vvar__2__x__66978,Vvar__3___24Anonymous__66980)
=> ( Vvar__3___24Anonymous__66979 = Vvar__3___24Anonymous__66980
& Vvar__2__x__66977 = Vvar__2__x__66978
& Vvar__1__P__66975 = Vvar__1__P__66976
& Vvar__0__A__66973 = Vvar__0__A__66974 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__153191,Vvar__0__A__153192,Vvar__1__P__153193,Vvar__1__P__153194,Vvar__2__Q__153195,Vvar__2__Q__153196,Vvar__3__x__153197,Vvar__3__x__153198,Vvar__4___24Anonymous__153199,Vvar__4___24Anonymous__153200,Vvar__5___24Anonymous__153201,Vvar__5___24Anonymous__153202] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__153191,Vvar__1__P__153193,Vvar__2__Q__153195,Vvar__3__x__153197,Vvar__4___24Anonymous__153199,Vvar__5___24Anonymous__153201) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__153192,Vvar__1__P__153194,Vvar__2__Q__153196,Vvar__3__x__153198,Vvar__4___24Anonymous__153200,Vvar__5___24Anonymous__153202)
=> ( Vvar__5___24Anonymous__153201 = Vvar__5___24Anonymous__153202
& Vvar__4___24Anonymous__153199 = Vvar__4___24Anonymous__153200
& Vvar__3__x__153197 = Vvar__3__x__153198
& Vvar__2__Q__153195 = Vvar__2__Q__153196
& Vvar__1__P__153193 = Vvar__1__P__153194
& Vvar__0__A__153191 = Vvar__0__A__153192 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__321,Vvar__0__A__322,Vvar__1__B__323,Vvar__1__B__324,Vvar__2___24Anonymous__325,Vvar__2___24Anonymous__326] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__321,Vvar__1__B__323,Vvar__2___24Anonymous__325) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__322,Vvar__1__B__324,Vvar__2___24Anonymous__326)
=> ( Vvar__2___24Anonymous__325 = Vvar__2___24Anonymous__326
& Vvar__1__B__323 = Vvar__1__B__324
& Vvar__0__A__321 = Vvar__0__A__322 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__327,Vvar__0__A__328,Vvar__1__B__329,Vvar__1__B__330,Vvar__2___24Anonymous__331,Vvar__2___24Anonymous__332] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__327,Vvar__1__B__329) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__328,Vvar__1__B__330)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__329 = Vvar__1__B__330
& Vvar__0__A__327 = Vvar__0__A__328 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__188,Vvar__0__A__189,Vvar__1__B__190,Vvar__1__B__191,Vvar__2___24Anonymous__192,Vvar__2___24Anonymous__193] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__188,Vvar__1__B__190) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__189,Vvar__1__B__191)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__190 = Vvar__1__B__191
& Vvar__0__A__188 = Vvar__0__A__189 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__194,Vvar__0__A__195,Vvar__1__B__196,Vvar__1__B__197,Vvar__2___24Anonymous__198,Vvar__2___24Anonymous__199] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__194,Vvar__1__B__196) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__195,Vvar__1__B__197)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__196 = Vvar__1__B__197
& Vvar__0__A__194 = Vvar__0__A__195 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__31535,Vvar__0___24Anonymous__31536] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31535) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31536)
=> Vvar__0___24Anonymous__31535 = Vvar__0___24Anonymous__31536 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__21,Vvar__0___24Anonymous__22] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__21) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22)
=> Vvar__0___24Anonymous__21 = Vvar__0___24Anonymous__22 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__19,Vvar__0___24Anonymous__20] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20)
=> Vvar__0___24Anonymous__19 = Vvar__0___24Anonymous__20 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__8,Vvar__0___24Anonymous__9] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__8) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__9)
=> Vvar__0___24Anonymous__8 = Vvar__0___24Anonymous__9 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__10,Vvar__0___24Anonymous__11] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__10) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11)
=> Vvar__0___24Anonymous__10 = Vvar__0___24Anonymous__11 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__153556,Vvar__0__p__153557,Vvar__1___24Anonymous__153558,Vvar__1___24Anonymous__153559] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__153556,Vvar__1___24Anonymous__153558) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__153557,Vvar__1___24Anonymous__153559)
=> ( Vvar__1___24Anonymous__153558 = Vvar__1___24Anonymous__153559
& Vvar__0__p__153556 = Vvar__0__p__153557 ) ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__54866,Vvar__0___24Anonymous__54867] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__54866) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__54867)
=> Vvar__0___24Anonymous__54866 = Vvar__0___24Anonymous__54867 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__32624,Vvar__0__Qnum__32625,Vvar__1__Qden__32626,Vvar__1__Qden__32627] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__32624,Vvar__1__Qden__32626) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__32625,Vvar__1__Qden__32627)
=> ( Vvar__1__Qden__32626 = Vvar__1__Qden__32627
& Vvar__0__Qnum__32624 = Vvar__0__Qnum__32625 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__152685,Vvar__0__neg__152686,Vvar__1__cond__neg__152687,Vvar__1__cond__neg__152688] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__152685) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__152686)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__152685 = Vvar__0__neg__152686 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__152664,Vvar__0__nonneg__152665,Vvar__1__cond__nonneg__152666,Vvar__1__cond__nonneg__152667] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__152664) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__152665)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__152664 = Vvar__0__nonneg__152665 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__152678,Vvar__0__nonpos__152679,Vvar__1__cond__nonpos__152680,Vvar__1__cond__nonpos__152681] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__152678) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__152679)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__152678 = Vvar__0__nonpos__152679 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__152692,Vvar__0__nonzero__152693,Vvar__1__cond__nonzero__152694,Vvar__1__cond__nonzero__152695] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__152692) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__152693)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__152692 = Vvar__0__nonzero__152693 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__152671,Vvar__0__pos__152672,Vvar__1__cond__pos__152673,Vvar__1__cond__pos__152674] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__152671) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__152672)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__152671 = Vvar__0__pos__152672 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__82537,Vvar__0__x__82538,Vvar__1__n__82539,Vvar__1__n__82540,Vvar__2___24Anonymous__82541,Vvar__2___24Anonymous__82542] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__82537,Vvar__1__n__82539) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__82538,Vvar__1__n__82540)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__82539 = Vvar__1__n__82540
& Vvar__0__x__82537 = Vvar__0__x__82538 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__82527,Vvar__0__x__82528,Vvar__1___24Anonymous__82529,Vvar__1___24Anonymous__82530] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__82527) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__82528)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__82527 = Vvar__0__x__82528 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__82531,Vvar__0__x__82532,Vvar__1__n__82533,Vvar__1__n__82534,Vvar__2___24Anonymous__82535,Vvar__2___24Anonymous__82536] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__82531,Vvar__1__n__82533) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__82532,Vvar__1__n__82534)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__82533 = Vvar__1__n__82534
& Vvar__0__x__82531 = Vvar__0__x__82532 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__1239,Vvar__0___24Anonymous__1240,Vvar__1___24Anonymous__1241,Vvar__1___24Anonymous__1242,Vvar__2___24Anonymous__1243,Vvar__2___24Anonymous__1244,Vvar__3___24Anonymous__1245,Vvar__3___24Anonymous__1246,Vvar__4___24Anonymous__1247,Vvar__4___24Anonymous__1248,Vvar__5___24Anonymous__1249,Vvar__5___24Anonymous__1250,Vvar__6___24Anonymous__1251,Vvar__6___24Anonymous__1252,Vvar__7___24Anonymous__1253,Vvar__7___24Anonymous__1254] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__1239,Vvar__1___24Anonymous__1241,Vvar__2___24Anonymous__1243,Vvar__3___24Anonymous__1245,Vvar__4___24Anonymous__1247,Vvar__5___24Anonymous__1249,Vvar__6___24Anonymous__1251,Vvar__7___24Anonymous__1253) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__1240,Vvar__1___24Anonymous__1242,Vvar__2___24Anonymous__1244,Vvar__3___24Anonymous__1246,Vvar__4___24Anonymous__1248,Vvar__5___24Anonymous__1250,Vvar__6___24Anonymous__1252,Vvar__7___24Anonymous__1254)
=> ( Vvar__7___24Anonymous__1253 = Vvar__7___24Anonymous__1254
& Vvar__6___24Anonymous__1251 = Vvar__6___24Anonymous__1252
& Vvar__5___24Anonymous__1249 = Vvar__5___24Anonymous__1250
& Vvar__4___24Anonymous__1247 = Vvar__4___24Anonymous__1248
& Vvar__3___24Anonymous__1245 = Vvar__3___24Anonymous__1246
& Vvar__2___24Anonymous__1243 = Vvar__2___24Anonymous__1244
& Vvar__1___24Anonymous__1241 = Vvar__1___24Anonymous__1242
& Vvar__0___24Anonymous__1239 = Vvar__0___24Anonymous__1240 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__34722,Vvar__0___24Anonymous__34723,Vvar__1___24Anonymous__34724,Vvar__1___24Anonymous__34725] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__34722,Vvar__1___24Anonymous__34724) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__34723,Vvar__1___24Anonymous__34725)
=> ( Vvar__1___24Anonymous__34724 = Vvar__1___24Anonymous__34725
& Vvar__0___24Anonymous__34722 = Vvar__0___24Anonymous__34723 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__82425,Vvar__0__X__82426,Vvar__1__lt__82427,Vvar__1__lt__82428,Vvar__2__eq__82429,Vvar__2__eq__82430,Vvar__3__x__82431,Vvar__3__x__82432,Vvar__4__y__82433,Vvar__4__y__82434,Vvar__5___24Anonymous__82435,Vvar__5___24Anonymous__82436] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__82425,Vvar__1__lt__82427,Vvar__2__eq__82429,Vvar__3__x__82431,Vvar__4__y__82433) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__82426,Vvar__1__lt__82428,Vvar__2__eq__82430,Vvar__3__x__82432,Vvar__4__y__82434)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__82433 = Vvar__4__y__82434
& Vvar__3__x__82431 = Vvar__3__x__82432
& Vvar__2__eq__82429 = Vvar__2__eq__82430
& Vvar__1__lt__82427 = Vvar__1__lt__82428
& Vvar__0__X__82425 = Vvar__0__X__82426 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__82437,Vvar__0__X__82438,Vvar__1__lt__82439,Vvar__1__lt__82440,Vvar__2__eq__82441,Vvar__2__eq__82442,Vvar__3__x__82443,Vvar__3__x__82444,Vvar__4__y__82445,Vvar__4__y__82446,Vvar__5___24Anonymous__82447,Vvar__5___24Anonymous__82448] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__82437,Vvar__1__lt__82439,Vvar__2__eq__82441,Vvar__3__x__82443,Vvar__4__y__82445) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__82438,Vvar__1__lt__82440,Vvar__2__eq__82442,Vvar__3__x__82444,Vvar__4__y__82446)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__82445 = Vvar__4__y__82446
& Vvar__3__x__82443 = Vvar__3__x__82444
& Vvar__2__eq__82441 = Vvar__2__eq__82442
& Vvar__1__lt__82439 = Vvar__1__lt__82440
& Vvar__0__X__82437 = Vvar__0__X__82438 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__82413,Vvar__0__X__82414,Vvar__1__lt__82415,Vvar__1__lt__82416,Vvar__2__eq__82417,Vvar__2__eq__82418,Vvar__3__x__82419,Vvar__3__x__82420,Vvar__4__y__82421,Vvar__4__y__82422,Vvar__5___24Anonymous__82423,Vvar__5___24Anonymous__82424] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__82413,Vvar__1__lt__82415,Vvar__2__eq__82417,Vvar__3__x__82419,Vvar__4__y__82421) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__82414,Vvar__1__lt__82416,Vvar__2__eq__82418,Vvar__3__x__82420,Vvar__4__y__82422)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__82421 = Vvar__4__y__82422
& Vvar__3__x__82419 = Vvar__3__x__82420
& Vvar__2__eq__82417 = Vvar__2__eq__82418
& Vvar__1__lt__82415 = Vvar__1__lt__82416
& Vvar__0__X__82413 = Vvar__0__X__82414 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__31797,Vvar__0__n__31798] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__31797) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__31798)
=> Vvar__0__n__31797 = Vvar__0__n__31798 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__31799,Vvar__0__n__31800,Vvar__1___24Anonymous__31801,Vvar__1___24Anonymous__31802] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__31799,Vvar__1___24Anonymous__31801) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__31800,Vvar__1___24Anonymous__31802)
=> ( Vvar__1___24Anonymous__31801 = Vvar__1___24Anonymous__31802
& Vvar__0__n__31799 = Vvar__0__n__31800 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__35516,Vvar__0__A__35517,Vvar__1__h__35518,Vvar__1__h__35519,Vvar__2__n__35520,Vvar__2__n__35521,Vvar__3___24Anonymous__35522,Vvar__3___24Anonymous__35523] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__35516,Vvar__1__h__35518,Vvar__2__n__35520,Vvar__3___24Anonymous__35522) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__35517,Vvar__1__h__35519,Vvar__2__n__35521,Vvar__3___24Anonymous__35523)
=> ( Vvar__3___24Anonymous__35522 = Vvar__3___24Anonymous__35523
& Vvar__2__n__35520 = Vvar__2__n__35521
& Vvar__1__h__35518 = Vvar__1__h__35519
& Vvar__0__A__35516 = Vvar__0__A__35517 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__35514,Vvar__0__A__35515] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__35514) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__35515)
=> Vvar__0__A__35514 = Vvar__0__A__35515 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__153351,Vvar__0__a__153352,Vvar__1__b__153353,Vvar__1__b__153354,Vvar__2__u__153355,Vvar__2__u__153356,Vvar__3__v__153357,Vvar__3__v__153358,Vvar__4__d__153359,Vvar__4__d__153360,Vvar__5___24Anonymous__153361,Vvar__5___24Anonymous__153362,Vvar__6___24Anonymous__153363,Vvar__6___24Anonymous__153364] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__153351,Vvar__1__b__153353,Vvar__2__u__153355,Vvar__3__v__153357,Vvar__4__d__153359) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__153352,Vvar__1__b__153354,Vvar__2__u__153356,Vvar__3__v__153358,Vvar__4__d__153360)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__153359 = Vvar__4__d__153360
& Vvar__3__v__153357 = Vvar__3__v__153358
& Vvar__2__u__153355 = Vvar__2__u__153356
& Vvar__1__b__153353 = Vvar__1__b__153354
& Vvar__0__a__153351 = Vvar__0__a__153352 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__153412,Vvar__0__x__153413,Vvar__1__p__153414,Vvar__1__p__153415,Vvar__2__q__153416,Vvar__2__q__153417,Vvar__3__r__153418,Vvar__3__r__153419,Vvar__4___24Anonymous__153420,Vvar__4___24Anonymous__153421,Vvar__5___24Anonymous__153422,Vvar__5___24Anonymous__153423,Vvar__6___24Anonymous__153424,Vvar__6___24Anonymous__153425] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__153412,Vvar__1__p__153414,Vvar__2__q__153416,Vvar__3__r__153418) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__153413,Vvar__1__p__153415,Vvar__2__q__153417,Vvar__3__r__153419)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__153418 = Vvar__3__r__153419
& Vvar__2__q__153416 = Vvar__2__q__153417
& Vvar__1__p__153414 = Vvar__1__p__153415
& Vvar__0__x__153412 = Vvar__0__x__153413 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__41022,Vvar__0__C__41023,Vvar__1___24Anonymous__41024,Vvar__1___24Anonymous__41025] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__41022,Vvar__1___24Anonymous__41024) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__41023,Vvar__1___24Anonymous__41025)
=> ( Vvar__1___24Anonymous__41024 = Vvar__1___24Anonymous__41025
& Vvar__0__C__41022 = Vvar__0__C__41023 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__41026,Vvar__0__C__41027,Vvar__1___24Anonymous__41028,Vvar__1___24Anonymous__41029,Vvar__2___24Anonymous__41030,Vvar__2___24Anonymous__41031] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__41026,Vvar__1___24Anonymous__41028,Vvar__2___24Anonymous__41030) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__41027,Vvar__1___24Anonymous__41029,Vvar__2___24Anonymous__41031)
=> ( Vvar__2___24Anonymous__41030 = Vvar__2___24Anonymous__41031
& Vvar__1___24Anonymous__41028 = Vvar__1___24Anonymous__41029
& Vvar__0__C__41026 = Vvar__0__C__41027 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__41018,Vvar__0__C__41019,Vvar__1___24Anonymous__41020,Vvar__1___24Anonymous__41021] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__41018,Vvar__1___24Anonymous__41020) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__41019,Vvar__1___24Anonymous__41021)
=> ( Vvar__1___24Anonymous__41020 = Vvar__1___24Anonymous__41021
& Vvar__0__C__41018 = Vvar__0__C__41019 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__41038,Vvar__0__C__41039,Vvar__1___24Anonymous__41040,Vvar__1___24Anonymous__41041,Vvar__2___24Anonymous__41042,Vvar__2___24Anonymous__41043] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__41038,Vvar__1___24Anonymous__41040,Vvar__2___24Anonymous__41042) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__41039,Vvar__1___24Anonymous__41041,Vvar__2___24Anonymous__41043)
=> ( Vvar__2___24Anonymous__41042 = Vvar__2___24Anonymous__41043
& Vvar__1___24Anonymous__41040 = Vvar__1___24Anonymous__41041
& Vvar__0__C__41038 = Vvar__0__C__41039 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__41044,Vvar__0__C__41045,Vvar__1___24Anonymous__41046,Vvar__1___24Anonymous__41047] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__41044,Vvar__1___24Anonymous__41046) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__41045,Vvar__1___24Anonymous__41047)
=> ( Vvar__1___24Anonymous__41046 = Vvar__1___24Anonymous__41047
& Vvar__0__C__41044 = Vvar__0__C__41045 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__41048,Vvar__0__C__41049,Vvar__1___24Anonymous__41050,Vvar__1___24Anonymous__41051,Vvar__2___24Anonymous__41052,Vvar__2___24Anonymous__41053] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__41048,Vvar__1___24Anonymous__41050,Vvar__2___24Anonymous__41052) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__41049,Vvar__1___24Anonymous__41051,Vvar__2___24Anonymous__41053)
=> ( Vvar__2___24Anonymous__41052 = Vvar__2___24Anonymous__41053
& Vvar__1___24Anonymous__41050 = Vvar__1___24Anonymous__41051
& Vvar__0__C__41048 = Vvar__0__C__41049 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__41032,Vvar__0__C__41033,Vvar__1___24Anonymous__41034,Vvar__1___24Anonymous__41035,Vvar__2___24Anonymous__41036,Vvar__2___24Anonymous__41037] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__41032,Vvar__1___24Anonymous__41034,Vvar__2___24Anonymous__41036) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__41033,Vvar__1___24Anonymous__41035,Vvar__2___24Anonymous__41037)
=> ( Vvar__2___24Anonymous__41036 = Vvar__2___24Anonymous__41037
& Vvar__1___24Anonymous__41034 = Vvar__1___24Anonymous__41035
& Vvar__0__C__41032 = Vvar__0__C__41033 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__41093,Vvar__0__C__41094,Vvar__1___24Anonymous__41095,Vvar__1___24Anonymous__41096,Vvar__2___24Anonymous__41097,Vvar__2___24Anonymous__41098,Vvar__3___24Anonymous__41099,Vvar__3___24Anonymous__41100] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__41093,Vvar__1___24Anonymous__41095,Vvar__2___24Anonymous__41097,Vvar__3___24Anonymous__41099) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__41094,Vvar__1___24Anonymous__41096,Vvar__2___24Anonymous__41098,Vvar__3___24Anonymous__41100)
=> ( Vvar__3___24Anonymous__41099 = Vvar__3___24Anonymous__41100
& Vvar__2___24Anonymous__41097 = Vvar__2___24Anonymous__41098
& Vvar__1___24Anonymous__41095 = Vvar__1___24Anonymous__41096
& Vvar__0__C__41093 = Vvar__0__C__41094 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__41083,Vvar__0__C__41084,Vvar__1___24Anonymous__41085,Vvar__1___24Anonymous__41086] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__41083,Vvar__1___24Anonymous__41085) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__41084,Vvar__1___24Anonymous__41086)
=> ( Vvar__1___24Anonymous__41085 = Vvar__1___24Anonymous__41086
& Vvar__0__C__41083 = Vvar__0__C__41084 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__41087,Vvar__0__C__41088,Vvar__1___24Anonymous__41089,Vvar__1___24Anonymous__41090,Vvar__2___24Anonymous__41091,Vvar__2___24Anonymous__41092] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__41087,Vvar__1___24Anonymous__41089,Vvar__2___24Anonymous__41091) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__41088,Vvar__1___24Anonymous__41090,Vvar__2___24Anonymous__41092)
=> ( Vvar__2___24Anonymous__41091 = Vvar__2___24Anonymous__41092
& Vvar__1___24Anonymous__41089 = Vvar__1___24Anonymous__41090
& Vvar__0__C__41087 = Vvar__0__C__41088 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__41121,Vvar__0___24Anonymous__41122,Vvar__1___24Anonymous__41123,Vvar__1___24Anonymous__41124] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__41121,Vvar__1___24Anonymous__41123) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__41122,Vvar__1___24Anonymous__41124)
=> ( Vvar__1___24Anonymous__41123 = Vvar__1___24Anonymous__41124
& Vvar__0___24Anonymous__41121 = Vvar__0___24Anonymous__41122 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__41117,Vvar__0___24Anonymous__41118,Vvar__1___24Anonymous__41119,Vvar__1___24Anonymous__41120] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__41117,Vvar__1___24Anonymous__41119) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__41118,Vvar__1___24Anonymous__41120)
=> ( Vvar__1___24Anonymous__41119 = Vvar__1___24Anonymous__41120
& Vvar__0___24Anonymous__41117 = Vvar__0___24Anonymous__41118 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__44756,Vvar__0__r__44757] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__44756) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__44757)
=> Vvar__0__r__44756 = Vvar__0__r__44757 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__44744,Vvar__0__r1__44745,Vvar__1__r2__44746,Vvar__1__r2__44747] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__44744,Vvar__1__r2__44746) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__44745,Vvar__1__r2__44747)
=> ( Vvar__1__r2__44746 = Vvar__1__r2__44747
& Vvar__0__r1__44744 = Vvar__0__r1__44745 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__44748,Vvar__0__r1__44749,Vvar__1__r2__44750,Vvar__1__r2__44751] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__44748,Vvar__1__r2__44750) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__44749,Vvar__1__r2__44751)
=> ( Vvar__1__r2__44750 = Vvar__1__r2__44751
& Vvar__0__r1__44748 = Vvar__0__r1__44749 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__44758,Vvar__0__r__44759] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__44758) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__44759)
=> Vvar__0__r__44758 = Vvar__0__r__44759 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__44740,Vvar__0__r1__44741,Vvar__1__r2__44742,Vvar__1__r2__44743] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__44740,Vvar__1__r2__44742) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__44741,Vvar__1__r2__44743)
=> ( Vvar__1__r2__44742 = Vvar__1__r2__44743
& Vvar__0__r1__44740 = Vvar__0__r1__44741 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__44752,Vvar__0__r1__44753,Vvar__1__z__44754,Vvar__1__z__44755] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__44752,Vvar__1__z__44754) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__44753,Vvar__1__z__44755)
=> ( Vvar__1__z__44754 = Vvar__1__z__44755
& Vvar__0__r1__44752 = Vvar__0__r1__44753 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__44736,Vvar__0__r__44737] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__44736) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__44737)
=> Vvar__0__r__44736 = Vvar__0__r__44737 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__44738,Vvar__0__r__44739] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__44738) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__44739)
=> Vvar__0__r__44738 = Vvar__0__r__44739 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__50274,Vvar__0__T__50275,Vvar__1__Flhs__50276,Vvar__1__Flhs__50277,Vvar__2__Fop__50278,Vvar__2__Fop__50279,Vvar__3__Frhs__50280,Vvar__3__Frhs__50281] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__50274,Vvar__1__Flhs__50276,Vvar__2__Fop__50278,Vvar__3__Frhs__50280) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__50275,Vvar__1__Flhs__50277,Vvar__2__Fop__50279,Vvar__3__Frhs__50281)
=> ( Vvar__3__Frhs__50280 = Vvar__3__Frhs__50281
& Vvar__2__Fop__50278 = Vvar__2__Fop__50279
& Vvar__1__Flhs__50276 = Vvar__1__Flhs__50277
& Vvar__0__T__50274 = Vvar__0__T__50275 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__50249,Vvar__0__C__50250,Vvar__1___24Anonymous__50251,Vvar__1___24Anonymous__50252,Vvar__2___24Anonymous__50253,Vvar__2___24Anonymous__50254] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__50249,Vvar__1___24Anonymous__50251,Vvar__2___24Anonymous__50253) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__50250,Vvar__1___24Anonymous__50252,Vvar__2___24Anonymous__50254)
=> ( Vvar__2___24Anonymous__50253 = Vvar__2___24Anonymous__50254
& Vvar__1___24Anonymous__50251 = Vvar__1___24Anonymous__50252
& Vvar__0__C__50249 = Vvar__0__C__50250 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__50255,Vvar__0__C__50256,Vvar__1___24Anonymous__50257,Vvar__1___24Anonymous__50258] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__50255,Vvar__1___24Anonymous__50257) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__50256,Vvar__1___24Anonymous__50258)
=> ( Vvar__1___24Anonymous__50257 = Vvar__1___24Anonymous__50258
& Vvar__0__C__50255 = Vvar__0__C__50256 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__50229,Vvar__0__C__50230,Vvar__1___24Anonymous__50231,Vvar__1___24Anonymous__50232] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__50229,Vvar__1___24Anonymous__50231) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__50230,Vvar__1___24Anonymous__50232)
=> ( Vvar__1___24Anonymous__50231 = Vvar__1___24Anonymous__50232
& Vvar__0__C__50229 = Vvar__0__C__50230 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__50237,Vvar__0__C__50238,Vvar__1___24Anonymous__50239,Vvar__1___24Anonymous__50240,Vvar__2___24Anonymous__50241,Vvar__2___24Anonymous__50242] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__50237,Vvar__1___24Anonymous__50239,Vvar__2___24Anonymous__50241) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__50238,Vvar__1___24Anonymous__50240,Vvar__2___24Anonymous__50242)
=> ( Vvar__2___24Anonymous__50241 = Vvar__2___24Anonymous__50242
& Vvar__1___24Anonymous__50239 = Vvar__1___24Anonymous__50240
& Vvar__0__C__50237 = Vvar__0__C__50238 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__50243,Vvar__0__C__50244,Vvar__1___24Anonymous__50245,Vvar__1___24Anonymous__50246,Vvar__2___24Anonymous__50247,Vvar__2___24Anonymous__50248] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__50243,Vvar__1___24Anonymous__50245,Vvar__2___24Anonymous__50247) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__50244,Vvar__1___24Anonymous__50246,Vvar__2___24Anonymous__50248)
=> ( Vvar__2___24Anonymous__50247 = Vvar__2___24Anonymous__50248
& Vvar__1___24Anonymous__50245 = Vvar__1___24Anonymous__50246
& Vvar__0__C__50243 = Vvar__0__C__50244 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__50233,Vvar__0__C__50234,Vvar__1___24Anonymous__50235,Vvar__1___24Anonymous__50236] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__50233,Vvar__1___24Anonymous__50235) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__50234,Vvar__1___24Anonymous__50236)
=> ( Vvar__1___24Anonymous__50235 = Vvar__1___24Anonymous__50236
& Vvar__0__C__50233 = Vvar__0__C__50234 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__50259,Vvar__0__C__50260] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__50259) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__50260)
=> Vvar__0__C__50259 = Vvar__0__C__50260 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__54582,Vvar__0__TA__54583,Vvar__1__TX__54584,Vvar__1__TX__54585,Vvar__2__AA__54586,Vvar__2__AA__54587,Vvar__3__AF__54588,Vvar__3__AF__54589,Vvar__4___24Anonymous__54590,Vvar__4___24Anonymous__54591,Vvar__5___24Anonymous__54592,Vvar__5___24Anonymous__54593] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__54582,Vvar__1__TX__54584,Vvar__2__AA__54586,Vvar__3__AF__54588,Vvar__4___24Anonymous__54590,Vvar__5___24Anonymous__54592) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__54583,Vvar__1__TX__54585,Vvar__2__AA__54587,Vvar__3__AF__54589,Vvar__4___24Anonymous__54591,Vvar__5___24Anonymous__54593)
=> ( Vvar__5___24Anonymous__54592 = Vvar__5___24Anonymous__54593
& Vvar__4___24Anonymous__54590 = Vvar__4___24Anonymous__54591
& Vvar__3__AF__54588 = Vvar__3__AF__54589
& Vvar__2__AA__54586 = Vvar__2__AA__54587
& Vvar__1__TX__54584 = Vvar__1__TX__54585
& Vvar__0__TA__54582 = Vvar__0__TA__54583 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__54594,Vvar__0__TA__54595,Vvar__1__TX__54596,Vvar__1__TX__54597,Vvar__2__AA__54598,Vvar__2__AA__54599,Vvar__3__AF__54600,Vvar__3__AF__54601,Vvar__4___24Anonymous__54602,Vvar__4___24Anonymous__54603,Vvar__5___24Anonymous__54604,Vvar__5___24Anonymous__54605] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__54594,Vvar__1__TX__54596,Vvar__2__AA__54598,Vvar__3__AF__54600,Vvar__4___24Anonymous__54602,Vvar__5___24Anonymous__54604) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__54595,Vvar__1__TX__54597,Vvar__2__AA__54599,Vvar__3__AF__54601,Vvar__4___24Anonymous__54603,Vvar__5___24Anonymous__54605)
=> ( Vvar__5___24Anonymous__54604 = Vvar__5___24Anonymous__54605
& Vvar__4___24Anonymous__54602 = Vvar__4___24Anonymous__54603
& Vvar__3__AF__54600 = Vvar__3__AF__54601
& Vvar__2__AA__54598 = Vvar__2__AA__54599
& Vvar__1__TX__54596 = Vvar__1__TX__54597
& Vvar__0__TA__54594 = Vvar__0__TA__54595 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__54606,Vvar__0__TA__54607,Vvar__1__TX__54608,Vvar__1__TX__54609,Vvar__2__AA__54610,Vvar__2__AA__54611,Vvar__3__AF__54612,Vvar__3__AF__54613,Vvar__4___24Anonymous__54614,Vvar__4___24Anonymous__54615,Vvar__5___24Anonymous__54616,Vvar__5___24Anonymous__54617] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__54606,Vvar__1__TX__54608,Vvar__2__AA__54610,Vvar__3__AF__54612,Vvar__4___24Anonymous__54614,Vvar__5___24Anonymous__54616) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__54607,Vvar__1__TX__54609,Vvar__2__AA__54611,Vvar__3__AF__54613,Vvar__4___24Anonymous__54615,Vvar__5___24Anonymous__54617)
=> ( Vvar__5___24Anonymous__54616 = Vvar__5___24Anonymous__54617
& Vvar__4___24Anonymous__54614 = Vvar__4___24Anonymous__54615
& Vvar__3__AF__54612 = Vvar__3__AF__54613
& Vvar__2__AA__54610 = Vvar__2__AA__54611
& Vvar__1__TX__54608 = Vvar__1__TX__54609
& Vvar__0__TA__54606 = Vvar__0__TA__54607 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__54564,Vvar__0__TA__54565,Vvar__1__TX__54566,Vvar__1__TX__54567,Vvar__2__AA__54568,Vvar__2__AA__54569,Vvar__3__AF__54570,Vvar__3__AF__54571] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__54564,Vvar__1__TX__54566,Vvar__2__AA__54568,Vvar__3__AF__54570) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__54565,Vvar__1__TX__54567,Vvar__2__AA__54569,Vvar__3__AF__54571)
=> ( Vvar__3__AF__54570 = Vvar__3__AF__54571
& Vvar__2__AA__54568 = Vvar__2__AA__54569
& Vvar__1__TX__54566 = Vvar__1__TX__54567
& Vvar__0__TA__54564 = Vvar__0__TA__54565 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__54628,Vvar__0__TA__54629,Vvar__1__TX__54630,Vvar__1__TX__54631,Vvar__2__AA__54632,Vvar__2__AA__54633,Vvar__3__AF__54634,Vvar__3__AF__54635,Vvar__4___24Anonymous__54636,Vvar__4___24Anonymous__54637,Vvar__5___24Anonymous__54638,Vvar__5___24Anonymous__54639,Vvar__6___24Anonymous__54640,Vvar__6___24Anonymous__54641] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__54628,Vvar__1__TX__54630,Vvar__2__AA__54632,Vvar__3__AF__54634,Vvar__4___24Anonymous__54636,Vvar__5___24Anonymous__54638,Vvar__6___24Anonymous__54640) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__54629,Vvar__1__TX__54631,Vvar__2__AA__54633,Vvar__3__AF__54635,Vvar__4___24Anonymous__54637,Vvar__5___24Anonymous__54639,Vvar__6___24Anonymous__54641)
=> ( Vvar__6___24Anonymous__54640 = Vvar__6___24Anonymous__54641
& Vvar__5___24Anonymous__54638 = Vvar__5___24Anonymous__54639
& Vvar__4___24Anonymous__54636 = Vvar__4___24Anonymous__54637
& Vvar__3__AF__54634 = Vvar__3__AF__54635
& Vvar__2__AA__54632 = Vvar__2__AA__54633
& Vvar__1__TX__54630 = Vvar__1__TX__54631
& Vvar__0__TA__54628 = Vvar__0__TA__54629 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__54618,Vvar__0__TA__54619,Vvar__1__TX__54620,Vvar__1__TX__54621,Vvar__2__AA__54622,Vvar__2__AA__54623,Vvar__3__AF__54624,Vvar__3__AF__54625,Vvar__4___24Anonymous__54626,Vvar__4___24Anonymous__54627] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__54618,Vvar__1__TX__54620,Vvar__2__AA__54622,Vvar__3__AF__54624,Vvar__4___24Anonymous__54626) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__54619,Vvar__1__TX__54621,Vvar__2__AA__54623,Vvar__3__AF__54625,Vvar__4___24Anonymous__54627)
=> ( Vvar__4___24Anonymous__54626 = Vvar__4___24Anonymous__54627
& Vvar__3__AF__54624 = Vvar__3__AF__54625
& Vvar__2__AA__54622 = Vvar__2__AA__54623
& Vvar__1__TX__54620 = Vvar__1__TX__54621
& Vvar__0__TA__54618 = Vvar__0__TA__54619 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__54556,Vvar__0__TA__54557,Vvar__1__TX__54558,Vvar__1__TX__54559,Vvar__2__AA__54560,Vvar__2__AA__54561,Vvar__3__AF__54562,Vvar__3__AF__54563] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__54556,Vvar__1__TX__54558,Vvar__2__AA__54560,Vvar__3__AF__54562) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__54557,Vvar__1__TX__54559,Vvar__2__AA__54561,Vvar__3__AF__54563)
=> ( Vvar__3__AF__54562 = Vvar__3__AF__54563
& Vvar__2__AA__54560 = Vvar__2__AA__54561
& Vvar__1__TX__54558 = Vvar__1__TX__54559
& Vvar__0__TA__54556 = Vvar__0__TA__54557 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__54572,Vvar__0__TA__54573,Vvar__1__TX__54574,Vvar__1__TX__54575,Vvar__2__AA__54576,Vvar__2__AA__54577,Vvar__3__AF__54578,Vvar__3__AF__54579,Vvar__4___24Anonymous__54580,Vvar__4___24Anonymous__54581] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__54572,Vvar__1__TX__54574,Vvar__2__AA__54576,Vvar__3__AF__54578,Vvar__4___24Anonymous__54580) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__54573,Vvar__1__TX__54575,Vvar__2__AA__54577,Vvar__3__AF__54579,Vvar__4___24Anonymous__54581)
=> ( Vvar__4___24Anonymous__54580 = Vvar__4___24Anonymous__54581
& Vvar__3__AF__54578 = Vvar__3__AF__54579
& Vvar__2__AA__54576 = Vvar__2__AA__54577
& Vvar__1__TX__54574 = Vvar__1__TX__54575
& Vvar__0__TA__54572 = Vvar__0__TA__54573 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__153243,Vvar__0__A__153244,Vvar__1___24Anonymous__153245,Vvar__1___24Anonymous__153246,Vvar__2___24Anonymous__153247,Vvar__2___24Anonymous__153248,Vvar__3___24Anonymous__153249,Vvar__3___24Anonymous__153250] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__153243,Vvar__1___24Anonymous__153245,Vvar__2___24Anonymous__153247,Vvar__3___24Anonymous__153249) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__153244,Vvar__1___24Anonymous__153246,Vvar__2___24Anonymous__153248,Vvar__3___24Anonymous__153250)
=> ( Vvar__3___24Anonymous__153249 = Vvar__3___24Anonymous__153250
& Vvar__2___24Anonymous__153247 = Vvar__2___24Anonymous__153248
& Vvar__1___24Anonymous__153245 = Vvar__1___24Anonymous__153246
& Vvar__0__A__153243 = Vvar__0__A__153244 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__153239,Vvar__0__A__153240,Vvar__1___24Anonymous__153241,Vvar__1___24Anonymous__153242] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__153239,Vvar__1___24Anonymous__153241) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__153240,Vvar__1___24Anonymous__153242)
=> ( Vvar__1___24Anonymous__153241 = Vvar__1___24Anonymous__153242
& Vvar__0__A__153239 = Vvar__0__A__153240 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__153237,Vvar__0__A__153238] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__153237) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__153238)
=> Vvar__0__A__153237 = Vvar__0__A__153238 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__54746,Vvar__0___24Anonymous__54747,Vvar__1___24Anonymous__54748,Vvar__1___24Anonymous__54749] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__54746,Vvar__1___24Anonymous__54748) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__54747,Vvar__1___24Anonymous__54749)
=> ( Vvar__1___24Anonymous__54748 = Vvar__1___24Anonymous__54749
& Vvar__0___24Anonymous__54746 = Vvar__0___24Anonymous__54747 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__54750,Vvar__0___24Anonymous__54751,Vvar__1___24Anonymous__54752,Vvar__1___24Anonymous__54753,Vvar__2___24Anonymous__54754,Vvar__2___24Anonymous__54755] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__54750,Vvar__1___24Anonymous__54752,Vvar__2___24Anonymous__54754) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__54751,Vvar__1___24Anonymous__54753,Vvar__2___24Anonymous__54755)
=> ( Vvar__2___24Anonymous__54754 = Vvar__2___24Anonymous__54755
& Vvar__1___24Anonymous__54752 = Vvar__1___24Anonymous__54753
& Vvar__0___24Anonymous__54750 = Vvar__0___24Anonymous__54751 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__54742,Vvar__0___24Anonymous__54743,Vvar__1___24Anonymous__54744,Vvar__1___24Anonymous__54745] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__54742,Vvar__1___24Anonymous__54744) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__54743,Vvar__1___24Anonymous__54745)
=> ( Vvar__1___24Anonymous__54744 = Vvar__1___24Anonymous__54745
& Vvar__0___24Anonymous__54742 = Vvar__0___24Anonymous__54743 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__42194,Vvar__0__C__42195] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__42194) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__42195)
=> Vvar__0__C__42194 = Vvar__0__C__42195 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__42192,Vvar__0__C__42193] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__42192) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__42193)
=> Vvar__0__C__42192 = Vvar__0__C__42193 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__42200,Vvar__0__C__42201,Vvar__1___24Anonymous__42202,Vvar__1___24Anonymous__42203] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__42200,Vvar__1___24Anonymous__42202) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__42201,Vvar__1___24Anonymous__42203)
=> ( Vvar__1___24Anonymous__42202 = Vvar__1___24Anonymous__42203
& Vvar__0__C__42200 = Vvar__0__C__42201 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__42204,Vvar__0__C__42205,Vvar__1___24Anonymous__42206,Vvar__1___24Anonymous__42207,Vvar__2___24Anonymous__42208,Vvar__2___24Anonymous__42209] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__42204,Vvar__1___24Anonymous__42206,Vvar__2___24Anonymous__42208) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__42205,Vvar__1___24Anonymous__42207,Vvar__2___24Anonymous__42209)
=> ( Vvar__2___24Anonymous__42208 = Vvar__2___24Anonymous__42209
& Vvar__1___24Anonymous__42206 = Vvar__1___24Anonymous__42207
& Vvar__0__C__42204 = Vvar__0__C__42205 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__42196,Vvar__0__C__42197,Vvar__1___24Anonymous__42198,Vvar__1___24Anonymous__42199] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__42196,Vvar__1___24Anonymous__42198) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__42197,Vvar__1___24Anonymous__42199)
=> ( Vvar__1___24Anonymous__42198 = Vvar__1___24Anonymous__42199
& Vvar__0__C__42196 = Vvar__0__C__42197 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__42230,Vvar__0__C__42231,Vvar__1___24Anonymous__42232,Vvar__1___24Anonymous__42233,Vvar__2___24Anonymous__42234,Vvar__2___24Anonymous__42235] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__42230,Vvar__1___24Anonymous__42232,Vvar__2___24Anonymous__42234) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__42231,Vvar__1___24Anonymous__42233,Vvar__2___24Anonymous__42235)
=> ( Vvar__2___24Anonymous__42234 = Vvar__2___24Anonymous__42235
& Vvar__1___24Anonymous__42232 = Vvar__1___24Anonymous__42233
& Vvar__0__C__42230 = Vvar__0__C__42231 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__42226,Vvar__0__C__42227,Vvar__1___24Anonymous__42228,Vvar__1___24Anonymous__42229] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__42226,Vvar__1___24Anonymous__42228) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__42227,Vvar__1___24Anonymous__42229)
=> ( Vvar__1___24Anonymous__42228 = Vvar__1___24Anonymous__42229
& Vvar__0__C__42226 = Vvar__0__C__42227 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__42216,Vvar__0__C__42217,Vvar__1___24Anonymous__42218,Vvar__1___24Anonymous__42219,Vvar__2___24Anonymous__42220,Vvar__2___24Anonymous__42221] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__42216,Vvar__1___24Anonymous__42218,Vvar__2___24Anonymous__42220) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__42217,Vvar__1___24Anonymous__42219,Vvar__2___24Anonymous__42221)
=> ( Vvar__2___24Anonymous__42220 = Vvar__2___24Anonymous__42221
& Vvar__1___24Anonymous__42218 = Vvar__1___24Anonymous__42219
& Vvar__0__C__42216 = Vvar__0__C__42217 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__42222,Vvar__0__C__42223,Vvar__1___24Anonymous__42224,Vvar__1___24Anonymous__42225] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__42222,Vvar__1___24Anonymous__42224) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__42223,Vvar__1___24Anonymous__42225)
=> ( Vvar__1___24Anonymous__42224 = Vvar__1___24Anonymous__42225
& Vvar__0__C__42222 = Vvar__0__C__42223 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__42236,Vvar__0__C__42237,Vvar__1___24Anonymous__42238,Vvar__1___24Anonymous__42239,Vvar__2___24Anonymous__42240,Vvar__2___24Anonymous__42241] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__42236,Vvar__1___24Anonymous__42238,Vvar__2___24Anonymous__42240) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__42237,Vvar__1___24Anonymous__42239,Vvar__2___24Anonymous__42241)
=> ( Vvar__2___24Anonymous__42240 = Vvar__2___24Anonymous__42241
& Vvar__1___24Anonymous__42238 = Vvar__1___24Anonymous__42239
& Vvar__0__C__42236 = Vvar__0__C__42237 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__42210,Vvar__0__C__42211,Vvar__1___24Anonymous__42212,Vvar__1___24Anonymous__42213,Vvar__2___24Anonymous__42214,Vvar__2___24Anonymous__42215] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__42210,Vvar__1___24Anonymous__42212,Vvar__2___24Anonymous__42214) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__42211,Vvar__1___24Anonymous__42213,Vvar__2___24Anonymous__42215)
=> ( Vvar__2___24Anonymous__42214 = Vvar__2___24Anonymous__42215
& Vvar__1___24Anonymous__42212 = Vvar__1___24Anonymous__42213
& Vvar__0__C__42210 = Vvar__0__C__42211 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__42248,Vvar__0__C__42249,Vvar__1__num__42250,Vvar__1__num__42251,Vvar__2__denum__42252,Vvar__2__denum__42253,Vvar__3__condition__42254,Vvar__3__condition__42255] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__42248,Vvar__1__num__42250,Vvar__2__denum__42252,Vvar__3__condition__42254) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__42249,Vvar__1__num__42251,Vvar__2__denum__42253,Vvar__3__condition__42255)
=> ( Vvar__3__condition__42254 = Vvar__3__condition__42255
& Vvar__2__denum__42252 = Vvar__2__denum__42253
& Vvar__1__num__42250 = Vvar__1__num__42251
& Vvar__0__C__42248 = Vvar__0__C__42249 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__42537,Vvar__0__C__42538,Vvar__1__rsplit__left__42539,Vvar__1__rsplit__left__42540,Vvar__2__rsplit__common__42541,Vvar__2__rsplit__common__42542,Vvar__3__rsplit__right__42543,Vvar__3__rsplit__right__42544] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__42537,Vvar__1__rsplit__left__42539,Vvar__2__rsplit__common__42541,Vvar__3__rsplit__right__42543) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__42538,Vvar__1__rsplit__left__42540,Vvar__2__rsplit__common__42542,Vvar__3__rsplit__right__42544)
=> ( Vvar__3__rsplit__right__42543 = Vvar__3__rsplit__right__42544
& Vvar__2__rsplit__common__42541 = Vvar__2__rsplit__common__42542
& Vvar__1__rsplit__left__42539 = Vvar__1__rsplit__left__42540
& Vvar__0__C__42537 = Vvar__0__C__42538 ) ) ).
fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
! [Vvar__0__hypo__type__152538,Vvar__0__hypo__type__152539,Vvar__1__hypo__proof__152540,Vvar__1__hypo__proof__152541] :
( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__152538,Vvar__1__hypo__proof__152540) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__152539,Vvar__1__hypo__proof__152541)
=> ( Vvar__1__hypo__proof__152540 = Vvar__1__hypo__proof__152541
& Vvar__0__hypo__type__152538 = Vvar__0__hypo__type__152539 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__33041,Vvar__0__C__33042] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__33041) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__33042)
=> Vvar__0__C__33041 = Vvar__0__C__33042 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__33039,Vvar__0__C__33040] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__33039) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__33040)
=> Vvar__0__C__33039 = Vvar__0__C__33040 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__33047,Vvar__0__C__33048,Vvar__1___24Anonymous__33049,Vvar__1___24Anonymous__33050] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__33047,Vvar__1___24Anonymous__33049) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__33048,Vvar__1___24Anonymous__33050)
=> ( Vvar__1___24Anonymous__33049 = Vvar__1___24Anonymous__33050
& Vvar__0__C__33047 = Vvar__0__C__33048 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__33051,Vvar__0__C__33052,Vvar__1___24Anonymous__33053,Vvar__1___24Anonymous__33054,Vvar__2___24Anonymous__33055,Vvar__2___24Anonymous__33056] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__33051,Vvar__1___24Anonymous__33053,Vvar__2___24Anonymous__33055) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__33052,Vvar__1___24Anonymous__33054,Vvar__2___24Anonymous__33056)
=> ( Vvar__2___24Anonymous__33055 = Vvar__2___24Anonymous__33056
& Vvar__1___24Anonymous__33053 = Vvar__1___24Anonymous__33054
& Vvar__0__C__33051 = Vvar__0__C__33052 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__33043,Vvar__0__C__33044,Vvar__1___24Anonymous__33045,Vvar__1___24Anonymous__33046] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__33043,Vvar__1___24Anonymous__33045) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__33044,Vvar__1___24Anonymous__33046)
=> ( Vvar__1___24Anonymous__33045 = Vvar__1___24Anonymous__33046
& Vvar__0__C__33043 = Vvar__0__C__33044 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__33063,Vvar__0__C__33064,Vvar__1___24Anonymous__33065,Vvar__1___24Anonymous__33066,Vvar__2___24Anonymous__33067,Vvar__2___24Anonymous__33068] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__33063,Vvar__1___24Anonymous__33065,Vvar__2___24Anonymous__33067) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__33064,Vvar__1___24Anonymous__33066,Vvar__2___24Anonymous__33068)
=> ( Vvar__2___24Anonymous__33067 = Vvar__2___24Anonymous__33068
& Vvar__1___24Anonymous__33065 = Vvar__1___24Anonymous__33066
& Vvar__0__C__33063 = Vvar__0__C__33064 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__33069,Vvar__0__C__33070,Vvar__1___24Anonymous__33071,Vvar__1___24Anonymous__33072] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__33069,Vvar__1___24Anonymous__33071) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__33070,Vvar__1___24Anonymous__33072)
=> ( Vvar__1___24Anonymous__33071 = Vvar__1___24Anonymous__33072
& Vvar__0__C__33069 = Vvar__0__C__33070 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__33073,Vvar__0__C__33074,Vvar__1___24Anonymous__33075,Vvar__1___24Anonymous__33076,Vvar__2___24Anonymous__33077,Vvar__2___24Anonymous__33078] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__33073,Vvar__1___24Anonymous__33075,Vvar__2___24Anonymous__33077) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__33074,Vvar__1___24Anonymous__33076,Vvar__2___24Anonymous__33078)
=> ( Vvar__2___24Anonymous__33077 = Vvar__2___24Anonymous__33078
& Vvar__1___24Anonymous__33075 = Vvar__1___24Anonymous__33076
& Vvar__0__C__33073 = Vvar__0__C__33074 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__33057,Vvar__0__C__33058,Vvar__1___24Anonymous__33059,Vvar__1___24Anonymous__33060,Vvar__2___24Anonymous__33061,Vvar__2___24Anonymous__33062] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__33057,Vvar__1___24Anonymous__33059,Vvar__2___24Anonymous__33061) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__33058,Vvar__1___24Anonymous__33060,Vvar__2___24Anonymous__33062)
=> ( Vvar__2___24Anonymous__33061 = Vvar__2___24Anonymous__33062
& Vvar__1___24Anonymous__33059 = Vvar__1___24Anonymous__33060
& Vvar__0__C__33057 = Vvar__0__C__33058 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__32696,Vvar__0__C__32697,Vvar__1___24Anonymous__32698,Vvar__1___24Anonymous__32699,Vvar__2___24Anonymous__32700,Vvar__2___24Anonymous__32701,Vvar__3___24Anonymous__32702,Vvar__3___24Anonymous__32703] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__32696,Vvar__1___24Anonymous__32698,Vvar__2___24Anonymous__32700,Vvar__3___24Anonymous__32702) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__32697,Vvar__1___24Anonymous__32699,Vvar__2___24Anonymous__32701,Vvar__3___24Anonymous__32703)
=> ( Vvar__3___24Anonymous__32702 = Vvar__3___24Anonymous__32703
& Vvar__2___24Anonymous__32700 = Vvar__2___24Anonymous__32701
& Vvar__1___24Anonymous__32698 = Vvar__1___24Anonymous__32699
& Vvar__0__C__32696 = Vvar__0__C__32697 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__32686,Vvar__0__C__32687,Vvar__1___24Anonymous__32688,Vvar__1___24Anonymous__32689] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__32686,Vvar__1___24Anonymous__32688) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__32687,Vvar__1___24Anonymous__32689)
=> ( Vvar__1___24Anonymous__32688 = Vvar__1___24Anonymous__32689
& Vvar__0__C__32686 = Vvar__0__C__32687 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__32690,Vvar__0__C__32691,Vvar__1___24Anonymous__32692,Vvar__1___24Anonymous__32693,Vvar__2___24Anonymous__32694,Vvar__2___24Anonymous__32695] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__32690,Vvar__1___24Anonymous__32692,Vvar__2___24Anonymous__32694) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__32691,Vvar__1___24Anonymous__32693,Vvar__2___24Anonymous__32695)
=> ( Vvar__2___24Anonymous__32694 = Vvar__2___24Anonymous__32695
& Vvar__1___24Anonymous__32692 = Vvar__1___24Anonymous__32693
& Vvar__0__C__32690 = Vvar__0__C__32691 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__32853,Vvar__0___24Anonymous__32854,Vvar__1___24Anonymous__32855,Vvar__1___24Anonymous__32856] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__32853,Vvar__1___24Anonymous__32855) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__32854,Vvar__1___24Anonymous__32856)
=> ( Vvar__1___24Anonymous__32855 = Vvar__1___24Anonymous__32856
& Vvar__0___24Anonymous__32853 = Vvar__0___24Anonymous__32854 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__32849,Vvar__0___24Anonymous__32850,Vvar__1___24Anonymous__32851,Vvar__1___24Anonymous__32852] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__32849,Vvar__1___24Anonymous__32851) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__32850,Vvar__1___24Anonymous__32852)
=> ( Vvar__1___24Anonymous__32851 = Vvar__1___24Anonymous__32852
& Vvar__0___24Anonymous__32849 = Vvar__0___24Anonymous__32850 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__34526,Vvar__0__R__34527,Vvar__1__req__34528,Vvar__1__req__34529,Vvar__2__reqb__34530,Vvar__2__reqb__34531,Vvar__3___24Anonymous__34532,Vvar__3___24Anonymous__34533] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34526,Vvar__1__req__34528,Vvar__2__reqb__34530) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34527,Vvar__1__req__34529,Vvar__2__reqb__34531)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__34530 = Vvar__2__reqb__34531
& Vvar__1__req__34528 = Vvar__1__req__34529
& Vvar__0__R__34526 = Vvar__0__R__34527 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__34534,Vvar__0__R__34535,Vvar__1__rO__34536,Vvar__1__rO__34537,Vvar__2__rI__34538,Vvar__2__rI__34539,Vvar__3__radd__34540,Vvar__3__radd__34541,Vvar__4__rmul__34542,Vvar__4__rmul__34543,Vvar__5__rsub__34544,Vvar__5__rsub__34545,Vvar__6__ropp__34546,Vvar__6__ropp__34547,Vvar__7__req__34548,Vvar__7__req__34549,Vvar__8__C__34550,Vvar__8__C__34551,Vvar__9__cO__34552,Vvar__9__cO__34553,Vvar__10__cI__34554,Vvar__10__cI__34555,Vvar__11__cadd__34556,Vvar__11__cadd__34557,Vvar__12__cmul__34558,Vvar__12__cmul__34559,Vvar__13__csub__34560,Vvar__13__csub__34561,Vvar__14__copp__34562,Vvar__14__copp__34563,Vvar__15__ceqb__34564,Vvar__15__ceqb__34565,Vvar__16__phi__34566,Vvar__16__phi__34567,Vvar__17___24Anonymous__34568,Vvar__17___24Anonymous__34569] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__34534,Vvar__1__rO__34536,Vvar__2__rI__34538,Vvar__3__radd__34540,Vvar__4__rmul__34542,Vvar__5__rsub__34544,Vvar__6__ropp__34546,Vvar__7__req__34548,Vvar__8__C__34550,Vvar__9__cO__34552,Vvar__10__cI__34554,Vvar__11__cadd__34556,Vvar__12__cmul__34558,Vvar__13__csub__34560,Vvar__14__copp__34562,Vvar__15__ceqb__34564,Vvar__16__phi__34566) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__34535,Vvar__1__rO__34537,Vvar__2__rI__34539,Vvar__3__radd__34541,Vvar__4__rmul__34543,Vvar__5__rsub__34545,Vvar__6__ropp__34547,Vvar__7__req__34549,Vvar__8__C__34551,Vvar__9__cO__34553,Vvar__10__cI__34555,Vvar__11__cadd__34557,Vvar__12__cmul__34559,Vvar__13__csub__34561,Vvar__14__copp__34563,Vvar__15__ceqb__34565,Vvar__16__phi__34567)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__34566 = Vvar__16__phi__34567
& Vvar__15__ceqb__34564 = Vvar__15__ceqb__34565
& Vvar__14__copp__34562 = Vvar__14__copp__34563
& Vvar__13__csub__34560 = Vvar__13__csub__34561
& Vvar__12__cmul__34558 = Vvar__12__cmul__34559
& Vvar__11__cadd__34556 = Vvar__11__cadd__34557
& Vvar__10__cI__34554 = Vvar__10__cI__34555
& Vvar__9__cO__34552 = Vvar__9__cO__34553
& Vvar__8__C__34550 = Vvar__8__C__34551
& Vvar__7__req__34548 = Vvar__7__req__34549
& Vvar__6__ropp__34546 = Vvar__6__ropp__34547
& Vvar__5__rsub__34544 = Vvar__5__rsub__34545
& Vvar__4__rmul__34542 = Vvar__4__rmul__34543
& Vvar__3__radd__34540 = Vvar__3__radd__34541
& Vvar__2__rI__34538 = Vvar__2__rI__34539
& Vvar__1__rO__34536 = Vvar__1__rO__34537
& Vvar__0__R__34534 = Vvar__0__R__34535 ) ) ).
fof('$_inj_Tait.Subst.mk_sub',axiom,
! [Vvar__0__support__336,Vvar__0__support__337,Vvar__1__shift__338,Vvar__1__shift__339] :
( cTait_2eSubst_2emk__sub___24a2(Vvar__0__support__336,Vvar__1__shift__338) = cTait_2eSubst_2emk__sub___24a2(Vvar__0__support__337,Vvar__1__shift__339)
=> ( Vvar__1__shift__338 = Vvar__1__shift__339
& Vvar__0__support__336 = Vvar__0__support__337 ) ) ).
fof('$_inj_Tait.Subst2.Joachimski.Dot',axiom,
! [Vvar__0___24Anonymous__1058,Vvar__0___24Anonymous__1059,Vvar__1___24Anonymous__1060,Vvar__1___24Anonymous__1061] :
( cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__1058,Vvar__1___24Anonymous__1060) = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__1059,Vvar__1___24Anonymous__1061)
=> ( Vvar__1___24Anonymous__1060 = Vvar__1___24Anonymous__1061
& Vvar__0___24Anonymous__1058 = Vvar__0___24Anonymous__1059 ) ) ).
fof('$_inj_Tait.Subst2.Joachimski.Up',axiom,
! [Vvar__0___24Anonymous__1062,Vvar__0___24Anonymous__1063] :
( cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__1062) = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__1063)
=> Vvar__0___24Anonymous__1062 = Vvar__0___24Anonymous__1063 ) ).
fof('$_inj_Tait.Term.Abs',axiom,
! [Vvar__0___24Anonymous__128,Vvar__0___24Anonymous__129,Vvar__1___24Anonymous__130,Vvar__1___24Anonymous__131] :
( cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__128,Vvar__1___24Anonymous__130) = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__129,Vvar__1___24Anonymous__131)
=> ( Vvar__1___24Anonymous__130 = Vvar__1___24Anonymous__131
& Vvar__0___24Anonymous__128 = Vvar__0___24Anonymous__129 ) ) ).
fof('$_inj_Tait.Term.App',axiom,
! [Vvar__0___24Anonymous__124,Vvar__0___24Anonymous__125,Vvar__1___24Anonymous__126,Vvar__1___24Anonymous__127] :
( cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__124,Vvar__1___24Anonymous__126) = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__125,Vvar__1___24Anonymous__127)
=> ( Vvar__1___24Anonymous__126 = Vvar__1___24Anonymous__127
& Vvar__0___24Anonymous__124 = Vvar__0___24Anonymous__125 ) ) ).
fof('$_inj_Tait.Term.Arrow',axiom,
! [Vvar__0___24Anonymous__211,Vvar__0___24Anonymous__212,Vvar__1___24Anonymous__213,Vvar__1___24Anonymous__214] :
( cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__211,Vvar__1___24Anonymous__213) = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__212,Vvar__1___24Anonymous__214)
=> ( Vvar__1___24Anonymous__213 = Vvar__1___24Anonymous__214
& Vvar__0___24Anonymous__211 = Vvar__0___24Anonymous__212 ) ) ).
fof('$_inj_Tait.Term.Var',axiom,
! [Vvar__0___24Anonymous__122,Vvar__0___24Anonymous__123] :
( cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__122) = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__123)
=> Vvar__0___24Anonymous__122 = Vvar__0___24Anonymous__123 ) ).
fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
! [Vvar__0__P__55098,Vvar__1__Q__55100,Vvar__2__init__55103,Vvar__3___24Anonymous__55104,Vvar__4___24Anonymous__55105] :
( c_24__type__55131___24t(Vvar__0__P__55098,Vvar__1__Q__55100,Vvar__2__init__55103,Vvar__3___24Anonymous__55104,Vvar__4___24Anonymous__55105,Vvar__0__P__55098)
=> ( c_24__type__55139___24t(Vvar__0__P__55098,Vvar__1__Q__55100,Vvar__2__init__55103,Vvar__3___24Anonymous__55104,Vvar__4___24Anonymous__55105,Vvar__1__Q__55100)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__55103)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__55104)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__55105)
=> ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__55098,Vvar__1__Q__55100,Vvar__2__init__55103,Vvar__3___24Anonymous__55104,Vvar__4___24Anonymous__55105)
=> ( ( Vvar__4___24Anonymous__55105 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__3___24Anonymous__55104 = Vvar__2__init__55103 )
| ? [Vvar__3__k__55119] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__55119)
& ? [Vvar__4__l__55120] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__55120)
& ? [Vvar__5__n__55121] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__55121)
& cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__55098,Vvar__1__Q__55100,Vvar__2__init__55103,Vvar__3__k__55119,Vvar__5__n__55121)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__55098,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__55119),Vvar__4__l__55120)
& p(happ(Vvar__1__Q__55100,Vvar__4__l__55120))
& Vvar__4___24Anonymous__55105 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__55121)
& Vvar__3___24Anonymous__55104 = Vvar__4__l__55120 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__55033,Vvar__1__k__55035,Vvar__2___24Anonymous__55036] :
( c_24__type__55050___24t(Vvar__0__P__55033,Vvar__1__k__55035,Vvar__2___24Anonymous__55036,Vvar__0__P__55033)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__55035)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__55036)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__55033,Vvar__1__k__55035,Vvar__2___24Anonymous__55036)
=> ( Vvar__2___24Anonymous__55036 = Vvar__1__k__55035
| ? [Vvar__2__l__55044] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__55044)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__55033,Vvar__1__k__55035,Vvar__2__l__55044)
& p(happ(Vvar__0__P__55033,Vvar__2__l__55044))
& Vvar__2___24Anonymous__55036 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__55044) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__55060,Vvar__1__k__55062,Vvar__2___24Anonymous__55063] :
( c_24__type__55079___24t(Vvar__0__Q__55060,Vvar__1__k__55062,Vvar__2___24Anonymous__55063,Vvar__0__Q__55060)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__55062)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__55063)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__55060,Vvar__1__k__55062,Vvar__2___24Anonymous__55063)
=> ( ? [Vvar__2__l__55068] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__55068)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__55060,Vvar__1__k__55062,Vvar__2__l__55068)
& Vvar__2___24Anonymous__55063 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__55068) )
| ? [Vvar__2__l__55073] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__55073)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__55062,Vvar__2__l__55073))
& p(happ(Vvar__0__Q__55060,Vvar__2__l__55073))
& Vvar__2___24Anonymous__55063 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__55073) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__63278] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63278)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__63278)
=> ( Vvar__0___24Anonymous__63278 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__63280] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__63280)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__63280)
& Vvar__0___24Anonymous__63278 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__63280) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__63282] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__63282)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__63282)
=> ? [Vvar__0__n__63284] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__63284)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__63284)
& Vvar__0___24Anonymous__63282 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__63284) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__31545,Vvar__1___24Anonymous__31546,VX31547] :
( cProp___24t(Vvar__0__P__31545)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__31546)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__31545,Vvar__1___24Anonymous__31546,VX31547)
=> ( ( p(Vvar__0__P__31545)
& Vvar__1___24Anonymous__31546 = cCoq_2eInit_2eDatatypes_2etrue
& VX31547 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31545) )
| ( ~ p(Vvar__0__P__31545)
& Vvar__1___24Anonymous__31546 = cCoq_2eInit_2eDatatypes_2efalse
& VX31547 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31545) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
! [Vvar__0___24Anonymous__153560,Vvar__1___24Anonymous__153561,Vvar__2___24Anonymous__153562] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__153560)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__153561)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__153562)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__153560,Vvar__1___24Anonymous__153561,Vvar__2___24Anonymous__153562)
=> ( ? [Vvar__0__x__153564] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__153564)
& Vvar__2___24Anonymous__153562 = Vvar__0__x__153564
& Vvar__1___24Anonymous__153561 = Vvar__0__x__153564
& Vvar__0___24Anonymous__153560 = Vvar__0__x__153564 )
| ? [Vvar__0__x__153565] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__153565)
& Vvar__2___24Anonymous__153562 = Vvar__0__x__153565
& Vvar__1___24Anonymous__153561 = cCoq_2eInit_2eDatatypes_2eEq
& Vvar__0___24Anonymous__153560 = Vvar__0__x__153565 )
| ? [Vvar__0__x__153566] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__153566)
& Vvar__2___24Anonymous__153562 = Vvar__0__x__153566
& Vvar__1___24Anonymous__153561 = Vvar__0__x__153566
& Vvar__0___24Anonymous__153560 = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0__x__153567] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__153567)
& Vvar__2___24Anonymous__153562 = Vvar__0__x__153567
& Vvar__1___24Anonymous__153561 = cCoq_2eInit_2eDatatypes_2eLt
& Vvar__0___24Anonymous__153560 = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0__x__153568] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__153568)
& Vvar__2___24Anonymous__153562 = Vvar__0__x__153568
& Vvar__1___24Anonymous__153561 = cCoq_2eInit_2eDatatypes_2eGt
& Vvar__0___24Anonymous__153560 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX37558] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX37558)
=> ( VX37558 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__37559] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__37559)
& ? [Vvar__1___24Anonymous__37560] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__37560)
& ? [Vvar__2___24Anonymous__37561] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__37561)
& VX37558 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37559,Vvar__1___24Anonymous__37560,Vvar__2___24Anonymous__37561) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX40813] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX40813)
=> ( VX40813 = cCoq_2eInit_2eByte_2ex00
| VX40813 = cCoq_2eInit_2eByte_2ex01
| VX40813 = cCoq_2eInit_2eByte_2ex02
| VX40813 = cCoq_2eInit_2eByte_2ex03
| VX40813 = cCoq_2eInit_2eByte_2ex04
| VX40813 = cCoq_2eInit_2eByte_2ex05
| VX40813 = cCoq_2eInit_2eByte_2ex06
| VX40813 = cCoq_2eInit_2eByte_2ex07
| VX40813 = cCoq_2eInit_2eByte_2ex08
| VX40813 = cCoq_2eInit_2eByte_2ex09
| VX40813 = cCoq_2eInit_2eByte_2ex0a
| VX40813 = cCoq_2eInit_2eByte_2ex0b
| VX40813 = cCoq_2eInit_2eByte_2ex0c
| VX40813 = cCoq_2eInit_2eByte_2ex0d
| VX40813 = cCoq_2eInit_2eByte_2ex0e
| VX40813 = cCoq_2eInit_2eByte_2ex0f
| VX40813 = cCoq_2eInit_2eByte_2ex10
| VX40813 = cCoq_2eInit_2eByte_2ex11
| VX40813 = cCoq_2eInit_2eByte_2ex12
| VX40813 = cCoq_2eInit_2eByte_2ex13
| VX40813 = cCoq_2eInit_2eByte_2ex14
| VX40813 = cCoq_2eInit_2eByte_2ex15
| VX40813 = cCoq_2eInit_2eByte_2ex16
| VX40813 = cCoq_2eInit_2eByte_2ex17
| VX40813 = cCoq_2eInit_2eByte_2ex18
| VX40813 = cCoq_2eInit_2eByte_2ex19
| VX40813 = cCoq_2eInit_2eByte_2ex1a
| VX40813 = cCoq_2eInit_2eByte_2ex1b
| VX40813 = cCoq_2eInit_2eByte_2ex1c
| VX40813 = cCoq_2eInit_2eByte_2ex1d
| VX40813 = cCoq_2eInit_2eByte_2ex1e
| VX40813 = cCoq_2eInit_2eByte_2ex1f
| VX40813 = cCoq_2eInit_2eByte_2ex20
| VX40813 = cCoq_2eInit_2eByte_2ex21
| VX40813 = cCoq_2eInit_2eByte_2ex22
| VX40813 = cCoq_2eInit_2eByte_2ex23
| VX40813 = cCoq_2eInit_2eByte_2ex24
| VX40813 = cCoq_2eInit_2eByte_2ex25
| VX40813 = cCoq_2eInit_2eByte_2ex26
| VX40813 = cCoq_2eInit_2eByte_2ex27
| VX40813 = cCoq_2eInit_2eByte_2ex28
| VX40813 = cCoq_2eInit_2eByte_2ex29
| VX40813 = cCoq_2eInit_2eByte_2ex2a
| VX40813 = cCoq_2eInit_2eByte_2ex2b
| VX40813 = cCoq_2eInit_2eByte_2ex2c
| VX40813 = cCoq_2eInit_2eByte_2ex2d
| VX40813 = cCoq_2eInit_2eByte_2ex2e
| VX40813 = cCoq_2eInit_2eByte_2ex2f
| VX40813 = cCoq_2eInit_2eByte_2ex30
| VX40813 = cCoq_2eInit_2eByte_2ex31
| VX40813 = cCoq_2eInit_2eByte_2ex32
| VX40813 = cCoq_2eInit_2eByte_2ex33
| VX40813 = cCoq_2eInit_2eByte_2ex34
| VX40813 = cCoq_2eInit_2eByte_2ex35
| VX40813 = cCoq_2eInit_2eByte_2ex36
| VX40813 = cCoq_2eInit_2eByte_2ex37
| VX40813 = cCoq_2eInit_2eByte_2ex38
| VX40813 = cCoq_2eInit_2eByte_2ex39
| VX40813 = cCoq_2eInit_2eByte_2ex3a
| VX40813 = cCoq_2eInit_2eByte_2ex3b
| VX40813 = cCoq_2eInit_2eByte_2ex3c
| VX40813 = cCoq_2eInit_2eByte_2ex3d
| VX40813 = cCoq_2eInit_2eByte_2ex3e
| VX40813 = cCoq_2eInit_2eByte_2ex3f
| VX40813 = cCoq_2eInit_2eByte_2ex40
| VX40813 = cCoq_2eInit_2eByte_2ex41
| VX40813 = cCoq_2eInit_2eByte_2ex42
| VX40813 = cCoq_2eInit_2eByte_2ex43
| VX40813 = cCoq_2eInit_2eByte_2ex44
| VX40813 = cCoq_2eInit_2eByte_2ex45
| VX40813 = cCoq_2eInit_2eByte_2ex46
| VX40813 = cCoq_2eInit_2eByte_2ex47
| VX40813 = cCoq_2eInit_2eByte_2ex48
| VX40813 = cCoq_2eInit_2eByte_2ex49
| VX40813 = cCoq_2eInit_2eByte_2ex4a
| VX40813 = cCoq_2eInit_2eByte_2ex4b
| VX40813 = cCoq_2eInit_2eByte_2ex4c
| VX40813 = cCoq_2eInit_2eByte_2ex4d
| VX40813 = cCoq_2eInit_2eByte_2ex4e
| VX40813 = cCoq_2eInit_2eByte_2ex4f
| VX40813 = cCoq_2eInit_2eByte_2ex50
| VX40813 = cCoq_2eInit_2eByte_2ex51
| VX40813 = cCoq_2eInit_2eByte_2ex52
| VX40813 = cCoq_2eInit_2eByte_2ex53
| VX40813 = cCoq_2eInit_2eByte_2ex54
| VX40813 = cCoq_2eInit_2eByte_2ex55
| VX40813 = cCoq_2eInit_2eByte_2ex56
| VX40813 = cCoq_2eInit_2eByte_2ex57
| VX40813 = cCoq_2eInit_2eByte_2ex58
| VX40813 = cCoq_2eInit_2eByte_2ex59
| VX40813 = cCoq_2eInit_2eByte_2ex5a
| VX40813 = cCoq_2eInit_2eByte_2ex5b
| VX40813 = cCoq_2eInit_2eByte_2ex5c
| VX40813 = cCoq_2eInit_2eByte_2ex5d
| VX40813 = cCoq_2eInit_2eByte_2ex5e
| VX40813 = cCoq_2eInit_2eByte_2ex5f
| VX40813 = cCoq_2eInit_2eByte_2ex60
| VX40813 = cCoq_2eInit_2eByte_2ex61
| VX40813 = cCoq_2eInit_2eByte_2ex62
| VX40813 = cCoq_2eInit_2eByte_2ex63
| VX40813 = cCoq_2eInit_2eByte_2ex64
| VX40813 = cCoq_2eInit_2eByte_2ex65
| VX40813 = cCoq_2eInit_2eByte_2ex66
| VX40813 = cCoq_2eInit_2eByte_2ex67
| VX40813 = cCoq_2eInit_2eByte_2ex68
| VX40813 = cCoq_2eInit_2eByte_2ex69
| VX40813 = cCoq_2eInit_2eByte_2ex6a
| VX40813 = cCoq_2eInit_2eByte_2ex6b
| VX40813 = cCoq_2eInit_2eByte_2ex6c
| VX40813 = cCoq_2eInit_2eByte_2ex6d
| VX40813 = cCoq_2eInit_2eByte_2ex6e
| VX40813 = cCoq_2eInit_2eByte_2ex6f
| VX40813 = cCoq_2eInit_2eByte_2ex70
| VX40813 = cCoq_2eInit_2eByte_2ex71
| VX40813 = cCoq_2eInit_2eByte_2ex72
| VX40813 = cCoq_2eInit_2eByte_2ex73
| VX40813 = cCoq_2eInit_2eByte_2ex74
| VX40813 = cCoq_2eInit_2eByte_2ex75
| VX40813 = cCoq_2eInit_2eByte_2ex76
| VX40813 = cCoq_2eInit_2eByte_2ex77
| VX40813 = cCoq_2eInit_2eByte_2ex78
| VX40813 = cCoq_2eInit_2eByte_2ex79
| VX40813 = cCoq_2eInit_2eByte_2ex7a
| VX40813 = cCoq_2eInit_2eByte_2ex7b
| VX40813 = cCoq_2eInit_2eByte_2ex7c
| VX40813 = cCoq_2eInit_2eByte_2ex7d
| VX40813 = cCoq_2eInit_2eByte_2ex7e
| VX40813 = cCoq_2eInit_2eByte_2ex7f
| VX40813 = cCoq_2eInit_2eByte_2ex80
| VX40813 = cCoq_2eInit_2eByte_2ex81
| VX40813 = cCoq_2eInit_2eByte_2ex82
| VX40813 = cCoq_2eInit_2eByte_2ex83
| VX40813 = cCoq_2eInit_2eByte_2ex84
| VX40813 = cCoq_2eInit_2eByte_2ex85
| VX40813 = cCoq_2eInit_2eByte_2ex86
| VX40813 = cCoq_2eInit_2eByte_2ex87
| VX40813 = cCoq_2eInit_2eByte_2ex88
| VX40813 = cCoq_2eInit_2eByte_2ex89
| VX40813 = cCoq_2eInit_2eByte_2ex8a
| VX40813 = cCoq_2eInit_2eByte_2ex8b
| VX40813 = cCoq_2eInit_2eByte_2ex8c
| VX40813 = cCoq_2eInit_2eByte_2ex8d
| VX40813 = cCoq_2eInit_2eByte_2ex8e
| VX40813 = cCoq_2eInit_2eByte_2ex8f
| VX40813 = cCoq_2eInit_2eByte_2ex90
| VX40813 = cCoq_2eInit_2eByte_2ex91
| VX40813 = cCoq_2eInit_2eByte_2ex92
| VX40813 = cCoq_2eInit_2eByte_2ex93
| VX40813 = cCoq_2eInit_2eByte_2ex94
| VX40813 = cCoq_2eInit_2eByte_2ex95
| VX40813 = cCoq_2eInit_2eByte_2ex96
| VX40813 = cCoq_2eInit_2eByte_2ex97
| VX40813 = cCoq_2eInit_2eByte_2ex98
| VX40813 = cCoq_2eInit_2eByte_2ex99
| VX40813 = cCoq_2eInit_2eByte_2ex9a
| VX40813 = cCoq_2eInit_2eByte_2ex9b
| VX40813 = cCoq_2eInit_2eByte_2ex9c
| VX40813 = cCoq_2eInit_2eByte_2ex9d
| VX40813 = cCoq_2eInit_2eByte_2ex9e
| VX40813 = cCoq_2eInit_2eByte_2ex9f
| VX40813 = cCoq_2eInit_2eByte_2exa0
| VX40813 = cCoq_2eInit_2eByte_2exa1
| VX40813 = cCoq_2eInit_2eByte_2exa2
| VX40813 = cCoq_2eInit_2eByte_2exa3
| VX40813 = cCoq_2eInit_2eByte_2exa4
| VX40813 = cCoq_2eInit_2eByte_2exa5
| VX40813 = cCoq_2eInit_2eByte_2exa6
| VX40813 = cCoq_2eInit_2eByte_2exa7
| VX40813 = cCoq_2eInit_2eByte_2exa8
| VX40813 = cCoq_2eInit_2eByte_2exa9
| VX40813 = cCoq_2eInit_2eByte_2exaa
| VX40813 = cCoq_2eInit_2eByte_2exab
| VX40813 = cCoq_2eInit_2eByte_2exac
| VX40813 = cCoq_2eInit_2eByte_2exad
| VX40813 = cCoq_2eInit_2eByte_2exae
| VX40813 = cCoq_2eInit_2eByte_2exaf
| VX40813 = cCoq_2eInit_2eByte_2exb0
| VX40813 = cCoq_2eInit_2eByte_2exb1
| VX40813 = cCoq_2eInit_2eByte_2exb2
| VX40813 = cCoq_2eInit_2eByte_2exb3
| VX40813 = cCoq_2eInit_2eByte_2exb4
| VX40813 = cCoq_2eInit_2eByte_2exb5
| VX40813 = cCoq_2eInit_2eByte_2exb6
| VX40813 = cCoq_2eInit_2eByte_2exb7
| VX40813 = cCoq_2eInit_2eByte_2exb8
| VX40813 = cCoq_2eInit_2eByte_2exb9
| VX40813 = cCoq_2eInit_2eByte_2exba
| VX40813 = cCoq_2eInit_2eByte_2exbb
| VX40813 = cCoq_2eInit_2eByte_2exbc
| VX40813 = cCoq_2eInit_2eByte_2exbd
| VX40813 = cCoq_2eInit_2eByte_2exbe
| VX40813 = cCoq_2eInit_2eByte_2exbf
| VX40813 = cCoq_2eInit_2eByte_2exc0
| VX40813 = cCoq_2eInit_2eByte_2exc1
| VX40813 = cCoq_2eInit_2eByte_2exc2
| VX40813 = cCoq_2eInit_2eByte_2exc3
| VX40813 = cCoq_2eInit_2eByte_2exc4
| VX40813 = cCoq_2eInit_2eByte_2exc5
| VX40813 = cCoq_2eInit_2eByte_2exc6
| VX40813 = cCoq_2eInit_2eByte_2exc7
| VX40813 = cCoq_2eInit_2eByte_2exc8
| VX40813 = cCoq_2eInit_2eByte_2exc9
| VX40813 = cCoq_2eInit_2eByte_2exca
| VX40813 = cCoq_2eInit_2eByte_2excb
| VX40813 = cCoq_2eInit_2eByte_2excc
| VX40813 = cCoq_2eInit_2eByte_2excd
| VX40813 = cCoq_2eInit_2eByte_2exce
| VX40813 = cCoq_2eInit_2eByte_2excf
| VX40813 = cCoq_2eInit_2eByte_2exd0
| VX40813 = cCoq_2eInit_2eByte_2exd1
| VX40813 = cCoq_2eInit_2eByte_2exd2
| VX40813 = cCoq_2eInit_2eByte_2exd3
| VX40813 = cCoq_2eInit_2eByte_2exd4
| VX40813 = cCoq_2eInit_2eByte_2exd5
| VX40813 = cCoq_2eInit_2eByte_2exd6
| VX40813 = cCoq_2eInit_2eByte_2exd7
| VX40813 = cCoq_2eInit_2eByte_2exd8
| VX40813 = cCoq_2eInit_2eByte_2exd9
| VX40813 = cCoq_2eInit_2eByte_2exda
| VX40813 = cCoq_2eInit_2eByte_2exdb
| VX40813 = cCoq_2eInit_2eByte_2exdc
| VX40813 = cCoq_2eInit_2eByte_2exdd
| VX40813 = cCoq_2eInit_2eByte_2exde
| VX40813 = cCoq_2eInit_2eByte_2exdf
| VX40813 = cCoq_2eInit_2eByte_2exe0
| VX40813 = cCoq_2eInit_2eByte_2exe1
| VX40813 = cCoq_2eInit_2eByte_2exe2
| VX40813 = cCoq_2eInit_2eByte_2exe3
| VX40813 = cCoq_2eInit_2eByte_2exe4
| VX40813 = cCoq_2eInit_2eByte_2exe5
| VX40813 = cCoq_2eInit_2eByte_2exe6
| VX40813 = cCoq_2eInit_2eByte_2exe7
| VX40813 = cCoq_2eInit_2eByte_2exe8
| VX40813 = cCoq_2eInit_2eByte_2exe9
| VX40813 = cCoq_2eInit_2eByte_2exea
| VX40813 = cCoq_2eInit_2eByte_2exeb
| VX40813 = cCoq_2eInit_2eByte_2exec
| VX40813 = cCoq_2eInit_2eByte_2exed
| VX40813 = cCoq_2eInit_2eByte_2exee
| VX40813 = cCoq_2eInit_2eByte_2exef
| VX40813 = cCoq_2eInit_2eByte_2exf0
| VX40813 = cCoq_2eInit_2eByte_2exf1
| VX40813 = cCoq_2eInit_2eByte_2exf2
| VX40813 = cCoq_2eInit_2eByte_2exf3
| VX40813 = cCoq_2eInit_2eByte_2exf4
| VX40813 = cCoq_2eInit_2eByte_2exf5
| VX40813 = cCoq_2eInit_2eByte_2exf6
| VX40813 = cCoq_2eInit_2eByte_2exf7
| VX40813 = cCoq_2eInit_2eByte_2exf8
| VX40813 = cCoq_2eInit_2eByte_2exf9
| VX40813 = cCoq_2eInit_2eByte_2exfa
| VX40813 = cCoq_2eInit_2eByte_2exfb
| VX40813 = cCoq_2eInit_2eByte_2exfc
| VX40813 = cCoq_2eInit_2eByte_2exfd
| VX40813 = cCoq_2eInit_2eByte_2exfe
| VX40813 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__37949,Vvar__1__Q__37950,Vvar__2___24Anonymous__37951] :
( cProp___24t(Vvar__0__P__37949)
=> ( cProp___24t(Vvar__1__Q__37950)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__37951)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__37949,Vvar__1__Q__37950,Vvar__2___24Anonymous__37951)
=> ( ( p(Vvar__0__P__37949)
& Vvar__2___24Anonymous__37951 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__37950)
& Vvar__2___24Anonymous__37951 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__31770,Vvar__1__Plt__31771,Vvar__2__Pgt__31772,Vvar__3___24Anonymous__31773] :
( cProp___24t(Vvar__0__Peq__31770)
=> ( cProp___24t(Vvar__1__Plt__31771)
=> ( cProp___24t(Vvar__2__Pgt__31772)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__31773)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__31770,Vvar__1__Plt__31771,Vvar__2__Pgt__31772,Vvar__3___24Anonymous__31773)
=> ( ( p(Vvar__0__Peq__31770)
& Vvar__3___24Anonymous__31773 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__31771)
& Vvar__3___24Anonymous__31773 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__31772)
& Vvar__3___24Anonymous__31773 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__82184,Vvar__1__Plt__82185,Vvar__2__Pgt__82186,Vvar__3___24Anonymous__82187,VX82188] :
( cProp___24t(Vvar__0__Peq__82184)
=> ( cProp___24t(Vvar__1__Plt__82185)
=> ( cProp___24t(Vvar__2__Pgt__82186)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__82187)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__82184,Vvar__1__Plt__82185,Vvar__2__Pgt__82186,Vvar__3___24Anonymous__82187,VX82188)
=> ( ( p(Vvar__0__Peq__82184)
& Vvar__3___24Anonymous__82187 = cCoq_2eInit_2eDatatypes_2eEq
& VX82188 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__82184,Vvar__1__Plt__82185,Vvar__2__Pgt__82186) )
| ( p(Vvar__1__Plt__82185)
& Vvar__3___24Anonymous__82187 = cCoq_2eInit_2eDatatypes_2eLt
& VX82188 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__82184,Vvar__1__Plt__82185,Vvar__2__Pgt__82186) )
| ( p(Vvar__2__Pgt__82186)
& Vvar__3___24Anonymous__82187 = cCoq_2eInit_2eDatatypes_2eGt
& VX82188 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__82184,Vvar__1__Plt__82185,Vvar__2__Pgt__82186) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX76] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX76)
=> ( VX76 = cCoq_2eInit_2eDatatypes_2etrue
| VX76 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX84] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX84)
=> ( VX84 = cCoq_2eInit_2eDatatypes_2eEq
| VX84 = cCoq_2eInit_2eDatatypes_2eLt
| VX84 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
! [Vvar__0___24Anonymous__152005] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__152005)
=> ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__152005)
=> Vvar__0___24Anonymous__152005 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
! [Vvar__0__A__152013,Vvar__1__a__152014,Vvar__2___24Anonymous__152015] :
( cType___24t(Vvar__0__A__152013)
=> ( t(Vvar__1__a__152014,Vvar__0__A__152013)
=> ( t(Vvar__2___24Anonymous__152015,Vvar__0__A__152013)
=> ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__152013,Vvar__1__a__152014,Vvar__2___24Anonymous__152015)
=> Vvar__2___24Anonymous__152015 = Vvar__1__a__152014 ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__696,VX697] :
( cType___24t(Vvar__0__A__696)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__696,VX697)
=> ( VX697 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__696)
| ? [Vvar__1___24Anonymous__700] :
( t(Vvar__1___24Anonymous__700,Vvar__0__A__696)
& ? [Vvar__2___24Anonymous__701] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__696,Vvar__2___24Anonymous__701)
& VX697 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__696,Vvar__1___24Anonymous__700,Vvar__2___24Anonymous__701) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX77] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX77)
=> ( VX77 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__78] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__78)
& VX77 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__78) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__31733,VX31734] :
( cType___24t(Vvar__0__A__31733)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__31733,VX31734)
=> ( ? [Vvar__1___24Anonymous__31736] :
( t(Vvar__1___24Anonymous__31736,Vvar__0__A__31733)
& VX31734 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__31733,Vvar__1___24Anonymous__31736) )
| VX31734 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__31733) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__31752,Vvar__1__B__31753,VX31754] :
( cType___24t(Vvar__0__A__31752)
=> ( cType___24t(Vvar__1__B__31753)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__31752,Vvar__1__B__31753,VX31754)
=> ? [Vvar__2___24Anonymous__31757] :
( t(Vvar__2___24Anonymous__31757,Vvar__0__A__31752)
& ? [Vvar__3___24Anonymous__31758] :
( t(Vvar__3___24Anonymous__31758,Vvar__1__B__31753)
& VX31754 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__31752,Vvar__1__B__31753,Vvar__2___24Anonymous__31757,Vvar__3___24Anonymous__31758) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__40815,Vvar__1__B__40816,VX40817] :
( cType___24t(Vvar__0__A__40815)
=> ( cType___24t(Vvar__1__B__40816)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__40815,Vvar__1__B__40816,VX40817)
=> ( ? [Vvar__2___24Anonymous__40820] :
( t(Vvar__2___24Anonymous__40820,Vvar__0__A__40815)
& VX40817 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__40815,Vvar__1__B__40816,Vvar__2___24Anonymous__40820) )
| ? [Vvar__2___24Anonymous__40823] :
( t(Vvar__2___24Anonymous__40823,Vvar__1__B__40816)
& VX40817 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__40815,Vvar__1__B__40816,Vvar__2___24Anonymous__40823) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX31731] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX31731)
=> VX31731 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
! [VX152023] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(VX152023)
=> ( ? [Vvar__0__i__152024] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__152024)
& ? [Vvar__1__f__152025] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__152025)
& VX152023 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__152024,Vvar__1__f__152025) ) )
| ? [Vvar__0__i__152026] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__152026)
& ? [Vvar__1__f__152027] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__152027)
& ? [Vvar__2__e__152028] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__152028)
& VX152023 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__152026,Vvar__1__f__152027,Vvar__2__e__152028) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX83384] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX83384)
=> ( ? [Vvar__0__d__83385] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__83385)
& VX83384 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__83385) )
| ? [Vvar__0__d__83386] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__83386)
& VX83384 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__83386) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX81040] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX81040)
=> ( VX81040 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__81041] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__81041)
& VX81040 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__81041) )
| ? [Vvar__0___24Anonymous__81042] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__81042)
& VX81040 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__81042) )
| ? [Vvar__0___24Anonymous__81043] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__81043)
& VX81040 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__81043) )
| ? [Vvar__0___24Anonymous__81044] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__81044)
& VX81040 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__81044) )
| ? [Vvar__0___24Anonymous__81045] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__81045)
& VX81040 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__81045) )
| ? [Vvar__0___24Anonymous__81046] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__81046)
& VX81040 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__81046) )
| ? [Vvar__0___24Anonymous__81047] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__81047)
& VX81040 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__81047) )
| ? [Vvar__0___24Anonymous__81048] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__81048)
& VX81040 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__81048) )
| ? [Vvar__0___24Anonymous__81049] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__81049)
& VX81040 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__81049) )
| ? [Vvar__0___24Anonymous__81050] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__81050)
& VX81040 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__81050) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__96,Vvar__1___24Anonymous__97] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__96)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__97)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__96,Vvar__1___24Anonymous__97))
=> ( Vvar__1___24Anonymous__97 = Vvar__0__n__96
| ? [Vvar__1__m__101] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__101)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__96,Vvar__1__m__101))
& Vvar__1___24Anonymous__97 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__101) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__34622,Vvar__1__P__34623,VX34626] :
( cType___24t(Vvar__0__A__34622)
=> ( c_24__type__34636___24t(Vvar__0__A__34622,Vvar__1__P__34623,Vvar__1__P__34623)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__34622,Vvar__1__P__34623,VX34626)
=> ? [Vvar__2__x__34631] :
( t(Vvar__2__x__34631,Vvar__0__A__34622)
& p(happ(Vvar__1__P__34623,Vvar__2__x__34631))
& VX34626 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__34622,Vvar__1__P__34623,Vvar__2__x__34631) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__153091,Vvar__1__P__153092,Vvar__2__Q__153095,VX153098] :
( cType___24t(Vvar__0__A__153091)
=> ( c_24__type__153115___24t(Vvar__0__A__153091,Vvar__1__P__153092,Vvar__2__Q__153095,Vvar__1__P__153092)
=> ( c_24__type__153123___24t(Vvar__0__A__153091,Vvar__1__P__153092,Vvar__2__Q__153095,Vvar__2__Q__153095)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__153091,Vvar__1__P__153092,Vvar__2__Q__153095,VX153098)
=> ? [Vvar__3__x__153106] :
( t(Vvar__3__x__153106,Vvar__0__A__153091)
& p(happ(Vvar__1__P__153092,Vvar__3__x__153106))
& p(happ(Vvar__2__Q__153095,Vvar__3__x__153106))
& VX153098 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__153091,Vvar__1__P__153092,Vvar__2__Q__153095,Vvar__3__x__153106) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__66950,Vvar__1__P__66951,VX66954] :
( cType___24t(Vvar__0__A__66950)
=> ( c_24__type__66964___24t(Vvar__0__A__66950,Vvar__1__P__66951,Vvar__1__P__66951)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__66950,Vvar__1__P__66951,VX66954)
=> ? [Vvar__2__x__66959] :
( t(Vvar__2__x__66959,Vvar__0__A__66950)
& ? [Vvar__3___24Anonymous__66960] :
( t(Vvar__3___24Anonymous__66960,happ(Vvar__1__P__66951,Vvar__2__x__66959))
& VX66954 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__66950,Vvar__1__P__66951,Vvar__2__x__66959,Vvar__3___24Anonymous__66960) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__153147,Vvar__1__P__153148,Vvar__2__Q__153151,VX153154] :
( cType___24t(Vvar__0__A__153147)
=> ( c_24__type__153171___24t(Vvar__0__A__153147,Vvar__1__P__153148,Vvar__2__Q__153151,Vvar__1__P__153148)
=> ( c_24__type__153179___24t(Vvar__0__A__153147,Vvar__1__P__153148,Vvar__2__Q__153151,Vvar__2__Q__153151)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__153147,Vvar__1__P__153148,Vvar__2__Q__153151,VX153154)
=> ? [Vvar__3__x__153162] :
( t(Vvar__3__x__153162,Vvar__0__A__153147)
& ? [Vvar__4___24Anonymous__153163] :
( t(Vvar__4___24Anonymous__153163,happ(Vvar__1__P__153148,Vvar__3__x__153162))
& ? [Vvar__5___24Anonymous__153164] :
( t(Vvar__5___24Anonymous__153164,happ(Vvar__2__Q__153151,Vvar__3__x__153162))
& VX153154 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__153147,Vvar__1__P__153148,Vvar__2__Q__153151,Vvar__3__x__153162,Vvar__4___24Anonymous__153163,Vvar__5___24Anonymous__153164) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__170,Vvar__1__B__171,VX172] :
( cProp___24t(Vvar__0__A__170)
=> ( cProp___24t(Vvar__1__B__171)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__170,Vvar__1__B__171,VX172)
=> ( ( p(Vvar__0__A__170)
& VX172 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__170,Vvar__1__B__171) )
| ( p(Vvar__1__B__171)
& VX172 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__170,Vvar__1__B__171) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__303,Vvar__1__B__304,VX305] :
( cType___24t(Vvar__0__A__303)
=> ( cProp___24t(Vvar__1__B__304)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__303,Vvar__1__B__304,VX305)
=> ( ? [Vvar__2___24Anonymous__308] :
( t(Vvar__2___24Anonymous__308,Vvar__0__A__303)
& VX305 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__303,Vvar__1__B__304,Vvar__2___24Anonymous__308) )
| ( p(Vvar__1__B__304)
& VX305 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__303,Vvar__1__B__304) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__81432,Vvar__1__R__81433,Vvar__2__x__81438] :
( cType___24t(Vvar__0__A__81432)
=> ( c_24__type__81467___24t(Vvar__0__A__81432,Vvar__1__R__81433,Vvar__2__x__81438,Vvar__1__R__81433)
=> ( t(Vvar__2__x__81438,Vvar__0__A__81432)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__81432,Vvar__1__R__81433,Vvar__2__x__81438)
=> ( ! [Vvar__var__var__var__var__3__y__81448__81450__81452__81454__81456] :
( t(Vvar__var__var__var__var__3__y__81448__81450__81452__81454__81456,Vvar__0__A__81432)
=> ( p(happ(happ(Vvar__1__R__81433,Vvar__var__var__var__var__3__y__81448__81450__81452__81454__81456),Vvar__2__x__81438))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__81432,Vvar__1__R__81433,Vvar__var__var__var__var__3__y__81448__81450__81452__81454__81456) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__73027,Vvar__1__a__73028,Vvar__2___24Anonymous__73029,Vvar__3___24Anonymous__73030] :
( cType___24t(Vvar__0__A__73027)
=> ( t(Vvar__1__a__73028,Vvar__0__A__73027)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73027,Vvar__2___24Anonymous__73029)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73027,Vvar__3___24Anonymous__73030)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__73027,Vvar__1__a__73028,Vvar__2___24Anonymous__73029,Vvar__3___24Anonymous__73030)
=> ( ? [Vvar__2__l__73034] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73027,Vvar__2__l__73034)
& Vvar__3___24Anonymous__73030 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73027,Vvar__1__a__73028,Vvar__2__l__73034)
& Vvar__2___24Anonymous__73029 = Vvar__2__l__73034 )
| ? [Vvar__2__x__73037] :
( t(Vvar__2__x__73037,Vvar__0__A__73027)
& ? [Vvar__3__l__73038] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73027,Vvar__3__l__73038)
& ? [Vvar__4__l_27__73039] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73027,Vvar__4__l_27__73039)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__73027,Vvar__1__a__73028,Vvar__3__l__73038,Vvar__4__l_27__73039)
& Vvar__3___24Anonymous__73030 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73027,Vvar__2__x__73037,Vvar__4__l_27__73039)
& Vvar__2___24Anonymous__73029 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73027,Vvar__2__x__73037,Vvar__3__l__73038) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__73130,Vvar__1__P__73131,Vvar__2___24Anonymous__73134] :
( cType___24t(Vvar__0__A__73130)
=> ( c_24__type__73154___24t(Vvar__0__A__73130,Vvar__1__P__73131,Vvar__2___24Anonymous__73134,Vvar__1__P__73131)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73130,Vvar__2___24Anonymous__73134)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__73130,Vvar__1__P__73131,Vvar__2___24Anonymous__73134)
=> ( ? [Vvar__2__x__73140] :
( t(Vvar__2__x__73140,Vvar__0__A__73130)
& ? [Vvar__3__l__73141] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73130,Vvar__3__l__73141)
& p(happ(Vvar__1__P__73131,Vvar__2__x__73140))
& Vvar__2___24Anonymous__73134 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73130,Vvar__2__x__73140,Vvar__3__l__73141) ) )
| ? [Vvar__2__x__73147] :
( t(Vvar__2__x__73147,Vvar__0__A__73130)
& ? [Vvar__3__l__73148] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73130,Vvar__3__l__73148)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__73130,Vvar__1__P__73131,Vvar__3__l__73148)
& Vvar__2___24Anonymous__73134 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73130,Vvar__2__x__73147,Vvar__3__l__73148) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__73289,Vvar__1__P__73290,Vvar__2___24Anonymous__73293] :
( cType___24t(Vvar__0__A__73289)
=> ( c_24__type__73311___24t(Vvar__0__A__73289,Vvar__1__P__73290,Vvar__2___24Anonymous__73293,Vvar__1__P__73290)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73289,Vvar__2___24Anonymous__73293)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__73289,Vvar__1__P__73290,Vvar__2___24Anonymous__73293)
=> ( Vvar__2___24Anonymous__73293 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__73289)
| ? [Vvar__2__x__73303] :
( t(Vvar__2__x__73303,Vvar__0__A__73289)
& ? [Vvar__3__l__73304] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73289,Vvar__3__l__73304)
& p(happ(Vvar__1__P__73290,Vvar__2__x__73303))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__73289,Vvar__1__P__73290,Vvar__3__l__73304)
& Vvar__2___24Anonymous__73293 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73289,Vvar__2__x__73303,Vvar__3__l__73304) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__73501,Vvar__1__B__73502,Vvar__2__R__73503,Vvar__3___24Anonymous__73508,Vvar__4___24Anonymous__73509] :
( cType___24t(Vvar__0__A__73501)
=> ( cType___24t(Vvar__1__B__73502)
=> ( c_24__type__73546___24t(Vvar__0__A__73501,Vvar__1__B__73502,Vvar__2__R__73503,Vvar__3___24Anonymous__73508,Vvar__4___24Anonymous__73509,Vvar__2__R__73503)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73501,Vvar__3___24Anonymous__73508)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__73502,Vvar__4___24Anonymous__73509)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__73501,Vvar__1__B__73502,Vvar__2__R__73503,Vvar__3___24Anonymous__73508,Vvar__4___24Anonymous__73509)
=> ( ( Vvar__4___24Anonymous__73509 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__73502)
& Vvar__3___24Anonymous__73508 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__73501) )
| ? [Vvar__3__x__73525] :
( t(Vvar__3__x__73525,Vvar__0__A__73501)
& ? [Vvar__4__y__73526] :
( t(Vvar__4__y__73526,Vvar__1__B__73502)
& ? [Vvar__5__l__73527] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73501,Vvar__5__l__73527)
& ? [Vvar__6__l_27__73528] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__73502,Vvar__6__l_27__73528)
& p(happ(happ(Vvar__2__R__73503,Vvar__3__x__73525),Vvar__4__y__73526))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__73501,Vvar__1__B__73502,Vvar__2__R__73503,Vvar__5__l__73527,Vvar__6__l_27__73528)
& Vvar__4___24Anonymous__73509 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__73502,Vvar__4__y__73526,Vvar__6__l_27__73528)
& Vvar__3___24Anonymous__73508 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73501,Vvar__3__x__73525,Vvar__5__l__73527) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__73614,Vvar__1__R__73615,Vvar__2___24Anonymous__73620] :
( cType___24t(Vvar__0__A__73614)
=> ( c_24__type__73647___24t(Vvar__0__A__73614,Vvar__1__R__73615,Vvar__2___24Anonymous__73620,Vvar__1__R__73615)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73614,Vvar__2___24Anonymous__73620)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__73614,Vvar__1__R__73615,Vvar__2___24Anonymous__73620)
=> ( Vvar__2___24Anonymous__73620 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__73614)
| ? [Vvar__2__a__73634] :
( t(Vvar__2__a__73634,Vvar__0__A__73614)
& ? [Vvar__3__l__73635] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73614,Vvar__3__l__73635)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__73614,happ(Vvar__1__R__73615,Vvar__2__a__73634),Vvar__3__l__73635)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__73614,Vvar__1__R__73615,Vvar__3__l__73635)
& Vvar__2___24Anonymous__73620 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73614,Vvar__2__a__73634,Vvar__3__l__73635) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__73061,Vvar__1___24Anonymous__73062] :
( cType___24t(Vvar__0__A__73061)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73061,Vvar__1___24Anonymous__73062)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__73061,Vvar__1___24Anonymous__73062)
=> ( Vvar__1___24Anonymous__73062 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__73061)
| ? [Vvar__1__x__73066] :
( t(Vvar__1__x__73066,Vvar__0__A__73061)
& ? [Vvar__2__l__73067] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73061,Vvar__2__l__73067)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__73061,Vvar__1__x__73066,Vvar__2__l__73067)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__73061,Vvar__2__l__73067)
& Vvar__1___24Anonymous__73062 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73061,Vvar__1__x__73066,Vvar__2__l__73067) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__53988,Vvar__1__eqA__53989,Vvar__2__x__53994,Vvar__3___24Anonymous__53995] :
( cType___24t(Vvar__0__A__53988)
=> ( c_24__type__54028___24t(Vvar__0__A__53988,Vvar__1__eqA__53989,Vvar__2__x__53994,Vvar__3___24Anonymous__53995,Vvar__1__eqA__53989)
=> ( t(Vvar__2__x__53994,Vvar__0__A__53988)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__53988,Vvar__3___24Anonymous__53995)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__53988,Vvar__1__eqA__53989,Vvar__2__x__53994,Vvar__3___24Anonymous__53995)
=> ( ? [Vvar__3__y__54004] :
( t(Vvar__3__y__54004,Vvar__0__A__53988)
& ? [Vvar__4__l__54005] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__53988,Vvar__4__l__54005)
& p(happ(happ(Vvar__1__eqA__53989,Vvar__2__x__53994),Vvar__3__y__54004))
& Vvar__3___24Anonymous__53995 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__53988,Vvar__3__y__54004,Vvar__4__l__54005) ) )
| ? [Vvar__3__y__54014] :
( t(Vvar__3__y__54014,Vvar__0__A__53988)
& ? [Vvar__4__l__54015] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__53988,Vvar__4__l__54015)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__53988,Vvar__1__eqA__53989,Vvar__2__x__53994,Vvar__4__l__54015)
& Vvar__3___24Anonymous__53995 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__53988,Vvar__3__y__54014,Vvar__4__l__54015) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__76533,Vvar__1__eqA__76534,Vvar__2___24Anonymous__76539] :
( cType___24t(Vvar__0__A__76533)
=> ( c_24__type__76566___24t(Vvar__0__A__76533,Vvar__1__eqA__76534,Vvar__2___24Anonymous__76539,Vvar__1__eqA__76534)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__76533,Vvar__2___24Anonymous__76539)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__76533,Vvar__1__eqA__76534,Vvar__2___24Anonymous__76539)
=> ( Vvar__2___24Anonymous__76539 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__76533)
| ? [Vvar__2__x__76553] :
( t(Vvar__2__x__76553,Vvar__0__A__76533)
& ? [Vvar__3__l__76554] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__76533,Vvar__3__l__76554)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__76533,Vvar__1__eqA__76534,Vvar__2__x__76553,Vvar__3__l__76554)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__76533,Vvar__1__eqA__76534,Vvar__3__l__76554)
& Vvar__2___24Anonymous__76539 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__76533,Vvar__2__x__76553,Vvar__3__l__76554) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__76618,Vvar__1__eqA__76619,Vvar__2___24Anonymous__76624,Vvar__3___24Anonymous__76625] :
( cType___24t(Vvar__0__A__76618)
=> ( c_24__type__76656___24t(Vvar__0__A__76618,Vvar__1__eqA__76619,Vvar__2___24Anonymous__76624,Vvar__3___24Anonymous__76625,Vvar__1__eqA__76619)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__76618,Vvar__2___24Anonymous__76624)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__76618,Vvar__3___24Anonymous__76625)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__76618,Vvar__1__eqA__76619,Vvar__2___24Anonymous__76624,Vvar__3___24Anonymous__76625)
=> ( ( Vvar__3___24Anonymous__76625 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__76618)
& Vvar__2___24Anonymous__76624 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__76618) )
| ? [Vvar__2__x__76639] :
( t(Vvar__2__x__76639,Vvar__0__A__76618)
& ? [Vvar__3__x_27__76640] :
( t(Vvar__3__x_27__76640,Vvar__0__A__76618)
& ? [Vvar__4__l__76641] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__76618,Vvar__4__l__76641)
& ? [Vvar__5__l_27__76642] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__76618,Vvar__5__l_27__76642)
& p(happ(happ(Vvar__1__eqA__76619,Vvar__2__x__76639),Vvar__3__x_27__76640))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__76618,Vvar__1__eqA__76619,Vvar__4__l__76641,Vvar__5__l_27__76642)
& Vvar__3___24Anonymous__76625 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__76618,Vvar__3__x_27__76640,Vvar__5__l_27__76642)
& Vvar__2___24Anonymous__76624 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__76618,Vvar__2__x__76639,Vvar__4__l__76641) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__152049,Vvar__1__P__152050,Vvar__2__p__152053,Vvar__3__x__152054,Vvar__4__q__152055,Vvar__5___24Anonymous__152056] :
( cType___24t(Vvar__0__U__152049)
=> ( c_24__type__152071___24t(Vvar__0__U__152049,Vvar__1__P__152050,Vvar__2__p__152053,Vvar__3__x__152054,Vvar__4__q__152055,Vvar__5___24Anonymous__152056,Vvar__1__P__152050)
=> ( t(Vvar__2__p__152053,Vvar__0__U__152049)
=> ( t(Vvar__3__x__152054,happ(Vvar__1__P__152050,Vvar__2__p__152053))
=> ( t(Vvar__4__q__152055,Vvar__0__U__152049)
=> ( t(Vvar__5___24Anonymous__152056,happ(Vvar__1__P__152050,Vvar__4__q__152055))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__152049,Vvar__1__P__152050,Vvar__2__p__152053,Vvar__3__x__152054,Vvar__4__q__152055,Vvar__5___24Anonymous__152056)
=> ( Vvar__5___24Anonymous__152056 = Vvar__3__x__152054
& Vvar__4__q__152055 = Vvar__2__p__152053 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__152073,Vvar__1__P__152074,Vvar__2__p__152077,Vvar__3__x__152078,Vvar__4__q__152079,Vvar__5__y__152080] :
( cType___24t(Vvar__0__U__152073)
=> ( c_24__type__152099___24t(Vvar__0__U__152073,Vvar__1__P__152074,Vvar__2__p__152077,Vvar__3__x__152078,Vvar__4__q__152079,Vvar__5__y__152080,Vvar__1__P__152074)
=> ( t(Vvar__2__p__152077,Vvar__0__U__152073)
=> ( t(Vvar__3__x__152078,happ(Vvar__1__P__152074,Vvar__2__p__152077))
=> ( t(Vvar__4__q__152079,Vvar__0__U__152073)
=> ( t(Vvar__5__y__152080,happ(Vvar__1__P__152074,Vvar__4__q__152079))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__152073,Vvar__1__P__152074,Vvar__2__p__152077,Vvar__3__x__152078,Vvar__4__q__152079,Vvar__5__y__152080)
=> ( Vvar__4__q__152079 = Vvar__2__p__152077
& Vvar__3__x__152078 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__152073,Vvar__4__q__152079,Vvar__1__P__152074,Vvar__5__y__152080,Vvar__2__p__152077)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX31532] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX31532)
=> ( VX31532 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__31533] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31533)
& VX31532 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31533) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX12] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX12)
=> ( VX12 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__13] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13)
& VX12 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13) )
| ? [Vvar__0___24Anonymous__14] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14)
& VX12 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__14) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1)
=> ( ? [Vvar__0___24Anonymous__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2)
& VX1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2) )
| ? [Vvar__0___24Anonymous__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3)
& VX1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3) )
| VX1 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [Vvar__0___24Anonymous__153495,VX153496] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__153495)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__153495,VX153496)
=> ( ( Vvar__0___24Anonymous__153495 = cCoq_2eNumbers_2eBinNums_2exH
& VX153496 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
| ? [Vvar__0__p__153497] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__153497)
& ? [Vvar__1___24Anonymous__153498] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__153497,Vvar__1___24Anonymous__153498)
& Vvar__0___24Anonymous__153495 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24153533___24a2(Vvar__0___24Anonymous__153495,Vvar__0__p__153497)
& VX153496 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__153497,Vvar__1___24Anonymous__153498) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX54862] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX54862)
=> ( VX54862 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__54863] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__54863)
& VX54862 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__54863) )
| VX54862 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX32621] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX32621)
=> ? [Vvar__0__Qnum__32622] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__32622)
& ? [Vvar__1__Qden__32623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__32623)
& VX32621 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__32622,Vvar__1__Qden__32623) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX152682] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX152682)
=> ? [Vvar__0__neg__152683] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__152683)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__152683,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX152682 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__152683) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX152661] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX152661)
=> ? [Vvar__0__nonneg__152662] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__152662)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__152662)
& VX152661 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__152662) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX152675] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX152675)
=> ? [Vvar__0__nonpos__152676] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__152676)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__152676,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX152675 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__152676) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX152689] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX152689)
=> ? [Vvar__0__nonzero__152690] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__152690)
& Vvar__0__nonzero__152690 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX152689 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__152690) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX152668] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX152668)
=> ? [Vvar__0__pos__152669] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__152669)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__152669)
& VX152668 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__152669) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__82454,Vvar__1___24Anonymous__82455,VX82456] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__82454)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__82455)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__82454,Vvar__1___24Anonymous__82455,VX82456)
=> ( ( Vvar__0__x__82454 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__82455 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX82456 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__82454) )
| ? [Vvar__1__n__82460] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__82460)
& Vvar__0__x__82454 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__82460)
& Vvar__1___24Anonymous__82455 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2482480___24a3(Vvar__0__x__82454,Vvar__1___24Anonymous__82455,Vvar__1__n__82460)
& VX82456 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__82454,Vvar__1__n__82460) )
| ? [Vvar__1__n__82465] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__82465)
& Vvar__0__x__82454 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__82465))
& Vvar__1___24Anonymous__82455 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2482497___24a3(Vvar__0__x__82454,Vvar__1___24Anonymous__82455,Vvar__1__n__82465)
& VX82456 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__82454,Vvar__1__n__82465) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__66406,Vvar__1__leA__66407,Vvar__2___24Anonymous__66412] :
( cType___24t(Vvar__0__A__66406)
=> ( c_24__type__66502___24t(Vvar__0__A__66406,Vvar__1__leA__66407,Vvar__2___24Anonymous__66412,Vvar__1__leA__66407)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__66406,Vvar__2___24Anonymous__66412)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__66406,Vvar__1__leA__66407,Vvar__2___24Anonymous__66412)
=> ( Vvar__2___24Anonymous__66412 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__66406)
| ? [Vvar__2__x__66426] :
( t(Vvar__2__x__66426,Vvar__0__A__66406)
& Vvar__2___24Anonymous__66412 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__66406,Vvar__2__x__66426,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__66406)) )
| ? [Vvar__2__x__66433] :
( t(Vvar__2__x__66433,Vvar__0__A__66406)
& ? [Vvar__3__y__66434] :
( t(Vvar__3__y__66434,Vvar__0__A__66406)
& ? [Vvar__4__l__66435] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__66406,Vvar__4__l__66435)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__66406,Vvar__1__leA__66407,Vvar__2__x__66433,Vvar__3__y__66434)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__66406,Vvar__1__leA__66407,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__66406,Vvar__4__l__66435,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__66406,Vvar__3__y__66434,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__66406))))
& Vvar__2___24Anonymous__66412 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2466700___24a6(Vvar__0__A__66406,Vvar__1__leA__66407,Vvar__2___24Anonymous__66412,Vvar__2__x__66433,Vvar__3__y__66434,Vvar__4__l__66435) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__73726,Vvar__1__leA__73727,Vvar__2___24Anonymous__73732,Vvar__3___24Anonymous__73733] :
( cType___24t(Vvar__0__A__73726)
=> ( c_24__type__73775___24t(Vvar__0__A__73726,Vvar__1__leA__73727,Vvar__2___24Anonymous__73732,Vvar__3___24Anonymous__73733,Vvar__1__leA__73727)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73726,Vvar__2___24Anonymous__73732)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73726,Vvar__3___24Anonymous__73733)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__73726,Vvar__1__leA__73727,Vvar__2___24Anonymous__73732,Vvar__3___24Anonymous__73733)
=> ( ? [Vvar__2__a__73741] :
( t(Vvar__2__a__73741,Vvar__0__A__73726)
& ? [Vvar__3__x__73742] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73726,Vvar__3__x__73742)
& Vvar__3___24Anonymous__73733 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73726,Vvar__2__a__73741,Vvar__3__x__73742)
& Vvar__2___24Anonymous__73732 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__73726) ) )
| ? [Vvar__2__a__73749] :
( t(Vvar__2__a__73749,Vvar__0__A__73726)
& ? [Vvar__3__b__73750] :
( t(Vvar__3__b__73750,Vvar__0__A__73726)
& p(happ(happ(Vvar__1__leA__73727,Vvar__2__a__73749),Vvar__3__b__73750))
& ? [Vvar__5__x__73752] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73726,Vvar__5__x__73752)
& ? [Vvar__6__y__73753] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73726,Vvar__6__y__73753)
& Vvar__3___24Anonymous__73733 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73726,Vvar__3__b__73750,Vvar__6__y__73753)
& Vvar__2___24Anonymous__73732 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73726,Vvar__2__a__73749,Vvar__5__x__73752) ) ) ) )
| ? [Vvar__2__a__73760] :
( t(Vvar__2__a__73760,Vvar__0__A__73726)
& ? [Vvar__3__x__73761] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73726,Vvar__3__x__73761)
& ? [Vvar__4__y__73762] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__73726,Vvar__4__y__73762)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__73726,Vvar__1__leA__73727,Vvar__3__x__73761,Vvar__4__y__73762)
& Vvar__3___24Anonymous__73733 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73726,Vvar__2__a__73760,Vvar__4__y__73762)
& Vvar__2___24Anonymous__73732 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__73726,Vvar__2__a__73760,Vvar__3__x__73761) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__66393,Vvar__1__R__66394,Vvar__2__x__66395,Vvar__3___24Anonymous__66396] :
( cType___24t(Vvar__0__A__66393)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__66393,Vvar__1__R__66394)
=> ( t(Vvar__2__x__66395,Vvar__0__A__66393)
=> ( t(Vvar__3___24Anonymous__66396,Vvar__0__A__66393)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__66393,Vvar__1__R__66394,Vvar__2__x__66395,Vvar__3___24Anonymous__66396)
=> ( ? [Vvar__3__y__66401] :
( t(Vvar__3__y__66401,Vvar__0__A__66393)
& p(happ(happ(Vvar__1__R__66394,Vvar__2__x__66395),Vvar__3__y__66401))
& Vvar__3___24Anonymous__66396 = Vvar__3__y__66401 )
| Vvar__3___24Anonymous__66396 = Vvar__2__x__66395 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__54115,Vvar__1__R__54116,Vvar__2__a__54121,Vvar__3___24Anonymous__54122] :
( cType___24t(Vvar__0__A__54115)
=> ( c_24__type__54152___24t(Vvar__0__A__54115,Vvar__1__R__54116,Vvar__2__a__54121,Vvar__3___24Anonymous__54122,Vvar__1__R__54116)
=> ( t(Vvar__2__a__54121,Vvar__0__A__54115)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__54115,Vvar__3___24Anonymous__54122)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__54115,Vvar__1__R__54116,Vvar__2__a__54121,Vvar__3___24Anonymous__54122)
=> ( Vvar__3___24Anonymous__54122 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__54115)
| ? [Vvar__3__b__54138] :
( t(Vvar__3__b__54138,Vvar__0__A__54115)
& ? [Vvar__4__l__54139] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__54115,Vvar__4__l__54139)
& p(happ(happ(Vvar__1__R__54116,Vvar__2__a__54121),Vvar__3__b__54138))
& Vvar__3___24Anonymous__54122 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__54115,Vvar__3__b__54138,Vvar__4__l__54139) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__77706,Vvar__1__R__77707,Vvar__2___24Anonymous__77712] :
( cType___24t(Vvar__0__A__77706)
=> ( c_24__type__77747___24t(Vvar__0__A__77706,Vvar__1__R__77707,Vvar__2___24Anonymous__77712,Vvar__1__R__77707)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__77706,Vvar__2___24Anonymous__77712)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__77706,Vvar__1__R__77707,Vvar__2___24Anonymous__77712)
=> ( Vvar__2___24Anonymous__77712 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__77706)
| ? [Vvar__2__a__77726] :
( t(Vvar__2__a__77726,Vvar__0__A__77706)
& Vvar__2___24Anonymous__77712 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__77706,Vvar__2__a__77726,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__77706)) )
| ? [Vvar__2__a__77733] :
( t(Vvar__2__a__77733,Vvar__0__A__77706)
& ? [Vvar__3__b__77734] :
( t(Vvar__3__b__77734,Vvar__0__A__77706)
& ? [Vvar__4__l__77735] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__77706,Vvar__4__l__77735)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__77706,Vvar__1__R__77707,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__77706,Vvar__3__b__77734,Vvar__4__l__77735))
& p(happ(happ(Vvar__1__R__77707,Vvar__2__a__77733),Vvar__3__b__77734))
& Vvar__2___24Anonymous__77712 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__77706,Vvar__2__a__77733,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__77706,Vvar__3__b__77734,Vvar__4__l__77735)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__54154,Vvar__1__R__54155,Vvar__2___24Anonymous__54160] :
( cType___24t(Vvar__0__A__54154)
=> ( c_24__type__54187___24t(Vvar__0__A__54154,Vvar__1__R__54155,Vvar__2___24Anonymous__54160,Vvar__1__R__54155)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__54154,Vvar__2___24Anonymous__54160)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__54154,Vvar__1__R__54155,Vvar__2___24Anonymous__54160)
=> ( Vvar__2___24Anonymous__54160 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__54154)
| ? [Vvar__2__a__54174] :
( t(Vvar__2__a__54174,Vvar__0__A__54154)
& ? [Vvar__3__l__54175] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__54154,Vvar__3__l__54175)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__54154,Vvar__1__R__54155,Vvar__3__l__54175)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__54154,Vvar__1__R__54155,Vvar__2__a__54174,Vvar__3__l__54175)
& Vvar__2___24Anonymous__54160 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__54154,Vvar__2__a__54174,Vvar__3__l__54175) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__77920,Vvar__1__R__77921,Vvar__2___24Anonymous__77926] :
( cType___24t(Vvar__0__A__77920)
=> ( c_24__type__77953___24t(Vvar__0__A__77920,Vvar__1__R__77921,Vvar__2___24Anonymous__77926,Vvar__1__R__77921)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__77920,Vvar__2___24Anonymous__77926)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__77920,Vvar__1__R__77921,Vvar__2___24Anonymous__77926)
=> ( Vvar__2___24Anonymous__77926 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__77920)
| ? [Vvar__2__a__77940] :
( t(Vvar__2__a__77940,Vvar__0__A__77920)
& ? [Vvar__3__l__77941] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__77920,Vvar__3__l__77941)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__77920,Vvar__1__R__77921,Vvar__3__l__77941)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__77920,happ(Vvar__1__R__77921,Vvar__2__a__77940),Vvar__3__l__77941)
& Vvar__2___24Anonymous__77926 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__77920,Vvar__2__a__77940,Vvar__3__l__77941) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX1230] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX1230)
=> ? [Vvar__0___24Anonymous__1231] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__1231)
& ? [Vvar__1___24Anonymous__1232] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__1232)
& ? [Vvar__2___24Anonymous__1233] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__1233)
& ? [Vvar__3___24Anonymous__1234] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__1234)
& ? [Vvar__4___24Anonymous__1235] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__1235)
& ? [Vvar__5___24Anonymous__1236] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__1236)
& ? [Vvar__6___24Anonymous__1237] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__1237)
& ? [Vvar__7___24Anonymous__1238] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__1238)
& VX1230 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__1231,Vvar__1___24Anonymous__1232,Vvar__2___24Anonymous__1233,Vvar__3___24Anonymous__1234,Vvar__4___24Anonymous__1235,Vvar__5___24Anonymous__1236,Vvar__6___24Anonymous__1237,Vvar__7___24Anonymous__1238) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX34717] :
( cCoq_2eStrings_2eString_2estring___24t(VX34717)
=> ( VX34717 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__34718] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__34718)
& ? [Vvar__1___24Anonymous__34719] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__34719)
& VX34717 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__34718,Vvar__1___24Anonymous__34719) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__82257,Vvar__1__lt__82258,Vvar__2__eq__82263,Vvar__3__x__82268,Vvar__4__y__82269,VX82270] :
( cType___24t(Vvar__0__X__82257)
=> ( c_24__type__82330___24t(Vvar__0__X__82257,Vvar__1__lt__82258,Vvar__2__eq__82263,Vvar__3__x__82268,Vvar__4__y__82269,Vvar__1__lt__82258)
=> ( c_24__type__82349___24t(Vvar__0__X__82257,Vvar__1__lt__82258,Vvar__2__eq__82263,Vvar__3__x__82268,Vvar__4__y__82269,Vvar__2__eq__82263)
=> ( t(Vvar__3__x__82268,Vvar__0__X__82257)
=> ( t(Vvar__4__y__82269,Vvar__0__X__82257)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__82257,Vvar__1__lt__82258,Vvar__2__eq__82263,Vvar__3__x__82268,Vvar__4__y__82269,VX82270)
=> ( ( p(happ(happ(Vvar__1__lt__82258,Vvar__3__x__82268),Vvar__4__y__82269))
& VX82270 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__82257,Vvar__1__lt__82258,Vvar__2__eq__82263,Vvar__3__x__82268,Vvar__4__y__82269) )
| ( p(happ(happ(Vvar__2__eq__82263,Vvar__3__x__82268),Vvar__4__y__82269))
& VX82270 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__82257,Vvar__1__lt__82258,Vvar__2__eq__82263,Vvar__3__x__82268,Vvar__4__y__82269) )
| ( p(happ(happ(Vvar__1__lt__82258,Vvar__4__y__82269),Vvar__3__x__82268))
& VX82270 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__82257,Vvar__1__lt__82258,Vvar__2__eq__82263,Vvar__3__x__82268,Vvar__4__y__82269) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__83764,Vvar__1___24Anonymous__83765] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__83764)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__83765)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__83764,Vvar__1___24Anonymous__83765)
=> ( ? [Vvar__0__a__83767] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__83767)
& ? [Vvar__1__s__83768] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__83768)
& Vvar__1___24Anonymous__83765 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__83767,Vvar__1__s__83768)
& Vvar__0___24Anonymous__83764 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__83769] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__83769)
& ? [Vvar__1__s1__83770] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__83770)
& ? [Vvar__2__s2__83771] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__83771)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__83770,Vvar__2__s2__83771)
& Vvar__1___24Anonymous__83765 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__83769,Vvar__2__s2__83771)
& Vvar__0___24Anonymous__83764 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__83769,Vvar__1__s1__83770) ) ) )
| ? [Vvar__0__a__83773] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__83773)
& ? [Vvar__1__b__83774] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__83774)
& ? [Vvar__2__s1__83775] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__83775)
& ? [Vvar__3__s2__83776] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__83776)
& p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__83773),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__83774)))
& Vvar__1___24Anonymous__83765 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__83774,Vvar__3__s2__83776)
& Vvar__0___24Anonymous__83764 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__83773,Vvar__2__s1__83775) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX82449] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX82449)
=> ( VX82449 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX82449 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX82449 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__31789,VX31790] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31789)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__31789,VX31790)
=> ( ? [Vvar__0__n__31791] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__31791)
& Vvar__0___24Anonymous__31789 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__31791)
& VX31790 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__31791) )
| ? [Vvar__0__n__31792] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__31792)
& ? [Vvar__1___24Anonymous__31793] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__31792,Vvar__1___24Anonymous__31793)
& Vvar__0___24Anonymous__31789 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__31792)
& VX31790 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__31792,Vvar__1___24Anonymous__31793) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__35498,Vvar__1___24Anonymous__35499,VX35500] :
( cType___24t(Vvar__0__A__35498)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__35499)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__35498,Vvar__1___24Anonymous__35499,VX35500)
=> ( ( Vvar__1___24Anonymous__35499 = cCoq_2eInit_2eDatatypes_2eO
& VX35500 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__35498) )
| ? [Vvar__1__h__35503] :
( t(Vvar__1__h__35503,Vvar__0__A__35498)
& ? [Vvar__2__n__35504] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__35504)
& ? [Vvar__3___24Anonymous__35505] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__35498,Vvar__2__n__35504,Vvar__3___24Anonymous__35505)
& Vvar__1___24Anonymous__35499 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__35504)
& VX35500 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__35498,Vvar__1__h__35503,Vvar__2__n__35504,Vvar__3___24Anonymous__35505) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__153365,Vvar__1__b__153366,Vvar__2__d__153367] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__153365)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__153366)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__153367)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__153365,Vvar__1__b__153366,Vvar__2__d__153367)
=> ? [Vvar__3__u__153372] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__153372)
& ? [Vvar__4__v__153373] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__153373)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__153372,Vvar__0__a__153365),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__153373,Vvar__1__b__153366)) = Vvar__2__d__153367
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__153340,Vvar__1__b__153341,VX153342] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__153340)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__153341)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__153340,Vvar__1__b__153341,VX153342)
=> ? [Vvar__2__u__153345] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__153345)
& ? [Vvar__3__v__153346] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__153346)
& ? [Vvar__4__d__153347] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__153347)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__153345,Vvar__0__a__153340),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__153346,Vvar__1__b__153341)) = Vvar__4__d__153347
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__153340,Vvar__1__b__153341,Vvar__4__d__153347)
& VX153342 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__153340,Vvar__1__b__153341,Vvar__2__u__153345,Vvar__3__v__153346,Vvar__4__d__153347) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__153312,Vvar__1__b__153313,Vvar__2__g__153314] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__153312)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__153313)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__153314)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__153312,Vvar__1__b__153313,Vvar__2__g__153314)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__153314,Vvar__0__a__153312)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__153314,Vvar__1__b__153313)
& ! [Vvar__var__var__var__var__5__x__153322__153325__153328__153331__153334] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__153322__153325__153328__153331__153334)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__153322__153325__153328__153331__153334,Vvar__0__a__153312)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__153322__153325__153328__153331__153334,Vvar__1__b__153313)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__153322__153325__153328__153331__153334,Vvar__2__g__153314) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__153375] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__153375)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__153375)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__153375))
& ! [Vvar__var__var__2__n__153380__153382__153384] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__153380__153382__153384)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__153380__153382__153384))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__153380__153382__153384,Vvar__0__p__153375)) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__153380__153382__153384,Vvar__0__p__153375) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__153388,Vvar__1__p__153389,VX153390] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__153388)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__153389)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__153388,Vvar__1__p__153389,VX153390)
=> ? [Vvar__2__q__153393] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__153393)
& ? [Vvar__3__r__153394] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__153394)
& Vvar__0__x__153388 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__153393,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__153389)),Vvar__3__r__153394)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__153394))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__153394,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__153389)))
& VX153390 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__153388,Vvar__1__p__153389,Vvar__2__q__153393,Vvar__3__r__153394) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__83393,Vvar__1__F__83394] :
( cType___24t(Vvar__0__T__83393)
=> ( t(Vvar__1__F__83394,Vvar__0__T__83393)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__83393,Vvar__1__F__83394)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
! [Vvar__0__T__152044,Vvar__1__F__152045] :
( cType___24t(Vvar__0__T__152044)
=> ( t(Vvar__1__F__152045,Vvar__0__T__152044)
=> ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__152044,Vvar__1__F__152045)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX41104] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX41104)
=> ( VX41104 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__41105] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41105)
& ? [Vvar__1___24Anonymous__41106] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__41106)
& VX41104 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__41105,Vvar__1___24Anonymous__41106) ) )
| ? [Vvar__0___24Anonymous__41107] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41107)
& ? [Vvar__1___24Anonymous__41108] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__41108)
& VX41104 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__41107,Vvar__1___24Anonymous__41108) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__40890,VX40891] :
( cType___24t(Vvar__0__C__40890)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__40890,VX40891)
=> ( ? [Vvar__1___24Anonymous__40893] :
( t(Vvar__1___24Anonymous__40893,Vvar__0__C__40890)
& VX40891 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__40890,Vvar__1___24Anonymous__40893) )
| ? [Vvar__1___24Anonymous__40895] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__40895)
& VX40891 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__40890,Vvar__1___24Anonymous__40895) )
| ? [Vvar__1___24Anonymous__40897] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__40890,Vvar__1___24Anonymous__40897)
& ? [Vvar__2___24Anonymous__40898] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__40890,Vvar__2___24Anonymous__40898)
& VX40891 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__40890,Vvar__1___24Anonymous__40897,Vvar__2___24Anonymous__40898) ) )
| ? [Vvar__1___24Anonymous__40900] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__40890,Vvar__1___24Anonymous__40900)
& ? [Vvar__2___24Anonymous__40901] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__40890,Vvar__2___24Anonymous__40901)
& VX40891 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__40890,Vvar__1___24Anonymous__40900,Vvar__2___24Anonymous__40901) ) )
| ? [Vvar__1___24Anonymous__40903] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__40890,Vvar__1___24Anonymous__40903)
& ? [Vvar__2___24Anonymous__40904] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__40890,Vvar__2___24Anonymous__40904)
& VX40891 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__40890,Vvar__1___24Anonymous__40903,Vvar__2___24Anonymous__40904) ) )
| ? [Vvar__1___24Anonymous__40906] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__40890,Vvar__1___24Anonymous__40906)
& VX40891 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__40890,Vvar__1___24Anonymous__40906) )
| ? [Vvar__1___24Anonymous__40908] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__40890,Vvar__1___24Anonymous__40908)
& ? [Vvar__2___24Anonymous__40909] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__40909)
& VX40891 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__40890,Vvar__1___24Anonymous__40908,Vvar__2___24Anonymous__40909) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__41054,VX41055] :
( cType___24t(Vvar__0__C__41054)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__41054,VX41055)
=> ( ? [Vvar__1___24Anonymous__41057] :
( t(Vvar__1___24Anonymous__41057,Vvar__0__C__41054)
& VX41055 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__41054,Vvar__1___24Anonymous__41057) )
| ? [Vvar__1___24Anonymous__41059] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__41059)
& ? [Vvar__2___24Anonymous__41060] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__41054,Vvar__2___24Anonymous__41060)
& VX41055 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__41054,Vvar__1___24Anonymous__41059,Vvar__2___24Anonymous__41060) ) )
| ? [Vvar__1___24Anonymous__41062] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__41054,Vvar__1___24Anonymous__41062)
& ? [Vvar__2___24Anonymous__41063] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__41063)
& ? [Vvar__3___24Anonymous__41064] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__41054,Vvar__3___24Anonymous__41064)
& VX41055 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__41054,Vvar__1___24Anonymous__41062,Vvar__2___24Anonymous__41063,Vvar__3___24Anonymous__41064) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__43523,Vvar__1__rO__43524,Vvar__2__rI__43525,Vvar__3__rplus__43526,Vvar__4__rtimes__43531,Vvar__5__rminus__43536,Vvar__6__ropp__43541,Vvar__7__req__43544,Vvar__8__rle__43549,Vvar__9__rlt__43554] :
( cType___24t(Vvar__0__R__43523)
=> ( t(Vvar__1__rO__43524,Vvar__0__R__43523)
=> ( t(Vvar__2__rI__43525,Vvar__0__R__43523)
=> ( c_24__type__43955___24t(Vvar__0__R__43523,Vvar__1__rO__43524,Vvar__2__rI__43525,Vvar__3__rplus__43526,Vvar__4__rtimes__43531,Vvar__5__rminus__43536,Vvar__6__ropp__43541,Vvar__7__req__43544,Vvar__8__rle__43549,Vvar__9__rlt__43554,Vvar__3__rplus__43526)
=> ( c_24__type__44056___24t(Vvar__0__R__43523,Vvar__1__rO__43524,Vvar__2__rI__43525,Vvar__3__rplus__43526,Vvar__4__rtimes__43531,Vvar__5__rminus__43536,Vvar__6__ropp__43541,Vvar__7__req__43544,Vvar__8__rle__43549,Vvar__9__rlt__43554,Vvar__4__rtimes__43531)
=> ( c_24__type__44157___24t(Vvar__0__R__43523,Vvar__1__rO__43524,Vvar__2__rI__43525,Vvar__3__rplus__43526,Vvar__4__rtimes__43531,Vvar__5__rminus__43536,Vvar__6__ropp__43541,Vvar__7__req__43544,Vvar__8__rle__43549,Vvar__9__rlt__43554,Vvar__5__rminus__43536)
=> ( c_24__type__44247___24t(Vvar__0__R__43523,Vvar__1__rO__43524,Vvar__2__rI__43525,Vvar__3__rplus__43526,Vvar__4__rtimes__43531,Vvar__5__rminus__43536,Vvar__6__ropp__43541,Vvar__7__req__43544,Vvar__8__rle__43549,Vvar__9__rlt__43554,Vvar__6__ropp__43541)
=> ( c_24__type__44348___24t(Vvar__0__R__43523,Vvar__1__rO__43524,Vvar__2__rI__43525,Vvar__3__rplus__43526,Vvar__4__rtimes__43531,Vvar__5__rminus__43536,Vvar__6__ropp__43541,Vvar__7__req__43544,Vvar__8__rle__43549,Vvar__9__rlt__43554,Vvar__7__req__43544)
=> ( c_24__type__44449___24t(Vvar__0__R__43523,Vvar__1__rO__43524,Vvar__2__rI__43525,Vvar__3__rplus__43526,Vvar__4__rtimes__43531,Vvar__5__rminus__43536,Vvar__6__ropp__43541,Vvar__7__req__43544,Vvar__8__rle__43549,Vvar__9__rlt__43554,Vvar__8__rle__43549)
=> ( c_24__type__44550___24t(Vvar__0__R__43523,Vvar__1__rO__43524,Vvar__2__rI__43525,Vvar__3__rplus__43526,Vvar__4__rtimes__43531,Vvar__5__rminus__43536,Vvar__6__ropp__43541,Vvar__7__req__43544,Vvar__8__rle__43549,Vvar__9__rlt__43554,Vvar__9__rlt__43554)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__43523,Vvar__1__rO__43524,Vvar__2__rI__43525,Vvar__3__rplus__43526,Vvar__4__rtimes__43531,Vvar__5__rminus__43536,Vvar__6__ropp__43541,Vvar__7__req__43544,Vvar__8__rle__43549,Vvar__9__rlt__43554)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__43523,Vvar__7__req__43544)
& ! [Vvar__var__var__var__var__11__x1__43598__43604__43709__43715__43721] :
( t(Vvar__var__var__var__var__11__x1__43598__43604__43709__43715__43721,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__12__x2__43599__43605__43710__43716__43722] :
( t(Vvar__var__var__var__var__12__x2__43599__43605__43710__43716__43722,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__11__x1__43598__43604__43709__43715__43721),Vvar__var__var__var__var__12__x2__43599__43605__43710__43716__43722))
=> ! [Vvar__var__var__var__var__14__y1__43600__43606__43711__43717__43723] :
( t(Vvar__var__var__var__var__14__y1__43600__43606__43711__43717__43723,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__15__y2__43601__43607__43712__43718__43724] :
( t(Vvar__var__var__var__var__15__y2__43601__43607__43712__43718__43724,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__14__y1__43600__43606__43711__43717__43723),Vvar__var__var__var__var__15__y2__43601__43607__43712__43718__43724))
=> p(happ(happ(Vvar__7__req__43544,happ(happ(Vvar__3__rplus__43526,Vvar__var__var__var__var__11__x1__43598__43604__43709__43715__43721),Vvar__var__var__var__var__14__y1__43600__43606__43711__43717__43723)),happ(happ(Vvar__3__rplus__43526,Vvar__var__var__var__var__12__x2__43599__43605__43710__43716__43722),Vvar__var__var__var__var__15__y2__43601__43607__43712__43718__43724))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__43611__43617__43727__43733__43739] :
( t(Vvar__var__var__var__var__12__x1__43611__43617__43727__43733__43739,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__13__x2__43612__43618__43728__43734__43740] :
( t(Vvar__var__var__var__var__13__x2__43612__43618__43728__43734__43740,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__12__x1__43611__43617__43727__43733__43739),Vvar__var__var__var__var__13__x2__43612__43618__43728__43734__43740))
=> ! [Vvar__var__var__var__var__15__y1__43613__43619__43729__43735__43741] :
( t(Vvar__var__var__var__var__15__y1__43613__43619__43729__43735__43741,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__16__y2__43614__43620__43730__43736__43742] :
( t(Vvar__var__var__var__var__16__y2__43614__43620__43730__43736__43742,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__15__y1__43613__43619__43729__43735__43741),Vvar__var__var__var__var__16__y2__43614__43620__43730__43736__43742))
=> p(happ(happ(Vvar__7__req__43544,happ(happ(Vvar__4__rtimes__43531,Vvar__var__var__var__var__12__x1__43611__43617__43727__43733__43739),Vvar__var__var__var__var__15__y1__43613__43619__43729__43735__43741)),happ(happ(Vvar__4__rtimes__43531,Vvar__var__var__var__var__13__x2__43612__43618__43728__43734__43740),Vvar__var__var__var__var__16__y2__43614__43620__43730__43736__43742))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__43624__43627__43745__43748__43751] :
( t(Vvar__var__var__var__var__13__x1__43624__43627__43745__43748__43751,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__14__x2__43625__43628__43746__43749__43752] :
( t(Vvar__var__var__var__var__14__x2__43625__43628__43746__43749__43752,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__13__x1__43624__43627__43745__43748__43751),Vvar__var__var__var__var__14__x2__43625__43628__43746__43749__43752))
=> p(happ(happ(Vvar__7__req__43544,happ(Vvar__6__ropp__43541,Vvar__var__var__var__var__13__x1__43624__43627__43745__43748__43751)),happ(Vvar__6__ropp__43541,Vvar__var__var__var__var__14__x2__43625__43628__43746__43749__43752))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__43631__43637__43754__43760__43766] :
( t(Vvar__var__var__var__var__14__x1__43631__43637__43754__43760__43766,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__15__x2__43632__43638__43755__43761__43767] :
( t(Vvar__var__var__var__var__15__x2__43632__43638__43755__43761__43767,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__14__x1__43631__43637__43754__43760__43766),Vvar__var__var__var__var__15__x2__43632__43638__43755__43761__43767))
=> ! [Vvar__var__var__var__var__17__y1__43633__43639__43756__43762__43768] :
( t(Vvar__var__var__var__var__17__y1__43633__43639__43756__43762__43768,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__18__y2__43634__43640__43757__43763__43769] :
( t(Vvar__var__var__var__var__18__y2__43634__43640__43757__43763__43769,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__17__y1__43633__43639__43756__43762__43768),Vvar__var__var__var__var__18__y2__43634__43640__43757__43763__43769))
=> ( p(happ(happ(Vvar__8__rle__43549,Vvar__var__var__var__var__14__x1__43631__43637__43754__43760__43766),Vvar__var__var__var__var__17__y1__43633__43639__43756__43762__43768))
<=> p(happ(happ(Vvar__8__rle__43549,Vvar__var__var__var__var__15__x2__43632__43638__43755__43761__43767),Vvar__var__var__var__var__18__y2__43634__43640__43757__43763__43769)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__43644__43650__43772__43778__43784] :
( t(Vvar__var__var__var__var__15__x1__43644__43650__43772__43778__43784,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__16__x2__43645__43651__43773__43779__43785] :
( t(Vvar__var__var__var__var__16__x2__43645__43651__43773__43779__43785,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__15__x1__43644__43650__43772__43778__43784),Vvar__var__var__var__var__16__x2__43645__43651__43773__43779__43785))
=> ! [Vvar__var__var__var__var__18__y1__43646__43652__43774__43780__43786] :
( t(Vvar__var__var__var__var__18__y1__43646__43652__43774__43780__43786,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__19__y2__43647__43653__43775__43781__43787] :
( t(Vvar__var__var__var__var__19__y2__43647__43653__43775__43781__43787,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__18__y1__43646__43652__43774__43780__43786),Vvar__var__var__var__var__19__y2__43647__43653__43775__43781__43787))
=> ( p(happ(happ(Vvar__9__rlt__43554,Vvar__var__var__var__var__15__x1__43644__43650__43772__43778__43784),Vvar__var__var__var__var__18__y1__43646__43652__43774__43780__43786))
<=> p(happ(happ(Vvar__9__rlt__43554,Vvar__var__var__var__var__16__x2__43645__43651__43773__43779__43785),Vvar__var__var__var__var__19__y2__43647__43653__43775__43781__43787)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__43523,Vvar__1__rO__43524,Vvar__2__rI__43525,Vvar__3__rplus__43526,Vvar__4__rtimes__43531,Vvar__5__rminus__43536,Vvar__6__ropp__43541,Vvar__7__req__43544)
& ! [Vvar__var__var__var__17__n__43658__43659__43790__43791] :
( t(Vvar__var__var__var__17__n__43658__43659__43790__43791,Vvar__0__R__43523)
=> p(happ(happ(Vvar__8__rle__43549,Vvar__var__var__var__17__n__43658__43659__43790__43791),Vvar__var__var__var__17__n__43658__43659__43790__43791)) )
& ! [Vvar__var__var__var__var__18__n__43661__43665__43792__43796__43800] :
( t(Vvar__var__var__var__var__18__n__43661__43665__43792__43796__43800,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__19__m__43662__43666__43793__43797__43801] :
( t(Vvar__var__var__var__var__19__m__43662__43666__43793__43797__43801,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__8__rle__43549,Vvar__var__var__var__var__18__n__43661__43665__43792__43796__43800),Vvar__var__var__var__var__19__m__43662__43666__43793__43797__43801))
=> ( p(happ(happ(Vvar__8__rle__43549,Vvar__var__var__var__var__19__m__43662__43666__43793__43797__43801),Vvar__var__var__var__var__18__n__43661__43665__43792__43796__43800))
=> p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__18__n__43661__43665__43792__43796__43800),Vvar__var__var__var__var__19__m__43662__43666__43793__43797__43801)) ) ) ) )
& ! [Vvar__var__var__var__19__n__43670__43675__43804__43809] :
( t(Vvar__var__var__var__19__n__43670__43675__43804__43809,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__20__m__43671__43676__43805__43810] :
( t(Vvar__var__var__var__20__m__43671__43676__43805__43810,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__21__p__43672__43677__43806__43811] :
( t(Vvar__var__var__var__21__p__43672__43677__43806__43811,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__8__rle__43549,Vvar__var__var__var__19__n__43670__43675__43804__43809),Vvar__var__var__var__20__m__43671__43676__43805__43810))
=> ( p(happ(happ(Vvar__8__rle__43549,Vvar__var__var__var__20__m__43671__43676__43805__43810),Vvar__var__var__var__21__p__43672__43677__43806__43811))
=> p(happ(happ(Vvar__8__rle__43549,Vvar__var__var__var__19__n__43670__43675__43804__43809),Vvar__var__var__var__21__p__43672__43677__43806__43811)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__43681__43683__43814__43816__43818__43820] :
( t(Vvar__var__var__var__var__var__20__n__43681__43683__43814__43816__43818__43820,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__var__21__m__43682__43684__43815__43817__43819__43821] :
( t(Vvar__var__var__var__var__var__21__m__43682__43684__43815__43817__43819__43821,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__9__rlt__43554,Vvar__var__var__var__var__var__20__n__43681__43683__43814__43816__43818__43820),Vvar__var__var__var__var__var__21__m__43682__43684__43815__43817__43819__43821))
<=> ( p(happ(happ(Vvar__8__rle__43549,Vvar__var__var__var__var__var__20__n__43681__43683__43814__43816__43818__43820),Vvar__var__var__var__var__var__21__m__43682__43684__43815__43817__43819__43821))
& ~ p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__var__20__n__43681__43683__43814__43816__43818__43820),Vvar__var__var__var__var__var__21__m__43682__43684__43815__43817__43819__43821)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__43686__43688__43822__43824__43826] :
( t(Vvar__var__var__var__var__21__n__43686__43688__43822__43824__43826,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__22__m__43687__43689__43823__43825__43827] :
( t(Vvar__var__var__var__var__22__m__43687__43689__43823__43825__43827,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__9__rlt__43554,Vvar__var__var__var__var__21__n__43686__43688__43822__43824__43826),Vvar__var__var__var__var__22__m__43687__43689__43823__43825__43827))
| p(happ(happ(Vvar__7__req__43544,Vvar__var__var__var__var__21__n__43686__43688__43822__43824__43826),Vvar__var__var__var__var__22__m__43687__43689__43823__43825__43827))
| p(happ(happ(Vvar__9__rlt__43554,Vvar__var__var__var__var__22__m__43687__43689__43823__43825__43827),Vvar__var__var__var__var__21__n__43686__43688__43822__43824__43826)) ) ) )
& ! [Vvar__var__var__var__var__22__n__43691__43695__43828__43832__43836] :
( t(Vvar__var__var__var__var__22__n__43691__43695__43828__43832__43836,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__23__m__43692__43696__43829__43833__43837] :
( t(Vvar__var__var__var__var__23__m__43692__43696__43829__43833__43837,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__24__p__43693__43697__43830__43834__43838] :
( t(Vvar__var__var__var__var__24__p__43693__43697__43830__43834__43838,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__8__rle__43549,Vvar__var__var__var__var__22__n__43691__43695__43828__43832__43836),Vvar__var__var__var__var__23__m__43692__43696__43829__43833__43837))
=> p(happ(happ(Vvar__8__rle__43549,happ(happ(Vvar__3__rplus__43526,Vvar__var__var__var__var__24__p__43693__43697__43830__43834__43838),Vvar__var__var__var__var__22__n__43691__43695__43828__43832__43836)),happ(happ(Vvar__3__rplus__43526,Vvar__var__var__var__var__24__p__43693__43697__43830__43834__43838),Vvar__var__var__var__var__23__m__43692__43696__43829__43833__43837))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__43700__43704__43840__43844__43848__43852] :
( t(Vvar__var__var__var__var__var__23__n__43700__43704__43840__43844__43848__43852,Vvar__0__R__43523)
=> ! [Vvar__var__var__var__var__var__24__m__43701__43705__43841__43845__43849__43853] :
( t(Vvar__var__var__var__var__var__24__m__43701__43705__43841__43845__43849__43853,Vvar__0__R__43523)
=> ( p(happ(happ(Vvar__9__rlt__43554,Vvar__1__rO__43524),Vvar__var__var__var__var__var__23__n__43700__43704__43840__43844__43848__43852))
=> ( p(happ(happ(Vvar__9__rlt__43554,Vvar__1__rO__43524),Vvar__var__var__var__var__var__24__m__43701__43705__43841__43845__43849__43853))
=> p(happ(happ(Vvar__9__rlt__43554,Vvar__1__rO__43524),happ(happ(Vvar__4__rtimes__43531,Vvar__var__var__var__var__var__23__n__43700__43704__43840__43844__43848__43852),Vvar__var__var__var__var__var__24__m__43701__43705__43841__43845__43849__43853))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__43544,Vvar__1__rO__43524),Vvar__2__rI__43525))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX44615] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX44615)
=> ( VX44615 = cCoq_2emicromega_2eRMicromega_2eC0
| VX44615 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__44616] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__44616)
& VX44615 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__44616) )
| ? [Vvar__0__r__44617] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__44617)
& VX44615 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__44617) )
| ? [Vvar__0__r1__44618] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__44618)
& ? [Vvar__1__r2__44619] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__44619)
& VX44615 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__44618,Vvar__1__r2__44619) ) )
| ? [Vvar__0__r1__44620] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__44620)
& ? [Vvar__1__r2__44621] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__44621)
& VX44615 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__44620,Vvar__1__r2__44621) ) )
| ? [Vvar__0__r1__44622] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__44622)
& ? [Vvar__1__r2__44623] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__44623)
& VX44615 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__44622,Vvar__1__r2__44623) ) )
| ? [Vvar__0__r1__44624] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__44624)
& ? [Vvar__1__z__44625] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__44625)
& VX44615 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__44624,Vvar__1__z__44625) ) )
| ? [Vvar__0__r__44626] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__44626)
& VX44615 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__44626) )
| ? [Vvar__0__r__44627] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__44627)
& VX44615 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__44627) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__50268,VX50269] :
( cType___24t(Vvar__0__T__50268)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__50268,VX50269)
=> ? [Vvar__1__Flhs__50271] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__50268,Vvar__1__Flhs__50271)
& ? [Vvar__2__Fop__50272] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__50272)
& ? [Vvar__3__Frhs__50273] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__50268,Vvar__3__Frhs__50273)
& VX50269 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__50268,Vvar__1__Flhs__50271,Vvar__2__Fop__50272,Vvar__3__Frhs__50273) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX50114] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX50114)
=> ( VX50114 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX50114 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX50114 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX50114 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX73944] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX73944)
=> ( VX73944 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX73944 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX73944 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX73944 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX73944 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX73944 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__50115,VX50116] :
( cType___24t(Vvar__0__C__50115)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__50115,VX50116)
=> ( ? [Vvar__1___24Anonymous__50118] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__50118)
& VX50116 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__50115,Vvar__1___24Anonymous__50118) )
| ? [Vvar__1___24Anonymous__50120] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__50115,Vvar__1___24Anonymous__50120)
& VX50116 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__50115,Vvar__1___24Anonymous__50120) )
| ? [Vvar__1___24Anonymous__50122] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__50115,Vvar__1___24Anonymous__50122)
& ? [Vvar__2___24Anonymous__50123] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__50115,Vvar__2___24Anonymous__50123)
& VX50116 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__50115,Vvar__1___24Anonymous__50122,Vvar__2___24Anonymous__50123) ) )
| ? [Vvar__1___24Anonymous__50125] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__50115,Vvar__1___24Anonymous__50125)
& ? [Vvar__2___24Anonymous__50126] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__50115,Vvar__2___24Anonymous__50126)
& VX50116 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__50115,Vvar__1___24Anonymous__50125,Vvar__2___24Anonymous__50126) ) )
| ? [Vvar__1___24Anonymous__50128] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__50115,Vvar__1___24Anonymous__50128)
& ? [Vvar__2___24Anonymous__50129] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__50115,Vvar__2___24Anonymous__50129)
& VX50116 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__50115,Vvar__1___24Anonymous__50128,Vvar__2___24Anonymous__50129) ) )
| ? [Vvar__1___24Anonymous__50131] :
( t(Vvar__1___24Anonymous__50131,Vvar__0__C__50115)
& VX50116 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__50115,Vvar__1___24Anonymous__50131) )
| VX50116 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__50115) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890] :
( cType___24t(Vvar__0__R__44821)
=> ( t(Vvar__1__rO__44822,Vvar__0__R__44821)
=> ( t(Vvar__2__rI__44823,Vvar__0__R__44821)
=> ( c_24__type__45354___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__3__rplus__44824)
=> ( c_24__type__45700___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__4__rtimes__44829)
=> ( c_24__type__46046___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__5__rminus__44834)
=> ( c_24__type__46369___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__6__ropp__44839)
=> ( c_24__type__46715___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__7__req__44842)
=> ( c_24__type__47061___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__8__rle__44847)
=> ( cType___24t(Vvar__9__C__44852)
=> ( t(Vvar__10__cO__44853,Vvar__9__C__44852)
=> ( t(Vvar__11__cI__44854,Vvar__9__C__44852)
=> ( c_24__type__47407___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__12__cplus__44855)
=> ( c_24__type__47753___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__13__ctimes__44860)
=> ( c_24__type__48099___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__14__cminus__44865)
=> ( c_24__type__48422___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__15__copp__44870)
=> ( c_24__type__48768___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__16__ceqb__44873)
=> ( c_24__type__49114___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__17__cleb__44878)
=> ( c_24__type__49437___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__18__phi__44883)
=> ( cType___24t(Vvar__19__E__44886)
=> ( c_24__type__49760___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__20__pow__phi__44887)
=> ( c_24__type__50106___24t(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890,Vvar__21__rpow__44890)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__8__rle__44847,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__17__cleb__44878,Vvar__18__phi__44883,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__44821,Vvar__1__rO__44822,Vvar__2__rI__44823,Vvar__3__rplus__44824,Vvar__4__rtimes__44829,Vvar__5__rminus__44834,Vvar__6__ropp__44839,Vvar__7__req__44842,Vvar__9__C__44852,Vvar__10__cO__44853,Vvar__11__cI__44854,Vvar__12__cplus__44855,Vvar__13__ctimes__44860,Vvar__14__cminus__44865,Vvar__15__copp__44870,Vvar__16__ceqb__44873,Vvar__18__phi__44883)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__44821,Vvar__2__rI__44823,Vvar__4__rtimes__44829,Vvar__7__req__44842,Vvar__19__E__44886,Vvar__20__pow__phi__44887,Vvar__21__rpow__44890)
& ! [Vvar__var__var__var__var__var__24__x__44973__44976__44986__44989__44992__44995] :
( t(Vvar__var__var__var__var__var__24__x__44973__44976__44986__44989__44992__44995,Vvar__9__C__44852)
=> ! [Vvar__var__var__var__var__var__25__y__44974__44977__44987__44990__44993__44996] :
( t(Vvar__var__var__var__var__var__25__y__44974__44977__44987__44990__44993__44996,Vvar__9__C__44852)
=> ( happ(happ(Vvar__16__ceqb__44873,Vvar__var__var__var__var__var__24__x__44973__44976__44986__44989__44992__44995),Vvar__var__var__var__var__var__25__y__44974__44977__44987__44990__44993__44996) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__44842,happ(Vvar__18__phi__44883,Vvar__var__var__var__var__var__24__x__44973__44976__44986__44989__44992__44995)),happ(Vvar__18__phi__44883,Vvar__var__var__var__var__var__25__y__44974__44977__44987__44990__44993__44996))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__44980__44983__44998__45001__45004__45007] :
( t(Vvar__var__var__var__var__var__25__x__44980__44983__44998__45001__45004__45007,Vvar__9__C__44852)
=> ! [Vvar__var__var__var__var__var__26__y__44981__44984__44999__45002__45005__45008] :
( t(Vvar__var__var__var__var__var__26__y__44981__44984__44999__45002__45005__45008,Vvar__9__C__44852)
=> ( happ(happ(Vvar__17__cleb__44878,Vvar__var__var__var__var__var__25__x__44980__44983__44998__45001__45004__45007),Vvar__var__var__var__var__var__26__y__44981__44984__44999__45002__45005__45008) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__44847,happ(Vvar__18__phi__44883,Vvar__var__var__var__var__var__25__x__44980__44983__44998__45001__45004__45007)),happ(Vvar__18__phi__44883,Vvar__var__var__var__var__var__26__y__44981__44984__44999__45002__45005__45008))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,VX54203] :
( cType___24t(Vvar__0__TA__54199)
=> ( cType___24t(Vvar__1__TX__54200)
=> ( cType___24t(Vvar__2__AA__54201)
=> ( cType___24t(Vvar__3__AF__54202)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,VX54203)
=> ( VX54203 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202)
| VX54203 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202)
| ? [Vvar__4___24Anonymous__54216] :
( t(Vvar__4___24Anonymous__54216,Vvar__1__TX__54200)
& VX54203 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__4___24Anonymous__54216) )
| ? [Vvar__4___24Anonymous__54221] :
( t(Vvar__4___24Anonymous__54221,Vvar__0__TA__54199)
& ? [Vvar__5___24Anonymous__54222] :
( t(Vvar__5___24Anonymous__54222,Vvar__2__AA__54201)
& VX54203 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__4___24Anonymous__54221,Vvar__5___24Anonymous__54222) ) )
| ? [Vvar__4___24Anonymous__54227] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__4___24Anonymous__54227)
& ? [Vvar__5___24Anonymous__54228] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__5___24Anonymous__54228)
& VX54203 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__4___24Anonymous__54227,Vvar__5___24Anonymous__54228) ) )
| ? [Vvar__4___24Anonymous__54233] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__4___24Anonymous__54233)
& ? [Vvar__5___24Anonymous__54234] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__5___24Anonymous__54234)
& VX54203 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__4___24Anonymous__54233,Vvar__5___24Anonymous__54234) ) )
| ? [Vvar__4___24Anonymous__54239] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__4___24Anonymous__54239)
& VX54203 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__4___24Anonymous__54239) )
| ? [Vvar__4___24Anonymous__54244] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__4___24Anonymous__54244)
& ? [Vvar__5___24Anonymous__54245] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__54202,Vvar__5___24Anonymous__54245)
& ? [Vvar__6___24Anonymous__54246] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__6___24Anonymous__54246)
& VX54203 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__54199,Vvar__1__TX__54200,Vvar__2__AA__54201,Vvar__3__AF__54202,Vvar__4___24Anonymous__54244,Vvar__5___24Anonymous__54245,Vvar__6___24Anonymous__54246) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__153214,VX153215] :
( cType___24t(Vvar__0__A__153214)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__153214,VX153215)
=> ( VX153215 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__153214)
| ? [Vvar__1___24Anonymous__153218] :
( t(Vvar__1___24Anonymous__153218,Vvar__0__A__153214)
& VX153215 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__153214,Vvar__1___24Anonymous__153218) )
| ? [Vvar__1___24Anonymous__153220] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__153214,Vvar__1___24Anonymous__153220)
& ? [Vvar__2___24Anonymous__153221] :
( t(Vvar__2___24Anonymous__153221,Vvar__0__A__153214)
& ? [Vvar__3___24Anonymous__153222] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__153214,Vvar__3___24Anonymous__153222)
& VX153215 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__153214,Vvar__1___24Anonymous__153220,Vvar__2___24Anonymous__153221,Vvar__3___24Anonymous__153222) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
! [Vvar__0___24Anonymous__153474] :
( cProp___24t(Vvar__0___24Anonymous__153474)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__153474)
=> ( ? [Vvar__0__P__153476] :
( cProp___24t(Vvar__0__P__153476)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__153476)
& Vvar__0___24Anonymous__153474 = Vvar__0__P__153476 )
| ? [Vvar__0__s__153478] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__153478)
& Vvar__0___24Anonymous__153474 = c_24__prop__153487___24a2(Vvar__0___24Anonymous__153474,Vvar__0__s__153478) )
| ? [Vvar__0__s1__153480] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__153480)
& ? [Vvar__1__s2__153481] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__153481)
& Vvar__0___24Anonymous__153474 = c_24__prop__153488___24a3(Vvar__0___24Anonymous__153474,Vvar__0__s1__153480,Vvar__1__s2__153481) ) )
| ? [Vvar__0__s1__153484] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__153484)
& ? [Vvar__1__s2__153485] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__153485)
& Vvar__0___24Anonymous__153474 = c_24__prop__153489___24a3(Vvar__0___24Anonymous__153474,Vvar__0__s1__153484,Vvar__1__s2__153485) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__153443] :
( cProp___24t(Vvar__0___24Anonymous__153443)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__153443)
=> ( ? [Vvar__0__S__153445] :
( cType___24t(Vvar__0__S__153445)
& ? [Vvar__1__x__153446] :
( t(Vvar__1__x__153446,Vvar__0__S__153445)
& ? [Vvar__2__y__153447] :
( t(Vvar__2__y__153447,Vvar__0__S__153445)
& Vvar__0___24Anonymous__153443 = c_24__prop__153467___24a4(Vvar__0___24Anonymous__153443,Vvar__0__S__153445,Vvar__1__x__153446,Vvar__2__y__153447) ) ) )
| ? [Vvar__0__x__153448] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__153448)
& ? [Vvar__1__y__153449] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__153449)
& Vvar__0___24Anonymous__153443 = c_24__prop__153468___24a3(Vvar__0___24Anonymous__153443,Vvar__0__x__153448,Vvar__1__y__153449) ) )
| ? [Vvar__0__x__153450] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__153450)
& ? [Vvar__1__s__153451] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__153451)
& Vvar__0___24Anonymous__153443 = c_24__prop__153469___24a3(Vvar__0___24Anonymous__153443,Vvar__0__x__153450,Vvar__1__s__153451) ) )
| Vvar__0___24Anonymous__153443 = c_24True
| Vvar__0___24Anonymous__153443 = c_24False
| ? [Vvar__0__P__153452] :
( cProp___24t(Vvar__0__P__153452)
& ? [Vvar__1__Q__153453] :
( cProp___24t(Vvar__1__Q__153453)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__153452)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__153453)
& Vvar__0___24Anonymous__153443 = c_24__prop__153470___24a3(Vvar__0___24Anonymous__153443,Vvar__0__P__153452,Vvar__1__Q__153453) ) )
| ? [Vvar__0__P__153456] :
( cProp___24t(Vvar__0__P__153456)
& ? [Vvar__1__Q__153457] :
( cProp___24t(Vvar__1__Q__153457)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__153456)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__153457)
& Vvar__0___24Anonymous__153443 = c_24__prop__153471___24a3(Vvar__0___24Anonymous__153443,Vvar__0__P__153456,Vvar__1__Q__153457) ) )
| ? [Vvar__0__P__153460] :
( cProp___24t(Vvar__0__P__153460)
& ? [Vvar__1__Q__153461] :
( cProp___24t(Vvar__1__Q__153461)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__153460)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__153461)
& Vvar__0___24Anonymous__153443 = c_24__prop__153472___24a3(Vvar__0___24Anonymous__153443,Vvar__0__P__153460,Vvar__1__Q__153461) ) )
| ? [Vvar__0__P__153465] :
( cProp___24t(Vvar__0__P__153465)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__153465)
& Vvar__0___24Anonymous__153443 = c_24__prop__153473___24a2(Vvar__0___24Anonymous__153443,Vvar__0__P__153465) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX54713] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX54713)
=> ( VX54713 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__54714] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__54714)
& ? [Vvar__1___24Anonymous__54715] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__54715)
& VX54713 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__54714,Vvar__1___24Anonymous__54715) ) )
| ? [Vvar__0___24Anonymous__54716] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__54716)
& ? [Vvar__1___24Anonymous__54717] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__54717)
& VX54713 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__54716,Vvar__1___24Anonymous__54717) ) )
| ? [Vvar__0___24Anonymous__54718] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__54718)
& ? [Vvar__1___24Anonymous__54719] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__54719)
& ? [Vvar__2___24Anonymous__54720] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__54720)
& VX54713 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__54718,Vvar__1___24Anonymous__54719,Vvar__2___24Anonymous__54720) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__153251,Vvar__1__env__153252,Vvar__2__env_27__153255,Vvar__3__x__153258] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__153251)
=> ( c_24__type__153279___24t(Vvar__0__fr__153251,Vvar__1__env__153252,Vvar__2__env_27__153255,Vvar__3__x__153258,Vvar__1__env__153252)
=> ( c_24__type__153288___24t(Vvar__0__fr__153251,Vvar__1__env__153252,Vvar__2__env_27__153255,Vvar__3__x__153258,Vvar__2__env_27__153255)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__153258)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__153251,Vvar__1__env__153252,Vvar__2__env_27__153255,Vvar__3__x__153258)
=> ( happ(Vvar__1__env__153252,Vvar__3__x__153258) = happ(Vvar__2__env_27__153255,Vvar__3__x__153258)
& happ(Vvar__1__env__153252,Vvar__3__x__153258) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__153255,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__153251,Vvar__3__x__153258))),happ(Vvar__2__env_27__153255,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__153251,Vvar__3__x__153258))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__153255,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__153251,Vvar__3__x__153258))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__153255,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__153251,Vvar__3__x__153258))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__41915,VX41916] :
( cType___24t(Vvar__0__C__41915)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,VX41916)
=> ( VX41916 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__41915)
| VX41916 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__41915)
| ? [Vvar__1___24Anonymous__41920] :
( t(Vvar__1___24Anonymous__41920,Vvar__0__C__41915)
& VX41916 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__41915,Vvar__1___24Anonymous__41920) )
| ? [Vvar__1___24Anonymous__41922] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__41922)
& VX41916 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__41915,Vvar__1___24Anonymous__41922) )
| ? [Vvar__1___24Anonymous__41924] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,Vvar__1___24Anonymous__41924)
& ? [Vvar__2___24Anonymous__41925] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,Vvar__2___24Anonymous__41925)
& VX41916 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__41915,Vvar__1___24Anonymous__41924,Vvar__2___24Anonymous__41925) ) )
| ? [Vvar__1___24Anonymous__41927] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,Vvar__1___24Anonymous__41927)
& ? [Vvar__2___24Anonymous__41928] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,Vvar__2___24Anonymous__41928)
& VX41916 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__41915,Vvar__1___24Anonymous__41927,Vvar__2___24Anonymous__41928) ) )
| ? [Vvar__1___24Anonymous__41930] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,Vvar__1___24Anonymous__41930)
& ? [Vvar__2___24Anonymous__41931] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,Vvar__2___24Anonymous__41931)
& VX41916 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__41915,Vvar__1___24Anonymous__41930,Vvar__2___24Anonymous__41931) ) )
| ? [Vvar__1___24Anonymous__41933] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,Vvar__1___24Anonymous__41933)
& VX41916 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__41915,Vvar__1___24Anonymous__41933) )
| ? [Vvar__1___24Anonymous__41935] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,Vvar__1___24Anonymous__41935)
& VX41916 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__41915,Vvar__1___24Anonymous__41935) )
| ? [Vvar__1___24Anonymous__41937] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,Vvar__1___24Anonymous__41937)
& ? [Vvar__2___24Anonymous__41938] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,Vvar__2___24Anonymous__41938)
& VX41916 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__41915,Vvar__1___24Anonymous__41937,Vvar__2___24Anonymous__41938) ) )
| ? [Vvar__1___24Anonymous__41940] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__41915,Vvar__1___24Anonymous__41940)
& ? [Vvar__2___24Anonymous__41941] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__41941)
& VX41916 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__41915,Vvar__1___24Anonymous__41940,Vvar__2___24Anonymous__41941) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__41125,Vvar__1__rO__41126,Vvar__2__rI__41127,Vvar__3__radd__41128,Vvar__4__rmul__41133,Vvar__5__rsub__41138,Vvar__6__ropp__41143,Vvar__7__rdiv__41146,Vvar__8__rinv__41151,Vvar__9__req__41154] :
( cType___24t(Vvar__0__R__41125)
=> ( t(Vvar__1__rO__41126,Vvar__0__R__41125)
=> ( t(Vvar__2__rI__41127,Vvar__0__R__41125)
=> ( c_24__type__41319___24t(Vvar__0__R__41125,Vvar__1__rO__41126,Vvar__2__rI__41127,Vvar__3__radd__41128,Vvar__4__rmul__41133,Vvar__5__rsub__41138,Vvar__6__ropp__41143,Vvar__7__rdiv__41146,Vvar__8__rinv__41151,Vvar__9__req__41154,Vvar__3__radd__41128)
=> ( c_24__type__41412___24t(Vvar__0__R__41125,Vvar__1__rO__41126,Vvar__2__rI__41127,Vvar__3__radd__41128,Vvar__4__rmul__41133,Vvar__5__rsub__41138,Vvar__6__ropp__41143,Vvar__7__rdiv__41146,Vvar__8__rinv__41151,Vvar__9__req__41154,Vvar__4__rmul__41133)
=> ( c_24__type__41505___24t(Vvar__0__R__41125,Vvar__1__rO__41126,Vvar__2__rI__41127,Vvar__3__radd__41128,Vvar__4__rmul__41133,Vvar__5__rsub__41138,Vvar__6__ropp__41143,Vvar__7__rdiv__41146,Vvar__8__rinv__41151,Vvar__9__req__41154,Vvar__5__rsub__41138)
=> ( c_24__type__41587___24t(Vvar__0__R__41125,Vvar__1__rO__41126,Vvar__2__rI__41127,Vvar__3__radd__41128,Vvar__4__rmul__41133,Vvar__5__rsub__41138,Vvar__6__ropp__41143,Vvar__7__rdiv__41146,Vvar__8__rinv__41151,Vvar__9__req__41154,Vvar__6__ropp__41143)
=> ( c_24__type__41680___24t(Vvar__0__R__41125,Vvar__1__rO__41126,Vvar__2__rI__41127,Vvar__3__radd__41128,Vvar__4__rmul__41133,Vvar__5__rsub__41138,Vvar__6__ropp__41143,Vvar__7__rdiv__41146,Vvar__8__rinv__41151,Vvar__9__req__41154,Vvar__7__rdiv__41146)
=> ( c_24__type__41762___24t(Vvar__0__R__41125,Vvar__1__rO__41126,Vvar__2__rI__41127,Vvar__3__radd__41128,Vvar__4__rmul__41133,Vvar__5__rsub__41138,Vvar__6__ropp__41143,Vvar__7__rdiv__41146,Vvar__8__rinv__41151,Vvar__9__req__41154,Vvar__8__rinv__41151)
=> ( c_24__type__41855___24t(Vvar__0__R__41125,Vvar__1__rO__41126,Vvar__2__rI__41127,Vvar__3__radd__41128,Vvar__4__rmul__41133,Vvar__5__rsub__41138,Vvar__6__ropp__41143,Vvar__7__rdiv__41146,Vvar__8__rinv__41151,Vvar__9__req__41154,Vvar__9__req__41154)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__41125,Vvar__1__rO__41126,Vvar__2__rI__41127,Vvar__3__radd__41128,Vvar__4__rmul__41133,Vvar__5__rsub__41138,Vvar__6__ropp__41143,Vvar__7__rdiv__41146,Vvar__8__rinv__41151,Vvar__9__req__41154)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__41125,Vvar__1__rO__41126,Vvar__2__rI__41127,Vvar__3__radd__41128,Vvar__4__rmul__41133,Vvar__5__rsub__41138,Vvar__6__ropp__41143,Vvar__9__req__41154)
& ~ p(happ(happ(Vvar__9__req__41154,Vvar__2__rI__41127),Vvar__1__rO__41126))
& ! [Vvar__var__var__var__var__var__var__12__p__41197__41199__41206__41208__41210__41212__41214] :
( t(Vvar__var__var__var__var__var__var__12__p__41197__41199__41206__41208__41210__41212__41214,Vvar__0__R__41125)
=> ! [Vvar__var__var__var__var__var__var__13__q__41198__41200__41207__41209__41211__41213__41215] :
( t(Vvar__var__var__var__var__var__var__13__q__41198__41200__41207__41209__41211__41213__41215,Vvar__0__R__41125)
=> p(happ(happ(Vvar__9__req__41154,happ(happ(Vvar__7__rdiv__41146,Vvar__var__var__var__var__var__var__12__p__41197__41199__41206__41208__41210__41212__41214),Vvar__var__var__var__var__var__var__13__q__41198__41200__41207__41209__41211__41213__41215)),happ(happ(Vvar__4__rmul__41133,Vvar__var__var__var__var__var__var__12__p__41197__41199__41206__41208__41210__41212__41214),happ(Vvar__8__rinv__41151,Vvar__var__var__var__var__var__var__13__q__41198__41200__41207__41209__41211__41213__41215)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__41202__41204__41216__41218__41220__41222__41224__41226] :
( t(Vvar__var__var__var__var__var__var__var__13__p__41202__41204__41216__41218__41220__41222__41224__41226,Vvar__0__R__41125)
=> ( ~ p(happ(happ(Vvar__9__req__41154,Vvar__var__var__var__var__var__var__var__13__p__41202__41204__41216__41218__41220__41222__41224__41226),Vvar__1__rO__41126))
=> p(happ(happ(Vvar__9__req__41154,happ(happ(Vvar__4__rmul__41133,happ(Vvar__8__rinv__41151,Vvar__var__var__var__var__var__var__var__13__p__41202__41204__41216__41218__41220__41222__41224__41226)),Vvar__var__var__var__var__var__var__var__13__p__41202__41204__41216__41218__41220__41222__41224__41226)),Vvar__2__rI__41127)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__42568,Vvar__1__rO__42569,Vvar__2__rI__42570,Vvar__3__radd__42571,Vvar__4__rmul__42576,Vvar__5__rsub__42581,Vvar__6__ropp__42586,Vvar__7__rdiv__42589,Vvar__8__rinv__42594,Vvar__9__req__42597] :
( cType___24t(Vvar__0__R__42568)
=> ( t(Vvar__1__rO__42569,Vvar__0__R__42568)
=> ( t(Vvar__2__rI__42570,Vvar__0__R__42568)
=> ( c_24__type__42762___24t(Vvar__0__R__42568,Vvar__1__rO__42569,Vvar__2__rI__42570,Vvar__3__radd__42571,Vvar__4__rmul__42576,Vvar__5__rsub__42581,Vvar__6__ropp__42586,Vvar__7__rdiv__42589,Vvar__8__rinv__42594,Vvar__9__req__42597,Vvar__3__radd__42571)
=> ( c_24__type__42855___24t(Vvar__0__R__42568,Vvar__1__rO__42569,Vvar__2__rI__42570,Vvar__3__radd__42571,Vvar__4__rmul__42576,Vvar__5__rsub__42581,Vvar__6__ropp__42586,Vvar__7__rdiv__42589,Vvar__8__rinv__42594,Vvar__9__req__42597,Vvar__4__rmul__42576)
=> ( c_24__type__42948___24t(Vvar__0__R__42568,Vvar__1__rO__42569,Vvar__2__rI__42570,Vvar__3__radd__42571,Vvar__4__rmul__42576,Vvar__5__rsub__42581,Vvar__6__ropp__42586,Vvar__7__rdiv__42589,Vvar__8__rinv__42594,Vvar__9__req__42597,Vvar__5__rsub__42581)
=> ( c_24__type__43030___24t(Vvar__0__R__42568,Vvar__1__rO__42569,Vvar__2__rI__42570,Vvar__3__radd__42571,Vvar__4__rmul__42576,Vvar__5__rsub__42581,Vvar__6__ropp__42586,Vvar__7__rdiv__42589,Vvar__8__rinv__42594,Vvar__9__req__42597,Vvar__6__ropp__42586)
=> ( c_24__type__43123___24t(Vvar__0__R__42568,Vvar__1__rO__42569,Vvar__2__rI__42570,Vvar__3__radd__42571,Vvar__4__rmul__42576,Vvar__5__rsub__42581,Vvar__6__ropp__42586,Vvar__7__rdiv__42589,Vvar__8__rinv__42594,Vvar__9__req__42597,Vvar__7__rdiv__42589)
=> ( c_24__type__43205___24t(Vvar__0__R__42568,Vvar__1__rO__42569,Vvar__2__rI__42570,Vvar__3__radd__42571,Vvar__4__rmul__42576,Vvar__5__rsub__42581,Vvar__6__ropp__42586,Vvar__7__rdiv__42589,Vvar__8__rinv__42594,Vvar__9__req__42597,Vvar__8__rinv__42594)
=> ( c_24__type__43298___24t(Vvar__0__R__42568,Vvar__1__rO__42569,Vvar__2__rI__42570,Vvar__3__radd__42571,Vvar__4__rmul__42576,Vvar__5__rsub__42581,Vvar__6__ropp__42586,Vvar__7__rdiv__42589,Vvar__8__rinv__42594,Vvar__9__req__42597,Vvar__9__req__42597)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__42568,Vvar__1__rO__42569,Vvar__2__rI__42570,Vvar__3__radd__42571,Vvar__4__rmul__42576,Vvar__5__rsub__42581,Vvar__6__ropp__42586,Vvar__7__rdiv__42589,Vvar__8__rinv__42594,Vvar__9__req__42597)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__42568,Vvar__1__rO__42569,Vvar__2__rI__42570,Vvar__3__radd__42571,Vvar__4__rmul__42576,Vvar__5__rsub__42581,Vvar__6__ropp__42586,Vvar__9__req__42597)
& ~ p(happ(happ(Vvar__9__req__42597,Vvar__2__rI__42570),Vvar__1__rO__42569))
& ! [Vvar__var__var__var__var__var__var__12__p__42640__42642__42649__42651__42653__42655__42657] :
( t(Vvar__var__var__var__var__var__var__12__p__42640__42642__42649__42651__42653__42655__42657,Vvar__0__R__42568)
=> ! [Vvar__var__var__var__var__var__var__13__q__42641__42643__42650__42652__42654__42656__42658] :
( t(Vvar__var__var__var__var__var__var__13__q__42641__42643__42650__42652__42654__42656__42658,Vvar__0__R__42568)
=> p(happ(happ(Vvar__9__req__42597,happ(happ(Vvar__7__rdiv__42589,Vvar__var__var__var__var__var__var__12__p__42640__42642__42649__42651__42653__42655__42657),Vvar__var__var__var__var__var__var__13__q__42641__42643__42650__42652__42654__42656__42658)),happ(happ(Vvar__4__rmul__42576,Vvar__var__var__var__var__var__var__12__p__42640__42642__42649__42651__42653__42655__42657),happ(Vvar__8__rinv__42594,Vvar__var__var__var__var__var__var__13__q__42641__42643__42650__42652__42654__42656__42658)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__42645__42647__42659__42661__42663__42665__42667__42669] :
( t(Vvar__var__var__var__var__var__var__var__13__p__42645__42647__42659__42661__42663__42665__42667__42669,Vvar__0__R__42568)
=> ( ~ p(happ(happ(Vvar__9__req__42597,Vvar__var__var__var__var__var__var__var__13__p__42645__42647__42659__42661__42663__42665__42667__42669),Vvar__1__rO__42569))
=> p(happ(happ(Vvar__9__req__42597,happ(happ(Vvar__4__rmul__42576,happ(Vvar__8__rinv__42594,Vvar__var__var__var__var__var__var__var__13__p__42645__42647__42659__42661__42663__42665__42667__42669)),Vvar__var__var__var__var__var__var__var__13__p__42645__42647__42659__42661__42663__42665__42667__42669)),Vvar__2__rI__42570)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__42242,VX42243] :
( cType___24t(Vvar__0__C__42242)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__42242,VX42243)
=> ? [Vvar__1__num__42245] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__42242,Vvar__1__num__42245)
& ? [Vvar__2__denum__42246] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__42242,Vvar__2__denum__42246)
& ? [Vvar__3__condition__42247] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__42242),Vvar__3__condition__42247)
& VX42243 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__42242,Vvar__1__num__42245,Vvar__2__denum__42246,Vvar__3__condition__42247) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__42531,VX42532] :
( cType___24t(Vvar__0__C__42531)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__42531,VX42532)
=> ? [Vvar__1__rsplit__left__42534] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__42531,Vvar__1__rsplit__left__42534)
& ? [Vvar__2__rsplit__common__42535] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__42531,Vvar__2__rsplit__common__42535)
& ? [Vvar__3__rsplit__right__42536] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__42531,Vvar__3__rsplit__right__42536)
& VX42532 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__42531,Vvar__1__rsplit__left__42534,Vvar__2__rsplit__common__42535,Vvar__3__rsplit__right__42536) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__152138,Vvar__1__rO__152139,Vvar__2__rI__152140,Vvar__3__radd__152141,Vvar__4__rmul__152146,Vvar__5__rdiv__152151,Vvar__6__rinv__152156,Vvar__7__req__152159] :
( cType___24t(Vvar__0__R__152138)
=> ( t(Vvar__1__rO__152139,Vvar__0__R__152138)
=> ( t(Vvar__2__rI__152140,Vvar__0__R__152138)
=> ( c_24__type__152286___24t(Vvar__0__R__152138,Vvar__1__rO__152139,Vvar__2__rI__152140,Vvar__3__radd__152141,Vvar__4__rmul__152146,Vvar__5__rdiv__152151,Vvar__6__rinv__152156,Vvar__7__req__152159,Vvar__3__radd__152141)
=> ( c_24__type__152349___24t(Vvar__0__R__152138,Vvar__1__rO__152139,Vvar__2__rI__152140,Vvar__3__radd__152141,Vvar__4__rmul__152146,Vvar__5__rdiv__152151,Vvar__6__rinv__152156,Vvar__7__req__152159,Vvar__4__rmul__152146)
=> ( c_24__type__152412___24t(Vvar__0__R__152138,Vvar__1__rO__152139,Vvar__2__rI__152140,Vvar__3__radd__152141,Vvar__4__rmul__152146,Vvar__5__rdiv__152151,Vvar__6__rinv__152156,Vvar__7__req__152159,Vvar__5__rdiv__152151)
=> ( c_24__type__152466___24t(Vvar__0__R__152138,Vvar__1__rO__152139,Vvar__2__rI__152140,Vvar__3__radd__152141,Vvar__4__rmul__152146,Vvar__5__rdiv__152151,Vvar__6__rinv__152156,Vvar__7__req__152159,Vvar__6__rinv__152156)
=> ( c_24__type__152529___24t(Vvar__0__R__152138,Vvar__1__rO__152139,Vvar__2__rI__152140,Vvar__3__radd__152141,Vvar__4__rmul__152146,Vvar__5__rdiv__152151,Vvar__6__rinv__152156,Vvar__7__req__152159,Vvar__7__req__152159)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__152138,Vvar__1__rO__152139,Vvar__2__rI__152140,Vvar__3__radd__152141,Vvar__4__rmul__152146,Vvar__5__rdiv__152151,Vvar__6__rinv__152156,Vvar__7__req__152159)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__152138,Vvar__1__rO__152139,Vvar__2__rI__152140,Vvar__3__radd__152141,Vvar__4__rmul__152146,Vvar__7__req__152159)
& ~ p(happ(happ(Vvar__7__req__152159,Vvar__2__rI__152140),Vvar__1__rO__152139))
& ! [Vvar__var__var__var__var__var__var__10__p__152194__152196__152203__152205__152207__152209__152211] :
( t(Vvar__var__var__var__var__var__var__10__p__152194__152196__152203__152205__152207__152209__152211,Vvar__0__R__152138)
=> ! [Vvar__var__var__var__var__var__var__11__q__152195__152197__152204__152206__152208__152210__152212] :
( t(Vvar__var__var__var__var__var__var__11__q__152195__152197__152204__152206__152208__152210__152212,Vvar__0__R__152138)
=> p(happ(happ(Vvar__7__req__152159,happ(happ(Vvar__5__rdiv__152151,Vvar__var__var__var__var__var__var__10__p__152194__152196__152203__152205__152207__152209__152211),Vvar__var__var__var__var__var__var__11__q__152195__152197__152204__152206__152208__152210__152212)),happ(happ(Vvar__4__rmul__152146,Vvar__var__var__var__var__var__var__10__p__152194__152196__152203__152205__152207__152209__152211),happ(Vvar__6__rinv__152156,Vvar__var__var__var__var__var__var__11__q__152195__152197__152204__152206__152208__152210__152212)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__152199__152201__152213__152215__152217__152219__152221__152223] :
( t(Vvar__var__var__var__var__var__var__var__11__p__152199__152201__152213__152215__152217__152219__152221__152223,Vvar__0__R__152138)
=> ( ~ p(happ(happ(Vvar__7__req__152159,Vvar__var__var__var__var__var__var__var__11__p__152199__152201__152213__152215__152217__152219__152221__152223),Vvar__1__rO__152139))
=> p(happ(happ(Vvar__7__req__152159,happ(happ(Vvar__4__rmul__152146,happ(Vvar__6__rinv__152156,Vvar__var__var__var__var__var__var__var__11__p__152199__152201__152213__152215__152217__152219__152221__152223)),Vvar__var__var__var__var__var__var__var__11__p__152199__152201__152213__152215__152217__152219__152221__152223)),Vvar__2__rI__152140)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
! [VX152535] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX152535)
=> ? [Vvar__0__hypo__type__152536] :
( cType___24t(Vvar__0__hypo__type__152536)
& ? [Vvar__1__hypo__proof__152537] :
( t(Vvar__1__hypo__proof__152537,Vvar__0__hypo__type__152536)
& VX152535 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__152536,Vvar__1__hypo__proof__152537) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX32836] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX32836)
=> ( VX32836 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__32837] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32837)
& ? [Vvar__1___24Anonymous__32838] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__32838)
& VX32836 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__32837,Vvar__1___24Anonymous__32838) ) )
| ? [Vvar__0___24Anonymous__32839] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32839)
& ? [Vvar__1___24Anonymous__32840] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__32840)
& VX32836 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__32839,Vvar__1___24Anonymous__32840) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__32857,VX32858] :
( cType___24t(Vvar__0__C__32857)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32857,VX32858)
=> ( VX32858 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__32857)
| VX32858 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__32857)
| ? [Vvar__1___24Anonymous__32862] :
( t(Vvar__1___24Anonymous__32862,Vvar__0__C__32857)
& VX32858 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__32857,Vvar__1___24Anonymous__32862) )
| ? [Vvar__1___24Anonymous__32864] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32864)
& VX32858 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__32857,Vvar__1___24Anonymous__32864) )
| ? [Vvar__1___24Anonymous__32866] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32857,Vvar__1___24Anonymous__32866)
& ? [Vvar__2___24Anonymous__32867] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32857,Vvar__2___24Anonymous__32867)
& VX32858 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__32857,Vvar__1___24Anonymous__32866,Vvar__2___24Anonymous__32867) ) )
| ? [Vvar__1___24Anonymous__32869] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32857,Vvar__1___24Anonymous__32869)
& ? [Vvar__2___24Anonymous__32870] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32857,Vvar__2___24Anonymous__32870)
& VX32858 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__32857,Vvar__1___24Anonymous__32869,Vvar__2___24Anonymous__32870) ) )
| ? [Vvar__1___24Anonymous__32872] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32857,Vvar__1___24Anonymous__32872)
& ? [Vvar__2___24Anonymous__32873] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32857,Vvar__2___24Anonymous__32873)
& VX32858 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__32857,Vvar__1___24Anonymous__32872,Vvar__2___24Anonymous__32873) ) )
| ? [Vvar__1___24Anonymous__32875] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32857,Vvar__1___24Anonymous__32875)
& VX32858 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__32857,Vvar__1___24Anonymous__32875) )
| ? [Vvar__1___24Anonymous__32877] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32857,Vvar__1___24Anonymous__32877)
& ? [Vvar__2___24Anonymous__32878] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__32878)
& VX32858 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__32857,Vvar__1___24Anonymous__32877,Vvar__2___24Anonymous__32878) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__32657,VX32658] :
( cType___24t(Vvar__0__C__32657)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__32657,VX32658)
=> ( ? [Vvar__1___24Anonymous__32660] :
( t(Vvar__1___24Anonymous__32660,Vvar__0__C__32657)
& VX32658 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__32657,Vvar__1___24Anonymous__32660) )
| ? [Vvar__1___24Anonymous__32662] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32662)
& ? [Vvar__2___24Anonymous__32663] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__32657,Vvar__2___24Anonymous__32663)
& VX32658 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__32657,Vvar__1___24Anonymous__32662,Vvar__2___24Anonymous__32663) ) )
| ? [Vvar__1___24Anonymous__32665] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__32657,Vvar__1___24Anonymous__32665)
& ? [Vvar__2___24Anonymous__32666] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__32666)
& ? [Vvar__3___24Anonymous__32667] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__32657,Vvar__3___24Anonymous__32667)
& VX32658 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__32657,Vvar__1___24Anonymous__32665,Vvar__2___24Anonymous__32666,Vvar__3___24Anonymous__32667) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__50336,Vvar__1__rO__50337,Vvar__2__rI__50338,Vvar__3__radd__50339,Vvar__4__rmul__50344,Vvar__5__rsub__50349,Vvar__6__ropp__50354,Vvar__7__req__50357] :
( cType___24t(Vvar__0__R__50336)
=> ( t(Vvar__1__rO__50337,Vvar__0__R__50336)
=> ( t(Vvar__2__rI__50338,Vvar__0__R__50336)
=> ( c_24__type__50585___24t(Vvar__0__R__50336,Vvar__1__rO__50337,Vvar__2__rI__50338,Vvar__3__radd__50339,Vvar__4__rmul__50344,Vvar__5__rsub__50349,Vvar__6__ropp__50354,Vvar__7__req__50357,Vvar__3__radd__50339)
=> ( c_24__type__50648___24t(Vvar__0__R__50336,Vvar__1__rO__50337,Vvar__2__rI__50338,Vvar__3__radd__50339,Vvar__4__rmul__50344,Vvar__5__rsub__50349,Vvar__6__ropp__50354,Vvar__7__req__50357,Vvar__4__rmul__50344)
=> ( c_24__type__50711___24t(Vvar__0__R__50336,Vvar__1__rO__50337,Vvar__2__rI__50338,Vvar__3__radd__50339,Vvar__4__rmul__50344,Vvar__5__rsub__50349,Vvar__6__ropp__50354,Vvar__7__req__50357,Vvar__5__rsub__50349)
=> ( c_24__type__50765___24t(Vvar__0__R__50336,Vvar__1__rO__50337,Vvar__2__rI__50338,Vvar__3__radd__50339,Vvar__4__rmul__50344,Vvar__5__rsub__50349,Vvar__6__ropp__50354,Vvar__7__req__50357,Vvar__6__ropp__50354)
=> ( c_24__type__50828___24t(Vvar__0__R__50336,Vvar__1__rO__50337,Vvar__2__rI__50338,Vvar__3__radd__50339,Vvar__4__rmul__50344,Vvar__5__rsub__50349,Vvar__6__ropp__50354,Vvar__7__req__50357,Vvar__7__req__50357)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__50336,Vvar__1__rO__50337,Vvar__2__rI__50338,Vvar__3__radd__50339,Vvar__4__rmul__50344,Vvar__5__rsub__50349,Vvar__6__ropp__50354,Vvar__7__req__50357)
=> ( ! [Vvar__var__var__var__var__var__8__x__50390__50391__50444__50445__50446__50447] :
( t(Vvar__var__var__var__var__var__8__x__50390__50391__50444__50445__50446__50447,Vvar__0__R__50336)
=> p(happ(happ(Vvar__7__req__50357,happ(happ(Vvar__3__radd__50339,Vvar__1__rO__50337),Vvar__var__var__var__var__var__8__x__50390__50391__50444__50445__50446__50447)),Vvar__var__var__var__var__var__8__x__50390__50391__50444__50445__50446__50447)) )
& ! [Vvar__var__var__var__var__9__x__50393__50395__50448__50450__50452] :
( t(Vvar__var__var__var__var__9__x__50393__50395__50448__50450__50452,Vvar__0__R__50336)
=> ! [Vvar__var__var__var__var__10__y__50394__50396__50449__50451__50453] :
( t(Vvar__var__var__var__var__10__y__50394__50396__50449__50451__50453,Vvar__0__R__50336)
=> p(happ(happ(Vvar__7__req__50357,happ(happ(Vvar__3__radd__50339,Vvar__var__var__var__var__9__x__50393__50395__50448__50450__50452),Vvar__var__var__var__var__10__y__50394__50396__50449__50451__50453)),happ(happ(Vvar__3__radd__50339,Vvar__var__var__var__var__10__y__50394__50396__50449__50451__50453),Vvar__var__var__var__var__9__x__50393__50395__50448__50450__50452))) ) )
& ! [Vvar__var__var__var__var__10__x__50398__50401__50454__50457__50460] :
( t(Vvar__var__var__var__var__10__x__50398__50401__50454__50457__50460,Vvar__0__R__50336)
=> ! [Vvar__var__var__var__var__11__y__50399__50402__50455__50458__50461] :
( t(Vvar__var__var__var__var__11__y__50399__50402__50455__50458__50461,Vvar__0__R__50336)
=> ! [Vvar__var__var__var__var__12__z__50400__50403__50456__50459__50462] :
( t(Vvar__var__var__var__var__12__z__50400__50403__50456__50459__50462,Vvar__0__R__50336)
=> p(happ(happ(Vvar__7__req__50357,happ(happ(Vvar__3__radd__50339,Vvar__var__var__var__var__10__x__50398__50401__50454__50457__50460),happ(happ(Vvar__3__radd__50339,Vvar__var__var__var__var__11__y__50399__50402__50455__50458__50461),Vvar__var__var__var__var__12__z__50400__50403__50456__50459__50462))),happ(happ(Vvar__3__radd__50339,happ(happ(Vvar__3__radd__50339,Vvar__var__var__var__var__10__x__50398__50401__50454__50457__50460),Vvar__var__var__var__var__11__y__50399__50402__50455__50458__50461)),Vvar__var__var__var__var__12__z__50400__50403__50456__50459__50462))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__50405__50406__50463__50464__50465__50466] :
( t(Vvar__var__var__var__var__var__11__x__50405__50406__50463__50464__50465__50466,Vvar__0__R__50336)
=> p(happ(happ(Vvar__7__req__50357,happ(happ(Vvar__4__rmul__50344,Vvar__2__rI__50338),Vvar__var__var__var__var__var__11__x__50405__50406__50463__50464__50465__50466)),Vvar__var__var__var__var__var__11__x__50405__50406__50463__50464__50465__50466)) )
& ! [Vvar__var__var__var__var__var__12__x__50408__50409__50467__50468__50469__50470] :
( t(Vvar__var__var__var__var__var__12__x__50408__50409__50467__50468__50469__50470,Vvar__0__R__50336)
=> p(happ(happ(Vvar__7__req__50357,happ(happ(Vvar__4__rmul__50344,Vvar__1__rO__50337),Vvar__var__var__var__var__var__12__x__50408__50409__50467__50468__50469__50470)),Vvar__1__rO__50337)) )
& ! [Vvar__var__var__var__var__13__x__50411__50413__50471__50473__50475] :
( t(Vvar__var__var__var__var__13__x__50411__50413__50471__50473__50475,Vvar__0__R__50336)
=> ! [Vvar__var__var__var__var__14__y__50412__50414__50472__50474__50476] :
( t(Vvar__var__var__var__var__14__y__50412__50414__50472__50474__50476,Vvar__0__R__50336)
=> p(happ(happ(Vvar__7__req__50357,happ(happ(Vvar__4__rmul__50344,Vvar__var__var__var__var__13__x__50411__50413__50471__50473__50475),Vvar__var__var__var__var__14__y__50412__50414__50472__50474__50476)),happ(happ(Vvar__4__rmul__50344,Vvar__var__var__var__var__14__y__50412__50414__50472__50474__50476),Vvar__var__var__var__var__13__x__50411__50413__50471__50473__50475))) ) )
& ! [Vvar__var__var__var__var__14__x__50416__50419__50477__50480__50483] :
( t(Vvar__var__var__var__var__14__x__50416__50419__50477__50480__50483,Vvar__0__R__50336)
=> ! [Vvar__var__var__var__var__15__y__50417__50420__50478__50481__50484] :
( t(Vvar__var__var__var__var__15__y__50417__50420__50478__50481__50484,Vvar__0__R__50336)
=> ! [Vvar__var__var__var__var__16__z__50418__50421__50479__50482__50485] :
( t(Vvar__var__var__var__var__16__z__50418__50421__50479__50482__50485,Vvar__0__R__50336)
=> p(happ(happ(Vvar__7__req__50357,happ(happ(Vvar__4__rmul__50344,Vvar__var__var__var__var__14__x__50416__50419__50477__50480__50483),happ(happ(Vvar__4__rmul__50344,Vvar__var__var__var__var__15__y__50417__50420__50478__50481__50484),Vvar__var__var__var__var__16__z__50418__50421__50479__50482__50485))),happ(happ(Vvar__4__rmul__50344,happ(happ(Vvar__4__rmul__50344,Vvar__var__var__var__var__14__x__50416__50419__50477__50480__50483),Vvar__var__var__var__var__15__y__50417__50420__50478__50481__50484)),Vvar__var__var__var__var__16__z__50418__50421__50479__50482__50485))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__50423__50426__50486__50489__50492__50495] :
( t(Vvar__var__var__var__var__var__15__x__50423__50426__50486__50489__50492__50495,Vvar__0__R__50336)
=> ! [Vvar__var__var__var__var__var__16__y__50424__50427__50487__50490__50493__50496] :
( t(Vvar__var__var__var__var__var__16__y__50424__50427__50487__50490__50493__50496,Vvar__0__R__50336)
=> ! [Vvar__var__var__var__var__var__17__z__50425__50428__50488__50491__50494__50497] :
( t(Vvar__var__var__var__var__var__17__z__50425__50428__50488__50491__50494__50497,Vvar__0__R__50336)
=> p(happ(happ(Vvar__7__req__50357,happ(happ(Vvar__4__rmul__50344,happ(happ(Vvar__3__radd__50339,Vvar__var__var__var__var__var__15__x__50423__50426__50486__50489__50492__50495),Vvar__var__var__var__var__var__16__y__50424__50427__50487__50490__50493__50496)),Vvar__var__var__var__var__var__17__z__50425__50428__50488__50491__50494__50497)),happ(happ(Vvar__3__radd__50339,happ(happ(Vvar__4__rmul__50344,Vvar__var__var__var__var__var__15__x__50423__50426__50486__50489__50492__50495),Vvar__var__var__var__var__var__17__z__50425__50428__50488__50491__50494__50497)),happ(happ(Vvar__4__rmul__50344,Vvar__var__var__var__var__var__16__y__50424__50427__50487__50490__50493__50496),Vvar__var__var__var__var__var__17__z__50425__50428__50488__50491__50494__50497)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__50430__50432__50498__50500__50502__50504] :
( t(Vvar__var__var__var__var__var__16__x__50430__50432__50498__50500__50502__50504,Vvar__0__R__50336)
=> ! [Vvar__var__var__var__var__var__17__y__50431__50433__50499__50501__50503__50505] :
( t(Vvar__var__var__var__var__var__17__y__50431__50433__50499__50501__50503__50505,Vvar__0__R__50336)
=> p(happ(happ(Vvar__7__req__50357,happ(Vvar__6__ropp__50354,happ(happ(Vvar__4__rmul__50344,Vvar__var__var__var__var__var__16__x__50430__50432__50498__50500__50502__50504),Vvar__var__var__var__var__var__17__y__50431__50433__50499__50501__50503__50505))),happ(happ(Vvar__4__rmul__50344,happ(Vvar__6__ropp__50354,Vvar__var__var__var__var__var__16__x__50430__50432__50498__50500__50502__50504)),Vvar__var__var__var__var__var__17__y__50431__50433__50499__50501__50503__50505))) ) )
& ! [Vvar__var__var__var__var__var__17__x__50435__50437__50506__50508__50510__50512] :
( t(Vvar__var__var__var__var__var__17__x__50435__50437__50506__50508__50510__50512,Vvar__0__R__50336)
=> ! [Vvar__var__var__var__var__var__18__y__50436__50438__50507__50509__50511__50513] :
( t(Vvar__var__var__var__var__var__18__y__50436__50438__50507__50509__50511__50513,Vvar__0__R__50336)
=> p(happ(happ(Vvar__7__req__50357,happ(Vvar__6__ropp__50354,happ(happ(Vvar__3__radd__50339,Vvar__var__var__var__var__var__17__x__50435__50437__50506__50508__50510__50512),Vvar__var__var__var__var__var__18__y__50436__50438__50507__50509__50511__50513))),happ(happ(Vvar__3__radd__50339,happ(Vvar__6__ropp__50354,Vvar__var__var__var__var__var__17__x__50435__50437__50506__50508__50510__50512)),happ(Vvar__6__ropp__50354,Vvar__var__var__var__var__var__18__y__50436__50438__50507__50509__50511__50513)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__50440__50442__50514__50516__50518__50520__50522] :
( t(Vvar__var__var__var__var__var__var__18__x__50440__50442__50514__50516__50518__50520__50522,Vvar__0__R__50336)
=> ! [Vvar__var__var__var__var__var__var__19__y__50441__50443__50515__50517__50519__50521__50523] :
( t(Vvar__var__var__var__var__var__var__19__y__50441__50443__50515__50517__50519__50521__50523,Vvar__0__R__50336)
=> p(happ(happ(Vvar__7__req__50357,happ(happ(Vvar__5__rsub__50349,Vvar__var__var__var__var__var__var__18__x__50440__50442__50514__50516__50518__50520__50522),Vvar__var__var__var__var__var__var__19__y__50441__50443__50515__50517__50519__50521__50523)),happ(happ(Vvar__3__radd__50339,Vvar__var__var__var__var__var__var__18__x__50440__50442__50514__50516__50518__50520__50522),happ(Vvar__6__ropp__50354,Vvar__var__var__var__var__var__var__19__y__50441__50443__50515__50517__50519__50521__50523)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__52903,Vvar__1__req__52904,Vvar__2__C__52909,Vvar__3__cadd__52910,Vvar__4__cmul__52915,Vvar__5__phi__52920,Vvar__6__cdiv__52923] :
( cType___24t(Vvar__0__R__52903)
=> ( c_24__type__53043___24t(Vvar__0__R__52903,Vvar__1__req__52904,Vvar__2__C__52909,Vvar__3__cadd__52910,Vvar__4__cmul__52915,Vvar__5__phi__52920,Vvar__6__cdiv__52923,Vvar__1__req__52904)
=> ( cType___24t(Vvar__2__C__52909)
=> ( c_24__type__53093___24t(Vvar__0__R__52903,Vvar__1__req__52904,Vvar__2__C__52909,Vvar__3__cadd__52910,Vvar__4__cmul__52915,Vvar__5__phi__52920,Vvar__6__cdiv__52923,Vvar__3__cadd__52910)
=> ( c_24__type__53143___24t(Vvar__0__R__52903,Vvar__1__req__52904,Vvar__2__C__52909,Vvar__3__cadd__52910,Vvar__4__cmul__52915,Vvar__5__phi__52920,Vvar__6__cdiv__52923,Vvar__4__cmul__52915)
=> ( c_24__type__53185___24t(Vvar__0__R__52903,Vvar__1__req__52904,Vvar__2__C__52909,Vvar__3__cadd__52910,Vvar__4__cmul__52915,Vvar__5__phi__52920,Vvar__6__cdiv__52923,Vvar__5__phi__52920)
=> ( c_24__type__53235___24t(Vvar__0__R__52903,Vvar__1__req__52904,Vvar__2__C__52909,Vvar__3__cadd__52910,Vvar__4__cmul__52915,Vvar__5__phi__52920,Vvar__6__cdiv__52923,Vvar__6__cdiv__52923)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__52903,Vvar__1__req__52904,Vvar__2__C__52909,Vvar__3__cadd__52910,Vvar__4__cmul__52915,Vvar__5__phi__52920,Vvar__6__cdiv__52923)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__52955__52960__52965__52970__52975__52980__52985__52990] :
( t(Vvar__var__var__var__var__var__var__var__7__a__52955__52960__52965__52970__52975__52980__52985__52990,Vvar__2__C__52909)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__52956__52961__52966__52971__52976__52981__52986__52991] :
( t(Vvar__var__var__var__var__var__var__var__8__b__52956__52961__52966__52971__52976__52981__52986__52991,Vvar__2__C__52909)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2453298___24a9(Vvar__0__R__52903,Vvar__1__req__52904,Vvar__2__C__52909,Vvar__3__cadd__52910,Vvar__4__cmul__52915,Vvar__5__phi__52920,Vvar__6__cdiv__52923,Vvar__var__var__var__var__var__var__var__7__a__52955__52960__52965__52970__52975__52980__52985__52990,Vvar__var__var__var__var__var__var__var__8__b__52956__52961__52966__52971__52976__52981__52986__52991) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__53318,Vvar__1__rI__53319,Vvar__2__rmul__53320,Vvar__3__req__53325,Vvar__4__Cpow__53330,Vvar__5__Cp__phi__53331,Vvar__6__rpow__53334] :
( cType___24t(Vvar__0__R__53318)
=> ( t(Vvar__1__rI__53319,Vvar__0__R__53318)
=> ( c_24__type__53420___24t(Vvar__0__R__53318,Vvar__1__rI__53319,Vvar__2__rmul__53320,Vvar__3__req__53325,Vvar__4__Cpow__53330,Vvar__5__Cp__phi__53331,Vvar__6__rpow__53334,Vvar__2__rmul__53320)
=> ( c_24__type__53464___24t(Vvar__0__R__53318,Vvar__1__rI__53319,Vvar__2__rmul__53320,Vvar__3__req__53325,Vvar__4__Cpow__53330,Vvar__5__Cp__phi__53331,Vvar__6__rpow__53334,Vvar__3__req__53325)
=> ( cType___24t(Vvar__4__Cpow__53330)
=> ( c_24__type__53500___24t(Vvar__0__R__53318,Vvar__1__rI__53319,Vvar__2__rmul__53320,Vvar__3__req__53325,Vvar__4__Cpow__53330,Vvar__5__Cp__phi__53331,Vvar__6__rpow__53334,Vvar__5__Cp__phi__53331)
=> ( c_24__type__53544___24t(Vvar__0__R__53318,Vvar__1__rI__53319,Vvar__2__rmul__53320,Vvar__3__req__53325,Vvar__4__Cpow__53330,Vvar__5__Cp__phi__53331,Vvar__6__rpow__53334,Vvar__6__rpow__53334)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__53318,Vvar__1__rI__53319,Vvar__2__rmul__53320,Vvar__3__req__53325,Vvar__4__Cpow__53330,Vvar__5__Cp__phi__53331,Vvar__6__rpow__53334)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__53362__53364__53366__53368__53370__53372__53374__53376] :
( t(Vvar__var__var__var__var__var__var__var__7__r__53362__53364__53366__53368__53370__53372__53374__53376,Vvar__0__R__53318)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__53363__53365__53367__53369__53371__53373__53375__53377] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__53363__53365__53367__53369__53371__53373__53375__53377)
=> p(happ(happ(Vvar__3__req__53325,happ(happ(Vvar__6__rpow__53334,Vvar__var__var__var__var__var__var__var__7__r__53362__53364__53366__53368__53370__53372__53374__53376),happ(Vvar__5__Cp__phi__53331,Vvar__var__var__var__var__var__var__var__8__n__53363__53365__53367__53369__53371__53373__53375__53377))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__53318,Vvar__1__rI__53319,Vvar__2__rmul__53320,Vvar__var__var__var__var__var__var__var__7__r__53362__53364__53366__53368__53370__53372__53374__53376,Vvar__var__var__var__var__var__var__var__8__n__53363__53365__53367__53369__53371__53373__53375__53377))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__37959,Vvar__1__radd__37960,Vvar__2__rmul__37965,Vvar__3__ropp__37970,Vvar__4__req__37973] :
( cType___24t(Vvar__0__R__37959)
=> ( c_24__type__38064___24t(Vvar__0__R__37959,Vvar__1__radd__37960,Vvar__2__rmul__37965,Vvar__3__ropp__37970,Vvar__4__req__37973,Vvar__1__radd__37960)
=> ( c_24__type__38094___24t(Vvar__0__R__37959,Vvar__1__radd__37960,Vvar__2__rmul__37965,Vvar__3__ropp__37970,Vvar__4__req__37973,Vvar__2__rmul__37965)
=> ( c_24__type__38118___24t(Vvar__0__R__37959,Vvar__1__radd__37960,Vvar__2__rmul__37965,Vvar__3__ropp__37970,Vvar__4__req__37973,Vvar__3__ropp__37970)
=> ( c_24__type__38148___24t(Vvar__0__R__37959,Vvar__1__radd__37960,Vvar__2__rmul__37965,Vvar__3__ropp__37970,Vvar__4__req__37973,Vvar__4__req__37973)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__37959,Vvar__1__radd__37960,Vvar__2__rmul__37965,Vvar__3__ropp__37970,Vvar__4__req__37973)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__38178___24a5(Vvar__0__R__37959,Vvar__1__radd__37960,Vvar__2__rmul__37965,Vvar__3__ropp__37970,Vvar__4__req__37973),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__37959,c_24__type__38202___24a5(Vvar__0__R__37959,Vvar__1__radd__37960,Vvar__2__rmul__37965,Vvar__3__ropp__37970,Vvar__4__req__37973),Vvar__4__req__37973,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__37959,Vvar__0__R__37959,Vvar__4__req__37973,Vvar__4__req__37973)),Vvar__1__radd__37960)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__38235___24a5(Vvar__0__R__37959,Vvar__1__radd__37960,Vvar__2__rmul__37965,Vvar__3__ropp__37970,Vvar__4__req__37973),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__37959,c_24__type__38259___24a5(Vvar__0__R__37959,Vvar__1__radd__37960,Vvar__2__rmul__37965,Vvar__3__ropp__37970,Vvar__4__req__37973),Vvar__4__req__37973,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__37959,Vvar__0__R__37959,Vvar__4__req__37973,Vvar__4__req__37973)),Vvar__2__rmul__37965)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__38286___24a5(Vvar__0__R__37959,Vvar__1__radd__37960,Vvar__2__rmul__37965,Vvar__3__ropp__37970,Vvar__4__req__37973),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__37959,Vvar__0__R__37959,Vvar__4__req__37973,Vvar__4__req__37973),Vvar__3__ropp__37970)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX34361] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX34361)
=> ( VX34361 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__34362] :
( cType___24t(Vvar__0__R__34362)
& ? [Vvar__1__req__34363] :
( c_24__type__32418___24t(Vvar__0__R__34362,Vvar__1__req__34363)
& ? [Vvar__2__reqb__34368] :
( c_24__type__32372___24t(Vvar__0__R__34362,Vvar__2__reqb__34368)
& ! [Vvar__var__3__x__34374__34377] :
( t(Vvar__var__3__x__34374__34377,Vvar__0__R__34362)
=> ! [Vvar__var__4__y__34375__34378] :
( t(Vvar__var__4__y__34375__34378,Vvar__0__R__34362)
=> ( happ(happ(Vvar__2__reqb__34368,Vvar__var__3__x__34374__34377),Vvar__var__4__y__34375__34378) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__34363,Vvar__var__3__x__34374__34377),Vvar__var__4__y__34375__34378)) ) ) )
& VX34361 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34362,Vvar__1__req__34363,Vvar__2__reqb__34368) ) ) )
| ? [Vvar__0__R__34380] :
( cType___24t(Vvar__0__R__34380)
& ? [Vvar__1__rO__34381] :
( t(Vvar__1__rO__34381,Vvar__0__R__34380)
& ? [Vvar__2__rI__34382] :
( t(Vvar__2__rI__34382,Vvar__0__R__34380)
& ? [Vvar__3__radd__34383] :
( c_24__type__32404___24t(Vvar__0__R__34380,Vvar__3__radd__34383)
& ? [Vvar__4__rmul__34388] :
( c_24__type__32404___24t(Vvar__0__R__34380,Vvar__4__rmul__34388)
& ? [Vvar__5__rsub__34393] :
( c_24__type__32404___24t(Vvar__0__R__34380,Vvar__5__rsub__34393)
& ? [Vvar__6__ropp__34398] :
( c_24__type__32413___24t(Vvar__0__R__34380,Vvar__6__ropp__34398)
& ? [Vvar__7__req__34401] :
( c_24__type__32418___24t(Vvar__0__R__34380,Vvar__7__req__34401)
& ? [Vvar__8__C__34406] :
( cType___24t(Vvar__8__C__34406)
& ? [Vvar__9__cO__34407] :
( t(Vvar__9__cO__34407,Vvar__8__C__34406)
& ? [Vvar__10__cI__34408] :
( t(Vvar__10__cI__34408,Vvar__8__C__34406)
& ? [Vvar__11__cadd__34409] :
( c_24__type__32425___24t(Vvar__0__R__34380,Vvar__8__C__34406,Vvar__11__cadd__34409)
& ? [Vvar__12__cmul__34414] :
( c_24__type__32425___24t(Vvar__0__R__34380,Vvar__8__C__34406,Vvar__12__cmul__34414)
& ? [Vvar__13__csub__34419] :
( c_24__type__32425___24t(Vvar__0__R__34380,Vvar__8__C__34406,Vvar__13__csub__34419)
& ? [Vvar__14__copp__34424] :
( c_24__type__32439___24t(Vvar__0__R__34380,Vvar__8__C__34406,Vvar__14__copp__34424)
& ? [Vvar__15__ceqb__34427] :
( c_24__type__32446___24t(Vvar__0__R__34380,Vvar__8__C__34406,Vvar__15__ceqb__34427)
& ? [Vvar__16__phi__34432] :
( c_24__type__32450___24t(Vvar__0__R__34380,Vvar__8__C__34406,Vvar__16__phi__34432)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__34380,Vvar__1__rO__34381,Vvar__2__rI__34382,Vvar__3__radd__34383,Vvar__4__rmul__34388,Vvar__5__rsub__34393,Vvar__6__ropp__34398,Vvar__7__req__34401,Vvar__8__C__34406,Vvar__9__cO__34407,Vvar__10__cI__34408,Vvar__11__cadd__34409,Vvar__12__cmul__34414,Vvar__13__csub__34419,Vvar__14__copp__34424,Vvar__15__ceqb__34427,Vvar__16__phi__34432)
& VX34361 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__34380,Vvar__1__rO__34381,Vvar__2__rI__34382,Vvar__3__radd__34383,Vvar__4__rmul__34388,Vvar__5__rsub__34393,Vvar__6__ropp__34398,Vvar__7__req__34401,Vvar__8__C__34406,Vvar__9__cO__34407,Vvar__10__cI__34408,Vvar__11__cadd__34409,Vvar__12__cmul__34414,Vvar__13__csub__34419,Vvar__14__copp__34424,Vvar__15__ceqb__34427,Vvar__16__phi__34432) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341] :
( cType___24t(Vvar__0__R__38289)
=> ( t(Vvar__1__rO__38290,Vvar__0__R__38289)
=> ( t(Vvar__2__rI__38291,Vvar__0__R__38289)
=> ( c_24__type__38685___24t(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341,Vvar__3__radd__38292)
=> ( c_24__type__38898___24t(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341,Vvar__4__rmul__38297)
=> ( c_24__type__39111___24t(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341,Vvar__5__rsub__38302)
=> ( c_24__type__39306___24t(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341,Vvar__6__ropp__38307)
=> ( c_24__type__39519___24t(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341,Vvar__7__req__38310)
=> ( cType___24t(Vvar__8__C__38315)
=> ( t(Vvar__9__cO__38316,Vvar__8__C__38315)
=> ( t(Vvar__10__cI__38317,Vvar__8__C__38315)
=> ( c_24__type__39732___24t(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341,Vvar__11__cadd__38318)
=> ( c_24__type__39945___24t(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341,Vvar__12__cmul__38323)
=> ( c_24__type__40158___24t(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341,Vvar__13__csub__38328)
=> ( c_24__type__40353___24t(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341,Vvar__14__copp__38333)
=> ( c_24__type__40566___24t(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341,Vvar__15__ceqb__38336)
=> ( c_24__type__40761___24t(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341,Vvar__16__phi__38341)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__38289,Vvar__1__rO__38290,Vvar__2__rI__38291,Vvar__3__radd__38292,Vvar__4__rmul__38297,Vvar__5__rsub__38302,Vvar__6__ropp__38307,Vvar__7__req__38310,Vvar__8__C__38315,Vvar__9__cO__38316,Vvar__10__cI__38317,Vvar__11__cadd__38318,Vvar__12__cmul__38323,Vvar__13__csub__38328,Vvar__14__copp__38333,Vvar__15__ceqb__38336,Vvar__16__phi__38341)
=> ( p(happ(happ(Vvar__7__req__38310,happ(Vvar__16__phi__38341,Vvar__9__cO__38316)),Vvar__1__rO__38290))
& p(happ(happ(Vvar__7__req__38310,happ(Vvar__16__phi__38341,Vvar__10__cI__38317)),Vvar__2__rI__38291))
& ! [Vvar__var__var__var__var__var__var__19__x__38403__38405__38427__38429__38431__38433__38435] :
( t(Vvar__var__var__var__var__var__var__19__x__38403__38405__38427__38429__38431__38433__38435,Vvar__8__C__38315)
=> ! [Vvar__var__var__var__var__var__var__20__y__38404__38406__38428__38430__38432__38434__38436] :
( t(Vvar__var__var__var__var__var__var__20__y__38404__38406__38428__38430__38432__38434__38436,Vvar__8__C__38315)
=> p(happ(happ(Vvar__7__req__38310,happ(Vvar__16__phi__38341,happ(happ(Vvar__11__cadd__38318,Vvar__var__var__var__var__var__var__19__x__38403__38405__38427__38429__38431__38433__38435),Vvar__var__var__var__var__var__var__20__y__38404__38406__38428__38430__38432__38434__38436))),happ(happ(Vvar__3__radd__38292,happ(Vvar__16__phi__38341,Vvar__var__var__var__var__var__var__19__x__38403__38405__38427__38429__38431__38433__38435)),happ(Vvar__16__phi__38341,Vvar__var__var__var__var__var__var__20__y__38404__38406__38428__38430__38432__38434__38436)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__38408__38410__38437__38439__38441__38443__38445] :
( t(Vvar__var__var__var__var__var__var__20__x__38408__38410__38437__38439__38441__38443__38445,Vvar__8__C__38315)
=> ! [Vvar__var__var__var__var__var__var__21__y__38409__38411__38438__38440__38442__38444__38446] :
( t(Vvar__var__var__var__var__var__var__21__y__38409__38411__38438__38440__38442__38444__38446,Vvar__8__C__38315)
=> p(happ(happ(Vvar__7__req__38310,happ(Vvar__16__phi__38341,happ(happ(Vvar__13__csub__38328,Vvar__var__var__var__var__var__var__20__x__38408__38410__38437__38439__38441__38443__38445),Vvar__var__var__var__var__var__var__21__y__38409__38411__38438__38440__38442__38444__38446))),happ(happ(Vvar__5__rsub__38302,happ(Vvar__16__phi__38341,Vvar__var__var__var__var__var__var__20__x__38408__38410__38437__38439__38441__38443__38445)),happ(Vvar__16__phi__38341,Vvar__var__var__var__var__var__var__21__y__38409__38411__38438__38440__38442__38444__38446)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__38413__38415__38447__38449__38451__38453__38455] :
( t(Vvar__var__var__var__var__var__var__21__x__38413__38415__38447__38449__38451__38453__38455,Vvar__8__C__38315)
=> ! [Vvar__var__var__var__var__var__var__22__y__38414__38416__38448__38450__38452__38454__38456] :
( t(Vvar__var__var__var__var__var__var__22__y__38414__38416__38448__38450__38452__38454__38456,Vvar__8__C__38315)
=> p(happ(happ(Vvar__7__req__38310,happ(Vvar__16__phi__38341,happ(happ(Vvar__12__cmul__38323,Vvar__var__var__var__var__var__var__21__x__38413__38415__38447__38449__38451__38453__38455),Vvar__var__var__var__var__var__var__22__y__38414__38416__38448__38450__38452__38454__38456))),happ(happ(Vvar__4__rmul__38297,happ(Vvar__16__phi__38341,Vvar__var__var__var__var__var__var__21__x__38413__38415__38447__38449__38451__38453__38455)),happ(Vvar__16__phi__38341,Vvar__var__var__var__var__var__var__22__y__38414__38416__38448__38450__38452__38454__38456)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__38418__38419__38457__38458__38459__38460__38461] :
( t(Vvar__var__var__var__var__var__var__22__x__38418__38419__38457__38458__38459__38460__38461,Vvar__8__C__38315)
=> p(happ(happ(Vvar__7__req__38310,happ(Vvar__16__phi__38341,happ(Vvar__14__copp__38333,Vvar__var__var__var__var__var__var__22__x__38418__38419__38457__38458__38459__38460__38461))),happ(Vvar__6__ropp__38307,happ(Vvar__16__phi__38341,Vvar__var__var__var__var__var__var__22__x__38418__38419__38457__38458__38459__38460__38461)))) )
& ! [Vvar__var__var__var__var__var__23__x__38421__38424__38462__38465__38468__38471] :
( t(Vvar__var__var__var__var__var__23__x__38421__38424__38462__38465__38468__38471,Vvar__8__C__38315)
=> ! [Vvar__var__var__var__var__var__24__y__38422__38425__38463__38466__38469__38472] :
( t(Vvar__var__var__var__var__var__24__y__38422__38425__38463__38466__38469__38472,Vvar__8__C__38315)
=> ( happ(happ(Vvar__15__ceqb__38336,Vvar__var__var__var__var__var__23__x__38421__38424__38462__38465__38468__38471),Vvar__var__var__var__var__var__24__y__38422__38425__38463__38466__38469__38472) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__38310,happ(Vvar__16__phi__38341,Vvar__var__var__var__var__var__23__x__38421__38424__38462__38465__38468__38471)),happ(Vvar__16__phi__38341,Vvar__var__var__var__var__var__24__y__38422__38425__38463__38466__38469__38472))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__50917,Vvar__1__rO__50918,Vvar__2__rI__50919,Vvar__3__radd__50920,Vvar__4__rmul__50925,Vvar__5__rsub__50930,Vvar__6__ropp__50935,Vvar__7__req__50938] :
( cType___24t(Vvar__0__R__50917)
=> ( t(Vvar__1__rO__50918,Vvar__0__R__50917)
=> ( t(Vvar__2__rI__50919,Vvar__0__R__50917)
=> ( c_24__type__51141___24t(Vvar__0__R__50917,Vvar__1__rO__50918,Vvar__2__rI__50919,Vvar__3__radd__50920,Vvar__4__rmul__50925,Vvar__5__rsub__50930,Vvar__6__ropp__50935,Vvar__7__req__50938,Vvar__3__radd__50920)
=> ( c_24__type__51204___24t(Vvar__0__R__50917,Vvar__1__rO__50918,Vvar__2__rI__50919,Vvar__3__radd__50920,Vvar__4__rmul__50925,Vvar__5__rsub__50930,Vvar__6__ropp__50935,Vvar__7__req__50938,Vvar__4__rmul__50925)
=> ( c_24__type__51267___24t(Vvar__0__R__50917,Vvar__1__rO__50918,Vvar__2__rI__50919,Vvar__3__radd__50920,Vvar__4__rmul__50925,Vvar__5__rsub__50930,Vvar__6__ropp__50935,Vvar__7__req__50938,Vvar__5__rsub__50930)
=> ( c_24__type__51321___24t(Vvar__0__R__50917,Vvar__1__rO__50918,Vvar__2__rI__50919,Vvar__3__radd__50920,Vvar__4__rmul__50925,Vvar__5__rsub__50930,Vvar__6__ropp__50935,Vvar__7__req__50938,Vvar__6__ropp__50935)
=> ( c_24__type__51384___24t(Vvar__0__R__50917,Vvar__1__rO__50918,Vvar__2__rI__50919,Vvar__3__radd__50920,Vvar__4__rmul__50925,Vvar__5__rsub__50930,Vvar__6__ropp__50935,Vvar__7__req__50938,Vvar__7__req__50938)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__50917,Vvar__1__rO__50918,Vvar__2__rI__50919,Vvar__3__radd__50920,Vvar__4__rmul__50925,Vvar__5__rsub__50930,Vvar__6__ropp__50935,Vvar__7__req__50938)
=> ( ! [Vvar__var__var__var__var__var__8__x__50971__50972__51015__51016__51017__51018] :
( t(Vvar__var__var__var__var__var__8__x__50971__50972__51015__51016__51017__51018,Vvar__0__R__50917)
=> p(happ(happ(Vvar__7__req__50938,happ(happ(Vvar__3__radd__50920,Vvar__1__rO__50918),Vvar__var__var__var__var__var__8__x__50971__50972__51015__51016__51017__51018)),Vvar__var__var__var__var__var__8__x__50971__50972__51015__51016__51017__51018)) )
& ! [Vvar__var__var__var__var__9__x__50974__50976__51019__51021__51023] :
( t(Vvar__var__var__var__var__9__x__50974__50976__51019__51021__51023,Vvar__0__R__50917)
=> ! [Vvar__var__var__var__var__10__y__50975__50977__51020__51022__51024] :
( t(Vvar__var__var__var__var__10__y__50975__50977__51020__51022__51024,Vvar__0__R__50917)
=> p(happ(happ(Vvar__7__req__50938,happ(happ(Vvar__3__radd__50920,Vvar__var__var__var__var__9__x__50974__50976__51019__51021__51023),Vvar__var__var__var__var__10__y__50975__50977__51020__51022__51024)),happ(happ(Vvar__3__radd__50920,Vvar__var__var__var__var__10__y__50975__50977__51020__51022__51024),Vvar__var__var__var__var__9__x__50974__50976__51019__51021__51023))) ) )
& ! [Vvar__var__var__var__var__10__x__50979__50982__51025__51028__51031] :
( t(Vvar__var__var__var__var__10__x__50979__50982__51025__51028__51031,Vvar__0__R__50917)
=> ! [Vvar__var__var__var__var__11__y__50980__50983__51026__51029__51032] :
( t(Vvar__var__var__var__var__11__y__50980__50983__51026__51029__51032,Vvar__0__R__50917)
=> ! [Vvar__var__var__var__var__12__z__50981__50984__51027__51030__51033] :
( t(Vvar__var__var__var__var__12__z__50981__50984__51027__51030__51033,Vvar__0__R__50917)
=> p(happ(happ(Vvar__7__req__50938,happ(happ(Vvar__3__radd__50920,Vvar__var__var__var__var__10__x__50979__50982__51025__51028__51031),happ(happ(Vvar__3__radd__50920,Vvar__var__var__var__var__11__y__50980__50983__51026__51029__51032),Vvar__var__var__var__var__12__z__50981__50984__51027__51030__51033))),happ(happ(Vvar__3__radd__50920,happ(happ(Vvar__3__radd__50920,Vvar__var__var__var__var__10__x__50979__50982__51025__51028__51031),Vvar__var__var__var__var__11__y__50980__50983__51026__51029__51032)),Vvar__var__var__var__var__12__z__50981__50984__51027__51030__51033))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__50986__50987__51034__51035__51036__51037] :
( t(Vvar__var__var__var__var__var__11__x__50986__50987__51034__51035__51036__51037,Vvar__0__R__50917)
=> p(happ(happ(Vvar__7__req__50938,happ(happ(Vvar__4__rmul__50925,Vvar__2__rI__50919),Vvar__var__var__var__var__var__11__x__50986__50987__51034__51035__51036__51037)),Vvar__var__var__var__var__var__11__x__50986__50987__51034__51035__51036__51037)) )
& ! [Vvar__var__var__var__var__12__x__50989__50991__51038__51040__51042] :
( t(Vvar__var__var__var__var__12__x__50989__50991__51038__51040__51042,Vvar__0__R__50917)
=> ! [Vvar__var__var__var__var__13__y__50990__50992__51039__51041__51043] :
( t(Vvar__var__var__var__var__13__y__50990__50992__51039__51041__51043,Vvar__0__R__50917)
=> p(happ(happ(Vvar__7__req__50938,happ(happ(Vvar__4__rmul__50925,Vvar__var__var__var__var__12__x__50989__50991__51038__51040__51042),Vvar__var__var__var__var__13__y__50990__50992__51039__51041__51043)),happ(happ(Vvar__4__rmul__50925,Vvar__var__var__var__var__13__y__50990__50992__51039__51041__51043),Vvar__var__var__var__var__12__x__50989__50991__51038__51040__51042))) ) )
& ! [Vvar__var__var__var__var__13__x__50994__50997__51044__51047__51050] :
( t(Vvar__var__var__var__var__13__x__50994__50997__51044__51047__51050,Vvar__0__R__50917)
=> ! [Vvar__var__var__var__var__14__y__50995__50998__51045__51048__51051] :
( t(Vvar__var__var__var__var__14__y__50995__50998__51045__51048__51051,Vvar__0__R__50917)
=> ! [Vvar__var__var__var__var__15__z__50996__50999__51046__51049__51052] :
( t(Vvar__var__var__var__var__15__z__50996__50999__51046__51049__51052,Vvar__0__R__50917)
=> p(happ(happ(Vvar__7__req__50938,happ(happ(Vvar__4__rmul__50925,Vvar__var__var__var__var__13__x__50994__50997__51044__51047__51050),happ(happ(Vvar__4__rmul__50925,Vvar__var__var__var__var__14__y__50995__50998__51045__51048__51051),Vvar__var__var__var__var__15__z__50996__50999__51046__51049__51052))),happ(happ(Vvar__4__rmul__50925,happ(happ(Vvar__4__rmul__50925,Vvar__var__var__var__var__13__x__50994__50997__51044__51047__51050),Vvar__var__var__var__var__14__y__50995__50998__51045__51048__51051)),Vvar__var__var__var__var__15__z__50996__50999__51046__51049__51052))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__51001__51004__51053__51056__51059__51062] :
( t(Vvar__var__var__var__var__var__14__x__51001__51004__51053__51056__51059__51062,Vvar__0__R__50917)
=> ! [Vvar__var__var__var__var__var__15__y__51002__51005__51054__51057__51060__51063] :
( t(Vvar__var__var__var__var__var__15__y__51002__51005__51054__51057__51060__51063,Vvar__0__R__50917)
=> ! [Vvar__var__var__var__var__var__16__z__51003__51006__51055__51058__51061__51064] :
( t(Vvar__var__var__var__var__var__16__z__51003__51006__51055__51058__51061__51064,Vvar__0__R__50917)
=> p(happ(happ(Vvar__7__req__50938,happ(happ(Vvar__4__rmul__50925,happ(happ(Vvar__3__radd__50920,Vvar__var__var__var__var__var__14__x__51001__51004__51053__51056__51059__51062),Vvar__var__var__var__var__var__15__y__51002__51005__51054__51057__51060__51063)),Vvar__var__var__var__var__var__16__z__51003__51006__51055__51058__51061__51064)),happ(happ(Vvar__3__radd__50920,happ(happ(Vvar__4__rmul__50925,Vvar__var__var__var__var__var__14__x__51001__51004__51053__51056__51059__51062),Vvar__var__var__var__var__var__16__z__51003__51006__51055__51058__51061__51064)),happ(happ(Vvar__4__rmul__50925,Vvar__var__var__var__var__var__15__y__51002__51005__51054__51057__51060__51063),Vvar__var__var__var__var__var__16__z__51003__51006__51055__51058__51061__51064)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__51008__51010__51065__51067__51069__51071__51073] :
( t(Vvar__var__var__var__var__var__var__15__x__51008__51010__51065__51067__51069__51071__51073,Vvar__0__R__50917)
=> ! [Vvar__var__var__var__var__var__var__16__y__51009__51011__51066__51068__51070__51072__51074] :
( t(Vvar__var__var__var__var__var__var__16__y__51009__51011__51066__51068__51070__51072__51074,Vvar__0__R__50917)
=> p(happ(happ(Vvar__7__req__50938,happ(happ(Vvar__5__rsub__50930,Vvar__var__var__var__var__var__var__15__x__51008__51010__51065__51067__51069__51071__51073),Vvar__var__var__var__var__var__var__16__y__51009__51011__51066__51068__51070__51072__51074)),happ(happ(Vvar__3__radd__50920,Vvar__var__var__var__var__var__var__15__x__51008__51010__51065__51067__51069__51071__51073),happ(Vvar__6__ropp__50935,Vvar__var__var__var__var__var__var__16__y__51009__51011__51066__51068__51070__51072__51074)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__51013__51014__51075__51076__51077__51078__51079] :
( t(Vvar__var__var__var__var__var__var__16__x__51013__51014__51075__51076__51077__51078__51079,Vvar__0__R__50917)
=> p(happ(happ(Vvar__7__req__50938,happ(happ(Vvar__3__radd__50920,Vvar__var__var__var__var__var__var__16__x__51013__51014__51075__51076__51077__51078__51079),happ(Vvar__6__ropp__50935,Vvar__var__var__var__var__var__var__16__x__51013__51014__51075__51076__51077__51078__51079))),Vvar__1__rO__50918)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__51657,Vvar__1__rO__51658,Vvar__2__rI__51659,Vvar__3__radd__51660,Vvar__4__rmul__51665,Vvar__5__req__51670,Vvar__6__C__51675,Vvar__7__cO__51676,Vvar__8__cI__51677,Vvar__9__cadd__51678,Vvar__10__cmul__51683,Vvar__11__ceqb__51688,Vvar__12__phi__51693] :
( cType___24t(Vvar__0__R__51657)
=> ( t(Vvar__1__rO__51658,Vvar__0__R__51657)
=> ( t(Vvar__2__rI__51659,Vvar__0__R__51657)
=> ( c_24__type__51910___24t(Vvar__0__R__51657,Vvar__1__rO__51658,Vvar__2__rI__51659,Vvar__3__radd__51660,Vvar__4__rmul__51665,Vvar__5__req__51670,Vvar__6__C__51675,Vvar__7__cO__51676,Vvar__8__cI__51677,Vvar__9__cadd__51678,Vvar__10__cmul__51683,Vvar__11__ceqb__51688,Vvar__12__phi__51693,Vvar__3__radd__51660)
=> ( c_24__type__52035___24t(Vvar__0__R__51657,Vvar__1__rO__51658,Vvar__2__rI__51659,Vvar__3__radd__51660,Vvar__4__rmul__51665,Vvar__5__req__51670,Vvar__6__C__51675,Vvar__7__cO__51676,Vvar__8__cI__51677,Vvar__9__cadd__51678,Vvar__10__cmul__51683,Vvar__11__ceqb__51688,Vvar__12__phi__51693,Vvar__4__rmul__51665)
=> ( c_24__type__52160___24t(Vvar__0__R__51657,Vvar__1__rO__51658,Vvar__2__rI__51659,Vvar__3__radd__51660,Vvar__4__rmul__51665,Vvar__5__req__51670,Vvar__6__C__51675,Vvar__7__cO__51676,Vvar__8__cI__51677,Vvar__9__cadd__51678,Vvar__10__cmul__51683,Vvar__11__ceqb__51688,Vvar__12__phi__51693,Vvar__5__req__51670)
=> ( cType___24t(Vvar__6__C__51675)
=> ( t(Vvar__7__cO__51676,Vvar__6__C__51675)
=> ( t(Vvar__8__cI__51677,Vvar__6__C__51675)
=> ( c_24__type__52285___24t(Vvar__0__R__51657,Vvar__1__rO__51658,Vvar__2__rI__51659,Vvar__3__radd__51660,Vvar__4__rmul__51665,Vvar__5__req__51670,Vvar__6__C__51675,Vvar__7__cO__51676,Vvar__8__cI__51677,Vvar__9__cadd__51678,Vvar__10__cmul__51683,Vvar__11__ceqb__51688,Vvar__12__phi__51693,Vvar__9__cadd__51678)
=> ( c_24__type__52410___24t(Vvar__0__R__51657,Vvar__1__rO__51658,Vvar__2__rI__51659,Vvar__3__radd__51660,Vvar__4__rmul__51665,Vvar__5__req__51670,Vvar__6__C__51675,Vvar__7__cO__51676,Vvar__8__cI__51677,Vvar__9__cadd__51678,Vvar__10__cmul__51683,Vvar__11__ceqb__51688,Vvar__12__phi__51693,Vvar__10__cmul__51683)
=> ( c_24__type__52535___24t(Vvar__0__R__51657,Vvar__1__rO__51658,Vvar__2__rI__51659,Vvar__3__radd__51660,Vvar__4__rmul__51665,Vvar__5__req__51670,Vvar__6__C__51675,Vvar__7__cO__51676,Vvar__8__cI__51677,Vvar__9__cadd__51678,Vvar__10__cmul__51683,Vvar__11__ceqb__51688,Vvar__12__phi__51693,Vvar__11__ceqb__51688)
=> ( c_24__type__52646___24t(Vvar__0__R__51657,Vvar__1__rO__51658,Vvar__2__rI__51659,Vvar__3__radd__51660,Vvar__4__rmul__51665,Vvar__5__req__51670,Vvar__6__C__51675,Vvar__7__cO__51676,Vvar__8__cI__51677,Vvar__9__cadd__51678,Vvar__10__cmul__51683,Vvar__11__ceqb__51688,Vvar__12__phi__51693,Vvar__12__phi__51693)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__51657,Vvar__1__rO__51658,Vvar__2__rI__51659,Vvar__3__radd__51660,Vvar__4__rmul__51665,Vvar__5__req__51670,Vvar__6__C__51675,Vvar__7__cO__51676,Vvar__8__cI__51677,Vvar__9__cadd__51678,Vvar__10__cmul__51683,Vvar__11__ceqb__51688,Vvar__12__phi__51693)
=> ( p(happ(happ(Vvar__5__req__51670,happ(Vvar__12__phi__51693,Vvar__7__cO__51676)),Vvar__1__rO__51658))
& p(happ(happ(Vvar__5__req__51670,happ(Vvar__12__phi__51693,Vvar__8__cI__51677)),Vvar__2__rI__51659))
& ! [Vvar__var__var__var__var__var__var__15__x__51739__51741__51755__51757__51759__51761__51763] :
( t(Vvar__var__var__var__var__var__var__15__x__51739__51741__51755__51757__51759__51761__51763,Vvar__6__C__51675)
=> ! [Vvar__var__var__var__var__var__var__16__y__51740__51742__51756__51758__51760__51762__51764] :
( t(Vvar__var__var__var__var__var__var__16__y__51740__51742__51756__51758__51760__51762__51764,Vvar__6__C__51675)
=> p(happ(happ(Vvar__5__req__51670,happ(Vvar__12__phi__51693,happ(happ(Vvar__9__cadd__51678,Vvar__var__var__var__var__var__var__15__x__51739__51741__51755__51757__51759__51761__51763),Vvar__var__var__var__var__var__var__16__y__51740__51742__51756__51758__51760__51762__51764))),happ(happ(Vvar__3__radd__51660,happ(Vvar__12__phi__51693,Vvar__var__var__var__var__var__var__15__x__51739__51741__51755__51757__51759__51761__51763)),happ(Vvar__12__phi__51693,Vvar__var__var__var__var__var__var__16__y__51740__51742__51756__51758__51760__51762__51764)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__51744__51746__51765__51767__51769__51771__51773] :
( t(Vvar__var__var__var__var__var__var__16__x__51744__51746__51765__51767__51769__51771__51773,Vvar__6__C__51675)
=> ! [Vvar__var__var__var__var__var__var__17__y__51745__51747__51766__51768__51770__51772__51774] :
( t(Vvar__var__var__var__var__var__var__17__y__51745__51747__51766__51768__51770__51772__51774,Vvar__6__C__51675)
=> p(happ(happ(Vvar__5__req__51670,happ(Vvar__12__phi__51693,happ(happ(Vvar__10__cmul__51683,Vvar__var__var__var__var__var__var__16__x__51744__51746__51765__51767__51769__51771__51773),Vvar__var__var__var__var__var__var__17__y__51745__51747__51766__51768__51770__51772__51774))),happ(happ(Vvar__4__rmul__51665,happ(Vvar__12__phi__51693,Vvar__var__var__var__var__var__var__16__x__51744__51746__51765__51767__51769__51771__51773)),happ(Vvar__12__phi__51693,Vvar__var__var__var__var__var__var__17__y__51745__51747__51766__51768__51770__51772__51774)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__51749__51752__51775__51778__51781__51784] :
( t(Vvar__var__var__var__var__var__17__x__51749__51752__51775__51778__51781__51784,Vvar__6__C__51675)
=> ! [Vvar__var__var__var__var__var__18__y__51750__51753__51776__51779__51782__51785] :
( t(Vvar__var__var__var__var__var__18__y__51750__51753__51776__51779__51782__51785,Vvar__6__C__51675)
=> ( happ(happ(Vvar__11__ceqb__51688,Vvar__var__var__var__var__var__17__x__51749__51752__51775__51778__51781__51784),Vvar__var__var__var__var__var__18__y__51750__51753__51776__51779__51782__51785) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__51670,happ(Vvar__12__phi__51693,Vvar__var__var__var__var__var__17__x__51749__51752__51775__51778__51781__51784)),happ(Vvar__12__phi__51693,Vvar__var__var__var__var__var__18__y__51750__51753__51776__51779__51782__51785))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__83437,Vvar__1__rO__83438,Vvar__2__rI__83439,Vvar__3__radd__83440,Vvar__4__rmul__83445,Vvar__5__req__83450] :
( cType___24t(Vvar__0__R__83437)
=> ( t(Vvar__1__rO__83438,Vvar__0__R__83437)
=> ( t(Vvar__2__rI__83439,Vvar__0__R__83437)
=> ( c_24__type__83605___24t(Vvar__0__R__83437,Vvar__1__rO__83438,Vvar__2__rI__83439,Vvar__3__radd__83440,Vvar__4__rmul__83445,Vvar__5__req__83450,Vvar__3__radd__83440)
=> ( c_24__type__83644___24t(Vvar__0__R__83437,Vvar__1__rO__83438,Vvar__2__rI__83439,Vvar__3__radd__83440,Vvar__4__rmul__83445,Vvar__5__req__83450,Vvar__4__rmul__83445)
=> ( c_24__type__83683___24t(Vvar__0__R__83437,Vvar__1__rO__83438,Vvar__2__rI__83439,Vvar__3__radd__83440,Vvar__4__rmul__83445,Vvar__5__req__83450,Vvar__5__req__83450)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__83437,Vvar__1__rO__83438,Vvar__2__rI__83439,Vvar__3__radd__83440,Vvar__4__rmul__83445,Vvar__5__req__83450)
=> ( ! [Vvar__var__var__var__var__var__6__n__83475__83476__83514__83515__83516__83517] :
( t(Vvar__var__var__var__var__var__6__n__83475__83476__83514__83515__83516__83517,Vvar__0__R__83437)
=> p(happ(happ(Vvar__5__req__83450,happ(happ(Vvar__3__radd__83440,Vvar__1__rO__83438),Vvar__var__var__var__var__var__6__n__83475__83476__83514__83515__83516__83517)),Vvar__var__var__var__var__var__6__n__83475__83476__83514__83515__83516__83517)) )
& ! [Vvar__var__var__var__var__7__n__83478__83480__83518__83520__83522] :
( t(Vvar__var__var__var__var__7__n__83478__83480__83518__83520__83522,Vvar__0__R__83437)
=> ! [Vvar__var__var__var__var__8__m__83479__83481__83519__83521__83523] :
( t(Vvar__var__var__var__var__8__m__83479__83481__83519__83521__83523,Vvar__0__R__83437)
=> p(happ(happ(Vvar__5__req__83450,happ(happ(Vvar__3__radd__83440,Vvar__var__var__var__var__7__n__83478__83480__83518__83520__83522),Vvar__var__var__var__var__8__m__83479__83481__83519__83521__83523)),happ(happ(Vvar__3__radd__83440,Vvar__var__var__var__var__8__m__83479__83481__83519__83521__83523),Vvar__var__var__var__var__7__n__83478__83480__83518__83520__83522))) ) )
& ! [Vvar__var__var__var__var__8__n__83483__83486__83524__83527__83530] :
( t(Vvar__var__var__var__var__8__n__83483__83486__83524__83527__83530,Vvar__0__R__83437)
=> ! [Vvar__var__var__var__var__9__m__83484__83487__83525__83528__83531] :
( t(Vvar__var__var__var__var__9__m__83484__83487__83525__83528__83531,Vvar__0__R__83437)
=> ! [Vvar__var__var__var__var__10__p__83485__83488__83526__83529__83532] :
( t(Vvar__var__var__var__var__10__p__83485__83488__83526__83529__83532,Vvar__0__R__83437)
=> p(happ(happ(Vvar__5__req__83450,happ(happ(Vvar__3__radd__83440,Vvar__var__var__var__var__8__n__83483__83486__83524__83527__83530),happ(happ(Vvar__3__radd__83440,Vvar__var__var__var__var__9__m__83484__83487__83525__83528__83531),Vvar__var__var__var__var__10__p__83485__83488__83526__83529__83532))),happ(happ(Vvar__3__radd__83440,happ(happ(Vvar__3__radd__83440,Vvar__var__var__var__var__8__n__83483__83486__83524__83527__83530),Vvar__var__var__var__var__9__m__83484__83487__83525__83528__83531)),Vvar__var__var__var__var__10__p__83485__83488__83526__83529__83532))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__83490__83491__83533__83534__83535__83536] :
( t(Vvar__var__var__var__var__var__9__n__83490__83491__83533__83534__83535__83536,Vvar__0__R__83437)
=> p(happ(happ(Vvar__5__req__83450,happ(happ(Vvar__4__rmul__83445,Vvar__2__rI__83439),Vvar__var__var__var__var__var__9__n__83490__83491__83533__83534__83535__83536)),Vvar__var__var__var__var__var__9__n__83490__83491__83533__83534__83535__83536)) )
& ! [Vvar__var__var__var__var__var__10__n__83493__83494__83537__83538__83539__83540] :
( t(Vvar__var__var__var__var__var__10__n__83493__83494__83537__83538__83539__83540,Vvar__0__R__83437)
=> p(happ(happ(Vvar__5__req__83450,happ(happ(Vvar__4__rmul__83445,Vvar__1__rO__83438),Vvar__var__var__var__var__var__10__n__83493__83494__83537__83538__83539__83540)),Vvar__1__rO__83438)) )
& ! [Vvar__var__var__var__var__11__n__83496__83498__83541__83543__83545] :
( t(Vvar__var__var__var__var__11__n__83496__83498__83541__83543__83545,Vvar__0__R__83437)
=> ! [Vvar__var__var__var__var__12__m__83497__83499__83542__83544__83546] :
( t(Vvar__var__var__var__var__12__m__83497__83499__83542__83544__83546,Vvar__0__R__83437)
=> p(happ(happ(Vvar__5__req__83450,happ(happ(Vvar__4__rmul__83445,Vvar__var__var__var__var__11__n__83496__83498__83541__83543__83545),Vvar__var__var__var__var__12__m__83497__83499__83542__83544__83546)),happ(happ(Vvar__4__rmul__83445,Vvar__var__var__var__var__12__m__83497__83499__83542__83544__83546),Vvar__var__var__var__var__11__n__83496__83498__83541__83543__83545))) ) )
& ! [Vvar__var__var__var__var__12__n__83501__83504__83547__83550__83553] :
( t(Vvar__var__var__var__var__12__n__83501__83504__83547__83550__83553,Vvar__0__R__83437)
=> ! [Vvar__var__var__var__var__13__m__83502__83505__83548__83551__83554] :
( t(Vvar__var__var__var__var__13__m__83502__83505__83548__83551__83554,Vvar__0__R__83437)
=> ! [Vvar__var__var__var__var__14__p__83503__83506__83549__83552__83555] :
( t(Vvar__var__var__var__var__14__p__83503__83506__83549__83552__83555,Vvar__0__R__83437)
=> p(happ(happ(Vvar__5__req__83450,happ(happ(Vvar__4__rmul__83445,Vvar__var__var__var__var__12__n__83501__83504__83547__83550__83553),happ(happ(Vvar__4__rmul__83445,Vvar__var__var__var__var__13__m__83502__83505__83548__83551__83554),Vvar__var__var__var__var__14__p__83503__83506__83549__83552__83555))),happ(happ(Vvar__4__rmul__83445,happ(happ(Vvar__4__rmul__83445,Vvar__var__var__var__var__12__n__83501__83504__83547__83550__83553),Vvar__var__var__var__var__13__m__83502__83505__83548__83551__83554)),Vvar__var__var__var__var__14__p__83503__83506__83549__83552__83555))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__83508__83511__83556__83559__83562__83565] :
( t(Vvar__var__var__var__var__var__13__n__83508__83511__83556__83559__83562__83565,Vvar__0__R__83437)
=> ! [Vvar__var__var__var__var__var__14__m__83509__83512__83557__83560__83563__83566] :
( t(Vvar__var__var__var__var__var__14__m__83509__83512__83557__83560__83563__83566,Vvar__0__R__83437)
=> ! [Vvar__var__var__var__var__var__15__p__83510__83513__83558__83561__83564__83567] :
( t(Vvar__var__var__var__var__var__15__p__83510__83513__83558__83561__83564__83567,Vvar__0__R__83437)
=> p(happ(happ(Vvar__5__req__83450,happ(happ(Vvar__4__rmul__83445,happ(happ(Vvar__3__radd__83440,Vvar__var__var__var__var__var__13__n__83508__83511__83556__83559__83562__83565),Vvar__var__var__var__var__var__14__m__83509__83512__83557__83560__83563__83566)),Vvar__var__var__var__var__var__15__p__83510__83513__83558__83561__83564__83567)),happ(happ(Vvar__3__radd__83440,happ(happ(Vvar__4__rmul__83445,Vvar__var__var__var__var__var__13__n__83508__83511__83556__83559__83562__83565),Vvar__var__var__var__var__var__15__p__83510__83513__83558__83561__83564__83567)),happ(happ(Vvar__4__rmul__83445,Vvar__var__var__var__var__var__14__m__83509__83512__83557__83560__83563__83566),Vvar__var__var__var__var__var__15__p__83510__83513__83558__83561__83564__83567)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__52809,Vvar__1__copp__52810,Vvar__2__ceqb__52813,Vvar__3__get__sign__52818] :
( cType___24t(Vvar__0__C__52809)
=> ( c_24__type__52865___24t(Vvar__0__C__52809,Vvar__1__copp__52810,Vvar__2__ceqb__52813,Vvar__3__get__sign__52818,Vvar__1__copp__52810)
=> ( c_24__type__52884___24t(Vvar__0__C__52809,Vvar__1__copp__52810,Vvar__2__ceqb__52813,Vvar__3__get__sign__52818,Vvar__2__ceqb__52813)
=> ( c_24__type__52898___24t(Vvar__0__C__52809,Vvar__1__copp__52810,Vvar__2__ceqb__52813,Vvar__3__get__sign__52818,Vvar__3__get__sign__52818)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__52809,Vvar__1__copp__52810,Vvar__2__ceqb__52813,Vvar__3__get__sign__52818)
=> ( ! [Vvar__var__var__var__var__var__4__c__52835__52838__52841__52844__52847__52850] :
( t(Vvar__var__var__var__var__var__4__c__52835__52838__52841__52844__52847__52850,Vvar__0__C__52809)
=> ! [Vvar__var__var__var__var__var__5__c_27__52836__52839__52842__52845__52848__52851] :
( t(Vvar__var__var__var__var__var__5__c_27__52836__52839__52842__52845__52848__52851,Vvar__0__C__52809)
=> ( happ(Vvar__3__get__sign__52818,Vvar__var__var__var__var__var__4__c__52835__52838__52841__52844__52847__52850) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__52809,Vvar__var__var__var__var__var__5__c_27__52836__52839__52842__52845__52848__52851)
=> happ(happ(Vvar__2__ceqb__52813,Vvar__var__var__var__var__var__4__c__52835__52838__52841__52844__52847__52850),happ(Vvar__1__copp__52810,Vvar__var__var__var__var__var__5__c_27__52836__52839__52842__52845__52848__52851)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__51435,Vvar__1__radd__51436,Vvar__2__rmul__51441,Vvar__3__req__51446] :
( cType___24t(Vvar__0__R__51435)
=> ( c_24__type__51521___24t(Vvar__0__R__51435,Vvar__1__radd__51436,Vvar__2__rmul__51441,Vvar__3__req__51446,Vvar__1__radd__51436)
=> ( c_24__type__51544___24t(Vvar__0__R__51435,Vvar__1__radd__51436,Vvar__2__rmul__51441,Vvar__3__req__51446,Vvar__2__rmul__51441)
=> ( c_24__type__51567___24t(Vvar__0__R__51435,Vvar__1__radd__51436,Vvar__2__rmul__51441,Vvar__3__req__51446,Vvar__3__req__51446)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__51435,Vvar__1__radd__51436,Vvar__2__rmul__51441,Vvar__3__req__51446)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__51590___24a4(Vvar__0__R__51435,Vvar__1__radd__51436,Vvar__2__rmul__51441,Vvar__3__req__51446),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__51435,c_24__type__51608___24a4(Vvar__0__R__51435,Vvar__1__radd__51436,Vvar__2__rmul__51441,Vvar__3__req__51446),Vvar__3__req__51446,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__51435,Vvar__0__R__51435,Vvar__3__req__51446,Vvar__3__req__51446)),Vvar__1__radd__51436)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__51634___24a4(Vvar__0__R__51435,Vvar__1__radd__51436,Vvar__2__rmul__51441,Vvar__3__req__51446),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__51435,c_24__type__51652___24a4(Vvar__0__R__51435,Vvar__1__radd__51436,Vvar__2__rmul__51441,Vvar__3__req__51446),Vvar__3__req__51446,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__51435,Vvar__0__R__51435,Vvar__3__req__51446,Vvar__3__req__51446)),Vvar__2__rmul__51441)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Eta.Eta',axiom,
! [Vvar__0___24Anonymous__121937,Vvar__1___24Anonymous__121938,Vvar__2___24Anonymous__121939,Vvar__3___24Anonymous__121940] :
( cTait_2eTyping_2econtext___24t(Vvar__0___24Anonymous__121937)
=> ( cTait_2eTerm_2etype___24t(Vvar__1___24Anonymous__121938)
=> ( cTait_2eTerm_2eterm___24t(Vvar__2___24Anonymous__121939)
=> ( cTait_2eTerm_2eterm___24t(Vvar__3___24Anonymous__121940)
=> ( cEta_2eEta___24a4(Vvar__0___24Anonymous__121937,Vvar__1___24Anonymous__121938,Vvar__2___24Anonymous__121939,Vvar__3___24Anonymous__121940)
=> ( ? [Vvar__0__rhos__121942] :
( cTait_2eTyping_2econtext___24t(Vvar__0__rhos__121942)
& ? [Vvar__1__r__121943] :
( cTait_2eTerm_2eterm___24t(Vvar__1__r__121943)
& Vvar__3___24Anonymous__121940 = Vvar__1__r__121943
& Vvar__2___24Anonymous__121939 = Vvar__1__r__121943
& Vvar__1___24Anonymous__121938 = cTait_2eTerm_2eIota
& Vvar__0___24Anonymous__121937 = Vvar__0__rhos__121942 ) )
| ? [Vvar__0__rhos__121944] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__0__rhos__121944)
& ? [Vvar__1__sigmas__121945] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__1__sigmas__121945)
& ? [Vvar__2__rho__121946] :
( cTait_2eTerm_2etype___24t(Vvar__2__rho__121946)
& ? [Vvar__3__sigma__121947] :
( cTait_2eTerm_2etype___24t(Vvar__3__sigma__121947)
& ? [Vvar__4__k__121948] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__k__121948)
& ? [Vvar__5__etak__121949] :
( cTait_2eTerm_2eterm___24t(Vvar__5__etak__121949)
& ? [Vvar__6__r__121950] :
( cTait_2eTerm_2eterm___24t(Vvar__6__r__121950)
& ? [Vvar__7__s__121951] :
( cTait_2eTerm_2eterm___24t(Vvar__7__s__121951)
& p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,Vvar__0__rhos__121944),Vvar__4__k__121948))
& cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,Vvar__0__rhos__121944,Vvar__1__sigmas__121945)) = Vvar__4__k__121948
& cEta_2eEta___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,Vvar__0__rhos__121944,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,Vvar__1__sigmas__121945,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,Vvar__2__rho__121946,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)))),Vvar__2__rho__121946,cTait_2eTerm_2eVar___24a1(Vvar__4__k__121948),Vvar__5__etak__121949)
& cEta_2eEta___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,Vvar__0__rhos__121944,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,Vvar__1__sigmas__121945,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,Vvar__2__rho__121946,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)))),Vvar__3__sigma__121947,cTait_2eTerm_2eApp___24a2(Vvar__6__r__121950,Vvar__5__etak__121949),Vvar__7__s__121951)
& Vvar__3___24Anonymous__121940 = cTait_2eTerm_2eAbs___24a2(Vvar__2__rho__121946,c_24__case__Tait_2eTerm_2eterm_24134937___24a6(Vvar__0___24Anonymous__121937,Vvar__1___24Anonymous__121938,Vvar__2___24Anonymous__121939,Vvar__3___24Anonymous__121940,Vvar__4__k__121948,Vvar__7__s__121951))
& Vvar__2___24Anonymous__121939 = Vvar__6__r__121950
& Vvar__1___24Anonymous__121938 = cTait_2eTerm_2eArrow___24a2(Vvar__2__rho__121946,Vvar__3__sigma__121947)
& Vvar__0___24Anonymous__121937 = Vvar__0__rhos__121944 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Eta.EtaExp',axiom,
! [Vvar__0___24Anonymous__83833,Vvar__1___24Anonymous__83834,Vvar__2___24Anonymous__83835,Vvar__3___24Anonymous__83836] :
( cTait_2eTyping_2econtext___24t(Vvar__0___24Anonymous__83833)
=> ( cTait_2eTerm_2etype___24t(Vvar__1___24Anonymous__83834)
=> ( cTait_2eTerm_2eterm___24t(Vvar__2___24Anonymous__83835)
=> ( cTait_2eTerm_2eterm___24t(Vvar__3___24Anonymous__83836)
=> ( cEta_2eEtaExp___24a4(Vvar__0___24Anonymous__83833,Vvar__1___24Anonymous__83834,Vvar__2___24Anonymous__83835,Vvar__3___24Anonymous__83836)
=> ( ? [Vvar__0__rhos__83838] :
( cTait_2eTyping_2econtext___24t(Vvar__0__rhos__83838)
& ? [Vvar__1__sigmas__83839] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__1__sigmas__83839)
& ? [Vvar__2__rs__83840] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__2__rs__83840)
& ? [Vvar__3__ss__83841] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__3__ss__83841)
& ? [Vvar__4__k__83842] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__k__83842)
& ? [Vvar__5__t__83843] :
( cTait_2eTerm_2eterm___24t(Vvar__5__t__83843)
& ? [Vvar__6__rho__83844] :
( cTait_2eTerm_2etype___24t(Vvar__6__rho__83844)
& cTait_2eTyping_2eTypJ___24a3(Vvar__0__rhos__83838,cTait_2eTerm_2eVar___24a1(Vvar__4__k__83842),cTait_2eApps_2earrows___24a2(Vvar__6__rho__83844,Vvar__1__sigmas__83839))
& cEta_2eEtaExps___24a4(Vvar__0__rhos__83838,Vvar__1__sigmas__83839,Vvar__2__rs__83840,Vvar__3__ss__83841)
& cEta_2eEta___24a4(Vvar__0__rhos__83838,Vvar__6__rho__83844,cTait_2eApps_2eapps___24a2(cTait_2eTerm_2eVar___24a1(Vvar__4__k__83842),Vvar__3__ss__83841),Vvar__5__t__83843)
& Vvar__3___24Anonymous__83836 = Vvar__5__t__83843
& Vvar__2___24Anonymous__83835 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2484376___24a6(Vvar__0___24Anonymous__83833,Vvar__1___24Anonymous__83834,Vvar__2___24Anonymous__83835,Vvar__3___24Anonymous__83836,Vvar__2__rs__83840,Vvar__4__k__83842)
& Vvar__1___24Anonymous__83834 = Vvar__6__rho__83844
& Vvar__0___24Anonymous__83833 = Vvar__0__rhos__83838 ) ) ) ) ) ) )
| ? [Vvar__0__rhos__83859] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__0__rhos__83859)
& ? [Vvar__1__sigmas__83860] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__1__sigmas__83860)
& ? [Vvar__2__rho__83861] :
( cTait_2eTerm_2etype___24t(Vvar__2__rho__83861)
& ? [Vvar__3__sigma__83862] :
( cTait_2eTerm_2etype___24t(Vvar__3__sigma__83862)
& ? [Vvar__4__r__83863] :
( cTait_2eTerm_2eterm___24t(Vvar__4__r__83863)
& ? [Vvar__5__s__83864] :
( cTait_2eTerm_2eterm___24t(Vvar__5__s__83864)
& ? [Vvar__6__k__83865] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__6__k__83865)
& p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,Vvar__0__rhos__83859),Vvar__6__k__83865))
& cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,Vvar__0__rhos__83859,Vvar__1__sigmas__83860)) = Vvar__6__k__83865
& cEta_2eEtaExp___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,Vvar__0__rhos__83859,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,Vvar__1__sigmas__83860,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,Vvar__2__rho__83861,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)))),Vvar__3__sigma__83862,Vvar__4__r__83863,Vvar__5__s__83864)
& Vvar__3___24Anonymous__83836 = cTait_2eTerm_2eAbs___24a2(Vvar__2__rho__83861,c_24__case__Tait_2eTerm_2eterm_2497196___24a6(Vvar__0___24Anonymous__83833,Vvar__1___24Anonymous__83834,Vvar__2___24Anonymous__83835,Vvar__3___24Anonymous__83836,Vvar__5__s__83864,Vvar__6__k__83865))
& Vvar__2___24Anonymous__83835 = cTait_2eTerm_2eAbs___24a2(Vvar__2__rho__83861,c_24__case__Tait_2eTerm_2eterm_2497196___24a6(Vvar__0___24Anonymous__83833,Vvar__1___24Anonymous__83834,Vvar__2___24Anonymous__83835,Vvar__3___24Anonymous__83836,Vvar__4__r__83863,Vvar__6__k__83865))
& Vvar__1___24Anonymous__83834 = cTait_2eTerm_2eArrow___24a2(Vvar__2__rho__83861,Vvar__3__sigma__83862)
& Vvar__0___24Anonymous__83833 = Vvar__0__rhos__83859 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Eta.EtaExps',axiom,
! [Vvar__0___24Anonymous__121900,Vvar__1___24Anonymous__121901,Vvar__2___24Anonymous__121902,Vvar__3___24Anonymous__121903] :
( cTait_2eTyping_2econtext___24t(Vvar__0___24Anonymous__121900)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__1___24Anonymous__121901)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__2___24Anonymous__121902)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__3___24Anonymous__121903)
=> ( cEta_2eEtaExps___24a4(Vvar__0___24Anonymous__121900,Vvar__1___24Anonymous__121901,Vvar__2___24Anonymous__121902,Vvar__3___24Anonymous__121903)
=> ( ? [Vvar__0__rhos__121905] :
( cTait_2eTyping_2econtext___24t(Vvar__0__rhos__121905)
& Vvar__3___24Anonymous__121903 = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)
& Vvar__2___24Anonymous__121902 = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)
& Vvar__1___24Anonymous__121901 = cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)
& Vvar__0___24Anonymous__121900 = Vvar__0__rhos__121905 )
| ? [Vvar__0__rhos__121906] :
( cTait_2eTyping_2econtext___24t(Vvar__0__rhos__121906)
& ? [Vvar__1__sigma__121907] :
( cTait_2eTerm_2etype___24t(Vvar__1__sigma__121907)
& ? [Vvar__2__sigmas__121908] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__2__sigmas__121908)
& ? [Vvar__3__r__121909] :
( cTait_2eTerm_2eterm___24t(Vvar__3__r__121909)
& ? [Vvar__4__s__121910] :
( cTait_2eTerm_2eterm___24t(Vvar__4__s__121910)
& ? [Vvar__5__rs__121911] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__5__rs__121911)
& ? [Vvar__6__ss__121912] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__6__ss__121912)
& cEta_2eEtaExp___24a4(Vvar__0__rhos__121906,Vvar__1__sigma__121907,Vvar__3__r__121909,Vvar__4__s__121910)
& cEta_2eEtaExps___24a4(Vvar__0__rhos__121906,Vvar__2__sigmas__121908,Vvar__5__rs__121911,Vvar__6__ss__121912)
& Vvar__3___24Anonymous__121903 = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__4__s__121910,Vvar__6__ss__121912)
& Vvar__2___24Anonymous__121902 = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,Vvar__3__r__121909,Vvar__5__rs__121911)
& Vvar__1___24Anonymous__121901 = cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,Vvar__1__sigma__121907,Vvar__2__sigmas__121908)
& Vvar__0___24Anonymous__121900 = Vvar__0__rhos__121906 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [VX152697] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX152697)
=> ( VX152697 = cHammer_2eTactics_2eReconstr_2eEmpty
| VX152697 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).
fof('$_inversion_Tait.Subst.substitution',axiom,
! [VX333] :
( cTait_2eSubst_2esubstitution___24t(VX333)
=> ? [Vvar__0__support__334] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vvar__0__support__334)
& ? [Vvar__1__shift__335] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__shift__335)
& VX333 = cTait_2eSubst_2emk__sub___24a2(Vvar__0__support__334,Vvar__1__shift__335) ) ) ) ).
fof('$_inversion_Tait.Subst2.Joachimski.substitution',axiom,
! [VX1051] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(VX1051)
=> ( ? [Vvar__0___24Anonymous__1052] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__1052)
& ? [Vvar__1___24Anonymous__1053] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vvar__1___24Anonymous__1053)
& VX1051 = cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vvar__0___24Anonymous__1052,Vvar__1___24Anonymous__1053) ) )
| ? [Vvar__0___24Anonymous__1054] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1054)
& VX1051 = cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vvar__0___24Anonymous__1054) ) ) ) ).
fof('$_inversion_Tait.Term.term',axiom,
! [VX106] :
( cTait_2eTerm_2eterm___24t(VX106)
=> ( ? [Vvar__0___24Anonymous__107] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__107)
& VX106 = cTait_2eTerm_2eVar___24a1(Vvar__0___24Anonymous__107) )
| ? [Vvar__0___24Anonymous__108] :
( cTait_2eTerm_2eterm___24t(Vvar__0___24Anonymous__108)
& ? [Vvar__1___24Anonymous__109] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__109)
& VX106 = cTait_2eTerm_2eApp___24a2(Vvar__0___24Anonymous__108,Vvar__1___24Anonymous__109) ) )
| ? [Vvar__0___24Anonymous__110] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__110)
& ? [Vvar__1___24Anonymous__111] :
( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__111)
& VX106 = cTait_2eTerm_2eAbs___24a2(Vvar__0___24Anonymous__110,Vvar__1___24Anonymous__111) ) ) ) ) ).
fof('$_inversion_Tait.Term.type',axiom,
! [VX206] :
( cTait_2eTerm_2etype___24t(VX206)
=> ( VX206 = cTait_2eTerm_2eIota
| ? [Vvar__0___24Anonymous__207] :
( cTait_2eTerm_2etype___24t(Vvar__0___24Anonymous__207)
& ? [Vvar__1___24Anonymous__208] :
( cTait_2eTerm_2etype___24t(Vvar__1___24Anonymous__208)
& VX206 = cTait_2eTerm_2eArrow___24a2(Vvar__0___24Anonymous__207,Vvar__1___24Anonymous__208) ) ) ) ) ).
fof('$_inversion_Tait.Typing.CorTyp',axiom,
! [Vvar__0___24Anonymous__1001,Vvar__1___24Anonymous__1002] :
( cTait_2eTyping_2econtext___24t(Vvar__0___24Anonymous__1001)
=> ( cTait_2eTerm_2eterm___24t(Vvar__1___24Anonymous__1002)
=> ( cTait_2eTyping_2eCorTyp___24a2(Vvar__0___24Anonymous__1001,Vvar__1___24Anonymous__1002)
=> ( ? [Vvar__0__rhos__1004] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__0__rhos__1004)
& ? [Vvar__1__n__1005] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__1005)
& p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__1__n__1005,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,Vvar__0__rhos__1004)))
& Vvar__1___24Anonymous__1002 = cTait_2eTerm_2eVar___24a1(Vvar__1__n__1005)
& Vvar__0___24Anonymous__1001 = Vvar__0__rhos__1004 ) )
| ? [Vvar__0__rhos__1007] :
( cTait_2eTyping_2econtext___24t(Vvar__0__rhos__1007)
& ? [Vvar__1__r__1008] :
( cTait_2eTerm_2eterm___24t(Vvar__1__r__1008)
& ? [Vvar__2__s__1009] :
( cTait_2eTerm_2eterm___24t(Vvar__2__s__1009)
& cTait_2eTyping_2eCorTyp___24a2(Vvar__0__rhos__1007,Vvar__1__r__1008)
& cTait_2eTyping_2eCorTyp___24a2(Vvar__0__rhos__1007,Vvar__2__s__1009)
& ? [Vvar__5__sigma__1012] :
( cTait_2eTerm_2etype___24t(Vvar__5__sigma__1012)
& cTait_2eTyping_2etyp___24a2(Vvar__0__rhos__1007,Vvar__1__r__1008) = cTait_2eTerm_2eArrow___24a2(cTait_2eTyping_2etyp___24a2(Vvar__0__rhos__1007,Vvar__2__s__1009),Vvar__5__sigma__1012)
& Vvar__1___24Anonymous__1002 = cTait_2eTerm_2eApp___24a2(Vvar__1__r__1008,Vvar__2__s__1009)
& Vvar__0___24Anonymous__1001 = Vvar__0__rhos__1007 ) ) ) )
| ? [Vvar__0__rhos__1014] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vvar__0__rhos__1014)
& ? [Vvar__1__rho__1015] :
( cTait_2eTerm_2etype___24t(Vvar__1__rho__1015)
& ? [Vvar__2__r__1016] :
( cTait_2eTerm_2eterm___24t(Vvar__2__r__1016)
& cTait_2eTyping_2eCorTyp___24a2(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,Vvar__1__rho__1015,Vvar__0__rhos__1014),Vvar__2__r__1016)
& Vvar__1___24Anonymous__1002 = cTait_2eTerm_2eAbs___24a2(Vvar__1__rho__1015,Vvar__2__r__1016)
& Vvar__0___24Anonymous__1001 = Vvar__0__rhos__1014 ) ) ) ) ) ) ) ).
fof('$_lam_152564',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__152564___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_152780',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__152780___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_152788',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__152788___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_152796',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__152796___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_152804',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__152804___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_26',axiom,
! [Vv__CANONICAL__0] : c_24__lam__26___24a1(Vv__CANONICAL__0) = c_24__type__28___24a1(Vv__CANONICAL__0) ).
fof('$_lam_30',axiom,
! [Vv__CANONICAL__0] : c_24__lam__30___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eSpecif_2eleft___24a3(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__0),cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eArith_2ePeanoNat_2eNat_2ele__0__l___24a1(Vv__CANONICAL__0)) ).
fof('$_lam_33372',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11] : c_24__lam__33372___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = c_24__let__11__subst__l__33300___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__11)) ).
fof('$_lam_414',axiom,
! [Vv__CANONICAL__0] : c_24__lam__414___24a1(Vv__CANONICAL__0) = c_24__type__416___24a1(Vv__CANONICAL__0) ).
fof('$_lam_422',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__422___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24__prop__424,c_24__prop__425,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eO)) )
| ? [Vvar__0___24Anonymous__423] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__423)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__423)
& c_24__lam__422___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eSpecif_2eright___24a3(c_24__prop__426___24a1(Vvar__0___24Anonymous__423),c_24__prop__427___24a1(Vvar__0___24Anonymous__423),cCoq_2eInit_2ePeano_2eO__S___24a1(Vvar__0___24Anonymous__423)) ) ) ) ).
fof('$_lam_507',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__507___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__510___24a1(Vv__CANONICAL__0),c_24__prop__511___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__0___24Anonymous__508] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__508)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__508)
& c_24__lam__507___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(c_24__prop__514___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__508),c_24__prop__515___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__508)) ) ) ) ) ).
fof('$_lam_53',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__53___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0))) )
| ? [Vvar__0___24Anonymous__54] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__54)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__54)
& c_24__lam__53___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a6(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__54),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__54,Vv__CANONICAL__0),c_24__lam__61___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__54),c_24__lam__64___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__54),c_24__lam__68___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__54),happ(Vv__CANONICAL__1,Vvar__0___24Anonymous__54)) ) ) ) ) ).
fof('$_lam_55008',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__55008___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0) ).
fof('$_lam_55011',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__55011___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ).
fof('$_lam_61',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__61___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1)),cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0))) ).
fof('$_lam_64',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__64___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eleft___24a3(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1)),cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0)),cCoq_2eArith_2eGt_2egt__le__S___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ).
fof('$_lam_64696',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__64696___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_66336',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__66336___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esig___24a2(Vv__CANONICAL__0,c_24__lam__66340___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_66340',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__66340___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0))) ) ).
fof('$_lam_68',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__68___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1)),cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0))) ).
fof('$_lam_72981',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__72981___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_836',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__836___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_prop_1223',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1223___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cTait_2eApps_2eright__app___24a1(Vv__CANONICAL__0) = cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_1224',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1224___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cTait_2eApps_2eright__app___24a1(Vv__CANONICAL__0) != cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_1225',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1225___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cTait_2eApps_2eright__app___24a1(Vv__CANONICAL__0) = cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_1226',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1226___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cTait_2eApps_2eright__app___24a1(Vv__CANONICAL__0) != cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_151',axiom,
! [V1__k,Vvar__0___24Anonymous__133] :
( p(c_24__prop__151___24a2(V1__k,Vvar__0___24Anonymous__133))
<=> Vvar__0___24Anonymous__133 = V1__k ) ).
fof('$_prop_152',axiom,
! [V1__k,Vvar__0___24Anonymous__133] :
( p(c_24__prop__152___24a2(V1__k,Vvar__0___24Anonymous__133))
<=> Vvar__0___24Anonymous__133 != V1__k ) ).
fof('$_prop_152020',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__152020___24a2(V0__A,V1__B))
<=> ( p(V0__A)
| p(V1__B) ) ) ).
fof('$_prop_152021',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__152021___24a2(V0__A,V1__B))
<=> ( p(V0__A)
& p(V1__B) ) ) ).
fof('$_prop_153',axiom,
! [V1__k,Vvar__0___24Anonymous__133] :
( p(c_24__prop__153___24a2(V1__k,Vvar__0___24Anonymous__133))
<=> Vvar__0___24Anonymous__133 = V1__k ) ).
fof('$_prop_153467',axiom,
! [Vvar__0___24Anonymous__153443,Vvar__0__S__153445,Vvar__1__x__153446,Vvar__2__y__153447] :
( p(c_24__prop__153467___24a4(Vvar__0___24Anonymous__153443,Vvar__0__S__153445,Vvar__1__x__153446,Vvar__2__y__153447))
<=> Vvar__1__x__153446 = Vvar__2__y__153447 ) ).
fof('$_prop_153468',axiom,
! [Vvar__0___24Anonymous__153443,Vvar__0__x__153448,Vvar__1__y__153449] :
( p(c_24__prop__153468___24a3(Vvar__0___24Anonymous__153443,Vvar__0__x__153448,Vvar__1__y__153449))
<=> Vvar__0__x__153448 = Vvar__1__y__153449 ) ).
fof('$_prop_153469',axiom,
! [Vvar__0___24Anonymous__153443,Vvar__0__x__153450,Vvar__1__s__153451] :
( p(c_24__prop__153469___24a3(Vvar__0___24Anonymous__153443,Vvar__0__x__153450,Vvar__1__s__153451))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__153450,Vvar__1__s__153451) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_153470',axiom,
! [Vvar__0___24Anonymous__153443,Vvar__0__P__153452,Vvar__1__Q__153453] :
( p(c_24__prop__153470___24a3(Vvar__0___24Anonymous__153443,Vvar__0__P__153452,Vvar__1__Q__153453))
<=> ( p(Vvar__0__P__153452)
& p(Vvar__1__Q__153453) ) ) ).
fof('$_prop_153471',axiom,
! [Vvar__0___24Anonymous__153443,Vvar__0__P__153456,Vvar__1__Q__153457] :
( p(c_24__prop__153471___24a3(Vvar__0___24Anonymous__153443,Vvar__0__P__153456,Vvar__1__Q__153457))
<=> ( p(Vvar__0__P__153456)
| p(Vvar__1__Q__153457) ) ) ).
fof('$_prop_153472',axiom,
! [Vvar__0___24Anonymous__153443,Vvar__0__P__153460,Vvar__1__Q__153461] :
( p(c_24__prop__153472___24a3(Vvar__0___24Anonymous__153443,Vvar__0__P__153460,Vvar__1__Q__153461))
<=> ( p(Vvar__0__P__153460)
=> p(Vvar__1__Q__153461) ) ) ).
fof('$_prop_153473',axiom,
! [Vvar__0___24Anonymous__153443,Vvar__0__P__153465] :
( p(c_24__prop__153473___24a2(Vvar__0___24Anonymous__153443,Vvar__0__P__153465))
<=> ~ p(Vvar__0__P__153465) ) ).
fof('$_prop_153487',axiom,
! [Vvar__0___24Anonymous__153474,Vvar__0__s__153478] :
( p(c_24__prop__153487___24a2(Vvar__0___24Anonymous__153474,Vvar__0__s__153478))
<=> ! [Vvar__1__a__153479] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__153479)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__153479,Vvar__0__s__153478) ) ) ).
fof('$_prop_153488',axiom,
! [Vvar__0___24Anonymous__153474,Vvar__0__s1__153480,Vvar__1__s2__153481] :
( p(c_24__prop__153488___24a3(Vvar__0___24Anonymous__153474,Vvar__0__s1__153480,Vvar__1__s2__153481))
<=> ! [Vvar__2__a__153482] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__153482)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__153482,Vvar__0__s1__153480)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__153482,Vvar__1__s2__153481) ) ) ) ).
fof('$_prop_153489',axiom,
! [Vvar__0___24Anonymous__153474,Vvar__0__s1__153484,Vvar__1__s2__153485] :
( p(c_24__prop__153489___24a3(Vvar__0___24Anonymous__153474,Vvar__0__s1__153484,Vvar__1__s2__153485))
<=> ! [Vvar__2__a__153486] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__153486)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__153486,Vvar__0__s1__153484)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__153486,Vvar__1__s2__153485) ) ) ) ).
fof('$_prop_154',axiom,
! [V1__k,Vvar__0___24Anonymous__133] :
( p(c_24__prop__154___24a2(V1__k,Vvar__0___24Anonymous__133))
<=> Vvar__0___24Anonymous__133 != V1__k ) ).
fof('$_prop_418',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__418___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_419',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__419___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_424',axiom,
( p(c_24__prop__424)
<=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_425',axiom,
( p(c_24__prop__425)
<=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_426',axiom,
! [Vvar__0___24Anonymous__423] :
( p(c_24__prop__426___24a1(Vvar__0___24Anonymous__423))
<=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__423) ) ).
fof('$_prop_427',axiom,
! [Vvar__0___24Anonymous__423] :
( p(c_24__prop__427___24a1(Vvar__0___24Anonymous__423))
<=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__423) ) ).
fof('$_prop_510',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__510___24a1(Vv__CANONICAL__0))
<=> cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_511',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__511___24a1(Vv__CANONICAL__0))
<=> cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0) != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_514',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__508] :
( p(c_24__prop__514___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__508))
<=> Vv__CANONICAL__0 = Vvar__0___24Anonymous__508 ) ).
fof('$_prop_515',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__508] :
( p(c_24__prop__515___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__508))
<=> Vv__CANONICAL__0 != Vvar__0___24Anonymous__508 ) ).
fof('$_prop_519',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__519___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_520',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__520___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_55000',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__55000___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_854',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__854___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_987',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__987___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_988',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__988___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_type_104',axiom,
! [Vvar__105] :
( c_24__type__104___24t(Vvar__105)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__105,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1041',axiom,
! [Vvar__1042] :
( c_24__type__1041___24t(Vvar__1042)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTyping_2econtext___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__1042,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1065',axiom,
! [Vvar__1066] :
( c_24__type__1065___24t(Vvar__1066)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eSubst2_2eJoachimski_2esubstitution___24t(happ(happ(Vvar__1066,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1067',axiom,
! [Vvar__1068] :
( c_24__type__1067___24t(Vvar__1068)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cTait_2eSubst2_2eJoachimski_2esubstitution___24t(happ(Vvar__1068,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1075',axiom,
! [Vv__CANONICAL__0,Vvar__1076] :
( c_24__type__1075___24t(Vv__CANONICAL__0,Vvar__1076)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__1076,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1091',axiom,
! [Vvar__1092] :
( c_24__type__1091___24t(Vvar__1092)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1093___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1101___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1104___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__1092,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1093',axiom,
! [Vvar__1094] :
( c_24__type__1093___24t(Vvar__1094)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__1094,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1101',axiom,
! [Vv__CANONICAL__0,Vvar__1102] :
( c_24__type__1101___24t(Vv__CANONICAL__0,Vvar__1102)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__2))
=> t(happ(happ(happ(Vvar__1102,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,cTait_2eSubst2_2eJoachimski_2eDot___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_type_1104',axiom,
! [Vv__CANONICAL__0,Vvar__1105] :
( c_24__type__1104___24t(Vv__CANONICAL__0,Vvar__1105)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__1105,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,cTait_2eSubst2_2eJoachimski_2eUp___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_type_1106',axiom,
! [Vvar__1107] :
( c_24__type__1106___24t(Vvar__1107)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1107,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1118',axiom,
! [Vvar__1119] :
( c_24__type__1118___24t(Vvar__1119)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cTait_2eSubst2_2eJoachimski_2esubstitution___24t(happ(happ(Vvar__1119,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1135',axiom,
! [Vvar__1136] :
( c_24__type__1135___24t(Vvar__1136)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__1136,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1146',axiom,
! [Vvar__1147] :
( c_24__type__1146___24t(Vvar__1147)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__1147,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1154',axiom,
! [Vvar__1155] :
( c_24__type__1154___24t(Vvar__1155)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eSubst2_2eJoachimski_2esubstitution___24t(happ(happ(Vvar__1155,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1164',axiom,
! [Vvar__1165] :
( c_24__type__1164___24t(Vvar__1165)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eSubst2_2eJoachimski_2esubstitution___24t(happ(happ(Vvar__1165,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1169',axiom,
! [Vvar__1170] :
( c_24__type__1169___24t(Vvar__1170)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eSubst2_2eJoachimski_2esubstitution___24t(happ(happ(Vvar__1170,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1228',axiom,
! [Vvar__1229] :
( c_24__type__1228___24t(Vvar__1229)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__1229,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_143330',axiom,
! [Vvar__143331] :
( c_24__type__143330___24t(Vvar__143331)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__143331,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_143341',axiom,
! [Vvar__143342] :
( c_24__type__143341___24t(Vvar__143342)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__143342,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_144520',axiom,
! [Vvar__144521] :
( c_24__type__144520___24t(Vvar__144521)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(Vvar__144521,Vv__CANONICAL__0)) ) ) ).
fof('$_type_144523',axiom,
! [Vvar__144524] :
( c_24__type__144523___24t(Vvar__144524)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__144524,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_144532',axiom,
! [Vvar__144533] :
( c_24__type__144532___24t(Vvar__144533)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__144533,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_144541',axiom,
! [Vvar__144542] :
( c_24__type__144541___24t(Vvar__144542)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__144542,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_144735',axiom,
! [Vvar__144736] :
( c_24__type__144735___24t(Vvar__144736)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__144736,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_144760',axiom,
! [Vvar__144761] :
( c_24__type__144760___24t(Vvar__144761)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__144761,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_144772',axiom,
! [Vvar__144773] :
( c_24__type__144772___24t(Vvar__144773)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__144773,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_144795',axiom,
! [Vvar__144796] :
( c_24__type__144795___24t(Vvar__144796)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__851___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__144796,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_144823',axiom,
! [Vvar__144824] :
( c_24__type__144823___24t(Vvar__144824)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__144824,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_144957',axiom,
! [Vvar__144958] :
( c_24__type__144957___24t(Vvar__144958)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32372___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32372___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__144958,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_145056',axiom,
! [Vvar__145057] :
( c_24__type__145056___24t(Vvar__145057)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32450___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__3,Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__145057,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_145201',axiom,
! [Vvar__145202] :
( c_24__type__145201___24t(Vvar__145202)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__145202,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_145206',axiom,
! [Vvar__145207] :
( c_24__type__145206___24t(Vvar__145207)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__145207,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_145211',axiom,
! [Vvar__145212] :
( c_24__type__145211___24t(Vvar__145212)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__145212,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_145217',axiom,
! [Vvar__145218] :
( c_24__type__145217___24t(Vvar__145218)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__145218,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_145219',axiom,
! [Vvar__145220] :
( c_24__type__145219___24t(Vvar__145220)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(Vvar__145220,Vv__CANONICAL__0)) ) ) ).
fof('$_type_145250',axiom,
! [Vvar__145251] :
( c_24__type__145250___24t(Vvar__145251)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__145254___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__145251,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_145254',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__145255] :
( c_24__type__145254___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__145255)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__145255,Vv__CANONICAL__2)) ) ) ).
fof('$_type_145288',axiom,
! [Vvar__145289] :
( c_24__type__145288___24t(Vvar__145289)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__145297___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__145289,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_145297',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__145298] :
( c_24__type__145297___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__145298)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(Vvar__145298,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_146833',axiom,
! [Vvar__146834] :
( c_24__type__146833___24t(Vvar__146834)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(happ(happ(Vvar__146834,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_149089',axiom,
! [Vvar__149090] :
( c_24__type__149089___24t(Vvar__149090)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__149090,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_149094',axiom,
! [Vvar__149095] :
( c_24__type__149094___24t(Vvar__149095)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__149095,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_150264',axiom,
! [Vvar__150265] :
( c_24__type__150264___24t(Vvar__150265)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__150272___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__150265,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_150272',axiom,
! [Vv__CANONICAL__0,Vvar__150273] :
( c_24__type__150272___24t(Vv__CANONICAL__0,Vvar__150273)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(Vvar__150273,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_150488',axiom,
! [Vvar__150489] :
( c_24__type__150488___24t(Vvar__150489)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__150489,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_150522',axiom,
! [Vvar__150523] :
( c_24__type__150522___24t(Vvar__150523)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__150523,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_151206',axiom,
! [Vvar__151207] :
( c_24__type__151206___24t(Vvar__151207)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__34643___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__81941___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__151207,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_151895',axiom,
! [Vv__CANONICAL__0,Vvar__151896] :
( c_24__type__151895___24t(Vv__CANONICAL__0,Vvar__151896)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__151896,Vv__CANONICAL__1)) ) ) ).
fof('$_type_151917',axiom,
! [Vvar__151918] :
( c_24__type__151917___24t(Vvar__151918)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__151919___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cTait_2eTerm_2eIota))
=> ! [Vv__CANONICAL__2] :
( c_24__type__151931___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__151918,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_151919',axiom,
! [Vvar__151920] :
( c_24__type__151919___24t(Vvar__151920)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__151920,Vv__CANONICAL__0)) ) ) ).
fof('$_type_151931',axiom,
! [Vv__CANONICAL__0,Vvar__151932] :
( c_24__type__151931___24t(Vv__CANONICAL__0,Vvar__151932)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__3] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__3))
=> t(happ(happ(happ(happ(Vvar__151932,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,cTait_2eTerm_2eArrow___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ) ) ).
fof('$_type_151933',axiom,
! [Vvar__151934] :
( c_24__type__151933___24t(Vvar__151934)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__151934,Vv__CANONICAL__0)) ) ) ).
fof('$_type_151973',axiom,
! [Vvar__151974] :
( c_24__type__151973___24t(Vvar__151974)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(happ(happ(Vvar__151974,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_151979',axiom,
! [Vvar__151980] :
( c_24__type__151979___24t(Vvar__151980)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(happ(happ(happ(Vvar__151980,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_152002',axiom,
! [Vvar__152003] :
( c_24__type__152002___24t(Vvar__152003)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__152003,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_152009',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__152010] :
( c_24__type__152009___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__152010)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__152010,Vv__CANONICAL__2)) ) ) ).
fof('$_type_152071',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__152072] :
( c_24__type__152071___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__152072)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__152072,Vv__CANONICAL__6)) ) ) ).
fof('$_type_152099',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__152100] :
( c_24__type__152099___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__152100)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__152100,Vv__CANONICAL__6)) ) ) ).
fof('$_type_152286',axiom,
! [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__152287] :
( c_24__type__152286___24t(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__152287)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__152287,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_152349',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__152350] :
( c_24__type__152349___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__152350)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__152350,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_152412',axiom,
! [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__152413] :
( c_24__type__152412___24t(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__152413)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__152413,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_152466',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__152467] :
( c_24__type__152466___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__152467)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__152467,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_152529',axiom,
! [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__152530] :
( c_24__type__152529___24t(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__152530)
<=> ! [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__152530,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_152591',axiom,
! [Vvar__152592] :
( c_24__type__152591___24t(Vvar__152592)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__152592,Vv__CANONICAL__0)) ) ) ).
fof('$_type_152699',axiom,
! [Vvar__152700] :
( c_24__type__152699___24t(Vvar__152700)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__152700,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_152847',axiom,
! [Vvar__152848] :
( c_24__type__152847___24t(Vvar__152848)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__152848,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_152867',axiom,
! [Vvar__152868] :
( c_24__type__152867___24t(Vvar__152868)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__152868,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_152935',axiom,
! [Vvar__152936] :
( c_24__type__152935___24t(Vvar__152936)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__32450___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__5,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__5,Vv__CANONICAL__8)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__152936,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_153115',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__153116] :
( c_24__type__153115___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__153116)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__153116,Vv__CANONICAL__3)) ) ) ).
fof('$_type_153123',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__153124] :
( c_24__type__153123___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__153124)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__153124,Vv__CANONICAL__3)) ) ) ).
fof('$_type_153131',axiom,
! [Vvar__153132] :
( c_24__type__153131___24t(Vvar__153132)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__34643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__34643___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__153132,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_153171',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__153172] :
( c_24__type__153171___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__153172)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__153172,Vv__CANONICAL__3)) ) ) ).
fof('$_type_153179',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__153180] :
( c_24__type__153179___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__153180)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__153180,Vv__CANONICAL__3)) ) ) ).
fof('$_type_153187',axiom,
! [Vvar__153188] :
( c_24__type__153187___24t(Vvar__153188)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__66971___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__66971___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__153188,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_153204',axiom,
! [Vvar__153205] :
( c_24__type__153204___24t(Vvar__153205)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ( p(c_24False)
=> t(happ(Vvar__153205,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_153211',axiom,
! [Vvar__153212] :
( c_24__type__153211___24t(Vvar__153212)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__153212,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_153279',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__153280] :
( c_24__type__153279___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__153280)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__153280,Vv__CANONICAL__4)) ) ) ).
fof('$_type_153288',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__153289] :
( c_24__type__153288___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__153289)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__153289,Vv__CANONICAL__4)) ) ) ).
fof('$_type_153310',axiom,
! [Vvar__153311] :
( c_24__type__153310___24t(Vvar__153311)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(happ(Vvar__153311,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_153410',axiom,
! [Vvar__153411] :
( c_24__type__153410___24t(Vvar__153411)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__153411,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_153552',axiom,
! [Vvar__153553] :
( c_24__type__153552___24t(Vvar__153553)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__153553,Vv__CANONICAL__0)) ) ) ).
fof('$_type_156',axiom,
! [Vvar__157] :
( c_24__type__156___24t(Vvar__157)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__157,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_159',axiom,
! [Vvar__160] :
( c_24__type__159___24t(Vvar__160)
<=> ! [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__160,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_161',axiom,
! [Vvar__162] :
( c_24__type__161___24t(Vvar__162)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__162,Vv__CANONICAL__0)) ) ) ).
fof('$_type_164',axiom,
! [Vvar__165] :
( c_24__type__164___24t(Vvar__165)
<=> ! [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__165,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_167',axiom,
! [Vvar__168] :
( c_24__type__167___24t(Vvar__168)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__168,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_180',axiom,
! [Vvar__181] :
( c_24__type__180___24t(Vvar__181)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__181,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_202',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__203] :
( c_24__type__202___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__203)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__203,Vv__CANONICAL__2)) ) ) ).
fof('$_type_215',axiom,
! [Vvar__216] :
( c_24__type__215___24t(Vvar__216)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cTait_2eTerm_2eterm___24t(happ(Vvar__216,Vv__CANONICAL__0)) ) ) ).
fof('$_type_218',axiom,
! [Vvar__219] :
( c_24__type__218___24t(Vvar__219)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__219,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_221',axiom,
! [Vvar__222] :
( c_24__type__221___24t(Vvar__222)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__222,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_223',axiom,
! [Vvar__224] :
( c_24__type__223___24t(Vvar__224)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__224,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23',axiom,
! [Vvar__24] :
( c_24__type__23___24t(Vvar__24)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__24,Vv__CANONICAL__0)) ) ) ).
fof('$_type_253',axiom,
! [Vvar__254] :
( c_24__type__253___24t(Vvar__254)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__254,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_278',axiom,
! [Vvar__279] :
( c_24__type__278___24t(Vvar__279)
<=> ! [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__279,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_28',axiom,
! [Vv__CANONICAL__0,Vvar__29] :
( c_24__type__28___24t(Vv__CANONICAL__0,Vvar__29)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(Vvar__29,Vv__CANONICAL__1)) ) ) ).
fof('$_type_283',axiom,
! [Vvar__284] :
( c_24__type__283___24t(Vvar__284)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,happ(happ(Vvar__284,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_290',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__291] :
( c_24__type__290___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__291)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__291,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_300',axiom,
! [Vv__CANONICAL__0,Vvar__301] :
( c_24__type__300___24t(Vv__CANONICAL__0,Vvar__301)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__301,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_313',axiom,
! [Vvar__314] :
( c_24__type__313___24t(Vvar__314)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__314,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31526',axiom,
! [Vvar__31527] :
( c_24__type__31526___24t(Vvar__31527)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__31527,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31537',axiom,
! [Vvar__31538] :
( c_24__type__31537___24t(Vvar__31538)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__31538,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31539',axiom,
! [Vvar__31540] :
( c_24__type__31539___24t(Vvar__31540)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__31540,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31553',axiom,
! [Vvar__31554] :
( c_24__type__31553___24t(Vvar__31554)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__31554,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31723',axiom,
! [Vvar__31724] :
( c_24__type__31723___24t(Vvar__31724)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__31724,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31748',axiom,
! [Vvar__31749] :
( c_24__type__31748___24t(Vvar__31749)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__31749,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31750',axiom,
! [Vvar__31751] :
( c_24__type__31750___24t(Vvar__31751)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__31751,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31760',axiom,
! [Vvar__31761] :
( c_24__type__31760___24t(Vvar__31761)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__31761,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31787',axiom,
! [Vvar__31788] :
( c_24__type__31787___24t(Vvar__31788)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__31788,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32372',axiom,
! [Vv__CANONICAL__0,Vvar__32373] :
( c_24__type__32372___24t(Vv__CANONICAL__0,Vvar__32373)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__32373,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_32396',axiom,
! [Vvar__32397] :
( c_24__type__32396___24t(Vvar__32397)
<=> ! [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__32372___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__32397,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_32404',axiom,
! [Vv__CANONICAL__0,Vvar__32405] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vvar__32405)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32405,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32413',axiom,
! [Vv__CANONICAL__0,Vvar__32414] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vvar__32414)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__32414,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_32418',axiom,
! [Vv__CANONICAL__0,Vvar__32419] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vvar__32419)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__32419,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_32425',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32426] :
( c_24__type__32425___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32426)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__32426,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_32439',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32440] :
( c_24__type__32439___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32440)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__32440,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_32446',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32447] :
( c_24__type__32446___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32447)
<=> ! [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__32447,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_32450',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32451] :
( c_24__type__32450___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32451)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__32451,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_32474',axiom,
! [Vvar__32475] :
( c_24__type__32474___24t(Vvar__32475)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32481___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__32475,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_32481',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32482] :
( c_24__type__32481___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32482)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32482,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32510',axiom,
! [Vvar__32511] :
( c_24__type__32510___24t(Vvar__32511)
<=> ! [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__32511,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32599',axiom,
! [Vvar__32600] :
( c_24__type__32599___24t(Vvar__32600)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__32600,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32629',axiom,
! [Vvar__32630] :
( c_24__type__32629___24t(Vvar__32630)
<=> ! [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__32630,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32633',axiom,
! [Vvar__32634] :
( c_24__type__32633___24t(Vvar__32634)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__32634,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32831',axiom,
! [Vvar__32832] :
( c_24__type__32831___24t(Vvar__32832)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32372___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__32832,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33270',axiom,
! [Vvar__33271] :
( c_24__type__33270___24t(Vvar__33271)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__32450___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__33287___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__33296___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__33271,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_33287',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33288] :
( c_24__type__33287___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33288)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__33288,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_33296',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33297] :
( c_24__type__33296___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33297)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__33297,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_33504',axiom,
! [Vvar__33505] :
( c_24__type__33504___24t(Vvar__33505)
<=> ! [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__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__32372___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__33522___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__33505,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),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('$_type_33522',axiom,
! [Vv__CANONICAL__0,Vvar__33523] :
( c_24__type__33522___24t(Vv__CANONICAL__0,Vvar__33523)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__33523,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_33760',axiom,
! [Vvar__33761] :
( c_24__type__33760___24t(Vvar__33761)
<=> ! [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__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__32450___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__33287___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__33296___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__33761,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),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('$_type_33945',axiom,
! [Vvar__33946] :
( c_24__type__33945___24t(Vvar__33946)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__32372___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__33522___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__33946,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_341',axiom,
! [Vvar__342] :
( c_24__type__341___24t(Vvar__342)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cTait_2eSubst_2esubstitution___24t(happ(happ(Vvar__342,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34203',axiom,
! [Vvar__34204] :
( c_24__type__34203___24t(Vvar__34204)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__10] :
( c_24__type__32446___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__32450___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__34224___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__7,Vv__CANONICAL__14)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__34204,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_34224',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34225] :
( c_24__type__34224___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34225)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__34225,Vv__CANONICAL__2)) ) ) ).
fof('$_type_34283',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34284] :
( c_24__type__34283___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34284)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__34284,Vv__CANONICAL__3)) ) ) ).
fof('$_type_34301',axiom,
! [Vvar__34302] :
( c_24__type__34301___24t(Vvar__34302)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32404___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__34302,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_34306',axiom,
! [Vvar__34307] :
( c_24__type__34306___24t(Vvar__34307)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__34307,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34314',axiom,
! [Vvar__34315] :
( c_24__type__34314___24t(Vvar__34315)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34315,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_346',axiom,
! [Vvar__347] :
( c_24__type__346___24t(Vvar__347)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eSubst_2esubstitution___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,happ(Vvar__347,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34636',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34637] :
( c_24__type__34636___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34637)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__34637,Vv__CANONICAL__2)) ) ) ).
fof('$_type_34640',axiom,
! [Vvar__34641] :
( c_24__type__34640___24t(Vvar__34641)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__34643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__34641,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34643',axiom,
! [Vv__CANONICAL__0,Vvar__34644] :
( c_24__type__34643___24t(Vv__CANONICAL__0,Vvar__34644)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__34644,Vv__CANONICAL__1)) ) ) ).
fof('$_type_34660',axiom,
! [Vvar__34661] :
( c_24__type__34660___24t(Vvar__34661)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__34643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__34661,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_34666',axiom,
! [Vvar__34667] :
( c_24__type__34666___24t(Vvar__34667)
<=> ! [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__34667,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_34671',axiom,
! [Vvar__34672] :
( c_24__type__34671___24t(Vvar__34672)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__34672,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_34697',axiom,
! [Vvar__34698] :
( c_24__type__34697___24t(Vvar__34698)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__34701___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__34708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__34715___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__34698,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('$_type_34701',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34702] :
( c_24__type__34701___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34702)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__34702,Vv__CANONICAL__2)) ) ) ).
fof('$_type_34708',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34709] :
( c_24__type__34708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34709)
<=> ( p(Vv__CANONICAL__0)
=> t(Vvar__34709,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_34715',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34716] :
( c_24__type__34715___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34716)
<=> ( p(Vv__CANONICAL__1)
=> t(Vvar__34716,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_34727',axiom,
! [Vvar__34728] :
( c_24__type__34727___24t(Vvar__34728)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__34728,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_348',axiom,
! [Vvar__349] :
( c_24__type__348___24t(Vvar__349)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eSubst_2esubstitution___24t(Vv__CANONICAL__0)
=> cTait_2eSubst_2esubstitution___24t(happ(Vvar__349,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35507',axiom,
! [Vvar__35508] :
( c_24__type__35507___24t(Vvar__35508)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__35508,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35524',axiom,
! [Vvar__35525] :
( c_24__type__35524___24t(Vvar__35525)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__35525,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35532',axiom,
! [Vvar__35533] :
( c_24__type__35532___24t(Vvar__35533)
<=> ! [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__35533,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_359',axiom,
! [Vvar__360] :
( c_24__type__359___24t(Vvar__360)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eSubst_2esubstitution___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__360,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_361',axiom,
! [Vvar__362] :
( c_24__type__361___24t(Vvar__362)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> cTait_2eSubst_2esubstitution___24t(happ(Vvar__362,Vv__CANONICAL__0)) ) ) ).
fof('$_type_363',axiom,
! [Vvar__364] :
( c_24__type__363___24t(Vvar__364)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cTait_2eSubst_2esubstitution___24t(happ(Vvar__364,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37257',axiom,
! [Vvar__37258] :
( c_24__type__37257___24t(Vvar__37258)
<=> ! [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__37258,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37293',axiom,
! [Vvar__37294] :
( c_24__type__37293___24t(Vvar__37294)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__37294,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37335',axiom,
! [Vvar__37336] :
( c_24__type__37335___24t(Vvar__37336)
<=> ! [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__37336,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37454',axiom,
! [Vvar__37455] :
( c_24__type__37454___24t(Vvar__37455)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__37455,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37554',axiom,
! [Vvar__37555] :
( c_24__type__37554___24t(Vvar__37555)
<=> ! [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__37555,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37574',axiom,
! [Vvar__37575] :
( c_24__type__37574___24t(Vvar__37575)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__37575,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37576',axiom,
! [Vvar__37577] :
( c_24__type__37576___24t(Vvar__37577)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__37577,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37621',axiom,
! [Vvar__37622] :
( c_24__type__37621___24t(Vvar__37622)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__37622,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37810',axiom,
! [Vvar__37811] :
( c_24__type__37810___24t(Vvar__37811)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(happ(Vvar__37811,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37812',axiom,
! [Vvar__37813] :
( c_24__type__37812___24t(Vvar__37813)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(Vvar__37813,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37872',axiom,
! [Vvar__37873] :
( c_24__type__37872___24t(Vvar__37873)
<=> ! [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__37873,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37877',axiom,
! [Vvar__37878] :
( c_24__type__37877___24t(Vvar__37878)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__37878,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37883',axiom,
! [Vvar__37884] :
( c_24__type__37883___24t(Vvar__37884)
<=> ! [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__37884,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37902',axiom,
! [Vvar__37903] :
( c_24__type__37902___24t(Vvar__37903)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__37903,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38064',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38065] :
( c_24__type__38064___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38065)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38065,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_38094',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38095] :
( c_24__type__38094___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38095)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38095,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_38118',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38119] :
( c_24__type__38118___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38119)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__38119,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_38148',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38149] :
( c_24__type__38148___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38149)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__38149,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_38178',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38179] :
( c_24__type__38178___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38179)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38179,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_38202',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38203] :
( c_24__type__38202___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38203)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__38203,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_38235',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38236] :
( c_24__type__38235___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38236)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38236,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_38259',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38260] :
( c_24__type__38259___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38260)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__38260,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_38286',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38287] :
( c_24__type__38286___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38287)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__38287,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_38685',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__38686] :
( c_24__type__38685___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__38686)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38686,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_387',axiom,
! [Vvar__388] :
( c_24__type__387___24t(Vvar__388)
<=> ! [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] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__2)
=> cTait_2eTerm_2eterm___24t(happ(happ(happ(Vvar__388,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38898',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__38899] :
( c_24__type__38898___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__38899)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38899,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_39111',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39112] :
( c_24__type__39111___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39112)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__39112,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_39306',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__39307] :
( c_24__type__39306___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__39307)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__39307,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_39519',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39520] :
( c_24__type__39519___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39520)
<=> ! [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__39520,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_39732',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__39733] :
( c_24__type__39732___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__39733)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__39733,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_39945',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39946] :
( c_24__type__39945___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39946)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__39946,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_40158',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__40159] :
( c_24__type__40158___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__40159)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__40159,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_40353',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__40354] :
( c_24__type__40353___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__40354)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__40354,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_40566',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__40567] :
( c_24__type__40566___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__40567)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__40567,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_40761',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__40762] :
( c_24__type__40761___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__40762)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__40762,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_40846',axiom,
! [Vvar__40847] :
( c_24__type__40846___24t(Vvar__40847)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__40847,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_40851',axiom,
! [Vvar__40852] :
( c_24__type__40851___24t(Vvar__40852)
<=> ! [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__40852,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_40859',axiom,
! [Vvar__40860] :
( c_24__type__40859___24t(Vvar__40860)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__40860,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_40871',axiom,
! [Vvar__40872] :
( c_24__type__40871___24t(Vvar__40872)
<=> ! [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__40872,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_40883',axiom,
! [Vvar__40884] :
( c_24__type__40883___24t(Vvar__40884)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__40884,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_40888',axiom,
! [Vv__CANONICAL__0,Vvar__40889] :
( c_24__type__40888___24t(Vv__CANONICAL__0,Vvar__40889)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__40889,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_41102',axiom,
! [Vvar__41103] :
( c_24__type__41102___24t(Vvar__41103)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__41103,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_41319',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__41320] :
( c_24__type__41319___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__41320)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__41320,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_41412',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__41413] :
( c_24__type__41412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__41413)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__41413,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_41505',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__41506] :
( c_24__type__41505___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__41506)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__41506,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_41587',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__41588] :
( c_24__type__41587___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__41588)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__41588,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_416',axiom,
! [Vv__CANONICAL__0,Vvar__417] :
( c_24__type__416___24t(Vv__CANONICAL__0,Vvar__417)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__418___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__419___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(Vvar__417,Vv__CANONICAL__1)) ) ) ).
fof('$_type_41680',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__41681] :
( c_24__type__41680___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__41681)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__41681,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_41762',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__41763] :
( c_24__type__41762___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__41763)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__41763,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_41855',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__41856] :
( c_24__type__41855___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__41856)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__41856,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_42265',axiom,
! [Vvar__42266] :
( c_24__type__42265___24t(Vvar__42266)
<=> ! [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__42266,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42285',axiom,
! [Vvar__42286] :
( c_24__type__42285___24t(Vvar__42286)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__42286,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42504',axiom,
! [Vvar__42505] :
( c_24__type__42504___24t(Vvar__42505)
<=> ! [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__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__32450___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__33287___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__33296___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__42505,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),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('$_type_42561',axiom,
! [Vvar__42562] :
( c_24__type__42561___24t(Vvar__42562)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__42566___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__42562,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_42566',axiom,
! [Vv__CANONICAL__0,Vvar__42567] :
( c_24__type__42566___24t(Vv__CANONICAL__0,Vvar__42567)
<=> ! [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__42567,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_42762',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__42763] :
( c_24__type__42762___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__42763)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__42763,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_42855',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__42856] :
( c_24__type__42855___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__42856)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__42856,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_42948',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__42949] :
( c_24__type__42948___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__42949)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__42949,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_43030',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__43031] :
( c_24__type__43030___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__43031)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__43031,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_43123',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43124] :
( c_24__type__43123___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43124)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__43124,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_43205',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__43206] :
( c_24__type__43205___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__43206)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__43206,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_43298',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43299] :
( c_24__type__43298___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43299)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__43299,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_43346',axiom,
! [Vvar__43347] :
( c_24__type__43346___24t(Vvar__43347)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__43347,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_43433',axiom,
! [Vvar__43434] :
( c_24__type__43433___24t(Vvar__43434)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__43434,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_43474',axiom,
! [Vvar__43475] :
( c_24__type__43474___24t(Vvar__43475)
<=> ! [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__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__43475,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_43492',axiom,
! [Vvar__43493] :
( c_24__type__43492___24t(Vvar__43493)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__43493,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_43519',axiom,
! [Vvar__43520] :
( c_24__type__43519___24t(Vvar__43520)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__851___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__43520,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_43955',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43956] :
( c_24__type__43955___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__43956)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__43956,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44056',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__44057] :
( c_24__type__44056___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__44057)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__44057,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44157',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__44158] :
( c_24__type__44157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__44158)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__44158,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44247',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__44248] :
( c_24__type__44247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__44248)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__44248,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_44348',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__44349] :
( c_24__type__44348___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__44349)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__44349,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_44449',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__44450] :
( c_24__type__44449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__44450)
<=> ! [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__44450,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_44550',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__44551] :
( c_24__type__44550___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__44551)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__44551,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_44602',axiom,
! [Vvar__44603] :
( c_24__type__44602___24t(Vvar__44603)
<=> ! [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__44603,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44607',axiom,
! [Vvar__44608] :
( c_24__type__44607___24t(Vvar__44608)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__44608,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44612',axiom,
! [Vvar__44613] :
( c_24__type__44612___24t(Vvar__44613)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__44613,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44761',axiom,
! [Vvar__44762] :
( c_24__type__44761___24t(Vvar__44762)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__44762,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44764',axiom,
! [Vvar__44765] :
( c_24__type__44764___24t(Vvar__44765)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__44765,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44767',axiom,
! [Vvar__44768] :
( c_24__type__44767___24t(Vvar__44768)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__44768,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44774',axiom,
! [Vvar__44775] :
( c_24__type__44774___24t(Vvar__44775)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__44775,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44792',axiom,
! [Vvar__44793] :
( c_24__type__44792___24t(Vvar__44793)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__34643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__44793,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_44818',axiom,
! [Vvar__44819] :
( c_24__type__44818___24t(Vvar__44819)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__34643___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__44819,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45354',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__45355] :
( c_24__type__45354___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__45355)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__45355,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_45700',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__45701] :
( c_24__type__45700___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__45701)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__45701,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_46046',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__46047] :
( c_24__type__46046___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__46047)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__46047,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_46369',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__46370] :
( c_24__type__46369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__46370)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__46370,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_46715',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__46716] :
( c_24__type__46715___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__46716)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__46716,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_47061',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__47062] :
( c_24__type__47061___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__47062)
<=> ! [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__47062,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_47407',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__47408] :
( c_24__type__47407___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__47408)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__47408,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_47753',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__47754] :
( c_24__type__47753___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__47754)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__47754,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_48099',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48100] :
( c_24__type__48099___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48100)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__48100,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_48422',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__48423] :
( c_24__type__48422___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__48423)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__48423,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_48768',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48769] :
( c_24__type__48768___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48769)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__48769,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_49114',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__49115] :
( c_24__type__49114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__49115)
<=> ! [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__49115,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_49437',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__49438] :
( c_24__type__49437___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__49438)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__49438,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_49760',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__49761] :
( c_24__type__49760___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__49761)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__49761,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_50106',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__50107] :
( c_24__type__50106___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__50107)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__50107,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_50283',axiom,
! [Vvar__50284] :
( c_24__type__50283___24t(Vvar__50284)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__50284,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_50288',axiom,
! [Vvar__50289] :
( c_24__type__50288___24t(Vvar__50289)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__50289,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_50296',axiom,
! [Vvar__50297] :
( c_24__type__50296___24t(Vvar__50297)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__50297,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_50299',axiom,
! [Vvar__50300] :
( c_24__type__50299___24t(Vvar__50300)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__50300,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_50302',axiom,
! [Vvar__50303] :
( c_24__type__50302___24t(Vvar__50303)
<=> ! [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__50303,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_50307',axiom,
! [Vvar__50308] :
( c_24__type__50307___24t(Vvar__50308)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__50308,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_50331',axiom,
! [Vvar__50332] :
( c_24__type__50331___24t(Vvar__50332)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32404___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__50332,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_50585',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__50586] :
( c_24__type__50585___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__50586)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__50586,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_50648',axiom,
! [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__50649] :
( c_24__type__50648___24t(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__50649)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__50649,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_50711',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__50712] :
( c_24__type__50711___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__50712)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__50712,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_50765',axiom,
! [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__50766] :
( c_24__type__50765___24t(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__50766)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__50766,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_50828',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__50829] :
( c_24__type__50828___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__50829)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__50829,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_51141',axiom,
! [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__51142] :
( c_24__type__51141___24t(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__51142)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__51142,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_51204',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__51205] :
( c_24__type__51204___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__51205)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__51205,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_51267',axiom,
! [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__51268] :
( c_24__type__51267___24t(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__51268)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__51268,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_51321',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__51322] :
( c_24__type__51321___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__51322)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__51322,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_51384',axiom,
! [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__51385] :
( c_24__type__51384___24t(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__51385)
<=> ! [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__51385,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_51521',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51522] :
( c_24__type__51521___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51522)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__51522,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_51544',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51545] :
( c_24__type__51544___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51545)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__51545,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_51567',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51568] :
( c_24__type__51567___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51568)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__51568,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_51590',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51591] :
( c_24__type__51590___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51591)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__51591,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_51608',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51609] :
( c_24__type__51608___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51609)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__51609,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_51634',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51635] :
( c_24__type__51634___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51635)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__51635,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_51652',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51653] :
( c_24__type__51652___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__51653)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__51653,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_517',axiom,
! [Vvar__518] :
( c_24__type__517___24t(Vvar__518)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__519___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__520___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__518,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_51910',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__51911] :
( c_24__type__51910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__51911)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__51911,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_52035',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52036] :
( c_24__type__52035___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52036)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__52036,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_52160',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52161] :
( c_24__type__52160___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52161)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__52161,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_52285',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52286] :
( c_24__type__52285___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52286)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__52286,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_52410',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52411] :
( c_24__type__52410___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52411)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__52411,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_52535',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52536] :
( c_24__type__52535___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52536)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__52536,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_52646',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52647] :
( c_24__type__52646___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__52647)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__52647,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_52865',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__52866] :
( c_24__type__52865___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__52866)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__52866,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_52884',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__52885] :
( c_24__type__52884___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__52885)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__52885,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_52898',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__52899] :
( c_24__type__52898___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__52899)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__52899,Vv__CANONICAL__4)) ) ) ).
fof('$_type_53043',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53044] :
( c_24__type__53043___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53044)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__53044,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_53093',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53094] :
( c_24__type__53093___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53094)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__53094,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_53143',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53144] :
( c_24__type__53143___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53144)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__53144,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_53185',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53186] :
( c_24__type__53185___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53186)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__53186,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_53235',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53236] :
( c_24__type__53235___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53236)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__53236,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_53311',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__53312] :
( c_24__type__53311___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__53312)
<=> ! [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__53312,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_534',axiom,
! [Vvar__535] :
( c_24__type__534___24t(Vvar__535)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__535,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_53420',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53421] :
( c_24__type__53420___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53421)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__53421,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53464',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53465] :
( c_24__type__53464___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53465)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__53465,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_53500',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53501] :
( c_24__type__53500___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53501)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__53501,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_53544',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53545] :
( c_24__type__53544___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__53545)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__53545,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53556',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__53557] :
( c_24__type__53556___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__53557)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__53557,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_53573',axiom,
! [Vvar__53574] :
( c_24__type__53573___24t(Vvar__53574)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__53574,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_538',axiom,
! [Vvar__539] :
( c_24__type__538___24t(Vvar__539)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__539,Vv__CANONICAL__0)) ) ) ).
fof('$_type_53983',axiom,
! [Vvar__53984] :
( c_24__type__53983___24t(Vvar__53984)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__53984,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_53986',axiom,
! [Vvar__53987] :
( c_24__type__53986___24t(Vvar__53987)
<=> ! [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__53987,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_54028',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__54029] :
( c_24__type__54028___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__54029)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__54029,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_54048',axiom,
! [Vvar__54049] :
( c_24__type__54048___24t(Vvar__54049)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32418___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__54058___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__54049,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_54058',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__54059] :
( c_24__type__54058___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__54059)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__54059,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_54108',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__54109] :
( c_24__type__54108___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__54109)
<=> ! [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__54109,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_54152',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__54153] :
( c_24__type__54152___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__54153)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__54153,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_54187',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__54188] :
( c_24__type__54187___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__54188)
<=> ! [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__54188,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_54192',axiom,
! [Vvar__54193] :
( c_24__type__54192___24t(Vvar__54193)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__54193,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_54197',axiom,
! [Vvar__54198] :
( c_24__type__54197___24t(Vvar__54198)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__54198,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_54253',axiom,
! [Vvar__54254] :
( c_24__type__54253___24t(Vvar__54254)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__54254,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_54691',axiom,
! [Vvar__54692] :
( c_24__type__54691___24t(Vvar__54692)
<=> ! [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__54698___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__54692,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_54698',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__54699] :
( c_24__type__54698___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__54699)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__54699,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_54707',axiom,
! [Vvar__54708] :
( c_24__type__54707___24t(Vvar__54708)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__54710___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__54708,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_54710',axiom,
! [Vv__CANONICAL__0,Vvar__54711] :
( c_24__type__54710___24t(Vv__CANONICAL__0,Vvar__54711)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__54711,Vv__CANONICAL__1)) ) ) ).
fof('$_type_54868',axiom,
! [Vvar__54869] :
( c_24__type__54868___24t(Vvar__54869)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__54869,Vv__CANONICAL__0)) ) ) ).
fof('$_type_54882',axiom,
! [Vvar__54883] :
( c_24__type__54882___24t(Vvar__54883)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__54883,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_54972',axiom,
! [Vvar__54973] :
( c_24__type__54972___24t(Vvar__54973)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__54973,Vv__CANONICAL__0)) ) ) ).
fof('$_type_55018',axiom,
! [Vvar__55019] :
( c_24__type__55018___24t(Vvar__55019)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__55019,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_55023',axiom,
! [Vvar__55024] :
( c_24__type__55023___24t(Vvar__55024)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTyping_2econtext___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,happ(happ(happ(Vvar__55024,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_55050',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55051] :
( c_24__type__55050___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55051)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__55051,Vv__CANONICAL__3)) ) ) ).
fof('$_type_55079',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55080] :
( c_24__type__55079___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55080)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__55080,Vv__CANONICAL__3)) ) ) ).
fof('$_type_55131',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__55132] :
( c_24__type__55131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__55132)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__55132,Vv__CANONICAL__5)) ) ) ).
fof('$_type_55139',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__55140] :
( c_24__type__55139___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__55140)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__55140,Vv__CANONICAL__5)) ) ) ).
fof('$_type_569',axiom,
! [Vvar__570] :
( c_24__type__569___24t(Vvar__570)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__570,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_572',axiom,
! [Vvar__573] :
( c_24__type__572___24t(Vvar__573)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__573,Vv__CANONICAL__0)) ) ) ).
fof('$_type_584',axiom,
! [Vvar__585] :
( c_24__type__584___24t(Vvar__585)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__585,Vv__CANONICAL__0)) ) ) ).
fof('$_type_593',axiom,
! [Vvar__594] :
( c_24__type__593___24t(Vvar__594)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> cTait_2eTerm_2eterm___24t(happ(Vvar__594,Vv__CANONICAL__0)) ) ) ).
fof('$_type_610',axiom,
! [Vvar__611] :
( c_24__type__610___24t(Vvar__611)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,happ(Vvar__611,Vv__CANONICAL__0)) ) ) ).
fof('$_type_621',axiom,
! [Vvar__622] :
( c_24__type__621___24t(Vvar__622)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__622,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_63243',axiom,
! [Vv__CANONICAL__0,Vvar__63244] :
( c_24__type__63243___24t(Vv__CANONICAL__0,Vvar__63244)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__63244,Vv__CANONICAL__1)) ) ) ).
fof('$_type_63256',axiom,
! [Vvar__63257] :
( c_24__type__63256___24t(Vvar__63257)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__31723___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__63261___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__63257,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_63261',axiom,
! [Vv__CANONICAL__0,Vvar__63262] :
( c_24__type__63261___24t(Vv__CANONICAL__0,Vvar__63262)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__63262,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_65779',axiom,
! [Vvar__65780] :
( c_24__type__65779___24t(Vvar__65780)
<=> ! [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__65780,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_65949',axiom,
! [Vvar__65950] :
( c_24__type__65949___24t(Vvar__65950)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,happ(Vvar__65950,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66198',axiom,
! [Vvar__66199] :
( c_24__type__66198___24t(Vvar__66199)
<=> ! [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__66199,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66210',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__66211] :
( c_24__type__66210___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__66211)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__66211,Vv__CANONICAL__2)) ) ) ).
fof('$_type_66235',axiom,
! [Vvar__66236] :
( c_24__type__66235___24t(Vvar__66236)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__66238___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__66250___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__66236,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_66238',axiom,
! [Vv__CANONICAL__0,Vvar__66239] :
( c_24__type__66238___24t(Vv__CANONICAL__0,Vvar__66239)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__66239,Vv__CANONICAL__1)) ) ) ).
fof('$_type_66250',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__66251] :
( c_24__type__66250___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__66251)
<=> ! [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__66251,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('$_type_66297',axiom,
! [Vvar__66298] :
( c_24__type__66297___24t(Vvar__66298)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__66298,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_66329',axiom,
! [Vvar__66330] :
( c_24__type__66329___24t(Vvar__66330)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( Vv__CANONICAL__1 != cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esigT___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),c_24__lam__66336___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__66330,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_66502',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__66503] :
( c_24__type__66502___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__66503)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__66503,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_66964',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__66965] :
( c_24__type__66964___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__66965)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__66965,Vv__CANONICAL__2)) ) ) ).
fof('$_type_66968',axiom,
! [Vvar__66969] :
( c_24__type__66968___24t(Vvar__66969)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__66971___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__66969,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66971',axiom,
! [Vv__CANONICAL__0,Vvar__66972] :
( c_24__type__66971___24t(Vv__CANONICAL__0,Vvar__66972)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__66972,Vv__CANONICAL__1)) ) ) ).
fof('$_type_66988',axiom,
! [Vvar__66989] :
( c_24__type__66988___24t(Vvar__66989)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__66971___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__66989,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_66992',axiom,
! [Vvar__66993] :
( c_24__type__66992___24t(Vvar__66993)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vv__CANONICAL__1)
=> cTait_2eTerm_2etype___24t(happ(happ(Vvar__66993,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_67372',axiom,
! [Vvar__67373] :
( c_24__type__67372___24t(Vvar__67373)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__32450___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__33287___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__33296___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__67373,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_67456',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67457] :
( c_24__type__67456___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67457)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__67457,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_67461',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67462] :
( c_24__type__67461___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67462)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> t(happ(Vvar__67462,Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ).
fof('$_type_68418',axiom,
! [Vvar__68419] :
( c_24__type__68418___24t(Vvar__68419)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32372___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__68419,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_68948',axiom,
! [Vvar__68949] :
( c_24__type__68948___24t(Vvar__68949)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__68949,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_690',axiom,
! [Vvar__691] :
( c_24__type__690___24t(Vvar__691)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__691,Vv__CANONICAL__0)) ) ) ).
fof('$_type_692',axiom,
! [Vvar__693] :
( c_24__type__692___24t(Vvar__693)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__693,Vv__CANONICAL__0)) ) ) ).
fof('$_type_69902',axiom,
! [Vvar__69903] :
( c_24__type__69902___24t(Vvar__69903)
<=> ! [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__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__32450___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__33287___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__33296___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__69903,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__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('$_type_69936',axiom,
! [Vvar__69937] :
( c_24__type__69936___24t(Vvar__69937)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__69937,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_70000',axiom,
! [Vvar__70001] :
( c_24__type__70000___24t(Vvar__70001)
<=> ! [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__70001,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_70057',axiom,
! [Vvar__70058] :
( c_24__type__70057___24t(Vvar__70058)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32372___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(Vvar__70058,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_702',axiom,
! [Vvar__703] :
( c_24__type__702___24t(Vvar__703)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__703,Vv__CANONICAL__0)) ) ) ).
fof('$_type_71',axiom,
! [Vvar__72] :
( c_24__type__71___24t(Vvar__72)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(happ(Vvar__72,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_71500',axiom,
! [Vvar__71501] :
( c_24__type__71500___24t(Vvar__71501)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__71501,Vv__CANONICAL__0)) ) ) ).
fof('$_type_716',axiom,
! [Vvar__717] :
( c_24__type__716___24t(Vvar__717)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__717,Vv__CANONICAL__0)) ) ) ).
fof('$_type_71693',axiom,
! [Vvar__71694] :
( c_24__type__71693___24t(Vvar__71694)
<=> ! [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__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__32413___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vv__CANONICAL__7)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__71694,Vv__CANONICAL__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('$_type_71722',axiom,
! [Vv__CANONICAL__0,Vvar__71723] :
( c_24__type__71722___24t(Vv__CANONICAL__0,Vvar__71723)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__71723,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_71731',axiom,
! [Vvar__71732] :
( c_24__type__71731___24t(Vvar__71732)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__71732,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_71887',axiom,
! [Vvar__71888] :
( c_24__type__71887___24t(Vvar__71888)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__71888,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_72039',axiom,
! [Vvar__72040] :
( c_24__type__72039___24t(Vvar__72040)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__72040,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_721',axiom,
! [Vvar__722] :
( c_24__type__721___24t(Vvar__722)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__722,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_724',axiom,
! [Vv__CANONICAL__0,Vvar__725] :
( c_24__type__724___24t(Vv__CANONICAL__0,Vvar__725)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__725,Vv__CANONICAL__1)) ) ) ).
fof('$_type_72844',axiom,
! [Vvar__72845] :
( c_24__type__72844___24t(Vvar__72845)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__72848___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__72845,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_72848',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__72849] :
( c_24__type__72848___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__72849)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__72849,Vv__CANONICAL__2)) ) ) ).
fof('$_type_72967',axiom,
! [Vvar__72968] :
( c_24__type__72967___24t(Vvar__72968)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__72968,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_72991',axiom,
! [Vvar__72992] :
( c_24__type__72991___24t(Vvar__72992)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__72992,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_73010',axiom,
! [Vvar__73011] :
( c_24__type__73010___24t(Vvar__73011)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__73011,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_73044',axiom,
! [Vv__CANONICAL__0,Vvar__73045] :
( c_24__type__73044___24t(Vv__CANONICAL__0,Vvar__73045)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__73045,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_73154',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73155] :
( c_24__type__73154___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73155)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__73155,Vv__CANONICAL__3)) ) ) ).
fof('$_type_73311',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73312] :
( c_24__type__73311___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73312)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__73312,Vv__CANONICAL__3)) ) ) ).
fof('$_type_73370',axiom,
! [Vvar__73371] :
( c_24__type__73370___24t(Vvar__73371)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__34643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__66238___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__4] :
( c_24__type__73389___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__73371,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ) ).
fof('$_type_73389',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73390] :
( c_24__type__73389___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73390)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(Vvar__73390,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ) ).
fof('$_type_73546',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__73547] :
( c_24__type__73546___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__73547)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__73547,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_73647',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73648] :
( c_24__type__73647___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73648)
<=> ! [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__73648,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_73678',axiom,
! [Vvar__73679] :
( c_24__type__73678___24t(Vvar__73679)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__73679,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_737',axiom,
! [Vvar__738] :
( c_24__type__737___24t(Vvar__738)
<=> ! [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__738,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_73705',axiom,
! [Vvar__73706] :
( c_24__type__73705___24t(Vvar__73706)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__73706,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_73708',axiom,
! [Vvar__73709] :
( c_24__type__73708___24t(Vvar__73709)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(Vvar__73709,Vv__CANONICAL__0)) ) ) ).
fof('$_type_73719',axiom,
! [Vvar__73720] :
( c_24__type__73719___24t(Vvar__73720)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__73720,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_73775',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__73776] :
( c_24__type__73775___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__73776)
<=> ! [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__73776,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_73927',axiom,
! [Vvar__73928] :
( c_24__type__73927___24t(Vvar__73928)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,happ(happ(Vvar__73928,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_74',axiom,
! [Vvar__75] :
( c_24__type__74___24t(Vvar__75)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__75,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_74744',axiom,
! [Vvar__74745] :
( c_24__type__74744___24t(Vvar__74745)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32450___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__4,Vv__CANONICAL__7)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__74745,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ).
fof('$_type_74754',axiom,
! [Vvar__74755] :
( c_24__type__74754___24t(Vvar__74755)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__74755,Vv__CANONICAL__0)) ) ) ).
fof('$_type_749',axiom,
! [Vvar__750] :
( c_24__type__749___24t(Vvar__750)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__750,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_760',axiom,
! [Vvar__761] :
( c_24__type__760___24t(Vvar__761)
<=> ! [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__761,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_76230',axiom,
! [Vvar__76231] :
( c_24__type__76230___24t(Vvar__76231)
<=> ! [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__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__32413___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__32446___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__32450___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__33287___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__33296___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__34283___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__76231,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),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_76566',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__76567] :
( c_24__type__76566___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__76567)
<=> ! [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__76567,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_76601',axiom,
! [Vvar__76602] :
( c_24__type__76601___24t(Vvar__76602)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__76602,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_76656',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__76657] :
( c_24__type__76656___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__76657)
<=> ! [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__76657,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_76711',axiom,
! [Vv__CANONICAL__0,Vvar__76712] :
( c_24__type__76711___24t(Vv__CANONICAL__0,Vvar__76712)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__76712,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_76762',axiom,
! [Vv__CANONICAL__0,Vvar__76763] :
( c_24__type__76762___24t(Vv__CANONICAL__0,Vvar__76763)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__76763,Vv__CANONICAL__1)) ) ) ).
fof('$_type_76770',axiom,
! [Vv__CANONICAL__0,Vvar__76771] :
( c_24__type__76770___24t(Vv__CANONICAL__0,Vvar__76771)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__76771,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_76822',axiom,
! [Vvar__76823] :
( c_24__type__76822___24t(Vvar__76823)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32418___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__76832___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__54058___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__76823,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_76832',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76833] :
( c_24__type__76832___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76833)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__76833,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_777',axiom,
! [Vvar__778] :
( c_24__type__777___24t(Vvar__778)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__290___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__778,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_77747',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77748] :
( c_24__type__77747___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77748)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__77748,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_77953',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77954] :
( c_24__type__77953___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__77954)
<=> ! [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__77954,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_78288',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78289] :
( c_24__type__78288___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78289)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__78289,Vv__CANONICAL__2)) ) ) ).
fof('$_type_78294',axiom,
! [Vvar__78295] :
( c_24__type__78294___24t(Vvar__78295)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__34643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__78295,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_78587',axiom,
! [Vvar__78588] :
( c_24__type__78587___24t(Vvar__78588)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eStrings_2eAscii_2eascii,Vv__CANONICAL__0)
=> cCoq_2eStrings_2eString_2estring___24t(happ(Vvar__78588,Vv__CANONICAL__0)) ) ) ).
fof('$_type_78602',axiom,
! [Vvar__78603] :
( c_24__type__78602___24t(Vvar__78603)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2eoption___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__78603,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_78734',axiom,
! [Vvar__78735] :
( c_24__type__78734___24t(Vvar__78735)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__78735,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_78761',axiom,
! [Vvar__78762] :
( c_24__type__78761___24t(Vvar__78762)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__78762,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_79039',axiom,
! [Vvar__79040] :
( c_24__type__79039___24t(Vvar__79040)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__79040,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_80125',axiom,
! [Vvar__80126] :
( c_24__type__80125___24t(Vvar__80126)
<=> ! [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__54698___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__80126,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_80154',axiom,
! [Vvar__80155] :
( c_24__type__80154___24t(Vvar__80155)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__54698___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__80155,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_803',axiom,
! [Vvar__804] :
( c_24__type__803___24t(Vvar__804)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__810___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__804,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_80308',axiom,
! [Vvar__80309] :
( c_24__type__80308___24t(Vvar__80309)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__80309,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_80510',axiom,
! [Vvar__80511] :
( c_24__type__80510___24t(Vvar__80511)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__80511,Vv__CANONICAL__0)) ) ) ).
fof('$_type_810',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__811] :
( c_24__type__810___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__811)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__811,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_81019',axiom,
! [Vvar__81020] :
( c_24__type__81019___24t(Vvar__81020)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__81020,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81467',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__81468] :
( c_24__type__81467___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__81468)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__81468,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_81901',axiom,
! [Vvar__81902] :
( c_24__type__81901___24t(Vvar__81902)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__81902,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81941',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__81942] :
( c_24__type__81941___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__81942)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__81942,Vv__CANONICAL__2)) ) ) ).
fof('$_type_82',axiom,
! [Vvar__83] :
( c_24__type__82___24t(Vvar__83)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__83,Vv__CANONICAL__0)) ) ) ).
fof('$_type_822',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__823] :
( c_24__type__822___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__823)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__823,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_82207',axiom,
! [Vvar__82208] :
( c_24__type__82207___24t(Vvar__82208)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__82208,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_82330',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__82331] :
( c_24__type__82330___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__82331)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__82331,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_82349',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__82350] :
( c_24__type__82349___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__82350)
<=> ! [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__82350,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_82369',axiom,
! [Vvar__82370] :
( c_24__type__82369___24t(Vvar__82370)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__32418___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__82370,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_82451',axiom,
! [Vvar__82452] :
( c_24__type__82451___24t(Vvar__82452)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__82452,Vv__CANONICAL__0)) ) ) ).
fof('$_type_82509',axiom,
! [Vvar__82510] :
( c_24__type__82509___24t(Vvar__82510)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__82510,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_82561',axiom,
! [Vvar__82562] :
( c_24__type__82561___24t(Vvar__82562)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32404___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__82562,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_83399',axiom,
! [Vvar__83400] :
( c_24__type__83399___24t(Vvar__83400)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__83400,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_83404',axiom,
! [Vvar__83405] :
( c_24__type__83404___24t(Vvar__83405)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__83405,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_83435',axiom,
! [Vvar__83436] :
( c_24__type__83435___24t(Vvar__83436)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__83436,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_83605',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__83606] :
( c_24__type__83605___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__83606)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__83606,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_83644',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__83645] :
( c_24__type__83644___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__83645)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__83645,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_83683',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__83684] :
( c_24__type__83683___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__83684)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__83684,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_83791',axiom,
! [Vvar__83792] :
( c_24__type__83791___24t(Vvar__83792)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTyping_2econtext___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__83792,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_83810',axiom,
! [Vvar__83811] :
( c_24__type__83810___24t(Vvar__83811)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTyping_2econtext___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__83811,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_848',axiom,
! [Vvar__849] :
( c_24__type__848___24t(Vvar__849)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__851___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__849,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_851',axiom,
! [Vv__CANONICAL__0,Vvar__852] :
( c_24__type__851___24t(Vv__CANONICAL__0,Vvar__852)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__852,Vv__CANONICAL__1)) ) ) ).
fof('$_type_858',axiom,
! [Vvar__859] :
( c_24__type__858___24t(Vvar__859)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eSubst_2esubstitution___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__859,Vv__CANONICAL__0)) ) ) ).
fof('$_type_861',axiom,
! [Vvar__862] :
( c_24__type__861___24t(Vvar__862)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2eterm___24t(happ(happ(Vvar__862,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_865',axiom,
! [Vvar__866] :
( c_24__type__865___24t(Vvar__866)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2etype___24t(happ(happ(Vvar__866,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_876',axiom,
! [Vv__CANONICAL__0,Vvar__877] :
( c_24__type__876___24t(Vv__CANONICAL__0,Vvar__877)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__877,Vv__CANONICAL__1)) ) ) ).
fof('$_type_915',axiom,
! [Vvar__916] :
( c_24__type__915___24t(Vvar__916)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__917___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__932___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__940___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__916,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_917',axiom,
! [Vvar__918] :
( c_24__type__917___24t(Vvar__918)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__918,Vv__CANONICAL__0)) ) ) ).
fof('$_type_92',axiom,
! [Vvar__93] :
( c_24__type__92___24t(Vvar__93)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__93,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_920',axiom,
! [Vv__CANONICAL__0,Vvar__921] :
( c_24__type__920___24t(Vv__CANONICAL__0,Vvar__921)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__921,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,cTait_2eTerm_2eVar___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_type_932',axiom,
! [Vv__CANONICAL__0,Vvar__933] :
( c_24__type__932___24t(Vv__CANONICAL__0,Vvar__933)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__3] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__3))
=> t(happ(happ(happ(happ(Vvar__933,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,cTait_2eTerm_2eApp___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ) ) ).
fof('$_type_94',axiom,
! [Vvar__95] :
( c_24__type__94___24t(Vvar__95)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__95,Vv__CANONICAL__0)) ) ) ).
fof('$_type_940',axiom,
! [Vv__CANONICAL__0,Vvar__941] :
( c_24__type__940___24t(Vv__CANONICAL__0,Vvar__941)
<=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__2))
=> t(happ(happ(happ(Vvar__941,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,cTait_2eTerm_2eAbs___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_type_982',axiom,
! [Vvar__983] :
( c_24__type__982___24t(Vvar__983)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2etype___24t(Vv__CANONICAL__0)
=> cTait_2eTerm_2etype___24t(happ(Vvar__983,Vv__CANONICAL__0)) ) ) ).
fof('$_type_985',axiom,
! [Vvar__986] :
( c_24__type__985___24t(Vvar__986)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__987___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__988___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__986,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_999',axiom,
! [Vvar__1000] :
( c_24__type__999___24t(Vvar__1000)
<=> ! [Vv__CANONICAL__0] :
( cTait_2eTyping_2econtext___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTait_2eTerm_2eterm___24t(Vv__CANONICAL__1)
=> cTait_2eTerm_2etype___24t(happ(happ(Vvar__1000,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_typeof_Coq.Arith.Compare_dec.le_gt_dec',axiom,
c_24__type__74___24t(cCoq_2eArith_2eCompare__dec_2ele__gt__dec) ).
fof('$_typeof_Coq.Arith.Compare_dec.le_lt_dec',axiom,
c_24__type__71___24t(cCoq_2eArith_2eCompare__dec_2ele__lt__dec) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__167___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq_dec',axiom,
c_24__type__517___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
c_24__type__167___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
c_24__type__167___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__54707___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__31539___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__164___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
c_24__type__152002___24t(cCoq_2eBool_2eBool_2eifb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__31553___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
c_24__type__37877___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__37872___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
c_24__type__37574___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__37621___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev',axiom,
c_24__type__37812___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
c_24__type__37810___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Byte.xbb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbb) ).
fof('$_typeof_Coq.Init.Byte.xbc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbc) ).
fof('$_typeof_Coq.Init.Byte.xbd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbd) ).
fof('$_typeof_Coq.Init.Byte.xbe',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbe) ).
fof('$_typeof_Coq.Init.Byte.xbf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbf) ).
fof('$_typeof_Coq.Init.Byte.xc0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc0) ).
fof('$_typeof_Coq.Init.Byte.xc1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc1) ).
fof('$_typeof_Coq.Init.Byte.xc2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc2) ).
fof('$_typeof_Coq.Init.Byte.xc3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc3) ).
fof('$_typeof_Coq.Init.Byte.xc4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc4) ).
fof('$_typeof_Coq.Init.Byte.xc5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc5) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__82207___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.Empty_set',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eEmpty__set) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.ID',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eID) ).
fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__31750___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__82___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__31748___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__164___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__749___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_typeof_Coq.Init.Datatypes.bool',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_typeof_Coq.Init.Datatypes.comparison',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2ecomparison) ).
fof('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__721___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__40871___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__40846___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__40851___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__737___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__702___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.list_rec',axiom,
c_24__type__66235___24t(cCoq_2eInit_2eDatatypes_2elist__rec) ).
fof('$_typeof_Coq.Init.Datatypes.list_rect',axiom,
c_24__type__66235___24t(cCoq_2eInit_2eDatatypes_2elist__rect) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__63256___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__690___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__716___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__702___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__164___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__40859___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__31760___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__40883___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__31760___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__164___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Decimal.decimal',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2edecimal) ).
fof('$_typeof_Coq.Init.Decimal.int',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2eint) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
c_24__type__152591___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__92___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__92___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__92___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__92___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__82___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__92___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.t',axiom,
cType___24t(cCoq_2eInit_2eNat_2et) ).
fof('$_typeof_Coq.Init.Nat.zero',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eNat_2ezero) ).
fof('$_typeof_Coq.Init.Peano.IsSucc',axiom,
c_24__type__692___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__167___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__167___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__167___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.except',axiom,
c_24__type__153204___24t(cCoq_2eInit_2eSpecif_2eexcept) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__34660___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__66988___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__54192___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__54197___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__34666___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__78294___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__34671___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__34640___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__153131___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__66968___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__153187___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__180___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
c_24__type__34697___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__313___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Lists.List.ForallPairs',axiom,
c_24__type__144823___24t(cCoq_2eLists_2eList_2eForallPairs) ).
fof('$_typeof_Coq.Lists.List.Forall_rect',axiom,
c_24__type__73370___24t(cCoq_2eLists_2eList_2eForall__rect) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__43492___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.concat',axiom,
c_24__type__72039___24t(cCoq_2eLists_2eList_2econcat) ).
fof('$_typeof_Coq.Lists.List.exists_last',axiom,
c_24__type__66329___24t(cCoq_2eLists_2eList_2eexists__last) ).
fof('$_typeof_Coq.Lists.List.existsb',axiom,
c_24__type__848___24t(cCoq_2eLists_2eList_2eexistsb) ).
fof('$_typeof_Coq.Lists.List.filter',axiom,
c_24__type__43519___24t(cCoq_2eLists_2eList_2efilter) ).
fof('$_typeof_Coq.Lists.List.find',axiom,
c_24__type__144795___24t(cCoq_2eLists_2eList_2efind) ).
fof('$_typeof_Coq.Lists.List.firstn',axiom,
c_24__type__73010___24t(cCoq_2eLists_2eList_2efirstn) ).
fof('$_typeof_Coq.Lists.List.flat_map',axiom,
c_24__type__72844___24t(cCoq_2eLists_2eList_2eflat__map) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__803___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__32474___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.forallb',axiom,
c_24__type__848___24t(cCoq_2eLists_2eList_2eforallb) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__144735___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.hd_error',axiom,
c_24__type__71731___24t(cCoq_2eLists_2eList_2ehd__error) ).
fof('$_typeof_Coq.Lists.List.incl',axiom,
c_24__type__72991___24t(cCoq_2eLists_2eList_2eincl) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__66297___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.lel',axiom,
c_24__type__72991___24t(cCoq_2eLists_2eList_2elel) ).
fof('$_typeof_Coq.Lists.List.list_prod',axiom,
c_24__type__72967___24t(cCoq_2eLists_2eList_2elist__prod) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__777___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__278___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.nth_default',axiom,
c_24__type__144772___24t(cCoq_2eLists_2eList_2enth__default) ).
fof('$_typeof_Coq.Lists.List.nth_error',axiom,
c_24__type__71887___24t(cCoq_2eLists_2eList_2enth__error) ).
fof('$_typeof_Coq.Lists.List.nth_ok',axiom,
c_24__type__144760___24t(cCoq_2eLists_2eList_2enth__ok) ).
fof('$_typeof_Coq.Lists.List.removelast',axiom,
c_24__type__760___24t(cCoq_2eLists_2eList_2eremovelast) ).
fof('$_typeof_Coq.Lists.List.repeat',axiom,
c_24__type__73678___24t(cCoq_2eLists_2eList_2erepeat) ).
fof('$_typeof_Coq.Lists.List.rev',axiom,
c_24__type__760___24t(cCoq_2eLists_2eList_2erev) ).
fof('$_typeof_Coq.Lists.List.rev\'',axiom,
c_24__type__760___24t(cCoq_2eLists_2eList_2erev_27) ).
fof('$_typeof_Coq.Lists.List.rev_append',axiom,
c_24__type__749___24t(cCoq_2eLists_2eList_2erev__append) ).
fof('$_typeof_Coq.Lists.List.seq',axiom,
c_24__type__283___24t(cCoq_2eLists_2eList_2eseq) ).
fof('$_typeof_Coq.Lists.List.skipn',axiom,
c_24__type__73010___24t(cCoq_2eLists_2eList_2eskipn) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__760___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Lists.SetoidList.equivlistA',axiom,
c_24__type__76601___24t(cCoq_2eLists_2eSetoidList_2eequivlistA) ).
fof('$_typeof_Coq.Lists.SetoidList.inclA',axiom,
c_24__type__76601___24t(cCoq_2eLists_2eSetoidList_2einclA) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__54048___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__54048___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__76822___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__76822___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__31787___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__37335___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__37335___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__37257___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__65779___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__32599___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__37257___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__37293___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__31537___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__23___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__23___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__161___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__161___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
c_24__type__153552___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__37554___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNeg',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__54868___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__37454___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
c_24__type__161___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__54882___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__82561___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
c_24__type__161___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__37454___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__161___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.t',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2et) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__44612___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qdiv',axiom,
c_24__type__73705___24t(cCoq_2eQArith_2eQArith__base_2eQdiv) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq',axiom,
c_24__type__32629___24t(cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq_bool',axiom,
c_24__type__32633___24t(cCoq_2eQArith_2eQArith__base_2eQeq__bool) ).
fof('$_typeof_Coq.QArith.QArith_base.Qinv',axiom,
c_24__type__73708___24t(cCoq_2eQArith_2eQArith__base_2eQinv) ).
fof('$_typeof_Coq.QArith.QArith_base.Qle',axiom,
c_24__type__32629___24t(cCoq_2eQArith_2eQArith__base_2eQle) ).
fof('$_typeof_Coq.QArith.QArith_base.Qlt',axiom,
c_24__type__32629___24t(cCoq_2eQArith_2eQArith__base_2eQlt) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__44602___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qminus',axiom,
c_24__type__73705___24t(cCoq_2eQArith_2eQArith__base_2eQminus) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmult',axiom,
c_24__type__73705___24t(cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__44607___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.QArith.QArith_base.Qopp',axiom,
c_24__type__73708___24t(cCoq_2eQArith_2eQArith__base_2eQopp) ).
fof('$_typeof_Coq.QArith.QArith_base.Qplus',axiom,
c_24__type__73705___24t(cCoq_2eQArith_2eQArith__base_2eQplus) ).
fof('$_typeof_Coq.QArith.QArith_base.Qpower',axiom,
c_24__type__73719___24t(cCoq_2eQArith_2eQArith__base_2eQpower) ).
fof('$_typeof_Coq.Reals.RIneq.negreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonposreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonposreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__44774___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__44761___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__44764___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__44767___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__44767___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__44761___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__44761___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__44764___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__44761___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__82451___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__82509___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__53983___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__702___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__53986___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__702___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Sets.Relations_1.Transitive',axiom,
c_24__type__81901___24t(cCoq_2eSets_2eRelations__1_2eTransitive) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).
fof('$_typeof_Coq.Strings.String.String',axiom,
c_24__type__34727___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.append',axiom,
c_24__type__153211___24t(cCoq_2eStrings_2eString_2eappend) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Strings.String.string_of_list_ascii',axiom,
c_24__type__78587___24t(cCoq_2eStrings_2eString_2estring__of__list__ascii) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__82369___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__37335___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__167___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__167___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
c_24__type__37554___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__37554___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__159___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLE',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLE) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLT) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__31723___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__35532___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__35524___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__35507___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.to_list',axiom,
c_24__type__80308___24t(cCoq_2eVectors_2eVectorDef_2eto__list) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__159___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__159___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__159___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__159___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__159___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__159___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__538___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__534___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__569___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gtb',axiom,
c_24__type__37883___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egtb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__37883___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__534___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__534___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__37902___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__572___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__538___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__534___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__66198___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__534___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__538___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.t',axiom,
cType___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2et) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__54972___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ezero) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__37883___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength',axiom,
c_24__type__81019___24t(cCoq_2eZArith_2eZcomplements_2eZlength) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength_aux',axiom,
c_24__type__153310___24t(cCoq_2eZArith_2eZcomplements_2eZlength__aux) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__94___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__94___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__31526___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__82509___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__153410___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__702___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__702___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__41102___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__702___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.QMicromega.QWitness',axiom,
cType___24t(cCoq_2emicromega_2eQMicromega_2eQWitness) ).
fof('$_typeof_Coq.micromega.RMicromega.RWitness',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRWitness) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__44818___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__44792___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__702___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__702___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpNEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__702___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__702___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__702___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzAdd',axiom,
c_24__type__145211___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__145217___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzIn',axiom,
c_24__type__83435___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzIn) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulC',axiom,
c_24__type__145206___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulE',axiom,
c_24__type__145211___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzSquare',axiom,
c_24__type__145201___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzZ',axiom,
c_24__type__145219___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzZ) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.cltb',axiom,
c_24__type__144957___24t(cCoq_2emicromega_2eRingMicromega_2ecltb) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
c_24__type__152847___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_pol',axiom,
c_24__type__145056___24t(cCoq_2emicromega_2eRingMicromega_2eeval__pol) ).
fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
c_24__type__32510___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).
fof('$_typeof_Coq.micromega.RingMicromega.map_option',axiom,
c_24__type__145250___24t(cCoq_2emicromega_2eRingMicromega_2emap__option) ).
fof('$_typeof_Coq.micromega.RingMicromega.map_option2',axiom,
c_24__type__145288___24t(cCoq_2emicromega_2eRingMicromega_2emap__option2) ).
fof('$_typeof_Coq.micromega.RingMicromega.nhyps_of_psatz',axiom,
c_24__type__73927___24t(cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.psubC',axiom,
c_24__type__152867___24t(cCoq_2emicromega_2eRingMicromega_2epsubC) ).
fof('$_typeof_Coq.micromega.Tauto.BFormula',axiom,
c_24__type__702___24t(cCoq_2emicromega_2eTauto_2eBFormula) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__54253___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.TFormula',axiom,
c_24__type__54253___24t(cCoq_2emicromega_2eTauto_2eTFormula) ).
fof('$_typeof_Coq.micromega.Tauto.and_cnf',axiom,
c_24__type__79039___24t(cCoq_2emicromega_2eTauto_2eand__cnf) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__31760___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.Tauto.cnf',axiom,
c_24__type__31760___24t(cCoq_2emicromega_2eTauto_2ecnf) ).
fof('$_typeof_Coq.micromega.Tauto.cnf_ff',axiom,
c_24__type__78761___24t(cCoq_2emicromega_2eTauto_2ecnf__ff) ).
fof('$_typeof_Coq.micromega.Tauto.cnf_tt',axiom,
c_24__type__78761___24t(cCoq_2emicromega_2eTauto_2ecnf__tt) ).
fof('$_typeof_Coq.micromega.Tauto.collect_annot',axiom,
c_24__type__78734___24t(cCoq_2emicromega_2eTauto_2ecollect__annot) ).
fof('$_typeof_Coq.micromega.Tauto.cons_id',axiom,
c_24__type__78602___24t(cCoq_2emicromega_2eTauto_2econs__id) ).
fof('$_typeof_Coq.micromega.Tauto.eval_clause',axiom,
c_24__type__80125___24t(cCoq_2emicromega_2eTauto_2eeval__clause) ).
fof('$_typeof_Coq.micromega.Tauto.eval_cnf',axiom,
c_24__type__80154___24t(cCoq_2emicromega_2eTauto_2eeval__cnf) ).
fof('$_typeof_Coq.micromega.Tauto.eval_f',axiom,
c_24__type__151206___24t(cCoq_2emicromega_2eTauto_2eeval__f) ).
fof('$_typeof_Coq.micromega.Tauto.eval_tt',axiom,
c_24__type__54691___24t(cCoq_2emicromega_2eTauto_2eeval__tt) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__702___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.CutProof',axiom,
c_24__type__151973___24t(cCoq_2emicromega_2eZMicromega_2eCutProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.EnumProof',axiom,
c_24__type__151979___24t(cCoq_2emicromega_2eZMicromega_2eEnumProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.RatProof',axiom,
c_24__type__151973___24t(cCoq_2emicromega_2eZMicromega_2eRatProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.MP.to_list',axiom,
c_24__type__65949___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eto__list) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZWitness',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZWitness) ).
fof('$_typeof_Coq.micromega.ZMicromega.make_conj',axiom,
c_24__type__44818___24t(cCoq_2emicromega_2eZMicromega_2emake__conj) ).
fof('$_typeof_Coq.micromega.ZMicromega.make_impl',axiom,
c_24__type__44792___24t(cCoq_2emicromega_2eZMicromega_2emake__impl) ).
fof('$_typeof_Coq.micromega.ZMicromega.valid_cut_sign',axiom,
c_24__type__80510___24t(cCoq_2emicromega_2eZMicromega_2evalid__cut__sign) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
c_24__type__572___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).
fof('$_typeof_Coq.setoid_ring.BinList.jump',axiom,
c_24__type__143330___24t(cCoq_2esetoid__ring_2eBinList_2ejump) ).
fof('$_typeof_Coq.setoid_ring.BinList.nth',axiom,
c_24__type__143341___24t(cCoq_2esetoid__ring_2eBinList_2enth) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEI',axiom,
c_24__type__144520___24t(cCoq_2esetoid__ring_2eField__theory_2eFEI) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEO',axiom,
c_24__type__144520___24t(cCoq_2esetoid__ring_2eField__theory_2eFEO) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__83399___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__83404___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__144523___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__83404___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__69902___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__144532___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__83404___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__144532___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEpow',axiom,
c_24__type__144541___24t(cCoq_2esetoid__ring_2eField__theory_2eFEpow) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__83404___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__702___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__42561___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEadd',axiom,
c_24__type__68418___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
c_24__type__67372___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEopp',axiom,
c_24__type__68948___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__42504___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__42285___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__42265___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__702___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__69936___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__42265___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__702___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
c_24__type__70000___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__common) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__70000___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__70000___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.split',axiom,
c_24__type__70057___24t(cCoq_2esetoid__ring_2eField__theory_2esplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__34306___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nsub',axiom,
c_24__type__37257___24t(cCoq_2esetoid__ring_2eInitialRing_2eNsub) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__43474___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiNword',axiom,
c_24__type__71693___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__43346___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__43346___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__43433___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.get_signZ',axiom,
c_24__type__71500___24t(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.hypo',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
c_24__type__32396___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__164___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.P0',axiom,
c_24__type__50283___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.P1',axiom,
c_24__type__50283___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP1) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__74754___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__74754___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__50302___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__50307___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__50299___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__33270___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__50307___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__149089___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__149094___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__50307___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__702___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__50296___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__50283___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__32831___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pequiv',axiom,
c_24__type__152935___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePequiv) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__50288___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__702___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi',axiom,
c_24__type__74744___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_dev',axiom,
c_24__type__34203___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__dev) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__76230___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
c_24__type__33760___24t(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkPinj',axiom,
c_24__type__50288___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkPinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkZmon',axiom,
c_24__type__146833___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkZmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__33945___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__150522___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_rec',axiom,
c_24__type__150264___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__33504___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.r_list_pow',axiom,
c_24__type__150488___24t(cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.vmon',axiom,
c_24__type__146833___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
c_24__type__146833___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__34314___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__34314___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__53573___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
c_24__type__31748___24t(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__34306___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__34301___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__50331___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).
fof('$_typeof_Eta.eta_red',axiom,
c_24__type__593___24t(cEta_2eeta__red) ).
fof('$_typeof_Eta.is_eta_core',axiom,
c_24__type__1228___24t(cEta_2eis__eta__core) ).
fof('$_typeof_Hammer.Tactics.Reconstr.ReconstrT',axiom,
cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).
fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
c_24__type__152699___24t(cHammer_2eTactics_2eReconstr_2erdone) ).
fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
c_24__type__152699___24t(cHammer_2eTactics_2eTactics_2erdone) ).
fof('$_typeof_Tait.Apps.apps',axiom,
c_24__type__621___24t(cTait_2eApps_2eapps) ).
fof('$_typeof_Tait.Apps.arrows',axiom,
c_24__type__66992___24t(cTait_2eApps_2earrows) ).
fof('$_typeof_Tait.Apps.get_apps',axiom,
c_24__type__610___24t(cTait_2eApps_2eget__apps) ).
fof('$_typeof_Tait.Apps.head_apps',axiom,
c_24__type__593___24t(cTait_2eApps_2ehead__apps) ).
fof('$_typeof_Tait.Apps.is_app',axiom,
c_24__type__584___24t(cTait_2eApps_2eis__app) ).
fof('$_typeof_Tait.Apps.left_app',axiom,
c_24__type__593___24t(cTait_2eApps_2eleft__app) ).
fof('$_typeof_Tait.Apps.right_app',axiom,
c_24__type__593___24t(cTait_2eApps_2eright__app) ).
fof('$_typeof_Tait.MoreList.consn',axiom,
c_24__type__55018___24t(cTait_2eMoreList_2econsn) ).
fof('$_typeof_Tait.MoreList.exists_last',axiom,
c_24__type__66329___24t(cTait_2eMoreList_2eexists__last) ).
fof('$_typeof_Tait.MoreList.existsb',axiom,
c_24__type__848___24t(cTait_2eMoreList_2eexistsb) ).
fof('$_typeof_Tait.MoreList.firstn',axiom,
c_24__type__73010___24t(cTait_2eMoreList_2efirstn) ).
fof('$_typeof_Tait.MoreList.last',axiom,
c_24__type__66297___24t(cTait_2eMoreList_2elast) ).
fof('$_typeof_Tait.MoreList.removelast',axiom,
c_24__type__760___24t(cTait_2eMoreList_2eremovelast) ).
fof('$_typeof_Tait.MoreList.rev_acc',axiom,
c_24__type__749___24t(cTait_2eMoreList_2erev__acc) ).
fof('$_typeof_Tait.MoreList.seq',axiom,
c_24__type__283___24t(cTait_2eMoreList_2eseq) ).
fof('$_typeof_Tait.Subst.id',axiom,
c_24__type__363___24t(cTait_2eSubst_2eid) ).
fof('$_typeof_Tait.Subst.mk_sub',axiom,
c_24__type__341___24t(cTait_2eSubst_2emk__sub) ).
fof('$_typeof_Tait.Subst.shift',axiom,
c_24__type__858___24t(cTait_2eSubst_2eshift) ).
fof('$_typeof_Tait.Subst.sub',axiom,
c_24__type__359___24t(cTait_2eSubst_2esub) ).
fof('$_typeof_Tait.Subst.sub1',axiom,
c_24__type__361___24t(cTait_2eSubst_2esub1) ).
fof('$_typeof_Tait.Subst.sub_swap0',axiom,
c_24__type__861___24t(cTait_2eSubst_2esub__swap0) ).
fof('$_typeof_Tait.Subst.sublift',axiom,
c_24__type__348___24t(cTait_2eSubst_2esublift) ).
fof('$_typeof_Tait.Subst.substitution',axiom,
cType___24t(cTait_2eSubst_2esubstitution) ).
fof('$_typeof_Tait.Subst.support',axiom,
c_24__type__346___24t(cTait_2eSubst_2esupport) ).
fof('$_typeof_Tait.Subst2.Joachimski.Dot',axiom,
c_24__type__1065___24t(cTait_2eSubst2_2eJoachimski_2eDot) ).
fof('$_typeof_Tait.Subst2.Joachimski.PushList',axiom,
c_24__type__1164___24t(cTait_2eSubst2_2eJoachimski_2ePushList) ).
fof('$_typeof_Tait.Subst2.Joachimski.Spare',axiom,
c_24__type__1169___24t(cTait_2eSubst2_2eJoachimski_2eSpare) ).
fof('$_typeof_Tait.Subst2.Joachimski.Up',axiom,
c_24__type__1067___24t(cTait_2eSubst2_2eJoachimski_2eUp) ).
fof('$_typeof_Tait.Subst2.Joachimski.comp',axiom,
c_24__type__1154___24t(cTait_2eSubst2_2eJoachimski_2ecomp) ).
fof('$_typeof_Tait.Subst2.Joachimski.comp\'',axiom,
c_24__type__1169___24t(cTait_2eSubst2_2eJoachimski_2ecomp_27) ).
fof('$_typeof_Tait.Subst2.Joachimski.sub',axiom,
c_24__type__1146___24t(cTait_2eSubst2_2eJoachimski_2esub) ).
fof('$_typeof_Tait.Subst2.Joachimski.sub\'',axiom,
c_24__type__1135___24t(cTait_2eSubst2_2eJoachimski_2esub_27) ).
fof('$_typeof_Tait.Subst2.Joachimski.sublift',axiom,
c_24__type__1118___24t(cTait_2eSubst2_2eJoachimski_2esublift) ).
fof('$_typeof_Tait.Subst2.Joachimski.substitution',axiom,
cType___24t(cTait_2eSubst2_2eJoachimski_2esubstitution) ).
fof('$_typeof_Tait.Subst2.Joachimski.substitution_rect',axiom,
c_24__type__1091___24t(cTait_2eSubst2_2eJoachimski_2esubstitution__rect) ).
fof('$_typeof_Tait.Subst2.above',axiom,
c_24__type__104___24t(cTait_2eSubst2_2eabove) ).
fof('$_typeof_Tait.Term.Abs',axiom,
c_24__type__221___24t(cTait_2eTerm_2eAbs) ).
fof('$_typeof_Tait.Term.App',axiom,
c_24__type__218___24t(cTait_2eTerm_2eApp) ).
fof('$_typeof_Tait.Term.Arrow',axiom,
c_24__type__865___24t(cTait_2eTerm_2eArrow) ).
fof('$_typeof_Tait.Term.Iota',axiom,
cTait_2eTerm_2etype___24t(cTait_2eTerm_2eIota) ).
fof('$_typeof_Tait.Term.Var',axiom,
c_24__type__215___24t(cTait_2eTerm_2eVar) ).
fof('$_typeof_Tait.Term.arrow_left',axiom,
c_24__type__982___24t(cTait_2eTerm_2earrow__left) ).
fof('$_typeof_Tait.Term.arrow_right',axiom,
c_24__type__982___24t(cTait_2eTerm_2earrow__right) ).
fof('$_typeof_Tait.Term.down',axiom,
c_24__type__253___24t(cTait_2eTerm_2edown) ).
fof('$_typeof_Tait.Term.dterm',axiom,
cTait_2eTerm_2eterm___24t(cTait_2eTerm_2edterm) ).
fof('$_typeof_Tait.Term.dtype',axiom,
cTait_2eTerm_2etype___24t(cTait_2eTerm_2edtype) ).
fof('$_typeof_Tait.Term.lift',axiom,
c_24__type__387___24t(cTait_2eTerm_2elift) ).
fof('$_typeof_Tait.Term.occurs',axiom,
c_24__type__156___24t(cTait_2eTerm_2eoccurs) ).
fof('$_typeof_Tait.Term.term',axiom,
cType___24t(cTait_2eTerm_2eterm) ).
fof('$_typeof_Tait.Term.term_dec',axiom,
c_24__type__985___24t(cTait_2eTerm_2eterm__dec) ).
fof('$_typeof_Tait.Term.term_rec',axiom,
c_24__type__915___24t(cTait_2eTerm_2eterm__rec) ).
fof('$_typeof_Tait.Term.term_rect',axiom,
c_24__type__915___24t(cTait_2eTerm_2eterm__rect) ).
fof('$_typeof_Tait.Term.type',axiom,
cType___24t(cTait_2eTerm_2etype) ).
fof('$_typeof_Tait.Term.type_rec',axiom,
c_24__type__151917___24t(cTait_2eTerm_2etype__rec) ).
fof('$_typeof_Tait.Term.type_rect',axiom,
c_24__type__151917___24t(cTait_2eTerm_2etype__rect) ).
fof('$_typeof_Tait.Term.up',axiom,
c_24__type__253___24t(cTait_2eTerm_2eup) ).
fof('$_typeof_Tait.Typing.TypJ',axiom,
c_24__type__1041___24t(cTait_2eTyping_2eTypJ) ).
fof('$_typeof_Tait.Typing.context',axiom,
cType___24t(cTait_2eTyping_2econtext) ).
fof('$_typeof_Tait.Typing.ext_ctx',axiom,
c_24__type__55023___24t(cTait_2eTyping_2eext__ctx) ).
fof('$_typeof_Tait.Typing.typ',axiom,
c_24__type__999___24t(cTait_2eTyping_2etyp) ).
fof('Coq.Arith.Compare_dec.dec_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.dec_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.dec_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.not_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Compare_dec.not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Compare_dec.not_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.gt_S_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),V0__n))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.gt_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)))
=> p(cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.Gt.gt_Sn_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO)) ) ).
fof('Coq.Arith.Gt.gt_irrefl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V0__n)) ) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.gt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Le.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Le.le_n_0_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO))
=> cCoq_2eInit_2eDatatypes_2eO = V0__n ) ) ).
fof('Coq.Arith.Le.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Lt.S_pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n))
=> V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2epred___24a1(V0__n)) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Lt.lt_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Minus.minus_diag_reverse',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eNat_2esub___24a2(V0__n,V0__n) ) ).
fof('Coq.Arith.Minus.minus_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.Minus.minus_plus',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),V0__n) = V1__m ) ) ).
fof('Coq.Arith.Minus.minus_plus_simpl_l_reverse',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m)) ) ) ) ).
fof('Coq.Arith.Minus.pred_of_minus',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2epred___24a1(V0__n) = cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ) ).
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.le_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_assoc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__p)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_succ_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO)) ) ).
fof('Coq.Arith.PeanoNat.Nat.nlt_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2esub___24a2(V1__m,V0__n),V0__n) = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_diag',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,V0__n) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.Peano_dec.dec_eq_nat',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__854___24a2(V0__n,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)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m))) ) ) ).
fof('Coq.Arith.Plus.le_plus_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m))) ) ) ).
fof('Coq.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.negb_sym',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ! [V1__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
=> ( V1__b_27 = cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b)
=> V0__b = cCoq_2eInit_2eDatatypes_2enegb___24a1(V1__b_27) ) ) ) ).
fof('Coq.Bool.Bool.orb_assoc',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ! [V2__b3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__b3)
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,cCoq_2eInit_2eDatatypes_2eorb___24a2(V1__b2,V2__b3)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2),V2__b3) ) ) ) ).
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_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_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.FSets.FSetPositive.PositiveSet.empty_1',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('Coq.FSets.FSetPositive.PositiveSet.tree_ind',axiom,
! [V0__P] :
( c_24__type__37576___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf))
=> ( ! [V2__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V2__t)
=> ( p(happ(V0__P,V2__t))
=> ! [V4__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V4__b)
=> ! [V5__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V5__t)
=> ( p(happ(V0__P,V5__t))
=> p(happ(V0__P,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V2__t,V4__b,V5__t))) ) ) ) ) )
=> ! [V3__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V3__t)
=> p(happ(V0__P,V3__t)) ) ) ) ) ).
fof('Coq.Init.Datatypes.andb_prop',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__a = cCoq_2eInit_2eDatatypes_2etrue
& V1__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__724___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.list_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__724___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__692___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__152009___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.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__300___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Init.Peano.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.Init.Peano.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Init.Peano.plus_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Init.Peano.plus_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).
fof('Coq.Init.Specif.sumbool_ind',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__202___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.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.Add_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V3__l,V4__l_27)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V4__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l)) ) ) ) ).
fof('Coq.Lists.List.Add_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__P] :
( c_24__type__73044___24t(V0__A,V2__P)
=> ( ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> p(happ(happ(V2__P,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l_27)
=> ( p(happ(happ(V2__P,V5__l),V6__l_27))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l_27))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l)
=> p(happ(happ(V2__P,V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l)
=> ? [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
& cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V4__l_27,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__P] :
( c_24__type__73044___24t(V0__A,V2__P)
=> ( ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> p(happ(happ(V2__P,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l_27)
=> ( p(happ(happ(V2__P,V5__l),V6__l_27))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l_27))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l)
=> p(happ(happ(V2__P,V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> ? [V5__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l1)
& ? [V6__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2)
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V5__l1,V6__l2)
& V3__l_27 = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V5__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V6__l2)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(happ(V1__P,V2__x))
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_exists',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eExists___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.Exists_impl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__34643___24t(V0__A,V2__Q)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
=> p(happ(V2__Q,V3__x)) ) )
=> ! [V4__xs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__xs)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V4__xs)
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V2__Q,V4__xs) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__724___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V3__x))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V5__l)
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l))) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__724___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V3__x))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V5__l)
=> ( p(happ(V2__P,V5__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l))) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V5__l)
=> p(happ(V2__P,V5__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.FOP_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.Forall2_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__54698___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__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l1_27)
=> ! [V6__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V6__l2_27)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V3__l1,V5__l1_27)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,V4__l2,V6__l2_27)
=> cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l1,V4__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,V5__l1_27,V6__l2_27)) ) ) ) ) ) ) ) ) ) ).
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__54698___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__54698___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__54698___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.Forall2_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__54698___24t(V0__A,V1__B,V2__R)
=> cCoq_2eLists_2eList_2eForall2___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)) ) ) ) ).
fof('Coq.Lists.List.ForallOrdPairs_ForallPairs',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> ( ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) )
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V1__R,V4__y),V3__x)) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V4__l)
=> cCoq_2eLists_2eList_2eForallPairs___24a3(V0__A,V1__R,V4__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.ForallOrdPairs_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V2__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V2__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__y,V2__l)
=> ( V4__x = V5__y
| p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.ForallPairs_ForallOrdPairs',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForallPairs___24a3(V0__A,V1__R,V2__l)
=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V1__R,V2__l) ) ) ) ) ).
fof('Coq.Lists.List.Forall_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(happ(V1__P,V2__x))
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_forall',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___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.Forall_impl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__34643___24t(V0__A,V2__Q)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(happ(V1__P,V3__a))
=> p(happ(V2__Q,V3__a)) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V4__l)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V2__Q,V4__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l))
=> p(happ(V1__P,V2__a)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_inv_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___24t(V0__A,V1__P)
=> ! [V2__x0] :
( t(V2__x0,V0__A)
=> ! [V3__xs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__xs)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x0,V3__xs))
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__xs) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__34643___24t(V0__A,V1__P)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.NoDup_Add',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l_27)
<=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l)
& ~ cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ).
fof('Coq.Lists.List.NoDup_remove',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))
& ~ 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.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_assoc',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__m,V3__n)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),V3__n) ) ) ) ) ).
fof('Coq.Lists.List.app_assoc_reverse',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),V3__n) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__m,V3__n)) ) ) ) ) ).
fof('Coq.Lists.List.app_comm_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__y)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,V2__y)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V1__x),V2__y) ) ) ) ) ).
fof('Coq.Lists.List.app_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_end',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> V1__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.app_nil_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),V1__l) = V1__l ) ) ).
fof('Coq.Lists.List.app_nil_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) = V1__l ) ) ).
fof('Coq.Lists.List.app_nth1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,V1__l,V3__d) ) ) ) ) ) ) ).
fof('Coq.Lists.List.app_nth2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2ege___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,cCoq_2eInit_2eNat_2esub___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)),V2__l_27,V3__d) ) ) ) ) ) ) ).
fof('Coq.Lists.List.concat_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V1__l1)
=> ! [V2__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V2__l2)
=> cCoq_2eLists_2eList_2econcat___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V1__l1,V2__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2econcat___24a2(V0__A,V1__l1),cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l2)) ) ) ) ).
fof('Coq.Lists.List.concat_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V2__l)
=> cCoq_2eLists_2eList_2econcat___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V1__x,V2__l)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,cCoq_2eLists_2eList_2econcat___24a2(V0__A,V2__l)) ) ) ) ).
fof('Coq.Lists.List.existsb_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__851___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.ext_in_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__290___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__290___24t(V0__A,V1__B,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V4__l)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__a,V4__l)
=> happ(V2__f,V6__a) = happ(V3__g,V6__a) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.firstn_all',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V1__l) = V1__l ) ) ).
fof('Coq.Lists.List.firstn_all2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),V1__n))
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l) = V2__l ) ) ) ) ).
fof('Coq.Lists.List.firstn_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l1),cCoq_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eNat_2esub___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l1)),V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.firstn_app_2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l1),V1__n),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.firstn_skipn',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l),cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V2__l)) = V2__l ) ) ) ).
fof('Coq.Lists.List.fold_left_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__810___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l_27)
=> ! [V5__i] :
( t(V5__i,V0__A)
=> cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,V3__l,V4__l_27),V5__i) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l_27,cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V3__l,V5__i)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.fold_right_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__54058___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ! [V5__i] :
( t(V5__i,V1__B)
=> cCoq_2eLists_2eList_2efold__right___24a5(V1__B,V0__A,V2__f,V5__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27)) = cCoq_2eLists_2eList_2efold__right___24a5(V1__B,V0__A,V2__f,cCoq_2eLists_2eList_2efold__right___24a5(V1__B,V0__A,V2__f,V5__i,V4__l_27),V3__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.forallb_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__851___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_iff',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_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27))
<=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__l_27) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_app_or',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m))
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.in_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l)) ) ) ) ).
fof('Coq.Lists.List.in_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))
=> ( V1__a = V2__b
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__290___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l)
=> cCoq_2eLists_2eList_2eIn___24a3(V1__B,happ(V2__f,V4__x),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_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.in_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__l)
<=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) ) ) ) ) ).
fof('Coq.Lists.List.in_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V2__l)
=> ? [V4__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
& ? [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V5__l2)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_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__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__m,V3__n)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m),V3__n) ) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_appl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__n,V2__m)) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_appr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__m,V3__n)) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V1__l) ) ) ).
fof('Coq.Lists.List.incl_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__m)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__m)) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_tran',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__m,V3__n)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n) ) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__b] :
( t(V1__b,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V2__l,V3__m)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__b,V3__m)) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_cons_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V3__l,V4__m)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__b,V4__m)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.lel_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V1__l) ) ) ).
fof('Coq.Lists.List.lel_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V2__m)
=> ( cCoq_2eLists_2eList_2elel___24a3(V0__A,V2__m,V3__n)
=> cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V3__n) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__290___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.map_ext',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__290___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__290___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> happ(V2__f,V4__a) = happ(V3__g,V4__a) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V5__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V5__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_ext_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__290___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__290___24t(V0__A,V1__B,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__a,V4__l)
=> happ(V2__f,V5__a) = happ(V3__g,V5__a) ) )
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V4__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_id',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V0__A,c_24__lam__64696___24a1(V0__A),V1__l) = V1__l ) ) ).
fof('Coq.Lists.List.map_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__290___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l) ) ) ) ) ).
fof('Coq.Lists.List.map_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__290___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__822___24t(V0__A,V1__B,V2__C,V4__g)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V1__B,V2__C,V4__g,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__f,V5__l)) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V2__C,c_24__lam__152564___24a5(V0__A,V1__B,V2__C,V3__f,V4__g),V5__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_error_app1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V3__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth__error___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V3__n) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)))
=> ? [V5__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l1)
& ? [V6__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2)
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V5__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,cCoq_2eLists_2eList_2enth___24a4(V0__A,V1__n,V2__l,V3__d),V6__l2))
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V5__l1) = V1__n ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.removelast_app',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)
=> ( V2__l_27 != cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
=> cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l_27)) ) ) ) ) ).
fof('Coq.Lists.List.rev_app_distr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__y)
=> cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,V2__y)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__y),cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__x)) ) ) ) ).
fof('Coq.Lists.List.rev_append_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V1__l,V2__l_27) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l),V2__l_27) ) ) ) ).
fof('Coq.Lists.List.rev_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__724___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.List.rev_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) ) ) ).
fof('Coq.Lists.List.rev_list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__724___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,cCoq_2eLists_2eList_2erev___24a2(V0__A,V4__l)))
=> p(happ(V1__P,cCoq_2eLists_2eList_2erev___24a2(V0__A,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,cCoq_2eLists_2eList_2erev___24a2(V0__A,V4__l))) ) ) ) ) ) ).
fof('Coq.Lists.List.rev_unit',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) ) ) ) ).
fof('Coq.Lists.List.seq_length',axiom,
! [V0__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__len)
=> ! [V1__start] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__start)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eLists_2eList_2eseq___24a2(V1__start,V0__len)) = V0__len ) ) ).
fof('Coq.Lists.List.skipn_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V2__l1),cCoq_2eLists_2eList_2eskipn___24a3(V0__A,cCoq_2eInit_2eNat_2esub___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l1)),V3__l2)) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_InfA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__ltA] :
( c_24__type__32418___24t(V0__A,V3__ltA)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ( ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V6__y,V4__l)
=> p(happ(happ(V3__ltA,V5__x),V6__y)) ) )
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V3__ltA,V5__x,V4__l) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_alt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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_altdef',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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)
<=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,happ(V1__eqA,V2__x),V3__l) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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_idem',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V3__l))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V3__l) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_app_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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_compat',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__76711___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__724___24a1(V0__A),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cProp,cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA),c_3c_3d_3e)),cCoq_2eLists_2eSetoidList_2eInA___24a2(V0__A,V1__eqA)) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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__32418___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__32418___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.InA_double_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,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.InA_eqA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__eqA,V4__x),V5__y))
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V5__y,V3__l) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__724___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(happ(happ(V1__eqA,V2__x),V4__y))
=> p(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__y,V5__l))) ) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V6__l)
=> ( p(happ(V3__P,V6__l))
=> p(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,V6__l))) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V6__l)
=> p(happ(V3__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_permute_heads',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__z,V5__l)))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__z,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V5__l))) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__p] :
( t(V2__p,V0__A)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__m)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__p,cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__m))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__p,V3__m) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__724___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( p(happ(happ(V1__eqA,V2__x),V4__y))
=> p(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__y,V5__l))) ) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V6__l)
=> ( p(happ(V3__P,V6__l))
=> p(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,V6__l))) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V6__l)
=> p(happ(V3__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V3__x,V2__l)
=> ? [V5__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l1)
& ? [V6__y] :
( t(V6__y,V0__A)
& ? [V7__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l2)
& p(happ(happ(V1__eqA,V3__x),V6__y))
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V5__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,V7__l2)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.In_InA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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.In_InfA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__32418___24t(V0__A,V1__ltA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__y,V2__l)
=> p(happ(happ(V1__ltA,V3__x),V4__y)) ) )
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V3__x,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InfA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__32418___24t(V0__A,V1__ltA)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__a,V2__l1)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__a,V3__l2)
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InfA_ltA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__32418___24t(V0__A,V1__ltA)
=> ( cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(V0__A,V1__ltA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__ltA,V4__x),V5__y))
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V5__y,V3__l)
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V4__x,V3__l) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V4__l_27)
=> ( ! [V7__x] :
( t(V7__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V7__x,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V7__x,V4__l_27)
=> p(c_24False) ) ) )
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V3__l)
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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__32418___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_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__ltA] :
( c_24__type__32418___24t(V0__A,V3__ltA)
=> ! [V4__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,V4__l1)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,V5__l2)
=> ( ! [V8__x] :
( t(V8__x,V0__A)
=> ! [V9__y] :
( t(V9__y,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V8__x,V4__l1)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V9__y,V5__l2)
=> p(happ(happ(V3__ltA,V8__x),V9__y)) ) ) ) )
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V3__ltA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,V5__l2)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.app_eqlistA_compat',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__76770___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),c_24__type__76762___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA))),cCoq_2eInit_2eDatatypes_2eapp___24a1(V0__A)) ) ) ).
fof('Coq.Lists.SetoidList.eqarefl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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.eqasym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V1__eqA) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1)
=> ! [V4__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1_27)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ! [V6__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V3__l1,V4__l1_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V5__l2,V6__l2_27)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l1,V5__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1_27,V6__l2_27)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__x_27] :
( t(V3__x_27,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l_27)
=> ( p(happ(happ(V1__eqA,V2__x),V3__x_27))
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V4__l,V5__l_27)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V4__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x_27,V5__l_27)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA)) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_equivlistA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2esubrelation___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V0__A,V1__eqA),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA)) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__P] :
( c_24__type__73044___24t(V0__A,V2__P)
=> ( p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__x_27] :
( t(V5__x_27,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27)
=> ( p(happ(happ(V1__eqA,V4__x),V5__x_27))
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V6__l,V7__l_27)
=> ( p(happ(happ(V2__P,V6__l),V7__l_27))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x_27,V7__l_27))) ) ) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V5__l,V6__l)
=> p(happ(happ(V2__P,V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l_27) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_rev_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V2__l1,V3__l1_27)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ! [V6__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V5__l2,V6__l2_27)
=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l1),V5__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V3__l1_27),V6__l2_27)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_NoDupA_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
=> ! [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ( p(happ(happ(V1__eqA,V6__x),V7__y))
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__x,V3__l))
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V7__y,V5__l2)))
=> ( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__x,V3__l),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V7__y,V5__l2)))
=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V3__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,V5__l2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_app_idem',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V2__l),V2__l) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_app_proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__76770___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),c_24__type__76762___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA))),cCoq_2eInit_2eDatatypes_2eapp___24a1(V0__A)) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_double_head',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlistA_permute_heads',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___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_2eequivlistA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V4__l))) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.equivlist_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V0__A,V1__eqA)) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_commutes',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__54108___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__54058___24t(V0__A,V3__B,V6__f)
=> ! [V7__i] :
( t(V7__i,V3__B)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__54058___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__32439___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V3__B,V4__eqB,V6__f)
=> ! [V10__s1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V10__s1)
=> ! [V11__s2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V11__s2)
=> ! [V12__x] :
( t(V12__x,V0__A)
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V10__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V12__x,V11__s2)))),happ(happ(V6__f,V12__x),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V10__s1,V11__s2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_commutes2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__54108___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__54058___24t(V0__A,V3__B,V6__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__54058___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__32439___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V3__B,V4__eqB,V6__f)
=> ! [V9__s1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V9__s1)
=> ! [V10__s2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V10__s2)
=> ! [V11__i] :
( t(V11__i,V3__B)
=> ! [V12__x] :
( t(V12__x,V0__A)
=> ! [V13__x_27] :
( t(V13__x_27,V0__A)
=> ( p(happ(happ(V1__eqA,V12__x),V13__x_27))
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V11__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V9__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V12__x,V10__s2)))),happ(happ(V6__f,V13__x_27),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V11__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V9__s1,V10__s2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_commutes_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__54108___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__54058___24t(V0__A,V3__B,V6__f)
=> ! [V7__i] :
( t(V7__i,V3__B)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__54058___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__32439___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ! [V9__R] :
( c_24__type__76832___24t(V0__A,V3__B,V9__R)
=> ( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V3__B,V4__eqB,V9__R,V6__f)
=> ! [V11__s1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V11__s1)
=> ! [V12__s2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V12__s2)
=> ! [V13__x] :
( t(V13__x,V0__A)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V9__R,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V11__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V13__x,V12__s2)))
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V11__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V13__x,V12__s2)))),happ(happ(V6__f,V13__x),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V7__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V11__s1,V12__s2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_commutes_restr2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__eqB] :
( c_24__type__54108___24t(V0__A,V3__B,V4__eqB)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V3__B,V4__eqB)
=> ! [V6__f] :
( c_24__type__54058___24t(V0__A,V3__B,V6__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__54058___24a2(V0__A,V3__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__32439___24a2(V0__A,V3__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V3__B,V3__B,V4__eqB,V4__eqB)),V6__f)
=> ! [V8__R] :
( c_24__type__76832___24t(V0__A,V3__B,V8__R)
=> ( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V3__B,V4__eqB,V8__R,V6__f)
=> ! [V10__s1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V10__s1)
=> ! [V11__s2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V11__s2)
=> ! [V12__x] :
( t(V12__x,V0__A)
=> ! [V13__i] :
( t(V13__i,V3__B)
=> ! [V14__j] :
( t(V14__j,V3__B)
=> ( p(happ(happ(V4__eqB,V13__i),V14__j))
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V0__A,V8__R,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V10__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V12__x,V11__s2)))
=> p(happ(happ(V4__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V13__i,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V10__s1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V12__x,V11__s2)))),happ(happ(V6__f,V12__x),cCoq_2eLists_2eList_2efold__right___24a5(V3__B,V0__A,V6__f,V14__j,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V10__s1,V11__s2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.fold_right_eqlistA2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__eqB] :
( c_24__type__54108___24t(V0__A,V2__B,V3__eqB)
=> ! [V4__f] :
( c_24__type__54058___24t(V0__A,V2__B,V4__f)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__54058___24a2(V0__A,V2__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__32439___24a2(V0__A,V2__B),V1__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V2__B,V2__B,V3__eqB,V3__eqB)),V4__f)
=> ! [V6__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__s)
=> ! [V7__s_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__s_27)
=> ! [V8__i] :
( t(V8__i,V2__B)
=> ! [V9__j] :
( t(V9__j,V2__B)
=> ( p(happ(happ(V3__eqB,V8__i),V9__j))
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V6__s,V7__s_27)
=> p(happ(happ(V3__eqB,cCoq_2eLists_2eList_2efold__right___24a5(V2__B,V0__A,V4__f,V8__i,V6__s)),cCoq_2eLists_2eList_2efold__right___24a5(V2__B,V0__A,V4__f,V9__j,V7__s_27))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.incl_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__32418___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eSetoidList_2einclA___24a4(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),V2__l) ) ) ) ).
fof('Coq.Logic.Decidable.dec_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__152021___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.dec_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__152020___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.imp_simp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( p(V0__A)
=> p(V1__B) )
=> ( ~ p(V0__A)
| p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
& p(V1__B) )
=> ( ~ p(V0__A)
| ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
& p(V1__B) )
=> p(c_24False) )
<=> ( p(V0__A)
=> ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ~ ( p(V0__A)
| p(V1__B) )
=> ( ~ p(V0__A)
& ~ p(V1__B) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__31526___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.add_comm',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) ) ) ).
fof('Coq.PArith.BinPos.Pos.peano_ind',axiom,
! [V0__P] :
( c_24__type__31526___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V2__p))) ) )
=> ! [V3__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> p(happ(V0__P,V3__p)) ) ) ) ) ).
fof('Coq.QArith.QArith_base.Q_Setoid',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('Coq.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.Qinv_comp',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__73708,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_2eQinv) ).
fof('Coq.QArith.QArith_base.Qmult_comp',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__73705,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,c_24__type__73708,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__73708,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__73705,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eQArith_2eQArith__base_2eQ,c_24__type__73708,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.Relations.Relation_Operators.Desc_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__32418___24t(V0__A,V1__leA)
=> ! [V2__P] :
( c_24__type__724___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__leA,V5__x,V6__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,V6__l)
=> p(happ(V2__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.Desc_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__32418___24t(V0__A,V1__leA)
=> ! [V2__P] :
( c_24__type__724___24t(V0__A,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__leA,V5__x,V6__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))
=> ( p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V7__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V6__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,V6__l)
=> p(happ(V2__P,V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.Lt_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__32418___24t(V0__A,V1__leA)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__leA,V2__a),V3__b))
=> ! [V5__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__x)
=> ! [V6__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__y)
=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V5__x),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__b,V6__y)) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.Lt_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__32418___24t(V0__A,V1__leA)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__x)
=> ! [V4__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,V3__x,V4__y)
=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__x),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.d_conc',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__leA] :
( c_24__type__32418___24t(V0__A,V1__leA)
=> ! [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_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__leA,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))))
=> cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V0__A,V1__leA,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))) ) ) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Build_Setoid_Theory',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__A,V1__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V1__Aeq,V3__x),V3__x)) ) ) ) ) ).
fof('Coq.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.Sorting.Sorted.HdRel_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(happ(V1__R,V2__a),V3__b))
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__b,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.HdRel_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__b,V4__l))
=> p(happ(happ(V1__R,V2__a),V3__b)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.HdRel_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ) ).
fof('Coq.Sorting.Sorted.SSorted_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_StronglySorted',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> ( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__A,V1__R)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V3__l)
=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V3__l) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V3__l)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__R,V2__a,V3__l)
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Sorted.Sorted_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Sorting.Sorted.StronglySorted_Sorted',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__32418___24t(V0__A,V1__R)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V0__A,V1__R,V2__l)
=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V0__A,V1__R,V2__l) ) ) ) ) ).
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.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__55000___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.ZArith.BinInt.Z.lt_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pos_sub_discr',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24153578___24a2(V0__p,V1__q) ) ) ).
fof('Coq.ZArith.Zbool.Zgt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> c_24__case__Coq_2eInit_2eDatatypes_2ebool_24153299___24a2(V0__n,V1__m) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_sub',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n)) ) ).
fof('Coq.ZArith.Znat.Nat2Z.is_nonneg',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n))) ) ).
fof('Coq.ZArith.Znat.inj_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__y) ) ) ) ).
fof('Coq.ZArith.Znat.inj_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_minus2',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.Znat.inj_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_le_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_lt_ge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.auxiliary.Zge_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zgt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zle_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zne_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_square_nonneg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__32404___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__32404___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__32404___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__32418___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__32418___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.ropp_morph_Proper',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__32404___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__32404___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__32404___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__32418___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__32418___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)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32413___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req),V6__ropp) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.rplus_morph_Proper',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__32404___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__32404___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__32404___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__32418___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__32418___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)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V3__rplus) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.rtimes_morph_Proper',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__32404___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__32404___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__32404___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__32418___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__32418___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)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V4__rtimes) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__34643___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__34643___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.make_conj_impl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__34643___24t(V0__A,V1__eval)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__g] :
( cProp___24t(V3__g)
=> ( ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V2__l)
=> p(V3__g) )
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V0__A,V1__eval,V2__l,V3__g) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__34643___24t(V0__A,V1__eval)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V2__l)
=> ! [V4__p] :
( t(V4__p,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__p,V2__l)
=> p(happ(V1__eval,V4__p)) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_impl_true',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__34643___24t(V0__A,V1__eval)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V0__A,V1__eval,V2__l,c_24True) ) ) ) ).
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__34643___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__34643___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.rle_morph_Proper',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__32404___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__32404___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__32404___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__32418___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__32418___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)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32418___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__34643___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,cProp,V7__req,c_3c_3d_3e)),V8__rle) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rlt_morph_Proper',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__32404___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__32404___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__32404___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__32418___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__32418___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)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32418___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__34643___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,cProp,V7__req,c_3c_3d_3e)),V9__rlt) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.ropp_morph_Proper',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__32404___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__32404___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__32404___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__32418___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__32418___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)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32413___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req),V6__ropp) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rplus_morph_Proper',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__32404___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__32404___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__32404___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__32418___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__32418___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)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V3__rplus) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rtimes_morph_Proper',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__32404___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__32404___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__32404___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__32418___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__32418___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)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V4__rtimes) ) ) ) ) ) ) ) ) ) ) ) ).
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__54698___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.ZMicromega.Vars.Facts.MP.Dec.F.E_ST',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive)) ).
fof('Coq.omega.OmegaLemmas.OMEGA17',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA19',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA5',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 = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA7',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ! [V3__t] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__t)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__z,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V3__t,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V3__t)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA10',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k1)
=> ! [V6__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__k2)
=> ! [V7__P] :
( c_24__type__94___24t(V7__P)
=> ( p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V6__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V6__k2)))))
=> p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V6__k2)))) ) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA11',axiom,
! [V0__v1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v1)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k1)
=> ! [V5__P] :
( c_24__type__94___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V4__k1)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l1,V4__k1),V3__l2))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,V1__c1),V2__l1),V4__k1),V3__l2))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA12',axiom,
! [V0__v2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v2)
=> ! [V1__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c2)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k2)
=> ! [V5__P] :
( c_24__type__94___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c2,V4__k2)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l2,V4__k2)))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,V1__c2),V3__l2),V4__k2)))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA13',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__94___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA14',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__94___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA15',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k2)
=> ! [V6__P] :
( c_24__type__94___24t(V6__P)
=> ( p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__c1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V5__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V5__k2)))))
=> p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V5__k2)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA16',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c)
=> ! [V2__l] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l)
=> ! [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__k)
=> ! [V4__P] :
( c_24__type__94___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c,V3__k)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l,V3__k))))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c),V2__l),V3__k))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__94___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_mult_distr_r',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__94___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_plus_distr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__94___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__94___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p)))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc_reverse',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__94___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_comm',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__94___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V0__x)))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_permute',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__94___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__94___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__94___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor3',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__94___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y),V0__x))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor4',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ! [V3__P] :
( c_24__type__94___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V2__z))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__94___24t(V2__P)
=> ( p(happ(V2__P,V1__y))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__94___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.intro_Z',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = V1__y
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.omega.OmegaLemmas.new_var',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& V0__x = V1__y ) ) ).
fof('Coq.setoid_ring.Field_theory.AF_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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__32404___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__32413___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__32418___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__32404___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__32413___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__32418___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__32404___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__32413___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__32418___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__32404___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__32413___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__32418___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__32404___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__32413___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__32418___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.NPEequiv_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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__phi] :
( c_24__type__32450___24t(V0__R,V9__C,V10__phi)
=> ! [V11__Cpow] :
( cType___24t(V11__Cpow)
=> ! [V12__Cp__phi] :
( c_24__type__33287___24t(V0__R,V9__C,V11__Cpow,V12__Cp__phi)
=> ! [V13__rpow] :
( c_24__type__33296___24t(V0__R,V9__C,V11__Cpow,V13__rpow)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V9__C),cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a13(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.NPEeval_ext',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__phi] :
( c_24__type__32450___24t(V0__R,V9__C,V10__phi)
=> ! [V11__Cpow] :
( cType___24t(V11__Cpow)
=> ! [V12__Cp__phi] :
( c_24__type__33287___24t(V0__R,V9__C,V11__Cpow,V12__Cp__phi)
=> ! [V13__rpow] :
( c_24__type__33296___24t(V0__R,V9__C,V11__Cpow,V13__rpow)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__67456___24a3(V0__R,V9__C,V11__Cpow),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__R),c_24__type__67461___24a3(V0__R,V9__C,V11__Cpow),c_3d___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__R)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V9__C),V0__R,cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a13(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow),V7__req)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a12(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.PCond_app',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__32450___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__33287___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__33296___24t(V0__R,V8__C,V10__Cpow,V12__rpow)
=> ! [V13__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V13__l)
=> ! [V14__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V14__l1)
=> ! [V15__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__l2)
=> ( 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,V13__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V14__l1,V15__l2))
<=> ( 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,V13__l,V14__l1)
& 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,V13__l,V15__l2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.PCond_cons',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__32450___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__33287___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__33296___24t(V0__R,V8__C,V10__Cpow,V12__rpow)
=> ! [V13__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V13__l)
=> ! [V14__a] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,V14__a)
=> ! [V15__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__l1)
=> ( 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,V13__l,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V14__a,V15__l1))
<=> ( ~ 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,V13__l,V14__a)),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,V13__l,V15__l1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ceqb_spec',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32425___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__32425___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__32425___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__32439___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__32446___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__32450___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__c] :
( t(V18__c,V8__C)
=> ! [V19__c_27] :
( t(V19__c_27,V8__C)
=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(happ(happ(V7__req,happ(V16__phi,V18__c)),happ(V16__phi,V19__c_27)),c_24True,happ(happ(V15__ceqb,V18__c),V19__c_27)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.cross_product_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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__32404___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__32413___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__32418___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( 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)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ( ~ p(happ(happ(V9__req,V15__b),V1__rO))
=> ( ~ p(happ(happ(V9__req,V17__d),V1__rO))
=> ( p(happ(happ(V9__req,happ(happ(V4__rmul,V14__a),V17__d)),happ(happ(V4__rmul,V16__c),V15__b)))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V14__a),V15__b)),happ(happ(V7__rdiv,V16__c),V17__d))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.radd_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__32418___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__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv1',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__32404___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__32413___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__32418___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,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)
=> ! [V13__r] :
( t(V13__r,V0__R)
=> p(happ(happ(V9__req,V13__r),happ(happ(V7__rdiv,V13__r),V2__rI))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv5',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__32404___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__32413___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__32418___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,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)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> p(happ(happ(V9__req,happ(V6__ropp,happ(happ(V7__rdiv,V13__a),V14__b))),happ(happ(V7__rdiv,happ(V6__ropp,V13__a)),V14__b))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv_r_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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__32404___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__32413___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__32418___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(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)
=> ! [V12__r] :
( t(V12__r,V0__R)
=> ( ~ p(happ(happ(V9__req,V12__r),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V12__r),V12__r)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rinv_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rinv] :
( c_24__type__32413___24t(V0__R,V1__rinv)
=> ! [V2__req] :
( c_24__type__32418___24t(V0__R,V2__req)
=> ( ! [V3__p] :
( t(V3__p,V0__R)
=> ! [V4__q] :
( t(V4__q,V0__R)
=> ( p(happ(happ(V2__req,V3__p),V4__q))
=> p(happ(happ(V2__req,happ(V1__rinv,V3__p)),happ(V1__rinv,V4__q))) ) ) )
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32413___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V2__req,V2__req),V1__rinv) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rinv_nz',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__32404___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__32413___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__32418___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,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)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__a),V1__rO))
=> ~ p(happ(happ(V9__req,happ(V8__rinv,V13__a)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__32418___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> ! [V6__x] :
( t(V6__x,V0__R)
=> ! [V7__y] :
( t(V7__y,V0__R)
=> ( p(happ(happ(V4__req,V6__x),V7__y))
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ( p(happ(happ(V4__req,V9__x),V10__y))
=> p(happ(happ(V4__req,happ(happ(V2__rmul,V6__x),V9__x)),happ(happ(V2__rmul,V7__y),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__32418___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__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_reg_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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__32404___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__32413___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__32418___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,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)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q1] :
( t(V14__q1,V0__R)
=> ! [V15__q2] :
( t(V15__q2,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__p),V1__rO))
=> ( p(happ(happ(V9__req,happ(happ(V4__rmul,V13__p),V14__q1)),happ(happ(V4__rmul,V13__p),V15__q2)))
=> p(happ(happ(V9__req,V14__q1),V15__q2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ropp_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__32418___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__32413___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.Ztriv_div_th',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__32418___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> ! [V3__zphi] :
( c_24__type__71722___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.get_signZ_th',axiom,
cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('Coq.setoid_ring.InitialRing.radd_ext5_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__32418___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__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32425___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__32425___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__32425___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__32439___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__32446___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__32450___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.RealField.R_power_theory',axiom,
cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRmult,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow) ).
fof('Coq.setoid_ring.Ring_polynom.ceqb_spec',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32425___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__32425___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__32425___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__32439___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__32446___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__32450___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__c] :
( t(V18__c,V8__C)
=> ! [V19__c_27] :
( t(V19__c_27,V8__C)
=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(happ(happ(V7__req,happ(V16__phi,V18__c)),happ(V16__phi,V19__c_27)),c_24True,happ(happ(V15__ceqb,V18__c),V19__c_27)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.radd_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__32418___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__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__32418___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__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.ropp_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__32418___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__32413___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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(V3__radd,V10__x),V1__rO)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_assoc',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),happ(happ(V3__radd,V10__y),V11__z))),happ(happ(V3__radd,happ(happ(V3__radd,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_assoc1',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z)),happ(happ(V3__radd,happ(happ(V3__radd,V11__y),V12__z)),V10__x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_assoc2',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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(V3__radd,happ(happ(V3__radd,V12__y),V11__x)),V13__z)),happ(happ(V3__radd,happ(happ(V3__radd,V12__y),V13__z)),V11__x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARdistr_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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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,happ(happ(V3__radd,V9__x),V10__y)),V11__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V9__x),V11__z)),happ(happ(V4__rmul,V10__y),V11__z)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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_assoc1',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V4__rmul,V10__x),V11__y)),V12__z)),happ(happ(V4__rmul,happ(happ(V4__rmul,V11__y),V12__z)),V10__x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc2',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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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,happ(happ(V4__rmul,V12__y),V11__x)),V13__z)),happ(happ(V4__rmul,happ(happ(V4__rmul,V12__y),V13__z)),V11__x))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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_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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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(V3__radd,V9__x),V10__y))),happ(happ(V3__radd,happ(V6__ropp,V9__x)),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARth_SRth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V7__req) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_s_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,c_3d___24a1(V0__R)) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).
fof('Coq.setoid_ring.Ring_theory.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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ! [V9__reqb] :
( c_24__type__32372___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.Radd_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__32418___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__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Rmul_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__32418___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__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.SReqe_Reqe',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__32418___24t(V0__R,V3__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,V3__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V0__R),V3__req) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.div_eucl_th',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__32418___24t(V0__R,V1__req)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__cadd] :
( c_24__type__32425___24t(V0__R,V2__C,V3__cadd)
=> ! [V4__cmul] :
( c_24__type__32425___24t(V0__R,V2__C,V4__cmul)
=> ! [V5__phi] :
( c_24__type__32450___24t(V0__R,V2__C,V5__phi)
=> ! [V6__cdiv] :
( c_24__type__53311___24t(V0__R,V2__C,V6__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V0__R,V1__req,V2__C,V3__cadd,V4__cmul,V5__phi,V6__cdiv)
=> ! [V8__a] :
( t(V8__a,V2__C)
=> ! [V9__b] :
( t(V9__b,V2__C)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_24150833___24a9(V0__R,V1__req,V2__C,V3__cadd,V4__cmul,V5__phi,V6__cdiv,V8__a,V9__b) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.get_sign_None_th',axiom,
! [V0__C] :
( cType___24t(V0__C)
=> ! [V1__copp] :
( c_24__type__32413___24t(V0__C,V1__copp)
=> ! [V2__ceqb] :
( c_24__type__32372___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__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__32413___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__32418___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___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__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___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__32413___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.mk_seqe',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__32404___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__32404___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__32418___24t(V0__R,V3__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V3__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V3__req,V3__req)),V1__radd)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32404___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__32413___24a1(V0__R),V3__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V3__req,V3__req)),V2__rmul)
=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,V3__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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32425___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__32425___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__32425___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__32439___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__32446___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__32450___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32425___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__32425___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__32425___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__32439___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__32446___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__32450___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32425___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__32425___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__32425___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__32439___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__32446___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__32450___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32425___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__32425___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__32425___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__32439___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__32446___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__32450___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32425___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__32425___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__32425___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__32439___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__32446___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__32450___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32425___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__32425___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__32425___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__32439___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__32446___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__32450___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__32404___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__32404___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__32404___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__32413___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__32418___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__32425___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__32425___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__32425___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__32439___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__32446___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__32450___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__32404___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__32418___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__53556___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__810___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('Eta.EtaExp_Abs',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__sigmas)
=> ! [V2__rho] :
( cTait_2eTerm_2etype___24t(V2__rho)
=> ! [V3__sigma] :
( cTait_2eTerm_2etype___24t(V3__sigma)
=> ! [V4__r] :
( cTait_2eTerm_2eterm___24t(V4__r)
=> ! [V5__s] :
( cTait_2eTerm_2eterm___24t(V5__s)
=> ! [V6__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__k)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos),V6__k))
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__rhos,V1__sigmas)) = V6__k
=> ( cEta_2eEtaExp___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V2__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)))),V3__sigma,V4__r,V5__s)
=> cEta_2eEtaExp___24a4(V0__rhos,cTait_2eTerm_2eArrow___24a2(V2__rho,V3__sigma),cTait_2eTerm_2eAbs___24a2(V2__rho,cTait_2eSubst_2esub__swap0___24a2(V4__r,V6__k)),cTait_2eTerm_2eAbs___24a2(V2__rho,cTait_2eSubst_2esub__swap0___24a2(V5__s,V6__k))) ) ) ) ) ) ) ) ) ) ) ).
fof('Eta.EtaExp_EtaExps_ind',axiom,
! [V0__P] :
( c_24__type__83810___24t(V0__P)
=> ! [V1__Q] :
( c_24__type__83791___24t(V1__Q)
=> ( ! [V2__rhos] :
( cTait_2eTyping_2econtext___24t(V2__rhos)
=> ! [V3__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V3__sigmas)
=> ! [V4__rs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V4__rs)
=> ! [V5__ss] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V5__ss)
=> ! [V6__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__k)
=> ! [V7__t] :
( cTait_2eTerm_2eterm___24t(V7__t)
=> ! [V8__rho] :
( cTait_2eTerm_2etype___24t(V8__rho)
=> ( cTait_2eTyping_2eTypJ___24a3(V2__rhos,cTait_2eTerm_2eVar___24a1(V6__k),cTait_2eApps_2earrows___24a2(V8__rho,V3__sigmas))
=> ( cEta_2eEtaExps___24a4(V2__rhos,V3__sigmas,V4__rs,V5__ss)
=> ( p(happ(happ(happ(happ(V1__Q,V2__rhos),V3__sigmas),V4__rs),V5__ss))
=> ( cEta_2eEta___24a4(V2__rhos,V8__rho,cTait_2eApps_2eapps___24a2(cTait_2eTerm_2eVar___24a1(V6__k),V5__ss),V7__t)
=> p(happ(happ(happ(happ(V0__P,V2__rhos),V8__rho),cTait_2eApps_2eapps___24a2(cTait_2eTerm_2eVar___24a1(V6__k),V4__rs)),V7__t)) ) ) ) ) ) ) ) ) ) ) )
=> ( ! [V3__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V3__rhos)
=> ! [V4__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V4__sigmas)
=> ! [V5__rho] :
( cTait_2eTerm_2etype___24t(V5__rho)
=> ! [V6__sigma] :
( cTait_2eTerm_2etype___24t(V6__sigma)
=> ! [V7__r] :
( cTait_2eTerm_2eterm___24t(V7__r)
=> ! [V8__s] :
( cTait_2eTerm_2eterm___24t(V8__s)
=> ! [V9__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V9__k)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V3__rhos),V9__k))
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V3__rhos,V4__sigmas)) = V9__k
=> ( cEta_2eEtaExp___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V3__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V4__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V5__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)))),V6__sigma,V7__r,V8__s)
=> ( p(happ(happ(happ(happ(V0__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V3__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V4__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V5__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype))))),V6__sigma),V7__r),V8__s))
=> p(happ(happ(happ(happ(V0__P,V3__rhos),cTait_2eTerm_2eArrow___24a2(V5__rho,V6__sigma)),cTait_2eTerm_2eAbs___24a2(V5__rho,cTait_2eSubst_2esub__swap0___24a2(V7__r,V9__k))),cTait_2eTerm_2eAbs___24a2(V5__rho,cTait_2eSubst_2esub__swap0___24a2(V8__s,V9__k)))) ) ) ) ) ) ) ) ) ) ) )
=> ( ! [V4__rhos] :
( cTait_2eTyping_2econtext___24t(V4__rhos)
=> p(happ(happ(happ(happ(V1__Q,V4__rhos),cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)),cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)),cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm))) )
=> ( ! [V5__rhos] :
( cTait_2eTyping_2econtext___24t(V5__rhos)
=> ! [V6__s] :
( cTait_2eTerm_2etype___24t(V6__s)
=> ! [V7__ss] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V7__ss)
=> ! [V8__r] :
( cTait_2eTerm_2eterm___24t(V8__r)
=> ! [V9__r_27] :
( cTait_2eTerm_2eterm___24t(V9__r_27)
=> ! [V10__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V10__l)
=> ! [V11__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V11__l_27)
=> ( cEta_2eEtaExp___24a4(V5__rhos,V6__s,V8__r,V9__r_27)
=> ( p(happ(happ(happ(happ(V0__P,V5__rhos),V6__s),V8__r),V9__r_27))
=> ( cEta_2eEtaExps___24a4(V5__rhos,V7__ss,V10__l,V11__l_27)
=> ( p(happ(happ(happ(happ(V1__Q,V5__rhos),V7__ss),V10__l),V11__l_27))
=> p(happ(happ(happ(happ(V1__Q,V5__rhos),cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V6__s,V7__ss)),cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,V8__r,V10__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,V9__r_27,V11__l_27))) ) ) ) ) ) ) ) ) ) ) )
=> ! [V6__rhos] :
( cTait_2eTyping_2econtext___24t(V6__rhos)
=> ! [V7__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V7__sigmas)
=> ! [V8__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V8__l)
=> ! [V9__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V9__l_27)
=> ( cEta_2eEtaExps___24a4(V6__rhos,V7__sigmas,V8__l,V9__l_27)
=> p(happ(happ(happ(happ(V1__Q,V6__rhos),V7__sigmas),V8__l),V9__l_27)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Eta.EtaExp_Var',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__sigmas)
=> ! [V2__rs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V2__rs)
=> ! [V3__ss] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V3__ss)
=> ! [V4__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__k)
=> ! [V5__t] :
( cTait_2eTerm_2eterm___24t(V5__t)
=> ! [V6__rho] :
( cTait_2eTerm_2etype___24t(V6__rho)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eVar___24a1(V4__k),cTait_2eApps_2earrows___24a2(V6__rho,V1__sigmas))
=> ( cEta_2eEtaExps___24a4(V0__rhos,V1__sigmas,V2__rs,V3__ss)
=> ( cEta_2eEta___24a4(V0__rhos,V6__rho,cTait_2eApps_2eapps___24a2(cTait_2eTerm_2eVar___24a1(V4__k),V3__ss),V5__t)
=> cEta_2eEtaExp___24a4(V0__rhos,V6__rho,cTait_2eApps_2eapps___24a2(cTait_2eTerm_2eVar___24a1(V4__k),V2__rs),V5__t) ) ) ) ) ) ) ) ) ) ) ).
fof('Eta.EtaExp_ind',axiom,
! [V0__P] :
( c_24__type__83810___24t(V0__P)
=> ( ! [V1__rhos] :
( cTait_2eTyping_2econtext___24t(V1__rhos)
=> ! [V2__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__sigmas)
=> ! [V3__rs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V3__rs)
=> ! [V4__ss] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V4__ss)
=> ! [V5__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__k)
=> ! [V6__t] :
( cTait_2eTerm_2eterm___24t(V6__t)
=> ! [V7__rho] :
( cTait_2eTerm_2etype___24t(V7__rho)
=> ( cTait_2eTyping_2eTypJ___24a3(V1__rhos,cTait_2eTerm_2eVar___24a1(V5__k),cTait_2eApps_2earrows___24a2(V7__rho,V2__sigmas))
=> ( cEta_2eEtaExps___24a4(V1__rhos,V2__sigmas,V3__rs,V4__ss)
=> ( cEta_2eEta___24a4(V1__rhos,V7__rho,cTait_2eApps_2eapps___24a2(cTait_2eTerm_2eVar___24a1(V5__k),V4__ss),V6__t)
=> p(happ(happ(happ(happ(V0__P,V1__rhos),V7__rho),cTait_2eApps_2eapps___24a2(cTait_2eTerm_2eVar___24a1(V5__k),V3__rs)),V6__t)) ) ) ) ) ) ) ) ) ) )
=> ( ! [V2__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__rhos)
=> ! [V3__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V3__sigmas)
=> ! [V4__rho] :
( cTait_2eTerm_2etype___24t(V4__rho)
=> ! [V5__sigma] :
( cTait_2eTerm_2etype___24t(V5__sigma)
=> ! [V6__r] :
( cTait_2eTerm_2eterm___24t(V6__r)
=> ! [V7__s] :
( cTait_2eTerm_2eterm___24t(V7__s)
=> ! [V8__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V8__k)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V2__rhos),V8__k))
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V2__rhos,V3__sigmas)) = V8__k
=> ( cEta_2eEtaExp___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V2__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V3__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V4__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)))),V5__sigma,V6__r,V7__s)
=> ( p(happ(happ(happ(happ(V0__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V2__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V3__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V4__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype))))),V5__sigma),V6__r),V7__s))
=> p(happ(happ(happ(happ(V0__P,V2__rhos),cTait_2eTerm_2eArrow___24a2(V4__rho,V5__sigma)),cTait_2eTerm_2eAbs___24a2(V4__rho,cTait_2eSubst_2esub__swap0___24a2(V6__r,V8__k))),cTait_2eTerm_2eAbs___24a2(V4__rho,cTait_2eSubst_2esub__swap0___24a2(V7__s,V8__k)))) ) ) ) ) ) ) ) ) ) ) )
=> ! [V3__c] :
( cTait_2eTyping_2econtext___24t(V3__c)
=> ! [V4__t] :
( cTait_2eTerm_2etype___24t(V4__t)
=> ! [V5__t] :
( cTait_2eTerm_2eterm___24t(V5__t)
=> ! [V6__t] :
( cTait_2eTerm_2eterm___24t(V6__t)
=> ( cEta_2eEtaExp___24a4(V3__c,V4__t,V5__t,V6__t)
=> p(happ(happ(happ(happ(V0__P,V3__c),V4__t),V5__t),V6__t)) ) ) ) ) ) ) ) ) ).
fof('Eta.EtaExps_app',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__s1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__s1)
=> ! [V2__s2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__s2)
=> ! [V3__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V3__l1)
=> ! [V4__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V4__l2)
=> ! [V5__l1_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V5__l1_27)
=> ! [V6__l2_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V6__l2_27)
=> ( cEta_2eEtaExps___24a4(V0__rhos,V1__s1,V3__l1,V5__l1_27)
=> ( cEta_2eEtaExps___24a4(V0__rhos,V2__s2,V4__l2,V6__l2_27)
=> cEta_2eEtaExps___24a4(V0__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__s1,V2__s2),cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2eterm,V3__l1,V4__l2),cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2eterm,V5__l1_27,V6__l2_27)) ) ) ) ) ) ) ) ) ) ).
fof('Eta.EtaExps_cons',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__sigma] :
( cTait_2eTerm_2etype___24t(V1__sigma)
=> ! [V2__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__sigmas)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__s] :
( cTait_2eTerm_2eterm___24t(V4__s)
=> ! [V5__rs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V5__rs)
=> ! [V6__ss] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V6__ss)
=> ( cEta_2eEtaExp___24a4(V0__rhos,V1__sigma,V3__r,V4__s)
=> ( cEta_2eEtaExps___24a4(V0__rhos,V2__sigmas,V5__rs,V6__ss)
=> cEta_2eEtaExps___24a4(V0__rhos,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V1__sigma,V2__sigmas),cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,V3__r,V5__rs),cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,V4__s,V6__ss)) ) ) ) ) ) ) ) ) ) ).
fof('Eta.EtaExps_ind',axiom,
! [V0__P] :
( c_24__type__83791___24t(V0__P)
=> ( ! [V1__rhos] :
( cTait_2eTyping_2econtext___24t(V1__rhos)
=> p(happ(happ(happ(happ(V0__P,V1__rhos),cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)),cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)),cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm))) )
=> ( ! [V2__rhos] :
( cTait_2eTyping_2econtext___24t(V2__rhos)
=> ! [V3__sigma] :
( cTait_2eTerm_2etype___24t(V3__sigma)
=> ! [V4__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V4__sigmas)
=> ! [V5__r] :
( cTait_2eTerm_2eterm___24t(V5__r)
=> ! [V6__s] :
( cTait_2eTerm_2eterm___24t(V6__s)
=> ! [V7__rs] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V7__rs)
=> ! [V8__ss] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V8__ss)
=> ( cEta_2eEtaExp___24a4(V2__rhos,V3__sigma,V5__r,V6__s)
=> ( cEta_2eEtaExps___24a4(V2__rhos,V4__sigmas,V7__rs,V8__ss)
=> ( p(happ(happ(happ(happ(V0__P,V2__rhos),V4__sigmas),V7__rs),V8__ss))
=> p(happ(happ(happ(happ(V0__P,V2__rhos),cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V3__sigma,V4__sigmas)),cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,V5__r,V7__rs)),cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,V6__s,V8__ss))) ) ) ) ) ) ) ) ) ) )
=> ! [V3__c] :
( cTait_2eTyping_2econtext___24t(V3__c)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V4__l)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V6__l)
=> ( cEta_2eEtaExps___24a4(V3__c,V4__l,V5__l,V6__l)
=> p(happ(happ(happ(happ(V0__P,V3__c),V4__l),V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Eta.EtaExps_last',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__sigmas)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V3__l)
=> ! [V4__r] :
( cTait_2eTerm_2eterm___24t(V4__r)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V5__l_27)
=> ! [V6__r_27] :
( cTait_2eTerm_2eterm___24t(V6__r_27)
=> ( cEta_2eEtaExps___24a4(V0__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V2__sigma,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype))),cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2eterm,V3__l,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,V4__r,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm))),cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2eterm,V5__l_27,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2eterm,V6__r_27,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm))))
=> ( cEta_2eEtaExps___24a4(V0__rhos,V1__sigmas,V3__l,V5__l_27)
& cEta_2eEtaExp___24a4(V0__rhos,V2__sigma,V4__r,V6__r_27) ) ) ) ) ) ) ) ) ) ).
fof('Eta.EtaExps_nil',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> cEta_2eEtaExps___24a4(V0__rhos,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype),cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm),cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2eterm)) ) ).
fof('Eta.EtaExps_rev',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__s)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V3__l_27)
=> ( cEta_2eEtaExps___24a4(V0__rhos,V1__s,V2__l,V3__l_27)
=> cEta_2eEtaExps___24a4(V0__rhos,cCoq_2eLists_2eList_2erev___24a2(cTait_2eTerm_2etype,V1__s),cCoq_2eLists_2eList_2erev___24a2(cTait_2eTerm_2eterm,V2__l),cCoq_2eLists_2eList_2erev___24a2(cTait_2eTerm_2eterm,V3__l_27)) ) ) ) ) ) ).
fof('Eta.Eta_Arrow',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__sigmas)
=> ! [V2__rho] :
( cTait_2eTerm_2etype___24t(V2__rho)
=> ! [V3__sigma] :
( cTait_2eTerm_2etype___24t(V3__sigma)
=> ! [V4__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__k)
=> ! [V5__etak] :
( cTait_2eTerm_2eterm___24t(V5__etak)
=> ! [V6__r] :
( cTait_2eTerm_2eterm___24t(V6__r)
=> ! [V7__s] :
( cTait_2eTerm_2eterm___24t(V7__s)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos),V4__k))
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__rhos,V1__sigmas)) = V4__k
=> ( cEta_2eEta___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V2__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)))),V2__rho,cTait_2eTerm_2eVar___24a1(V4__k),V5__etak)
=> ( cEta_2eEta___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V2__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)))),V3__sigma,cTait_2eTerm_2eApp___24a2(V6__r,V5__etak),V7__s)
=> cEta_2eEta___24a4(V0__rhos,cTait_2eTerm_2eArrow___24a2(V2__rho,V3__sigma),V6__r,cTait_2eTerm_2eAbs___24a2(V2__rho,cTait_2eSubst_2esub__swap0___24a2(V7__s,V4__k))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Eta.Eta_Iota',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__r] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> cEta_2eEta___24a4(V0__rhos,cTait_2eTerm_2eIota,V1__r,V1__r) ) ) ).
fof('Eta.Eta_ind',axiom,
! [V0__P] :
( c_24__type__83810___24t(V0__P)
=> ( ! [V1__rhos] :
( cTait_2eTyping_2econtext___24t(V1__rhos)
=> ! [V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> p(happ(happ(happ(happ(V0__P,V1__rhos),cTait_2eTerm_2eIota),V2__r),V2__r)) ) )
=> ( ! [V2__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__rhos)
=> ! [V3__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V3__sigmas)
=> ! [V4__rho] :
( cTait_2eTerm_2etype___24t(V4__rho)
=> ! [V5__sigma] :
( cTait_2eTerm_2etype___24t(V5__sigma)
=> ! [V6__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__k)
=> ! [V7__etak] :
( cTait_2eTerm_2eterm___24t(V7__etak)
=> ! [V8__r] :
( cTait_2eTerm_2eterm___24t(V8__r)
=> ! [V9__s] :
( cTait_2eTerm_2eterm___24t(V9__s)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V2__rhos),V6__k))
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V2__rhos,V3__sigmas)) = V6__k
=> ( cEta_2eEta___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V2__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V3__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V4__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)))),V4__rho,cTait_2eTerm_2eVar___24a1(V6__k),V7__etak)
=> ( p(happ(happ(happ(happ(V0__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V2__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V3__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V4__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype))))),V4__rho),cTait_2eTerm_2eVar___24a1(V6__k)),V7__etak))
=> ( cEta_2eEta___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V2__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V3__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V4__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype)))),V5__sigma,cTait_2eTerm_2eApp___24a2(V8__r,V7__etak),V9__s)
=> ( p(happ(happ(happ(happ(V0__P,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V2__rhos,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V3__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V4__rho,cCoq_2eInit_2eDatatypes_2enil___24a1(cTait_2eTerm_2etype))))),V5__sigma),cTait_2eTerm_2eApp___24a2(V8__r,V7__etak)),V9__s))
=> p(happ(happ(happ(happ(V0__P,V2__rhos),cTait_2eTerm_2eArrow___24a2(V4__rho,V5__sigma)),V8__r),cTait_2eTerm_2eAbs___24a2(V4__rho,cTait_2eSubst_2esub__swap0___24a2(V9__s,V6__k)))) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [V3__c] :
( cTait_2eTyping_2econtext___24t(V3__c)
=> ! [V4__t] :
( cTait_2eTerm_2etype___24t(V4__t)
=> ! [V5__t] :
( cTait_2eTerm_2eterm___24t(V5__t)
=> ! [V6__t] :
( cTait_2eTerm_2eterm___24t(V6__t)
=> ( cEta_2eEta___24a4(V3__c,V4__t,V5__t,V6__t)
=> p(happ(happ(happ(happ(V0__P,V3__c),V4__t),V5__t),V6__t)) ) ) ) ) ) ) ) ) ).
fof('Eta.eta_red_occurs',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> cTait_2eTerm_2eoccurs___24a2(V1__k,cEta_2eeta__red___24a1(V0__r)) = cTait_2eTerm_2eoccurs___24a2(V1__k,V0__r) ) ) ).
fof('Eta.term2_ind',axiom,
! [V0__P] :
( c_24__type__223___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(V0__P,cTait_2eTerm_2eVar___24a1(V1__n))) )
=> ( ! [V2__t1] :
( cTait_2eTerm_2eterm___24t(V2__t1)
=> ! [V3__t2] :
( cTait_2eTerm_2eterm___24t(V3__t2)
=> ( p(happ(V0__P,V2__t1))
=> ( p(happ(V0__P,V3__t2))
=> p(happ(V0__P,cTait_2eTerm_2eApp___24a2(V2__t1,V3__t2))) ) ) ) )
=> ( ! [V3__rho] :
( cTait_2eTerm_2etype___24t(V3__rho)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(happ(V0__P,cTait_2eTerm_2eAbs___24a2(V3__rho,cTait_2eTerm_2eVar___24a1(V4__n)))) ) )
=> ( ! [V4__rho] :
( cTait_2eTerm_2etype___24t(V4__rho)
=> ! [V5__t1] :
( cTait_2eTerm_2eterm___24t(V5__t1)
=> ! [V6__t2] :
( cTait_2eTerm_2eterm___24t(V6__t2)
=> ( p(happ(V0__P,V5__t1))
=> ( p(happ(V0__P,V6__t2))
=> p(happ(V0__P,cTait_2eTerm_2eAbs___24a2(V4__rho,cTait_2eTerm_2eApp___24a2(V5__t1,V6__t2)))) ) ) ) ) )
=> ( ! [V5__rho] :
( cTait_2eTerm_2etype___24t(V5__rho)
=> ! [V6__sigma] :
( cTait_2eTerm_2etype___24t(V6__sigma)
=> ! [V7__t] :
( cTait_2eTerm_2eterm___24t(V7__t)
=> ( p(happ(V0__P,cTait_2eTerm_2eAbs___24a2(V6__sigma,V7__t)))
=> p(happ(V0__P,cTait_2eTerm_2eAbs___24a2(V5__rho,cTait_2eTerm_2eAbs___24a2(V6__sigma,V7__t)))) ) ) ) )
=> ! [V6__t] :
( cTait_2eTerm_2eterm___24t(V6__t)
=> p(happ(V0__P,V6__t)) ) ) ) ) ) ) ) ).
fof('Tait.Apps.CorTyp_apps',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V0__l)
=> ! [V1__r] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ! [V2__rhos] :
( cTait_2eTyping_2econtext___24t(V2__rhos)
=> ( cTait_2eTyping_2eCorTyp___24a2(V2__rhos,cTait_2eApps_2eapps___24a2(V1__r,V0__l))
=> cTait_2eTyping_2eCorTyp___24a2(V2__rhos,V1__r) ) ) ) ) ).
fof('Tait.Apps.TypJ_apps',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V0__l)
=> ! [V1__r] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ! [V2__r_27] :
( cTait_2eTerm_2eterm___24t(V2__r_27)
=> ! [V3__rhos] :
( cTait_2eTyping_2econtext___24t(V3__rhos)
=> ! [V4__rho] :
( cTait_2eTerm_2etype___24t(V4__rho)
=> ! [V5__sigma] :
( cTait_2eTerm_2etype___24t(V5__sigma)
=> ( cTait_2eTyping_2eTypJ___24a3(V3__rhos,V1__r,V5__sigma)
=> ( cTait_2eTyping_2eTypJ___24a3(V3__rhos,V2__r_27,V5__sigma)
=> ( cTait_2eTyping_2eTypJ___24a3(V3__rhos,cTait_2eApps_2eapps___24a2(V1__r,V0__l),V4__rho)
=> cTait_2eTyping_2eTypJ___24a3(V3__rhos,cTait_2eApps_2eapps___24a2(V2__r_27,V0__l),V4__rho) ) ) ) ) ) ) ) ) ) ).
fof('Tait.Apps.apps_app',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V2__l_27)
=> cTait_2eApps_2eapps___24a2(cTait_2eApps_2eapps___24a2(V0__r,V1__l),V2__l_27) = cTait_2eApps_2eapps___24a2(V0__r,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2eterm,V1__l,V2__l_27)) ) ) ) ).
fof('Tait.Apps.apps_form_unique1',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__r_27] :
( cTait_2eTerm_2eterm___24t(V1__r_27)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V3__l_27)
=> ( cTait_2eApps_2eapps___24a2(V0__r,V2__l) = cTait_2eApps_2eapps___24a2(V1__r_27,V3__l_27)
=> ( cTait_2eApps_2eis__app___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2efalse
=> ( cTait_2eApps_2eis__app___24a1(V1__r_27) = cCoq_2eInit_2eDatatypes_2efalse
=> V0__r = V1__r_27 ) ) ) ) ) ) ) ).
fof('Tait.Apps.apps_form_unique2',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__r_27] :
( cTait_2eTerm_2eterm___24t(V1__r_27)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V3__l_27)
=> ( cTait_2eApps_2eapps___24a2(V0__r,V2__l) = cTait_2eApps_2eapps___24a2(V1__r_27,V3__l_27)
=> ( cTait_2eApps_2eis__app___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2efalse
=> ( cTait_2eApps_2eis__app___24a1(V1__r_27) = cCoq_2eInit_2eDatatypes_2efalse
=> V2__l = V3__l_27 ) ) ) ) ) ) ) ).
fof('Tait.Apps.arrows_app',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__l)
=> ! [V1__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__l_27)
=> ! [V2__rho] :
( cTait_2eTerm_2etype___24t(V2__rho)
=> cTait_2eApps_2earrows___24a2(V2__rho,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__l,V1__l_27)) = cTait_2eApps_2earrows___24a2(cTait_2eApps_2earrows___24a2(V2__rho,V1__l_27),V0__l) ) ) ) ).
fof('Tait.Apps.head_apps_not_App',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__r1] :
( cTait_2eTerm_2eterm___24t(V1__r1)
=> ! [V2__r2] :
( cTait_2eTerm_2eterm___24t(V2__r2)
=> cTait_2eApps_2ehead__apps___24a1(V0__r) != cTait_2eTerm_2eApp___24a2(V1__r1,V2__r2) ) ) ) ).
fof('Tait.MoreList.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('Tait.MoreList.app_nth1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,V1__l,V3__d) ) ) ) ) ) ) ).
fof('Tait.MoreList.app_nth2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2ege___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,cCoq_2eInit_2eNat_2esub___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)),V2__l_27,V3__d) ) ) ) ) ) ) ).
fof('Tait.MoreList.consn_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cTait_2eMoreList_2econsn___24a4(V0__A,V1__n,V2__a,V3__l)) = cCoq_2eInit_2eNat_2eadd___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l)) ) ) ) ) ).
fof('Tait.MoreList.consn_nth1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__k)
=> ! [V5__d] :
( t(V5__d,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V4__k,V1__n))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__k,cTait_2eMoreList_2econsn___24a4(V0__A,V1__n,V2__a,V3__l),V5__d) = V2__a ) ) ) ) ) ) ) ).
fof('Tait.MoreList.existsb_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__851___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__d] :
( t(V4__d,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V3__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)))
=> ( cTait_2eMoreList_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('Tait.MoreList.fold_left_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__810___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l_27)
=> ! [V5__a] :
( t(V5__a,V0__A)
=> cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,V3__l,V4__l_27),V5__a) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l_27,cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V3__l,V5__a)) ) ) ) ) ) ) ).
fof('Tait.MoreList.map_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__290___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l_27)) ) ) ) ) ) ).
fof('Tait.MoreList.map_ext',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__290___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__290___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> happ(V2__f,V4__a) = happ(V3__g,V4__a) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V5__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V5__l) ) ) ) ) ) ) ).
fof('Tait.MoreList.map_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__290___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l) ) ) ) ) ).
fof('Tait.MoreList.map_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__290___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__822___24t(V0__A,V1__B,V2__C,V4__g)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V1__B,V2__C,V4__g,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__f,V5__l)) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V2__C,c_24__lam__836___24a5(V0__A,V1__B,V2__C,V3__f,V4__g),V5__l) ) ) ) ) ) ) ).
fof('Tait.MoreList.map_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__290___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__d] :
( t(V4__d,V0__A)
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> cCoq_2eLists_2eList_2enth___24a4(V1__B,V5__n,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l),happ(V2__f,V4__d)) = happ(V2__f,cCoq_2eLists_2eList_2enth___24a4(V0__A,V5__n,V3__l,V4__d)) ) ) ) ) ) ) ).
fof('Tait.MoreList.nth_indep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ! [V4__d_27] :
( t(V4__d_27,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V4__d_27) ) ) ) ) ) ) ).
fof('Tait.MoreList.nth_overflow',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V2__n))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V3__d) = V3__d ) ) ) ) ) ).
fof('Tait.MoreList.rev_acc_rev',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)
=> cTait_2eMoreList_2erev__acc___24a3(V0__A,V1__l,V2__l_27) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l),V2__l_27) ) ) ) ).
fof('Tait.MoreList.rev_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) ) ) ).
fof('Tait.MoreList.seq_length',axiom,
! [V0__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__len)
=> ! [V1__start] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__start)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2enat,cTait_2eMoreList_2eseq___24a2(V1__start,V0__len)) = V0__len ) ) ).
fof('Tait.MoreList.seq_nth',axiom,
! [V0__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__len)
=> ! [V1__start] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__start)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__d] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__d)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__n,V0__len))
=> cCoq_2eLists_2eList_2enth___24a4(cCoq_2eInit_2eDatatypes_2enat,V2__n,cTait_2eMoreList_2eseq___24a2(V1__start,V0__len),V3__d) = cCoq_2eInit_2eNat_2eadd___24a2(V1__start,V2__n) ) ) ) ) ) ).
fof('Tait.MoreList.seq_shift',axiom,
! [V0__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__len)
=> ! [V1__start] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__start)
=> cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eS,cTait_2eMoreList_2eseq___24a2(V1__start,V0__len)) = cTait_2eMoreList_2eseq___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__start),V0__len) ) ) ).
fof('Tait.Subst.map_up',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,V0__l)
=> cCoq_2eLists_2eList_2emap___24a4(cTait_2eTerm_2eterm,cTait_2eTerm_2eterm,cTait_2eTerm_2eup___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2enat,cTait_2eTerm_2eterm,cTait_2eTerm_2eVar,V0__l)) = cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2enat,cTait_2eTerm_2eterm,cTait_2eTerm_2eVar,cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eS,V0__l)) ) ).
fof('Tait.Subst.sub_id',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> cTait_2eSubst_2esub___24a2(V0__r,cTait_2eSubst_2eid___24a1(V1__k)) = V0__r ) ) ).
fof('Tait.Subst.sublift_id',axiom,
! [V0__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__k)
=> cTait_2eSubst_2esublift___24a1(cTait_2eSubst_2eid___24a1(V0__k)) = cTait_2eSubst_2eid___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__k)) ) ).
fof('Tait.Subst2.Joachimski.SubLiftComp',axiom,
! [V0__theta] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V0__theta)
=> ! [V1__theta_27] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V1__theta_27)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V2__l)
=> cTait_2eSubst2_2eJoachimski_2ecomp___24a2(cTait_2eSubst2_2eJoachimski_2esublift___24a2(V0__theta,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2eterm,V2__l)),cTait_2eSubst2_2eJoachimski_2ePushList___24a2(V2__l,V1__theta_27)) = cTait_2eSubst2_2eJoachimski_2ecomp___24a2(V0__theta,V1__theta_27) ) ) ) ).
fof('Tait.Subst2.Joachimski.SubSub',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__theta] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V1__theta)
=> ! [V2__theta_27] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V2__theta_27)
=> cTait_2eSubst2_2eJoachimski_2esub___24a2(cTait_2eSubst2_2eJoachimski_2esub___24a2(V0__r,V1__theta),V2__theta_27) = cTait_2eSubst2_2eJoachimski_2esub___24a2(V0__r,cTait_2eSubst2_2eJoachimski_2ecomp___24a2(V1__theta,V2__theta_27)) ) ) ) ).
fof('Tait.Subst2.Joachimski.UpPushList',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V0__l)
=> ! [V1__theta] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V1__theta)
=> cTait_2eSubst2_2eJoachimski_2ecomp___24a2(cTait_2eSubst2_2eJoachimski_2eUp___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2eterm,V0__l)),cTait_2eSubst2_2eJoachimski_2ePushList___24a2(V0__l,V1__theta)) = V1__theta ) ) ).
fof('Tait.Subst2.Joachimski.subliftId',axiom,
! [V0__theta] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V0__theta)
=> cTait_2eSubst2_2eJoachimski_2esublift___24a2(V0__theta,cCoq_2eInit_2eDatatypes_2eO) = V0__theta ) ).
fof('Tait.Subst2.Joachimski.substitution_ind',axiom,
! [V0__P] :
( c_24__type__1106___24t(V0__P)
=> ( ! [V1__t] :
( cTait_2eTerm_2eterm___24t(V1__t)
=> ! [V2__s] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V2__s)
=> ( p(happ(V0__P,V2__s))
=> p(happ(V0__P,cTait_2eSubst2_2eJoachimski_2eDot___24a2(V1__t,V2__s))) ) ) )
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> p(happ(V0__P,cTait_2eSubst2_2eJoachimski_2eUp___24a1(V2__n))) )
=> ! [V3__s] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V3__s)
=> p(happ(V0__P,V3__s)) ) ) ) ) ).
fof('Tait.Subst2.above_sub',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__rs] :
( cTait_2eSubst_2esubstitution___24t(V1__rs)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2eterm,V2__l)
=> ! [V3__d] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__d)
=> ( cTait_2eSubst2_2eabove___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2eterm,cTait_2eSubst_2esupport___24a1(V1__rs)),V0__r)
=> cTait_2eSubst_2esub___24a2(V0__r,cTait_2eSubst_2emk__sub___24a2(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2eterm,cTait_2eSubst_2esupport___24a1(V1__rs),V2__l),V3__d)) = cTait_2eSubst_2esub___24a2(V0__r,V1__rs) ) ) ) ) ) ).
fof('Tait.Term.down_up',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
=> cTait_2eTerm_2edown___24a2(V1__l,cTait_2eTerm_2eup___24a2(V1__l,V0__r)) = V0__r ) ) ).
fof('Tait.Term.lift_lift',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
=> ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ! [V3__k_27] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k_27)
=> cTait_2eTerm_2elift___24a3(V1__l,V3__k_27,cTait_2eTerm_2elift___24a3(V1__l,V2__k,V0__r)) = cTait_2eTerm_2elift___24a3(V1__l,cCoq_2eInit_2eNat_2eadd___24a2(V2__k,V3__k_27),V0__r) ) ) ) ) ).
fof('Tait.Term.lift_lift2',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k)
=> cTait_2eTerm_2elift___24a3(cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__n),V3__k,cTait_2eTerm_2elift___24a3(V1__m,V2__n,V0__r)) = cTait_2eTerm_2elift___24a3(V1__m,cCoq_2eInit_2eNat_2eadd___24a2(V2__n,V3__k),V0__r) ) ) ) ) ).
fof('Tait.Term.lift_lift3',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__m_27] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m_27)
=> ! [V4__n_27] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n_27)
=> cTait_2eTerm_2elift___24a3(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V3__m_27),V2__n),V4__n_27,cTait_2eTerm_2elift___24a3(V1__m,V2__n,V0__r)) = cTait_2eTerm_2elift___24a3(V1__m,V2__n,cTait_2eTerm_2elift___24a3(cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V3__m_27),V4__n_27,V0__r)) ) ) ) ) ) ).
fof('Tait.Term.lift_null',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
=> cTait_2eTerm_2elift___24a3(V1__l,cCoq_2eInit_2eDatatypes_2eO,V0__r) = V0__r ) ) ).
fof('Tait.Term.lift_occurs',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V2__n,V3__k))
=> cTait_2eTerm_2eoccurs___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__l,V3__k),cTait_2eTerm_2elift___24a3(V2__n,V1__l,V0__r)) = cTait_2eTerm_2eoccurs___24a2(V3__k,V0__r) ) ) ) ) ) ).
fof('Tait.Term.lift_up',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
=> cTait_2eTerm_2eup___24a2(V1__l,V0__r) = cTait_2eTerm_2elift___24a3(V1__l,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),V0__r) ) ) ).
fof('Tait.Term.term_ind',axiom,
! [V0__P] :
( c_24__type__223___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(V0__P,cTait_2eTerm_2eVar___24a1(V1__n))) )
=> ( ! [V2__t] :
( cTait_2eTerm_2eterm___24t(V2__t)
=> ( p(happ(V0__P,V2__t))
=> ! [V4__t] :
( cTait_2eTerm_2eterm___24t(V4__t)
=> ( p(happ(V0__P,V4__t))
=> p(happ(V0__P,cTait_2eTerm_2eApp___24a2(V2__t,V4__t))) ) ) ) )
=> ( ! [V3__t] :
( cTait_2eTerm_2etype___24t(V3__t)
=> ! [V4__t] :
( cTait_2eTerm_2eterm___24t(V4__t)
=> ( p(happ(V0__P,V4__t))
=> p(happ(V0__P,cTait_2eTerm_2eAbs___24a2(V3__t,V4__t))) ) ) )
=> ! [V4__t] :
( cTait_2eTerm_2eterm___24t(V4__t)
=> p(happ(V0__P,V4__t)) ) ) ) ) ) ).
fof('Tait.Term.type_ind',axiom,
! [V0__P] :
( c_24__type__151933___24t(V0__P)
=> ( p(happ(V0__P,cTait_2eTerm_2eIota))
=> ( ! [V2__t] :
( cTait_2eTerm_2etype___24t(V2__t)
=> ( p(happ(V0__P,V2__t))
=> ! [V4__t] :
( cTait_2eTerm_2etype___24t(V4__t)
=> ( p(happ(V0__P,V4__t))
=> p(happ(V0__P,cTait_2eTerm_2eArrow___24a2(V2__t,V4__t))) ) ) ) )
=> ! [V3__t] :
( cTait_2eTerm_2etype___24t(V3__t)
=> p(happ(V0__P,V3__t)) ) ) ) ) ).
fof('Tait.Typing.CorAbs',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__r] :
( cTait_2eTerm_2eterm___24t(V2__r)
=> ( cTait_2eTyping_2eCorTyp___24a2(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V1__rho,V0__rhos),V2__r)
=> cTait_2eTyping_2eCorTyp___24a2(V0__rhos,cTait_2eTerm_2eAbs___24a2(V1__rho,V2__r)) ) ) ) ) ).
fof('Tait.Typing.CorApp',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__r] :
( cTait_2eTerm_2eterm___24t(V1__r)
=> ! [V2__s] :
( cTait_2eTerm_2eterm___24t(V2__s)
=> ( cTait_2eTyping_2eCorTyp___24a2(V0__rhos,V1__r)
=> ( cTait_2eTyping_2eCorTyp___24a2(V0__rhos,V2__s)
=> ! [V5__sigma] :
( cTait_2eTerm_2etype___24t(V5__sigma)
=> ( cTait_2eTyping_2etyp___24a2(V0__rhos,V1__r) = cTait_2eTerm_2eArrow___24a2(cTait_2eTyping_2etyp___24a2(V0__rhos,V2__s),V5__sigma)
=> cTait_2eTyping_2eCorTyp___24a2(V0__rhos,cTait_2eTerm_2eApp___24a2(V1__r,V2__s)) ) ) ) ) ) ) ) ).
fof('Tait.Typing.CorVar',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos)))
=> cTait_2eTyping_2eCorTyp___24a2(V0__rhos,cTait_2eTerm_2eVar___24a1(V1__n)) ) ) ) ).
fof('Tait.Typing.SubRed',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__s] :
( cTait_2eTerm_2eterm___24t(V4__s)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eApp___24a2(cTait_2eTerm_2eAbs___24a2(V2__sigma,V3__r),V4__s),V1__rho)
=> cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eSubst_2esub___24a2(V3__r,cTait_2eSubst_2esub1___24a1(V4__s)),V1__rho) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_Abs',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__mu] :
( cTait_2eTerm_2etype___24t(V3__mu)
=> ! [V4__r] :
( cTait_2eTerm_2eterm___24t(V4__r)
=> ( V2__sigma = cTait_2eTerm_2eArrow___24a2(V1__rho,V3__mu)
=> ( cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V1__rho,V0__rhos),V4__r,V3__mu)
=> cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eAbs___24a2(V1__rho,V4__r),V2__sigma) ) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_App',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__s] :
( cTait_2eTerm_2eterm___24t(V4__s)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,V3__r,cTait_2eTerm_2eArrow___24a2(V1__rho,V2__sigma))
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,V4__s,V1__rho)
=> cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eApp___24a2(V3__r,V4__s),V2__sigma) ) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_App_inv1',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__s] :
( cTait_2eTerm_2eterm___24t(V4__s)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eApp___24a2(V3__r,V4__s),V1__rho)
=> ( V2__sigma = cTait_2eTyping_2etyp___24a2(V0__rhos,V4__s)
=> cTait_2eTyping_2eTypJ___24a3(V0__rhos,V3__r,cTait_2eTerm_2eArrow___24a2(V2__sigma,V1__rho)) ) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_App_inv2',axiom,
! [V0__rhos] :
( cTait_2eTyping_2econtext___24t(V0__rhos)
=> ! [V1__rho] :
( cTait_2eTerm_2etype___24t(V1__rho)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__s] :
( cTait_2eTerm_2eterm___24t(V4__s)
=> ( cTait_2eTyping_2eTypJ___24a3(V0__rhos,cTait_2eTerm_2eApp___24a2(V3__r,V4__s),V1__rho)
=> ( V2__sigma = cTait_2eTyping_2etyp___24a2(V0__rhos,V4__s)
=> cTait_2eTyping_2eTypJ___24a3(V0__rhos,V4__s,V2__sigma) ) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_ext_ctx',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__rhos] :
( cTait_2eTyping_2econtext___24t(V1__rhos)
=> ! [V2__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__sigmas)
=> ! [V3__rho] :
( cTait_2eTerm_2etype___24t(V3__rho)
=> ( cTait_2eTyping_2eTypJ___24a3(V1__rhos,V0__r,V3__rho)
=> cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__rhos,V2__sigmas),V0__r,V3__rho) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_red_ctx',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__rhos)
=> ! [V2__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__sigmas)
=> ! [V3__rho] :
( cTait_2eTerm_2etype___24t(V3__rho)
=> ( cTait_2eSubst2_2eabove___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V1__rhos),V0__r)
=> ( cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__rhos,V2__sigmas),V0__r,V3__rho)
=> cTait_2eTyping_2eTypJ___24a3(V1__rhos,V0__r,V3__rho) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_sub1',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__rhos)
=> ! [V2__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__sigmas)
=> ! [V3__mus] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V3__mus)
=> ! [V4__rho] :
( cTait_2eTerm_2etype___24t(V4__rho)
=> ! [V5__rs] :
( cTait_2eSubst_2esubstitution___24t(V5__rs)
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V1__rhos) = cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2eterm,cTait_2eSubst_2esupport___24a1(V5__rs))
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V3__mus) = cTait_2eSubst_2eshift___24a1(V5__rs)
=> ( cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__rhos,V2__sigmas),V0__r,V4__rho)
=> ( ! [V9__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V9__n)
=> ! [V10__d] :
( cTait_2eTerm_2eterm___24t(V10__d)
=> ! [V11__d_27] :
( cTait_2eTerm_2etype___24t(V11__d_27)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V9__n,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V1__rhos)))
=> cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V3__mus,V2__sigmas),cCoq_2eLists_2eList_2enth___24a4(cTait_2eTerm_2eterm,V9__n,cTait_2eSubst_2esupport___24a1(V5__rs),V10__d),cCoq_2eLists_2eList_2enth___24a4(cTait_2eTerm_2etype,V9__n,V1__rhos,V11__d_27)) ) ) ) )
=> cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V3__mus,V2__sigmas),cTait_2eSubst_2esub___24a2(V0__r,V5__rs),V4__rho) ) ) ) ) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_sub2',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__sigmas] :
( cTait_2eTyping_2econtext___24t(V1__sigmas)
=> ! [V2__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__rhos)
=> ! [V3__rho] :
( cTait_2eTerm_2etype___24t(V3__rho)
=> ! [V4__rs] :
( cTait_2eSubst_2esubstitution___24t(V4__rs)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V2__rhos),cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2eterm,cTait_2eSubst_2esupport___24a1(V4__rs))))
=> ( cTait_2eTyping_2eTypJ___24a3(V2__rhos,V0__r,V3__rho)
=> ( ! [V7__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V7__n)
=> ! [V8__d] :
( cTait_2eTerm_2eterm___24t(V8__d)
=> ! [V9__d_27] :
( cTait_2eTerm_2etype___24t(V9__d_27)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V7__n,cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V2__rhos)))
=> cTait_2eTyping_2eTypJ___24a3(V1__sigmas,cCoq_2eLists_2eList_2enth___24a4(cTait_2eTerm_2eterm,V7__n,cTait_2eSubst_2esupport___24a1(V4__rs),V8__d),cCoq_2eLists_2eList_2enth___24a4(cTait_2eTerm_2etype,V7__n,V2__rhos,V9__d_27)) ) ) ) )
=> cTait_2eTyping_2eTypJ___24a3(V1__sigmas,cTait_2eSubst_2esub___24a2(V0__r,V4__rs),V3__rho) ) ) ) ) ) ) ) ) ).
fof('Tait.Typing.TypJ_up',axiom,
! [V0__r] :
( cTait_2eTerm_2eterm___24t(V0__r)
=> ! [V1__sigmas] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__sigmas)
=> ! [V2__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V2__rhos)
=> ! [V3__rho] :
( cTait_2eTerm_2etype___24t(V3__rho)
=> ! [V4__sigma] :
( cTait_2eTerm_2etype___24t(V4__sigma)
=> ! [V5__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__k)
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V1__sigmas) = V5__k
=> ( cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__sigmas,V2__rhos),V0__r,V3__rho)
=> cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V1__sigmas,cCoq_2eInit_2eDatatypes_2econs___24a3(cTait_2eTerm_2etype,V4__sigma,V2__rhos)),cTait_2eTerm_2eup___24a2(V5__k,V0__r),V3__rho) ) ) ) ) ) ) ) ) ).
fof('Tait.Typing.ext_ctx_TypJ',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__rho] :
( cTait_2eTerm_2etype___24t(V2__rho)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos),V1__k))
=> cTait_2eTyping_2eTypJ___24a3(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__rhos,cTait_2eTyping_2eext__ctx___24a3(V0__rhos,V1__k,V2__rho)),cTait_2eTerm_2eVar___24a1(V1__k),V2__rho) ) ) ) ) ).
fof('Tait.Typing.ext_ctx_last',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__rho] :
( cTait_2eTerm_2etype___24t(V2__rho)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos),V1__k))
=> cTait_2eMoreList_2elast___24a3(cTait_2eTerm_2etype,cTait_2eTyping_2eext__ctx___24a3(V0__rhos,V1__k,V2__rho),cTait_2eTerm_2edtype) = V2__rho ) ) ) ) ).
fof('Tait.Typing.ext_ctx_length',axiom,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__rho] :
( cTait_2eTerm_2etype___24t(V2__rho)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,V0__rhos),V1__k))
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cTait_2eTerm_2etype,cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__rhos,cTait_2eTyping_2eext__ctx___24a3(V0__rhos,V1__k,V2__rho))) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__k) ) ) ) ) ).
fof('$adef_Coq.QArith.QArith_base.Qlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQlt,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.seq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eseq,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eseq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$153578_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24153578,V_24X1),V_24X2))
<=> c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24153578___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_153471_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__153471,V_24X1),V_24X2),V_24X3) = c_24__prop__153471___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_fix_80294_v_CANONICAL_2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__fix__80294__v__CANONICAL__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__fix__80294__v__CANONICAL__2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.None_$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_153467_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__153467,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__153467___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pequiv_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePequiv,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9))
<=> cCoq_2esetoid__ring_2eRing__polynom_2ePequiv___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.repeat_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2erepeat,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2erepeat___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_519_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__519,V_24X1),V_24X2) = c_24__prop__519___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_18_mkmult_pow_75952_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__75952,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__75952___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
fof('$adef_Coq.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_$_case_Coq.Init.Datatypes.list$100174_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24100174___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.Exists_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eExists,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eExists___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.cons_id_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eTauto_2econs__id,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eTauto_2econs__id___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.setoid_ring.Field_theory.NPEequiv_$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('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$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('$adef_Tait.MoreList.consn_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTait_2eMoreList_2econsn,V_24X1),V_24X2),V_24X3),V_24X4) = cTait_2eMoreList_2econsn___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.eval_pol_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__pol,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.psubC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2epsubC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2epsubC___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_1225_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1225,V_24X1),V_24X2) = c_24__prop__1225___24a2(V_24X1,V_24X2) ).
fof('$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.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.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.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_$_case_Coq.Init.Specif.sumbool$1214_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esumbool_241214,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_241214___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.List.nth_error_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2enth__error,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2enth__error___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$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('$adef_$_case_Coq.Init.Datatypes.list$66700_$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_2466700,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2466700___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.DeclConstant.GT_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eGT,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eGT___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sorting.Sorted.LocallySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eLocallySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_18_mkmult_pow_75952_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__75952,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__75952___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.Lists.SetoidList.inclA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2einclA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2einclA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Decimal.Pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.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_$_let_11_subst_l_33300_$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__33300,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__33300___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$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('$adef_$_prop_1226_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1226,V_24X1),V_24X2) = c_24__prop__1226___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_4_r\'_1198_1200_1204_$a1',axiom,
! [V_24X1] : happ(c_24__let__var__var__4__r_27__1198__1200__1204,V_24X1) = c_24__let__var__var__4__r_27__1198__1200__1204___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).
fof('$adef_Tait.MoreList.firstn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eMoreList_2efirstn,V_24X1),V_24X2),V_24X3) = cTait_2eMoreList_2efirstn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Tait.MoreList.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eMoreList_2elast,V_24X1),V_24X2),V_24X3) = cTait_2eMoreList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rec,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.collect_annot_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2ecollect__annot,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2ecollect__annot___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.Tauto.eval_f_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__f,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Decimal.D6_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_102516_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__102516__v__CANONICAL__0,V_24X1) = c_24__fix__102516__v__CANONICAL__0___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$101466_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_24101466,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24101466___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_152020_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__152020,V_24X1),V_24X2) = c_24__prop__152020___24a2(V_24X1,V_24X2) ).
fof('$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_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_$_prop_510_$a1',axiom,
! [V_24X1] : happ(c_24__prop__510,V_24X1) = c_24__prop__510___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$82502_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2482502,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2482502___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D4_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Specif.sumbool_$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('$adef_$_prop_153_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__153,V_24X1),V_24X2) = c_24__prop__153___24a2(V_24X1,V_24X2) ).
fof('$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_Tait.Term.up_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2eup,V_24X1) = cTait_2eTerm_2eup___24a1(V_24X1) ).
fof('$adef_$_lam_55008_$a1',axiom,
! [V_24X1] : happ(c_24__lam__55008,V_24X1) = c_24__lam__55008___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkpow_$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('$adef_$_lam_55011_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__55011,V_24X1),V_24X2) = c_24__lam__55011___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).
fof('$adef_Tait.MoreList.rev_acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eMoreList_2erev__acc,V_24X1),V_24X2),V_24X3) = cTait_2eMoreList_2erev__acc___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).
fof('$adef_$_prop_55000_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__55000,V_24X1),V_24X2) = c_24__prop__55000___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.micromega.EnvRing.PsubC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePsubC,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePsubC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Gt.gt_le_S_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eGt_2egt__le__S,V_24X1),V_24X2) = cCoq_2eArith_2eGt_2egt__le__S___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.existsb_$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('$adef_$_lam_53_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__53,V_24X1),V_24X2),V_24X3) = c_24__lam__53___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.ct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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_$_prop_153473_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__153473,V_24X1),V_24X2) = c_24__prop__153473___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.hd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2ehd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_427_$a1',axiom,
! [V_24X1] : happ(c_24__prop__427,V_24X1) = c_24__prop__427___24a1(V_24X1) ).
fof('$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_$_case_Coq.Init.Datatypes.list$84376_$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_2484376,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2484376___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Init.Datatypes.nat_rec_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rec,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2enat__rec___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_854_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__854,V_24X1),V_24X2) = c_24__prop__854___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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_Coq.Structures.OrderedType.LT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_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.Lists.List.skipn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eskipn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eskipn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_152796_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__152796,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__152796___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.rev_append_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_$_lam_64696_$a1',axiom,
! [V_24X1] : happ(c_24__lam__64696,V_24X1) = c_24__lam__64696___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).
fof('$adef_$_prop_418_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__418,V_24X1),V_24X2) = c_24__prop__418___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Between.exists_between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Tait.Apps.head_apps_$a1',axiom,
! [V_24X1] : happ(cTait_2eApps_2ehead__apps,V_24X1) = cTait_2eApps_2ehead__apps___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('$adef_Tait.Term.Abs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2eAbs,V_24X1),V_24X2) = cTait_2eTerm_2eAbs___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.identity_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eidentity,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eidentity___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_154_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__154,V_24X1),V_24X2) = c_24__prop__154___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.BFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eTauto_2eBFormula,V_24X1) = cCoq_2emicromega_2eTauto_2eBFormula___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_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.micromega.Tauto.and_cnf_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eand__cnf,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eand__cnf___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$82480_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2482480,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2482480___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEadd_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEadd,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.micromega.Tauto.cnf_ff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf__ff,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf__ff___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.TFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.interp_PElist_$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('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkPinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkPinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.QArith.QArith_base.Qle_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQle,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$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('$adef_Hammer.Tactics.Reconstr.rdone_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHammer_2eTactics_2eReconstr_2erdone,V_24X1),V_24X2))
<=> cHammer_2eTactics_2eReconstr_2erdone___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkZmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkZmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sumbool_rec_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rec,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Lists.SetoidList.transpose2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$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('$adef_Coq.Vectors.VectorDef.to_list_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eto__list,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2eto__list___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Strings.String.append_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eappend,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eappend___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Subst2.Joachimski.substitution_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTait_2eSubst2_2eJoachimski_2esubstitution__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cTait_2eSubst2_2eJoachimski_2esubstitution__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Tait.Term.term_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2eterm__dec,V_24X1),V_24X2) = cTait_2eTerm_2eterm__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.equivlistA_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eSetoidList_2eequivlistA,V_24X1),V_24X2) = cCoq_2eLists_2eSetoidList_2eequivlistA___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Forall2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eList_2eForall2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Tait.Subst.mk_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst_2emk__sub,V_24X1),V_24X2) = cTait_2eSubst_2emk__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$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('$adef_$_prop_152021_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__152021,V_24X1),V_24X2) = c_24__prop__152021___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Term.Var_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2eVar,V_24X1) = cTait_2eTerm_2eVar___24a1(V_24X1) ).
fof('$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_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.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.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.Morphism_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eMorphism,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.P0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eP0,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).
fof('$adef_Tait.Term.lift_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eTerm_2elift,V_24X1),V_24X2),V_24X3) = cTait_2eTerm_2elift___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Term.type_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTait_2eTerm_2etype__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cTait_2eTerm_2etype__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.condition_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2econdition,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
fof('$adef_Coq.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.Lists.List.rev\'_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2erev_27,V_24X1),V_24X2) = cCoq_2eLists_2eList_2erev_27___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_153549_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__153549__v__CANONICAL__0,V_24X1) = c_24__fix__153549__v__CANONICAL__0___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_$_lam_61_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__61,V_24X1),V_24X2) = c_24__lam__61___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V_24X1) ).
fof('$adef_$_let_17_mkopp_pow_75951_$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__75951,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__75951___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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$101187_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_24101187,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24101187___24a1(V_24X1) ).
fof('$adef_$_lam_66340_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__66340,V_24X1),V_24X2),V_24X3) = c_24__lam__66340___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Tait.Term.term$134937_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Tait_2eTerm_2eterm_24134937,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Tait_2eTerm_2eterm_24134937___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$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('$adef_Coq.setoid_ring.Ring_polynom.P1_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eP1,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2eP1___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
<=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).
fof('$adef_Coq.Lists.List.ForallOrdPairs_$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('$adef_Coq.Init.Logic_Type.notT_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eLogic__Type_2enotT,V_24X1))
<=> cCoq_2eInit_2eLogic__Type_2enotT___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEc_$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('$adef_Coq.Classes.Morphisms.Proper_$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('$adef_Tait.Term.App_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2eApp,V_24X1),V_24X2) = cTait_2eTerm_2eApp___24a2(V_24X1,V_24X2) ).
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('$adef_Tait.Subst.sub_swap0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst_2esub__swap0,V_24X1),V_24X2) = cTait_2eSubst_2esub__swap0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_$_let_var_v_CANONICAL_4_509_513_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__var__v__CANONICAL__4__509__513,V_24X1),V_24X2),V_24X3) = c_24__let__var__v__CANONICAL__4__509__513___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Logic.eq_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eeq__refl,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.List.ForallPairs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallPairs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForallPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_prop_426_$a1',axiom,
! [V_24X1] : happ(c_24__prop__426,V_24X1) = c_24__prop__426___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.rev_$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('$adef_Coq.Bool.Bool.ifb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eBool_2eifb,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eBool_2eifb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_6_p_50317_50320_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__50317__50320,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__50317__50320___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Numbers.BinNums.positive$153533_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24153533,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24153533___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('$adef_Tait.Term.term_rec_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2eterm__rec,V_24X1) = cTait_2eTerm_2eterm__rec___24a1(V_24X1) ).
fof('$adef_$_lam_152804_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__152804,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__152804___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.cons_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2econs___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_$_lam_66340_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__66340,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__66340___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$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_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) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___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('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mknegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$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('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.InA_$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('$adef_$_lam_414_$a1',axiom,
! [V_24X1] : happ(c_24__lam__414,V_24X1) = c_24__lam__414___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_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_Tait.Subst2.Joachimski.comp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2ecomp,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2ecomp___24a2(V_24X1,V_24X2) ).
fof('$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.Lists.List.firstn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efirstn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efirstn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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$1207_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_241207,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_241207___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_let_16_mkpow_75950_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__75950,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__75950___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_case_Tait.Term.term$101877_$a1',axiom,
! [V_24X1] : happ(c_24__case__Tait_2eTerm_2eterm_24101877,V_24X1) = c_24__case__Tait_2eTerm_2eterm_24101877___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('$adef_Coq.Classes.RelationClasses.Symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eSymmetric,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_$_lam_152788_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__152788,V_24X1),V_24X2),V_24X3) = c_24__lam__152788___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.flat_map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2eflat__map,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2eflat__map___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_Tait.Typing.CorTyp_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTait_2eTyping_2eCorTyp,V_24X1),V_24X2))
<=> cTait_2eTyping_2eCorTyp___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_$_prop_987_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__987,V_24X1),V_24X2) = c_24__prop__987___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Subst.sub1_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst_2esub1,V_24X1) = cTait_2eSubst_2esub1___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.Pphi_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.QArith.QArith_base.Qdiv_$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('$adef_$_lam_55011_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__55011,V_24X1),V_24X2),V_24X3) = c_24__lam__55011___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_152564_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__152564,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__152564___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Tait.Subst.sublift_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst_2esublift,V_24X1) = cTait_2eSubst_2esublift___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_$_prop_153488_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__153488,V_24X1),V_24X2),V_24X3) = c_24__prop__153488___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_Tait.Term.arrow_left_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2earrow__left,V_24X1) = cTait_2eTerm_2earrow__left___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.eq_dec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qpower_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQpower,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_836_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__836,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__836___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$82497_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2482497,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2482497___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sumbool_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_152780_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__152780,V_24X1),V_24X2),V_24X3) = c_24__lam__152780___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Tait.MoreList.seq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eMoreList_2eseq,V_24X1),V_24X2) = cTait_2eMoreList_2eseq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_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_Tait.Apps.apps_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eApps_2eapps,V_24X1),V_24X2) = cTait_2eApps_2eapps___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Tait.Term.term$97196_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Tait_2eTerm_2eterm_2497196,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Tait_2eTerm_2eterm_2497196___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_422_$a1',axiom,
! [V_24X1] : happ(c_24__lam__422,V_24X1) = c_24__lam__422___24a1(V_24X1) ).
fof('$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_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.setoid_ring.Field_theory.rsplit_common_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__common,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qpower_positive_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQpower__positive,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQpower__positive___24a2(V_24X1,V_24X2) ).
fof('$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_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_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ).
fof('$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.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D7_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).
fof('$adef_Coq.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.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.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Even.even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
<=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_66336_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__66336,V_24X1),V_24X2) = c_24__lam__66336___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('$adef_Coq.QArith.QArith_base.Qmult_$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('$adef_$_lam_836_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__836,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__836___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Decimal.D0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_lam_55008_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__55008,V_24X1),V_24X2) = c_24__lam__55008___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompLtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
<=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).
fof('$adef_$_prop_419_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__419,V_24X1),V_24X2) = c_24__prop__419___24a2(V_24X1,V_24X2) ).
fof('$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_Coq.micromega.VarMap.Branch_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).
fof('$adef_$_prop_1224_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1224,V_24X1),V_24X2) = c_24__prop__1224___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.list_prod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2elist__prod,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2elist__prod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$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('$adef_Tait.Apps.left_app_$a1',axiom,
! [V_24X1] : happ(cTait_2eApps_2eleft__app,V_24X1) = cTait_2eApps_2eleft__app___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.lel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2elel,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2elel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Eta.EtaExp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cEta_2eEtaExp,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cEta_2eEtaExp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_507_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__507,V_24X1),V_24X2),V_24X3) = c_24__lam__507___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_153469_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__153469,V_24X1),V_24X2),V_24X3) = c_24__prop__153469___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('$adef_Tait.Term.type_rec_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2etype__rec,V_24X1) = cTait_2eTerm_2etype__rec___24a1(V_24X1) ).
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('$adef_$_prop_515_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__515,V_24X1),V_24X2) = c_24__prop__515___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33372_$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__33372,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__33372___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Tait.Subst.shift_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst_2eshift,V_24X1) = cTait_2eSubst_2eshift___24a1(V_24X1) ).
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('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.rev_append_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2erev__append,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2erev__append___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Peano.IsSucc_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2ePeano_2eIsSucc,V_24X1))
<=> cCoq_2eInit_2ePeano_2eIsSucc___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Datatypes.eq_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eDatatypes_2eeq__true,V_24X1))
<=> cCoq_2eInit_2eDatatypes_2eeq__true___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Subst.swap0_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst_2eswap0,V_24X1) = cTait_2eSubst_2eswap0___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('$adef_Coq.micromega.ZMicromega.valid_cut_sign_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2evalid__cut__sign,V_24X1) = cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.concat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2econcat,V_24X1),V_24X2) = cCoq_2eLists_2eList_2econcat___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_153472_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__153472,V_24X1),V_24X2),V_24X3) = c_24__prop__153472___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.Decimal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDecimal_2eDecimal,V_24X1),V_24X2) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).
fof('$adef_Tait.Subst2.Joachimski.Dot_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2eDot,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2eDot___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_152796_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__152796,V_24X1),V_24X2),V_24X3) = c_24__lam__152796___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Compare_dec.le_lt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2ele__lt__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Term.term_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cTait_2eTerm_2eterm__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cTait_2eTerm_2eterm__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_dev_$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('$adef_Coq.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_Tait.Typing.TypJ_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTait_2eTyping_2eTypJ,V_24X1),V_24X2),V_24X3))
<=> cTait_2eTyping_2eTypJ___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.r_list_pow_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2er__list__pow___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Tait.Subst2.above_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTait_2eSubst2_2eabove,V_24X1),V_24X2))
<=> cTait_2eSubst2_2eabove___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.ge_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ege__bool,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQminus,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.mknonnegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).
fof('$adef_Tait.Typing.ext_ctx_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eTyping_2eext__ctx,V_24X1),V_24X2),V_24X3) = cTait_2eTyping_2eext__ctx___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Tait.Subst2.Joachimski.Spare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2eSpare,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2eSpare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.le_0_l_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2ele__0__l,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2ele__0__l___24a1(V_24X1) ).
fof('$adef_$_lam_30_$a1',axiom,
! [V_24X1] : happ(c_24__lam__30,V_24X1) = c_24__lam__30___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.reflect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Relations_1.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$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.Arith.Between.between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ebetween,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ebetween___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Subst.id_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst_2eid,V_24X1) = cTait_2eSubst_2eid___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEopp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEopp,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_$_lam_64_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__64,V_24X1),V_24X2) = c_24__lam__64___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zcomplements.Zlength_aux_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eZArith_2eZcomplements_2eZlength__aux,V_24X1),V_24X2),V_24X3) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.gtb_$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('$adef_$_case_Coq.Init.Datatypes.nat$101511_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24101511,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24101511___24a1(V_24X1) ).
fof('$adef_$_fix_54827_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__54827__1__add__carry,V_24X1),V_24X2) = c_24__fix__54827__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zcomplements.Zlength_aux_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZcomplements_2eZlength__aux,V_24X1) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a1(V_24X1) ).
fof('$adef_Coq.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_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.Specif.exist2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.map_option2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_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_$_fix_84413_v_CANONICAL_0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__84413__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__84413__v__CANONICAL__0___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('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_fix_105972_v_CANONICAL_0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__105972__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__105972__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_66336_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__66336,V_24X1),V_24X2),V_24X3) = c_24__lam__66336___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_153468_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__153468,V_24X1),V_24X2),V_24X3) = c_24__prop__153468___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Tait.MoreList.removelast_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eMoreList_2eremovelast,V_24X1),V_24X2) = cTait_2eMoreList_2eremovelast___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sumbool_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.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_$_prop_153489_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__153489,V_24X1),V_24X2),V_24X3) = c_24__prop__153489___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Hammer.Tactics.Tactics.rdone_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHammer_2eTactics_2eTactics_2erdone,V_24X1),V_24X2))
<=> cHammer_2eTactics_2eTactics_2erdone___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$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('$adef_$_fix_101566_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__101566__v__CANONICAL__0,V_24X1) = c_24__fix__101566__v__CANONICAL__0___24a1(V_24X1) ).
fof('$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_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_Tait.Term.occurs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2eoccurs,V_24X1),V_24X2) = cTait_2eTerm_2eoccurs___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_102016_v_CANONICAL_0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__102016__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__102016__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.BinList.jump_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2ejump,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ).
fof('$adef_Eta.eta_red_$a1',axiom,
! [V_24X1] : happ(cEta_2eeta__red,V_24X1) = cEta_2eeta__red___24a1(V_24X1) ).
fof('$adef_Tait.Apps.is_app_$a1',axiom,
! [V_24X1] : happ(cTait_2eApps_2eis__app,V_24X1) = cTait_2eApps_2eis__app___24a1(V_24X1) ).
fof('$adef_Coq.Strings.String.string_of_list_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eString_2estring__of__list__ascii,V_24X1) = cCoq_2eStrings_2eString_2estring__of__list__ascii___24a1(V_24X1) ).
fof('$adef_$_fix_66832_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__66832__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__66832__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.Neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.nhyps_of_psatz_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2enhyps__of__psatz___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Subst2.Joachimski.PushList_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2ePushList,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2ePushList___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.get_signZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ,V_24X1) = cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V_24X1) ).
fof('$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_Coq.micromega.RingMicromega.eval_op1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$153299_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24153299,V_24X1),V_24X2))
<=> c_24__case__Coq_2eInit_2eDatatypes_2ebool_24153299___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Decimal.D9_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiNword_$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_2eInitialRing_2egen__phiNword,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiNword___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Classes.RelationClasses.Reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eReflexive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Eta.Eta_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cEta_2eEta,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cEta_2eEta___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_$_prop_151_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__151,V_24X1),V_24X2) = c_24__prop__151___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.MoreList.existsb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTait_2eMoreList_2eexistsb,V_24X1),V_24X2),V_24X3) = cTait_2eMoreList_2eexistsb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.Wf_nat.ltof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2eltof,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eArith_2eWf__nat_2eltof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_26_$a1',axiom,
! [V_24X1] : happ(c_24__lam__26,V_24X1) = c_24__lam__26___24a1(V_24X1) ).
fof('$adef_$_prop_153470_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__153470,V_24X1),V_24X2),V_24X3) = c_24__prop__153470___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Tait.Typing.typ_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTyping_2etyp,V_24X1),V_24X2) = cTait_2eTyping_2etyp___24a2(V_24X1,V_24X2) ).
fof('$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_$_case_Coq.Init.Datatypes.prod$53298_$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_2453298,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_2453298___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.InA_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2) = cCoq_2eLists_2eSetoidList_2eInA___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('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.O_S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2ePeano_2eO__S,V_24X1) = cCoq_2eInit_2ePeano_2eO__S___24a1(V_24X1) ).
fof('$adef_$_prop_153487_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__153487,V_24X1),V_24X2) = c_24__prop__153487___24a2(V_24X1,V_24X2) ).
fof('$adef_Eta.is_eta_core_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cEta_2eis__eta__core,V_24X1),V_24X2) = cEta_2eis__eta__core___24a2(V_24X1,V_24X2) ).
fof('$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_Tait.Subst2.Joachimski.sub\'_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2esub_27,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2esub_27___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_152780_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__152780,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__152780___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_let_17_mkopp_pow_75951_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__75951,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__75951___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEequiv_$a13',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13) = cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ).
fof('$adef_Coq.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_$_lam_64696_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__64696,V_24X1),V_24X2) = c_24__lam__64696___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33372_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__33372,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__33372___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.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_Tait.Term.term_rect_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2eterm__rect,V_24X1) = cTait_2eTerm_2eterm__rect___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_$_lam_72981_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__72981,V_24X1),V_24X2),V_24X3) = c_24__lam__72981___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.Computational_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$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('$adef_$_prop_988_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__988,V_24X1),V_24X2) = c_24__prop__988___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Term.type_rect_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2etype__rect,V_24X1) = cTait_2eTerm_2etype__rect___24a1(V_24X1) ).
fof('$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.micromega.Tauto.cnf_tt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf__tt,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_rec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__rec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.Lists.List.nth_ok_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth__ok,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth__ok___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_152_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__152,V_24X1),V_24X2) = c_24__prop__152___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Tait.Term.Arrow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2eArrow,V_24X1),V_24X2) = cTait_2eTerm_2eArrow___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.subrelation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eRelationClasses_2esubrelation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eRelationClasses_2esubrelation___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Tait.Subst2.Joachimski.Up_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst2_2eJoachimski_2eUp,V_24X1) = cTait_2eSubst2_2eJoachimski_2eUp___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.eqlistA_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2) = cCoq_2eLists_2eSetoidList_2eeqlistA___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.clause_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2eclause,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___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('$adef_Coq.Arith.Compare_dec.le_gt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2ele__gt__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2ele__gt__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.removelast_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eremovelast,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eremovelast___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_16_mkpow_75950_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__75950,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__75950___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Tait.Term.up_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2eup,V_24X1),V_24X2) = cTait_2eTerm_2eup___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_152564_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__152564,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__152564___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Tait.Subst2.Joachimski.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2esub,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2esub___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Decimal.D5_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.hd_error_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2ehd__error,V_24X1),V_24X2) = cCoq_2eLists_2eList_2ehd__error___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_514_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__514,V_24X1),V_24X2) = c_24__prop__514___24a2(V_24X1,V_24X2) ).
fof('$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.Arith.PeanoNat.Nat.eq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec,V_24X1),V_24X2) = cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_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_$_fix_101530_v_CANONICAL_0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__101530__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__101530__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.PeanoView_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.DecimalExp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDecimal_2eDecimalExp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.N_$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('$adef_Tait.Subst2.Joachimski.comp\'_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2ecomp_27,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2ecomp_27___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znat.neq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnat_2eneq,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnat_2eneq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Lists.SetoidList.equivlistA_$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('$adef_Coq.Init.Nat.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.existT2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$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('$adef_Tait.Apps.right_app_$a1',axiom,
! [V_24X1] : happ(cTait_2eApps_2eright__app,V_24X1) = cTait_2eApps_2eright__app___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.mkhypo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eInitialRing_2emkhypo,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(V_24X1,V_24X2) ).
fof('$adef_Tait.Apps.arrows_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eApps_2earrows,V_24X1),V_24X2) = cTait_2eApps_2earrows___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
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('$adef_Eta.EtaExps_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cEta_2eEtaExps,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cEta_2eEtaExps___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
<=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).
fof('$adef_$_lam_152804_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__152804,V_24X1),V_24X2),V_24X3) = c_24__lam__152804___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_default_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth__default,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth__default___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_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_Tait.Subst.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst_2esub,V_24X1),V_24X2) = cTait_2eSubst_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.tl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2etl,V_24X1),V_24X2) = cCoq_2eLists_2eList_2etl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_prop_511_$a1',axiom,
! [V_24X1] : happ(c_24__prop__511,V_24X1) = c_24__prop__511___24a1(V_24X1) ).
fof('$adef_$_lam_152788_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__152788,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__152788___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_let_var_6_p_50319_50321_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__50319__50321,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__50319__50321___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('$adef_Tait.Subst2.Joachimski.sublift_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eSubst2_2eJoachimski_2esublift,V_24X1),V_24X2) = cTait_2eSubst2_2eJoachimski_2esublift___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('$adef_Tait.Subst.support_$a1',axiom,
! [V_24X1] : happ(cTait_2eSubst_2esupport,V_24X1) = cTait_2eSubst_2esupport___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('$adef_Tait.Term.arrow_right_$a1',axiom,
! [V_24X1] : happ(cTait_2eTerm_2earrow__right,V_24X1) = cTait_2eTerm_2earrow__right___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.map_option_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Decimal.D3_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).
fof('$adef_$_lam_72981_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__72981,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__72981___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_prop_520_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__520,V_24X1),V_24X2) = c_24__prop__520___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$150833_$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_24150833,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_24150833___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.right_$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('$adef_Coq.NArith.BinNatDef.N.eqb_$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('$adef_Coq.setoid_ring.Field_theory.denum_$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('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Tait.Term.down_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTait_2eTerm_2edown,V_24X1),V_24X2) = cTait_2eTerm_2edown___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.incl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eincl,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eincl___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_61_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__61,V_24X1),V_24X2),V_24X3) = c_24__lam__61___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Tait.Apps.get_apps_$a1',axiom,
! [V_24X1] : happ(cTait_2eApps_2eget__apps,V_24X1) = cTait_2eApps_2eget__apps___24a1(V_24X1) ).
fof('$adef_$_prop_1223_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1223,V_24X1),V_24X2) = c_24__prop__1223___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_103877_v_CANONICAL_0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__103877__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__103877__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$66787_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2466787,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2466787___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_68_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__68,V_24X1),V_24X2) = c_24__lam__68___24a2(V_24X1,V_24X2) ).
fof('$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_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ).
fof('$tdef_$_type_538',axiom,
! [V_24Y] :
( c_24__type__538___24t(V_24Y)
<=> t(V_24Y,c_24__type__538) ) ).
fof('$tdef_$_type_51544',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__51544___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__51544___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_915',axiom,
! [V_24Y] :
( c_24__type__915___24t(V_24Y)
<=> t(V_24Y,c_24__type__915) ) ).
fof('$tdef_$_type_153288',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__153288___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__153288___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_51608',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__51608___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__51608___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_145254',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__145254___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__145254___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_39111',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__39111___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__39111___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_53556',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__53556___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__53556___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_38202',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__38202___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__38202___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_41587',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__41587___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__41587___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.VarMap.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).
fof('$tdef_$_type_51384',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__51384___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__51384___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_40353',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__40353___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__40353___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Init.Specif.sigT2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1146',axiom,
! [V_24Y] :
( c_24__type__1146___24t(V_24Y)
<=> t(V_24Y,c_24__type__1146) ) ).
fof('$tdef_$_type_74744',axiom,
! [V_24Y] :
( c_24__type__74744___24t(V_24Y)
<=> t(V_24Y,c_24__type__74744) ) ).
fof('$tdef_$_type_23',axiom,
! [V_24Y] :
( c_24__type__23___24t(V_24Y)
<=> t(V_24Y,c_24__type__23) ) ).
fof('$tdef_Tait.Term.term',axiom,
! [V_24Y] :
( cTait_2eTerm_2eterm___24t(V_24Y)
<=> t(V_24Y,cTait_2eTerm_2eterm) ) ).
fof('$tdef_$_type_31760',axiom,
! [V_24Y] :
( c_24__type__31760___24t(V_24Y)
<=> t(V_24Y,c_24__type__31760) ) ).
fof('$tdef_$_type_31526',axiom,
! [V_24Y] :
( c_24__type__31526___24t(V_24Y)
<=> t(V_24Y,c_24__type__31526) ) ).
fof('$tdef_$_type_73775',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__73775___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__73775___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_44818',axiom,
! [V_24Y] :
( c_24__type__44818___24t(V_24Y)
<=> t(V_24Y,c_24__type__44818) ) ).
fof('$tdef_$_type_77953',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__77953___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__77953___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_143341',axiom,
! [V_24Y] :
( c_24__type__143341___24t(V_24Y)
<=> t(V_24Y,c_24__type__143341) ) ).
fof('$tdef_$_type_940',axiom,
! [V_24X1,V_24Y] :
( c_24__type__940___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__940___24a1(V_24X1)) ) ).
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_$_type_145288',axiom,
! [V_24Y] :
( c_24__type__145288___24t(V_24Y)
<=> t(V_24Y,c_24__type__145288) ) ).
fof('$tdef_$_type_42566',axiom,
! [V_24X1,V_24Y] :
( c_24__type__42566___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__42566___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34314',axiom,
! [V_24Y] :
( c_24__type__34314___24t(V_24Y)
<=> t(V_24Y,c_24__type__34314) ) ).
fof('$tdef_$_type_34224',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34224___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34224___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1106',axiom,
! [V_24Y] :
( c_24__type__1106___24t(V_24Y)
<=> t(V_24Y,c_24__type__1106) ) ).
fof('$tdef_$_type_37335',axiom,
! [V_24Y] :
( c_24__type__37335___24t(V_24Y)
<=> t(V_24Y,c_24__type__37335) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1101',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1101___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1101___24a1(V_24X1)) ) ).
fof('$tdef_$_type_876',axiom,
! [V_24X1,V_24Y] :
( c_24__type__876___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__876___24a1(V_24X1)) ) ).
fof('$tdef_$_type_37877',axiom,
! [V_24Y] :
( c_24__type__37877___24t(V_24Y)
<=> t(V_24Y,c_24__type__37877) ) ).
fof('$tdef_$_type_44761',axiom,
! [V_24Y] :
( c_24__type__44761___24t(V_24Y)
<=> t(V_24Y,c_24__type__44761) ) ).
fof('$tdef_$_type_78288',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__78288___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__78288___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_80154',axiom,
! [V_24Y] :
( c_24__type__80154___24t(V_24Y)
<=> t(V_24Y,c_24__type__80154) ) ).
fof('$tdef_$_type_33760',axiom,
! [V_24Y] :
( c_24__type__33760___24t(V_24Y)
<=> t(V_24Y,c_24__type__33760) ) ).
fof('$tdef_$_type_73647',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__73647___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__73647___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_77747',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__77747___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__77747___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_43492',axiom,
! [V_24Y] :
( c_24__type__43492___24t(V_24Y)
<=> t(V_24Y,c_24__type__43492) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ) ).
fof('$tdef_$_type_71731',axiom,
! [V_24Y] :
( c_24__type__71731___24t(V_24Y)
<=> t(V_24Y,c_24__type__71731) ) ).
fof('$tdef_$_type_54192',axiom,
! [V_24Y] :
( c_24__type__54192___24t(V_24Y)
<=> t(V_24Y,c_24__type__54192) ) ).
fof('$tdef_$_type_78602',axiom,
! [V_24Y] :
( c_24__type__78602___24t(V_24Y)
<=> t(V_24Y,c_24__type__78602) ) ).
fof('$tdef_$_type_53043',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__53043___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__53043___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_37293',axiom,
! [V_24Y] :
( c_24__type__37293___24t(V_24Y)
<=> t(V_24Y,c_24__type__37293) ) ).
fof('$tdef_$_type_51910',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__51910___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__51910___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_153123',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__153123___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__153123___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_145219',axiom,
! [V_24Y] :
( c_24__type__145219___24t(V_24Y)
<=> t(V_24Y,c_24__type__145219) ) ).
fof('$tdef_$_type_44449',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__44449___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__44449___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$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('$tdef_$_type_985',axiom,
! [V_24Y] :
( c_24__type__985___24t(V_24Y)
<=> t(V_24Y,c_24__type__985) ) ).
fof('$tdef_$_type_44348',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__44348___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__44348___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_45700',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__45700___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__45700___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_40883',axiom,
! [V_24Y] :
( c_24__type__40883___24t(V_24Y)
<=> t(V_24Y,c_24__type__40883) ) ).
fof('$tdef_$_type_48768',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__48768___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__48768___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_76566',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__76566___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__76566___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Init.Specif.sig2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_44774',axiom,
! [V_24Y] :
( c_24__type__44774___24t(V_24Y)
<=> t(V_24Y,c_24__type__44774) ) ).
fof('$tdef_$_type_144772',axiom,
! [V_24Y] :
( c_24__type__144772___24t(V_24Y)
<=> t(V_24Y,c_24__type__144772) ) ).
fof('$tdef_$_type_32418',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32418___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32418___24a1(V_24X1)) ) ).
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_$_type_55139',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__55139___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__55139___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_152466',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__152466___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__152466___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_41319',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__41319___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__41319___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34643',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34643___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34643___24a1(V_24X1)) ) ).
fof('$tdef_$_type_66198',axiom,
! [V_24Y] :
( c_24__type__66198___24t(V_24Y)
<=> t(V_24Y,c_24__type__66198) ) ).
fof('$tdef_$_type_65949',axiom,
! [V_24Y] :
( c_24__type__65949___24t(V_24Y)
<=> t(V_24Y,c_24__type__65949) ) ).
fof('$tdef_$_type_55079',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__55079___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__55079___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_39519',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__39519___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__39519___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_861',axiom,
! [V_24Y] :
( c_24__type__861___24t(V_24Y)
<=> t(V_24Y,c_24__type__861) ) ).
fof('$tdef_$_type_143330',axiom,
! [V_24Y] :
( c_24__type__143330___24t(V_24Y)
<=> t(V_24Y,c_24__type__143330) ) ).
fof('$tdef_$_type_48099',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__48099___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__48099___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_66297',axiom,
! [V_24Y] :
( c_24__type__66297___24t(V_24Y)
<=> t(V_24Y,c_24__type__66297) ) ).
fof('$tdef_$_type_290',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__290___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__290___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32446',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32446___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32446___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_73546',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__73546___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__73546___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_53983',axiom,
! [V_24Y] :
( c_24__type__53983___24t(V_24Y)
<=> t(V_24Y,c_24__type__53983) ) ).
fof('$tdef_$_type_78761',axiom,
! [V_24Y] :
( c_24__type__78761___24t(V_24Y)
<=> t(V_24Y,c_24__type__78761) ) ).
fof('$tdef_$_type_152591',axiom,
! [V_24Y] :
( c_24__type__152591___24t(V_24Y)
<=> t(V_24Y,c_24__type__152591) ) ).
fof('$tdef_$_type_150272',axiom,
! [V_24X1,V_24Y] :
( c_24__type__150272___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__150272___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1135',axiom,
! [V_24Y] :
( c_24__type__1135___24t(V_24Y)
<=> t(V_24Y,c_24__type__1135) ) ).
fof('$tdef_$_type_917',axiom,
! [V_24Y] :
( c_24__type__917___24t(V_24Y)
<=> t(V_24Y,c_24__type__917) ) ).
fof('$tdef_$_type_76711',axiom,
! [V_24X1,V_24Y] :
( c_24__type__76711___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__76711___24a1(V_24X1)) ) ).
fof('$tdef_$_type_70000',axiom,
! [V_24Y] :
( c_24__type__70000___24t(V_24Y)
<=> t(V_24Y,c_24__type__70000) ) ).
fof('$tdef_$_type_83399',axiom,
! [V_24Y] :
( c_24__type__83399___24t(V_24Y)
<=> t(V_24Y,c_24__type__83399) ) ).
fof('$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_621',axiom,
! [V_24Y] :
( c_24__type__621___24t(V_24Y)
<=> t(V_24Y,c_24__type__621) ) ).
fof('$tdef_$_type_83644',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__83644___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__83644___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_54698',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__54698___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__54698___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_39945',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__39945___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__39945___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_76770',axiom,
! [V_24X1,V_24Y] :
( c_24__type__76770___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__76770___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1)) ) ).
fof('$tdef_$_type_83605',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__83605___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__83605___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Tait.Subst.substitution',axiom,
! [V_24Y] :
( cTait_2eSubst_2esubstitution___24t(V_24Y)
<=> t(V_24Y,cTait_2eSubst_2esubstitution) ) ).
fof('$tdef_$_type_313',axiom,
! [V_24Y] :
( c_24__type__313___24t(V_24Y)
<=> t(V_24Y,c_24__type__313) ) ).
fof('$tdef_$_type_145297',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__145297___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__145297___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_52160',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__52160___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__52160___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_40851',axiom,
! [V_24Y] :
( c_24__type__40851___24t(V_24Y)
<=> t(V_24Y,c_24__type__40851) ) ).
fof('$tdef_$_type_153310',axiom,
! [V_24Y] :
( c_24__type__153310___24t(V_24Y)
<=> t(V_24Y,c_24__type__153310) ) ).
fof('$tdef_$_type_52646',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__52646___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__52646___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_76656',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__76656___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__76656___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_37810',axiom,
! [V_24Y] :
( c_24__type__37810___24t(V_24Y)
<=> t(V_24Y,c_24__type__37810) ) ).
fof('$tdef_$_type_144735',axiom,
! [V_24Y] :
( c_24__type__144735___24t(V_24Y)
<=> t(V_24Y,c_24__type__144735) ) ).
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_$_type_150522',axiom,
! [V_24Y] :
( c_24__type__150522___24t(V_24Y)
<=> t(V_24Y,c_24__type__150522) ) ).
fof('$tdef_$_type_82',axiom,
! [V_24Y] :
( c_24__type__82___24t(V_24Y)
<=> t(V_24Y,c_24__type__82) ) ).
fof('$tdef_$_type_54187',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__54187___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__54187___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_83810',axiom,
! [V_24Y] :
( c_24__type__83810___24t(V_24Y)
<=> t(V_24Y,c_24__type__83810) ) ).
fof('$tdef_$_type_52535',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__52535___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__52535___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_53464',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__53464___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__53464___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$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_42762',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__42762___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__42762___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_43123',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__43123___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__43123___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_37812',axiom,
! [V_24Y] :
( c_24__type__37812___24t(V_24Y)
<=> t(V_24Y,c_24__type__37812) ) ).
fof('$tdef_$_type_71500',axiom,
! [V_24Y] :
( c_24__type__71500___24t(V_24Y)
<=> t(V_24Y,c_24__type__71500) ) ).
fof('$tdef_$_type_34727',axiom,
! [V_24Y] :
( c_24__type__34727___24t(V_24Y)
<=> t(V_24Y,c_24__type__34727) ) ).
fof('$tdef_$_type_223',axiom,
! [V_24Y] :
( c_24__type__223___24t(V_24Y)
<=> t(V_24Y,c_24__type__223) ) ).
fof('$tdef_$_type_54152',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__54152___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__54152___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_42504',axiom,
! [V_24Y] :
( c_24__type__42504___24t(V_24Y)
<=> t(V_24Y,c_24__type__42504) ) ).
fof('$tdef_$_type_72967',axiom,
! [V_24Y] :
( c_24__type__72967___24t(V_24Y)
<=> t(V_24Y,c_24__type__72967) ) ).
fof('$tdef_$_type_152529',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__152529___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__152529___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_43298',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__43298___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__43298___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_803',axiom,
! [V_24Y] :
( c_24__type__803___24t(V_24Y)
<=> t(V_24Y,c_24__type__803) ) ).
fof('$tdef_$_type_52285',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__52285___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__52285___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_32629',axiom,
! [V_24Y] :
( c_24__type__32629___24t(V_24Y)
<=> t(V_24Y,c_24__type__32629) ) ).
fof('$tdef_$_type_218',axiom,
! [V_24Y] :
( c_24__type__218___24t(V_24Y)
<=> t(V_24Y,c_24__type__218) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.hypo',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2ehypo) ) ).
fof('$tdef_$_type_34666',axiom,
! [V_24Y] :
( c_24__type__34666___24t(V_24Y)
<=> t(V_24Y,c_24__type__34666) ) ).
fof('$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_40846',axiom,
! [V_24Y] :
( c_24__type__40846___24t(V_24Y)
<=> t(V_24Y,c_24__type__40846) ) ).
fof('$tdef_$_type_144523',axiom,
! [V_24Y] :
( c_24__type__144523___24t(V_24Y)
<=> t(V_24Y,c_24__type__144523) ) ).
fof('$tdef_$_type_53544',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__53544___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__53544___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_52865',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__52865___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__52865___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_82330',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__82330___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__82330___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_$_type_79039',axiom,
! [V_24Y] :
( c_24__type__79039___24t(V_24Y)
<=> t(V_24Y,c_24__type__79039) ) ).
fof('$tdef_$_type_72039',axiom,
! [V_24Y] :
( c_24__type__72039___24t(V_24Y)
<=> t(V_24Y,c_24__type__72039) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Decimal.int',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).
fof('$tdef_$_type_31723',axiom,
! [V_24Y] :
( c_24__type__31723___24t(V_24Y)
<=> t(V_24Y,c_24__type__31723) ) ).
fof('$tdef_$_type_153187',axiom,
! [V_24Y] :
( c_24__type__153187___24t(V_24Y)
<=> t(V_24Y,c_24__type__153187) ) ).
fof('$tdef_$_type_53093',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__53093___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__53093___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Strings.String.string',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eString_2estring___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eString_2estring) ) ).
fof('$tdef_$_type_65779',axiom,
! [V_24Y] :
( c_24__type__65779___24t(V_24Y)
<=> t(V_24Y,c_24__type__65779) ) ).
fof('$tdef_$_type_73389',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__73389___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__73389___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_38094',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__38094___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__38094___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_152071',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__152071___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__152071___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_35507',axiom,
! [V_24Y] :
( c_24__type__35507___24t(V_24Y)
<=> t(V_24Y,c_24__type__35507) ) ).
fof('$tdef_$_type_848',axiom,
! [V_24Y] :
( c_24__type__848___24t(V_24Y)
<=> t(V_24Y,c_24__type__848) ) ).
fof('$tdef_$_type_43519',axiom,
! [V_24Y] :
( c_24__type__43519___24t(V_24Y)
<=> t(V_24Y,c_24__type__43519) ) ).
fof('$tdef_$_type_253',axiom,
! [V_24Y] :
( c_24__type__253___24t(V_24Y)
<=> t(V_24Y,c_24__type__253) ) ).
fof('$tdef_$_type_50307',axiom,
! [V_24Y] :
( c_24__type__50307___24t(V_24Y)
<=> t(V_24Y,c_24__type__50307) ) ).
fof('$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_348',axiom,
! [V_24Y] :
( c_24__type__348___24t(V_24Y)
<=> t(V_24Y,c_24__type__348) ) ).
fof('$tdef_$_type_151931',axiom,
! [V_24X1,V_24Y] :
( c_24__type__151931___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__151931___24a1(V_24X1)) ) ).
fof('$tdef_$_type_38148',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__38148___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__38148___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_44607',axiom,
! [V_24Y] :
( c_24__type__44607___24t(V_24Y)
<=> t(V_24Y,c_24__type__44607) ) ).
fof('$tdef_$_type_43030',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__43030___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__43030___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_82561',axiom,
! [V_24Y] :
( c_24__type__82561___24t(V_24Y)
<=> t(V_24Y,c_24__type__82561) ) ).
fof('$tdef_$_type_149094',axiom,
! [V_24Y] :
( c_24__type__149094___24t(V_24Y)
<=> t(V_24Y,c_24__type__149094) ) ).
fof('$tdef_$_type_34203',axiom,
! [V_24Y] :
( c_24__type__34203___24t(V_24Y)
<=> t(V_24Y,c_24__type__34203) ) ).
fof('$tdef_$_type_51267',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__51267___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__51267___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_49760',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__49760___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__49760___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_68418',axiom,
! [V_24Y] :
( c_24__type__68418___24t(V_24Y)
<=> t(V_24Y,c_24__type__68418) ) ).
fof('$tdef_$_type_45354',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__45354___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__45354___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_46046',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__46046___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__46046___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('$tdef_Tait.Term.type',axiom,
! [V_24Y] :
( cTait_2eTerm_2etype___24t(V_24Y)
<=> t(V_24Y,cTait_2eTerm_2etype) ) ).
fof('$tdef_$_type_54868',axiom,
! [V_24Y] :
( c_24__type__54868___24t(V_24Y)
<=> t(V_24Y,c_24__type__54868) ) ).
fof('$tdef_$_type_38064',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__38064___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__38064___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_37554',axiom,
! [V_24Y] :
( c_24__type__37554___24t(V_24Y)
<=> t(V_24Y,c_24__type__37554) ) ).
fof('$tdef_$_type_341',axiom,
! [V_24Y] :
( c_24__type__341___24t(V_24Y)
<=> t(V_24Y,c_24__type__341) ) ).
fof('$tdef_$_type_66992',axiom,
! [V_24Y] :
( c_24__type__66992___24t(V_24Y)
<=> t(V_24Y,c_24__type__66992) ) ).
fof('$tdef_$_type_359',axiom,
! [V_24Y] :
( c_24__type__359___24t(V_24Y)
<=> t(V_24Y,c_24__type__359) ) ).
fof('$tdef_$_type_156',axiom,
! [V_24Y] :
( c_24__type__156___24t(V_24Y)
<=> t(V_24Y,c_24__type__156) ) ).
fof('$tdef_$_type_1154',axiom,
! [V_24Y] :
( c_24__type__1154___24t(V_24Y)
<=> t(V_24Y,c_24__type__1154) ) ).
fof('$tdef_$_type_83791',axiom,
! [V_24Y] :
( c_24__type__83791___24t(V_24Y)
<=> t(V_24Y,c_24__type__83791) ) ).
fof('$tdef_$_type_34708',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__34708___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__34708___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_53143',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__53143___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__53143___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_865',axiom,
! [V_24Y] :
( c_24__type__865___24t(V_24Y)
<=> t(V_24Y,c_24__type__865) ) ).
fof('$tdef_$_type_584',axiom,
! [V_24Y] :
( c_24__type__584___24t(V_24Y)
<=> t(V_24Y,c_24__type__584) ) ).
fof('$tdef_$_type_810',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__810___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__810___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34306',axiom,
! [V_24Y] :
( c_24__type__34306___24t(V_24Y)
<=> t(V_24Y,c_24__type__34306) ) ).
fof('$tdef_Coq.Structures.OrderedType.Compare',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( cCoq_2eStructures_2eOrderedType_2eCompare___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Init.Specif.sumor',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumor___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_41102',axiom,
! [V_24Y] :
( c_24__type__41102___24t(V_24Y)
<=> t(V_24Y,c_24__type__41102) ) ).
fof('$tdef_$_type_72991',axiom,
! [V_24Y] :
( c_24__type__72991___24t(V_24Y)
<=> t(V_24Y,c_24__type__72991) ) ).
fof('$tdef_$_type_569',axiom,
! [V_24Y] :
( c_24__type__569___24t(V_24Y)
<=> t(V_24Y,c_24__type__569) ) ).
fof('$tdef_$_type_31553',axiom,
! [V_24Y] :
( c_24__type__31553___24t(V_24Y)
<=> t(V_24Y,c_24__type__31553) ) ).
fof('$tdef_$_type_41505',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__41505___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__41505___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_69902',axiom,
! [V_24Y] :
( c_24__type__69902___24t(V_24Y)
<=> t(V_24Y,c_24__type__69902) ) ).
fof('$tdef_$_type_94',axiom,
! [V_24Y] :
( c_24__type__94___24t(V_24Y)
<=> t(V_24Y,c_24__type__94) ) ).
fof('$tdef_$_type_72844',axiom,
! [V_24Y] :
( c_24__type__72844___24t(V_24Y)
<=> t(V_24Y,c_24__type__72844) ) ).
fof('$tdef_$_type_38178',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__38178___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__38178___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_43474',axiom,
! [V_24Y] :
( c_24__type__43474___24t(V_24Y)
<=> t(V_24Y,c_24__type__43474) ) ).
fof('$tdef_$_type_69936',axiom,
! [V_24Y] :
( c_24__type__69936___24t(V_24Y)
<=> t(V_24Y,c_24__type__69936) ) ).
fof('$tdef_$_type_34697',axiom,
! [V_24Y] :
( c_24__type__34697___24t(V_24Y)
<=> t(V_24Y,c_24__type__34697) ) ).
fof('$tdef_Tait.Typing.context',axiom,
! [V_24Y] :
( cTait_2eTyping_2econtext___24t(V_24Y)
<=> t(V_24Y,cTait_2eTyping_2econtext) ) ).
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_$_type_73010',axiom,
! [V_24Y] :
( c_24__type__73010___24t(V_24Y)
<=> t(V_24Y,c_24__type__73010) ) ).
fof('$tdef_$_type_149089',axiom,
! [V_24Y] :
( c_24__type__149089___24t(V_24Y)
<=> t(V_24Y,c_24__type__149089) ) ).
fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).
fof('$tdef_$_type_67461',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__67461___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__67461___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_153211',axiom,
! [V_24Y] :
( c_24__type__153211___24t(V_24Y)
<=> t(V_24Y,c_24__type__153211) ) ).
fof('$tdef_$_type_43346',axiom,
! [V_24Y] :
( c_24__type__43346___24t(V_24Y)
<=> t(V_24Y,c_24__type__43346) ) ).
fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_$_type_50302',axiom,
! [V_24Y] :
( c_24__type__50302___24t(V_24Y)
<=> t(V_24Y,c_24__type__50302) ) ).
fof('$tdef_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [V_24X1,V_24Y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).
fof('$tdef_$_type_73311',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__73311___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__73311___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_54707',axiom,
! [V_24Y] :
( c_24__type__54707___24t(V_24Y)
<=> t(V_24Y,c_24__type__54707) ) ).
fof('$tdef_$_type_66250',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__66250___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__66250___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_50283',axiom,
! [V_24Y] :
( c_24__type__50283___24t(V_24Y)
<=> t(V_24Y,c_24__type__50283) ) ).
fof('$tdef_$_type_37454',axiom,
! [V_24Y] :
( c_24__type__37454___24t(V_24Y)
<=> t(V_24Y,c_24__type__37454) ) ).
fof('$tdef_$_type_152867',axiom,
! [V_24Y] :
( c_24__type__152867___24t(V_24Y)
<=> t(V_24Y,c_24__type__152867) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ) ).
fof('$tdef_$_type_73705',axiom,
! [V_24Y] :
( c_24__type__73705___24t(V_24Y)
<=> t(V_24Y,c_24__type__73705) ) ).
fof('$tdef_$_type_724',axiom,
! [V_24X1,V_24Y] :
( c_24__type__724___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__724___24a1(V_24X1)) ) ).
fof('$tdef_$_type_63256',axiom,
! [V_24Y] :
( c_24__type__63256___24t(V_24Y)
<=> t(V_24Y,c_24__type__63256) ) ).
fof('$tdef_$_type_54710',axiom,
! [V_24X1,V_24Y] :
( c_24__type__54710___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__54710___24a1(V_24X1)) ) ).
fof('$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_40761',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__40761___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__40761___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_152099',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__152099___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__152099___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_50331',axiom,
! [V_24Y] :
( c_24__type__50331___24t(V_24Y)
<=> t(V_24Y,c_24__type__50331) ) ).
fof('$tdef_$_type_32372',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32372___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32372___24a1(V_24X1)) ) ).
fof('$tdef_$_type_38118',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__38118___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__38118___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
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_$_type_53235',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__53235___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__53235___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_32599',axiom,
! [V_24Y] :
( c_24__type__32599___24t(V_24Y)
<=> t(V_24Y,c_24__type__32599) ) ).
fof('$tdef_$_type_152412',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__152412___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__152412___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_300',axiom,
! [V_24X1,V_24Y] :
( c_24__type__300___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__300___24a1(V_24X1)) ) ).
fof('$tdef_$_type_777',axiom,
! [V_24Y] :
( c_24__type__777___24t(V_24Y)
<=> t(V_24Y,c_24__type__777) ) ).
fof('$tdef_$_type_48422',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__48422___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__48422___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.NArith.BinNatDef.N.t',axiom,
! [V_24Y] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNArith_2eBinNatDef_2eN_2et) ) ).
fof('$tdef_Coq.Init.Datatypes.ID',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).
fof('$tdef_$_type_34715',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__34715___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__34715___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_78294',axiom,
! [V_24Y] :
( c_24__type__78294___24t(V_24Y)
<=> t(V_24Y,c_24__type__78294) ) ).
fof('$tdef_$_type_37576',axiom,
! [V_24Y] :
( c_24__type__37576___24t(V_24Y)
<=> t(V_24Y,c_24__type__37576) ) ).
fof('$tdef_$_type_40566',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__40566___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__40566___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_34701',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34701___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34701___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ) ).
fof('$tdef_Coq.micromega.Tauto.clause',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2emicromega_2eTauto_2eclause___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_278',axiom,
! [V_24Y] :
( c_24__type__278___24t(V_24Y)
<=> t(V_24Y,c_24__type__278) ) ).
fof('$tdef_$_type_68948',axiom,
! [V_24Y] :
( c_24__type__68948___24t(V_24Y)
<=> t(V_24Y,c_24__type__68948) ) ).
fof('$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_1075',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1075___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1075___24a1(V_24X1)) ) ).
fof('$tdef_$_type_82451',axiom,
! [V_24Y] :
( c_24__type__82451___24t(V_24Y)
<=> t(V_24Y,c_24__type__82451) ) ).
fof('$tdef_$_type_167',axiom,
! [V_24Y] :
( c_24__type__167___24t(V_24Y)
<=> t(V_24Y,c_24__type__167) ) ).
fof('$tdef_$_type_38685',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__38685___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__38685___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_28',axiom,
! [V_24X1,V_24Y] :
( c_24__type__28___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__28___24a1(V_24X1)) ) ).
fof('$tdef_$_type_66235',axiom,
! [V_24Y] :
( c_24__type__66235___24t(V_24Y)
<=> t(V_24Y,c_24__type__66235) ) ).
fof('$tdef_$_type_221',axiom,
! [V_24Y] :
( c_24__type__221___24t(V_24Y)
<=> t(V_24Y,c_24__type__221) ) ).
fof('$tdef_$_type_145211',axiom,
! [V_24Y] :
( c_24__type__145211___24t(V_24Y)
<=> t(V_24Y,c_24__type__145211) ) ).
fof('$tdef_$_type_153410',axiom,
! [V_24Y] :
( c_24__type__153410___24t(V_24Y)
<=> t(V_24Y,c_24__type__153410) ) ).
fof('$tdef_$_type_32450',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32450___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32450___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_39306',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__39306___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__39306___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_53420',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__53420___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__53420___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_53573',axiom,
! [V_24Y] :
( c_24__type__53573___24t(V_24Y)
<=> t(V_24Y,c_24__type__53573) ) ).
fof('$tdef_$_type_35532',axiom,
! [V_24Y] :
( c_24__type__35532___24t(V_24Y)
<=> t(V_24Y,c_24__type__35532) ) ).
fof('$tdef_$_type_83404',axiom,
! [V_24Y] :
( c_24__type__83404___24t(V_24Y)
<=> t(V_24Y,c_24__type__83404) ) ).
fof('$tdef_$_type_144532',axiom,
! [V_24Y] :
( c_24__type__144532___24t(V_24Y)
<=> t(V_24Y,c_24__type__144532) ) ).
fof('$tdef_$_type_33504',axiom,
! [V_24Y] :
( c_24__type__33504___24t(V_24Y)
<=> t(V_24Y,c_24__type__33504) ) ).
fof('$tdef_$_type_593',axiom,
! [V_24Y] :
( c_24__type__593___24t(V_24Y)
<=> t(V_24Y,c_24__type__593) ) ).
fof('$tdef_$_type_51590',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__51590___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__51590___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_44792',axiom,
! [V_24Y] :
( c_24__type__44792___24t(V_24Y)
<=> t(V_24Y,c_24__type__44792) ) ).
fof('$tdef_$_type_37902',axiom,
! [V_24Y] :
( c_24__type__37902___24t(V_24Y)
<=> t(V_24Y,c_24__type__37902) ) ).
fof('$tdef_$_type_72848',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__72848___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__72848___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_44612',axiom,
! [V_24Y] :
( c_24__type__44612___24t(V_24Y)
<=> t(V_24Y,c_24__type__44612) ) ).
fof('$tdef_$_type_32510',axiom,
! [V_24Y] :
( c_24__type__32510___24t(V_24Y)
<=> t(V_24Y,c_24__type__32510) ) ).
fof('$tdef_$_type_32831',axiom,
! [V_24Y] :
( c_24__type__32831___24t(V_24Y)
<=> t(V_24Y,c_24__type__32831) ) ).
fof('$tdef_$_type_152847',axiom,
! [V_24Y] :
( c_24__type__152847___24t(V_24Y)
<=> t(V_24Y,c_24__type__152847) ) ).
fof('$tdef_Coq.ZArith.Znumtheory.Euclid',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_$_type_82509',axiom,
! [V_24Y] :
( c_24__type__82509___24t(V_24Y)
<=> t(V_24Y,c_24__type__82509) ) ).
fof('$tdef_$_type_82369',axiom,
! [V_24Y] :
( c_24__type__82369___24t(V_24Y)
<=> t(V_24Y,c_24__type__82369) ) ).
fof('$tdef_$_type_73708',axiom,
! [V_24Y] :
( c_24__type__73708___24t(V_24Y)
<=> t(V_24Y,c_24__type__73708) ) ).
fof('$tdef_$_type_721',axiom,
! [V_24Y] :
( c_24__type__721___24t(V_24Y)
<=> t(V_24Y,c_24__type__721) ) ).
fof('$tdef_$_type_982',axiom,
! [V_24Y] :
( c_24__type__982___24t(V_24Y)
<=> t(V_24Y,c_24__type__982) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).
fof('$tdef_$_type_42285',axiom,
! [V_24Y] :
( c_24__type__42285___24t(V_24Y)
<=> t(V_24Y,c_24__type__42285) ) ).
fof('$tdef_$_type_55018',axiom,
! [V_24Y] :
( c_24__type__55018___24t(V_24Y)
<=> t(V_24Y,c_24__type__55018) ) ).
fof('$tdef_$_type_180',axiom,
! [V_24Y] :
( c_24__type__180___24t(V_24Y)
<=> t(V_24Y,c_24__type__180) ) ).
fof('$tdef_Coq.micromega.EnvRing.Mon',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).
fof('$tdef_$_type_80308',axiom,
! [V_24Y] :
( c_24__type__80308___24t(V_24Y)
<=> t(V_24Y,c_24__type__80308) ) ).
fof('$tdef_$_type_73678',axiom,
! [V_24Y] :
( c_24__type__73678___24t(V_24Y)
<=> t(V_24Y,c_24__type__73678) ) ).
fof('$tdef_$_type_40859',axiom,
! [V_24Y] :
( c_24__type__40859___24t(V_24Y)
<=> t(V_24Y,c_24__type__40859) ) ).
fof('$tdef_Coq.Reals.RIneq.nonposreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonposreal) ) ).
fof('$tdef_$_type_31539',axiom,
! [V_24Y] :
( c_24__type__31539___24t(V_24Y)
<=> t(V_24Y,c_24__type__31539) ) ).
fof('$tdef_$_type_749',axiom,
! [V_24Y] :
( c_24__type__749___24t(V_24Y)
<=> t(V_24Y,c_24__type__749) ) ).
fof('$tdef_$_type_73044',axiom,
! [V_24X1,V_24Y] :
( c_24__type__73044___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__73044___24a1(V_24X1)) ) ).
fof('$tdef_$_type_161',axiom,
! [V_24Y] :
( c_24__type__161___24t(V_24Y)
<=> t(V_24Y,c_24__type__161) ) ).
fof('$tdef_$_type_41762',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__41762___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__41762___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_737',axiom,
! [V_24Y] :
( c_24__type__737___24t(V_24Y)
<=> t(V_24Y,c_24__type__737) ) ).
fof('$tdef_$_type_851',axiom,
! [V_24X1,V_24Y] :
( c_24__type__851___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__851___24a1(V_24X1)) ) ).
fof('$tdef_$_type_145201',axiom,
! [V_24Y] :
( c_24__type__145201___24t(V_24Y)
<=> t(V_24Y,c_24__type__145201) ) ).
fof('$tdef_$_type_51634',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__51634___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__51634___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_42265',axiom,
! [V_24Y] :
( c_24__type__42265___24t(V_24Y)
<=> t(V_24Y,c_24__type__42265) ) ).
fof('$tdef_$_type_34283',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__34283___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__34283___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_104',axiom,
! [V_24Y] :
( c_24__type__104___24t(V_24Y)
<=> t(V_24Y,c_24__type__104) ) ).
fof('$tdef_Coq.Reals.RIneq.posreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).
fof('$tdef_$_type_1164',axiom,
! [V_24Y] :
( c_24__type__1164___24t(V_24Y)
<=> t(V_24Y,c_24__type__1164) ) ).
fof('$tdef_$_type_44157',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__44157___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__44157___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.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_46715',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__46715___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__46715___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Decimal.decimal',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2edecimal) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ) ).
fof('$tdef_$_type_50106',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__50106___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__50106___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_151895',axiom,
! [V_24X1,V_24Y] :
( c_24__type__151895___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__151895___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.QMicromega.QWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eQMicromega_2eQWitness) ) ).
fof('$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_153115',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__153115___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__153115___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_55023',axiom,
! [V_24Y] :
( c_24__type__55023___24t(V_24Y)
<=> t(V_24Y,c_24__type__55023) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.t',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2et) ) ).
fof('$tdef_$_type_37883',axiom,
! [V_24Y] :
( c_24__type__37883___24t(V_24Y)
<=> t(V_24Y,c_24__type__37883) ) ).
fof('$tdef_$_type_41855',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__41855___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__41855___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_73719',axiom,
! [V_24Y] :
( c_24__type__73719___24t(V_24Y)
<=> t(V_24Y,c_24__type__73719) ) ).
fof('$tdef_$_type_50288',axiom,
! [V_24Y] :
( c_24__type__50288___24t(V_24Y)
<=> t(V_24Y,c_24__type__50288) ) ).
fof('$tdef_$_type_34640',axiom,
! [V_24Y] :
( c_24__type__34640___24t(V_24Y)
<=> t(V_24Y,c_24__type__34640) ) ).
fof('$tdef_$_type_1067',axiom,
! [V_24Y] :
( c_24__type__1067___24t(V_24Y)
<=> t(V_24Y,c_24__type__1067) ) ).
fof('$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_517',axiom,
! [V_24Y] :
( c_24__type__517___24t(V_24Y)
<=> t(V_24Y,c_24__type__517) ) ).
fof('$tdef_$_type_164',axiom,
! [V_24Y] :
( c_24__type__164___24t(V_24Y)
<=> t(V_24Y,c_24__type__164) ) ).
fof('$tdef_$_type_920',axiom,
! [V_24X1,V_24Y] :
( c_24__type__920___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__920___24a1(V_24X1)) ) ).
fof('$tdef_$_type_153179',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__153179___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__153179___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_33296',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33296___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33296___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_152699',axiom,
! [V_24Y] :
( c_24__type__152699___24t(V_24Y)
<=> t(V_24Y,c_24__type__152699) ) ).
fof('$tdef_$_type_151979',axiom,
! [V_24Y] :
( c_24__type__151979___24t(V_24Y)
<=> t(V_24Y,c_24__type__151979) ) ).
fof('$tdef_$_type_50585',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__50585___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__50585___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_1041',axiom,
! [V_24Y] :
( c_24__type__1041___24t(V_24Y)
<=> t(V_24Y,c_24__type__1041) ) ).
fof('$tdef_$_type_50765',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__50765___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__50765___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_152286',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__152286___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__152286___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_44550',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__44550___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__44550___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
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_$_type_41680',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__41680___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__41680___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_150488',axiom,
! [V_24Y] :
( c_24__type__150488___24t(V_24Y)
<=> t(V_24Y,c_24__type__150488) ) ).
fof('$tdef_$_type_32481',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32481___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32481___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_153279',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__153279___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__153279___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_40871',axiom,
! [V_24Y] :
( c_24__type__40871___24t(V_24Y)
<=> t(V_24Y,c_24__type__40871) ) ).
fof('$tdef_$_type_53311',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__53311___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__53311___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_145250',axiom,
! [V_24Y] :
( c_24__type__145250___24t(V_24Y)
<=> t(V_24Y,c_24__type__145250) ) ).
fof('$tdef_$_type_54972',axiom,
! [V_24Y] :
( c_24__type__54972___24t(V_24Y)
<=> t(V_24Y,c_24__type__54972) ) ).
fof('$tdef_$_type_38259',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__38259___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__38259___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_51567',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__51567___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__51567___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_534',axiom,
! [V_24Y] :
( c_24__type__534___24t(V_24Y)
<=> t(V_24Y,c_24__type__534) ) ).
fof('$tdef_$_type_52884',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__52884___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__52884___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_$_type_44767',axiom,
! [V_24Y] :
( c_24__type__44767___24t(V_24Y)
<=> t(V_24Y,c_24__type__44767) ) ).
fof('$tdef_$_type_151973',axiom,
! [V_24Y] :
( c_24__type__151973___24t(V_24Y)
<=> t(V_24Y,c_24__type__151973) ) ).
fof('$tdef_Coq.ZArith.BinIntDef.Z.t',axiom,
! [V_24Y] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eBinIntDef_2eZ_2et) ) ).
fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$tdef_$_type_80125',axiom,
! [V_24Y] :
( c_24__type__80125___24t(V_24Y)
<=> t(V_24Y,c_24__type__80125) ) ).
fof('$tdef_$_type_76601',axiom,
! [V_24Y] :
( c_24__type__76601___24t(V_24Y)
<=> t(V_24Y,c_24__type__76601) ) ).
fof('$tdef_$_type_215',axiom,
! [V_24Y] :
( c_24__type__215___24t(V_24Y)
<=> t(V_24Y,c_24__type__215) ) ).
fof('$tdef_$_type_31748',axiom,
! [V_24Y] :
( c_24__type__31748___24t(V_24Y)
<=> t(V_24Y,c_24__type__31748) ) ).
fof('$tdef_$_type_145217',axiom,
! [V_24Y] :
( c_24__type__145217___24t(V_24Y)
<=> t(V_24Y,c_24__type__145217) ) ).
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_$_type_1093',axiom,
! [V_24Y] :
( c_24__type__1093___24t(V_24Y)
<=> t(V_24Y,c_24__type__1093) ) ).
fof('$tdef_$_type_1091',axiom,
! [V_24Y] :
( c_24__type__1091___24t(V_24Y)
<=> t(V_24Y,c_24__type__1091) ) ).
fof('$tdef_$_type_361',axiom,
! [V_24Y] :
( c_24__type__361___24t(V_24Y)
<=> t(V_24Y,c_24__type__361) ) ).
fof('$tdef_$_type_34671',axiom,
! [V_24Y] :
( c_24__type__34671___24t(V_24Y)
<=> t(V_24Y,c_24__type__34671) ) ).
fof('$tdef_$_type_144760',axiom,
! [V_24Y] :
( c_24__type__144760___24t(V_24Y)
<=> t(V_24Y,c_24__type__144760) ) ).
fof('$tdef_$_type_40888',axiom,
! [V_24X1,V_24Y] :
( c_24__type__40888___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__40888___24a1(V_24X1)) ) ).
fof('$tdef_$_type_152349',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__152349___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__152349___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).
fof('$tdef_$_type_33287',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33287___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33287___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_202',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__202___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__202___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_53500',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__53500___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__53500___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_$_type_63261',axiom,
! [V_24X1,V_24Y] :
( c_24__type__63261___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__63261___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_32396',axiom,
! [V_24Y] :
( c_24__type__32396___24t(V_24Y)
<=> t(V_24Y,c_24__type__32396) ) ).
fof('$tdef_$_type_153171',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__153171___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__153171___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1228',axiom,
! [V_24Y] :
( c_24__type__1228___24t(V_24Y)
<=> t(V_24Y,c_24__type__1228) ) ).
fof('$tdef_$_type_81467',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__81467___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__81467___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_144957',axiom,
! [V_24Y] :
( c_24__type__144957___24t(V_24Y)
<=> t(V_24Y,c_24__type__144957) ) ).
fof('$tdef_$_type_34301',axiom,
! [V_24Y] :
( c_24__type__34301___24t(V_24Y)
<=> t(V_24Y,c_24__type__34301) ) ).
fof('$tdef_$_type_416',axiom,
! [V_24X1,V_24Y] :
( c_24__type__416___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__416___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1118',axiom,
! [V_24Y] :
( c_24__type__1118___24t(V_24Y)
<=> t(V_24Y,c_24__type__1118) ) ).
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_$_type_44247',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__44247___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__44247___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_54028',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__54028___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__54028___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_153204',axiom,
! [V_24Y] :
( c_24__type__153204___24t(V_24Y)
<=> t(V_24Y,c_24__type__153204) ) ).
fof('$tdef_$_type_74',axiom,
! [V_24Y] :
( c_24__type__74___24t(V_24Y)
<=> t(V_24Y,c_24__type__74) ) ).
fof('$tdef_$_type_49437',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__49437___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__49437___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Nat.t',axiom,
! [V_24Y] :
( cCoq_2eInit_2eNat_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eNat_2et) ) ).
fof('$tdef_$_type_83683',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__83683___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__83683___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_31750',axiom,
! [V_24Y] :
( c_24__type__31750___24t(V_24Y)
<=> t(V_24Y,c_24__type__31750) ) ).
fof('$tdef_$_type_610',axiom,
! [V_24Y] :
( c_24__type__610___24t(V_24Y)
<=> t(V_24Y,c_24__type__610) ) ).
fof('$tdef_$_type_145056',axiom,
! [V_24Y] :
( c_24__type__145056___24t(V_24Y)
<=> t(V_24Y,c_24__type__145056) ) ).
fof('$tdef_$_type_73927',axiom,
! [V_24Y] :
( c_24__type__73927___24t(V_24Y)
<=> t(V_24Y,c_24__type__73927) ) ).
fof('$tdef_$_type_153131',axiom,
! [V_24Y] :
( c_24__type__153131___24t(V_24Y)
<=> t(V_24Y,c_24__type__153131) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.linear',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1)) ) ).
fof('$tdef_$_type_51521',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__51521___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__51521___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Init.Decimal.uint',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2euint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2euint) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_150264',axiom,
! [V_24Y] :
( c_24__type__150264___24t(V_24Y)
<=> t(V_24Y,c_24__type__150264) ) ).
fof('$tdef_$_type_41412',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__41412___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__41412___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_73154',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__73154___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__73154___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_690',axiom,
! [V_24Y] :
( c_24__type__690___24t(V_24Y)
<=> t(V_24Y,c_24__type__690) ) ).
fof('$tdef_$_type_53185',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__53185___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__53185___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_33522',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33522___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33522___24a1(V_24X1)) ) ).
fof('$tdef_$_type_151206',axiom,
! [V_24Y] :
( c_24__type__151206___24t(V_24Y)
<=> t(V_24Y,c_24__type__151206) ) ).
fof('$tdef_$_type_82207',axiom,
! [V_24Y] :
( c_24__type__82207___24t(V_24Y)
<=> t(V_24Y,c_24__type__82207) ) ).
fof('$tdef_$_type_66502',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__66502___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__66502___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_76832',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__76832___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__76832___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_145206',axiom,
! [V_24Y] :
( c_24__type__145206___24t(V_24Y)
<=> t(V_24Y,c_24__type__145206) ) ).
fof('$tdef_$_type_50299',axiom,
! [V_24Y] :
( c_24__type__50299___24t(V_24Y)
<=> t(V_24Y,c_24__type__50299) ) ).
fof('$tdef_$_type_146833',axiom,
! [V_24Y] :
( c_24__type__146833___24t(V_24Y)
<=> t(V_24Y,c_24__type__146833) ) ).
fof('$tdef_$_type_81019',axiom,
! [V_24Y] :
( c_24__type__81019___24t(V_24Y)
<=> t(V_24Y,c_24__type__81019) ) ).
fof('$tdef_$_type_32633',axiom,
! [V_24Y] :
( c_24__type__32633___24t(V_24Y)
<=> t(V_24Y,c_24__type__32633) ) ).
fof('$tdef_$_type_82349',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__82349___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__82349___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_74754',axiom,
! [V_24Y] :
( c_24__type__74754___24t(V_24Y)
<=> t(V_24Y,c_24__type__74754) ) ).
fof('$tdef_$_type_43205',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__43205___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__43205___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_66238',axiom,
! [V_24X1,V_24Y] :
( c_24__type__66238___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__66238___24a1(V_24X1)) ) ).
fof('$tdef_$_type_55050',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__55050___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__55050___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_66971',axiom,
! [V_24X1,V_24Y] :
( c_24__type__66971___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__66971___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1065',axiom,
! [V_24Y] :
( c_24__type__1065___24t(V_24Y)
<=> t(V_24Y,c_24__type__1065) ) ).
fof('$tdef_$_type_43433',axiom,
! [V_24Y] :
( c_24__type__43433___24t(V_24Y)
<=> t(V_24Y,c_24__type__43433) ) ).
fof('$tdef_$_type_42948',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__42948___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__42948___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_283',axiom,
! [V_24Y] :
( c_24__type__283___24t(V_24Y)
<=> t(V_24Y,c_24__type__283) ) ).
fof('$tdef_$_type_51321',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__51321___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__51321___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_858',axiom,
! [V_24Y] :
( c_24__type__858___24t(V_24Y)
<=> t(V_24Y,c_24__type__858) ) ).
fof('$tdef_$_type_52410',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__52410___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__52410___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_$_type_716',axiom,
! [V_24Y] :
( c_24__type__716___24t(V_24Y)
<=> t(V_24Y,c_24__type__716) ) ).
fof('$tdef_$_type_31787',axiom,
! [V_24Y] :
( c_24__type__31787___24t(V_24Y)
<=> t(V_24Y,c_24__type__31787) ) ).
fof('$tdef_$_type_152935',axiom,
! [V_24Y] :
( c_24__type__152935___24t(V_24Y)
<=> t(V_24Y,c_24__type__152935) ) ).
fof('$tdef_$_type_46369',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__46369___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__46369___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_80510',axiom,
! [V_24Y] :
( c_24__type__80510___24t(V_24Y)
<=> t(V_24Y,c_24__type__80510) ) ).
fof('$tdef_$_type_760',axiom,
! [V_24Y] :
( c_24__type__760___24t(V_24Y)
<=> t(V_24Y,c_24__type__760) ) ).
fof('$tdef_$_type_66988',axiom,
! [V_24Y] :
( c_24__type__66988___24t(V_24Y)
<=> t(V_24Y,c_24__type__66988) ) ).
fof('$tdef_$_type_144795',axiom,
! [V_24Y] :
( c_24__type__144795___24t(V_24Y)
<=> t(V_24Y,c_24__type__144795) ) ).
fof('$tdef_$_type_81901',axiom,
! [V_24Y] :
( c_24__type__81901___24t(V_24Y)
<=> t(V_24Y,c_24__type__81901) ) ).
fof('$tdef_$_type_692',axiom,
! [V_24Y] :
( c_24__type__692___24t(V_24Y)
<=> t(V_24Y,c_24__type__692) ) ).
fof('$tdef_$_type_151919',axiom,
! [V_24Y] :
( c_24__type__151919___24t(V_24Y)
<=> t(V_24Y,c_24__type__151919) ) ).
fof('$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_33945',axiom,
! [V_24Y] :
( c_24__type__33945___24t(V_24Y)
<=> t(V_24Y,c_24__type__33945) ) ).
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_$_type_47407',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__47407___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__47407___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_32425',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32425___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32425___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_51204',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__51204___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__51204___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_572',axiom,
! [V_24Y] :
( c_24__type__572___24t(V_24Y)
<=> t(V_24Y,c_24__type__572) ) ).
fof('$tdef_$_type_71887',axiom,
! [V_24Y] :
( c_24__type__71887___24t(V_24Y)
<=> t(V_24Y,c_24__type__71887) ) ).
fof('$tdef_$_type_54048',axiom,
! [V_24Y] :
( c_24__type__54048___24t(V_24Y)
<=> t(V_24Y,c_24__type__54048) ) ).
fof('$tdef_$_type_44056',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__44056___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__44056___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_144823',axiom,
! [V_24Y] :
( c_24__type__144823___24t(V_24Y)
<=> t(V_24Y,c_24__type__144823) ) ).
fof('$tdef_$_type_51141',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__51141___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__51141___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_73370',axiom,
! [V_24Y] :
( c_24__type__73370___24t(V_24Y)
<=> t(V_24Y,c_24__type__73370) ) ).
fof('$tdef_$_type_54691',axiom,
! [V_24Y] :
( c_24__type__54691___24t(V_24Y)
<=> t(V_24Y,c_24__type__54691) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ) ).
fof('$tdef_$_type_71722',axiom,
! [V_24X1,V_24Y] :
( c_24__type__71722___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__71722___24a1(V_24X1)) ) ).
fof('$tdef_$_type_38286',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__38286___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__38286___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_37872',axiom,
! [V_24Y] :
( c_24__type__37872___24t(V_24Y)
<=> t(V_24Y,c_24__type__37872) ) ).
fof('$tdef_$_type_63243',axiom,
! [V_24X1,V_24Y] :
( c_24__type__63243___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__63243___24a1(V_24X1)) ) ).
fof('$tdef_$_type_66329',axiom,
! [V_24Y] :
( c_24__type__66329___24t(V_24Y)
<=> t(V_24Y,c_24__type__66329) ) ).
fof('$tdef_$_type_53986',axiom,
! [V_24Y] :
( c_24__type__53986___24t(V_24Y)
<=> t(V_24Y,c_24__type__53986) ) ).
fof('$tdef_$_type_51652',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__51652___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__51652___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_31537',axiom,
! [V_24Y] :
( c_24__type__31537___24t(V_24Y)
<=> t(V_24Y,c_24__type__31537) ) ).
fof('$tdef_$_type_78587',axiom,
! [V_24Y] :
( c_24__type__78587___24t(V_24Y)
<=> t(V_24Y,c_24__type__78587) ) ).
fof('$tdef_$_type_66968',axiom,
! [V_24Y] :
( c_24__type__66968___24t(V_24Y)
<=> t(V_24Y,c_24__type__66968) ) ).
fof('$tdef_$_type_54108',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__54108___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__54108___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_152002',axiom,
! [V_24Y] :
( c_24__type__152002___24t(V_24Y)
<=> t(V_24Y,c_24__type__152002) ) ).
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_$_type_999',axiom,
! [V_24Y] :
( c_24__type__999___24t(V_24Y)
<=> t(V_24Y,c_24__type__999) ) ).
fof('$tdef_$_type_81941',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__81941___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__81941___24a2(V_24X1,V_24X2)) ) ).
fof('$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_78734',axiom,
! [V_24Y] :
( c_24__type__78734___24t(V_24Y)
<=> t(V_24Y,c_24__type__78734) ) ).
fof('$tdef_$_type_37574',axiom,
! [V_24Y] :
( c_24__type__37574___24t(V_24Y)
<=> t(V_24Y,c_24__type__37574) ) ).
fof('$tdef_$_type_42561',axiom,
! [V_24Y] :
( c_24__type__42561___24t(V_24Y)
<=> t(V_24Y,c_24__type__42561) ) ).
fof('$tdef_$_type_387',axiom,
! [V_24Y] :
( c_24__type__387___24t(V_24Y)
<=> t(V_24Y,c_24__type__387) ) ).
fof('$tdef_$_type_71',axiom,
! [V_24Y] :
( c_24__type__71___24t(V_24Y)
<=> t(V_24Y,c_24__type__71) ) ).
fof('$tdef_$_type_822',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__822___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__822___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_42855',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__42855___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__42855___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32474',axiom,
! [V_24Y] :
( c_24__type__32474___24t(V_24Y)
<=> t(V_24Y,c_24__type__32474) ) ).
fof('$tdef_$_type_66210',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__66210___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__66210___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_47753',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__47753___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__47753___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_37621',axiom,
! [V_24Y] :
( c_24__type__37621___24t(V_24Y)
<=> t(V_24Y,c_24__type__37621) ) ).
fof('$tdef_$_type_83435',axiom,
! [V_24Y] :
( c_24__type__83435___24t(V_24Y)
<=> t(V_24Y,c_24__type__83435) ) ).
fof('$tdef_$_type_50648',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__50648___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__50648___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_152009',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__152009___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__152009___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_54058',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__54058___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__54058___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_52898',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__52898___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__52898___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_159',axiom,
! [V_24Y] :
( c_24__type__159___24t(V_24Y)
<=> t(V_24Y,c_24__type__159) ) ).
fof('$tdef_$_type_702',axiom,
! [V_24Y] :
( c_24__type__702___24t(V_24Y)
<=> t(V_24Y,c_24__type__702) ) ).
fof('$tdef_$_type_67456',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__67456___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__67456___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_52035',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__52035___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__52035___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_32413',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32413___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32413___24a1(V_24X1)) ) ).
fof('$tdef_$_type_932',axiom,
! [V_24X1,V_24Y] :
( c_24__type__932___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__932___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34660',axiom,
! [V_24Y] :
( c_24__type__34660___24t(V_24Y)
<=> t(V_24Y,c_24__type__34660) ) ).
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_37257',axiom,
! [V_24Y] :
( c_24__type__37257___24t(V_24Y)
<=> t(V_24Y,c_24__type__37257) ) ).
fof('$tdef_$_type_70057',axiom,
! [V_24Y] :
( c_24__type__70057___24t(V_24Y)
<=> t(V_24Y,c_24__type__70057) ) ).
fof('$tdef_$_type_153552',axiom,
! [V_24Y] :
( c_24__type__153552___24t(V_24Y)
<=> t(V_24Y,c_24__type__153552) ) ).
fof('$tdef_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [V_24Y] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(V_24Y)
<=> t(V_24Y,cHammer_2eTactics_2eReconstr_2eReconstrT) ) ).
fof('$tdef_$_type_39732',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__39732___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__39732___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_50828',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__50828___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__50828___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_44602',axiom,
! [V_24Y] :
( c_24__type__44602___24t(V_24Y)
<=> t(V_24Y,c_24__type__44602) ) ).
fof('$tdef_$_type_43955',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__43955___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__43955___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_76822',axiom,
! [V_24Y] :
( c_24__type__76822___24t(V_24Y)
<=> t(V_24Y,c_24__type__76822) ) ).
fof('$tdef_$_type_54882',axiom,
! [V_24Y] :
( c_24__type__54882___24t(V_24Y)
<=> t(V_24Y,c_24__type__54882) ) ).
fof('$tdef_Coq.micromega.RMicromega.RWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRWitness) ) ).
fof('$tdef_$_type_54197',axiom,
! [V_24Y] :
( c_24__type__54197___24t(V_24Y)
<=> t(V_24Y,c_24__type__54197) ) ).
fof('$tdef_$_type_144520',axiom,
! [V_24Y] :
( c_24__type__144520___24t(V_24Y)
<=> t(V_24Y,c_24__type__144520) ) ).
fof('$tdef_Coq.Sets.Relations_1.Relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_76230',axiom,
! [V_24Y] :
( c_24__type__76230___24t(V_24Y)
<=> t(V_24Y,c_24__type__76230) ) ).
fof('$tdef_$_type_33270',axiom,
! [V_24Y] :
( c_24__type__33270___24t(V_24Y)
<=> t(V_24Y,c_24__type__33270) ) ).
fof('$tdef_$_type_144541',axiom,
! [V_24Y] :
( c_24__type__144541___24t(V_24Y)
<=> t(V_24Y,c_24__type__144541) ) ).
fof('$tdef_$_type_363',axiom,
! [V_24Y] :
( c_24__type__363___24t(V_24Y)
<=> t(V_24Y,c_24__type__363) ) ).
fof('$tdef_$_type_44764',axiom,
! [V_24Y] :
( c_24__type__44764___24t(V_24Y)
<=> t(V_24Y,c_24__type__44764) ) ).
fof('$tdef_$_type_346',axiom,
! [V_24Y] :
( c_24__type__346___24t(V_24Y)
<=> t(V_24Y,c_24__type__346) ) ).
fof('$tdef_$_type_40158',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__40158___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__40158___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_1104',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1104___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1104___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34636',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34636___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34636___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_38898',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__38898___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__38898___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('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).
fof('$tdef_$_type_32404',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32404___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32404___24a1(V_24X1)) ) ).
fof('$tdef_$_type_92',axiom,
! [V_24Y] :
( c_24__type__92___24t(V_24Y)
<=> t(V_24Y,c_24__type__92) ) ).
fof('$tdef_$_type_54253',axiom,
! [V_24Y] :
( c_24__type__54253___24t(V_24Y)
<=> t(V_24Y,c_24__type__54253) ) ).
fof('$tdef_$_type_50296',axiom,
! [V_24Y] :
( c_24__type__50296___24t(V_24Y)
<=> t(V_24Y,c_24__type__50296) ) ).
fof('$tdef_$_type_76762',axiom,
! [V_24X1,V_24Y] :
( c_24__type__76762___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__76762___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32439',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32439___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32439___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_49114',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__49114___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__49114___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_71693',axiom,
! [V_24Y] :
( c_24__type__71693___24t(V_24Y)
<=> t(V_24Y,c_24__type__71693) ) ).
fof('$tdef_$_type_38235',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__38235___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__38235___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_55131',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__55131___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__55131___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_151933',axiom,
! [V_24Y] :
( c_24__type__151933___24t(V_24Y)
<=> t(V_24Y,c_24__type__151933) ) ).
fof('$tdef_$_type_66964',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__66964___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__66964___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_50711',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__50711___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__50711___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).
fof('$tdef_$_type_151917',axiom,
! [V_24Y] :
( c_24__type__151917___24t(V_24Y)
<=> t(V_24Y,c_24__type__151917) ) ).
fof('$tdef_Tait.Subst2.Joachimski.substitution',axiom,
! [V_24Y] :
( cTait_2eSubst2_2eJoachimski_2esubstitution___24t(V_24Y)
<=> t(V_24Y,cTait_2eSubst2_2eJoachimski_2esubstitution) ) ).
fof('$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('$tdef_Coq.Reals.RIneq.negreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enegreal) ) ).
fof('$tdef_$_type_47061',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__47061___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__47061___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_35524',axiom,
! [V_24Y] :
( c_24__type__35524___24t(V_24Y)
<=> t(V_24Y,c_24__type__35524) ) ).
fof('$tdef_$_type_1169',axiom,
! [V_24Y] :
( c_24__type__1169___24t(V_24Y)
<=> t(V_24Y,c_24__type__1169) ) ).
fof('$tdef_$_type_67372',axiom,
! [V_24Y] :
( c_24__type__67372___24t(V_24Y)
<=> t(V_24Y,c_24__type__67372) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__rhos] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V0__rhos)
=> ! [V1__mus] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cTait_2eTerm_2etype,V1__mus)
=> ! [V2__sigma] :
( cTait_2eTerm_2etype___24t(V2__sigma)
=> ! [V3__r] :
( cTait_2eTerm_2eterm___24t(V3__r)
=> ! [V4__r_27] :
( cTait_2eTerm_2eterm___24t(V4__r_27)
=> ( cEta_2eEta___24a4(cCoq_2eInit_2eDatatypes_2eapp___24a3(cTait_2eTerm_2etype,V0__rhos,V1__mus),V2__sigma,V3__r,V4__r_27)
=> cEta_2eEta___24a4(V0__rhos,V2__sigma,V3__r,V4__r_27) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------