TPTP Problem File: SEV670+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SEV670+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - RTopology bounded real net has cluster point
% 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 : RTopology.bounded.real.net.has.cluster.point.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 2973 (1117 unt; 0 def)
% Number of atoms : 9404 (1906 equ)
% Maximal formula atoms : 76 ( 3 avg)
% Number of connectives : 6543 ( 112 ~; 220 |;1136 &)
% (1070 <=>;4005 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 6 avg)
% Maximal term depth : 19 ( 1 avg)
% Number of predicates : 576 ( 575 usr; 0 prp; 1-15 aty)
% Number of functors : 1571 (1571 usr; 968 con; 0-16 aty)
% Number of variables : 7824 (7380 !; 444 ?)
% 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$9399',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ( c_24__type__9400___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__9376__9392___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249399___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__7__down__9374__9390___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) )
| ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__9376__9392___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249399___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__9__z__9376__9392___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$9428',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ( c_24__type__9400___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__9405__9421___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249428___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__9__z__9405__9421___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) )
| ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__9405__9421___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249428___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__8__up__9404__9420___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$9466',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ( c_24__type__9400___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__9443__9459___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249466___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__7__down__9441__9457___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) )
| ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__9443__9459___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_249466___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__9__z__9443__9459___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ) ) ) ) ) ).
fof('$_case_Topology.TopologicalSpaces.TopologicalSpace$64651',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__1)
=> ( c_24__type__64707___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ? [Vvar__0__point__set__64652] :
( cType___24t(Vvar__0__point__set__64652)
& ? [Vvar__1__open__64653] :
( c_24__type__64711___24t(Vv__CANONICAL__1,Vvar__0__point__set__64652,Vvar__1__open__64653)
& ! [Vvar__var__2__F__64657__64661] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__point__set__64652,Vvar__var__2__F__64657__64661)
=> ( ! [Vvar__var__3__S__64658__64662] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__64652,Vvar__var__3__S__64658__64662)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__point__set__64652),Vvar__var__2__F__64657__64661,Vvar__var__3__S__64658__64662)
=> p(happ(Vvar__1__open__64653,Vvar__var__3__S__64658__64662)) ) )
=> p(happ(Vvar__1__open__64653,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__point__set__64652,Vvar__var__2__F__64657__64661))) ) )
& ! [Vvar__var__3__U__64666__64670] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__64652,Vvar__var__3__U__64666__64670)
=> ! [Vvar__var__4__V__64667__64671] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__64652,Vvar__var__4__V__64667__64671)
=> ( p(happ(Vvar__1__open__64653,Vvar__var__3__U__64666__64670))
=> ( p(happ(Vvar__1__open__64653,Vvar__var__4__V__64667__64671))
=> p(happ(Vvar__1__open__64653,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__point__set__64652,Vvar__var__3__U__64666__64670,Vvar__var__4__V__64667__64671))) ) ) ) )
& p(happ(Vvar__1__open__64653,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__point__set__64652)))
& happ(Vv__CANONICAL__2,Vv__CANONICAL__3) = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__64652,Vvar__1__open__64653)
& c_24__case__Topology_2eTopologicalSpaces_2eTopologicalSpace_2464651___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vvar__0__point__set__64652 ) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_1683',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__1683___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_2187',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__2190] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2190)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2190)
& c_24__let__16__mkpow__2187___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__2191] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2191)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2191)
& c_24__let__16__mkpow__2187___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__2187___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_mkopp_pow_2188',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__2188___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__2187___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_2189',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__2189___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__2187___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_var_7_down_9374_9390',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9373] : c_24__let__var__7__down__9374__9390___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9373) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9373) ).
fof('$_def_$_let_var_7_down_9403_9419',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9402] : c_24__let__var__7__down__9403__9419___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9402) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9402) ).
fof('$_def_$_let_var_7_down_9441_9457',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9440] : c_24__let__var__7__down__9441__9457___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9440) = c_24__fix__9439__0__Dichotomy__lb___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9440) ).
fof('$_def_$_let_var_8_up_9375_9391',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9373] : c_24__let__var__8__up__9375__9391___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9373) = c_24__fix__9372__1__Dichotomy__ub___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9373) ).
fof('$_def_$_let_var_8_up_9404_9420',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9402] : c_24__let__var__8__up__9404__9420___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9402) = c_24__fix__9372__1__Dichotomy__ub___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9402) ).
fof('$_def_$_let_var_8_up_9442_9458',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9440] : c_24__let__var__8__up__9442__9458___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9440) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__ub___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9440) ).
fof('$_def_$_let_var_9_z_9376_9392',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9373] : c_24__let__var__9__z__9376__9392___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9373) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(c_24__let__var__7__down__9374__9390___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9373),c_24__let__var__8__up__9375__9391___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9373)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('$_def_$_let_var_9_z_9405_9421',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9402] : c_24__let__var__9__z__9405__9421___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9402) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(c_24__let__var__7__down__9403__9419___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9402),c_24__let__var__8__up__9404__9420___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9402)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('$_def_$_let_var_9_z_9443_9459',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9440] : c_24__let__var__9__z__9443__9459___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9440) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(c_24__let__var__7__down__9441__9457___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9440),c_24__let__var__8__up__9442__9458___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9440)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('$_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('$_def_Coq.Arith.Factorial.fact',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__6044] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6044)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6044)
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6044),cCoq_2eArith_2eFactorial_2efact___24a1(Vvar__0___24Anonymous__6044)) ) ) ) ).
fof('$_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__2846] :
( t(Vvar__1___24Anonymous__2846,V0__A)
& ? [Vvar__2___24Anonymous__2847] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__2847)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2846,Vvar__2___24Anonymous__2847)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__2846,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__2847,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__6487] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6487)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6487)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__6487,V2__m)) ) ) ) ).
fof('$_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__13255] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13255)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13255)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__13258] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13258)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13258)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__13255,Vvar__0___24Anonymous__13258)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__6492] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6492)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6492)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__6492,V2__m)) ) ) ) ).
fof('$_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__4452] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4452)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4452)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__4452 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__6495] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6495)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6495)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__6498] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6498)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6498)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__6495,Vvar__0___24Anonymous__6498) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ).
fof('$_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('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__318___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__312] :
( t(Vvar__2__x__312,V0__A)
& p(happ(V1__P,Vvar__2__x__312))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__312)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__312 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT1',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__26692___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__26686] :
( t(Vvar__2__x__26686,V0__A)
& ? [Vvar__3___24Anonymous__26687] :
( t(Vvar__3___24Anonymous__26687,happ(V1__P,Vvar__2__x__26686))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__26686,Vvar__3___24Anonymous__26687)
& cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__26686 ) ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT2',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__26715___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__26709] :
( t(Vvar__2__x__26709,V0__A)
& ? [Vvar__3___24Anonymous__26710] :
( t(Vvar__3___24Anonymous__26710,happ(V1__P,Vvar__2__x__26709))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__26709,Vvar__3___24Anonymous__26710)
& cCoq_2eInit_2eSpecif_2eprojT2___24a3(V0__A,V1__P,V2__x) = Vvar__3___24Anonymous__26710 ) ) ) ) ) ).
fof('$_def_Coq.Init.Specif.sigT_rec',axiom,
! [V0__A,V1__P,V2__P] : cCoq_2eInit_2eSpecif_2esigT__rec___24a3(V0__A,V1__P,V2__P) = cCoq_2eInit_2eSpecif_2esigT__rect___24a3(V0__A,V1__P,V2__P) ).
fof('$_def_Coq.Init.Specif.sigT_rect',axiom,
! [V0__A,V1__P,V2__P,V3__f,V4__s] :
( cType___24t(V0__A)
=> ( c_24__type__26572___24t(V0__A,V1__P,V2__P,V1__P)
=> ( c_24__type__26580___24t(V0__A,V1__P,V2__P,V2__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V4__s)
=> ? [Vvar__2__x__26564] :
( t(Vvar__2__x__26564,V0__A)
& ? [Vvar__3___24Anonymous__26565] :
( t(Vvar__3___24Anonymous__26565,happ(V1__P,Vvar__2__x__26564))
& V4__s = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__26564,Vvar__3___24Anonymous__26565)
& cCoq_2eInit_2eSpecif_2esigT__rect___24a5(V0__A,V1__P,V2__P,V3__f,V4__s) = happ(happ(V3__f,Vvar__2__x__26564),Vvar__3___24Anonymous__26565) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Specif.sig_rec',axiom,
! [V0__A,V1__P,V2__P] : cCoq_2eInit_2eSpecif_2esig__rec___24a3(V0__A,V1__P,V2__P) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V0__A,V1__P,V2__P) ).
fof('$_def_Coq.Init.Specif.sumbool_rec',axiom,
! [V0__A,V1__B,V2__P] : cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V0__A,V1__B,V2__P) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V0__A,V1__B,V2__P) ).
fof('$_def_Coq.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__10095] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10095)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10095)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__10098] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10098)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10098)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__10095,Vvar__0___24Anonymous__10098)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__10116] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10116)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10116)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
| ? [Vvar__0___24Anonymous__10119] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10119)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10119)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__10116,V1__b) ) ) ) ) ) ) ) ).
fof('$_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__10108] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10108)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10108)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__10109] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10109)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10109)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__10112] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10112)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10112)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__10109,Vvar__0___24Anonymous__10112) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__10102] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10102)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10102)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__10105] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10105)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10105)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__10102,Vvar__0___24Anonymous__10105)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__10123] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10123)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__10123)
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__10123)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__2620] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2620)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2620)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__2620) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
! [V0__x] : cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd,V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('$_def_Coq.Reals.AltSeries.positivity_seq',axiom,
! [V0__Un] :
( cCoq_2eReals_2eAltSeries_2epositivity__seq___24a1(V0__Un)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(V0__Un,V1__n))) ) ) ).
fof('$_def_Coq.Reals.AltSeries.tg_alt',axiom,
! [V0__Un,V1__i] : cCoq_2eReals_2eAltSeries_2etg__alt___24a2(V0__Un,V1__i) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__i),happ(V0__Un,V1__i)) ).
fof('$_def_Coq.Reals.NewtonInt.Newton_integrable',axiom,
! [V0__f,V1__a,V2__b] : cCoq_2eReals_2eNewtonInt_2eNewton__integrable___24a3(V0__f,V1__a,V2__b) = cCoq_2eInit_2eSpecif_2esig___24a2(c_24__type__795,c_24__lam__6509___24a3(V0__f,V1__a,V2__b)) ).
fof('$_def_Coq.Reals.PSeries_reg.Boule',axiom,
! [V0__x,V1__r,V2__y] :
( cCoq_2eReals_2ePSeries__reg_2eBoule___24a3(V0__x,V1__r,V2__y)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V2__y,V0__x)),cCoq_2eReals_2eRIneq_2epos___24a1(V1__r))) ) ).
fof('$_def_Coq.Reals.PartSum.Cauchy_crit_series',axiom,
! [V0__An] :
( cCoq_2eReals_2ePartSum_2eCauchy__crit__series___24a1(V0__An)
<=> cCoq_2eReals_2eRseries_2eCauchy__crit___24a1(c_24__lam__14596___24a1(V0__An)) ) ).
fof('$_def_Coq.Reals.PartSum.SP',axiom,
! [V0__fn,V1__N,V2__x] : cCoq_2eReals_2ePartSum_2eSP___24a3(V0__fn,V1__N,V2__x) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__7140___24a2(V0__fn,V2__x),V1__N) ).
fof('$_def_Coq.Reals.RIneq.Rsqr',axiom,
! [V0__r] : cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r) ).
fof('$_def_Coq.Reals.RIneq.neg',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V0__n)
=> ? [Vvar__0__neg__14654] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__14654)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__14654,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& V0__n = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__14654)
& cCoq_2eReals_2eRIneq_2eneg___24a1(V0__n) = Vvar__0__neg__14654 ) ) ).
fof('$_def_Coq.Reals.RIneq.nonneg',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V0__n)
=> ? [Vvar__0__nonneg__6649] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__6649)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__6649))
& V0__n = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__6649)
& cCoq_2eReals_2eRIneq_2enonneg___24a1(V0__n) = Vvar__0__nonneg__6649 ) ) ).
fof('$_def_Coq.Reals.RIneq.pos',axiom,
! [V0__p] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V0__p)
=> ? [Vvar__0__pos__6664] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__6664)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__6664))
& V0__p = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__6664)
& cCoq_2eReals_2eRIneq_2epos___24a1(V0__p) = Vvar__0__pos__6664 ) ) ).
fof('$_def_Coq.Reals.RList.FF',axiom,
! [V0__l,V1__f] :
( cCoq_2eReals_2eRList_2eRlist___24t(V0__l)
=> ( ( V0__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2eFF___24a2(V0__l,V1__f) = cCoq_2eReals_2eRList_2enil )
| ? [Vvar__0___24Anonymous__6742] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__6742)
& ? [Vvar__1___24Anonymous__6743] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__6743)
& V0__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__6742,Vvar__1___24Anonymous__6743)
& cCoq_2eReals_2eRList_2eFF___24a2(V0__l,V1__f) = cCoq_2eReals_2eRList_2eapp__Rlist___24a2(cCoq_2eReals_2eRList_2emid__Rlist___24a2(Vvar__1___24Anonymous__6743,Vvar__0___24Anonymous__6742),V1__f) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.In',axiom,
! [V1__x,V2__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V2__l)
=> ( ( V2__l = cCoq_2eReals_2eRList_2enil
& ( cCoq_2eReals_2eRList_2eIn___24a2(V1__x,V2__l)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__6700] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__6700)
& ? [Vvar__1___24Anonymous__6701] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__6701)
& V2__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__6700,Vvar__1___24Anonymous__6701)
& ( cCoq_2eReals_2eRList_2eIn___24a2(V1__x,V2__l)
<=> ( V1__x = Vvar__0___24Anonymous__6700
| cCoq_2eReals_2eRList_2eIn___24a2(V1__x,Vvar__1___24Anonymous__6701) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.Rlength',axiom,
! [V1__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2eRlength___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__4528] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__4528)
& ? [Vvar__1___24Anonymous__4529] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__4529)
& V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__4528,Vvar__1___24Anonymous__4529)
& cCoq_2eReals_2eRList_2eRlength___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eReals_2eRList_2eRlength___24a1(Vvar__1___24Anonymous__4529)) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.Rlist_rec',axiom,
! [V0__P] : cCoq_2eReals_2eRList_2eRlist__rec___24a1(V0__P) = cCoq_2eReals_2eRList_2eRlist__rect___24a1(V0__P) ).
fof('$_def_Coq.Reals.RList.Rtail',axiom,
! [V0__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V0__l)
=> ( ( V0__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2eRtail___24a1(V0__l) = cCoq_2eReals_2eRList_2enil )
| ? [Vvar__0___24Anonymous__6737] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__6737)
& ? [Vvar__1___24Anonymous__6738] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__6738)
& V0__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__6737,Vvar__1___24Anonymous__6738)
& cCoq_2eReals_2eRList_2eRtail___24a1(V0__l) = Vvar__1___24Anonymous__6738 ) ) ) ) ).
fof('$_def_Coq.Reals.RList.app_Rlist',axiom,
! [V1__l,V2__f] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2eapp__Rlist___24a2(V1__l,V2__f) = cCoq_2eReals_2eRList_2enil )
| ? [Vvar__0___24Anonymous__6725] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__6725)
& ? [Vvar__1___24Anonymous__6726] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__6726)
& V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__6725,Vvar__1___24Anonymous__6726)
& cCoq_2eReals_2eRList_2eapp__Rlist___24a2(V1__l,V2__f) = cCoq_2eReals_2eRList_2econs___24a2(happ(V2__f,Vvar__0___24Anonymous__6725),cCoq_2eReals_2eRList_2eapp__Rlist___24a2(Vvar__1___24Anonymous__6726,V2__f)) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.cons_ORlist',axiom,
! [V1__k,V2__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__k)
=> ( ( V1__k = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2econs__ORlist___24a2(V1__k,V2__l) = V2__l )
| ? [Vvar__0___24Anonymous__6718] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__6718)
& ? [Vvar__1___24Anonymous__6719] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__6719)
& V1__k = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__6718,Vvar__1___24Anonymous__6719)
& cCoq_2eReals_2eRList_2econs__ORlist___24a2(V1__k,V2__l) = cCoq_2eReals_2eRList_2econs__ORlist___24a2(Vvar__1___24Anonymous__6719,cCoq_2eReals_2eRList_2einsert___24a2(V2__l,Vvar__0___24Anonymous__6718)) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.cons_Rlist',axiom,
! [V1__l,V2__k] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2econs__Rlist___24a2(V1__l,V2__k) = V2__k )
| ? [Vvar__0___24Anonymous__14693] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__14693)
& ? [Vvar__1___24Anonymous__14694] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__14694)
& V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__14693,Vvar__1___24Anonymous__14694)
& cCoq_2eReals_2eRList_2econs__Rlist___24a2(V1__l,V2__k) = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__14693,cCoq_2eReals_2eRList_2econs__Rlist___24a2(Vvar__1___24Anonymous__14694,V2__k)) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.ordered_Rlist',axiom,
! [V0__l] :
( cCoq_2eReals_2eRList_2eordered__Rlist___24a1(V0__l)
<=> ! [V1__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__i,cCoq_2eInit_2eNat_2epred___24a1(cCoq_2eReals_2eRList_2eRlength___24a1(V0__l))))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRList_2epos__Rl___24a2(V0__l,V1__i),cCoq_2eReals_2eRList_2epos__Rl___24a2(V0__l,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__i)))) ) ) ) ).
fof('$_def_Coq.Reals.RList.pos_Rl',axiom,
! [V1__l,V2__i] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2epos__Rl___24a2(V1__l,V2__i) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__4534] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__4534)
& ? [Vvar__1___24Anonymous__4535] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__4535)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
=> ( V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__4534,Vvar__1___24Anonymous__4535)
& ( ( V2__i = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRList_2epos__Rl___24a2(V1__l,V2__i) = Vvar__0___24Anonymous__4534 )
| ? [Vvar__0___24Anonymous__4541] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4541)
& V2__i = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4541)
& cCoq_2eReals_2eRList_2epos__Rl___24a2(V1__l,V2__i) = cCoq_2eReals_2eRList_2epos__Rl___24a2(Vvar__1___24Anonymous__4535,Vvar__0___24Anonymous__4541) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.R_sqrt.sqrt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__x) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__x) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x) = cCoq_2eReals_2eRsqrt__def_2eRsqrt___24a1(cCoq_2eReals_2eRIneq_2emknonnegreal___24a2(V0__x,cCoq_2eReals_2eRIneq_2eRge__le___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))) ) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.antiderivative',axiom,
! [V0__f,V1__g,V2__a,V3__b] :
( cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(V0__f,V1__g,V2__a,V3__b)
<=> ( ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V4__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V4__x,V3__b)) )
=> ? [V6__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V1__g,V4__x,V6__pr)
& happ(V0__f,V4__x) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V1__g,V4__x,V6__pr) ) ) )
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V3__b)) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.comp',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f1,V1__f2,V2__x) = happ(V0__f1,happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.constant_D_eq',axiom,
! [V0__f,V1__D,V2__c] :
( cCoq_2eReals_2eRanalysis1_2econstant__D__eq___24a3(V0__f,V1__D,V2__c)
<=> ! [V3__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__x)
=> ( p(happ(V1__D,V3__x))
=> happ(V0__f,V3__x) = V2__c ) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.continuity',axiom,
! [V0__f] :
( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V0__f)
<=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V1__x) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.continuity_pt',axiom,
! [V0__f,V1__x0] :
( cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V1__x0)
<=> cCoq_2eReals_2eRderiv_2econtinue__in___24a3(V0__f,cCoq_2eReals_2eRanalysis1_2eno__cond,V1__x0) ) ).
fof('$_def_Coq.Reals.Ranalysis1.d1',axiom,
! [V0__d] :
( cCoq_2eReals_2eRanalysis1_2eDifferential___24t(V0__d)
=> ? [Vvar__0__d1__14722] :
( c_24__type__795___24t(Vvar__0__d1__14722)
& ? [Vvar__1__cond__diff__14724] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(Vvar__0__d1__14722,Vvar__1__cond__diff__14724)
& V0__d = cCoq_2eReals_2eRanalysis1_2emkDifferential___24a2(Vvar__0__d1__14722,Vvar__1__cond__diff__14724)
& cCoq_2eReals_2eRanalysis1_2ed1___24a1(V0__d) = Vvar__0__d1__14722 ) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.decreasing',axiom,
! [V0__f] :
( cCoq_2eReals_2eRanalysis1_2edecreasing___24a1(V0__f)
<=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__x,V2__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__y),happ(V0__f,V1__x))) ) ) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.derivable',axiom,
! [V0__f] : cCoq_2eReals_2eRanalysis1_2ederivable___24a1(V0__f) = c_24__type__6878___24a1(V0__f) ).
fof('$_def_Coq.Reals.Ranalysis1.derivable_pt',axiom,
! [V0__f,V1__x] : cCoq_2eReals_2eRanalysis1_2ederivable__pt___24a2(V0__f,V1__x) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__6873___24a2(V0__f,V1__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.derivable_pt_abs',axiom,
! [V0__f,V1__x,V2__l] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs___24a3(V0__f,V1__x,V2__l)
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f,V1__x,V2__l) ) ).
fof('$_def_Coq.Reals.Ranalysis1.derivable_pt_lim',axiom,
! [V0__f,V1__x,V2__l] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f,V1__x,V2__l)
<=> ! [V3__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V3__eps))
=> ? [V5__delta] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V5__delta)
& ! [V6__h] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__h)
=> ( V6__h != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V6__h),cCoq_2eReals_2eRIneq_2epos___24a1(V5__delta)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V0__f,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__x,V6__h)),happ(V0__f,V1__x)),V6__h),V2__l)),V3__eps)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.derive',axiom,
! [V0__f,V1__pr,V2__x] : cCoq_2eReals_2eRanalysis1_2ederive___24a3(V0__f,V1__pr,V2__x) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V2__x,happ(V1__pr,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.derive_pt',axiom,
! [V0__f,V1__x,V2__pr] : cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V2__pr) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__6873___24a2(V0__f,V1__x),V2__pr) ).
fof('$_def_Coq.Reals.Ranalysis1.fct_cte',axiom,
! [V0__a,V1__x] : cCoq_2eReals_2eRanalysis1_2efct__cte___24a2(V0__a,V1__x) = V0__a ).
fof('$_def_Coq.Reals.Ranalysis1.id',axiom,
! [V0__x] : cCoq_2eReals_2eRanalysis1_2eid___24a1(V0__x) = V0__x ).
fof('$_def_Coq.Reals.Ranalysis1.increasing',axiom,
! [V0__f] :
( cCoq_2eReals_2eRanalysis1_2eincreasing___24a1(V0__f)
<=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__x,V2__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V1__x),happ(V0__f,V2__y))) ) ) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.minus_fct',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2eminus__fct___24a3(V0__f1,V1__f2,V2__x) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V0__f1,V2__x),happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.mult_fct',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2emult__fct___24a3(V0__f1,V1__f2,V2__x) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(V0__f1,V2__x),happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.no_cond',axiom,
! [V0__x] :
( cCoq_2eReals_2eRanalysis1_2eno__cond___24a1(V0__x)
<=> p(c_24True) ) ).
fof('$_def_Coq.Reals.Ranalysis1.opp_fct',axiom,
! [V0__f,V1__x] : cCoq_2eReals_2eRanalysis1_2eopp__fct___24a2(V0__f,V1__x) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(happ(V0__f,V1__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.plus_fct',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2eplus__fct___24a3(V0__f1,V1__f2,V2__x) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(V0__f1,V2__x),happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.pow_fct',axiom,
! [V0__n,V1__y] : cCoq_2eReals_2eRanalysis1_2epow__fct___24a2(V0__n,V1__y) = cCoq_2eReals_2eRpow__def_2epow___24a2(V1__y,V0__n) ).
fof('$_def_Coq.Reals.Ratan.Datan_seq',axiom,
! [V0__x,V1__n] : cCoq_2eReals_2eRatan_2eDatan__seq___24a2(V0__x,V1__n) = cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__n)) ).
fof('$_def_Coq.Reals.Ratan.Ratan_seq',axiom,
! [V0__x,V1__n] : cCoq_2eReals_2eRatan_2eRatan__seq___24a2(V0__x,V1__n) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__n),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__n),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))) ).
fof('$_def_Coq.Reals.Raxioms.INR',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__7258] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7258)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7258)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7258)
& ( ( Vvar__0___24Anonymous__7258 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__7261] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7261)
& Vvar__0___24Anonymous__7258 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7261)
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(Vvar__0___24Anonymous__7258),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Raxioms.bound',axiom,
! [V0__E] :
( cCoq_2eReals_2eRaxioms_2ebound___24a1(V0__E)
<=> ? [V1__m] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__m)
& cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V0__E,V1__m) ) ) ).
fof('$_def_Coq.Reals.Raxioms.is_lub',axiom,
! [V0__E,V1__m] :
( cCoq_2eReals_2eRaxioms_2eis__lub___24a2(V0__E,V1__m)
<=> ( cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V0__E,V1__m)
& ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ( cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V0__E,V2__b)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__m,V2__b)) ) ) ) ) ).
fof('$_def_Coq.Reals.Raxioms.is_upper_bound',axiom,
! [V0__E,V1__m] :
( cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V0__E,V1__m)
<=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ( p(happ(V0__E,V2__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__x,V1__m)) ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rabs',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__r) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) )
| ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__r) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = V0__r ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rmax',axiom,
! [V0__x,V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__7284___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V1__y )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__7285___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V0__x ) ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rmin',axiom,
! [V0__x,V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__791___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V0__x )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__792___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V1__y ) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.IPR',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__7334] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7334)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7334)
& cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__7334)) )
| ? [Vvar__0___24Anonymous__7335] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7335)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7335)
& cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__7335) )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eR1 ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.IPR_2',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__14829] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14829)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__14829)
& cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V1__p) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eR1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__14829))) )
| ? [Vvar__0___24Anonymous__14830] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14830)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__14830)
& cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V1__p) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eR1),cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__14830)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V1__p) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eR1) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__300] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__300)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__300)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__300) )
| ? [Vvar__0___24Anonymous__301] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__301)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__301)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__301)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rderiv.D_x',axiom,
! [V0__D,V1__y,V2__x] :
( cCoq_2eReals_2eRderiv_2eD__x___24a3(V0__D,V1__y,V2__x)
<=> ( p(happ(V0__D,V2__x))
& V1__y != V2__x ) ) ).
fof('$_def_Coq.Reals.Rderiv.continue_in',axiom,
! [V0__f,V1__D,V2__x0] :
( cCoq_2eReals_2eRderiv_2econtinue__in___24a3(V0__f,V1__D,V2__x0)
<=> cCoq_2eReals_2eRlimit_2elimit1__in___24a4(V0__f,cCoq_2eReals_2eRderiv_2eD__x___24a2(V1__D,V2__x0),happ(V0__f,V2__x0),V2__x0) ) ).
fof('$_def_Coq.Reals.Rfunctions.R_dist',axiom,
! [V0__x,V1__y] : cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V0__x,V1__y) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__x,V1__y)) ).
fof('$_def_Coq.Reals.Rfunctions.sum_f_R0',axiom,
! [V1__f,V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ( V2__N = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,V2__N) = happ(V1__f,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__7378] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7378)
& V2__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7378)
& cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,V2__N) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,Vvar__0___24Anonymous__7378),happ(V1__f,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7378))) ) ) ) ).
fof('$_def_Coq.Reals.RiemannInt.RinvN',axiom,
! [V0__N] : cCoq_2eReals_2eRiemannInt_2eRinvN___24a1(V0__N) = cCoq_2eReals_2eRIneq_2emkposreal___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__N),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRiemannInt_2eRinvN__pos___24a1(V0__N)) ).
fof('$_def_Coq.Reals.RiemannInt.c1',axiom,
! [V0__c] :
( cCoq_2eReals_2eRiemannInt_2eC1__fun___24t(V0__c)
=> ? [Vvar__0__c1__73128] :
( c_24__type__795___24t(Vvar__0__c1__73128)
& ? [Vvar__1__diff0__73130] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(Vvar__0__c1__73128,Vvar__1__diff0__73130)
& cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(cCoq_2eReals_2eRanalysis1_2ederive___24a2(Vvar__0__c1__73128,Vvar__1__diff0__73130))
& V0__c = cCoq_2eReals_2eRiemannInt_2emkC1___24a2(Vvar__0__c1__73128,Vvar__1__diff0__73130)
& cCoq_2eReals_2eRiemannInt_2ec1___24a1(V0__c) = Vvar__0__c1__73128 ) ) ) ).
fof('$_def_Coq.Reals.RiemannInt_SF.Int_SF',axiom,
! [V1__l,V2__k] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V1__l,V2__k) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__8049] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__8049)
& ? [Vvar__1___24Anonymous__8050] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__8050)
& ( cCoq_2eReals_2eRList_2eRlist___24t(V2__k)
=> ( V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__8049,Vvar__1___24Anonymous__8050)
& ( ( V2__k = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V1__l,V2__k) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__8064] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__8064)
& ? [Vvar__1___24Anonymous__8065] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__8065)
& ( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__8065)
=> ( V2__k = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__8064,Vvar__1___24Anonymous__8065)
& ( ( Vvar__1___24Anonymous__8065 = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V1__l,V2__k) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__8073] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__8073)
& ? [Vvar__1___24Anonymous__8074] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__8074)
& Vvar__1___24Anonymous__8065 = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__8073,Vvar__1___24Anonymous__8074)
& cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V1__l,V2__k) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(Vvar__0___24Anonymous__8049,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(Vvar__0___24Anonymous__8073,Vvar__0___24Anonymous__8064)),cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(Vvar__1___24Anonymous__8050,cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__8073,Vvar__1___24Anonymous__8074))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.RiemannInt_SF.IsStepFun',axiom,
! [V0__f,V1__a,V2__b] : cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24a3(V0__f,V1__a,V2__b) = cCoq_2eInit_2eSpecif_2esigT___24a2(cCoq_2eReals_2eRList_2eRlist,c_24__lam__7944___24a3(V0__f,V1__a,V2__b)) ).
fof('$_def_Coq.Reals.RiemannInt_SF.Nbound',axiom,
! [V0__I] :
( cCoq_2eReals_2eRiemannInt__SF_2eNbound___24a1(V0__I)
<=> ? [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
& ! [V2__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
=> ( p(happ(V0__I,V2__i))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V2__i,V1__n)) ) ) ) ) ).
fof('$_def_Coq.Reals.RiemannInt_SF.RiemannInt_SF',axiom,
! [V0__a,V1__b,V2__f] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__a,V1__b) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b),c_24__prop__8087___24a2(V0__a,V1__b))
& cCoq_2eReals_2eRiemannInt__SF_2eRiemannInt__SF___24a3(V0__a,V1__b,V2__f) = cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(cCoq_2eReals_2eRiemannInt__SF_2esubdivision__val___24a3(V0__a,V1__b,V2__f),cCoq_2eReals_2eRiemannInt__SF_2esubdivision___24a3(V0__a,V1__b,V2__f)) )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__a,V1__b) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b),c_24__prop__8088___24a2(V0__a,V1__b))
& cCoq_2eReals_2eRiemannInt__SF_2eRiemannInt__SF___24a3(V0__a,V1__b,V2__f) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(cCoq_2eReals_2eRiemannInt__SF_2esubdivision__val___24a3(V0__a,V1__b,V2__f),cCoq_2eReals_2eRiemannInt__SF_2esubdivision___24a3(V0__a,V1__b,V2__f))) ) ) ) ) ).
fof('$_def_Coq.Reals.RiemannInt_SF.co_interval',axiom,
! [V0__a,V1__b,V2__x] :
( cCoq_2eReals_2eRiemannInt__SF_2eco__interval___24a3(V0__a,V1__b,V2__x)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V2__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__x,V1__b)) ) ) ).
fof('$_def_Coq.Reals.RiemannInt_SF.fe',axiom,
! [V0__a,V1__b,V2__s] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(V0__a,V1__b,V2__s)
=> ? [Vvar__2__fe__7986] :
( c_24__type__7959___24t(V0__a,V1__b,Vvar__2__fe__7986)
& ? [Vvar__3__pre__7989] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vvar__2__fe__7986,V0__a,V1__b,Vvar__3__pre__7989)
& V2__s = cCoq_2eReals_2eRiemannInt__SF_2emkStepFun___24a4(V0__a,V1__b,Vvar__2__fe__7986,Vvar__3__pre__7989)
& cCoq_2eReals_2eRiemannInt__SF_2efe___24a3(V0__a,V1__b,V2__s) = Vvar__2__fe__7986 ) ) ) ) ) ).
fof('$_def_Coq.Reals.RiemannInt_SF.is_subdivision',axiom,
! [V0__f,V1__a,V2__b,V3__l] : cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24a4(V0__f,V1__a,V2__b,V3__l) = cCoq_2eInit_2eSpecif_2esigT___24a2(cCoq_2eReals_2eRList_2eRlist,c_24__lam__7932___24a4(V0__f,V1__a,V2__b,V3__l)) ).
fof('$_def_Coq.Reals.RiemannInt_SF.open_interval',axiom,
! [V0__a,V1__b,V2__x] :
( cCoq_2eReals_2eRiemannInt__SF_2eopen__interval___24a3(V0__a,V1__b,V2__x)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V2__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__x,V1__b)) ) ) ).
fof('$_def_Coq.Reals.RiemannInt_SF.pre',axiom,
! [V0__a,V1__b,V2__s] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(V0__a,V1__b,V2__s)
=> ? [Vvar__2__fe__63147] :
( c_24__type__7959___24t(V0__a,V1__b,Vvar__2__fe__63147)
& ? [Vvar__3__pre__63150] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vvar__2__fe__63147,V0__a,V1__b,Vvar__3__pre__63150)
& V2__s = cCoq_2eReals_2eRiemannInt__SF_2emkStepFun___24a4(V0__a,V1__b,Vvar__2__fe__63147,Vvar__3__pre__63150)
& cCoq_2eReals_2eRiemannInt__SF_2epre___24a3(V0__a,V1__b,V2__s) = Vvar__3__pre__63150 ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rlimit.Base',axiom,
! [V0__m] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V0__m)
=> ? [Vvar__0__Base__9098] :
( cType___24t(Vvar__0__Base__9098)
& ? [Vvar__1__dist__9099] :
( c_24__type__25___24t(Vvar__0__Base__9098,Vvar__1__dist__9099)
& ! [Vvar__var__2__x__9105__9107] :
( t(Vvar__var__2__x__9105__9107,Vvar__0__Base__9098)
=> ! [Vvar__var__3__y__9106__9108] :
( t(Vvar__var__3__y__9106__9108,Vvar__0__Base__9098)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__dist__9099,Vvar__var__2__x__9105__9107),Vvar__var__3__y__9106__9108),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
& ! [Vvar__var__3__x__9110__9112] :
( t(Vvar__var__3__x__9110__9112,Vvar__0__Base__9098)
=> ! [Vvar__var__4__y__9111__9113] :
( t(Vvar__var__4__y__9111__9113,Vvar__0__Base__9098)
=> happ(happ(Vvar__1__dist__9099,Vvar__var__3__x__9110__9112),Vvar__var__4__y__9111__9113) = happ(happ(Vvar__1__dist__9099,Vvar__var__4__y__9111__9113),Vvar__var__3__x__9110__9112) ) )
& ! [Vvar__var__4__x__9115__9117] :
( t(Vvar__var__4__x__9115__9117,Vvar__0__Base__9098)
=> ! [Vvar__var__5__y__9116__9118] :
( t(Vvar__var__5__y__9116__9118,Vvar__0__Base__9098)
=> ( happ(happ(Vvar__1__dist__9099,Vvar__var__4__x__9115__9117),Vvar__var__5__y__9116__9118) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vvar__var__4__x__9115__9117 = Vvar__var__5__y__9116__9118 ) ) )
& ! [Vvar__var__5__x__9120__9123] :
( t(Vvar__var__5__x__9120__9123,Vvar__0__Base__9098)
=> ! [Vvar__var__6__y__9121__9124] :
( t(Vvar__var__6__y__9121__9124,Vvar__0__Base__9098)
=> ! [Vvar__var__7__z__9122__9125] :
( t(Vvar__var__7__z__9122__9125,Vvar__0__Base__9098)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__dist__9099,Vvar__var__5__x__9120__9123),Vvar__var__6__y__9121__9124),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__dist__9099,Vvar__var__5__x__9120__9123),Vvar__var__7__z__9122__9125),happ(happ(Vvar__1__dist__9099,Vvar__var__7__z__9122__9125),Vvar__var__6__y__9121__9124)))) ) ) )
& V0__m = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__9098,Vvar__1__dist__9099)
& cCoq_2eReals_2eRlimit_2eBase___24a1(V0__m) = Vvar__0__Base__9098 ) ) ) ).
fof('$_def_Coq.Reals.Rlimit.R_met',axiom,
cCoq_2eReals_2eRlimit_2eR__met = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a6(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRfunctions_2eR__dist,cCoq_2eReals_2eRfunctions_2eR__dist__pos,cCoq_2eReals_2eRfunctions_2eR__dist__sym,cCoq_2eReals_2eRfunctions_2eR__dist__refl,cCoq_2eReals_2eRfunctions_2eR__dist__tri) ).
fof('$_def_Coq.Reals.Rlimit.dist',axiom,
! [V0__m] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V0__m)
=> ? [Vvar__0__Base__9190] :
( cType___24t(Vvar__0__Base__9190)
& ? [Vvar__1__dist__9191] :
( c_24__type__25___24t(Vvar__0__Base__9190,Vvar__1__dist__9191)
& ! [Vvar__var__2__x__9197__9199] :
( t(Vvar__var__2__x__9197__9199,Vvar__0__Base__9190)
=> ! [Vvar__var__3__y__9198__9200] :
( t(Vvar__var__3__y__9198__9200,Vvar__0__Base__9190)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__dist__9191,Vvar__var__2__x__9197__9199),Vvar__var__3__y__9198__9200),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
& ! [Vvar__var__3__x__9202__9204] :
( t(Vvar__var__3__x__9202__9204,Vvar__0__Base__9190)
=> ! [Vvar__var__4__y__9203__9205] :
( t(Vvar__var__4__y__9203__9205,Vvar__0__Base__9190)
=> happ(happ(Vvar__1__dist__9191,Vvar__var__3__x__9202__9204),Vvar__var__4__y__9203__9205) = happ(happ(Vvar__1__dist__9191,Vvar__var__4__y__9203__9205),Vvar__var__3__x__9202__9204) ) )
& ! [Vvar__var__4__x__9207__9209] :
( t(Vvar__var__4__x__9207__9209,Vvar__0__Base__9190)
=> ! [Vvar__var__5__y__9208__9210] :
( t(Vvar__var__5__y__9208__9210,Vvar__0__Base__9190)
=> ( happ(happ(Vvar__1__dist__9191,Vvar__var__4__x__9207__9209),Vvar__var__5__y__9208__9210) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vvar__var__4__x__9207__9209 = Vvar__var__5__y__9208__9210 ) ) )
& ! [Vvar__var__5__x__9212__9215] :
( t(Vvar__var__5__x__9212__9215,Vvar__0__Base__9190)
=> ! [Vvar__var__6__y__9213__9216] :
( t(Vvar__var__6__y__9213__9216,Vvar__0__Base__9190)
=> ! [Vvar__var__7__z__9214__9217] :
( t(Vvar__var__7__z__9214__9217,Vvar__0__Base__9190)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__dist__9191,Vvar__var__5__x__9212__9215),Vvar__var__6__y__9213__9216),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__dist__9191,Vvar__var__5__x__9212__9215),Vvar__var__7__z__9214__9217),happ(happ(Vvar__1__dist__9191,Vvar__var__7__z__9214__9217),Vvar__var__6__y__9213__9216)))) ) ) )
& V0__m = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__9190,Vvar__1__dist__9191)
& cCoq_2eReals_2eRlimit_2edist___24a1(V0__m) = Vvar__1__dist__9191 ) ) ) ).
fof('$_def_Coq.Reals.Rlimit.limit1_in',axiom,
! [V0__f,V1__D,V2__l,V3__x0] :
( cCoq_2eReals_2eRlimit_2elimit1__in___24a4(V0__f,V1__D,V2__l,V3__x0)
<=> cCoq_2eReals_2eRlimit_2elimit__in___24a6(cCoq_2eReals_2eRlimit_2eR__met,cCoq_2eReals_2eRlimit_2eR__met,V0__f,V1__D,V3__x0,V2__l) ) ).
fof('$_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__2504] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2504)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2504)
& 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__2504)) ) ) ) ).
fof('$_def_Coq.Reals.Rpower.Rpower',axiom,
! [V0__x,V1__y] : cCoq_2eReals_2eRpower_2eRpower___24a2(V0__x,V1__y) = cCoq_2eReals_2eRtrigo__def_2eexp___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__y,cCoq_2eReals_2eRpower_2eln___24a1(V0__x))) ).
fof('$_def_Coq.Reals.Rprod.prod_f_R0',axiom,
! [V1__f,V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ( V2__N = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V1__f,V2__N) = happ(V1__f,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__26255] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26255)
& V2__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26255)
& cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V1__f,V2__N) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V1__f,Vvar__0___24Anonymous__26255),happ(V1__f,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26255))) ) ) ) ).
fof('$_def_Coq.Reals.Rseries.Cauchy_crit',axiom,
! [V0__Un] :
( cCoq_2eReals_2eRseries_2eCauchy__crit___24a1(V0__Un)
<=> ! [V1__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V3__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__N)
& ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V4__n,V3__N)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V5__m,V3__N)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRfunctions_2eR__dist___24a2(happ(V0__Un,V4__n),happ(V0__Un,V5__m)),V1__eps)) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rseries.EUn',axiom,
! [V0__Un,V1__r] :
( cCoq_2eReals_2eRseries_2eEUn___24a2(V0__Un,V1__r)
<=> ? [V2__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
& V1__r = happ(V0__Un,V2__i) ) ) ).
fof('$_def_Coq.Reals.Rseries.Un_cv',axiom,
! [V0__Un,V1__l] :
( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V1__l)
<=> ! [V2__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V2__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V4__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__N)
& ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V5__n,V4__N)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRfunctions_2eR__dist___24a2(happ(V0__Un,V5__n),V1__l),V2__eps)) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rseries.Un_growing',axiom,
! [V0__Un] :
( cCoq_2eReals_2eRseries_2eUn__growing___24a1(V0__Un)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,V1__n),happ(V0__Un,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)))) ) ) ).
fof('$_def_Coq.Reals.Rsigma.sigma',axiom,
! [V0__f,V1__low,V2__high] : cCoq_2eReals_2eRsigma_2esigma___24a3(V0__f,V1__low,V2__high) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__9366___24a2(V0__f,V1__low),cCoq_2eInit_2eNat_2esub___24a2(V2__high,V1__low)) ).
fof('$_def_Coq.Reals.Rsqrt_def.Dichotomy_lb',axiom,
! [V2__x,V3__y,V4__P,V5__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__N)
=> ( ( V5__N = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V2__x,V3__y,V4__P,V5__N) = V2__x )
| ? [Vvar__0___24Anonymous__9373] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9373)
& V5__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9373)
& cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V2__x,V3__y,V4__P,V5__N) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249399___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9373) ) ) ) ).
fof('$_def_Coq.Reals.Rsqrt_def.dicho_lb',axiom,
! [V0__x,V1__y,V2__P,V3__N] : cCoq_2eReals_2eRsqrt__def_2edicho__lb___24a4(V0__x,V1__y,V2__P,V3__N) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V0__x,V1__y,V2__P,V3__N) ).
fof('$_def_Coq.Reals.Rsqrt_def.dicho_up',axiom,
! [V0__x,V1__y,V2__P,V3__N] : cCoq_2eReals_2eRsqrt__def_2edicho__up___24a4(V0__x,V1__y,V2__P,V3__N) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__ub___24a4(V0__x,V1__y,V2__P,V3__N) ).
fof('$_def_Coq.Reals.Rsqrt_def.pow_2_n',axiom,
! [V0__n] : cCoq_2eReals_2eRsqrt__def_2epow__2__n___24a1(V0__n) = cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V0__n) ).
fof('$_def_Coq.Reals.Rtopology.adherence',axiom,
! [V0__D,V1__x] :
( cCoq_2eReals_2eRtopology_2eadherence___24a2(V0__D,V1__x)
<=> cCoq_2eReals_2eRtopology_2epoint__adherent___24a2(V0__D,V1__x) ) ).
fof('$_def_Coq.Reals.Rtopology.bounded',axiom,
! [V0__D] :
( cCoq_2eReals_2eRtopology_2ebounded___24a1(V0__D)
<=> ? [V1__m] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__m)
& ? [V2__M] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__M)
& ! [V3__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__x)
=> ( p(happ(V0__D,V3__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__m,V3__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V3__x,V2__M)) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rtopology.closed_set',axiom,
! [V0__D] :
( cCoq_2eReals_2eRtopology_2eclosed__set___24a1(V0__D)
<=> cCoq_2eReals_2eRtopology_2eopen__set___24a1(cCoq_2eReals_2eRtopology_2ecomplementary___24a1(V0__D)) ) ).
fof('$_def_Coq.Reals.Rtopology.compact',axiom,
! [V0__X] :
( cCoq_2eReals_2eRtopology_2ecompact___24a1(V0__X)
<=> ! [V1__f] :
( cCoq_2eReals_2eRtopology_2efamily___24t(V1__f)
=> ( cCoq_2eReals_2eRtopology_2ecovering__open__set___24a2(V0__X,V1__f)
=> ? [V3__D] :
( c_24__type__332___24t(V3__D)
& cCoq_2eReals_2eRtopology_2ecovering__finite___24a2(V0__X,cCoq_2eReals_2eRtopology_2esubfamily___24a2(V1__f,V3__D)) ) ) ) ) ).
fof('$_def_Coq.Reals.Rtopology.disc',axiom,
! [V0__x,V1__delta,V2__y] :
( cCoq_2eReals_2eRtopology_2edisc___24a3(V0__x,V1__delta,V2__y)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V2__y,V0__x)),cCoq_2eReals_2eRIneq_2epos___24a1(V1__delta))) ) ).
fof('$_def_Coq.Reals.Rtopology.eq_Dom',axiom,
! [V0__D1,V1__D2] :
( cCoq_2eReals_2eRtopology_2eeq__Dom___24a2(V0__D1,V1__D2)
<=> ( cCoq_2eReals_2eRtopology_2eincluded___24a2(V0__D1,V1__D2)
& cCoq_2eReals_2eRtopology_2eincluded___24a2(V1__D2,V0__D1) ) ) ).
fof('$_def_Coq.Reals.Rtopology.f',axiom,
! [V0__f] :
( cCoq_2eReals_2eRtopology_2efamily___24t(V0__f)
=> ? [Vvar__0__ind__9708] :
( c_24__type__332___24t(Vvar__0__ind__9708)
& ? [Vvar__1__f__9710] :
( c_24__type__297___24t(Vvar__1__f__9710)
& ! [Vvar__var__2__x__9716__9719] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__var__2__x__9716__9719)
=> ( ? [Vvar__var__3__y__9717__9720] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__var__3__y__9717__9720)
& p(happ(happ(Vvar__1__f__9710,Vvar__var__2__x__9716__9719),Vvar__var__3__y__9717__9720)) )
=> p(happ(Vvar__0__ind__9708,Vvar__var__2__x__9716__9719)) ) )
& V0__f = cCoq_2eReals_2eRtopology_2emkfamily___24a2(Vvar__0__ind__9708,Vvar__1__f__9710)
& cCoq_2eReals_2eRtopology_2ef___24a1(V0__f) = Vvar__1__f__9710 ) ) ) ).
fof('$_def_Coq.Reals.Rtopology.image_dir',axiom,
! [V0__f,V1__D,V2__x] :
( cCoq_2eReals_2eRtopology_2eimage__dir___24a3(V0__f,V1__D,V2__x)
<=> ? [V3__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__y)
& V2__x = happ(V0__f,V3__y)
& p(happ(V1__D,V3__y)) ) ) ).
fof('$_def_Coq.Reals.Rtopology.included',axiom,
! [V0__D1,V1__D2] :
( cCoq_2eReals_2eRtopology_2eincluded___24a2(V0__D1,V1__D2)
<=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ( p(happ(V0__D1,V2__x))
=> p(happ(V1__D2,V2__x)) ) ) ) ).
fof('$_def_Coq.Reals.Rtopology.ind',axiom,
! [V0__f] :
( cCoq_2eReals_2eRtopology_2efamily___24t(V0__f)
=> ? [Vvar__0__ind__9675] :
( c_24__type__332___24t(Vvar__0__ind__9675)
& ? [Vvar__1__f__9677] :
( c_24__type__297___24t(Vvar__1__f__9677)
& ! [Vvar__var__2__x__9683__9686] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__var__2__x__9683__9686)
=> ( ? [Vvar__var__3__y__9684__9687] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__var__3__y__9684__9687)
& p(happ(happ(Vvar__1__f__9677,Vvar__var__2__x__9683__9686),Vvar__var__3__y__9684__9687)) )
=> p(happ(Vvar__0__ind__9675,Vvar__var__2__x__9683__9686)) ) )
& V0__f = cCoq_2eReals_2eRtopology_2emkfamily___24a2(Vvar__0__ind__9675,Vvar__1__f__9677)
& cCoq_2eReals_2eRtopology_2eind___24a1(V0__f) = Vvar__0__ind__9675 ) ) ) ).
fof('$_def_Coq.Reals.Rtopology.intersection_domain',axiom,
! [V0__D1,V1__D2,V2__c] :
( cCoq_2eReals_2eRtopology_2eintersection__domain___24a3(V0__D1,V1__D2,V2__c)
<=> ( p(happ(V0__D1,V2__c))
& p(happ(V1__D2,V2__c)) ) ) ).
fof('$_def_Coq.Reals.Rtopology.neighbourhood',axiom,
! [V0__V,V1__x] :
( cCoq_2eReals_2eRtopology_2eneighbourhood___24a2(V0__V,V1__x)
<=> ? [V2__delta] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V2__delta)
& cCoq_2eReals_2eRtopology_2eincluded___24a2(cCoq_2eReals_2eRtopology_2edisc___24a2(V1__x,V2__delta),V0__V) ) ) ).
fof('$_def_Coq.Reals.Rtopology.point_adherent',axiom,
! [V0__D,V1__x] :
( cCoq_2eReals_2eRtopology_2epoint__adherent___24a2(V0__D,V1__x)
<=> ! [V2__V] :
( c_24__type__332___24t(V2__V)
=> ( cCoq_2eReals_2eRtopology_2eneighbourhood___24a2(V2__V,V1__x)
=> ? [V4__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__y)
& cCoq_2eReals_2eRtopology_2eintersection__domain___24a3(V2__V,V0__D,V4__y) ) ) ) ) ).
fof('$_def_Coq.Reals.Rtrigo1.PI',axiom,
cCoq_2eReals_2eRtrigo1_2ePI = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eReals_2eRtrigo1_2ePI2) ).
fof('$_def_Coq.Reals.Rtrigo1.cos_lb',axiom,
! [V0__a] : cCoq_2eReals_2eRtrigo1_2ecos__lb___24a1(V0__a) = cCoq_2eReals_2eRtrigo__alt_2ecos__approx___24a2(V0__a,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))) ).
fof('$_def_Coq.Reals.Rtrigo1.cos_ub',axiom,
! [V0__a] : cCoq_2eReals_2eRtrigo1_2ecos__ub___24a1(V0__a) = cCoq_2eReals_2eRtrigo__alt_2ecos__approx___24a2(V0__a,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))) ).
fof('$_def_Coq.Reals.Rtrigo1.sin_lb',axiom,
! [V0__a] : cCoq_2eReals_2eRtrigo1_2esin__lb___24a1(V0__a) = cCoq_2eReals_2eRtrigo__alt_2esin__approx___24a2(V0__a,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))) ).
fof('$_def_Coq.Reals.Rtrigo1.sin_ub',axiom,
! [V0__a] : cCoq_2eReals_2eRtrigo1_2esin__ub___24a1(V0__a) = cCoq_2eReals_2eRtrigo__alt_2esin__approx___24a2(V0__a,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))) ).
fof('$_def_Coq.Reals.Rtrigo1.tan',axiom,
! [V0__x] : cCoq_2eReals_2eRtrigo1_2etan___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x)) ).
fof('$_def_Coq.Reals.Rtrigo_alt.cos_approx',axiom,
! [V0__a,V1__n] : cCoq_2eReals_2eRtrigo__alt_2ecos__approx___24a2(V0__a,V1__n) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eRtrigo__alt_2ecos__term___24a1(V0__a),V1__n) ).
fof('$_def_Coq.Reals.Rtrigo_alt.sin_approx',axiom,
! [V0__a,V1__n] : cCoq_2eReals_2eRtrigo__alt_2esin__approx___24a2(V0__a,V1__n) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eRtrigo__alt_2esin__term___24a1(V0__a),V1__n) ).
fof('$_def_Coq.Reals.Rtrigo_def.cos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ? [Vvar__2__x__9835] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2__x__9835)
& c_24__lam__9839___24a2(V0__x,Vvar__2__x__9835)
& cCoq_2eReals_2eRtrigo__def_2eexist__cos___24a1(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x)) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__9839___24a1(V0__x),Vvar__2__x__9835)
& cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x) = Vvar__2__x__9835 ) ) ).
fof('$_def_Coq.Reals.Rtrigo_def.cos_in',axiom,
! [V0__x,V1__l] :
( cCoq_2eReals_2eRtrigo__def_2ecos__in___24a2(V0__x,V1__l)
<=> cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(c_24__lam__9820___24a1(V0__x),V1__l) ) ).
fof('$_def_Coq.Reals.Rtrigo_def.exp',axiom,
! [V0__x] : cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V0__x) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__9818___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2eexist__exp___24a1(V0__x)) ).
fof('$_def_Coq.Reals.Rtrigo_def.sin',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ? [Vvar__2__x__9850] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2__x__9850)
& c_24__lam__9854___24a2(V0__x,Vvar__2__x__9850)
& cCoq_2eReals_2eRtrigo__def_2eexist__sin___24a1(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x)) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__9854___24a1(V0__x),Vvar__2__x__9850)
& cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,Vvar__2__x__9850) ) ) ).
fof('$_def_Coq.Reals.Rtrigo_def.sin_in',axiom,
! [V0__x,V1__l] :
( cCoq_2eReals_2eRtrigo__def_2esin__in___24a2(V0__x,V1__l)
<=> cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(c_24__lam__79426___24a1(V0__x),V1__l) ) ).
fof('$_def_Coq.Reals.SeqProp.Un_decreasing',axiom,
! [V0__Un] :
( cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(V0__Un)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)),happ(V0__Un,V1__n))) ) ) ).
fof('$_def_Coq.Reals.SeqProp.has_lb',axiom,
! [V0__Un] :
( cCoq_2eReals_2eSeqProp_2ehas__lb___24a1(V0__Un)
<=> cCoq_2eReals_2eRaxioms_2ebound___24a1(cCoq_2eReals_2eRseries_2eEUn___24a1(cCoq_2eReals_2eSeqProp_2eopp__seq___24a1(V0__Un))) ) ).
fof('$_def_Coq.Reals.SeqProp.has_ub',axiom,
! [V0__Un] :
( cCoq_2eReals_2eSeqProp_2ehas__ub___24a1(V0__Un)
<=> cCoq_2eReals_2eRaxioms_2ebound___24a1(cCoq_2eReals_2eRseries_2eEUn___24a1(V0__Un)) ) ).
fof('$_def_Coq.Reals.SeqProp.opp_seq',axiom,
! [V0__Un,V1__n] : cCoq_2eReals_2eSeqProp_2eopp__seq___24a2(V0__Un,V1__n) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(happ(V0__Un,V1__n)) ).
fof('$_def_Coq.Relations.Relation_Definitions.reflexive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__4012___24a1(V0__A) ).
fof('$_def_Coq.Relations.Relation_Definitions.transitive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Sets.Ensembles.Complement',axiom,
! [V0__U,V1__A,V2__x] :
( cCoq_2eSets_2eEnsembles_2eComplement___24a3(V0__U,V1__A,V2__x)
<=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V2__x) ) ).
fof('$_def_Coq.Sets.Ensembles.Ensemble',axiom,
! [V0__U] : cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U) = c_24__type__327___24a1(V0__U) ).
fof('$_def_Coq.Sets.Ensembles.In',axiom,
! [V0__U,V1__A,V2__x] :
( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V2__x)
<=> p(happ(V1__A,V2__x)) ) ).
fof('$_def_Coq.Sets.Ensembles.Included',axiom,
! [V0__U,V1__B,V2__C] :
( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__B,V2__C)
<=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x) ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.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__2623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2623)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2623)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__2627] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2627)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2627)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2623,Vvar__0___24Anonymous__2627)) )
| ? [Vvar__0___24Anonymous__2628] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2628)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2628)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__2623,Vvar__0___24Anonymous__2628) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2629] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2629)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2629)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__2633] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2633)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2633)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__2633,Vvar__0___24Anonymous__2629) )
| ? [Vvar__0___24Anonymous__2634] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2634)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2634)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2629,Vvar__0___24Anonymous__2634)) ) ) ) ) ) ) ) ).
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__2656] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2656)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2656)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__2657] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2657)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2657)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__2658] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2658)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2658)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__2662] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2662)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2662)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__2658,Vvar__0___24Anonymous__2662) )
| ? [Vvar__0___24Anonymous__2663] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2663)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2663)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__2664] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2664)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2664)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__2668] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2668)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2668)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__2669] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2669)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2669)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__2664,Vvar__0___24Anonymous__2669)) ) ) ) ) ) ) ) ).
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.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__2643] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2643)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2643)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__2647] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2647)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2647)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2643,Vvar__0___24Anonymous__2647)) )
| ? [Vvar__0___24Anonymous__2648] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2648)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2648)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2643,Vvar__0___24Anonymous__2648)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2649] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2649)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2649)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__2653] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2653)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2653)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2649,Vvar__0___24Anonymous__2653)) )
| ? [Vvar__0___24Anonymous__2654] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2654)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2654)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2649,Vvar__0___24Anonymous__2654)) ) ) ) ) ) ) ) ).
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__10133] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10133)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__10133)
& 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__10133)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__2638] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2638)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2638)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2638) )
| ? [Vvar__0___24Anonymous__2639] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2639)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2639)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2639) ) ) ) ).
fof('$_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__2673] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2673)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2673)
& ( ( 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__2683] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2683)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2673)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2683)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2683)
& ? [Vvar__2___24Anonymous__2691] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2691)
& ? [Vvar__3___24Anonymous__2692] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2692)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2673,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2683)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2691,Vvar__3___24Anonymous__2692)
& 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__2691),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2692)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2694] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2694)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2673)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2694)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2694)
& ? [Vvar__2___24Anonymous__2702] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2702)
& ? [Vvar__3___24Anonymous__2703] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2703)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2673,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2694)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2702,Vvar__3___24Anonymous__2703)
& 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__2702)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2703)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2705] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2705)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2705)
& ( ( 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__2715] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2715)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2705)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2715)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2715)
& ? [Vvar__2___24Anonymous__2723] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2723)
& ? [Vvar__3___24Anonymous__2724] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2724)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2705,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2715)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2723,Vvar__3___24Anonymous__2724)
& 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__2723)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2724))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2726] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2726)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2705)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2726)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2726)
& ? [Vvar__2___24Anonymous__2734] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2734)
& ? [Vvar__3___24Anonymous__2735] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2735)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2705,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2726)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2734,Vvar__3___24Anonymous__2735)
& 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__2734),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2735))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.micromega.QMicromega.QWitness',axiom,
! [Vvar__4507] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(Vvar__4507)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__4507) ) ).
fof('$_def_Coq.micromega.RMicromega.RTautoChecker',axiom,
! [V0__f,V1__w] : cCoq_2emicromega_2eRMicromega_2eRTautoChecker___24a2(V0__f,V1__w) = cCoq_2emicromega_2eTauto_2etauto__checker___24a11(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2eunit,cCoq_2emicromega_2eRMicromega_2erunsat,cCoq_2emicromega_2eRMicromega_2erdeduce,cCoq_2emicromega_2eRMicromega_2eRnormalise___24a1(cCoq_2eInit_2eDatatypes_2eunit),cCoq_2emicromega_2eRMicromega_2eRnegate___24a1(cCoq_2eInit_2eDatatypes_2eunit),cCoq_2emicromega_2eRMicromega_2eRWitness,c_24__lam__4697,cCoq_2emicromega_2eTauto_2emap__bformula___24a7(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2emicromega_2eRingMicromega_2emap__Formula___24a3(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2emicromega_2eRMicromega_2eRcst,cCoq_2emicromega_2eRMicromega_2eQ__of__Rcst),V0__f),V1__w) ).
fof('$_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.VarMap.find',axiom,
! [V0__A,V1__default,V3__vm,V4__p] :
( cType___24t(V0__A)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,V3__vm)
=> ( ( V3__vm = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V0__A)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = V1__default )
| ? [Vvar__1___24Anonymous__5749] :
( t(Vvar__1___24Anonymous__5749,V0__A)
& V3__vm = cCoq_2emicromega_2eVarMap_2eElt___24a2(V0__A,Vvar__1___24Anonymous__5749)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = Vvar__1___24Anonymous__5749 )
| ? [Vvar__1___24Anonymous__5751] :
( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,Vvar__1___24Anonymous__5751)
& ? [Vvar__2___24Anonymous__5752] :
( t(Vvar__2___24Anonymous__5752,V0__A)
& ? [Vvar__3___24Anonymous__5753] :
( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,Vvar__3___24Anonymous__5753)
& ( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> ( V3__vm = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V0__A,Vvar__1___24Anonymous__5751,Vvar__2___24Anonymous__5752,Vvar__3___24Anonymous__5753)
& ( ? [Vvar__0___24Anonymous__5766] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5766)
& V4__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__5766)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,Vvar__3___24Anonymous__5753,Vvar__0___24Anonymous__5766) )
| ? [Vvar__0___24Anonymous__5767] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5767)
& V4__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__5767)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,Vvar__1___24Anonymous__5751,Vvar__0___24Anonymous__5767) )
| ( V4__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = Vvar__2___24Anonymous__5752 ) ) ) ) ) ) ) ) ) ) ) ).
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__3447] :
( t(Vvar__1___24Anonymous__3447,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__3447)
& 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__3447) )
| ? [Vvar__1___24Anonymous__3449] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3449)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__3449)
& 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__3449,V15__l) )
| ? [Vvar__1___24Anonymous__3451] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__3451)
& ? [Vvar__2___24Anonymous__3452] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__3452)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__3451,Vvar__2___24Anonymous__3452)
& 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__3451)),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__3452)) ) )
| ? [Vvar__1___24Anonymous__3455] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__3455)
& ? [Vvar__2___24Anonymous__3456] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__3456)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__3455,Vvar__2___24Anonymous__3456)
& 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__3455)),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__3456)) ) )
| ? [Vvar__1___24Anonymous__3459] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__3459)
& ? [Vvar__2___24Anonymous__3460] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__3460)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__3459,Vvar__2___24Anonymous__3460)
& 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__3459)),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__3460)) ) )
| ? [Vvar__1___24Anonymous__3463] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__3463)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__3463)
& 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__3463)) )
| ? [Vvar__1___24Anonymous__3465] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__3465)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__3465)
& 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__3465)) )
| ? [Vvar__1___24Anonymous__3467] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__3467)
& ? [Vvar__2___24Anonymous__3468] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__3468)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__3467,Vvar__2___24Anonymous__3468)
& 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__3467)),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__3468)) ) )
| ? [Vvar__1___24Anonymous__3471] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__3471)
& ? [Vvar__2___24Anonymous__3472] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__3472)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__3471,Vvar__2___24Anonymous__3472)
& 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__3471)),happ(V12__Cp__phi,Vvar__2___24Anonymous__3472)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__4246] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__4246)
& ? [Vvar__2___24Anonymous__4247] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__4247)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__4246,Vvar__2___24Anonymous__4247)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__4246),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__4247,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fcons2',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l] : cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons1___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e),V10__l) ).
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__3784] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__3784)
& ? [Vvar__2___24Anonymous__3785] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__3785)
& ( 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__3785)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__3784,Vvar__2___24Anonymous__3785)
& ( ( Vvar__2___24Anonymous__3785 = 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__3784)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__3796] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__3796)
& ? [Vvar__2___24Anonymous__3797] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__3797)
& Vvar__2___24Anonymous__3785 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__3796,Vvar__2___24Anonymous__3797)
& ( 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__3784)),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__3785) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__3771] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__3771)
& ? [Vvar__2__denum__3772] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__3772)
& ? [Vvar__3__condition__3773] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__3773)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__3771,Vvar__2__denum__3772,Vvar__3__condition__3773)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__3773 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__3762] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__3762)
& ? [Vvar__2__denum__3763] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__3763)
& ? [Vvar__3__condition__3764] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__3764)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__3762,Vvar__2__denum__3763,Vvar__3__condition__3764)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__3763 ) ) ) ) ) ).
fof('$_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__3751] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__3751)
& ? [Vvar__2__denum__3752] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__3752)
& ? [Vvar__3__condition__3753] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__3753)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__3751,Vvar__2__denum__3752,Vvar__3__condition__3753)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__3751 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.get_signZ',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__532] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__532)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__532)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__533] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__533)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__533)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__533)) ) ) ) ).
fof('$_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__1461] :
( t(Vvar__1___24Anonymous__1461,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__1461)
& 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__1461) )
| ? [Vvar__1___24Anonymous__1463] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1463)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__1463)
& 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__1463,V13__l) )
| ? [Vvar__1___24Anonymous__1465] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__1465)
& ? [Vvar__2___24Anonymous__1466] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__1466)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__1465,Vvar__2___24Anonymous__1466)
& 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__1465)),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__1466)) ) )
| ? [Vvar__1___24Anonymous__1469] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__1469)
& ? [Vvar__2___24Anonymous__1470] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__1470)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__1469,Vvar__2___24Anonymous__1470)
& 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__1469)),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__1470)) ) )
| ? [Vvar__1___24Anonymous__1473] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__1473)
& ? [Vvar__2___24Anonymous__1474] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__1474)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__1473,Vvar__2___24Anonymous__1474)
& 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__1473)),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__1474)) ) )
| ? [Vvar__1___24Anonymous__1477] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__1477)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__1477)
& 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__1477)) )
| ? [Vvar__1___24Anonymous__1479] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__1479)
& ? [Vvar__2___24Anonymous__1480] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__1480)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__1479,Vvar__2___24Anonymous__1480)
& 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__1479)),happ(V10__Cp__phi,Vvar__2___24Anonymous__1480)) ) ) ) ) ) ) ) ).
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__4980] :
( t(Vvar__1___24Anonymous__4980,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__4980)
& ( ? [Vvar__1___24Anonymous__4990] :
( t(Vvar__1___24Anonymous__4990,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__4990)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__4980),Vvar__1___24Anonymous__4990) )
| ? [Vvar__1___24Anonymous__4992] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__4992)
& ? [Vvar__2___24Anonymous__4993] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__4993)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__4992,Vvar__2___24Anonymous__4993)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__4996] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__4996)
& ? [Vvar__2___24Anonymous__4997] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__4997)
& ? [Vvar__3___24Anonymous__4998] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__4998)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__4996,Vvar__2___24Anonymous__4997,Vvar__3___24Anonymous__4998)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__5003] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5003)
& ? [Vvar__2___24Anonymous__5004] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__5004)
& ( 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__5003,Vvar__2___24Anonymous__5004)
& ( ? [Vvar__1___24Anonymous__5024] :
( t(Vvar__1___24Anonymous__5024,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__5024)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__5026] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5026)
& ? [Vvar__2___24Anonymous__5027] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__5027)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5003)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5026)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__5026,Vvar__2___24Anonymous__5027)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__5003,Vvar__1___24Anonymous__5026) = 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__5004,Vvar__2___24Anonymous__5027) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__5003,Vvar__1___24Anonymous__5026) = 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__5003,Vvar__1___24Anonymous__5026) = 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__5032] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__5032)
& ? [Vvar__2___24Anonymous__5033] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5033)
& ? [Vvar__3___24Anonymous__5034] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__5034)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__5032,Vvar__2___24Anonymous__5033,Vvar__3___24Anonymous__5034)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__5039] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__5039)
& ? [Vvar__2___24Anonymous__5040] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5040)
& ? [Vvar__3___24Anonymous__5041] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__5041)
& ( 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__5039,Vvar__2___24Anonymous__5040,Vvar__3___24Anonymous__5041)
& ( ? [Vvar__1___24Anonymous__5074] :
( t(Vvar__1___24Anonymous__5074,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__5074)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__5076] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5076)
& ? [Vvar__2___24Anonymous__5077] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__5077)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__5076,Vvar__2___24Anonymous__5077)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__5080] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__5080)
& ? [Vvar__2___24Anonymous__5081] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5081)
& ? [Vvar__3___24Anonymous__5082] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__5082)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5040)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5081)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__5080,Vvar__2___24Anonymous__5081,Vvar__3___24Anonymous__5082)
& ( ( cType___24t(V0__C)
=> ( c_24__type__1902___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__5039)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__5080)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__5040,Vvar__2___24Anonymous__5081) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__5039,Vvar__1___24Anonymous__5080) = 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__5041,Vvar__3___24Anonymous__5082) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__5039,Vvar__1___24Anonymous__5080) = 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__5040,Vvar__2___24Anonymous__5081) = 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__5040,Vvar__2___24Anonymous__5081) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__2187___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__2188___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__2189___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
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__1913] :
( 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__1913)
& ? [Vvar__2___24Anonymous__1914] :
( 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__1914)
& ( 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__1913)
=> ( 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__1913,Vvar__2___24Anonymous__1914)
& ? [Vvar__2___24Anonymous__1930] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__1930)
& ? [Vvar__3___24Anonymous__1931] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__1931)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__1652___24t(V0__C,V3__cadd)
=> ( c_24__type__1652___24t(V0__C,V4__cmul)
=> ( c_24__type__1652___24t(V0__C,V5__csub)
=> ( c_24__type__1661___24t(V0__C,V6__copp)
=> ( c_24__type__1902___24t(V0__C,V7__ceqb)
=> ( c_24__type__1907___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__1930)
=> ( Vvar__1___24Anonymous__1913 = 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__1930,Vvar__3___24Anonymous__1931)
& ( ? [Vvar__1___24Anonymous__1939] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__1939)
& 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__1930)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__1939)
& 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__1939,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__1931)),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__1914)) )
| ( 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__1930)) = 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__1914) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__1755___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_RTopology.RTop',axiom,
cRTopology_2eRTop = cTopology_2eOrderTopology_2eOrderTopology___24a2(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_def_RTopology.R_metric',axiom,
! [V0__x,V1__y] : cRTopology_2eR__metric___24a2(V0__x,V1__y) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__y,V0__x)) ).
fof('$_def_Topology.Compactness.compact',axiom,
! [V0__X] :
( cTopology_2eCompactness_2ecompact___24a1(V0__X)
<=> ! [V1__C] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__C)
=> ( ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__C,V2__U)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V2__U) ) )
=> ( cZornsLemma_2eFamilies_2eFamilyUnion___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__C) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X))
=> ? [V4__C_27] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__C_27)
& cCoq_2eSets_2eFinite__sets_2eFinite___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V4__C_27)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V4__C_27,V1__C)
& cZornsLemma_2eFamilies_2eFamilyUnion___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__C_27) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)) ) ) ) ) ) ).
fof('$_def_Topology.Completeness.cauchy',axiom,
! [V0__X,V1__d,V2__x] :
( cTopology_2eCompleteness_2ecauchy___24a3(V0__X,V1__d,V2__x)
<=> ! [V3__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V3__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V5__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__N)
& ! [V6__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__m)
=> ! [V7__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V7__n)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V6__m,V5__N)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V7__n,V5__N)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(V1__d,happ(V2__x,V6__m)),happ(V2__x,V7__n)),V3__eps)) ) ) ) ) ) ) ) ) ).
fof('$_def_Topology.Continuity.continuous_at',axiom,
! [V0__X,V1__Y,V2__f,V3__x] :
( cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x)
<=> ! [V4__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V4__V)
=> ( cTopology_2eNeighborhoods_2eneighborhood___24a3(V1__Y,V4__V,happ(V2__f,V3__x))
=> cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f,V4__V),V3__x) ) ) ) ).
fof('$_def_Topology.CountabilityAxioms.first_countable',axiom,
! [V0__X] :
( cTopology_2eCountabilityAxioms_2efirst__countable___24a1(V0__X)
<=> ! [V1__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ? [V2__NBx] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__NBx)
& cTopology_2eNeighborhoodBases_2eneighborhood__basis___24a3(V0__X,V2__NBx,V1__x)
& cZornsLemma_2eCountableTypes_2eCountable___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V2__NBx) ) ) ) ).
fof('$_def_Topology.DirectedSets.DS_ord',axiom,
! [V0__d] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__d)
=> ? [Vvar__0__DS__set__2884] :
( cType___24t(Vvar__0__DS__set__2884)
& ? [Vvar__1__DS__ord__2885] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__DS__set__2884,Vvar__1__DS__ord__2885)
& cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__DS__set__2884,Vvar__1__DS__ord__2885)
& ! [Vvar__var__3__i__2888__2891] :
( t(Vvar__var__3__i__2888__2891,Vvar__0__DS__set__2884)
=> ! [Vvar__var__4__j__2890__2893] :
( t(Vvar__var__4__j__2890__2893,Vvar__0__DS__set__2884)
=> ? [Vvar__var__5__k__2889__2892] :
( t(Vvar__var__5__k__2889__2892,Vvar__0__DS__set__2884)
& p(happ(happ(Vvar__1__DS__ord__2885,Vvar__var__3__i__2888__2891),Vvar__var__5__k__2889__2892))
& p(happ(happ(Vvar__1__DS__ord__2885,Vvar__var__4__j__2890__2893),Vvar__var__5__k__2889__2892)) ) ) )
& V0__d = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__2884,Vvar__1__DS__ord__2885)
& cTopology_2eDirectedSets_2eDS__ord___24a1(V0__d) = Vvar__1__DS__ord__2885 ) ) ) ).
fof('$_def_Topology.DirectedSets.DS_set',axiom,
! [V0__d] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__d)
=> ? [Vvar__0__DS__set__2854] :
( cType___24t(Vvar__0__DS__set__2854)
& ? [Vvar__1__DS__ord__2855] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__DS__set__2854,Vvar__1__DS__ord__2855)
& cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__DS__set__2854,Vvar__1__DS__ord__2855)
& ! [Vvar__var__3__i__2858__2861] :
( t(Vvar__var__3__i__2858__2861,Vvar__0__DS__set__2854)
=> ! [Vvar__var__4__j__2860__2863] :
( t(Vvar__var__4__j__2860__2863,Vvar__0__DS__set__2854)
=> ? [Vvar__var__5__k__2859__2862] :
( t(Vvar__var__5__k__2859__2862,Vvar__0__DS__set__2854)
& p(happ(happ(Vvar__1__DS__ord__2855,Vvar__var__3__i__2858__2861),Vvar__var__5__k__2859__2862))
& p(happ(happ(Vvar__1__DS__ord__2855,Vvar__var__4__j__2860__2863),Vvar__var__5__k__2859__2862)) ) ) )
& V0__d = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__2854,Vvar__1__DS__ord__2855)
& cTopology_2eDirectedSets_2eDS__set___24a1(V0__d) = Vvar__0__DS__set__2854 ) ) ) ).
fof('$_def_Topology.DirectedSets.eventually',axiom,
! [V0__I,V1__P] :
( cTopology_2eDirectedSets_2eeventually___24a2(V0__I,V1__P)
<=> ? [V2__i] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__I,V2__i)
& ! [V3__j] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__I,V3__j)
=> ( cTopology_2eDirectedSets_2eDS__ord___24a3(V0__I,V2__i,V3__j)
=> p(happ(V1__P,V3__j)) ) ) ) ) ).
fof('$_def_Topology.DirectedSets.exists_arbitrarily_large',axiom,
! [V0__I,V1__P] :
( cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V0__I,V1__P)
<=> ! [V2__i] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__I,V2__i)
=> ? [V3__j] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__I,V3__j)
& cTopology_2eDirectedSets_2eDS__ord___24a3(V0__I,V2__i,V3__j)
& p(happ(V1__P,V3__j)) ) ) ) ).
fof('$_def_Topology.FilterLimits.filter_cluster_point',axiom,
! [V0__X,V1__F,V2__x0] :
( cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V1__F,V2__x0)
<=> ! [V3__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F),V3__S)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V3__S),V2__x0) ) ) ) ).
fof('$_def_Topology.FilterLimits.filter_limit',axiom,
! [V0__X,V1__F,V2__x0] :
( cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,V1__F,V2__x0)
<=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eFilterLimits_2eneighborhood__filter___24a2(V0__X,V2__x0)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)) ) ).
fof('$_def_Topology.Filters.filter_family',axiom,
! [V0__X,V1__f] :
( cType___24t(V0__X)
=> ( cTopology_2eFilters_2eFilter___24t(V0__X,V1__f)
=> ? [Vvar__1__filter__family__64845] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,Vvar__1__filter__family__64845)
& ! [Vvar__var__var__2__S1__64847__64851__64866] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,Vvar__var__var__2__S1__64847__64851__64866)
=> ! [Vvar__var__var__3__S2__64848__64852__64867] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,Vvar__var__var__3__S2__64848__64852__64867)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__64845,Vvar__var__var__2__S1__64847__64851__64866)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__64845,Vvar__var__var__3__S2__64848__64852__64867)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__64845,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,Vvar__var__var__2__S1__64847__64851__64866,Vvar__var__var__3__S2__64848__64852__64867)) ) ) ) )
& ! [Vvar__var__var__3__S1__64856__64860__64870] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,Vvar__var__var__3__S1__64856__64860__64870)
=> ! [Vvar__var__var__4__S2__64857__64861__64871] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,Vvar__var__var__4__S2__64857__64861__64871)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__64845,Vvar__var__var__3__S1__64856__64860__64870)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,Vvar__var__var__3__S1__64856__64860__64870,Vvar__var__var__4__S2__64857__64861__64871)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__64845,Vvar__var__var__4__S2__64857__64861__64871) ) ) ) )
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__64845,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X))
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__64845,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__X))
& V1__f = cTopology_2eFilters_2eBuild__Filter___24a2(V0__X,Vvar__1__filter__family__64845)
& cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f) = Vvar__1__filter__family__64845 ) ) ) ).
fof('$_def_Topology.FiltersAndNets.filter_to_net',axiom,
! [V0__X,V1__F] : cTopology_2eFiltersAndNets_2efilter__to__net___24a2(V0__X,V1__F) = cTopology_2eFiltersAndNets_2eftn__x___24a2(V0__X,V1__F) ).
fof('$_def_Topology.FiltersAndNets.net_tail',axiom,
! [V0__X,V1__J,V2__x,V3__j] : cTopology_2eFiltersAndNets_2enet__tail___24a4(V0__X,V1__J,V2__x,V3__j) = cCoq_2eSets_2eImage_2eIm___24a4(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J),c_24__lam__68442___24a3(V0__X,V1__J,V3__j)),V2__x) ).
fof('$_def_Topology.FiltersAndNets.tail_filter_basis',axiom,
! [V0__X,V1__J,V2__x] : cTopology_2eFiltersAndNets_2etail__filter__basis___24a3(V0__X,V1__J,V2__x) = cCoq_2eSets_2eImage_2eIm___24a4(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J),cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J)),cTopology_2eFiltersAndNets_2enet__tail___24a3(V0__X,V1__J,V2__x)) ).
fof('$_def_Topology.InteriorsClosures.closure',axiom,
! [V0__X,V1__S] : cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S) = cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),c_24__lam__901___24a2(V0__X,V1__S))) ).
fof('$_def_Topology.MetricSpaces.metrizes',axiom,
! [V0__X,V1__d] :
( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
<=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V0__X,cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__d,V2__x),V2__x) ) ) ).
fof('$_def_Topology.MetricSpaces.open_ball',axiom,
! [V0__X,V1__d,V2__x0,V3__r] : cTopology_2eMetricSpaces_2eopen__ball___24a4(V0__X,V1__d,V2__x0,V3__r) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,c_24__lam__548___24a4(V0__X,V1__d,V2__x0,V3__r)) ).
fof('$_def_Topology.Neighborhoods.neighborhood',axiom,
! [V0__X,V1__N,V2__x] :
( cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,V1__N,V2__x)
<=> ? [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
& cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,V3__U,V2__x)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U,V1__N) ) ) ).
fof('$_def_Topology.Neighborhoods.open_neighborhood',axiom,
! [V0__X,V1__U,V2__x] :
( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,V1__U,V2__x)
<=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V1__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U,V2__x) ) ) ).
fof('$_def_Topology.Nets.Net',axiom,
! [V0__I,V1__X] : cTopology_2eNets_2eNet___24a2(V0__I,V1__X) = c_24__type__4472___24a2(V0__I,V1__X) ).
fof('$_def_Topology.Nets.cluster_point_subnet',axiom,
! [V0__X,V1__I,V2__x,V3__x0,V5__iU] : cTopology_2eNets_2ecluster__point__subnet___24a5(V0__X,V1__I,V2__x,V3__x0,V5__iU) = happ(V2__x,cTopology_2eNets_2ecps__i___24a5(V0__X,V1__I,V2__x,V3__x0,V5__iU)) ).
fof('$_def_Topology.Nets.cluster_point_subnet_DS',axiom,
! [V0__X,V1__I,V2__x,V3__x0] : cTopology_2eNets_2ecluster__point__subnet__DS___24a4(V0__X,V1__I,V2__x,V3__x0) = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(cTopology_2eNets_2ecluster__point__subnet__DS__set___24a4(V0__X,V1__I,V2__x,V3__x0),cTopology_2eNets_2ecluster__point__subnet__DS__ord___24a4(V0__X,V1__I,V2__x,V3__x0)) ).
fof('$_def_Topology.Nets.cluster_point_subnet_DS_ord',axiom,
! [V0__X,V1__I,V2__x,V3__x0,V4__iU1,V5__iU2] :
( cTopology_2eNets_2ecluster__point__subnet__DS__ord___24a6(V0__X,V1__I,V2__x,V3__x0,V4__iU1,V5__iU2)
<=> ( cTopology_2eDirectedSets_2eDS__ord___24a3(V1__I,cTopology_2eNets_2ecps__i___24a5(V0__X,V1__I,V2__x,V3__x0,V4__iU1),cTopology_2eNets_2ecps__i___24a5(V0__X,V1__I,V2__x,V3__x0,V5__iU2))
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eNets_2ecps__U___24a5(V0__X,V1__I,V2__x,V3__x0,V5__iU2),cTopology_2eNets_2ecps__U___24a5(V0__X,V1__I,V2__x,V3__x0,V4__iU1)) ) ) ).
fof('$_def_Topology.Nets.cps_U',axiom,
! [V0__X,V1__I,V2__x,V3__x0,V4__c] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(V0__X,V1__I,V2__x,V3__x0,V4__c)
=> ? [Vvar__4__cps__i__69564] :
( cTopology_2eDirectedSets_2eDS__set___24t(V1__I,Vvar__4__cps__i__69564)
& ? [Vvar__5__cps__U__69565] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__5__cps__U__69565)
& cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,Vvar__5__cps__U__69565,V3__x0)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__5__cps__U__69565,happ(V2__x,Vvar__4__cps__i__69564))
& V4__c = cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(V0__X,V1__I,V2__x,V3__x0,Vvar__4__cps__i__69564,Vvar__5__cps__U__69565)
& cTopology_2eNets_2ecps__U___24a5(V0__X,V1__I,V2__x,V3__x0,V4__c) = Vvar__5__cps__U__69565 ) ) ) ) ) ) ) ).
fof('$_def_Topology.Nets.cps_i',axiom,
! [V0__X,V1__I,V2__x,V3__x0,V4__c] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(V0__X,V1__I,V2__x,V3__x0,V4__c)
=> ? [Vvar__4__cps__i__69526] :
( cTopology_2eDirectedSets_2eDS__set___24t(V1__I,Vvar__4__cps__i__69526)
& ? [Vvar__5__cps__U__69527] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__5__cps__U__69527)
& cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,Vvar__5__cps__U__69527,V3__x0)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__5__cps__U__69527,happ(V2__x,Vvar__4__cps__i__69526))
& V4__c = cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(V0__X,V1__I,V2__x,V3__x0,Vvar__4__cps__i__69526,Vvar__5__cps__U__69527)
& cTopology_2eNets_2ecps__i___24a5(V0__X,V1__I,V2__x,V3__x0,V4__c) = Vvar__4__cps__i__69526 ) ) ) ) ) ) ) ).
fof('$_def_Topology.Nets.neighborhood_net',axiom,
! [V0__X,V1__x,V2__x] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ( cTopology_2eNets_2eneighborhood__net__DS__set___24t(V0__X,V1__x,V2__x)
=> ? [Vvar__2__U__69247] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__69247)
& ? [Vvar__3__y__69248] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,Vvar__3__y__69248)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,Vvar__2__U__69247)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__69247,V1__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__69247,Vvar__3__y__69248)
& V2__x = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(V0__X,V1__x,Vvar__2__U__69247,Vvar__3__y__69248)
& cTopology_2eNets_2eneighborhood__net___24a3(V0__X,V1__x,V2__x) = Vvar__3__y__69248 ) ) ) ) ) ).
fof('$_def_Topology.Nets.neighborhood_net_DS_ord',axiom,
! [V0__X,V1__x,V2__Uy,V3__Vz] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ( cTopology_2eNets_2eneighborhood__net__DS__set___24t(V0__X,V1__x,V2__Uy)
=> ? [Vvar__2__U__69166] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__69166)
& ? [Vvar__3__y__69167] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,Vvar__3__y__69167)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,Vvar__2__U__69166)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__69166,V1__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__69166,Vvar__3__y__69167)
& ( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ( cTopology_2eNets_2eneighborhood__net__DS__set___24t(V0__X,V1__x,V3__Vz)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__69166)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,Vvar__3__y__69167)
=> ( V2__Uy = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(V0__X,V1__x,Vvar__2__U__69166,Vvar__3__y__69167)
& ? [Vvar__2__U__69215] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__69215)
& ? [Vvar__3__y__69216] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,Vvar__3__y__69216)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,Vvar__2__U__69215)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__69215,V1__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__69215,Vvar__3__y__69216)
& V3__Vz = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(V0__X,V1__x,Vvar__2__U__69215,Vvar__3__y__69216)
& ( cTopology_2eNets_2eneighborhood__net__DS__ord___24a4(V0__X,V1__x,V2__Uy,V3__Vz)
<=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__69215,Vvar__2__U__69166) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Topology.Nets.net_cluster_point',axiom,
! [V0__I,V1__X,V2__x,V3__x0] :
( cTopology_2eNets_2enet__cluster__point___24a4(V0__I,V1__X,V2__x,V3__x0)
<=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V4__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V1__X,V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V4__U,V3__x0)
=> cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V0__I,c_24__lam__284___24a4(V0__I,V1__X,V2__x,V4__U)) ) ) ) ) ).
fof('$_def_Topology.Nets.net_limit',axiom,
! [V0__I,V1__X,V2__x,V3__x0] :
( cTopology_2eNets_2enet__limit___24a4(V0__I,V1__X,V2__x,V3__x0)
<=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V4__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V1__X,V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V4__U,V3__x0)
=> cTopology_2eDirectedSets_2eeventually___24a2(V0__I,c_24__lam__284___24a4(V0__I,V1__X,V2__x,V4__U)) ) ) ) ) ).
fof('$_def_Topology.SeparatednessAxioms.Hausdorff',axiom,
! [V0__X] :
( cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X)
<=> ! [V1__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ! [V2__y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__y)
=> ( V1__x != V2__y
=> ? [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
& ? [V5__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V5__V)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V4__U)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V5__V)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V1__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V5__V,V2__y)
& cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V5__V) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)) ) ) ) ) ) ) ).
fof('$_def_Topology.SupInf.is_glb',axiom,
! [V0__E,V1__m] :
( cTopology_2eSupInf_2eis__glb___24a2(V0__E,V1__m)
<=> ( cTopology_2eSupInf_2eis__lower__bound___24a2(V0__E,V1__m)
& ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ( cTopology_2eSupInf_2eis__lower__bound___24a2(V0__E,V2__b)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__b,V1__m)) ) ) ) ) ).
fof('$_def_Topology.SupInf.is_lower_bound',axiom,
! [V0__E,V1__m] :
( cTopology_2eSupInf_2eis__lower__bound___24a2(V0__E,V1__m)
<=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ( p(happ(V0__E,V2__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V2__x,V1__m)) ) ) ) ).
fof('$_def_Topology.TopologicalSpaces.closed',axiom,
! [V0__X,V1__F] :
( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__F)
<=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)) ) ).
fof('$_def_Topology.TopologicalSpaces.open',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> ? [Vvar__0__point__set__2549] :
( cType___24t(Vvar__0__point__set__2549)
& ? [Vvar__1__open__2550] :
( c_24__type__375___24t(Vvar__0__point__set__2549,Vvar__1__open__2550)
& ! [Vvar__var__2__F__2554__2558] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__point__set__2549,Vvar__var__2__F__2554__2558)
=> ( ! [Vvar__var__3__S__2555__2559] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__2549,Vvar__var__3__S__2555__2559)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__point__set__2549),Vvar__var__2__F__2554__2558,Vvar__var__3__S__2555__2559)
=> p(happ(Vvar__1__open__2550,Vvar__var__3__S__2555__2559)) ) )
=> p(happ(Vvar__1__open__2550,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__point__set__2549,Vvar__var__2__F__2554__2558))) ) )
& ! [Vvar__var__3__U__2563__2567] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__2549,Vvar__var__3__U__2563__2567)
=> ! [Vvar__var__4__V__2564__2568] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__2549,Vvar__var__4__V__2564__2568)
=> ( p(happ(Vvar__1__open__2550,Vvar__var__3__U__2563__2567))
=> ( p(happ(Vvar__1__open__2550,Vvar__var__4__V__2564__2568))
=> p(happ(Vvar__1__open__2550,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__point__set__2549,Vvar__var__3__U__2563__2567,Vvar__var__4__V__2564__2568))) ) ) ) )
& p(happ(Vvar__1__open__2550,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__point__set__2549)))
& V0__t = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__2549,Vvar__1__open__2550)
& cTopology_2eTopologicalSpaces_2eopen___24a1(V0__t) = Vvar__1__open__2550 ) ) ) ).
fof('$_def_Topology.TopologicalSpaces.point_set',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> ? [Vvar__0__point__set__397] :
( cType___24t(Vvar__0__point__set__397)
& ? [Vvar__1__open__398] :
( c_24__type__375___24t(Vvar__0__point__set__397,Vvar__1__open__398)
& ! [Vvar__var__2__F__402__406] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__point__set__397,Vvar__var__2__F__402__406)
=> ( ! [Vvar__var__3__S__403__407] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__397,Vvar__var__3__S__403__407)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__point__set__397),Vvar__var__2__F__402__406,Vvar__var__3__S__403__407)
=> p(happ(Vvar__1__open__398,Vvar__var__3__S__403__407)) ) )
=> p(happ(Vvar__1__open__398,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__point__set__397,Vvar__var__2__F__402__406))) ) )
& ! [Vvar__var__3__U__411__415] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__397,Vvar__var__3__U__411__415)
=> ! [Vvar__var__4__V__412__416] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__397,Vvar__var__4__V__412__416)
=> ( p(happ(Vvar__1__open__398,Vvar__var__3__U__411__415))
=> ( p(happ(Vvar__1__open__398,Vvar__var__4__V__412__416))
=> p(happ(Vvar__1__open__398,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__point__set__397,Vvar__var__3__U__411__415,Vvar__var__4__V__412__416))) ) ) ) )
& p(happ(Vvar__1__open__398,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__point__set__397)))
& V0__t = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__397,Vvar__1__open__398)
& cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t) = Vvar__0__point__set__397 ) ) ) ).
fof('$_def_Topology.WeakTopology.WeakTopology',axiom,
! [V0__X,V1__A,V2__Y,V3__f] : cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,V1__A,V2__Y,V3__f) = cTopology_2eSubbases_2eBuild__TopologicalSpace__from__subbasis___24a2(V0__X,cTopology_2eWeakTopology_2eweak__topology__subbasis___24a4(V0__X,V1__A,V2__Y,V3__f)) ).
fof('$_def_ZornsLemma.CountableTypes.Countable',axiom,
! [V0__X,V1__S] :
( cZornsLemma_2eCountableTypes_2eCountable___24a2(V0__X,V1__S)
<=> cZornsLemma_2eCountableTypes_2eCountableT___24a1(cCoq_2eInit_2eSpecif_2esig___24a2(V0__X,c_24__lam__824___24a2(V0__X,V1__S))) ) ).
fof('$_def_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble',axiom,
! [V0__X,V1__P] : cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,V1__P) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V0__X,V1__P) ).
fof('$_def_ZornsLemma.Families.Family',axiom,
! [V0__T] : cZornsLemma_2eFamilies_2eFamily___24a1(V0__T) = cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T)) ).
fof('$_def_ZornsLemma.FunctionProperties.injective',axiom,
! [V0__X,V1__Y,V2__f] :
( cZornsLemma_2eFunctionProperties_2einjective___24a3(V0__X,V1__Y,V2__f)
<=> ! [V3__x1] :
( t(V3__x1,V0__X)
=> ! [V4__x2] :
( t(V4__x2,V0__X)
=> ( happ(V2__f,V3__x1) = happ(V2__f,V4__x2)
=> V3__x1 = V4__x2 ) ) ) ) ).
fof('$_def_ZornsLemma.InverseImage.inverse_image',axiom,
! [V0__X,V1__Y,V2__f,V3__T] : cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,c_24__lam__6382___24a4(V0__X,V1__Y,V2__f,V3__T)) ).
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__49] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__49) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__2831,Vvar__1___24Anonymous__2832,Vvar__0__A__2833] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__2831,Vvar__1___24Anonymous__2832) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__2833) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__472,Vvar__0__A__473,Vvar__1___24Anonymous__474,Vvar__2___24Anonymous__475] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__472) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__473,Vvar__1___24Anonymous__474,Vvar__2___24Anonymous__475) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__5195,Vvar__1__B__5196,Vvar__2___24Anonymous__5197,Vvar__0__A__5198,Vvar__1__B__5199,Vvar__2___24Anonymous__5200] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__5195,Vvar__1__B__5196,Vvar__2___24Anonymous__5197) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__5198,Vvar__1__B__5199) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__5165,Vvar__1__B__5166,Vvar__2___24Anonymous__5167,Vvar__0__A__5168,Vvar__1__B__5169,Vvar__2___24Anonymous__5170] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__5165,Vvar__1__B__5166) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__5168,Vvar__1__B__5169) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__5861] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5861) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__7] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__804,Vvar__0___24Anonymous__805] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__804) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__805) ).
fof('$_discrim_Coq.Reals.RList.nil$Coq.Reals.RList.cons',axiom,
! [Vvar__0___24Anonymous__4521,Vvar__1___24Anonymous__4522] : cCoq_2eReals_2eRList_2enil != cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__4521,Vvar__1___24Anonymous__4522) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__3047,Vvar__1___24Anonymous__3048,Vvar__0__C__3049,Vvar__1___24Anonymous__3050] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__3047,Vvar__1___24Anonymous__3048) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__3049,Vvar__1___24Anonymous__3050) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__11005,Vvar__1___24Anonymous__11006,Vvar__0__C__11007,Vvar__1___24Anonymous__11008,Vvar__2___24Anonymous__11009] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__11005,Vvar__1___24Anonymous__11006) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__11007,Vvar__1___24Anonymous__11008,Vvar__2___24Anonymous__11009) ).
fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).
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__1063,Vvar__1___24Anonymous__1064,Vvar__0__C__1065,Vvar__1___24Anonymous__1066] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__1063,Vvar__1___24Anonymous__1064) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__1065,Vvar__1___24Anonymous__1066) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__5562,Vvar__1__TX__5563,Vvar__2__AA__5564,Vvar__3__AF__5565,Vvar__0__TA__5566,Vvar__1__TX__5567,Vvar__2__AA__5568,Vvar__3__AF__5569] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__5562,Vvar__1__TX__5563,Vvar__2__AA__5564,Vvar__3__AF__5565) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__5566,Vvar__1__TX__5567,Vvar__2__AA__5568,Vvar__3__AF__5569) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__5717,Vvar__0__A__5718,Vvar__1___24Anonymous__5719] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__5717) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__5718,Vvar__1___24Anonymous__5719) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__3376,Vvar__0__C__3377] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3376) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3377) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__1400,Vvar__0__C__1401] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1400) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1401) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__1160,Vvar__1___24Anonymous__1161,Vvar__0__C__1162,Vvar__1___24Anonymous__1163,Vvar__2___24Anonymous__1164] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1160,Vvar__1___24Anonymous__1161) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1162,Vvar__1___24Anonymous__1163,Vvar__2___24Anonymous__1164) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__1210,Vvar__1___24Anonymous__1211] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1210,Vvar__1___24Anonymous__1211) ).
fof('$_fix_9372_1_Dichotomy_ub',axiom,
! [V2__x,V3__y,V4__P,V5__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__N)
=> ( ( V5__N = cCoq_2eInit_2eDatatypes_2eO
& c_24__fix__9372__1__Dichotomy__ub___24a4(V2__x,V3__y,V4__P,V5__N) = V3__y )
| ? [Vvar__0___24Anonymous__9402] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9402)
& V5__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9402)
& c_24__fix__9372__1__Dichotomy__ub___24a4(V2__x,V3__y,V4__P,V5__N) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249428___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9402) ) ) ) ).
fof('$_fix_9439_0_Dichotomy_lb',axiom,
! [V2__x,V3__y,V4__P,V5__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__N)
=> ( ( V5__N = cCoq_2eInit_2eDatatypes_2eO
& c_24__fix__9439__0__Dichotomy__lb___24a4(V2__x,V3__y,V4__P,V5__N) = V2__x )
| ? [Vvar__0___24Anonymous__9440] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9440)
& V5__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9440)
& c_24__fix__9439__0__Dichotomy__lb___24a4(V2__x,V3__y,V4__P,V5__N) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249466___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__9440) ) ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__2838,Vvar__0__A__2839] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__2838) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__2839)
=> Vvar__0__A__2838 = Vvar__0__A__2839 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__50,Vvar__0___24Anonymous__51] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__50) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__51)
=> Vvar__0___24Anonymous__50 = Vvar__0___24Anonymous__51 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__2834,Vvar__0__A__2835,Vvar__1___24Anonymous__2836,Vvar__1___24Anonymous__2837] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__2834,Vvar__1___24Anonymous__2836) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__2835,Vvar__1___24Anonymous__2837)
=> ( Vvar__1___24Anonymous__2836 = Vvar__1___24Anonymous__2837
& Vvar__0__A__2834 = Vvar__0__A__2835 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__478,Vvar__0__A__479,Vvar__1___24Anonymous__480,Vvar__1___24Anonymous__481,Vvar__2___24Anonymous__482,Vvar__2___24Anonymous__483] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__478,Vvar__1___24Anonymous__480,Vvar__2___24Anonymous__482) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__479,Vvar__1___24Anonymous__481,Vvar__2___24Anonymous__483)
=> ( Vvar__2___24Anonymous__482 = Vvar__2___24Anonymous__483
& Vvar__1___24Anonymous__480 = Vvar__1___24Anonymous__481
& Vvar__0__A__478 = Vvar__0__A__479 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__476,Vvar__0__A__477] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__476) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__477)
=> Vvar__0__A__476 = Vvar__0__A__477 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__866,Vvar__0__A__867,Vvar__1__B__868,Vvar__1__B__869,Vvar__2___24Anonymous__870,Vvar__2___24Anonymous__871,Vvar__3___24Anonymous__872,Vvar__3___24Anonymous__873] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__866,Vvar__1__B__868,Vvar__2___24Anonymous__870,Vvar__3___24Anonymous__872) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__867,Vvar__1__B__869,Vvar__2___24Anonymous__871,Vvar__3___24Anonymous__873)
=> ( Vvar__3___24Anonymous__872 = Vvar__3___24Anonymous__873
& Vvar__2___24Anonymous__870 = Vvar__2___24Anonymous__871
& Vvar__1__B__868 = Vvar__1__B__869
& Vvar__0__A__866 = Vvar__0__A__867 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__2529,Vvar__0__A__2530,Vvar__1__P__2531,Vvar__1__P__2532,Vvar__2__x__2533,Vvar__2__x__2534,Vvar__3___24Anonymous__2535,Vvar__3___24Anonymous__2536] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2529,Vvar__1__P__2531,Vvar__2__x__2533) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2530,Vvar__1__P__2532,Vvar__2__x__2534)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__2533 = Vvar__2__x__2534
& Vvar__1__P__2531 = Vvar__1__P__2532
& Vvar__0__A__2529 = Vvar__0__A__2530 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__10024,Vvar__0__A__10025,Vvar__1__P__10026,Vvar__1__P__10027,Vvar__2__x__10028,Vvar__2__x__10029,Vvar__3___24Anonymous__10030,Vvar__3___24Anonymous__10031] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__10024,Vvar__1__P__10026,Vvar__2__x__10028,Vvar__3___24Anonymous__10030) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__10025,Vvar__1__P__10027,Vvar__2__x__10029,Vvar__3___24Anonymous__10031)
=> ( Vvar__3___24Anonymous__10030 = Vvar__3___24Anonymous__10031
& Vvar__2__x__10028 = Vvar__2__x__10029
& Vvar__1__P__10026 = Vvar__1__P__10027
& Vvar__0__A__10024 = Vvar__0__A__10025 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__5201,Vvar__0__A__5202,Vvar__1__B__5203,Vvar__1__B__5204,Vvar__2___24Anonymous__5205,Vvar__2___24Anonymous__5206] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__5201,Vvar__1__B__5203,Vvar__2___24Anonymous__5205) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__5202,Vvar__1__B__5204,Vvar__2___24Anonymous__5206)
=> ( Vvar__2___24Anonymous__5205 = Vvar__2___24Anonymous__5206
& Vvar__1__B__5203 = Vvar__1__B__5204
& Vvar__0__A__5201 = Vvar__0__A__5202 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__5207,Vvar__0__A__5208,Vvar__1__B__5209,Vvar__1__B__5210,Vvar__2___24Anonymous__5211,Vvar__2___24Anonymous__5212] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__5207,Vvar__1__B__5209) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__5208,Vvar__1__B__5210)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__5209 = Vvar__1__B__5210
& Vvar__0__A__5207 = Vvar__0__A__5208 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__5171,Vvar__0__A__5172,Vvar__1__B__5173,Vvar__1__B__5174,Vvar__2___24Anonymous__5175,Vvar__2___24Anonymous__5176] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__5171,Vvar__1__B__5173) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__5172,Vvar__1__B__5174)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__5173 = Vvar__1__B__5174
& Vvar__0__A__5171 = Vvar__0__A__5172 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__5177,Vvar__0__A__5178,Vvar__1__B__5179,Vvar__1__B__5180,Vvar__2___24Anonymous__5181,Vvar__2___24Anonymous__5182] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__5177,Vvar__1__B__5179) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__5178,Vvar__1__B__5180)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__5179 = Vvar__1__B__5180
& Vvar__0__A__5177 = Vvar__0__A__5178 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__5862,Vvar__0___24Anonymous__5863] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5862) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5863)
=> Vvar__0___24Anonymous__5862 = Vvar__0___24Anonymous__5863 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__10,Vvar__0___24Anonymous__11] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11)
=> Vvar__0___24Anonymous__10 = Vvar__0___24Anonymous__11 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__8,Vvar__0___24Anonymous__9] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__8) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__9)
=> Vvar__0___24Anonymous__8 = Vvar__0___24Anonymous__9 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__806,Vvar__0___24Anonymous__807] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__806) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__807)
=> Vvar__0___24Anonymous__806 = Vvar__0___24Anonymous__807 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__808,Vvar__0___24Anonymous__809] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__808) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__809)
=> Vvar__0___24Anonymous__808 = Vvar__0___24Anonymous__809 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__4500,Vvar__0__Qnum__4501,Vvar__1__Qden__4502,Vvar__1__Qden__4503] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__4500,Vvar__1__Qden__4502) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__4501,Vvar__1__Qden__4503)
=> ( Vvar__1__Qden__4502 = Vvar__1__Qden__4503
& Vvar__0__Qnum__4500 = Vvar__0__Qnum__4501 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__14650,Vvar__0__neg__14651,Vvar__1__cond__neg__14652,Vvar__1__cond__neg__14653] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__14650) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__14651)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__14650 = Vvar__0__neg__14651 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__6645,Vvar__0__nonneg__6646,Vvar__1__cond__nonneg__6647,Vvar__1__cond__nonneg__6648] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__6645) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__6646)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__6645 = Vvar__0__nonneg__6646 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__6672,Vvar__0__nonpos__6673,Vvar__1__cond__nonpos__6674,Vvar__1__cond__nonpos__6675] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__6672) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__6673)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__6672 = Vvar__0__nonpos__6673 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__6657,Vvar__0__pos__6658,Vvar__1__cond__pos__6659,Vvar__1__cond__pos__6660] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__6657) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__6658)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__6657 = Vvar__0__pos__6658 ) ) ).
fof('$_inj_Coq.Reals.RList.cons',axiom,
! [Vvar__0___24Anonymous__4523,Vvar__0___24Anonymous__4524,Vvar__1___24Anonymous__4525,Vvar__1___24Anonymous__4526] :
( cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__4523,Vvar__1___24Anonymous__4525) = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__4524,Vvar__1___24Anonymous__4526)
=> ( Vvar__1___24Anonymous__4525 = Vvar__1___24Anonymous__4526
& Vvar__0___24Anonymous__4523 = Vvar__0___24Anonymous__4524 ) ) ).
fof('$_inj_Coq.Reals.Ranalysis1.mkDifferential',axiom,
! [Vvar__0__d1__14715,Vvar__0__d1__14716,Vvar__1__cond__diff__14717,Vvar__1__cond__diff__14718] :
( cCoq_2eReals_2eRanalysis1_2emkDifferential___24a2(Vvar__0__d1__14715,Vvar__1__cond__diff__14717) = cCoq_2eReals_2eRanalysis1_2emkDifferential___24a2(Vvar__0__d1__14716,Vvar__1__cond__diff__14718)
=> ( Vvar__1__cond__diff__14717 = Vvar__1__cond__diff__14718
& Vvar__0__d1__14715 = Vvar__0__d1__14716 ) ) ).
fof('$_inj_Coq.Reals.RiemannInt.mkC1',axiom,
! [Vvar__0__c1__15181,Vvar__0__c1__15182,Vvar__1__diff0__15183,Vvar__1__diff0__15184,Vvar__2__cont1__15185,Vvar__2__cont1__15186] :
( cCoq_2eReals_2eRiemannInt_2emkC1___24a2(Vvar__0__c1__15181,Vvar__1__diff0__15183) = cCoq_2eReals_2eRiemannInt_2emkC1___24a2(Vvar__0__c1__15182,Vvar__1__diff0__15184)
=> ( c_24Proof = c_24Proof
& Vvar__1__diff0__15183 = Vvar__1__diff0__15184
& Vvar__0__c1__15181 = Vvar__0__c1__15182 ) ) ).
fof('$_inj_Coq.Reals.RiemannInt_SF.mkStepFun',axiom,
! [Vvar__0__a__7964,Vvar__0__a__7965,Vvar__1__b__7966,Vvar__1__b__7967,Vvar__2__fe__7968,Vvar__2__fe__7969,Vvar__3__pre__7970,Vvar__3__pre__7971] :
( cCoq_2eReals_2eRiemannInt__SF_2emkStepFun___24a4(Vvar__0__a__7964,Vvar__1__b__7966,Vvar__2__fe__7968,Vvar__3__pre__7970) = cCoq_2eReals_2eRiemannInt__SF_2emkStepFun___24a4(Vvar__0__a__7965,Vvar__1__b__7967,Vvar__2__fe__7969,Vvar__3__pre__7971)
=> ( Vvar__3__pre__7970 = Vvar__3__pre__7971
& Vvar__2__fe__7968 = Vvar__2__fe__7969
& Vvar__1__b__7966 = Vvar__1__b__7967
& Vvar__0__a__7964 = Vvar__0__a__7965 ) ) ).
fof('$_inj_Coq.Reals.Rlimit.Build_Metric_Space',axiom,
! [Vvar__0__Base__9015,Vvar__0__Base__9016,Vvar__1__dist__9017,Vvar__1__dist__9018,Vvar__2__dist__pos__9019,Vvar__2__dist__pos__9020,Vvar__3__dist__sym__9021,Vvar__3__dist__sym__9022,Vvar__4__dist__refl__9023,Vvar__4__dist__refl__9024,Vvar__5__dist__tri__9025,Vvar__5__dist__tri__9026] :
( cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__9015,Vvar__1__dist__9017) = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__9016,Vvar__1__dist__9018)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__dist__9017 = Vvar__1__dist__9018
& Vvar__0__Base__9015 = Vvar__0__Base__9016 ) ) ).
fof('$_inj_Coq.Reals.Rtopology.mkfamily',axiom,
! [Vvar__0__ind__9648,Vvar__0__ind__9649,Vvar__1__f__9650,Vvar__1__f__9651,Vvar__2__cond__fam__9652,Vvar__2__cond__fam__9653] :
( cCoq_2eReals_2eRtopology_2emkfamily___24a2(Vvar__0__ind__9648,Vvar__1__f__9650) = cCoq_2eReals_2eRtopology_2emkfamily___24a2(Vvar__0__ind__9649,Vvar__1__f__9651)
=> ( c_24Proof = c_24Proof
& Vvar__1__f__9650 = Vvar__1__f__9651
& Vvar__0__ind__9648 = Vvar__0__ind__9649 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__3055,Vvar__0__C__3056,Vvar__1___24Anonymous__3057,Vvar__1___24Anonymous__3058] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__3055,Vvar__1___24Anonymous__3057) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__3056,Vvar__1___24Anonymous__3058)
=> ( Vvar__1___24Anonymous__3057 = Vvar__1___24Anonymous__3058
& Vvar__0__C__3055 = Vvar__0__C__3056 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__3059,Vvar__0__C__3060,Vvar__1___24Anonymous__3061,Vvar__1___24Anonymous__3062,Vvar__2___24Anonymous__3063,Vvar__2___24Anonymous__3064] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__3059,Vvar__1___24Anonymous__3061,Vvar__2___24Anonymous__3063) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__3060,Vvar__1___24Anonymous__3062,Vvar__2___24Anonymous__3064)
=> ( Vvar__2___24Anonymous__3063 = Vvar__2___24Anonymous__3064
& Vvar__1___24Anonymous__3061 = Vvar__1___24Anonymous__3062
& Vvar__0__C__3059 = Vvar__0__C__3060 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__3051,Vvar__0__C__3052,Vvar__1___24Anonymous__3053,Vvar__1___24Anonymous__3054] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__3051,Vvar__1___24Anonymous__3053) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__3052,Vvar__1___24Anonymous__3054)
=> ( Vvar__1___24Anonymous__3053 = Vvar__1___24Anonymous__3054
& Vvar__0__C__3051 = Vvar__0__C__3052 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__3071,Vvar__0__C__3072,Vvar__1___24Anonymous__3073,Vvar__1___24Anonymous__3074,Vvar__2___24Anonymous__3075,Vvar__2___24Anonymous__3076] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__3071,Vvar__1___24Anonymous__3073,Vvar__2___24Anonymous__3075) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__3072,Vvar__1___24Anonymous__3074,Vvar__2___24Anonymous__3076)
=> ( Vvar__2___24Anonymous__3075 = Vvar__2___24Anonymous__3076
& Vvar__1___24Anonymous__3073 = Vvar__1___24Anonymous__3074
& Vvar__0__C__3071 = Vvar__0__C__3072 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__3077,Vvar__0__C__3078,Vvar__1___24Anonymous__3079,Vvar__1___24Anonymous__3080] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__3077,Vvar__1___24Anonymous__3079) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__3078,Vvar__1___24Anonymous__3080)
=> ( Vvar__1___24Anonymous__3079 = Vvar__1___24Anonymous__3080
& Vvar__0__C__3077 = Vvar__0__C__3078 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__3081,Vvar__0__C__3082,Vvar__1___24Anonymous__3083,Vvar__1___24Anonymous__3084,Vvar__2___24Anonymous__3085,Vvar__2___24Anonymous__3086] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__3081,Vvar__1___24Anonymous__3083,Vvar__2___24Anonymous__3085) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__3082,Vvar__1___24Anonymous__3084,Vvar__2___24Anonymous__3086)
=> ( Vvar__2___24Anonymous__3085 = Vvar__2___24Anonymous__3086
& Vvar__1___24Anonymous__3083 = Vvar__1___24Anonymous__3084
& Vvar__0__C__3081 = Vvar__0__C__3082 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__3065,Vvar__0__C__3066,Vvar__1___24Anonymous__3067,Vvar__1___24Anonymous__3068,Vvar__2___24Anonymous__3069,Vvar__2___24Anonymous__3070] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__3065,Vvar__1___24Anonymous__3067,Vvar__2___24Anonymous__3069) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__3066,Vvar__1___24Anonymous__3068,Vvar__2___24Anonymous__3070)
=> ( Vvar__2___24Anonymous__3069 = Vvar__2___24Anonymous__3070
& Vvar__1___24Anonymous__3067 = Vvar__1___24Anonymous__3068
& Vvar__0__C__3065 = Vvar__0__C__3066 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__11020,Vvar__0__C__11021,Vvar__1___24Anonymous__11022,Vvar__1___24Anonymous__11023,Vvar__2___24Anonymous__11024,Vvar__2___24Anonymous__11025,Vvar__3___24Anonymous__11026,Vvar__3___24Anonymous__11027] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__11020,Vvar__1___24Anonymous__11022,Vvar__2___24Anonymous__11024,Vvar__3___24Anonymous__11026) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__11021,Vvar__1___24Anonymous__11023,Vvar__2___24Anonymous__11025,Vvar__3___24Anonymous__11027)
=> ( Vvar__3___24Anonymous__11026 = Vvar__3___24Anonymous__11027
& Vvar__2___24Anonymous__11024 = Vvar__2___24Anonymous__11025
& Vvar__1___24Anonymous__11022 = Vvar__1___24Anonymous__11023
& Vvar__0__C__11020 = Vvar__0__C__11021 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__11010,Vvar__0__C__11011,Vvar__1___24Anonymous__11012,Vvar__1___24Anonymous__11013] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__11010,Vvar__1___24Anonymous__11012) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__11011,Vvar__1___24Anonymous__11013)
=> ( Vvar__1___24Anonymous__11012 = Vvar__1___24Anonymous__11013
& Vvar__0__C__11010 = Vvar__0__C__11011 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__11014,Vvar__0__C__11015,Vvar__1___24Anonymous__11016,Vvar__1___24Anonymous__11017,Vvar__2___24Anonymous__11018,Vvar__2___24Anonymous__11019] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__11014,Vvar__1___24Anonymous__11016,Vvar__2___24Anonymous__11018) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__11015,Vvar__1___24Anonymous__11017,Vvar__2___24Anonymous__11019)
=> ( Vvar__2___24Anonymous__11018 = Vvar__2___24Anonymous__11019
& Vvar__1___24Anonymous__11016 = Vvar__1___24Anonymous__11017
& Vvar__0__C__11014 = Vvar__0__C__11015 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__4686,Vvar__0__r__4687] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__4686) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__4687)
=> Vvar__0__r__4686 = Vvar__0__r__4687 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__4674,Vvar__0__r1__4675,Vvar__1__r2__4676,Vvar__1__r2__4677] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__4674,Vvar__1__r2__4676) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__4675,Vvar__1__r2__4677)
=> ( Vvar__1__r2__4676 = Vvar__1__r2__4677
& Vvar__0__r1__4674 = Vvar__0__r1__4675 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__4678,Vvar__0__r1__4679,Vvar__1__r2__4680,Vvar__1__r2__4681] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__4678,Vvar__1__r2__4680) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__4679,Vvar__1__r2__4681)
=> ( Vvar__1__r2__4680 = Vvar__1__r2__4681
& Vvar__0__r1__4678 = Vvar__0__r1__4679 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__4688,Vvar__0__r__4689] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__4688) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__4689)
=> Vvar__0__r__4688 = Vvar__0__r__4689 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__4670,Vvar__0__r1__4671,Vvar__1__r2__4672,Vvar__1__r2__4673] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__4670,Vvar__1__r2__4672) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__4671,Vvar__1__r2__4673)
=> ( Vvar__1__r2__4672 = Vvar__1__r2__4673
& Vvar__0__r1__4670 = Vvar__0__r1__4671 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__4682,Vvar__0__r1__4683,Vvar__1__z__4684,Vvar__1__z__4685] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__4682,Vvar__1__z__4684) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__4683,Vvar__1__z__4685)
=> ( Vvar__1__z__4684 = Vvar__1__z__4685
& Vvar__0__r1__4682 = Vvar__0__r1__4683 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__4666,Vvar__0__r__4667] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__4666) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__4667)
=> Vvar__0__r__4666 = Vvar__0__r__4667 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__4668,Vvar__0__r__4669] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__4668) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__4669)
=> Vvar__0__r__4668 = Vvar__0__r__4669 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__1120,Vvar__0__T__1121,Vvar__1__Flhs__1122,Vvar__1__Flhs__1123,Vvar__2__Fop__1124,Vvar__2__Fop__1125,Vvar__3__Frhs__1126,Vvar__3__Frhs__1127] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__1120,Vvar__1__Flhs__1122,Vvar__2__Fop__1124,Vvar__3__Frhs__1126) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__1121,Vvar__1__Flhs__1123,Vvar__2__Fop__1125,Vvar__3__Frhs__1127)
=> ( Vvar__3__Frhs__1126 = Vvar__3__Frhs__1127
& Vvar__2__Fop__1124 = Vvar__2__Fop__1125
& Vvar__1__Flhs__1122 = Vvar__1__Flhs__1123
& Vvar__0__T__1120 = Vvar__0__T__1121 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__1087,Vvar__0__C__1088,Vvar__1___24Anonymous__1089,Vvar__1___24Anonymous__1090,Vvar__2___24Anonymous__1091,Vvar__2___24Anonymous__1092] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__1087,Vvar__1___24Anonymous__1089,Vvar__2___24Anonymous__1091) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__1088,Vvar__1___24Anonymous__1090,Vvar__2___24Anonymous__1092)
=> ( Vvar__2___24Anonymous__1091 = Vvar__2___24Anonymous__1092
& Vvar__1___24Anonymous__1089 = Vvar__1___24Anonymous__1090
& Vvar__0__C__1087 = Vvar__0__C__1088 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__1093,Vvar__0__C__1094,Vvar__1___24Anonymous__1095,Vvar__1___24Anonymous__1096] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__1093,Vvar__1___24Anonymous__1095) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__1094,Vvar__1___24Anonymous__1096)
=> ( Vvar__1___24Anonymous__1095 = Vvar__1___24Anonymous__1096
& Vvar__0__C__1093 = Vvar__0__C__1094 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__1067,Vvar__0__C__1068,Vvar__1___24Anonymous__1069,Vvar__1___24Anonymous__1070] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__1067,Vvar__1___24Anonymous__1069) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__1068,Vvar__1___24Anonymous__1070)
=> ( Vvar__1___24Anonymous__1069 = Vvar__1___24Anonymous__1070
& Vvar__0__C__1067 = Vvar__0__C__1068 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__1075,Vvar__0__C__1076,Vvar__1___24Anonymous__1077,Vvar__1___24Anonymous__1078,Vvar__2___24Anonymous__1079,Vvar__2___24Anonymous__1080] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__1075,Vvar__1___24Anonymous__1077,Vvar__2___24Anonymous__1079) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__1076,Vvar__1___24Anonymous__1078,Vvar__2___24Anonymous__1080)
=> ( Vvar__2___24Anonymous__1079 = Vvar__2___24Anonymous__1080
& Vvar__1___24Anonymous__1077 = Vvar__1___24Anonymous__1078
& Vvar__0__C__1075 = Vvar__0__C__1076 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__1081,Vvar__0__C__1082,Vvar__1___24Anonymous__1083,Vvar__1___24Anonymous__1084,Vvar__2___24Anonymous__1085,Vvar__2___24Anonymous__1086] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__1081,Vvar__1___24Anonymous__1083,Vvar__2___24Anonymous__1085) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__1082,Vvar__1___24Anonymous__1084,Vvar__2___24Anonymous__1086)
=> ( Vvar__2___24Anonymous__1085 = Vvar__2___24Anonymous__1086
& Vvar__1___24Anonymous__1083 = Vvar__1___24Anonymous__1084
& Vvar__0__C__1081 = Vvar__0__C__1082 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__1071,Vvar__0__C__1072,Vvar__1___24Anonymous__1073,Vvar__1___24Anonymous__1074] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__1071,Vvar__1___24Anonymous__1073) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__1072,Vvar__1___24Anonymous__1074)
=> ( Vvar__1___24Anonymous__1073 = Vvar__1___24Anonymous__1074
& Vvar__0__C__1071 = Vvar__0__C__1072 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__1097,Vvar__0__C__1098] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__1097) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__1098)
=> Vvar__0__C__1097 = Vvar__0__C__1098 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__5596,Vvar__0__TA__5597,Vvar__1__TX__5598,Vvar__1__TX__5599,Vvar__2__AA__5600,Vvar__2__AA__5601,Vvar__3__AF__5602,Vvar__3__AF__5603,Vvar__4___24Anonymous__5604,Vvar__4___24Anonymous__5605,Vvar__5___24Anonymous__5606,Vvar__5___24Anonymous__5607] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__5596,Vvar__1__TX__5598,Vvar__2__AA__5600,Vvar__3__AF__5602,Vvar__4___24Anonymous__5604,Vvar__5___24Anonymous__5606) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__5597,Vvar__1__TX__5599,Vvar__2__AA__5601,Vvar__3__AF__5603,Vvar__4___24Anonymous__5605,Vvar__5___24Anonymous__5607)
=> ( Vvar__5___24Anonymous__5606 = Vvar__5___24Anonymous__5607
& Vvar__4___24Anonymous__5604 = Vvar__4___24Anonymous__5605
& Vvar__3__AF__5602 = Vvar__3__AF__5603
& Vvar__2__AA__5600 = Vvar__2__AA__5601
& Vvar__1__TX__5598 = Vvar__1__TX__5599
& Vvar__0__TA__5596 = Vvar__0__TA__5597 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__5608,Vvar__0__TA__5609,Vvar__1__TX__5610,Vvar__1__TX__5611,Vvar__2__AA__5612,Vvar__2__AA__5613,Vvar__3__AF__5614,Vvar__3__AF__5615,Vvar__4___24Anonymous__5616,Vvar__4___24Anonymous__5617,Vvar__5___24Anonymous__5618,Vvar__5___24Anonymous__5619] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__5608,Vvar__1__TX__5610,Vvar__2__AA__5612,Vvar__3__AF__5614,Vvar__4___24Anonymous__5616,Vvar__5___24Anonymous__5618) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__5609,Vvar__1__TX__5611,Vvar__2__AA__5613,Vvar__3__AF__5615,Vvar__4___24Anonymous__5617,Vvar__5___24Anonymous__5619)
=> ( Vvar__5___24Anonymous__5618 = Vvar__5___24Anonymous__5619
& Vvar__4___24Anonymous__5616 = Vvar__4___24Anonymous__5617
& Vvar__3__AF__5614 = Vvar__3__AF__5615
& Vvar__2__AA__5612 = Vvar__2__AA__5613
& Vvar__1__TX__5610 = Vvar__1__TX__5611
& Vvar__0__TA__5608 = Vvar__0__TA__5609 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__5620,Vvar__0__TA__5621,Vvar__1__TX__5622,Vvar__1__TX__5623,Vvar__2__AA__5624,Vvar__2__AA__5625,Vvar__3__AF__5626,Vvar__3__AF__5627,Vvar__4___24Anonymous__5628,Vvar__4___24Anonymous__5629,Vvar__5___24Anonymous__5630,Vvar__5___24Anonymous__5631] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__5620,Vvar__1__TX__5622,Vvar__2__AA__5624,Vvar__3__AF__5626,Vvar__4___24Anonymous__5628,Vvar__5___24Anonymous__5630) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__5621,Vvar__1__TX__5623,Vvar__2__AA__5625,Vvar__3__AF__5627,Vvar__4___24Anonymous__5629,Vvar__5___24Anonymous__5631)
=> ( Vvar__5___24Anonymous__5630 = Vvar__5___24Anonymous__5631
& Vvar__4___24Anonymous__5628 = Vvar__4___24Anonymous__5629
& Vvar__3__AF__5626 = Vvar__3__AF__5627
& Vvar__2__AA__5624 = Vvar__2__AA__5625
& Vvar__1__TX__5622 = Vvar__1__TX__5623
& Vvar__0__TA__5620 = Vvar__0__TA__5621 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__5578,Vvar__0__TA__5579,Vvar__1__TX__5580,Vvar__1__TX__5581,Vvar__2__AA__5582,Vvar__2__AA__5583,Vvar__3__AF__5584,Vvar__3__AF__5585] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__5578,Vvar__1__TX__5580,Vvar__2__AA__5582,Vvar__3__AF__5584) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__5579,Vvar__1__TX__5581,Vvar__2__AA__5583,Vvar__3__AF__5585)
=> ( Vvar__3__AF__5584 = Vvar__3__AF__5585
& Vvar__2__AA__5582 = Vvar__2__AA__5583
& Vvar__1__TX__5580 = Vvar__1__TX__5581
& Vvar__0__TA__5578 = Vvar__0__TA__5579 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__5642,Vvar__0__TA__5643,Vvar__1__TX__5644,Vvar__1__TX__5645,Vvar__2__AA__5646,Vvar__2__AA__5647,Vvar__3__AF__5648,Vvar__3__AF__5649,Vvar__4___24Anonymous__5650,Vvar__4___24Anonymous__5651,Vvar__5___24Anonymous__5652,Vvar__5___24Anonymous__5653,Vvar__6___24Anonymous__5654,Vvar__6___24Anonymous__5655] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__5642,Vvar__1__TX__5644,Vvar__2__AA__5646,Vvar__3__AF__5648,Vvar__4___24Anonymous__5650,Vvar__5___24Anonymous__5652,Vvar__6___24Anonymous__5654) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__5643,Vvar__1__TX__5645,Vvar__2__AA__5647,Vvar__3__AF__5649,Vvar__4___24Anonymous__5651,Vvar__5___24Anonymous__5653,Vvar__6___24Anonymous__5655)
=> ( Vvar__6___24Anonymous__5654 = Vvar__6___24Anonymous__5655
& Vvar__5___24Anonymous__5652 = Vvar__5___24Anonymous__5653
& Vvar__4___24Anonymous__5650 = Vvar__4___24Anonymous__5651
& Vvar__3__AF__5648 = Vvar__3__AF__5649
& Vvar__2__AA__5646 = Vvar__2__AA__5647
& Vvar__1__TX__5644 = Vvar__1__TX__5645
& Vvar__0__TA__5642 = Vvar__0__TA__5643 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__5632,Vvar__0__TA__5633,Vvar__1__TX__5634,Vvar__1__TX__5635,Vvar__2__AA__5636,Vvar__2__AA__5637,Vvar__3__AF__5638,Vvar__3__AF__5639,Vvar__4___24Anonymous__5640,Vvar__4___24Anonymous__5641] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__5632,Vvar__1__TX__5634,Vvar__2__AA__5636,Vvar__3__AF__5638,Vvar__4___24Anonymous__5640) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__5633,Vvar__1__TX__5635,Vvar__2__AA__5637,Vvar__3__AF__5639,Vvar__4___24Anonymous__5641)
=> ( Vvar__4___24Anonymous__5640 = Vvar__4___24Anonymous__5641
& Vvar__3__AF__5638 = Vvar__3__AF__5639
& Vvar__2__AA__5636 = Vvar__2__AA__5637
& Vvar__1__TX__5634 = Vvar__1__TX__5635
& Vvar__0__TA__5632 = Vvar__0__TA__5633 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__5570,Vvar__0__TA__5571,Vvar__1__TX__5572,Vvar__1__TX__5573,Vvar__2__AA__5574,Vvar__2__AA__5575,Vvar__3__AF__5576,Vvar__3__AF__5577] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__5570,Vvar__1__TX__5572,Vvar__2__AA__5574,Vvar__3__AF__5576) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__5571,Vvar__1__TX__5573,Vvar__2__AA__5575,Vvar__3__AF__5577)
=> ( Vvar__3__AF__5576 = Vvar__3__AF__5577
& Vvar__2__AA__5574 = Vvar__2__AA__5575
& Vvar__1__TX__5572 = Vvar__1__TX__5573
& Vvar__0__TA__5570 = Vvar__0__TA__5571 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__5586,Vvar__0__TA__5587,Vvar__1__TX__5588,Vvar__1__TX__5589,Vvar__2__AA__5590,Vvar__2__AA__5591,Vvar__3__AF__5592,Vvar__3__AF__5593,Vvar__4___24Anonymous__5594,Vvar__4___24Anonymous__5595] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__5586,Vvar__1__TX__5588,Vvar__2__AA__5590,Vvar__3__AF__5592,Vvar__4___24Anonymous__5594) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__5587,Vvar__1__TX__5589,Vvar__2__AA__5591,Vvar__3__AF__5593,Vvar__4___24Anonymous__5595)
=> ( Vvar__4___24Anonymous__5594 = Vvar__4___24Anonymous__5595
& Vvar__3__AF__5592 = Vvar__3__AF__5593
& Vvar__2__AA__5590 = Vvar__2__AA__5591
& Vvar__1__TX__5588 = Vvar__1__TX__5589
& Vvar__0__TA__5586 = Vvar__0__TA__5587 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__5726,Vvar__0__A__5727,Vvar__1___24Anonymous__5728,Vvar__1___24Anonymous__5729,Vvar__2___24Anonymous__5730,Vvar__2___24Anonymous__5731,Vvar__3___24Anonymous__5732,Vvar__3___24Anonymous__5733] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__5726,Vvar__1___24Anonymous__5728,Vvar__2___24Anonymous__5730,Vvar__3___24Anonymous__5732) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__5727,Vvar__1___24Anonymous__5729,Vvar__2___24Anonymous__5731,Vvar__3___24Anonymous__5733)
=> ( Vvar__3___24Anonymous__5732 = Vvar__3___24Anonymous__5733
& Vvar__2___24Anonymous__5730 = Vvar__2___24Anonymous__5731
& Vvar__1___24Anonymous__5728 = Vvar__1___24Anonymous__5729
& Vvar__0__A__5726 = Vvar__0__A__5727 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__5722,Vvar__0__A__5723,Vvar__1___24Anonymous__5724,Vvar__1___24Anonymous__5725] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__5722,Vvar__1___24Anonymous__5724) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__5723,Vvar__1___24Anonymous__5725)
=> ( Vvar__1___24Anonymous__5724 = Vvar__1___24Anonymous__5725
& Vvar__0__A__5722 = Vvar__0__A__5723 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__5720,Vvar__0__A__5721] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__5720) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__5721)
=> Vvar__0__A__5720 = Vvar__0__A__5721 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__3380,Vvar__0__C__3381] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3380) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3381)
=> Vvar__0__C__3380 = Vvar__0__C__3381 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__3378,Vvar__0__C__3379] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3378) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3379)
=> Vvar__0__C__3378 = Vvar__0__C__3379 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__3386,Vvar__0__C__3387,Vvar__1___24Anonymous__3388,Vvar__1___24Anonymous__3389] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3386,Vvar__1___24Anonymous__3388) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3387,Vvar__1___24Anonymous__3389)
=> ( Vvar__1___24Anonymous__3388 = Vvar__1___24Anonymous__3389
& Vvar__0__C__3386 = Vvar__0__C__3387 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__3390,Vvar__0__C__3391,Vvar__1___24Anonymous__3392,Vvar__1___24Anonymous__3393,Vvar__2___24Anonymous__3394,Vvar__2___24Anonymous__3395] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3390,Vvar__1___24Anonymous__3392,Vvar__2___24Anonymous__3394) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3391,Vvar__1___24Anonymous__3393,Vvar__2___24Anonymous__3395)
=> ( Vvar__2___24Anonymous__3394 = Vvar__2___24Anonymous__3395
& Vvar__1___24Anonymous__3392 = Vvar__1___24Anonymous__3393
& Vvar__0__C__3390 = Vvar__0__C__3391 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__3382,Vvar__0__C__3383,Vvar__1___24Anonymous__3384,Vvar__1___24Anonymous__3385] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3382,Vvar__1___24Anonymous__3384) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3383,Vvar__1___24Anonymous__3385)
=> ( Vvar__1___24Anonymous__3384 = Vvar__1___24Anonymous__3385
& Vvar__0__C__3382 = Vvar__0__C__3383 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__3416,Vvar__0__C__3417,Vvar__1___24Anonymous__3418,Vvar__1___24Anonymous__3419,Vvar__2___24Anonymous__3420,Vvar__2___24Anonymous__3421] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3416,Vvar__1___24Anonymous__3418,Vvar__2___24Anonymous__3420) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3417,Vvar__1___24Anonymous__3419,Vvar__2___24Anonymous__3421)
=> ( Vvar__2___24Anonymous__3420 = Vvar__2___24Anonymous__3421
& Vvar__1___24Anonymous__3418 = Vvar__1___24Anonymous__3419
& Vvar__0__C__3416 = Vvar__0__C__3417 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__3412,Vvar__0__C__3413,Vvar__1___24Anonymous__3414,Vvar__1___24Anonymous__3415] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3412,Vvar__1___24Anonymous__3414) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3413,Vvar__1___24Anonymous__3415)
=> ( Vvar__1___24Anonymous__3414 = Vvar__1___24Anonymous__3415
& Vvar__0__C__3412 = Vvar__0__C__3413 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__3402,Vvar__0__C__3403,Vvar__1___24Anonymous__3404,Vvar__1___24Anonymous__3405,Vvar__2___24Anonymous__3406,Vvar__2___24Anonymous__3407] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3402,Vvar__1___24Anonymous__3404,Vvar__2___24Anonymous__3406) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3403,Vvar__1___24Anonymous__3405,Vvar__2___24Anonymous__3407)
=> ( Vvar__2___24Anonymous__3406 = Vvar__2___24Anonymous__3407
& Vvar__1___24Anonymous__3404 = Vvar__1___24Anonymous__3405
& Vvar__0__C__3402 = Vvar__0__C__3403 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__3408,Vvar__0__C__3409,Vvar__1___24Anonymous__3410,Vvar__1___24Anonymous__3411] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3408,Vvar__1___24Anonymous__3410) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3409,Vvar__1___24Anonymous__3411)
=> ( Vvar__1___24Anonymous__3410 = Vvar__1___24Anonymous__3411
& Vvar__0__C__3408 = Vvar__0__C__3409 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__3422,Vvar__0__C__3423,Vvar__1___24Anonymous__3424,Vvar__1___24Anonymous__3425,Vvar__2___24Anonymous__3426,Vvar__2___24Anonymous__3427] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3422,Vvar__1___24Anonymous__3424,Vvar__2___24Anonymous__3426) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3423,Vvar__1___24Anonymous__3425,Vvar__2___24Anonymous__3427)
=> ( Vvar__2___24Anonymous__3426 = Vvar__2___24Anonymous__3427
& Vvar__1___24Anonymous__3424 = Vvar__1___24Anonymous__3425
& Vvar__0__C__3422 = Vvar__0__C__3423 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__3396,Vvar__0__C__3397,Vvar__1___24Anonymous__3398,Vvar__1___24Anonymous__3399,Vvar__2___24Anonymous__3400,Vvar__2___24Anonymous__3401] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3396,Vvar__1___24Anonymous__3398,Vvar__2___24Anonymous__3400) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3397,Vvar__1___24Anonymous__3399,Vvar__2___24Anonymous__3401)
=> ( Vvar__2___24Anonymous__3400 = Vvar__2___24Anonymous__3401
& Vvar__1___24Anonymous__3398 = Vvar__1___24Anonymous__3399
& Vvar__0__C__3396 = Vvar__0__C__3397 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__3733,Vvar__0__C__3734,Vvar__1__num__3735,Vvar__1__num__3736,Vvar__2__denum__3737,Vvar__2__denum__3738,Vvar__3__condition__3739,Vvar__3__condition__3740] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__3733,Vvar__1__num__3735,Vvar__2__denum__3737,Vvar__3__condition__3739) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__3734,Vvar__1__num__3736,Vvar__2__denum__3738,Vvar__3__condition__3740)
=> ( Vvar__3__condition__3739 = Vvar__3__condition__3740
& Vvar__2__denum__3737 = Vvar__2__denum__3738
& Vvar__1__num__3735 = Vvar__1__num__3736
& Vvar__0__C__3733 = Vvar__0__C__3734 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__1404,Vvar__0__C__1405] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1404) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1405)
=> Vvar__0__C__1404 = Vvar__0__C__1405 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__1402,Vvar__0__C__1403] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1402) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1403)
=> Vvar__0__C__1402 = Vvar__0__C__1403 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__1410,Vvar__0__C__1411,Vvar__1___24Anonymous__1412,Vvar__1___24Anonymous__1413] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__1410,Vvar__1___24Anonymous__1412) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__1411,Vvar__1___24Anonymous__1413)
=> ( Vvar__1___24Anonymous__1412 = Vvar__1___24Anonymous__1413
& Vvar__0__C__1410 = Vvar__0__C__1411 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__1414,Vvar__0__C__1415,Vvar__1___24Anonymous__1416,Vvar__1___24Anonymous__1417,Vvar__2___24Anonymous__1418,Vvar__2___24Anonymous__1419] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__1414,Vvar__1___24Anonymous__1416,Vvar__2___24Anonymous__1418) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__1415,Vvar__1___24Anonymous__1417,Vvar__2___24Anonymous__1419)
=> ( Vvar__2___24Anonymous__1418 = Vvar__2___24Anonymous__1419
& Vvar__1___24Anonymous__1416 = Vvar__1___24Anonymous__1417
& Vvar__0__C__1414 = Vvar__0__C__1415 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__1406,Vvar__0__C__1407,Vvar__1___24Anonymous__1408,Vvar__1___24Anonymous__1409] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__1406,Vvar__1___24Anonymous__1408) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__1407,Vvar__1___24Anonymous__1409)
=> ( Vvar__1___24Anonymous__1408 = Vvar__1___24Anonymous__1409
& Vvar__0__C__1406 = Vvar__0__C__1407 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__1426,Vvar__0__C__1427,Vvar__1___24Anonymous__1428,Vvar__1___24Anonymous__1429,Vvar__2___24Anonymous__1430,Vvar__2___24Anonymous__1431] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__1426,Vvar__1___24Anonymous__1428,Vvar__2___24Anonymous__1430) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__1427,Vvar__1___24Anonymous__1429,Vvar__2___24Anonymous__1431)
=> ( Vvar__2___24Anonymous__1430 = Vvar__2___24Anonymous__1431
& Vvar__1___24Anonymous__1428 = Vvar__1___24Anonymous__1429
& Vvar__0__C__1426 = Vvar__0__C__1427 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__1432,Vvar__0__C__1433,Vvar__1___24Anonymous__1434,Vvar__1___24Anonymous__1435] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__1432,Vvar__1___24Anonymous__1434) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__1433,Vvar__1___24Anonymous__1435)
=> ( Vvar__1___24Anonymous__1434 = Vvar__1___24Anonymous__1435
& Vvar__0__C__1432 = Vvar__0__C__1433 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__1436,Vvar__0__C__1437,Vvar__1___24Anonymous__1438,Vvar__1___24Anonymous__1439,Vvar__2___24Anonymous__1440,Vvar__2___24Anonymous__1441] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__1436,Vvar__1___24Anonymous__1438,Vvar__2___24Anonymous__1440) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__1437,Vvar__1___24Anonymous__1439,Vvar__2___24Anonymous__1441)
=> ( Vvar__2___24Anonymous__1440 = Vvar__2___24Anonymous__1441
& Vvar__1___24Anonymous__1438 = Vvar__1___24Anonymous__1439
& Vvar__0__C__1436 = Vvar__0__C__1437 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__1420,Vvar__0__C__1421,Vvar__1___24Anonymous__1422,Vvar__1___24Anonymous__1423,Vvar__2___24Anonymous__1424,Vvar__2___24Anonymous__1425] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__1420,Vvar__1___24Anonymous__1422,Vvar__2___24Anonymous__1424) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__1421,Vvar__1___24Anonymous__1423,Vvar__2___24Anonymous__1425)
=> ( Vvar__2___24Anonymous__1424 = Vvar__2___24Anonymous__1425
& Vvar__1___24Anonymous__1422 = Vvar__1___24Anonymous__1423
& Vvar__0__C__1420 = Vvar__0__C__1421 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__1175,Vvar__0__C__1176,Vvar__1___24Anonymous__1177,Vvar__1___24Anonymous__1178,Vvar__2___24Anonymous__1179,Vvar__2___24Anonymous__1180,Vvar__3___24Anonymous__1181,Vvar__3___24Anonymous__1182] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1175,Vvar__1___24Anonymous__1177,Vvar__2___24Anonymous__1179,Vvar__3___24Anonymous__1181) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1176,Vvar__1___24Anonymous__1178,Vvar__2___24Anonymous__1180,Vvar__3___24Anonymous__1182)
=> ( Vvar__3___24Anonymous__1181 = Vvar__3___24Anonymous__1182
& Vvar__2___24Anonymous__1179 = Vvar__2___24Anonymous__1180
& Vvar__1___24Anonymous__1177 = Vvar__1___24Anonymous__1178
& Vvar__0__C__1175 = Vvar__0__C__1176 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__1165,Vvar__0__C__1166,Vvar__1___24Anonymous__1167,Vvar__1___24Anonymous__1168] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1165,Vvar__1___24Anonymous__1167) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1166,Vvar__1___24Anonymous__1168)
=> ( Vvar__1___24Anonymous__1167 = Vvar__1___24Anonymous__1168
& Vvar__0__C__1165 = Vvar__0__C__1166 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__1169,Vvar__0__C__1170,Vvar__1___24Anonymous__1171,Vvar__1___24Anonymous__1172,Vvar__2___24Anonymous__1173,Vvar__2___24Anonymous__1174] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1169,Vvar__1___24Anonymous__1171,Vvar__2___24Anonymous__1173) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1170,Vvar__1___24Anonymous__1172,Vvar__2___24Anonymous__1174)
=> ( Vvar__2___24Anonymous__1173 = Vvar__2___24Anonymous__1174
& Vvar__1___24Anonymous__1171 = Vvar__1___24Anonymous__1172
& Vvar__0__C__1169 = Vvar__0__C__1170 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__1216,Vvar__0___24Anonymous__1217,Vvar__1___24Anonymous__1218,Vvar__1___24Anonymous__1219] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1216,Vvar__1___24Anonymous__1218) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1217,Vvar__1___24Anonymous__1219)
=> ( Vvar__1___24Anonymous__1218 = Vvar__1___24Anonymous__1219
& Vvar__0___24Anonymous__1216 = Vvar__0___24Anonymous__1217 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__1212,Vvar__0___24Anonymous__1213,Vvar__1___24Anonymous__1214,Vvar__1___24Anonymous__1215] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1212,Vvar__1___24Anonymous__1214) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1213,Vvar__1___24Anonymous__1215)
=> ( Vvar__1___24Anonymous__1214 = Vvar__1___24Anonymous__1215
& Vvar__0___24Anonymous__1212 = Vvar__0___24Anonymous__1213 ) ) ).
fof('$_inj_Topology.DirectedSets.Build_DirectedSet',axiom,
! [Vvar__0__DS__set__6026,Vvar__0__DS__set__6027,Vvar__1__DS__ord__6028,Vvar__1__DS__ord__6029,Vvar__2__DS__ord__cond__6030,Vvar__2__DS__ord__cond__6031,Vvar__3__DS__join__cond__6032,Vvar__3__DS__join__cond__6033] :
( cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__6026,Vvar__1__DS__ord__6028) = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__6027,Vvar__1__DS__ord__6029)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__DS__ord__6028 = Vvar__1__DS__ord__6029
& Vvar__0__DS__set__6026 = Vvar__0__DS__set__6027 ) ) ).
fof('$_inj_Topology.Filters.Build_Filter',axiom,
! [Vvar__0__X__13036,Vvar__0__X__13037,Vvar__1__filter__family__13038,Vvar__1__filter__family__13039,Vvar__2__filter__intersection__13040,Vvar__2__filter__intersection__13041,Vvar__3__filter__upward__closed__13042,Vvar__3__filter__upward__closed__13043,Vvar__4__filter__full__13044,Vvar__4__filter__full__13045,Vvar__5__filter__empty__13046,Vvar__5__filter__empty__13047] :
( cTopology_2eFilters_2eBuild__Filter___24a2(Vvar__0__X__13036,Vvar__1__filter__family__13038) = cTopology_2eFilters_2eBuild__Filter___24a2(Vvar__0__X__13037,Vvar__1__filter__family__13039)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__filter__family__13038 = Vvar__1__filter__family__13039
& Vvar__0__X__13036 = Vvar__0__X__13037 ) ) ).
fof('$_inj_Topology.FiltersAndNets.Build_filter_to_net_DS_set',axiom,
! [Vvar__0__X__68492,Vvar__0__X__68493,Vvar__1__F__68494,Vvar__1__F__68495,Vvar__2__ftn__S__68496,Vvar__2__ftn__S__68497,Vvar__3__ftn__x__68498,Vvar__3__ftn__x__68499,Vvar__4__ftn__S__in__F__68500,Vvar__4__ftn__S__in__F__68501,Vvar__5__ftn__x__in__S__68502,Vvar__5__ftn__x__in__S__68503] :
( cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set___24a4(Vvar__0__X__68492,Vvar__1__F__68494,Vvar__2__ftn__S__68496,Vvar__3__ftn__x__68498) = cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set___24a4(Vvar__0__X__68493,Vvar__1__F__68495,Vvar__2__ftn__S__68497,Vvar__3__ftn__x__68499)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__ftn__x__68498 = Vvar__3__ftn__x__68499
& Vvar__2__ftn__S__68496 = Vvar__2__ftn__S__68497
& Vvar__1__F__68494 = Vvar__1__F__68495
& Vvar__0__X__68492 = Vvar__0__X__68493 ) ) ).
fof('$_inj_Topology.Nets.Build_cluster_point_subnet_DS_set',axiom,
! [Vvar__0__X__69472,Vvar__0__X__69473,Vvar__1__I__69474,Vvar__1__I__69475,Vvar__2__x__69476,Vvar__2__x__69477,Vvar__3__x0__69478,Vvar__3__x0__69479,Vvar__4__cps__i__69480,Vvar__4__cps__i__69481,Vvar__5__cps__U__69482,Vvar__5__cps__U__69483,Vvar__6__cps__U__open__neigh__69484,Vvar__6__cps__U__open__neigh__69485,Vvar__7__cps__xi__in__U__69486,Vvar__7__cps__xi__in__U__69487] :
( cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(Vvar__0__X__69472,Vvar__1__I__69474,Vvar__2__x__69476,Vvar__3__x0__69478,Vvar__4__cps__i__69480,Vvar__5__cps__U__69482) = cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(Vvar__0__X__69473,Vvar__1__I__69475,Vvar__2__x__69477,Vvar__3__x0__69479,Vvar__4__cps__i__69481,Vvar__5__cps__U__69483)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__5__cps__U__69482 = Vvar__5__cps__U__69483
& Vvar__4__cps__i__69480 = Vvar__4__cps__i__69481
& Vvar__3__x0__69478 = Vvar__3__x0__69479
& Vvar__2__x__69476 = Vvar__2__x__69477
& Vvar__1__I__69474 = Vvar__1__I__69475
& Vvar__0__X__69472 = Vvar__0__X__69473 ) ) ).
fof('$_inj_Topology.Nets.intro_neighborhood_net_DS',axiom,
! [Vvar__0__X__68991,Vvar__0__X__68992,Vvar__1__x__68993,Vvar__1__x__68994,Vvar__2__U__68995,Vvar__2__U__68996,Vvar__3__y__68997,Vvar__3__y__68998,Vvar__4___24Anonymous__68999,Vvar__4___24Anonymous__69000,Vvar__5___24Anonymous__69001,Vvar__5___24Anonymous__69002,Vvar__6___24Anonymous__69003,Vvar__6___24Anonymous__69004] :
( cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(Vvar__0__X__68991,Vvar__1__x__68993,Vvar__2__U__68995,Vvar__3__y__68997) = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(Vvar__0__X__68992,Vvar__1__x__68994,Vvar__2__U__68996,Vvar__3__y__68998)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__y__68997 = Vvar__3__y__68998
& Vvar__2__U__68995 = Vvar__2__U__68996
& Vvar__1__x__68993 = Vvar__1__x__68994
& Vvar__0__X__68991 = Vvar__0__X__68992 ) ) ).
fof('$_inj_Topology.TopologicalSpaces.Build_TopologicalSpace',axiom,
! [Vvar__0__point__set__387,Vvar__0__point__set__388,Vvar__1__open__389,Vvar__1__open__390,Vvar__2__open__family__union__391,Vvar__2__open__family__union__392,Vvar__3__open__intersection2__393,Vvar__3__open__intersection2__394,Vvar__4__open__full__395,Vvar__4__open__full__396] :
( cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__387,Vvar__1__open__389) = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__388,Vvar__1__open__390)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__open__389 = Vvar__1__open__390
& Vvar__0__point__set__387 = Vvar__0__point__set__388 ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX2823] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX2823)
=> ( VX2823 = cCoq_2eInit_2eDatatypes_2etrue
| VX2823 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX874] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX874)
=> ( VX874 = cCoq_2eInit_2eDatatypes_2eEq
| VX874 = cCoq_2eInit_2eDatatypes_2eLt
| VX874 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__464,VX465] :
( cType___24t(Vvar__0__A__464)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__464,VX465)
=> ( VX465 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__464)
| ? [Vvar__1___24Anonymous__468] :
( t(Vvar__1___24Anonymous__468,Vvar__0__A__464)
& ? [Vvar__2___24Anonymous__469] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__464,Vvar__2___24Anonymous__469)
& VX465 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__464,Vvar__1___24Anonymous__468,Vvar__2___24Anonymous__469) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX47] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX47)
=> ( VX47 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__48] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__48)
& VX47 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__48) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__2826,VX2827] :
( cType___24t(Vvar__0__A__2826)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__2826,VX2827)
=> ( ? [Vvar__1___24Anonymous__2829] :
( t(Vvar__1___24Anonymous__2829,Vvar__0__A__2826)
& VX2827 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__2826,Vvar__1___24Anonymous__2829) )
| VX2827 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__2826) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__856,Vvar__1__B__857,VX858] :
( cType___24t(Vvar__0__A__856)
=> ( cType___24t(Vvar__1__B__857)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__856,Vvar__1__B__857,VX858)
=> ? [Vvar__2___24Anonymous__861] :
( t(Vvar__2___24Anonymous__861,Vvar__0__A__856)
& ? [Vvar__3___24Anonymous__862] :
( t(Vvar__3___24Anonymous__862,Vvar__1__B__857)
& VX858 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__856,Vvar__1__B__857,Vvar__2___24Anonymous__861,Vvar__3___24Anonymous__862) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX2822] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX2822)
=> VX2822 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__6598,Vvar__1___24Anonymous__6599] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__6598)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__6599)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__6598,Vvar__1___24Anonymous__6599))
=> ( Vvar__1___24Anonymous__6599 = Vvar__0__n__6598
| ? [Vvar__1__m__6603] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__6603)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__6598,Vvar__1__m__6603))
& Vvar__1___24Anonymous__6599 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__6603) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__2508,Vvar__1__P__2509,VX2512] :
( cType___24t(Vvar__0__A__2508)
=> ( c_24__type__2522___24t(Vvar__0__A__2508,Vvar__1__P__2509,Vvar__1__P__2509)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__2508,Vvar__1__P__2509,VX2512)
=> ? [Vvar__2__x__2517] :
( t(Vvar__2__x__2517,Vvar__0__A__2508)
& p(happ(Vvar__1__P__2509,Vvar__2__x__2517))
& VX2512 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2508,Vvar__1__P__2509,Vvar__2__x__2517) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__10001,Vvar__1__P__10002,VX10005] :
( cType___24t(Vvar__0__A__10001)
=> ( c_24__type__10015___24t(Vvar__0__A__10001,Vvar__1__P__10002,Vvar__1__P__10002)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__10001,Vvar__1__P__10002,VX10005)
=> ? [Vvar__2__x__10010] :
( t(Vvar__2__x__10010,Vvar__0__A__10001)
& ? [Vvar__3___24Anonymous__10011] :
( t(Vvar__3___24Anonymous__10011,happ(Vvar__1__P__10002,Vvar__2__x__10010))
& VX10005 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__10001,Vvar__1__P__10002,Vvar__2__x__10010,Vvar__3___24Anonymous__10011) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__5153,Vvar__1__B__5154,VX5155] :
( cProp___24t(Vvar__0__A__5153)
=> ( cProp___24t(Vvar__1__B__5154)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__5153,Vvar__1__B__5154,VX5155)
=> ( ( p(Vvar__0__A__5153)
& VX5155 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__5153,Vvar__1__B__5154) )
| ( p(Vvar__1__B__5154)
& VX5155 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__5153,Vvar__1__B__5154) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__5183,Vvar__1__B__5184,VX5185] :
( cType___24t(Vvar__0__A__5183)
=> ( cProp___24t(Vvar__1__B__5184)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__5183,Vvar__1__B__5184,VX5185)
=> ( ? [Vvar__2___24Anonymous__5188] :
( t(Vvar__2___24Anonymous__5188,Vvar__0__A__5183)
& VX5185 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__5183,Vvar__1__B__5184,Vvar__2___24Anonymous__5188) )
| ( p(Vvar__1__B__5184)
& VX5185 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__5183,Vvar__1__B__5184) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX5859] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX5859)
=> ( VX5859 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__5860] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5860)
& VX5859 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5860) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX1)
=> ( VX1 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2)
& VX1 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2) )
| ? [Vvar__0___24Anonymous__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3)
& VX1 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX799] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX799)
=> ( ? [Vvar__0___24Anonymous__800] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__800)
& VX799 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__800) )
| ? [Vvar__0___24Anonymous__801] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__801)
& VX799 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__801) )
| VX799 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX4497] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX4497)
=> ? [Vvar__0__Qnum__4498] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__4498)
& ? [Vvar__1__Qden__4499] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__4499)
& VX4497 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__4498,Vvar__1__Qden__4499) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX14647] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX14647)
=> ? [Vvar__0__neg__14648] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__14648)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__14648,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& VX14647 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__14648) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX6642] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX6642)
=> ? [Vvar__0__nonneg__6643] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__6643)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__6643))
& VX6642 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__6643) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX6669] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX6669)
=> ? [Vvar__0__nonpos__6670] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__6670)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__6670,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& VX6669 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__6670) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX6654] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX6654)
=> ? [Vvar__0__pos__6655] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__6655)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__6655))
& VX6654 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__6655) ) ) ).
fof('$_inversion_Coq.Reals.RList.Rlist',axiom,
! [VX4518] :
( cCoq_2eReals_2eRList_2eRlist___24t(VX4518)
=> ( VX4518 = cCoq_2eReals_2eRList_2enil
| ? [Vvar__0___24Anonymous__4519] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__4519)
& ? [Vvar__1___24Anonymous__4520] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__4520)
& VX4518 = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__4519,Vvar__1___24Anonymous__4520) ) ) ) ) ).
fof('$_inversion_Coq.Reals.Ranalysis1.Differential',axiom,
! [VX14711] :
( cCoq_2eReals_2eRanalysis1_2eDifferential___24t(VX14711)
=> ? [Vvar__0__d1__14712] :
( c_24__type__795___24t(Vvar__0__d1__14712)
& ? [Vvar__1__cond__diff__14714] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(Vvar__0__d1__14712,Vvar__1__cond__diff__14714)
& VX14711 = cCoq_2eReals_2eRanalysis1_2emkDifferential___24a2(Vvar__0__d1__14712,Vvar__1__cond__diff__14714) ) ) ) ).
fof('$_inversion_Coq.Reals.RiemannInt.C1_fun',axiom,
! [VX15176] :
( cCoq_2eReals_2eRiemannInt_2eC1__fun___24t(VX15176)
=> ? [Vvar__0__c1__15177] :
( c_24__type__795___24t(Vvar__0__c1__15177)
& ? [Vvar__1__diff0__15179] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(Vvar__0__c1__15177,Vvar__1__diff0__15179)
& cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(cCoq_2eReals_2eRanalysis1_2ederive___24a2(Vvar__0__c1__15177,Vvar__1__diff0__15179))
& VX15176 = cCoq_2eReals_2eRiemannInt_2emkC1___24a2(Vvar__0__c1__15177,Vvar__1__diff0__15179) ) ) ) ).
fof('$_inversion_Coq.Reals.RiemannInt_SF.StepFun',axiom,
! [Vvar__0__a__7948,Vvar__1__b__7949,VX7950] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__a__7948)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__1__b__7949)
=> ( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(Vvar__0__a__7948,Vvar__1__b__7949,VX7950)
=> ? [Vvar__2__fe__7953] :
( c_24__type__7959___24t(Vvar__0__a__7948,Vvar__1__b__7949,Vvar__2__fe__7953)
& ? [Vvar__3__pre__7956] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vvar__2__fe__7953,Vvar__0__a__7948,Vvar__1__b__7949,Vvar__3__pre__7956)
& VX7950 = cCoq_2eReals_2eRiemannInt__SF_2emkStepFun___24a4(Vvar__0__a__7948,Vvar__1__b__7949,Vvar__2__fe__7953,Vvar__3__pre__7956) ) ) ) ) ) ).
fof('$_inversion_Coq.Reals.Rlimit.Metric_Space',axiom,
! [VX8974] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(VX8974)
=> ? [Vvar__0__Base__8975] :
( cType___24t(Vvar__0__Base__8975)
& ? [Vvar__1__dist__8976] :
( c_24__type__25___24t(Vvar__0__Base__8975,Vvar__1__dist__8976)
& ! [Vvar__var__2__x__8982__8984] :
( t(Vvar__var__2__x__8982__8984,Vvar__0__Base__8975)
=> ! [Vvar__var__3__y__8983__8985] :
( t(Vvar__var__3__y__8983__8985,Vvar__0__Base__8975)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__dist__8976,Vvar__var__2__x__8982__8984),Vvar__var__3__y__8983__8985),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
& ! [Vvar__var__3__x__8987__8989] :
( t(Vvar__var__3__x__8987__8989,Vvar__0__Base__8975)
=> ! [Vvar__var__4__y__8988__8990] :
( t(Vvar__var__4__y__8988__8990,Vvar__0__Base__8975)
=> happ(happ(Vvar__1__dist__8976,Vvar__var__3__x__8987__8989),Vvar__var__4__y__8988__8990) = happ(happ(Vvar__1__dist__8976,Vvar__var__4__y__8988__8990),Vvar__var__3__x__8987__8989) ) )
& ! [Vvar__var__4__x__8992__8994] :
( t(Vvar__var__4__x__8992__8994,Vvar__0__Base__8975)
=> ! [Vvar__var__5__y__8993__8995] :
( t(Vvar__var__5__y__8993__8995,Vvar__0__Base__8975)
=> ( happ(happ(Vvar__1__dist__8976,Vvar__var__4__x__8992__8994),Vvar__var__5__y__8993__8995) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vvar__var__4__x__8992__8994 = Vvar__var__5__y__8993__8995 ) ) )
& ! [Vvar__var__5__x__8997__9000] :
( t(Vvar__var__5__x__8997__9000,Vvar__0__Base__8975)
=> ! [Vvar__var__6__y__8998__9001] :
( t(Vvar__var__6__y__8998__9001,Vvar__0__Base__8975)
=> ! [Vvar__var__7__z__8999__9002] :
( t(Vvar__var__7__z__8999__9002,Vvar__0__Base__8975)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__dist__8976,Vvar__var__5__x__8997__9000),Vvar__var__6__y__8998__9001),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__dist__8976,Vvar__var__5__x__8997__9000),Vvar__var__7__z__8999__9002),happ(happ(Vvar__1__dist__8976,Vvar__var__7__z__8999__9002),Vvar__var__6__y__8998__9001)))) ) ) )
& VX8974 = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__8975,Vvar__1__dist__8976) ) ) ) ).
fof('$_inversion_Coq.Reals.Rtopology.family',axiom,
! [VX9628] :
( cCoq_2eReals_2eRtopology_2efamily___24t(VX9628)
=> ? [Vvar__0__ind__9629] :
( c_24__type__332___24t(Vvar__0__ind__9629)
& ? [Vvar__1__f__9631] :
( c_24__type__297___24t(Vvar__1__f__9631)
& ! [Vvar__var__2__x__9637__9640] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__var__2__x__9637__9640)
=> ( ? [Vvar__var__3__y__9638__9641] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__var__3__y__9638__9641)
& p(happ(happ(Vvar__1__f__9631,Vvar__var__2__x__9637__9640),Vvar__var__3__y__9638__9641)) )
=> p(happ(Vvar__0__ind__9629,Vvar__var__2__x__9637__9640)) ) )
& VX9628 = cCoq_2eReals_2eRtopology_2emkfamily___24a2(Vvar__0__ind__9629,Vvar__1__f__9631) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__69994,Vvar__1__R__69995] :
( cType___24t(Vvar__0__A__69994)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__69994,Vvar__1__R__69995)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__69994,Vvar__1__R__69995)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__69994,Vvar__1__R__69995)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__69994,Vvar__1__R__69995)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Full_set',axiom,
! [Vvar__0__U__10962,Vvar__1___24Anonymous__10963] :
( cType___24t(Vvar__0__U__10962)
=> ( t(Vvar__1___24Anonymous__10963,Vvar__0__U__10962)
=> ( cCoq_2eSets_2eEnsembles_2eFull__set___24a2(Vvar__0__U__10962,Vvar__1___24Anonymous__10963)
=> ? [Vvar__1__x__10966] :
( t(Vvar__1__x__10966,Vvar__0__U__10962)
& Vvar__1___24Anonymous__10963 = Vvar__1__x__10966 ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Inhabited',axiom,
! [Vvar__0__U__54,Vvar__1__B__55] :
( cType___24t(Vvar__0__U__54)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__54,Vvar__1__B__55)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__54,Vvar__1__B__55)
=> ? [Vvar__2__x__59] :
( t(Vvar__2__x__59,Vvar__0__U__54)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__54,Vvar__1__B__55,Vvar__2__x__59)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Intersection',axiom,
! [Vvar__0__U__502,Vvar__1__B__503,Vvar__2__C__504,Vvar__1___24Anonymous__505] :
( cType___24t(Vvar__0__U__502)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__502,Vvar__1__B__503)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__502,Vvar__2__C__504)
=> ( t(Vvar__1___24Anonymous__505,Vvar__0__U__502)
=> ( cCoq_2eSets_2eEnsembles_2eIntersection___24a4(Vvar__0__U__502,Vvar__1__B__503,Vvar__2__C__504,Vvar__1___24Anonymous__505)
=> ? [Vvar__3__x__510] :
( t(Vvar__3__x__510,Vvar__0__U__502)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__502,Vvar__1__B__503,Vvar__3__x__510)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__502,Vvar__2__C__504,Vvar__3__x__510)
& Vvar__1___24Anonymous__505 = Vvar__3__x__510 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Singleton',axiom,
! [Vvar__0__U__10967,Vvar__1__x__10968,Vvar__1___24Anonymous__10969] :
( cType___24t(Vvar__0__U__10967)
=> ( t(Vvar__1__x__10968,Vvar__0__U__10967)
=> ( t(Vvar__1___24Anonymous__10969,Vvar__0__U__10967)
=> ( cCoq_2eSets_2eEnsembles_2eSingleton___24a3(Vvar__0__U__10967,Vvar__1__x__10968,Vvar__1___24Anonymous__10969)
=> Vvar__1___24Anonymous__10969 = Vvar__1__x__10968 ) ) ) ) ).
fof('$_inversion_Coq.Sets.Image.Im',axiom,
! [Vvar__0__U__61,Vvar__1__V__62,Vvar__2__X__63,Vvar__3__f__64,Vvar__1___24Anonymous__67] :
( cType___24t(Vvar__0__U__61)
=> ( cType___24t(Vvar__1__V__62)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__61,Vvar__2__X__63)
=> ( c_24__type__87___24t(Vvar__0__U__61,Vvar__1__V__62,Vvar__2__X__63,Vvar__3__f__64,Vvar__1___24Anonymous__67,Vvar__3__f__64)
=> ( t(Vvar__1___24Anonymous__67,Vvar__1__V__62)
=> ( cCoq_2eSets_2eImage_2eIm___24a5(Vvar__0__U__61,Vvar__1__V__62,Vvar__2__X__63,Vvar__3__f__64,Vvar__1___24Anonymous__67)
=> ? [Vvar__4__x__75] :
( t(Vvar__4__x__75,Vvar__0__U__61)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__61,Vvar__2__X__63,Vvar__4__x__75)
& ? [Vvar__6__y__77] :
( t(Vvar__6__y__77,Vvar__1__V__62)
& Vvar__6__y__77 = happ(Vvar__3__f__64,Vvar__4__x__75)
& Vvar__1___24Anonymous__67 = Vvar__6__y__77 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__2923,VX2924] :
( cType___24t(Vvar__0__C__2923)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2923,VX2924)
=> ( ? [Vvar__1___24Anonymous__2926] :
( t(Vvar__1___24Anonymous__2926,Vvar__0__C__2923)
& VX2924 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__2923,Vvar__1___24Anonymous__2926) )
| ? [Vvar__1___24Anonymous__2928] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__2928)
& VX2924 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__2923,Vvar__1___24Anonymous__2928) )
| ? [Vvar__1___24Anonymous__2930] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2923,Vvar__1___24Anonymous__2930)
& ? [Vvar__2___24Anonymous__2931] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2923,Vvar__2___24Anonymous__2931)
& VX2924 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__2923,Vvar__1___24Anonymous__2930,Vvar__2___24Anonymous__2931) ) )
| ? [Vvar__1___24Anonymous__2933] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2923,Vvar__1___24Anonymous__2933)
& ? [Vvar__2___24Anonymous__2934] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2923,Vvar__2___24Anonymous__2934)
& VX2924 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__2923,Vvar__1___24Anonymous__2933,Vvar__2___24Anonymous__2934) ) )
| ? [Vvar__1___24Anonymous__2936] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2923,Vvar__1___24Anonymous__2936)
& ? [Vvar__2___24Anonymous__2937] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2923,Vvar__2___24Anonymous__2937)
& VX2924 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__2923,Vvar__1___24Anonymous__2936,Vvar__2___24Anonymous__2937) ) )
| ? [Vvar__1___24Anonymous__2939] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2923,Vvar__1___24Anonymous__2939)
& VX2924 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__2923,Vvar__1___24Anonymous__2939) )
| ? [Vvar__1___24Anonymous__2941] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__2923,Vvar__1___24Anonymous__2941)
& ? [Vvar__2___24Anonymous__2942] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2942)
& VX2924 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__2923,Vvar__1___24Anonymous__2941,Vvar__2___24Anonymous__2942) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__10981,VX10982] :
( cType___24t(Vvar__0__C__10981)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__10981,VX10982)
=> ( ? [Vvar__1___24Anonymous__10984] :
( t(Vvar__1___24Anonymous__10984,Vvar__0__C__10981)
& VX10982 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__10981,Vvar__1___24Anonymous__10984) )
| ? [Vvar__1___24Anonymous__10986] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10986)
& ? [Vvar__2___24Anonymous__10987] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__10981,Vvar__2___24Anonymous__10987)
& VX10982 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__10981,Vvar__1___24Anonymous__10986,Vvar__2___24Anonymous__10987) ) )
| ? [Vvar__1___24Anonymous__10989] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__10981,Vvar__1___24Anonymous__10989)
& ? [Vvar__2___24Anonymous__10990] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__10990)
& ? [Vvar__3___24Anonymous__10991] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__10981,Vvar__3___24Anonymous__10991)
& VX10982 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__10981,Vvar__1___24Anonymous__10989,Vvar__2___24Anonymous__10990,Vvar__3___24Anonymous__10991) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX4545] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX4545)
=> ( VX4545 = cCoq_2emicromega_2eRMicromega_2eC0
| VX4545 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__4546] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__4546)
& VX4545 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__4546) )
| ? [Vvar__0__r__4547] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__4547)
& VX4545 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__4547) )
| ? [Vvar__0__r1__4548] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__4548)
& ? [Vvar__1__r2__4549] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__4549)
& VX4545 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__4548,Vvar__1__r2__4549) ) )
| ? [Vvar__0__r1__4550] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__4550)
& ? [Vvar__1__r2__4551] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__4551)
& VX4545 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__4550,Vvar__1__r2__4551) ) )
| ? [Vvar__0__r1__4552] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__4552)
& ? [Vvar__1__r2__4553] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__4553)
& VX4545 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__4552,Vvar__1__r2__4553) ) )
| ? [Vvar__0__r1__4554] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__4554)
& ? [Vvar__1__z__4555] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__4555)
& VX4545 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__4554,Vvar__1__z__4555) ) )
| ? [Vvar__0__r__4556] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__4556)
& VX4545 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__4556) )
| ? [Vvar__0__r__4557] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__4557)
& VX4545 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__4557) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__1114,VX1115] :
( cType___24t(Vvar__0__T__1114)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__1114,VX1115)
=> ? [Vvar__1__Flhs__1117] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__1114,Vvar__1__Flhs__1117)
& ? [Vvar__2__Fop__1118] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__1118)
& ? [Vvar__3__Frhs__1119] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__1114,Vvar__3__Frhs__1119)
& VX1115 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__1114,Vvar__1__Flhs__1117,Vvar__2__Fop__1118,Vvar__3__Frhs__1119) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX1113] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX1113)
=> ( VX1113 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX1113 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX1113 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX1113 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX1113 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX1113 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__953,VX954] :
( cType___24t(Vvar__0__C__953)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__953,VX954)
=> ( ? [Vvar__1___24Anonymous__956] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__956)
& VX954 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__953,Vvar__1___24Anonymous__956) )
| ? [Vvar__1___24Anonymous__958] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__953,Vvar__1___24Anonymous__958)
& VX954 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__953,Vvar__1___24Anonymous__958) )
| ? [Vvar__1___24Anonymous__960] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__953,Vvar__1___24Anonymous__960)
& ? [Vvar__2___24Anonymous__961] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__953,Vvar__2___24Anonymous__961)
& VX954 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__953,Vvar__1___24Anonymous__960,Vvar__2___24Anonymous__961) ) )
| ? [Vvar__1___24Anonymous__963] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__953,Vvar__1___24Anonymous__963)
& ? [Vvar__2___24Anonymous__964] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__953,Vvar__2___24Anonymous__964)
& VX954 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__953,Vvar__1___24Anonymous__963,Vvar__2___24Anonymous__964) ) )
| ? [Vvar__1___24Anonymous__966] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__953,Vvar__1___24Anonymous__966)
& ? [Vvar__2___24Anonymous__967] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__953,Vvar__2___24Anonymous__967)
& VX954 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__953,Vvar__1___24Anonymous__966,Vvar__2___24Anonymous__967) ) )
| ? [Vvar__1___24Anonymous__969] :
( t(Vvar__1___24Anonymous__969,Vvar__0__C__953)
& VX954 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__953,Vvar__1___24Anonymous__969) )
| VX954 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__953) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,VX5217] :
( cType___24t(Vvar__0__TA__5213)
=> ( cType___24t(Vvar__1__TX__5214)
=> ( cType___24t(Vvar__2__AA__5215)
=> ( cType___24t(Vvar__3__AF__5216)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,VX5217)
=> ( VX5217 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216)
| VX5217 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216)
| ? [Vvar__4___24Anonymous__5230] :
( t(Vvar__4___24Anonymous__5230,Vvar__1__TX__5214)
& VX5217 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__4___24Anonymous__5230) )
| ? [Vvar__4___24Anonymous__5235] :
( t(Vvar__4___24Anonymous__5235,Vvar__0__TA__5213)
& ? [Vvar__5___24Anonymous__5236] :
( t(Vvar__5___24Anonymous__5236,Vvar__2__AA__5215)
& VX5217 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__4___24Anonymous__5235,Vvar__5___24Anonymous__5236) ) )
| ? [Vvar__4___24Anonymous__5241] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__4___24Anonymous__5241)
& ? [Vvar__5___24Anonymous__5242] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__5___24Anonymous__5242)
& VX5217 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__4___24Anonymous__5241,Vvar__5___24Anonymous__5242) ) )
| ? [Vvar__4___24Anonymous__5247] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__4___24Anonymous__5247)
& ? [Vvar__5___24Anonymous__5248] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__5___24Anonymous__5248)
& VX5217 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__4___24Anonymous__5247,Vvar__5___24Anonymous__5248) ) )
| ? [Vvar__4___24Anonymous__5253] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__4___24Anonymous__5253)
& VX5217 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__4___24Anonymous__5253) )
| ? [Vvar__4___24Anonymous__5258] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__4___24Anonymous__5258)
& ? [Vvar__5___24Anonymous__5259] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__5216,Vvar__5___24Anonymous__5259)
& ? [Vvar__6___24Anonymous__5260] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__6___24Anonymous__5260)
& VX5217 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__5213,Vvar__1__TX__5214,Vvar__2__AA__5215,Vvar__3__AF__5216,Vvar__4___24Anonymous__5258,Vvar__5___24Anonymous__5259,Vvar__6___24Anonymous__5260) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__5697,VX5698] :
( cType___24t(Vvar__0__A__5697)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__5697,VX5698)
=> ( VX5698 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__5697)
| ? [Vvar__1___24Anonymous__5701] :
( t(Vvar__1___24Anonymous__5701,Vvar__0__A__5697)
& VX5698 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__5697,Vvar__1___24Anonymous__5701) )
| ? [Vvar__1___24Anonymous__5703] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__5697,Vvar__1___24Anonymous__5703)
& ? [Vvar__2___24Anonymous__5704] :
( t(Vvar__2___24Anonymous__5704,Vvar__0__A__5697)
& ? [Vvar__3___24Anonymous__5705] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__5697,Vvar__3___24Anonymous__5705)
& VX5698 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__5697,Vvar__1___24Anonymous__5703,Vvar__2___24Anonymous__5704,Vvar__3___24Anonymous__5705) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__3101,VX3102] :
( cType___24t(Vvar__0__C__3101)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,VX3102)
=> ( VX3102 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3101)
| VX3102 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3101)
| ? [Vvar__1___24Anonymous__3106] :
( t(Vvar__1___24Anonymous__3106,Vvar__0__C__3101)
& VX3102 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3101,Vvar__1___24Anonymous__3106) )
| ? [Vvar__1___24Anonymous__3108] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3108)
& VX3102 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3101,Vvar__1___24Anonymous__3108) )
| ? [Vvar__1___24Anonymous__3110] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,Vvar__1___24Anonymous__3110)
& ? [Vvar__2___24Anonymous__3111] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,Vvar__2___24Anonymous__3111)
& VX3102 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3101,Vvar__1___24Anonymous__3110,Vvar__2___24Anonymous__3111) ) )
| ? [Vvar__1___24Anonymous__3113] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,Vvar__1___24Anonymous__3113)
& ? [Vvar__2___24Anonymous__3114] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,Vvar__2___24Anonymous__3114)
& VX3102 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3101,Vvar__1___24Anonymous__3113,Vvar__2___24Anonymous__3114) ) )
| ? [Vvar__1___24Anonymous__3116] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,Vvar__1___24Anonymous__3116)
& ? [Vvar__2___24Anonymous__3117] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,Vvar__2___24Anonymous__3117)
& VX3102 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3101,Vvar__1___24Anonymous__3116,Vvar__2___24Anonymous__3117) ) )
| ? [Vvar__1___24Anonymous__3119] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,Vvar__1___24Anonymous__3119)
& VX3102 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3101,Vvar__1___24Anonymous__3119) )
| ? [Vvar__1___24Anonymous__3121] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,Vvar__1___24Anonymous__3121)
& VX3102 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3101,Vvar__1___24Anonymous__3121) )
| ? [Vvar__1___24Anonymous__3123] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,Vvar__1___24Anonymous__3123)
& ? [Vvar__2___24Anonymous__3124] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,Vvar__2___24Anonymous__3124)
& VX3102 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3101,Vvar__1___24Anonymous__3123,Vvar__2___24Anonymous__3124) ) )
| ? [Vvar__1___24Anonymous__3126] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3101,Vvar__1___24Anonymous__3126)
& ? [Vvar__2___24Anonymous__3127] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__3127)
& VX3102 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3101,Vvar__1___24Anonymous__3126,Vvar__2___24Anonymous__3127) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__3727,VX3728] :
( cType___24t(Vvar__0__C__3727)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__3727,VX3728)
=> ? [Vvar__1__num__3730] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3727,Vvar__1__num__3730)
& ? [Vvar__2__denum__3731] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3727,Vvar__2__denum__3731)
& ? [Vvar__3__condition__3732] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__3727),Vvar__3__condition__3732)
& VX3728 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__3727,Vvar__1__num__3730,Vvar__2__denum__3731,Vvar__3__condition__3732) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX1199] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX1199)
=> ( VX1199 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__1200] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1200)
& ? [Vvar__1___24Anonymous__1201] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__1201)
& VX1199 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1200,Vvar__1___24Anonymous__1201) ) )
| ? [Vvar__0___24Anonymous__1202] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1202)
& ? [Vvar__1___24Anonymous__1203] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__1203)
& VX1199 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1202,Vvar__1___24Anonymous__1203) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__1220,VX1221] :
( cType___24t(Vvar__0__C__1220)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1220,VX1221)
=> ( VX1221 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1220)
| VX1221 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1220)
| ? [Vvar__1___24Anonymous__1225] :
( t(Vvar__1___24Anonymous__1225,Vvar__0__C__1220)
& VX1221 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__1220,Vvar__1___24Anonymous__1225) )
| ? [Vvar__1___24Anonymous__1227] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1227)
& VX1221 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__1220,Vvar__1___24Anonymous__1227) )
| ? [Vvar__1___24Anonymous__1229] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1220,Vvar__1___24Anonymous__1229)
& ? [Vvar__2___24Anonymous__1230] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1220,Vvar__2___24Anonymous__1230)
& VX1221 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__1220,Vvar__1___24Anonymous__1229,Vvar__2___24Anonymous__1230) ) )
| ? [Vvar__1___24Anonymous__1232] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1220,Vvar__1___24Anonymous__1232)
& ? [Vvar__2___24Anonymous__1233] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1220,Vvar__2___24Anonymous__1233)
& VX1221 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__1220,Vvar__1___24Anonymous__1232,Vvar__2___24Anonymous__1233) ) )
| ? [Vvar__1___24Anonymous__1235] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1220,Vvar__1___24Anonymous__1235)
& ? [Vvar__2___24Anonymous__1236] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1220,Vvar__2___24Anonymous__1236)
& VX1221 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__1220,Vvar__1___24Anonymous__1235,Vvar__2___24Anonymous__1236) ) )
| ? [Vvar__1___24Anonymous__1238] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1220,Vvar__1___24Anonymous__1238)
& VX1221 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__1220,Vvar__1___24Anonymous__1238) )
| ? [Vvar__1___24Anonymous__1240] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1220,Vvar__1___24Anonymous__1240)
& ? [Vvar__2___24Anonymous__1241] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__1241)
& VX1221 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__1220,Vvar__1___24Anonymous__1240,Vvar__2___24Anonymous__1241) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__1136,VX1137] :
( cType___24t(Vvar__0__C__1136)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1136,VX1137)
=> ( ? [Vvar__1___24Anonymous__1139] :
( t(Vvar__1___24Anonymous__1139,Vvar__0__C__1136)
& VX1137 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1136,Vvar__1___24Anonymous__1139) )
| ? [Vvar__1___24Anonymous__1141] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1141)
& ? [Vvar__2___24Anonymous__1142] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1136,Vvar__2___24Anonymous__1142)
& VX1137 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1136,Vvar__1___24Anonymous__1141,Vvar__2___24Anonymous__1142) ) )
| ? [Vvar__1___24Anonymous__1144] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1136,Vvar__1___24Anonymous__1144)
& ? [Vvar__2___24Anonymous__1145] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1145)
& ? [Vvar__3___24Anonymous__1146] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1136,Vvar__3___24Anonymous__1146)
& VX1137 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1136,Vvar__1___24Anonymous__1144,Vvar__2___24Anonymous__1145,Vvar__3___24Anonymous__1146) ) ) ) ) ) ) ).
fof('$_inversion_Topology.DirectedSets.DirectedSet',axiom,
! [VX6012] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(VX6012)
=> ? [Vvar__0__DS__set__6013] :
( cType___24t(Vvar__0__DS__set__6013)
& ? [Vvar__1__DS__ord__6014] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__DS__set__6013,Vvar__1__DS__ord__6014)
& cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__DS__set__6013,Vvar__1__DS__ord__6014)
& ! [Vvar__var__3__i__6017__6020] :
( t(Vvar__var__3__i__6017__6020,Vvar__0__DS__set__6013)
=> ! [Vvar__var__4__j__6019__6022] :
( t(Vvar__var__4__j__6019__6022,Vvar__0__DS__set__6013)
=> ? [Vvar__var__5__k__6018__6021] :
( t(Vvar__var__5__k__6018__6021,Vvar__0__DS__set__6013)
& p(happ(happ(Vvar__1__DS__ord__6014,Vvar__var__3__i__6017__6020),Vvar__var__5__k__6018__6021))
& p(happ(happ(Vvar__1__DS__ord__6014,Vvar__var__4__j__6019__6022),Vvar__var__5__k__6018__6021)) ) ) )
& VX6012 = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__6013,Vvar__1__DS__ord__6014) ) ) ) ).
fof('$_inversion_Topology.Filters.Filter',axiom,
! [Vvar__0__X__12996,VX12997] :
( cType___24t(Vvar__0__X__12996)
=> ( cTopology_2eFilters_2eFilter___24t(Vvar__0__X__12996,VX12997)
=> ? [Vvar__1__filter__family__12999] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__X__12996,Vvar__1__filter__family__12999)
& ! [Vvar__var__var__2__S1__13001__13005__13020] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__12996,Vvar__var__var__2__S1__13001__13005__13020)
=> ! [Vvar__var__var__3__S2__13002__13006__13021] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__12996,Vvar__var__var__3__S2__13002__13006__13021)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__12996),Vvar__1__filter__family__12999,Vvar__var__var__2__S1__13001__13005__13020)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__12996),Vvar__1__filter__family__12999,Vvar__var__var__3__S2__13002__13006__13021)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__12996),Vvar__1__filter__family__12999,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__X__12996,Vvar__var__var__2__S1__13001__13005__13020,Vvar__var__var__3__S2__13002__13006__13021)) ) ) ) )
& ! [Vvar__var__var__3__S1__13010__13014__13024] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__12996,Vvar__var__var__3__S1__13010__13014__13024)
=> ! [Vvar__var__var__4__S2__13011__13015__13025] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__12996,Vvar__var__var__4__S2__13011__13015__13025)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__12996),Vvar__1__filter__family__12999,Vvar__var__var__3__S1__13010__13014__13024)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__X__12996,Vvar__var__var__3__S1__13010__13014__13024,Vvar__var__var__4__S2__13011__13015__13025)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__12996),Vvar__1__filter__family__12999,Vvar__var__var__4__S2__13011__13015__13025) ) ) ) )
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__12996),Vvar__1__filter__family__12999,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__X__12996))
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__12996),Vvar__1__filter__family__12999,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vvar__0__X__12996))
& VX12997 = cTopology_2eFilters_2eBuild__Filter___24a2(Vvar__0__X__12996,Vvar__1__filter__family__12999) ) ) ) ).
fof('$_inversion_Topology.FiltersAndNets.filter_to_net_DS_set',axiom,
! [Vvar__0__X__68480,Vvar__1__F__68481,VX68482] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__68480)
=> ( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__68480),Vvar__1__F__68481)
=> ( cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(Vvar__0__X__68480,Vvar__1__F__68481,VX68482)
=> ? [Vvar__2__ftn__S__68485] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__68480),Vvar__2__ftn__S__68485)
& ? [Vvar__3__ftn__x__68486] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__68480,Vvar__3__ftn__x__68486)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__68480)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__68480),Vvar__1__F__68481),Vvar__2__ftn__S__68485)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__68480),Vvar__2__ftn__S__68485,Vvar__3__ftn__x__68486)
& VX68482 = cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set___24a4(Vvar__0__X__68480,Vvar__1__F__68481,Vvar__2__ftn__S__68485,Vvar__3__ftn__x__68486) ) ) ) ) ) ).
fof('$_inversion_Topology.MetricSpaces.metric',axiom,
! [Vvar__0__X__93,Vvar__1__d__94] :
( cType___24t(Vvar__0__X__93)
=> ( c_24__type__162___24t(Vvar__0__X__93,Vvar__1__d__94,Vvar__1__d__94)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(Vvar__0__X__93,Vvar__1__d__94)
=> ( ! [Vvar__var__var__var__2__x__107__109__133__135] :
( t(Vvar__var__var__var__2__x__107__109__133__135,Vvar__0__X__93)
=> ! [Vvar__var__var__var__3__y__108__110__134__136] :
( t(Vvar__var__var__var__3__y__108__110__134__136,Vvar__0__X__93)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__d__94,Vvar__var__var__var__2__x__107__109__133__135),Vvar__var__var__var__3__y__108__110__134__136),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
& ! [Vvar__var__var__var__3__x__112__114__137__139] :
( t(Vvar__var__var__var__3__x__112__114__137__139,Vvar__0__X__93)
=> ! [Vvar__var__var__var__4__y__113__115__138__140] :
( t(Vvar__var__var__var__4__y__113__115__138__140,Vvar__0__X__93)
=> happ(happ(Vvar__1__d__94,Vvar__var__var__var__3__x__112__114__137__139),Vvar__var__var__var__4__y__113__115__138__140) = happ(happ(Vvar__1__d__94,Vvar__var__var__var__4__y__113__115__138__140),Vvar__var__var__var__3__x__112__114__137__139) ) )
& ! [Vvar__var__var__var__4__x__117__120__141__144] :
( t(Vvar__var__var__var__4__x__117__120__141__144,Vvar__0__X__93)
=> ! [Vvar__var__var__var__5__y__119__122__143__146] :
( t(Vvar__var__var__var__5__y__119__122__143__146,Vvar__0__X__93)
=> ! [Vvar__var__var__var__6__z__118__121__142__145] :
( t(Vvar__var__var__var__6__z__118__121__142__145,Vvar__0__X__93)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__d__94,Vvar__var__var__var__4__x__117__120__141__144),Vvar__var__var__var__6__z__118__121__142__145),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__d__94,Vvar__var__var__var__4__x__117__120__141__144),Vvar__var__var__var__5__y__119__122__143__146),happ(happ(Vvar__1__d__94,Vvar__var__var__var__5__y__119__122__143__146),Vvar__var__var__var__6__z__118__121__142__145)))) ) ) )
& ! [Vvar__var__var__var__5__x__124__125__147__148] :
( t(Vvar__var__var__var__5__x__124__125__147__148,Vvar__0__X__93)
=> happ(happ(Vvar__1__d__94,Vvar__var__var__var__5__x__124__125__147__148),Vvar__var__var__var__5__x__124__125__147__148) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
& ! [Vvar__var__var__var__6__x__127__130__149__152] :
( t(Vvar__var__var__var__6__x__127__130__149__152,Vvar__0__X__93)
=> ! [Vvar__var__var__var__7__y__128__131__150__153] :
( t(Vvar__var__var__var__7__y__128__131__150__153,Vvar__0__X__93)
=> ( happ(happ(Vvar__1__d__94,Vvar__var__var__var__6__x__127__130__149__152),Vvar__var__var__var__7__y__128__131__150__153) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> Vvar__var__var__var__6__x__127__130__149__152 = Vvar__var__var__var__7__y__128__131__150__153 ) ) )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Topology.MetricSpaces.metric_topology_neighborhood_basis',axiom,
! [Vvar__0__X__563,Vvar__1__d__564,Vvar__2__x__569,Vvar__1___24Anonymous__570] :
( cType___24t(Vvar__0__X__563)
=> ( c_24__type__601___24t(Vvar__0__X__563,Vvar__1__d__564,Vvar__2__x__569,Vvar__1___24Anonymous__570,Vvar__1__d__564)
=> ( t(Vvar__2__x__569,Vvar__0__X__563)
=> ( c_24__type__612___24t(Vvar__0__X__563,Vvar__1__d__564,Vvar__2__x__569,Vvar__1___24Anonymous__570,Vvar__1___24Anonymous__570)
=> ( cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis___24a4(Vvar__0__X__563,Vvar__1__d__564,Vvar__2__x__569,Vvar__1___24Anonymous__570)
=> ? [Vvar__3__r__581] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__3__r__581)
& p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(Vvar__3__r__581,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& Vvar__1___24Anonymous__570 = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(Vvar__0__X__563,c_24__lam__624___24a5(Vvar__0__X__563,Vvar__1__d__564,Vvar__2__x__569,Vvar__1___24Anonymous__570,Vvar__3__r__581)) ) ) ) ) ) ) ).
fof('$_inversion_Topology.MetricSpaces.metrizable',axiom,
! [Vvar__0__X__224] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__224)
=> ( cTopology_2eMetricSpaces_2emetrizable___24a1(Vvar__0__X__224)
=> ? [Vvar__1__d__227] :
( c_24__type__222___24t(Vvar__0__X__224,Vvar__1__d__227)
& cTopology_2eMetricSpaces_2emetric___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__224),Vvar__1__d__227)
& cTopology_2eMetricSpaces_2emetrizes___24a2(Vvar__0__X__224,Vvar__1__d__227)
& p(c_24True) ) ) ) ).
fof('$_inversion_Topology.NeighborhoodBases.open_neighborhood_basis',axiom,
! [Vvar__0__X__906,Vvar__1__NB__907,Vvar__2__x__908] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__906)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__906),Vvar__1__NB__907)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__906,Vvar__2__x__908)
=> ( cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(Vvar__0__X__906,Vvar__1__NB__907,Vvar__2__x__908)
=> ( ! [Vvar__var__var__var__var__3__U__914__916__925__927__929] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__906),Vvar__var__var__var__var__3__U__914__916__925__927__929)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__906)),Vvar__1__NB__907,Vvar__var__var__var__var__3__U__914__916__925__927__929)
=> cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(Vvar__0__X__906,Vvar__var__var__var__var__3__U__914__916__925__927__929,Vvar__2__x__908) ) )
& ! [Vvar__var__var__var__var__4__U__919__922__931__934__937] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__906),Vvar__var__var__var__var__4__U__919__922__931__934__937)
=> ( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(Vvar__0__X__906,Vvar__var__var__var__var__4__U__919__922__931__934__937,Vvar__2__x__908)
=> ? [Vvar__var__var__var__var__6__V__920__923__932__935__938] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__906),Vvar__var__var__var__var__6__V__920__923__932__935__938)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__906)),Vvar__1__NB__907,Vvar__var__var__var__var__6__V__920__923__932__935__938)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__906),Vvar__var__var__var__var__6__V__920__923__932__935__938,Vvar__var__var__var__var__4__U__919__922__931__934__937) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Topology.Nets.Subnet',axiom,
! [Vvar__0__X__69305,Vvar__1__I__69306,Vvar__2__x__69307,Vvar__3__J__69308,Vvar__4___24Anonymous__69309] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__69305)
=> ( cTopology_2eDirectedSets_2eDirectedSet___24t(Vvar__1__I__69306)
=> ( cTopology_2eNets_2eNet___24t(Vvar__1__I__69306,Vvar__0__X__69305,Vvar__2__x__69307)
=> ( cTopology_2eDirectedSets_2eDirectedSet___24t(Vvar__3__J__69308)
=> ( cTopology_2eNets_2eNet___24t(Vvar__3__J__69308,Vvar__0__X__69305,Vvar__4___24Anonymous__69309)
=> ( cTopology_2eNets_2eSubnet___24a5(Vvar__0__X__69305,Vvar__1__I__69306,Vvar__2__x__69307,Vvar__3__J__69308,Vvar__4___24Anonymous__69309)
=> ? [Vvar__4__h__69315] :
( c_24__type__69350___24t(Vvar__0__X__69305,Vvar__1__I__69306,Vvar__2__x__69307,Vvar__3__J__69308,Vvar__4___24Anonymous__69309,Vvar__4__h__69315)
& ! [Vvar__var__var__var__5__j1__69319__69322__69333__69336] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vvar__3__J__69308,Vvar__var__var__var__5__j1__69319__69322__69333__69336)
=> ! [Vvar__var__var__var__6__j2__69320__69323__69334__69337] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vvar__3__J__69308,Vvar__var__var__var__6__j2__69320__69323__69334__69337)
=> ( cTopology_2eDirectedSets_2eDS__ord___24a3(Vvar__3__J__69308,Vvar__var__var__var__5__j1__69319__69322__69333__69336,Vvar__var__var__var__6__j2__69320__69323__69334__69337)
=> cTopology_2eDirectedSets_2eDS__ord___24a3(Vvar__1__I__69306,happ(Vvar__4__h__69315,Vvar__var__var__var__5__j1__69319__69322__69333__69336),happ(Vvar__4__h__69315,Vvar__var__var__var__6__j2__69320__69323__69334__69337)) ) ) )
& cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(Vvar__1__I__69306,c_24__lam__69373___24a6(Vvar__0__X__69305,Vvar__1__I__69306,Vvar__2__x__69307,Vvar__3__J__69308,Vvar__4___24Anonymous__69309,Vvar__4__h__69315))
& Vvar__4___24Anonymous__69309 = c_24__lam__69387___24a6(Vvar__0__X__69305,Vvar__1__I__69306,Vvar__2__x__69307,Vvar__3__J__69308,Vvar__4___24Anonymous__69309,Vvar__4__h__69315) ) ) ) ) ) ) ) ).
fof('$_inversion_Topology.Nets.cluster_point_subnet_DS_set',axiom,
! [Vvar__0__X__69451,Vvar__1__I__69452,Vvar__2__x__69453,Vvar__3__x0__69454,VX69455] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__69451)
=> ( cTopology_2eDirectedSets_2eDirectedSet___24t(Vvar__1__I__69452)
=> ( cTopology_2eNets_2eNet___24t(Vvar__1__I__69452,Vvar__0__X__69451,Vvar__2__x__69453)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__69451,Vvar__3__x0__69454)
=> ( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vvar__0__X__69451,Vvar__1__I__69452,Vvar__2__x__69453,Vvar__3__x0__69454,VX69455)
=> ? [Vvar__4__cps__i__69460] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vvar__1__I__69452,Vvar__4__cps__i__69460)
& ? [Vvar__5__cps__U__69461] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__69451),Vvar__5__cps__U__69461)
& cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(Vvar__0__X__69451,Vvar__5__cps__U__69461,Vvar__3__x0__69454)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__69451),Vvar__5__cps__U__69461,happ(Vvar__2__x__69453,Vvar__4__cps__i__69460))
& VX69455 = cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(Vvar__0__X__69451,Vvar__1__I__69452,Vvar__2__x__69453,Vvar__3__x0__69454,Vvar__4__cps__i__69460,Vvar__5__cps__U__69461) ) ) ) ) ) ) ) ).
fof('$_inversion_Topology.Nets.neighborhood_net_DS_set',axiom,
! [Vvar__0__X__68978,Vvar__1__x__68979,VX68980] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__68978)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__68978,Vvar__1__x__68979)
=> ( cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vvar__0__X__68978,Vvar__1__x__68979,VX68980)
=> ? [Vvar__2__U__68983] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__68978),Vvar__2__U__68983)
& ? [Vvar__3__y__68984] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__68978,Vvar__3__y__68984)
& cTopology_2eTopologicalSpaces_2eopen___24a2(Vvar__0__X__68978,Vvar__2__U__68983)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__68978),Vvar__2__U__68983,Vvar__1__x__68979)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__68978),Vvar__2__U__68983,Vvar__3__y__68984)
& VX68980 = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(Vvar__0__X__68978,Vvar__1__x__68979,Vvar__2__U__68983,Vvar__3__y__68984) ) ) ) ) ) ).
fof('$_inversion_Topology.OpenBases.B_open',axiom,
! [Vvar__0__X__63460,Vvar__1__B__63461,Vvar__2___24Anonymous__63462] :
( cType___24t(Vvar__0__X__63460)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__X__63460,Vvar__1__B__63461)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__63460,Vvar__2___24Anonymous__63462)
=> ( cTopology_2eOpenBases_2eB__open___24a3(Vvar__0__X__63460,Vvar__1__B__63461,Vvar__2___24Anonymous__63462)
=> ? [Vvar__2__F__63466] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__X__63460,Vvar__2__F__63466)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__63460),Vvar__2__F__63466,Vvar__1__B__63461)
& Vvar__2___24Anonymous__63462 = cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__X__63460,Vvar__2__F__63466) ) ) ) ) ) ).
fof('$_inversion_Topology.OpenBases.open_basis',axiom,
! [Vvar__0__X__69617,Vvar__1__B__69618] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__69617)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__69617),Vvar__1__B__69618)
=> ( cTopology_2eOpenBases_2eopen__basis___24a2(Vvar__0__X__69617,Vvar__1__B__69618)
=> ( ! [Vvar__var__var__var__2__V__69623__69625__69638__69640] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__69617),Vvar__var__var__var__2__V__69623__69625__69638__69640)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__69617)),Vvar__1__B__69618,Vvar__var__var__var__2__V__69623__69625__69638__69640)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(Vvar__0__X__69617,Vvar__var__var__var__2__V__69623__69625__69638__69640) ) )
& ! [Vvar__var__var__var__3__x__69629__69634__69643__69648] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__69617,Vvar__var__var__var__3__x__69629__69634__69643__69648)
=> ! [Vvar__var__var__var__4__U__69628__69633__69642__69647] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__69617),Vvar__var__var__var__4__U__69628__69633__69642__69647)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(Vvar__0__X__69617,Vvar__var__var__var__4__U__69628__69633__69642__69647)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__69617),Vvar__var__var__var__4__U__69628__69633__69642__69647,Vvar__var__var__var__3__x__69629__69634__69643__69648)
=> ? [Vvar__var__var__var__7__V__69630__69635__69644__69649] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__69617),Vvar__var__var__var__7__V__69630__69635__69644__69649)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__69617)),Vvar__1__B__69618,Vvar__var__var__var__7__V__69630__69635__69644__69649)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__69617),Vvar__var__var__var__7__V__69630__69635__69644__69649,Vvar__var__var__var__4__U__69628__69633__69642__69647)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__69617),Vvar__var__var__var__7__V__69630__69635__69644__69649,Vvar__var__var__var__3__x__69629__69634__69643__69648) ) ) ) ) )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Topology.OrderTopology.order_topology_subbasis',axiom,
! [Vvar__0__X__69669,Vvar__1__R__69670,Vvar__1___24Anonymous__69671] :
( cType___24t(Vvar__0__X__69669)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__X__69669,Vvar__1__R__69670)
=> ( c_24__type__69692___24t(Vvar__0__X__69669,Vvar__1__R__69670,Vvar__1___24Anonymous__69671,Vvar__1___24Anonymous__69671)
=> ( cTopology_2eOrderTopology_2eorder__topology__subbasis___24a3(Vvar__0__X__69669,Vvar__1__R__69670,Vvar__1___24Anonymous__69671)
=> ( ? [Vvar__2__x__69677] :
( t(Vvar__2__x__69677,Vvar__0__X__69669)
& Vvar__1___24Anonymous__69671 = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(Vvar__0__X__69669,c_24__lam__69700___24a4(Vvar__0__X__69669,Vvar__1__R__69670,Vvar__1___24Anonymous__69671,Vvar__2__x__69677)) )
| ? [Vvar__2__x__69683] :
( t(Vvar__2__x__69683,Vvar__0__X__69669)
& Vvar__1___24Anonymous__69671 = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(Vvar__0__X__69669,c_24__lam__69707___24a4(Vvar__0__X__69669,Vvar__1__R__69670,Vvar__1___24Anonymous__69671,Vvar__2__x__69683)) ) ) ) ) ) ) ).
fof('$_inversion_Topology.Subbases.subbasis',axiom,
! [Vvar__0__X__70114,Vvar__1__SB__70115] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__70114)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__70114),Vvar__1__SB__70115)
=> ( cTopology_2eSubbases_2esubbasis___24a2(Vvar__0__X__70114,Vvar__1__SB__70115)
=> ( ! [Vvar__var__var__var__2__U__70120__70122__70141__70143] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__70114),Vvar__var__var__var__2__U__70120__70122__70141__70143)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__70114)),Vvar__1__SB__70115,Vvar__var__var__var__2__U__70120__70122__70141__70143)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(Vvar__0__X__70114,Vvar__var__var__var__2__U__70120__70122__70141__70143) ) )
& ! [Vvar__var__var__var__3__U__70125__70133__70145__70153] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__70114),Vvar__var__var__var__3__U__70125__70133__70145__70153)
=> ! [Vvar__var__var__var__4__x__70126__70134__70146__70154] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__70114,Vvar__var__var__var__4__x__70126__70134__70146__70154)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__70114),Vvar__var__var__var__3__U__70125__70133__70145__70153,Vvar__var__var__var__4__x__70126__70134__70146__70154)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(Vvar__0__X__70114,Vvar__var__var__var__3__U__70125__70133__70145__70153)
=> ? [Vvar__var__var__var__7__A__70127__70135__70147__70155] :
( cType___24t(Vvar__var__var__var__7__A__70127__70135__70147__70155)
& cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(Vvar__var__var__var__7__A__70127__70135__70147__70155)
& ? [Vvar__var__var__var__8__V__70129__70137__70149__70157] :
( c_24__type__70166___24t(Vvar__0__X__70114,Vvar__1__SB__70115,Vvar__var__var__var__7__A__70127__70135__70147__70155,Vvar__var__var__var__8__V__70129__70137__70149__70157)
& ! [Vvar__var__var__var__9__a__70130__70138__70150__70158] :
( t(Vvar__var__var__var__9__a__70130__70138__70150__70158,Vvar__var__var__var__7__A__70127__70135__70147__70155)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__70114)),Vvar__1__SB__70115,happ(Vvar__var__var__var__8__V__70129__70137__70149__70157,Vvar__var__var__var__9__a__70130__70138__70150__70158)) )
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__70114),cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(Vvar__var__var__var__7__A__70127__70135__70147__70155,cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__70114),Vvar__var__var__var__8__V__70129__70137__70149__70157),Vvar__var__var__var__4__x__70126__70134__70146__70154)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__70114),cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(Vvar__var__var__var__7__A__70127__70135__70147__70155,cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__70114),Vvar__var__var__var__8__V__70129__70137__70149__70157),Vvar__var__var__var__3__U__70125__70133__70145__70153) ) ) ) ) ) )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Topology.TopologicalSpaces.TopologicalSpace',axiom,
! [VX350] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(VX350)
=> ? [Vvar__0__point__set__351] :
( cType___24t(Vvar__0__point__set__351)
& ? [Vvar__1__open__352] :
( c_24__type__375___24t(Vvar__0__point__set__351,Vvar__1__open__352)
& ! [Vvar__var__2__F__356__360] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__point__set__351,Vvar__var__2__F__356__360)
=> ( ! [Vvar__var__3__S__357__361] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__351,Vvar__var__3__S__357__361)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__point__set__351),Vvar__var__2__F__356__360,Vvar__var__3__S__357__361)
=> p(happ(Vvar__1__open__352,Vvar__var__3__S__357__361)) ) )
=> p(happ(Vvar__1__open__352,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__point__set__351,Vvar__var__2__F__356__360))) ) )
& ! [Vvar__var__3__U__365__369] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__351,Vvar__var__3__U__365__369)
=> ! [Vvar__var__4__V__366__370] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__351,Vvar__var__4__V__366__370)
=> ( p(happ(Vvar__1__open__352,Vvar__var__3__U__365__369))
=> ( p(happ(Vvar__1__open__352,Vvar__var__4__V__366__370))
=> p(happ(Vvar__1__open__352,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__point__set__351,Vvar__var__3__U__365__369,Vvar__var__4__V__366__370))) ) ) ) )
& p(happ(Vvar__1__open__352,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__point__set__351)))
& VX350 = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__351,Vvar__1__open__352) ) ) ) ).
fof('$_inversion_Topology.WeakTopology.weak_topology_subbasis',axiom,
! [Vvar__0__X__64213,Vvar__1__A__64214,Vvar__2__Y__64215,Vvar__3__f__64218,Vvar__1___24Anonymous__64223] :
( cType___24t(Vvar__0__X__64213)
=> ( cType___24t(Vvar__1__A__64214)
=> ( c_24__type__64321___24t(Vvar__0__X__64213,Vvar__1__A__64214,Vvar__2__Y__64215,Vvar__3__f__64218,Vvar__1___24Anonymous__64223,Vvar__2__Y__64215)
=> ( c_24__type__64346___24t(Vvar__0__X__64213,Vvar__1__A__64214,Vvar__2__Y__64215,Vvar__3__f__64218,Vvar__1___24Anonymous__64223,Vvar__3__f__64218)
=> ( c_24__type__64365___24t(Vvar__0__X__64213,Vvar__1__A__64214,Vvar__2__Y__64215,Vvar__3__f__64218,Vvar__1___24Anonymous__64223,Vvar__1___24Anonymous__64223)
=> ( cTopology_2eWeakTopology_2eweak__topology__subbasis___24a5(Vvar__0__X__64213,Vvar__1__A__64214,Vvar__2__Y__64215,Vvar__3__f__64218,Vvar__1___24Anonymous__64223)
=> ? [Vvar__4__a__64237] :
( t(Vvar__4__a__64237,Vvar__1__A__64214)
& ? [Vvar__5__V__64238] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(happ(Vvar__2__Y__64215,Vvar__4__a__64237)),Vvar__5__V__64238)
& cTopology_2eTopologicalSpaces_2eopen___24a2(happ(Vvar__2__Y__64215,Vvar__4__a__64237),Vvar__5__V__64238)
& Vvar__1___24Anonymous__64223 = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(Vvar__0__X__64213,c_24__lam__64547___24a7(Vvar__0__X__64213,Vvar__1__A__64214,Vvar__2__Y__64215,Vvar__3__f__64218,Vvar__1___24Anonymous__64223,Vvar__4__a__64237,Vvar__5__V__64238)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.CountableTypes.CountableT',axiom,
! [Vvar__0__X__10648] :
( cType___24t(Vvar__0__X__10648)
=> ( cZornsLemma_2eCountableTypes_2eCountableT___24a1(Vvar__0__X__10648)
=> ? [Vvar__1__f__10651] :
( c_24__type__10657___24t(Vvar__0__X__10648,Vvar__1__f__10651)
& cZornsLemma_2eFunctionProperties_2einjective___24a3(Vvar__0__X__10648,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__f__10651)
& p(c_24True) ) ) ) ).
fof('$_inversion_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction',axiom,
! [Vvar__0__X__513,Vvar__1__P__514,Vvar__2__x__517] :
( cType___24t(Vvar__0__X__513)
=> ( c_24__type__529___24t(Vvar__0__X__513,Vvar__1__P__514,Vvar__2__x__517,Vvar__1__P__514)
=> ( t(Vvar__2__x__517,Vvar__0__X__513)
=> ( cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a3(Vvar__0__X__513,Vvar__1__P__514,Vvar__2__x__517)
=> ( p(happ(Vvar__1__P__514,Vvar__2__x__517))
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.Families.FamilyUnion',axiom,
! [Vvar__0__T__883,Vvar__1__F__884,Vvar__1___24Anonymous__885] :
( cType___24t(Vvar__0__T__883)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__T__883,Vvar__1__F__884)
=> ( t(Vvar__1___24Anonymous__885,Vvar__0__T__883)
=> ( cZornsLemma_2eFamilies_2eFamilyUnion___24a3(Vvar__0__T__883,Vvar__1__F__884,Vvar__1___24Anonymous__885)
=> ? [Vvar__2__S__889] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__T__883,Vvar__2__S__889)
& ? [Vvar__3__x__890] :
( t(Vvar__3__x__890,Vvar__0__T__883)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__T__883),Vvar__1__F__884,Vvar__2__S__889)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__T__883,Vvar__2__S__889,Vvar__3__x__890)
& Vvar__1___24Anonymous__885 = Vvar__3__x__890 ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.FiniteIntersections.finite_intersections',axiom,
! [Vvar__0__X__63716,Vvar__1__S__63717,Vvar__1___24Anonymous__63718] :
( cType___24t(Vvar__0__X__63716)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__X__63716,Vvar__1__S__63717)
=> ( c_24__type__63739___24t(Vvar__0__X__63716,Vvar__1__S__63717,Vvar__1___24Anonymous__63718,Vvar__1___24Anonymous__63718)
=> ( cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a3(Vvar__0__X__63716,Vvar__1__S__63717,Vvar__1___24Anonymous__63718)
=> ( Vvar__1___24Anonymous__63718 = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__X__63716)
| ? [Vvar__2__U__63726] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__63716,Vvar__2__U__63726)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__63716),Vvar__1__S__63717,Vvar__2__U__63726)
& Vvar__1___24Anonymous__63718 = Vvar__2__U__63726 )
| ? [Vvar__2__U__63730] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__63716,Vvar__2__U__63730)
& ? [Vvar__3__V__63731] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__63716,Vvar__3__V__63731)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__63716),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(Vvar__0__X__63716,Vvar__1__S__63717),Vvar__2__U__63730)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__63716),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(Vvar__0__X__63716,Vvar__1__S__63717),Vvar__3__V__63731)
& Vvar__1___24Anonymous__63718 = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__X__63716,Vvar__2__U__63730,Vvar__3__V__63731) ) ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.IndexedFamilies.IndexedIntersection',axiom,
! [Vvar__0__A__65303,Vvar__1__T__65304,Vvar__2__F__65305,Vvar__1___24Anonymous__65306] :
( cType___24t(Vvar__0__A__65303)
=> ( cType___24t(Vvar__1__T__65304)
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(Vvar__0__A__65303,Vvar__1__T__65304,Vvar__2__F__65305)
=> ( t(Vvar__1___24Anonymous__65306,Vvar__1__T__65304)
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a4(Vvar__0__A__65303,Vvar__1__T__65304,Vvar__2__F__65305,Vvar__1___24Anonymous__65306)
=> ? [Vvar__3__x__65311] :
( t(Vvar__3__x__65311,Vvar__1__T__65304)
& ! [Vvar__var__var__var__var__4__a__65313__65314__65315__65316__65317] :
( t(Vvar__var__var__var__var__4__a__65313__65314__65315__65316__65317,Vvar__0__A__65303)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__1__T__65304,happ(Vvar__2__F__65305,Vvar__var__var__var__var__4__a__65313__65314__65315__65316__65317),Vvar__3__x__65311) )
& Vvar__1___24Anonymous__65306 = Vvar__3__x__65311 ) ) ) ) ) ) ).
fof('$_lam_14596',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__14596___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ).
fof('$_lam_15052',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__15052___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ).
fof('$_lam_1755',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__1755___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__1683___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('$_lam_26270',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__26270___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_26274',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__26274___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1)) ) ) ).
fof('$_lam_284',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__284___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__1),Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ).
fof('$_lam_41709',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( c_24__lam__41709___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__6)),Vv__CANONICAL__5)) ) ).
fof('$_lam_4420',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( c_24__lam__4420___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__6)),Vv__CANONICAL__5)) ) ).
fof('$_lam_4435',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( c_24__lam__4435___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__6)),Vv__CANONICAL__5)) ) ).
fof('$_lam_4491',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__4491___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ) ).
fof('$_lam_4697',axiom,
! [Vv__CANONICAL__0] : c_24__lam__4697___24a1(Vv__CANONICAL__0) = cCoq_2emicromega_2eRMicromega_2eRWeakChecker___24a1(cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2eunit),cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2efst___24a2(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2eunit),Vv__CANONICAL__0)) ).
fof('$_lam_548',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__548___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__4),Vv__CANONICAL__3)) ) ).
fof('$_lam_5813',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__5813___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__5815___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_5815',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__5815___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ).
fof('$_lam_61712',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__61712___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eReals_2ePartSum_2eSP___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1) ).
fof('$_lam_624',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__624___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__5),Vv__CANONICAL__4)) ) ).
fof('$_lam_63032',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__63032___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ).
fof('$_lam_63142',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__63142___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( p(happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
& ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( p(happ(Vv__CANONICAL__0,Vv__CANONICAL__2))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_lam_63257',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__63257___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_6382',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__6382___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ).
fof('$_lam_64547',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] :
( c_24__lam__64547___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(c_24__case__Topology_2eTopologicalSpaces_2eTopologicalSpace_2464651___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__6,happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__5),Vv__CANONICAL__7)) ) ).
fof('$_lam_6461',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( c_24__lam__6461___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__6)),Vv__CANONICAL__5)) ) ).
fof('$_lam_6509',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__6509___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__2)
| cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__2,Vv__CANONICAL__1) ) ) ).
fof('$_lam_6593',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__6593___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__1) ).
fof('$_lam_68442',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__68442___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cTopology_2eDirectedSets_2eDS__ord___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ).
fof('$_lam_6873',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__6873___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ) ).
fof('$_lam_68792',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__68792___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0)) ) ).
fof('$_lam_69289',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__69289___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__2,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_69373',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( c_24__lam__69373___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
<=> ? [Vv__CANONICAL__7] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__3,Vv__CANONICAL__7)
& happ(Vv__CANONICAL__5,Vv__CANONICAL__7) = Vv__CANONICAL__6 ) ) ).
fof('$_lam_69387',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__69387___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(Vv__CANONICAL__2,happ(Vv__CANONICAL__5,Vv__CANONICAL__6)) ).
fof('$_lam_69423',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__69423___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ? [Vv__CANONICAL__5] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__2,Vv__CANONICAL__5)
& happ(Vv__CANONICAL__3,Vv__CANONICAL__5) = Vv__CANONICAL__4 ) ) ).
fof('$_lam_69435',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__69435___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__2,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_69700',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__69700___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
& Vv__CANONICAL__4 != Vv__CANONICAL__3 ) ) ).
fof('$_lam_69707',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__69707___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
& Vv__CANONICAL__4 != Vv__CANONICAL__3 ) ) ).
fof('$_lam_6987',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__6987___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0) ).
fof('$_lam_70066',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__70066___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(cCoq_2eReals_2eRsqrt__def_2edicho__lb___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3) ) ).
fof('$_lam_70086',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__70086___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(cCoq_2eReals_2eRsqrt__def_2edicho__up___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3) ) ).
fof('$_lam_7048',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__7048___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__7051___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__1) ).
fof('$_lam_7051',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__7051___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_7104',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__7104___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__4))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__4,Vv__CANONICAL__2))
& happ(Vv__CANONICAL__0,Vv__CANONICAL__4) = Vv__CANONICAL__3 ) ) ).
fof('$_lam_7140',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__7140___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__1) ).
fof('$_lam_7248',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__7248___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eAltSeries_2etg__alt___24a1(cCoq_2eReals_2eRatan_2eRatan__seq___24a1(Vv__CANONICAL__1)),Vv__CANONICAL__0) ).
fof('$_lam_7275',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__7275___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRaxioms_2eis__lub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ).
fof('$_lam_72851',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__72851___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0)) ) ).
fof('$_lam_72876',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__72876___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0)) ) ).
fof('$_lam_73344',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__73344___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1)) ) ) ).
fof('$_lam_7680',axiom,
! [Vv__CANONICAL__0] : c_24__lam__7680___24a1(Vv__CANONICAL__0) = cCoq_2eReals_2eRIneq_2epos___24a1(cCoq_2eReals_2eRiemannInt_2eRinvN___24a1(Vv__CANONICAL__0)) ).
fof('$_lam_7856',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__7856___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__5),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__5))) ).
fof('$_lam_78771',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__78771___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ).
fof('$_lam_78784',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__78784___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ).
fof('$_lam_78791',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__78791___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_78796',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__78796___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_78820',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__78820___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ? [Vv__CANONICAL__5] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__2,Vv__CANONICAL__5)
& happ(Vv__CANONICAL__3,Vv__CANONICAL__5) = Vv__CANONICAL__4 ) ) ).
fof('$_lam_78832',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__78832___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__2,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_78897',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] : c_24__lam__78897___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__6),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)) ).
fof('$_lam_78940',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] : c_24__lam__78940___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__6),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)) ).
fof('$_lam_79168',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__79168___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__2,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_79311',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__79311___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__79313___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_79313',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__79313___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ).
fof('$_lam_7932',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__7932___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) ) ).
fof('$_lam_79320',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__79320___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__5815___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2) ) ).
fof('$_lam_79419',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__79419___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__2) ) ).
fof('$_lam_79426',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__79426___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRtrigo__def_2esin__n___24a1(Vv__CANONICAL__1),cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_7944',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__7944___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_824',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__824___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ) ).
fof('$_lam_8348',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__8348___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRiemannInt__SF_2efe___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_901',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__901___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__2) ) ) ).
fof('$_lam_9336',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__9336___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2eReals_2eRtrigo__def_2eexp___24a1(Vv__CANONICAL__1) ) ).
fof('$_lam_9366',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__9366___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_9551',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__9551___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2))
& happ(Vv__CANONICAL__0,Vv__CANONICAL__3) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('$_lam_9584',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__9584___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__1))
& Vv__CANONICAL__0 = cCoq_2eReals_2eRIneq_2eRsqr___24a1(Vv__CANONICAL__1) ) ) ).
fof('$_lam_9818',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__9818___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRtrigo__def_2eexp__in___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ).
fof('$_lam_9820',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__9820___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRtrigo__def_2ecos__n___24a1(Vv__CANONICAL__1),cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_9826',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__9826___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRtrigo__def_2ecos__in___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ).
fof('$_lam_9839',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__9839___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRtrigo__def_2ecos__in___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_9854',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__9854___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRtrigo__def_2esin__in___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_9869',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__9869___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ).
fof('$_lam_9942',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__9942___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_9949',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__9949___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_prop_10051',axiom,
! [V0__C] :
( p(c_24__prop__10051___24a1(V0__C))
<=> ~ p(V0__C) ) ).
fof('$_prop_10055',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__10055___24a1(Vv__CANONICAL__0))
<=> ~ p(Vv__CANONICAL__0) ) ).
fof('$_prop_10056',axiom,
! [V0__C] :
( p(c_24__prop__10056___24a1(V0__C))
<=> ~ p(V0__C) ) ).
fof('$_prop_14634',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__14634___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_14642',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__14642___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_14643',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__14643___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_4704',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__4704___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_61722',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__61722___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_61735',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3] :
( p(c_24__prop__61735___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3)) ) ) ).
fof('$_prop_61736',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__61736___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__1))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_prop_6638',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__6638___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_7284',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__7284___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_7285',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__7285___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_791',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__791___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_792',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__792___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_8087',axiom,
! [V0__a,V1__b] :
( p(c_24__prop__8087___24a2(V0__a,V1__b))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b)) ) ).
fof('$_prop_8088',axiom,
! [V0__a,V1__b] :
( p(c_24__prop__8088___24a2(V0__a,V1__b))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b)) ) ).
fof('$_type_10015',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10016] :
( c_24__type__10015___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10016)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__10016,Vv__CANONICAL__2)) ) ) ).
fof('$_type_10019',axiom,
! [Vvar__10020] :
( c_24__type__10019___24t(Vvar__10020)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10022___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__10020,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10022',axiom,
! [Vv__CANONICAL__0,Vvar__10023] :
( c_24__type__10022___24t(Vv__CANONICAL__0,Vvar__10023)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__10023,Vv__CANONICAL__1)) ) ) ).
fof('$_type_10039',axiom,
! [Vvar__10040] :
( c_24__type__10039___24t(Vvar__10040)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10022___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__10040,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_10053',axiom,
! [Vv__CANONICAL__0,Vvar__10054] :
( c_24__type__10053___24t(Vv__CANONICAL__0,Vvar__10054)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,c_24__prop__10055___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__10054,Vv__CANONICAL__1)) ) ) ).
fof('$_type_10068',axiom,
! [Vvar__10069] :
( c_24__type__10068___24t(Vvar__10069)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__10069,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_10085',axiom,
! [Vvar__10086] :
( c_24__type__10085___24t(Vvar__10086)
<=> ! [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)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__10086,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_10087',axiom,
! [Vvar__10088] :
( c_24__type__10087___24t(Vvar__10088)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(Vvar__10088,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10100',axiom,
! [Vvar__10101] :
( c_24__type__10100___24t(Vvar__10101)
<=> ! [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__10101,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10114',axiom,
! [Vvar__10115] :
( c_24__type__10114___24t(Vvar__10115)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__10115,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10121',axiom,
! [Vvar__10122] :
( c_24__type__10121___24t(Vvar__10122)
<=> ! [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__10122,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10124',axiom,
! [Vvar__10125] :
( c_24__type__10124___24t(Vvar__10125)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__10125,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10126',axiom,
! [Vvar__10127] :
( c_24__type__10126___24t(Vvar__10127)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__10127,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10134',axiom,
! [Vvar__10135] :
( c_24__type__10134___24t(Vvar__10135)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__10135,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10517',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10518] :
( c_24__type__10517___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10518)
<=> ! [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__10518,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_10657',axiom,
! [Vv__CANONICAL__0,Vvar__10658] :
( c_24__type__10657___24t(Vv__CANONICAL__0,Vvar__10658)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__10658,Vv__CANONICAL__1)) ) ) ).
fof('$_type_10713',axiom,
! [Vvar__10714] :
( c_24__type__10713___24t(Vvar__10714)
<=> ! [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__10714,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10731',axiom,
! [Vvar__10732] :
( c_24__type__10731___24t(Vvar__10732)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__10732,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1100',axiom,
! [Vvar__1101] :
( c_24__type__1100___24t(Vvar__1101)
<=> ! [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__1101,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11029',axiom,
! [Vvar__11030] :
( c_24__type__11029___24t(Vvar__11030)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__11030,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1105',axiom,
! [Vvar__1106] :
( c_24__type__1105___24t(Vvar__1106)
<=> ! [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__1106,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1111',axiom,
! [Vvar__1112] :
( c_24__type__1111___24t(Vvar__1112)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__1112,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1134',axiom,
! [Vvar__1135] :
( c_24__type__1134___24t(Vvar__1135)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__1135,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1184',axiom,
! [Vvar__1185] :
( c_24__type__1184___24t(Vvar__1185)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__1185,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1189',axiom,
! [Vvar__1190] :
( c_24__type__1189___24t(Vvar__1190)
<=> ! [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__1190,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1197',axiom,
! [Vvar__1198] :
( c_24__type__1197___24t(Vvar__1198)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__1198,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_13083',axiom,
! [Vvar__13084] :
( c_24__type__13083___24t(Vvar__13084)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__91___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__13084,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1443',axiom,
! [Vvar__1444] :
( c_24__type__1443___24t(Vvar__1444)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__1444,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1446',axiom,
! [Vvar__1447] :
( c_24__type__1446___24t(Vvar__1447)
<=> ! [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__1447,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1451',axiom,
! [Vvar__1452] :
( c_24__type__1451___24t(Vvar__1452)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1452,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14603',axiom,
! [Vvar__14604] :
( c_24__type__14603___24t(Vvar__14604)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__6580___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__14604,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14632',axiom,
! [Vvar__14633] :
( c_24__type__14632___24t(Vvar__14633)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__14634___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__14633,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14636',axiom,
! [Vvar__14637] :
( c_24__type__14636___24t(Vvar__14637)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(happ(Vvar__14637,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14640',axiom,
! [Vvar__14641] :
( c_24__type__14640___24t(Vvar__14641)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__14642___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__14643___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__14641,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14645',axiom,
! [Vvar__14646] :
( c_24__type__14645___24t(Vvar__14646)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__0))
=> cCoq_2eReals_2eRIneq_2enonnegreal___24t(happ(Vvar__14646,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_14657',axiom,
! [Vvar__14658] :
( c_24__type__14657___24t(Vvar__14658)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__14658,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14727',axiom,
! [Vvar__14728] :
( c_24__type__14727___24t(Vvar__14728)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRanalysis1_2eDifferential___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__14728,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14744',axiom,
! [Vvar__14745] :
( c_24__type__14744___24t(Vvar__14745)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__795___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2emult__fct___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__14745,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_14748',axiom,
! [Vvar__14749] :
( c_24__type__14748___24t(Vvar__14749)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRanalysis1_2ederivable___24t(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(Vv__CANONICAL__0),happ(Vvar__14749,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14798',axiom,
! [Vvar__14799] :
( c_24__type__14798___24t(Vvar__14799)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7308___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__14805___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__14812___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__14799,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ) ) ) ) ).
fof('$_type_14805',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14806] :
( c_24__type__14805___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14806)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(Vvar__14806,happ(Vv__CANONICAL__2,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14812',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14813] :
( c_24__type__14812___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14813)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0))
=> t(Vvar__14813,happ(Vv__CANONICAL__2,Vv__CANONICAL__1)) ) ) ).
fof('$_type_15009',axiom,
! [Vvar__15010] :
( c_24__type__15009___24t(Vvar__15010)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__15010,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_15012',axiom,
! [Vvar__15013] :
( c_24__type__15012___24t(Vvar__15013)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__15013,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15033',axiom,
! [Vvar__15034] :
( c_24__type__15033___24t(Vvar__15034)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__4)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__4))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__4,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__4) ) )
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(Vvar__15034,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ).
fof('$_type_15047',axiom,
! [Vvar__15048] :
( c_24__type__15047___24t(Vvar__15048)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(c_24__lam__15052___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(Vvar__15048,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_15091',axiom,
! [Vvar__15092] :
( c_24__type__15091___24t(Vvar__15092)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__4)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__4))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__4,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__4) ) )
=> ! [Vv__CANONICAL__5] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__5)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__5))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__5,Vv__CANONICAL__2))
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,happ(happ(happ(happ(Vvar__15092,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_15123',axiom,
! [Vvar__15124] :
( c_24__type__15123___24t(Vvar__15124)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> ! [Vv__CANONICAL__6] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__7)
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__15124,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_15140',axiom,
! [Vvar__15141] :
( c_24__type__15140___24t(Vvar__15141)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__15141,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_15157',axiom,
! [Vvar__15158] :
( c_24__type__15157___24t(Vvar__15158)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__15158,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_15203',axiom,
! [Vvar__15204] :
( c_24__type__15203___24t(Vvar__15204)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__5979___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__15204,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15225',axiom,
! [Vvar__15226] :
( c_24__type__15225___24t(Vvar__15226)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__15226,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_15255',axiom,
! [Vvar__15256] :
( c_24__type__15255___24t(Vvar__15256)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> ! [Vv__CANONICAL__6] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__7)
=> cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__15256,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_15272',axiom,
! [Vvar__15273] :
( c_24__type__15272___24t(Vvar__15273)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__15273,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_15289',axiom,
! [Vvar__15290] :
( c_24__type__15289___24t(Vvar__15290)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__15290,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_15306',axiom,
! [Vvar__15307] :
( c_24__type__15306___24t(Vvar__15307)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
=> cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__15307,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_162',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__163] :
( c_24__type__162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__163)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__163,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_1647',axiom,
! [Vvar__1648] :
( c_24__type__1647___24t(Vvar__1648)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1661___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1665___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__1670___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1679___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__1648,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1652',axiom,
! [Vv__CANONICAL__0,Vvar__1653] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vvar__1653)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1653,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1661',axiom,
! [Vv__CANONICAL__0,Vvar__1662] :
( c_24__type__1661___24t(Vv__CANONICAL__0,Vvar__1662)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__1662,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_1665',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1666] :
( c_24__type__1665___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1666)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__1666,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_1670',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1671] :
( c_24__type__1670___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1671)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__1671,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_1679',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1680] :
( c_24__type__1679___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1680)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__1680,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1887',axiom,
! [Vvar__1888] :
( c_24__type__1887___24t(Vvar__1888)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1661___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1902___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1907___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__1888,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1902',axiom,
! [Vv__CANONICAL__0,Vvar__1903] :
( c_24__type__1902___24t(Vv__CANONICAL__0,Vvar__1903)
<=> ! [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__1903,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1907',axiom,
! [Vv__CANONICAL__0,Vvar__1908] :
( c_24__type__1907___24t(Vv__CANONICAL__0,Vvar__1908)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__1908,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_20',axiom,
! [Vvar__21] :
( c_24__type__20___24t(Vvar__21)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__25___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__28___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__21,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2067',axiom,
! [Vvar__2068] :
( c_24__type__2067___24t(Vvar__2068)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1661___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1902___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1907___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__2068,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_217',axiom,
! [Vvar__218] :
( c_24__type__217___24t(Vvar__218)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__222___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__218,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_222',axiom,
! [Vv__CANONICAL__0,Vvar__223] :
( c_24__type__222___24t(Vv__CANONICAL__0,Vvar__223)
<=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__223,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_2467',axiom,
! [Vvar__2468] :
( c_24__type__2467___24t(Vvar__2468)
<=> ! [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__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1661___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__2484___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1665___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__1670___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__1679___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__2501___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__2468,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),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('$_type_2484',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2485] :
( c_24__type__2484___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2485)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2485,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_25',axiom,
! [Vv__CANONICAL__0,Vvar__26] :
( c_24__type__25___24t(Vv__CANONICAL__0,Vvar__26)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__26,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_2501',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2502] :
( c_24__type__2501___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2502)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__2502,Vv__CANONICAL__3)) ) ) ).
fof('$_type_2506',axiom,
! [Vvar__2507] :
( c_24__type__2506___24t(Vvar__2507)
<=> ! [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__2507,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2522',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2523] :
( c_24__type__2522___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2523)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2523,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2526',axiom,
! [Vvar__2527] :
( c_24__type__2526___24t(Vvar__2527)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2527,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2544',axiom,
! [Vvar__2545] :
( c_24__type__2544___24t(Vvar__2545)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__2545,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_2615',axiom,
! [Vvar__2616] :
( c_24__type__2615___24t(Vvar__2616)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2616,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2618',axiom,
! [Vvar__2619] :
( c_24__type__2618___24t(Vvar__2619)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2619,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2621',axiom,
! [Vvar__2622] :
( c_24__type__2621___24t(Vvar__2622)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__2622,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2636',axiom,
! [Vvar__2637] :
( c_24__type__2636___24t(Vvar__2637)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__2637,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2640',axiom,
! [Vvar__2641] :
( c_24__type__2640___24t(Vvar__2641)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__2641,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26572',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26573] :
( c_24__type__26572___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26573)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__26573,Vv__CANONICAL__3)) ) ) ).
fof('$_type_26580',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26581] :
( c_24__type__26580___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26581)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cType___24t(happ(Vvar__26581,Vv__CANONICAL__3)) ) ) ).
fof('$_type_26602',axiom,
! [Vvar__26603] :
( c_24__type__26602___24t(Vvar__26603)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10022___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__26608___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__26620___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__26603,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_26608',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26609] :
( c_24__type__26608___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26609)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__26609,Vv__CANONICAL__2)) ) ) ).
fof('$_type_26620',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26621] :
( c_24__type__26620___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26621)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(Vvar__26621,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexistT___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ).
fof('$_type_26692',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26693] :
( c_24__type__26692___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26693)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__26693,Vv__CANONICAL__2)) ) ) ).
fof('$_type_26698',axiom,
! [Vvar__26699] :
( c_24__type__26698___24t(Vvar__26699)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10022___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__26699,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_2671',axiom,
! [Vvar__2672] :
( c_24__type__2671___24t(Vvar__2672)
<=> ! [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__2672,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26715',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26716] :
( c_24__type__26715___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26716)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__26716,Vv__CANONICAL__2)) ) ) ).
fof('$_type_26721',axiom,
! [Vvar__26722] :
( c_24__type__26721___24t(Vvar__26722)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10022___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__26722,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2eprojT1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_type_26727',axiom,
! [Vvar__26728] :
( c_24__type__26727___24t(Vvar__26728)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__26728,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_26732',axiom,
! [Vvar__26733] :
( c_24__type__26732___24t(Vvar__26733)
<=> ! [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__26733,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_26753',axiom,
! [Vvar__26754] :
( c_24__type__26753___24t(Vvar__26754)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(Vvar__26754,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_26765',axiom,
! [Vvar__26766] :
( c_24__type__26765___24t(Vvar__26766)
<=> ! [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_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__26766,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_27271',axiom,
! [Vvar__27272] :
( c_24__type__27271___24t(Vvar__27272)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__27272,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2738',axiom,
! [Vvar__2739] :
( c_24__type__2738___24t(Vvar__2739)
<=> ! [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__2739,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28',axiom,
! [Vv__CANONICAL__0,Vvar__29] :
( c_24__type__28___24t(Vv__CANONICAL__0,Vvar__29)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__29,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_2824',axiom,
! [Vvar__2825] :
( c_24__type__2824___24t(Vvar__2825)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__2825,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2840',axiom,
! [Vvar__2841] :
( c_24__type__2840___24t(Vvar__2841)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__2841,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2852',axiom,
! [Vvar__2853] :
( c_24__type__2852___24t(Vvar__2853)
<=> ! [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__2853,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2882',axiom,
! [Vvar__2883] :
( c_24__type__2882___24t(Vvar__2883)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__2883,Vv__CANONICAL__0)) ) ) ).
fof('$_type_291',axiom,
! [Vvar__292] :
( c_24__type__291___24t(Vvar__292)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__292,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2912',axiom,
! [Vvar__2913] :
( c_24__type__2912___24t(Vvar__2913)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cTopology_2eDirectedSets_2eDS__set___24a1(Vv__CANONICAL__0),happ(Vvar__2913,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2916',axiom,
! [Vvar__2917] :
( c_24__type__2916___24t(Vvar__2917)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2919___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2917,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2919',axiom,
! [Vv__CANONICAL__0,Vvar__2920] :
( c_24__type__2919___24t(Vv__CANONICAL__0,Vvar__2920)
<=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__2920,Vv__CANONICAL__1)) ) ) ).
fof('$_type_294',axiom,
! [Vvar__295] :
( c_24__type__294___24t(Vvar__295)
<=> ! [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__295,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_297',axiom,
! [Vvar__298] :
( c_24__type__297___24t(Vvar__298)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__298,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_302',axiom,
! [Vvar__303] :
( c_24__type__302___24t(Vvar__303)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__303,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3088',axiom,
! [Vvar__3089] :
( c_24__type__3088___24t(Vvar__3089)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__3089,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3091',axiom,
! [Vvar__3092] :
( c_24__type__3091___24t(Vvar__3092)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__3092,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3096',axiom,
! [Vvar__3097] :
( c_24__type__3096___24t(Vvar__3097)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__3097,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_318',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__319] :
( c_24__type__318___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__319)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__319,Vv__CANONICAL__2)) ) ) ).
fof('$_type_324',axiom,
! [Vvar__325] :
( c_24__type__324___24t(Vvar__325)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__325,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_327',axiom,
! [Vv__CANONICAL__0,Vvar__328] :
( c_24__type__327___24t(Vv__CANONICAL__0,Vvar__328)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__328,Vv__CANONICAL__1)) ) ) ).
fof('$_type_330',axiom,
! [Vvar__331] :
( c_24__type__330___24t(Vvar__331)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__332___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__331,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_332',axiom,
! [Vvar__333] :
( c_24__type__332___24t(Vvar__333)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__333,Vv__CANONICAL__0)) ) ) ).
fof('$_type_334',axiom,
! [Vvar__335] :
( c_24__type__334___24t(Vvar__335)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__332___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__335,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3429',axiom,
! [Vvar__3430] :
( c_24__type__3429___24t(Vvar__3430)
<=> ! [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__3430,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3432',axiom,
! [Vvar__3433] :
( c_24__type__3432___24t(Vvar__3433)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__3433,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3437',axiom,
! [Vvar__3438] :
( c_24__type__3437___24t(Vvar__3438)
<=> ! [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__3438,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3699',axiom,
! [Vvar__3700] :
( c_24__type__3699___24t(Vvar__3700)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1661___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1661___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__1665___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1670___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__1679___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__9,Vv__CANONICAL__15)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__3700,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_3747',axiom,
! [Vvar__3748] :
( c_24__type__3747___24t(Vvar__3748)
<=> ! [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__3748,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_375',axiom,
! [Vv__CANONICAL__0,Vvar__376] :
( c_24__type__375___24t(Vv__CANONICAL__0,Vvar__376)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__376,Vv__CANONICAL__1)) ) ) ).
fof('$_type_3758',axiom,
! [Vvar__3759] :
( c_24__type__3758___24t(Vvar__3759)
<=> ! [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__3759,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3778',axiom,
! [Vvar__3779] :
( c_24__type__3778___24t(Vvar__3779)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__3779,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3997',axiom,
! [Vvar__3998] :
( c_24__type__3997___24t(Vvar__3998)
<=> ! [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__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1661___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__4012___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__1665___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1670___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1679___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__3998,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),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('$_type_4012',axiom,
! [Vv__CANONICAL__0,Vvar__4013] :
( c_24__type__4012___24t(Vv__CANONICAL__0,Vvar__4013)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__4013,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_4258',axiom,
! [Vvar__4259] :
( c_24__type__4258___24t(Vvar__4259)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4263___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__4259,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4263',axiom,
! [Vv__CANONICAL__0,Vvar__4264] :
( c_24__type__4263___24t(Vv__CANONICAL__0,Vvar__4264)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__4264,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_4385',axiom,
! [Vvar__4386] :
( c_24__type__4385___24t(Vvar__4386)
<=> ! [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__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1652___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1661___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1902___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1907___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__10)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__4386,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_4472',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4473] :
( c_24__type__4472___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4473)
<=> ! [Vv__CANONICAL__2] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,happ(Vvar__4473,Vv__CANONICAL__2)) ) ) ).
fof('$_type_4475',axiom,
! [Vvar__4476] :
( c_24__type__4475___24t(Vvar__4476)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__4476,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4494',axiom,
! [Vvar__4495] :
( c_24__type__4494___24t(Vvar__4495)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4495,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4505',axiom,
! [Vvar__4506] :
( c_24__type__4505___24t(Vvar__4506)
<=> ! [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__4506,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4509',axiom,
! [Vv__CANONICAL__0,Vvar__4510] :
( c_24__type__4509___24t(Vv__CANONICAL__0,Vvar__4510)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__4510,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_4531',axiom,
! [Vvar__4532] :
( c_24__type__4531___24t(Vvar__4532)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__4532,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4543',axiom,
! [Vvar__4544] :
( c_24__type__4543___24t(Vvar__4544)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__4544,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_462',axiom,
! [Vvar__463] :
( c_24__type__462___24t(Vvar__463)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__463,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4690',axiom,
! [Vvar__4691] :
( c_24__type__4690___24t(Vvar__4691)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__4691,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4692',axiom,
! [Vvar__4693] :
( c_24__type__4692___24t(Vvar__4693)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__4693,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4699',axiom,
! [Vvar__4700] :
( c_24__type__4699___24t(Vvar__4700)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eTauto_2eBFormula___24t(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eRMicromega_2eRWitness,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__4700,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_470',axiom,
! [Vvar__471] :
( c_24__type__470___24t(Vvar__471)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__471,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4702',axiom,
! [Vvar__4703] :
( c_24__type__4702___24t(Vvar__4703)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__4704___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eReals_2eRdefinitions_2eRgt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__4703,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_484',axiom,
! [Vvar__485] :
( c_24__type__484___24t(Vvar__485)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__485,Vv__CANONICAL__0)) ) ) ).
fof('$_type_489',axiom,
! [Vvar__490] :
( c_24__type__489___24t(Vvar__490)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__490,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_495',axiom,
! [Vvar__496] :
( c_24__type__495___24t(Vvar__496)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__496,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_500',axiom,
! [Vvar__501] :
( c_24__type__500___24t(Vvar__501)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__501,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5104',axiom,
! [Vvar__5105] :
( c_24__type__5104___24t(Vvar__5105)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1902___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__5105,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_5113',axiom,
! [Vvar__5114] :
( c_24__type__5113___24t(Vvar__5114)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__5115___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__5114,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5115',axiom,
! [Vvar__5116] :
( c_24__type__5115___24t(Vvar__5116)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__5116,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5117',axiom,
! [Vvar__5118] :
( c_24__type__5117___24t(Vvar__5118)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__5115___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5118,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5163',axiom,
! [Vvar__5164] :
( c_24__type__5163___24t(Vvar__5164)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__5164,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5193',axiom,
! [Vvar__5194] :
( c_24__type__5193___24t(Vvar__5194)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__5194,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5267',axiom,
! [Vvar__5268] :
( c_24__type__5267___24t(Vvar__5268)
<=> ! [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__5268,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_529',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__530] :
( c_24__type__529___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__530)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__530,Vv__CANONICAL__3)) ) ) ).
fof('$_type_534',axiom,
! [Vvar__535] :
( c_24__type__534___24t(Vvar__535)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__535,Vv__CANONICAL__0)) ) ) ).
fof('$_type_558',axiom,
! [Vvar__559] :
( c_24__type__558___24t(Vvar__559)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__25___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__559,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_5671',axiom,
! [Vvar__5672] :
( c_24__type__5671___24t(Vvar__5672)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__5672,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_5694',axiom,
! [Vvar__5695] :
( c_24__type__5694___24t(Vvar__5695)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__3,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(happ(Vvar__5695,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_5735',axiom,
! [Vvar__5736] :
( c_24__type__5735___24t(Vvar__5736)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(happ(Vvar__5736,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5743',axiom,
! [Vvar__5744] :
( c_24__type__5743___24t(Vvar__5744)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__5744,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_5774',axiom,
! [Vvar__5775] :
( c_24__type__5774___24t(Vvar__5775)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__5775,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_5817',axiom,
! [Vvar__5818] :
( c_24__type__5817___24t(Vvar__5818)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__5115___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__5818,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5851',axiom,
! [Vvar__5852] :
( c_24__type__5851___24t(Vvar__5852)
<=> ! [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__5852,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5864',axiom,
! [Vvar__5865] :
( c_24__type__5864___24t(Vvar__5865)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__5865,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5948',axiom,
! [Vvar__5949] :
( c_24__type__5948___24t(Vvar__5949)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5952___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__5949,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_5952',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5953] :
( c_24__type__5952___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5953)
<=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,happ(Vvar__5953,Vv__CANONICAL__2)) ) ) ).
fof('$_type_5979',axiom,
! [Vvar__5980] :
( c_24__type__5979___24t(Vvar__5980)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5980,Vv__CANONICAL__0)) ) ) ).
fof('$_type_601',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__602] :
( c_24__type__601___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__602)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__602,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_6038',axiom,
! [Vvar__6039] :
( c_24__type__6038___24t(Vvar__6039)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__6039,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6052',axiom,
! [Vvar__6053] :
( c_24__type__6052___24t(Vvar__6053)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__6053,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6058',axiom,
! [Vvar__6059] :
( c_24__type__6058___24t(Vvar__6059)
<=> ! [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__6059,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_612',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__613] :
( c_24__type__612___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__613)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__613,Vv__CANONICAL__4)) ) ) ).
fof('$_type_61720',axiom,
! [Vvar__61721] :
( c_24__type__61720___24t(Vvar__61721)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__61722___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__61721,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_61733',axiom,
! [Vvar__61734] :
( c_24__type__61733___24t(Vvar__61734)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)) )
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__61735___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3),c_24__prop__61736___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(Vvar__61734,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ).
fof('$_type_61740',axiom,
! [Vvar__61741] :
( c_24__type__61740___24t(Vvar__61741)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRIneq_2enegreal___24t(happ(Vvar__61741,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_61768',axiom,
! [Vvar__61769] :
( c_24__type__61768___24t(Vvar__61769)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__795___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eReals_2eRanalysis1_2ederivable___24t(cCoq_2eReals_2eRanalysis1_2eminus__fct___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__61769,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_61790',axiom,
! [Vvar__61791] :
( c_24__type__61790___24t(Vvar__61791)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1)) )
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2eid,Vv__CANONICAL__2,happ(happ(happ(Vvar__61791,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_61844',axiom,
! [Vvar__61845] :
( c_24__type__61844___24t(Vvar__61845)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) ) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__9551___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__61845,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ) ) ).
fof('$_type_62162',axiom,
! [Vvar__62163] :
( c_24__type__62162___24t(Vvar__62163)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__795___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__4))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__3))) )
=> ( ! [Vv__CANONICAL__7] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__7)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__7))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__7,happ(Vv__CANONICAL__0,Vv__CANONICAL__3)))
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__7) = cCoq_2eReals_2eRanalysis1_2eid___24a1(Vv__CANONICAL__7) ) ) )
=> ( ! [Vv__CANONICAL__8] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__8)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__8))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__8,happ(Vv__CANONICAL__0,Vv__CANONICAL__3)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,Vv__CANONICAL__8)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__1,Vv__CANONICAL__8),Vv__CANONICAL__3)) ) ) ) )
=> ( ! [Vv__CANONICAL__9] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__10)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__2,Vv__CANONICAL__9))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__9,Vv__CANONICAL__10))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__10,Vv__CANONICAL__3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__9),happ(Vv__CANONICAL__0,Vv__CANONICAL__10))) ) ) ) ) )
=> ! [Vv__CANONICAL__10] :
( c_24__type__62182___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__10)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__4),happ(happ(happ(happ(happ(happ(Vvar__62163,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__10)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_62182',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__62183] :
( c_24__type__62182___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__62183)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,happ(Vvar__62183,Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_62517',axiom,
! [Vvar__62518] :
( c_24__type__62517___24t(Vvar__62518)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__5115___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRseries_2eCauchy__crit___24a1(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__9869___24a1(Vv__CANONICAL__0),happ(Vvar__62518,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_63133',axiom,
! [Vvar__63134] :
( c_24__type__63133___24t(Vvar__63134)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__5979___24t(Vv__CANONICAL__0)
=> ( ? [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
& p(happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) )
=> ( cCoq_2eReals_2eRiemannInt__SF_2eNbound___24a1(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2enat,c_24__lam__63142___24a1(Vv__CANONICAL__0),happ(Vvar__63134,Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_type_63157',axiom,
! [Vvar__63158] :
( c_24__type__63157___24t(Vvar__63158)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(cCoq_2eReals_2eRiemannInt__SF_2efe___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__63158,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_63274',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__63275] :
( c_24__type__63274___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__63275)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__63275,Vv__CANONICAL__2)) ) ) ).
fof('$_type_63280',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__63281] :
( c_24__type__63280___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__63281)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__63281,Vv__CANONICAL__2)) ) ) ).
fof('$_type_63308',axiom,
! [Vvar__63309] :
( c_24__type__63308___24t(Vvar__63309)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__63312___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__63319___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__63326___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__63309,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_63312',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__63313] :
( c_24__type__63312___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__63313)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__63313,Vv__CANONICAL__2)) ) ) ).
fof('$_type_63319',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__63320] :
( c_24__type__63319___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__63320)
<=> ( p(Vv__CANONICAL__0)
=> t(Vvar__63320,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_63326',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__63327] :
( c_24__type__63326___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__63327)
<=> ( p(Vv__CANONICAL__1)
=> t(Vvar__63327,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_63385',axiom,
! [Vvar__63386] :
( c_24__type__63385___24t(Vvar__63386)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__63386,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_63416',axiom,
! [Vvar__63417] :
( c_24__type__63416___24t(Vvar__63417)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__4)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__4))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__4,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__4) ) )
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(Vvar__63417,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ).
fof('$_type_63481',axiom,
! [Vvar__63482] :
( c_24__type__63481___24t(Vvar__63482)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__63482,Vv__CANONICAL__0)) ) ) ).
fof('$_type_63488',axiom,
! [Vvar__63489] :
( c_24__type__63488___24t(Vvar__63489)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__63489,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_63739',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__63740] :
( c_24__type__63739___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__63740)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__63740,Vv__CANONICAL__3)) ) ) ).
fof('$_type_6391',axiom,
! [Vvar__6392] :
( c_24__type__6391___24t(Vvar__6392)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__91___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__6392,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_64321',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__64322] :
( c_24__type__64321___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__64322)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(Vvar__64322,Vv__CANONICAL__5)) ) ) ).
fof('$_type_64346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__64347] :
( c_24__type__64346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__64347)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__5),happ(happ(Vvar__64347,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_64365',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__64366] :
( c_24__type__64365___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__64366)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__64366,Vv__CANONICAL__5)) ) ) ).
fof('$_type_64707',axiom,
! [Vv__CANONICAL__0,Vvar__64708] :
( c_24__type__64707___24t(Vv__CANONICAL__0,Vvar__64708)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(Vvar__64708,Vv__CANONICAL__1)) ) ) ).
fof('$_type_64711',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__64712] :
( c_24__type__64711___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__64712)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__64712,Vv__CANONICAL__2)) ) ) ).
fof('$_type_64738',axiom,
! [Vvar__64739] :
( c_24__type__64738___24t(Vvar__64739)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__64707___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__64750___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(happ(happ(happ(Vvar__64739,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_64750',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__64751] :
( c_24__type__64750___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__64751)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__64751,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_6489',axiom,
! [Vvar__6490] :
( c_24__type__6489___24t(Vvar__6490)
<=> ! [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__6490,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64905',axiom,
! [Vvar__64906] :
( c_24__type__64905___24t(Vvar__64906)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cZornsLemma_2eFamilies_2eFamily___24t(Vv__CANONICAL__0,happ(happ(Vvar__64906,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6513',axiom,
! [Vvar__6514] :
( c_24__type__6513___24t(Vvar__6514)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__6514,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6562',axiom,
! [Vvar__6563] :
( c_24__type__6562___24t(Vvar__6563)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__6563,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6567',axiom,
! [Vvar__6568] :
( c_24__type__6567___24t(Vvar__6568)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__6568,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6580',axiom,
! [Vvar__6581] :
( c_24__type__6580___24t(Vvar__6581)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__6581,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6636',axiom,
! [Vvar__6637] :
( c_24__type__6636___24t(Vvar__6637)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__6638___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__6637,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6640',axiom,
! [Vvar__6641] :
( c_24__type__6640___24t(Vvar__6641)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(happ(Vvar__6641,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6652',axiom,
! [Vvar__6653] :
( c_24__type__6652___24t(Vvar__6653)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__6653,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6662',axiom,
! [Vvar__6663] :
( c_24__type__6662___24t(Vvar__6663)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__0))
=> cCoq_2eReals_2eRIneq_2eposreal___24t(happ(Vvar__6663,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_6667',axiom,
! [Vvar__6668] :
( c_24__type__6667___24t(Vvar__6668)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__6668,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6689',axiom,
! [Vvar__6690] :
( c_24__type__6689___24t(Vvar__6690)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRList_2eRlist___24t(happ(happ(Vvar__6690,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6691',axiom,
! [Vvar__6692] :
( c_24__type__6691___24t(Vvar__6692)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__6692,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6704',axiom,
! [Vvar__6705] :
( c_24__type__6704___24t(Vvar__6705)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__6705,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6722',axiom,
! [Vvar__6723] :
( c_24__type__6722___24t(Vvar__6723)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRList_2eRlist___24t(happ(happ(Vvar__6723,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6730',axiom,
! [Vvar__6731] :
( c_24__type__6730___24t(Vvar__6731)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__795___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRList_2eRlist___24t(happ(happ(Vvar__6731,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6740',axiom,
! [Vvar__6741] :
( c_24__type__6740___24t(Vvar__6741)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRList_2eRlist___24t(happ(Vvar__6741,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6750',axiom,
! [Vvar__6751] :
( c_24__type__6750___24t(Vvar__6751)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(happ(Vvar__6751,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6794',axiom,
! [Vvar__6795] :
( c_24__type__6794___24t(Vvar__6795)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__6795,Vv__CANONICAL__0)) ) ) ).
fof('$_type_68131',axiom,
! [Vvar__68132] :
( c_24__type__68131___24t(Vvar__68132)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ? [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__5))
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) )
=> cTopology_2eDirectedSets_2eDirectedSet___24t(happ(happ(Vvar__68132,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ).
fof('$_type_6818',axiom,
! [Vvar__6819] :
( c_24__type__6818___24t(Vvar__6819)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__795___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__6819,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6821',axiom,
! [Vvar__6822] :
( c_24__type__6821___24t(Vvar__6822)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__6822,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_68257',axiom,
! [Vvar__68258] :
( c_24__type__68257___24t(Vvar__68258)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__68258,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_68449',axiom,
! [Vvar__68450] :
( c_24__type__68449___24t(Vvar__68450)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__68450,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_68454',axiom,
! [Vvar__68455] :
( c_24__type__68454___24t(Vvar__68455)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(happ(happ(Vvar__68455,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_68490',axiom,
! [Vvar__68491] :
( c_24__type__68490___24t(Vvar__68491)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__68491,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6851',axiom,
! [Vvar__6852] :
( c_24__type__6851___24t(Vvar__6852)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__6852,Vv__CANONICAL__0)) ) ) ).
fof('$_type_68519',axiom,
! [Vvar__68520] :
( c_24__type__68519___24t(Vvar__68520)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__68520,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ).
fof('$_type_6857',axiom,
! [Vvar__6858] :
( c_24__type__6857___24t(Vvar__6858)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__332___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__6858,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6860',axiom,
! [Vvar__6861] :
( c_24__type__6860___24t(Vvar__6861)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__6861,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6866',axiom,
! [Vvar__6867] :
( c_24__type__6866___24t(Vvar__6867)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__6867,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6875',axiom,
! [Vvar__6876] :
( c_24__type__6875___24t(Vvar__6876)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__6876,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6878',axiom,
! [Vv__CANONICAL__0,Vvar__6879] :
( c_24__type__6878___24t(Vv__CANONICAL__0,Vvar__6879)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(Vvar__6879,Vv__CANONICAL__1)) ) ) ).
fof('$_type_6880',axiom,
! [Vvar__6881] :
( c_24__type__6880___24t(Vvar__6881)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__6881,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6887',axiom,
! [Vvar__6888] :
( c_24__type__6887___24t(Vvar__6888)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__6888,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6892',axiom,
! [Vvar__6893] :
( c_24__type__6892___24t(Vvar__6893)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__6893,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_68989',axiom,
! [Vvar__68990] :
( c_24__type__68989___24t(Vvar__68990)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__68990,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6901',axiom,
! [Vvar__6902] :
( c_24__type__6901___24t(Vvar__6902)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__795___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__6902,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_69026',axiom,
! [Vvar__69027] :
( c_24__type__69026___24t(Vvar__69027)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__69027,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ) ).
fof('$_type_69236',axiom,
! [Vvar__69237] :
( c_24__type__69236___24t(Vvar__69237)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__69237,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_69278',axiom,
! [Vvar__69279] :
( c_24__type__69278___24t(Vvar__69279)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cTopology_2eNets_2eNet___24t(cTopology_2eNets_2eneighborhood__net__DS___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__0,happ(happ(Vvar__69279,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_69350',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__69351] :
( c_24__type__69350___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__69351)
<=> ! [Vv__CANONICAL__5] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__3,Vv__CANONICAL__5)
=> cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__1,happ(Vvar__69351,Vv__CANONICAL__5)) ) ) ).
fof('$_type_69406',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__69407] :
( c_24__type__69406___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__69407)
<=> ! [Vv__CANONICAL__3] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__1,happ(Vvar__69407,Vv__CANONICAL__3)) ) ) ).
fof('$_type_6944',axiom,
! [Vvar__6945] :
( c_24__type__6944___24t(Vvar__6945)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__795___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2eplus__fct___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__6945,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_69470',axiom,
! [Vvar__69471] :
( c_24__type__69470___24t(Vvar__69471)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__69471,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_6949',axiom,
! [Vvar__6950] :
( c_24__type__6949___24t(Vvar__6950)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2eopp__fct___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,happ(happ(happ(Vvar__6950,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_69516',axiom,
! [Vvar__69517] :
( c_24__type__69516___24t(Vvar__69517)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__5)
=> ( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__5,happ(Vv__CANONICAL__2,Vv__CANONICAL__4))
=> cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__69517,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_69554',axiom,
! [Vvar__69555] :
( c_24__type__69554___24t(Vvar__69555)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__1,happ(happ(happ(happ(happ(Vvar__69555,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_69584',axiom,
! [Vvar__69585] :
( c_24__type__69584___24t(Vvar__69585)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(happ(Vvar__69585,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_69601',axiom,
! [Vvar__69602] :
( c_24__type__69601___24t(Vvar__69602)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__69602,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_69615',axiom,
! [Vvar__69616] :
( c_24__type__69615___24t(Vvar__69616)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eDirectedSets_2eDirectedSet___24t(happ(happ(happ(happ(Vvar__69616,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ).
fof('$_type_6962',axiom,
! [Vvar__6963] :
( c_24__type__6962___24t(Vvar__6963)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__795___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2eminus__fct___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__6963,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_6965',axiom,
! [Vvar__6966] :
( c_24__type__6965___24t(Vvar__6966)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,happ(happ(Vvar__6966,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_69692',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__69693] :
( c_24__type__69692___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__69693)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__69693,Vv__CANONICAL__3)) ) ) ).
fof('$_type_6975',axiom,
! [Vvar__6976] :
( c_24__type__6975___24t(Vvar__6976)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2eid,Vv__CANONICAL__0,happ(Vvar__6976,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6989',axiom,
! [Vvar__6990] :
( c_24__type__6989___24t(Vvar__6990)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRanalysis1_2ederivable___24t(c_24__lam__6987___24a1(Vv__CANONICAL__0),happ(Vvar__6990,Vv__CANONICAL__0)) ) ) ).
fof('$_type_69989',axiom,
! [Vvar__69990] :
( c_24__type__69989___24t(Vvar__69990)
<=> ! [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__69990,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_70044',axiom,
! [Vvar__70045] :
( c_24__type__70044___24t(Vvar__70045)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__0))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__9336___24a1(Vv__CANONICAL__0),happ(Vvar__70045,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_70059',axiom,
! [Vvar__70060] :
( c_24__type__70059___24t(Vvar__70060)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__9400___24t(Vv__CANONICAL__2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__70066___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__70060,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_70079',axiom,
! [Vvar__70080] :
( c_24__type__70079___24t(Vvar__70080)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__9400___24t(Vv__CANONICAL__2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__70086___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__70080,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_70166',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__70167] :
( c_24__type__70166___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__70167)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__2)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(Vvar__70167,Vv__CANONICAL__3)) ) ) ).
fof('$_type_7096',axiom,
! [Vvar__7097] :
( c_24__type__7096___24t(Vvar__7097)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__2))) )
=> ( ! [Vv__CANONICAL__6] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__6)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__6))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__6,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__6) ) )
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__7104___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(Vvar__7097,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ) ).
fof('$_type_7271',axiom,
! [Vvar__7272] :
( c_24__type__7271___24t(Vvar__7272)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__332___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRaxioms_2ebound___24a1(Vv__CANONICAL__0)
=> ( ? [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
& p(happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) )
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__7275___24a1(Vv__CANONICAL__0),happ(Vvar__7272,Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_type_7306',axiom,
! [Vvar__7307] :
( c_24__type__7306___24t(Vvar__7307)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7308___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__7315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__7322___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__7307,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ) ) ) ) ).
fof('$_type_7308',axiom,
! [Vvar__7309] :
( c_24__type__7308___24t(Vvar__7309)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__7309,Vv__CANONICAL__0)) ) ) ).
fof('$_type_73136',axiom,
! [Vvar__73137] :
( c_24__type__73136___24t(Vvar__73137)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRiemannInt_2eC1__fun___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__73137,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7315',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__7316] :
( c_24__type__7315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__7316)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0))
=> t(Vvar__7316,happ(Vv__CANONICAL__2,Vv__CANONICAL__0)) ) ) ).
fof('$_type_73179',axiom,
! [Vvar__73180] :
( c_24__type__73179___24t(Vvar__73180)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__795___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__795___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__5)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__7] :
( cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__3,Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__8)
=> cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__3,Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eReals_2eRList_2econs__ORlist___24a2(Vv__CANONICAL__4,Vv__CANONICAL__5),happ(happ(happ(happ(happ(happ(happ(happ(Vvar__73180,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_7322',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__7323] :
( c_24__type__7322___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__7323)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(Vvar__7323,happ(Vv__CANONICAL__2,Vv__CANONICAL__1)) ) ) ).
fof('$_type_7324',axiom,
! [Vvar__7325] :
( c_24__type__7324___24t(Vvar__7325)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),happ(Vvar__7325,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7336',axiom,
! [Vvar__7337] :
( c_24__type__7336___24t(Vvar__7337)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__7337,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7341',axiom,
! [Vvar__7342] :
( c_24__type__7341___24t(Vvar__7342)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__332___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__7342,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7537',axiom,
! [Vvar__7538] :
( c_24__type__7537___24t(Vvar__7538)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRIneq_2eposreal___24t(happ(Vvar__7538,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7848',axiom,
! [Vvar__7849] :
( c_24__type__7848___24t(Vvar__7849)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__795___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(c_24__lam__7856___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(happ(Vvar__7849,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_78747',axiom,
! [Vvar__78748] :
( c_24__type__78747___24t(Vvar__78748)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eNets_2eNet___24t(cTopology_2eNets_2ecluster__point__subnet__DS___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__78748,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ).
fof('$_type_78754',axiom,
! [Vvar__78755] :
( c_24__type__78754___24t(Vvar__78755)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cTopology_2eNets_2eNet___24t(cTopology_2eFiltersAndNets_2efilter__to__net__DS___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__0,happ(happ(Vvar__78755,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_78800',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78801] :
( c_24__type__78800___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78801)
<=> ! [Vv__CANONICAL__3] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__78801,Vv__CANONICAL__3)) ) ) ).
fof('$_type_78868',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78869] :
( c_24__type__78868___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78869)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__78869,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_78880',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78881] :
( c_24__type__78880___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78881)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__78881,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_78923',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78924] :
( c_24__type__78923___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__78924)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__78924,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_7896',axiom,
! [Vvar__7897] :
( c_24__type__7896___24t(Vvar__7897)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__7897,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_79198',axiom,
! [Vvar__79199] :
( c_24__type__79198___24t(Vvar__79199)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__5115___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2ePartSum_2eCauchy__crit__series___24a1(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__5813___24a1(Vv__CANONICAL__0),happ(Vvar__79199,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_79221',axiom,
! [Vvar__79222] :
( c_24__type__79221___24t(Vvar__79222)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__79223___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eReals_2eRList_2enil))
=> ! [Vv__CANONICAL__2] :
( c_24__type__79231___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__79222,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_79223',axiom,
! [Vvar__79224] :
( c_24__type__79223___24t(Vvar__79224)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__79224,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7923',axiom,
! [Vvar__7924] :
( c_24__type__7923___24t(Vvar__7924)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__7924,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_79231',axiom,
! [Vv__CANONICAL__0,Vvar__79232] :
( c_24__type__79231___24t(Vv__CANONICAL__0,Vvar__79232)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__2))
=> t(happ(happ(happ(Vvar__79232,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,cCoq_2eReals_2eRList_2econs___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_type_79274',axiom,
! [Vvar__79275] :
( c_24__type__79274___24t(Vvar__79275)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__795___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__795___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__5)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__7] :
( cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__3,Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__8)
=> cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eReals_2eRList_2econs__ORlist___24a2(Vv__CANONICAL__4,Vv__CANONICAL__5),happ(happ(happ(happ(happ(happ(happ(happ(Vvar__79275,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_79305',axiom,
! [Vvar__79306] :
( c_24__type__79305___24t(Vvar__79306)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__5115___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5115___24t(Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) )
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__79311___24a1(Vv__CANONICAL__1),Vv__CANONICAL__3)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__79320___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(Vvar__79306,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_79352',axiom,
! [Vvar__79353] :
( c_24__type__79352___24t(Vvar__79353)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRIneq_2enonposreal___24t(happ(Vvar__79353,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_79371',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__79372] :
( c_24__type__79371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__79372)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2))
=> cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,happ(Vvar__79372,Vv__CANONICAL__3)) ) ) ) ) ).
fof('$_type_7939',axiom,
! [Vvar__7940] :
( c_24__type__7939___24t(Vvar__7940)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__7940,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_79409',axiom,
! [Vvar__79410] :
( c_24__type__79409___24t(Vvar__79410)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__4)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__4))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__4,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__4) ) )
=> cCoq_2eInit_2eSpecif_2esig___24t(c_24__type__795,c_24__lam__79419___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__79410,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ).
fof('$_type_795',axiom,
! [Vvar__796] :
( c_24__type__795___24t(Vvar__796)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__796,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7959',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7960] :
( c_24__type__7959___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7960)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__7960,Vv__CANONICAL__2)) ) ) ).
fof('$_type_7962',axiom,
! [Vvar__7963] :
( c_24__type__7962___24t(Vvar__7963)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__7963,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7980',axiom,
! [Vvar__7981] :
( c_24__type__7980___24t(Vvar__7981)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__795___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__7981,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_7999',axiom,
! [Vvar__8000] :
( c_24__type__7999___24t(Vvar__8000)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(happ(Vvar__8000,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8077',axiom,
! [Vvar__8078] :
( c_24__type__8077___24t(Vvar__8078)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__8078,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8092',axiom,
! [Vvar__8093] :
( c_24__type__8092___24t(Vvar__8093)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__8093,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8097',axiom,
! [Vvar__8098] :
( c_24__type__8097___24t(Vvar__8098)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__8098,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_810',axiom,
! [Vvar__811] :
( c_24__type__810___24t(Vvar__811)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__811,Vv__CANONICAL__0)) ) ) ).
fof('$_type_812',axiom,
! [Vvar__813] :
( c_24__type__812___24t(Vvar__813)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__813,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8137',axiom,
! [Vvar__8138] :
( c_24__type__8137___24t(Vvar__8138)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__795___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__795___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__3,Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__7)
=> cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eReals_2eRList_2econs__ORlist___24a2(Vv__CANONICAL__4,Vv__CANONICAL__5),happ(happ(happ(happ(happ(happ(happ(happ(Vvar__8138,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_8172',axiom,
! [Vvar__8173] :
( c_24__type__8172___24t(Vvar__8173)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__795___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__795___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__3,Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__7)
=> cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(Vv__CANONICAL__3,Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eReals_2eRList_2econs__ORlist___24a2(Vv__CANONICAL__4,Vv__CANONICAL__5),happ(happ(happ(happ(happ(happ(happ(happ(Vvar__8173,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_8343',axiom,
! [Vvar__8344] :
( c_24__type__8343___24t(Vvar__8344)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(c_24__lam__8348___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__8344,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8356',axiom,
! [Vvar__8357] :
( c_24__type__8356___24t(Vvar__8357)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__8357,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_864',axiom,
! [Vvar__865] :
( c_24__type__864___24t(Vvar__865)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__865,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_87',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88] :
( c_24__type__87___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__88,Vv__CANONICAL__5),Vv__CANONICAL__1) ) ) ).
fof('$_type_876',axiom,
! [Vvar__877] :
( c_24__type__876___24t(Vvar__877)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(Vvar__877,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_880',axiom,
! [Vvar__881] :
( c_24__type__880___24t(Vvar__881)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(Vvar__881,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_897',axiom,
! [Vvar__898] :
( c_24__type__897___24t(Vvar__898)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(happ(Vvar__898,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9084',axiom,
! [Vvar__9085] :
( c_24__type__9084___24t(Vvar__9085)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__25___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
=> ( ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4) = happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3) ) )
=> ( ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ( happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vv__CANONICAL__4 = Vv__CANONICAL__5 ) ) )
=> ( ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__5),Vv__CANONICAL__6),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__5),Vv__CANONICAL__7),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__7),Vv__CANONICAL__6)))) ) ) )
=> cCoq_2eReals_2eRlimit_2eMetric__Space___24t(happ(happ(Vvar__9085,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ) ).
fof('$_type_91',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__92] :
( c_24__type__91___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__92)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__92,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_9188',axiom,
! [Vvar__9189] :
( c_24__type__9188___24t(Vvar__9189)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__9189,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9283',axiom,
! [Vvar__9284] :
( c_24__type__9283___24t(Vvar__9284)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__9284,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9322',axiom,
! [Vvar__9323] :
( c_24__type__9322___24t(Vvar__9323)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__332___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__9323,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_9370',axiom,
! [Vvar__9371] :
( c_24__type__9370___24t(Vvar__9371)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__5115___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__9371,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9400',axiom,
! [Vvar__9401] :
( c_24__type__9400___24t(Vvar__9401)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__9401,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9437',axiom,
! [Vvar__9438] :
( c_24__type__9437___24t(Vvar__9438)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__9400___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(happ(Vvar__9438,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_948',axiom,
! [Vvar__949] :
( c_24__type__948___24t(Vvar__949)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__949,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9546',axiom,
! [Vvar__9547] :
( c_24__type__9546___24t(Vvar__9547)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__9551___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__9547,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ) ) ).
fof('$_type_9573',axiom,
! [Vvar__9574] :
( c_24__type__9573___24t(Vvar__9574)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__795___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__9551___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__9574,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ) ).
fof('$_type_9581',axiom,
! [Vvar__9582] :
( c_24__type__9581___24t(Vvar__9582)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__0))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__9584___24a1(Vv__CANONICAL__0),happ(Vvar__9582,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_9602',axiom,
! [Vvar__9603] :
( c_24__type__9602___24t(Vvar__9603)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__332___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__332___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__9603,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9613',axiom,
! [Vvar__9614] :
( c_24__type__9613___24t(Vvar__9614)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__332___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__332___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__9614,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9668',axiom,
! [Vvar__9669] :
( c_24__type__9668___24t(Vvar__9669)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__332___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__297___24t(Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( ? [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) )
=> p(happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) )
=> cCoq_2eReals_2eRtopology_2efamily___24t(happ(happ(Vvar__9669,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_9706',axiom,
! [Vvar__9707] :
( c_24__type__9706___24t(Vvar__9707)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRtopology_2efamily___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__9707,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9741',axiom,
! [Vvar__9742] :
( c_24__type__9741___24t(Vvar__9742)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRtopology_2efamily___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__9742,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9823',axiom,
! [Vvar__9824] :
( c_24__type__9823___24t(Vvar__9824)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__9826___24a1(Vv__CANONICAL__0),happ(Vvar__9824,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9866',axiom,
! [Vvar__9867] :
( c_24__type__9866___24t(Vvar__9867)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__5115___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRseries_2eUn__growing___24a1(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eSeqProp_2ehas__ub___24a1(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__9869___24a1(Vv__CANONICAL__0),happ(Vvar__9867,Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_type_9957',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9958] :
( c_24__type__9957___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9958)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__9958,Vv__CANONICAL__2)) ) ) ).
fof('$_type_9981',axiom,
! [Vvar__9982] :
( c_24__type__9981___24t(Vvar__9982)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__9987___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__9999___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__9982,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_9987',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9988] :
( c_24__type__9987___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9988)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__9988,Vv__CANONICAL__2)) ) ) ).
fof('$_type_9999',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10000] :
( c_24__type__9999___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10000)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(Vvar__10000,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexist___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ).
fof('$_typeof_Coq.Arith.Compare_dec.le_gt_dec',axiom,
c_24__type__63385___24t(cCoq_2eArith_2eCompare__dec_2ele__gt__dec) ).
fof('$_typeof_Coq.Arith.Factorial.fact',axiom,
c_24__type__2824___24t(cCoq_2eArith_2eFactorial_2efact) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__2840___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__2824___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__10713___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__2852___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__489___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__470___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__484___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__470___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__10731___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__864___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.true',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2etrue) ).
fof('$_typeof_Coq.Init.Datatypes.tt',axiom,
cCoq_2eInit_2eDatatypes_2eunit___24t(cCoq_2eInit_2eDatatypes_2ett) ).
fof('$_typeof_Coq.Init.Datatypes.unit',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__6489___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__6489___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__6489___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__2824___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__6489___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__4494___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__4494___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__4494___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__2544___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__10039___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__26727___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__324___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.projT1',axiom,
c_24__type__26698___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).
fof('$_typeof_Coq.Init.Specif.projT2',axiom,
c_24__type__26721___24t(cCoq_2eInit_2eSpecif_2eprojT2) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__26732___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__2526___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__10019___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT_rec',axiom,
c_24__type__26602___24t(cCoq_2eInit_2eSpecif_2esigT__rec) ).
fof('$_typeof_Coq.Init.Specif.sigT_rect',axiom,
c_24__type__26602___24t(cCoq_2eInit_2eSpecif_2esigT__rect) ).
fof('$_typeof_Coq.Init.Specif.sig_rec',axiom,
c_24__type__9981___24t(cCoq_2eInit_2eSpecif_2esig__rec) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__5163___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
c_24__type__63308___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__5193___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__10100___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__10121___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__10114___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__10100___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.of_nat',axiom,
c_24__type__10124___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__2621___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('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__5864___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__812___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__812___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__810___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__810___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
c_24__type__10126___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__4505___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.Reals.AltSeries.positivity_seq',axiom,
c_24__type__5117___24t(cCoq_2eReals_2eAltSeries_2epositivity__seq) ).
fof('$_typeof_Coq.Reals.AltSeries.tg_alt',axiom,
c_24__type__5817___24t(cCoq_2eReals_2eAltSeries_2etg__alt) ).
fof('$_typeof_Coq.Reals.NewtonInt.Newton_integrable',axiom,
c_24__type__6513___24t(cCoq_2eReals_2eNewtonInt_2eNewton__integrable) ).
fof('$_typeof_Coq.Reals.PSeries_reg.Boule',axiom,
c_24__type__6567___24t(cCoq_2eReals_2ePSeries__reg_2eBoule) ).
fof('$_typeof_Coq.Reals.PartSum.Cauchy_crit_series',axiom,
c_24__type__5117___24t(cCoq_2eReals_2ePartSum_2eCauchy__crit__series) ).
fof('$_typeof_Coq.Reals.PartSum.SP',axiom,
c_24__type__14603___24t(cCoq_2eReals_2ePartSum_2eSP) ).
fof('$_typeof_Coq.Reals.PartSum.cv_cauchy_2',axiom,
c_24__type__79198___24t(cCoq_2eReals_2ePartSum_2ecv__cauchy__2) ).
fof('$_typeof_Coq.Reals.RIneq.Req_EM_T',axiom,
c_24__type__14640___24t(cCoq_2eReals_2eRIneq_2eReq__EM__T) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_dec',axiom,
c_24__type__6636___24t(cCoq_2eReals_2eRIneq_2eRle__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_lt_dec',axiom,
c_24__type__6640___24t(cCoq_2eReals_2eRIneq_2eRle__lt__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_lt_or_eq_dec',axiom,
c_24__type__61720___24t(cCoq_2eReals_2eRIneq_2eRle__lt__or__eq__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rlt_dec',axiom,
c_24__type__14632___24t(cCoq_2eReals_2eRIneq_2eRlt__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rlt_le_dec',axiom,
c_24__type__14636___24t(cCoq_2eReals_2eRIneq_2eRlt__le__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.inser_trans_R',axiom,
c_24__type__61733___24t(cCoq_2eReals_2eRIneq_2einser__trans__R) ).
fof('$_typeof_Coq.Reals.RIneq.mknegreal',axiom,
c_24__type__61740___24t(cCoq_2eReals_2eRIneq_2emknegreal) ).
fof('$_typeof_Coq.Reals.RIneq.mknonnegreal',axiom,
c_24__type__14645___24t(cCoq_2eReals_2eRIneq_2emknonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.mknonposreal',axiom,
c_24__type__79352___24t(cCoq_2eReals_2eRIneq_2emknonposreal) ).
fof('$_typeof_Coq.Reals.RIneq.mkposreal',axiom,
c_24__type__6662___24t(cCoq_2eReals_2eRIneq_2emkposreal) ).
fof('$_typeof_Coq.Reals.RIneq.neg',axiom,
c_24__type__14657___24t(cCoq_2eReals_2eRIneq_2eneg) ).
fof('$_typeof_Coq.Reals.RIneq.negreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonneg',axiom,
c_24__type__6652___24t(cCoq_2eReals_2eRIneq_2enonneg) ).
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('$_typeof_Coq.Reals.RIneq.pos',axiom,
c_24__type__6667___24t(cCoq_2eReals_2eRIneq_2epos) ).
fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).
fof('$_typeof_Coq.Reals.RList.FF',axiom,
c_24__type__6730___24t(cCoq_2eReals_2eRList_2eFF) ).
fof('$_typeof_Coq.Reals.RList.In',axiom,
c_24__type__6704___24t(cCoq_2eReals_2eRList_2eIn) ).
fof('$_typeof_Coq.Reals.RList.Rlength',axiom,
c_24__type__4531___24t(cCoq_2eReals_2eRList_2eRlength) ).
fof('$_typeof_Coq.Reals.RList.Rlist',axiom,
cType___24t(cCoq_2eReals_2eRList_2eRlist) ).
fof('$_typeof_Coq.Reals.RList.Rlist_rec',axiom,
c_24__type__79221___24t(cCoq_2eReals_2eRList_2eRlist__rec) ).
fof('$_typeof_Coq.Reals.RList.Rtail',axiom,
c_24__type__6740___24t(cCoq_2eReals_2eRList_2eRtail) ).
fof('$_typeof_Coq.Reals.RList.app_Rlist',axiom,
c_24__type__6730___24t(cCoq_2eReals_2eRList_2eapp__Rlist) ).
fof('$_typeof_Coq.Reals.RList.cons',axiom,
c_24__type__6689___24t(cCoq_2eReals_2eRList_2econs) ).
fof('$_typeof_Coq.Reals.RList.cons_ORlist',axiom,
c_24__type__6722___24t(cCoq_2eReals_2eRList_2econs__ORlist) ).
fof('$_typeof_Coq.Reals.RList.cons_Rlist',axiom,
c_24__type__6722___24t(cCoq_2eReals_2eRList_2econs__Rlist) ).
fof('$_typeof_Coq.Reals.RList.nil',axiom,
cCoq_2eReals_2eRList_2eRlist___24t(cCoq_2eReals_2eRList_2enil) ).
fof('$_typeof_Coq.Reals.RList.ordered_Rlist',axiom,
c_24__type__6691___24t(cCoq_2eReals_2eRList_2eordered__Rlist) ).
fof('$_typeof_Coq.Reals.RList.pos_Rl',axiom,
c_24__type__4543___24t(cCoq_2eReals_2eRList_2epos__Rl) ).
fof('$_typeof_Coq.Reals.R_sqrt.sqrt',axiom,
c_24__type__795___24t(cCoq_2eReals_2eR__sqrt_2esqrt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.Differential',axiom,
cType___24t(cCoq_2eReals_2eRanalysis1_2eDifferential) ).
fof('$_typeof_Coq.Reals.Ranalysis1.antiderivative',axiom,
c_24__type__6901___24t(cCoq_2eReals_2eRanalysis1_2eantiderivative) ).
fof('$_typeof_Coq.Reals.Ranalysis1.comp',axiom,
c_24__type__6818___24t(cCoq_2eReals_2eRanalysis1_2ecomp) ).
fof('$_typeof_Coq.Reals.Ranalysis1.constant_D_eq',axiom,
c_24__type__6857___24t(cCoq_2eReals_2eRanalysis1_2econstant__D__eq) ).
fof('$_typeof_Coq.Reals.Ranalysis1.continuity',axiom,
c_24__type__6851___24t(cCoq_2eReals_2eRanalysis1_2econtinuity) ).
fof('$_typeof_Coq.Reals.Ranalysis1.continuity_pt',axiom,
c_24__type__6860___24t(cCoq_2eReals_2eRanalysis1_2econtinuity__pt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.d1',axiom,
c_24__type__14727___24t(cCoq_2eReals_2eRanalysis1_2ed1) ).
fof('$_typeof_Coq.Reals.Ranalysis1.decreasing',axiom,
c_24__type__6851___24t(cCoq_2eReals_2eRanalysis1_2edecreasing) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable',axiom,
c_24__type__6880___24t(cCoq_2eReals_2eRanalysis1_2ederivable) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_Rsqr',axiom,
cCoq_2eReals_2eRanalysis1_2ederivable___24t(cCoq_2eReals_2eRIneq_2eRsqr,cCoq_2eReals_2eRanalysis1_2ederivable__Rsqr) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_const',axiom,
c_24__type__14748___24t(cCoq_2eReals_2eRanalysis1_2ederivable__const) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_id',axiom,
cCoq_2eReals_2eRanalysis1_2ederivable___24t(cCoq_2eReals_2eRanalysis1_2eid,cCoq_2eReals_2eRanalysis1_2ederivable__id) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_minus',axiom,
c_24__type__61768___24t(cCoq_2eReals_2eRanalysis1_2ederivable__minus) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pow',axiom,
c_24__type__6989___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pow) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt',axiom,
c_24__type__6875___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_abs',axiom,
c_24__type__6866___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_const',axiom,
c_24__type__6965___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__const) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_id',axiom,
c_24__type__6975___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__id) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_lim',axiom,
c_24__type__6866___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_minus',axiom,
c_24__type__6962___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__minus) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_mult',axiom,
c_24__type__14744___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__mult) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_opp',axiom,
c_24__type__6949___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__opp) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_plus',axiom,
c_24__type__6944___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__plus) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derive',axiom,
c_24__type__6892___24t(cCoq_2eReals_2eRanalysis1_2ederive) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derive_pt',axiom,
c_24__type__6887___24t(cCoq_2eReals_2eRanalysis1_2ederive__pt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.fct_cte',axiom,
c_24__type__294___24t(cCoq_2eReals_2eRanalysis1_2efct__cte) ).
fof('$_typeof_Coq.Reals.Ranalysis1.id',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRanalysis1_2eid) ).
fof('$_typeof_Coq.Reals.Ranalysis1.increasing',axiom,
c_24__type__6851___24t(cCoq_2eReals_2eRanalysis1_2eincreasing) ).
fof('$_typeof_Coq.Reals.Ranalysis1.minus_fct',axiom,
c_24__type__6818___24t(cCoq_2eReals_2eRanalysis1_2eminus__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.mult_fct',axiom,
c_24__type__6818___24t(cCoq_2eReals_2eRanalysis1_2emult__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.no_cond',axiom,
c_24__type__332___24t(cCoq_2eReals_2eRanalysis1_2eno__cond) ).
fof('$_typeof_Coq.Reals.Ranalysis1.opp_fct',axiom,
c_24__type__6821___24t(cCoq_2eReals_2eRanalysis1_2eopp__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.plus_fct',axiom,
c_24__type__6818___24t(cCoq_2eReals_2eRanalysis1_2eplus__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.pow_fct',axiom,
c_24__type__6580___24t(cCoq_2eReals_2eRanalysis1_2epow__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis4.derivable_exp',axiom,
cCoq_2eReals_2eRanalysis1_2ederivable___24t(cCoq_2eReals_2eRtrigo__def_2eexp,cCoq_2eReals_2eRanalysis4_2ederivable__exp) ).
fof('$_typeof_Coq.Reals.Ranalysis5.IVT_interv',axiom,
c_24__type__61844___24t(cCoq_2eReals_2eRanalysis5_2eIVT__interv) ).
fof('$_typeof_Coq.Reals.Ranalysis5.derivable_pt_id_interv',axiom,
c_24__type__61790___24t(cCoq_2eReals_2eRanalysis5_2ederivable__pt__id__interv) ).
fof('$_typeof_Coq.Reals.Ranalysis5.derivable_pt_recip_interv_prelim1',axiom,
c_24__type__62162___24t(cCoq_2eReals_2eRanalysis5_2ederivable__pt__recip__interv__prelim1) ).
fof('$_typeof_Coq.Reals.Ranalysis5.f_interv_is_interv',axiom,
c_24__type__7096___24t(cCoq_2eReals_2eRanalysis5_2ef__interv__is__interv) ).
fof('$_typeof_Coq.Reals.Ratan.Datan_seq',axiom,
c_24__type__2506___24t(cCoq_2eReals_2eRatan_2eDatan__seq) ).
fof('$_typeof_Coq.Reals.Ratan.Ratan_seq',axiom,
c_24__type__2506___24t(cCoq_2eReals_2eRatan_2eRatan__seq) ).
fof('$_typeof_Coq.Reals.Raxioms.INR',axiom,
c_24__type__5115___24t(cCoq_2eReals_2eRaxioms_2eINR) ).
fof('$_typeof_Coq.Reals.Raxioms.bound',axiom,
c_24__type__334___24t(cCoq_2eReals_2eRaxioms_2ebound) ).
fof('$_typeof_Coq.Reals.Raxioms.completeness',axiom,
c_24__type__7271___24t(cCoq_2eReals_2eRaxioms_2ecompleteness) ).
fof('$_typeof_Coq.Reals.Raxioms.is_lub',axiom,
c_24__type__330___24t(cCoq_2eReals_2eRaxioms_2eis__lub) ).
fof('$_typeof_Coq.Reals.Raxioms.is_upper_bound',axiom,
c_24__type__330___24t(cCoq_2eReals_2eRaxioms_2eis__upper__bound) ).
fof('$_typeof_Coq.Reals.Raxioms.total_order_T',axiom,
c_24__type__4702___24t(cCoq_2eReals_2eRaxioms_2etotal__order__T) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rabs',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRbasic__fun_2eRabs) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rcase_abs',axiom,
c_24__type__7324___24t(cCoq_2eReals_2eRbasic__fun_2eRcase__abs) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmax',axiom,
c_24__type__294___24t(cCoq_2eReals_2eRbasic__fun_2eRmax) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmax_case_strong',axiom,
c_24__type__7306___24t(cCoq_2eReals_2eRbasic__fun_2eRmax__case__strong) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmin',axiom,
c_24__type__294___24t(cCoq_2eReals_2eRbasic__fun_2eRmin) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmin_case_strong',axiom,
c_24__type__14798___24t(cCoq_2eReals_2eRbasic__fun_2eRmin__case__strong) ).
fof('$_typeof_Coq.Reals.Rcomplete.R_complete',axiom,
c_24__type__62517___24t(cCoq_2eReals_2eRcomplete_2eR__complete) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IPR',axiom,
c_24__type__7336___24t(cCoq_2eReals_2eRdefinitions_2eIPR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IPR_2',axiom,
c_24__type__7336___24t(cCoq_2eReals_2eRdefinitions_2eIPR__2) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__302___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
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__294___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__297___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__297___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__297___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__297___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__294___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__294___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__294___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__6794___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rderiv.D_x',axiom,
c_24__type__7341___24t(cCoq_2eReals_2eRderiv_2eD__x) ).
fof('$_typeof_Coq.Reals.Rderiv.continue_in',axiom,
c_24__type__6857___24t(cCoq_2eReals_2eRderiv_2econtinue__in) ).
fof('$_typeof_Coq.Reals.Rfunctions.R_dist',axiom,
c_24__type__294___24t(cCoq_2eReals_2eRfunctions_2eR__dist) ).
fof('$_typeof_Coq.Reals.Rfunctions.sum_f_R0',axiom,
c_24__type__5817___24t(cCoq_2eReals_2eRfunctions_2esum__f__R0) ).
fof('$_typeof_Coq.Reals.RiemannInt.C1_fun',axiom,
cType___24t(cCoq_2eReals_2eRiemannInt_2eC1__fun) ).
fof('$_typeof_Coq.Reals.RiemannInt.FTC_P1',axiom,
c_24__type__15091___24t(cCoq_2eReals_2eRiemannInt_2eFTC__P1) ).
fof('$_typeof_Coq.Reals.RiemannInt.RiemannInt_P1',axiom,
c_24__type__15009___24t(cCoq_2eReals_2eRiemannInt_2eRiemannInt__P1) ).
fof('$_typeof_Coq.Reals.RiemannInt.RiemannInt_P10',axiom,
c_24__type__7848___24t(cCoq_2eReals_2eRiemannInt_2eRiemannInt__P10) ).
fof('$_typeof_Coq.Reals.RiemannInt.RiemannInt_P14',axiom,
c_24__type__7896___24t(cCoq_2eReals_2eRiemannInt_2eRiemannInt__P14) ).
fof('$_typeof_Coq.Reals.RiemannInt.RiemannInt_P16',axiom,
c_24__type__15047___24t(cCoq_2eReals_2eRiemannInt_2eRiemannInt__P16) ).
fof('$_typeof_Coq.Reals.RiemannInt.RiemannInt_P21',axiom,
c_24__type__15123___24t(cCoq_2eReals_2eRiemannInt_2eRiemannInt__P21) ).
fof('$_typeof_Coq.Reals.RiemannInt.RiemannInt_P22',axiom,
c_24__type__15140___24t(cCoq_2eReals_2eRiemannInt_2eRiemannInt__P22) ).
fof('$_typeof_Coq.Reals.RiemannInt.RiemannInt_P23',axiom,
c_24__type__15157___24t(cCoq_2eReals_2eRiemannInt_2eRiemannInt__P23) ).
fof('$_typeof_Coq.Reals.RiemannInt.RiemannInt_P30',axiom,
c_24__type__79409___24t(cCoq_2eReals_2eRiemannInt_2eRiemannInt__P30) ).
fof('$_typeof_Coq.Reals.RiemannInt.RiemannInt_P6',axiom,
c_24__type__63416___24t(cCoq_2eReals_2eRiemannInt_2eRiemannInt__P6) ).
fof('$_typeof_Coq.Reals.RiemannInt.RiemannInt_P7',axiom,
c_24__type__15012___24t(cCoq_2eReals_2eRiemannInt_2eRiemannInt__P7) ).
fof('$_typeof_Coq.Reals.RiemannInt.RinvN',axiom,
c_24__type__7537___24t(cCoq_2eReals_2eRiemannInt_2eRinvN) ).
fof('$_typeof_Coq.Reals.RiemannInt.c1',axiom,
c_24__type__73136___24t(cCoq_2eReals_2eRiemannInt_2ec1) ).
fof('$_typeof_Coq.Reals.RiemannInt.continuity_implies_RiemannInt',axiom,
c_24__type__15033___24t(cCoq_2eReals_2eRiemannInt_2econtinuity__implies__RiemannInt) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.Int_SF',axiom,
c_24__type__8077___24t(cCoq_2eReals_2eRiemannInt__SF_2eInt__SF) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.IsStepFun',axiom,
c_24__type__6513___24t(cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.Nbound',axiom,
c_24__type__15203___24t(cCoq_2eReals_2eRiemannInt__SF_2eNbound) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.Nzorn',axiom,
c_24__type__63133___24t(cCoq_2eReals_2eRiemannInt__SF_2eNzorn) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.RiemannInt_SF',axiom,
c_24__type__8092___24t(cCoq_2eReals_2eRiemannInt__SF_2eRiemannInt__SF) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun',axiom,
c_24__type__7962___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun_P22',axiom,
c_24__type__79274___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun__P22) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun_P23',axiom,
c_24__type__8137___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun__P23) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun_P24',axiom,
c_24__type__73179___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun__P24) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun_P25',axiom,
c_24__type__8172___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun__P25) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun_P32',axiom,
c_24__type__8343___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun__P32) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun_P4',axiom,
c_24__type__8097___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun__P4) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun_P41',axiom,
c_24__type__15255___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun__P41) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun_P44',axiom,
c_24__type__15272___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun__P44) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun_P45',axiom,
c_24__type__15289___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun__P45) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun_P46',axiom,
c_24__type__15306___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun__P46) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun_P6',axiom,
c_24__type__15225___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun__P6) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.co_interval',axiom,
c_24__type__7923___24t(cCoq_2eReals_2eRiemannInt__SF_2eco__interval) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.fe',axiom,
c_24__type__7999___24t(cCoq_2eReals_2eRiemannInt__SF_2efe) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.is_subdivision',axiom,
c_24__type__7939___24t(cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.mkStepFun',axiom,
c_24__type__7980___24t(cCoq_2eReals_2eRiemannInt__SF_2emkStepFun) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.open_interval',axiom,
c_24__type__7923___24t(cCoq_2eReals_2eRiemannInt__SF_2eopen__interval) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.pre',axiom,
c_24__type__63157___24t(cCoq_2eReals_2eRiemannInt__SF_2epre) ).
fof('$_typeof_Coq.Reals.Rlimit.Base',axiom,
c_24__type__9188___24t(cCoq_2eReals_2eRlimit_2eBase) ).
fof('$_typeof_Coq.Reals.Rlimit.Build_Metric_Space',axiom,
c_24__type__9084___24t(cCoq_2eReals_2eRlimit_2eBuild__Metric__Space) ).
fof('$_typeof_Coq.Reals.Rlimit.Metric_Space',axiom,
cType___24t(cCoq_2eReals_2eRlimit_2eMetric__Space) ).
fof('$_typeof_Coq.Reals.Rlimit.R_met',axiom,
cCoq_2eReals_2eRlimit_2eMetric__Space___24t(cCoq_2eReals_2eRlimit_2eR__met) ).
fof('$_typeof_Coq.Reals.Rlimit.dist',axiom,
c_24__type__9283___24t(cCoq_2eReals_2eRlimit_2edist) ).
fof('$_typeof_Coq.Reals.Rlimit.limit1_in',axiom,
c_24__type__9322___24t(cCoq_2eReals_2eRlimit_2elimit1__in) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__2506___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Reals.Rpower.Rpower',axiom,
c_24__type__294___24t(cCoq_2eReals_2eRpower_2eRpower) ).
fof('$_typeof_Coq.Reals.Rpower.ln_exists1',axiom,
c_24__type__70044___24t(cCoq_2eReals_2eRpower_2eln__exists1) ).
fof('$_typeof_Coq.Reals.Rprod.prod_f_R0',axiom,
c_24__type__5817___24t(cCoq_2eReals_2eRprod_2eprod__f__R0) ).
fof('$_typeof_Coq.Reals.Rseries.Cauchy_crit',axiom,
c_24__type__5117___24t(cCoq_2eReals_2eRseries_2eCauchy__crit) ).
fof('$_typeof_Coq.Reals.Rseries.EUn',axiom,
c_24__type__5113___24t(cCoq_2eReals_2eRseries_2eEUn) ).
fof('$_typeof_Coq.Reals.Rseries.Un_cv',axiom,
c_24__type__5113___24t(cCoq_2eReals_2eRseries_2eUn__cv) ).
fof('$_typeof_Coq.Reals.Rseries.Un_growing',axiom,
c_24__type__5117___24t(cCoq_2eReals_2eRseries_2eUn__growing) ).
fof('$_typeof_Coq.Reals.Rsigma.sigma',axiom,
c_24__type__9370___24t(cCoq_2eReals_2eRsigma_2esigma) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.Dichotomy_lb',axiom,
c_24__type__9437___24t(cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.Dichotomy_ub',axiom,
c_24__type__9437___24t(cCoq_2eReals_2eRsqrt__def_2eDichotomy__ub) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.IVT',axiom,
c_24__type__9546___24t(cCoq_2eReals_2eRsqrt__def_2eIVT) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.IVT_cor',axiom,
c_24__type__9573___24t(cCoq_2eReals_2eRsqrt__def_2eIVT__cor) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.Rsqrt_exists',axiom,
c_24__type__9581___24t(cCoq_2eReals_2eRsqrt__def_2eRsqrt__exists) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.dicho_lb',axiom,
c_24__type__9437___24t(cCoq_2eReals_2eRsqrt__def_2edicho__lb) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.dicho_lb_cv',axiom,
c_24__type__70059___24t(cCoq_2eReals_2eRsqrt__def_2edicho__lb__cv) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.dicho_up',axiom,
c_24__type__9437___24t(cCoq_2eReals_2eRsqrt__def_2edicho__up) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.dicho_up_cv',axiom,
c_24__type__70079___24t(cCoq_2eReals_2eRsqrt__def_2edicho__up__cv) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.pow_2_n',axiom,
c_24__type__5115___24t(cCoq_2eReals_2eRsqrt__def_2epow__2__n) ).
fof('$_typeof_Coq.Reals.Rtopology.adherence',axiom,
c_24__type__330___24t(cCoq_2eReals_2eRtopology_2eadherence) ).
fof('$_typeof_Coq.Reals.Rtopology.bounded',axiom,
c_24__type__334___24t(cCoq_2eReals_2eRtopology_2ebounded) ).
fof('$_typeof_Coq.Reals.Rtopology.closed_set',axiom,
c_24__type__334___24t(cCoq_2eReals_2eRtopology_2eclosed__set) ).
fof('$_typeof_Coq.Reals.Rtopology.compact',axiom,
c_24__type__334___24t(cCoq_2eReals_2eRtopology_2ecompact) ).
fof('$_typeof_Coq.Reals.Rtopology.disc',axiom,
c_24__type__6567___24t(cCoq_2eReals_2eRtopology_2edisc) ).
fof('$_typeof_Coq.Reals.Rtopology.eq_Dom',axiom,
c_24__type__9602___24t(cCoq_2eReals_2eRtopology_2eeq__Dom) ).
fof('$_typeof_Coq.Reals.Rtopology.f',axiom,
c_24__type__9741___24t(cCoq_2eReals_2eRtopology_2ef) ).
fof('$_typeof_Coq.Reals.Rtopology.family',axiom,
cType___24t(cCoq_2eReals_2eRtopology_2efamily) ).
fof('$_typeof_Coq.Reals.Rtopology.image_dir',axiom,
c_24__type__6857___24t(cCoq_2eReals_2eRtopology_2eimage__dir) ).
fof('$_typeof_Coq.Reals.Rtopology.included',axiom,
c_24__type__9602___24t(cCoq_2eReals_2eRtopology_2eincluded) ).
fof('$_typeof_Coq.Reals.Rtopology.ind',axiom,
c_24__type__9706___24t(cCoq_2eReals_2eRtopology_2eind) ).
fof('$_typeof_Coq.Reals.Rtopology.intersection_domain',axiom,
c_24__type__9613___24t(cCoq_2eReals_2eRtopology_2eintersection__domain) ).
fof('$_typeof_Coq.Reals.Rtopology.mkfamily',axiom,
c_24__type__9668___24t(cCoq_2eReals_2eRtopology_2emkfamily) ).
fof('$_typeof_Coq.Reals.Rtopology.neighbourhood',axiom,
c_24__type__330___24t(cCoq_2eReals_2eRtopology_2eneighbourhood) ).
fof('$_typeof_Coq.Reals.Rtopology.point_adherent',axiom,
c_24__type__330___24t(cCoq_2eReals_2eRtopology_2epoint__adherent) ).
fof('$_typeof_Coq.Reals.Rtrigo1.PI',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRtrigo1_2ePI) ).
fof('$_typeof_Coq.Reals.Rtrigo1.cos_lb',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRtrigo1_2ecos__lb) ).
fof('$_typeof_Coq.Reals.Rtrigo1.cos_ub',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRtrigo1_2ecos__ub) ).
fof('$_typeof_Coq.Reals.Rtrigo1.sin_lb',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRtrigo1_2esin__lb) ).
fof('$_typeof_Coq.Reals.Rtrigo1.sin_ub',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRtrigo1_2esin__ub) ).
fof('$_typeof_Coq.Reals.Rtrigo1.tan',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRtrigo1_2etan) ).
fof('$_typeof_Coq.Reals.Rtrigo_alt.cos_approx',axiom,
c_24__type__2506___24t(cCoq_2eReals_2eRtrigo__alt_2ecos__approx) ).
fof('$_typeof_Coq.Reals.Rtrigo_alt.sin_approx',axiom,
c_24__type__2506___24t(cCoq_2eReals_2eRtrigo__alt_2esin__approx) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.cos',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRtrigo__def_2ecos) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.cos_in',axiom,
c_24__type__297___24t(cCoq_2eReals_2eRtrigo__def_2ecos__in) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.exist_cos',axiom,
c_24__type__9823___24t(cCoq_2eReals_2eRtrigo__def_2eexist__cos) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.exp',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRtrigo__def_2eexp) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.sin',axiom,
c_24__type__795___24t(cCoq_2eReals_2eRtrigo__def_2esin) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.sin_in',axiom,
c_24__type__297___24t(cCoq_2eReals_2eRtrigo__def_2esin__in) ).
fof('$_typeof_Coq.Reals.SeqProp.Un_decreasing',axiom,
c_24__type__5117___24t(cCoq_2eReals_2eSeqProp_2eUn__decreasing) ).
fof('$_typeof_Coq.Reals.SeqProp.growing_cv',axiom,
c_24__type__9866___24t(cCoq_2eReals_2eSeqProp_2egrowing__cv) ).
fof('$_typeof_Coq.Reals.SeqProp.has_lb',axiom,
c_24__type__5117___24t(cCoq_2eReals_2eSeqProp_2ehas__lb) ).
fof('$_typeof_Coq.Reals.SeqProp.has_ub',axiom,
c_24__type__5117___24t(cCoq_2eReals_2eSeqProp_2ehas__ub) ).
fof('$_typeof_Coq.Reals.SeqProp.opp_seq',axiom,
c_24__type__5817___24t(cCoq_2eReals_2eSeqProp_2eopp__seq) ).
fof('$_typeof_Coq.Reals.SeqSeries.Rseries_CV_comp',axiom,
c_24__type__79305___24t(cCoq_2eReals_2eSeqSeries_2eRseries__CV__comp) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__69989___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__470___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__69989___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Sets.Ensembles.Complement',axiom,
c_24__type__876___24t(cCoq_2eSets_2eEnsembles_2eComplement) ).
fof('$_typeof_Coq.Sets.Ensembles.Ensemble',axiom,
c_24__type__470___24t(cCoq_2eSets_2eEnsembles_2eEnsemble) ).
fof('$_typeof_Coq.Sets.Ensembles.In',axiom,
c_24__type__495___24t(cCoq_2eSets_2eEnsembles_2eIn) ).
fof('$_typeof_Coq.Sets.Ensembles.Included',axiom,
c_24__type__500___24t(cCoq_2eSets_2eEnsembles_2eIncluded) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__5851___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__5851___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__5851___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__5851___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__5851___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__2636___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__2671___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__2618___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__2636___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__10134___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__2640___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__2738___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__2636___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__2640___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__2618___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__3091___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEadd',axiom,
c_24__type__3096___24t(cCoq_2emicromega_2eEnvRing_2ePEadd) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__3088___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PEmul',axiom,
c_24__type__3096___24t(cCoq_2emicromega_2eEnvRing_2ePEmul) ).
fof('$_typeof_Coq.micromega.EnvRing.PEopp',axiom,
c_24__type__6038___24t(cCoq_2emicromega_2eEnvRing_2ePEopp) ).
fof('$_typeof_Coq.micromega.EnvRing.PEsub',axiom,
c_24__type__3096___24t(cCoq_2emicromega_2eEnvRing_2ePEsub) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__470___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__11029___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__470___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.QMicromega.QWitness',axiom,
cType___24t(cCoq_2emicromega_2eQMicromega_2eQWitness) ).
fof('$_typeof_Coq.micromega.RMicromega.CInv',axiom,
c_24__type__4692___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).
fof('$_typeof_Coq.micromega.RMicromega.CMult',axiom,
c_24__type__6750___24t(cCoq_2emicromega_2eRMicromega_2eCMult) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__4690___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.RTautoChecker',axiom,
c_24__type__4699___24t(cCoq_2emicromega_2eRMicromega_2eRTautoChecker) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.RingMicromega.Build_Formula',axiom,
c_24__type__1134___24t(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__470___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_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.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('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__470___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzAdd',axiom,
c_24__type__1105___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__1111___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzIn',axiom,
c_24__type__1100___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzIn) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulC',axiom,
c_24__type__27271___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulE',axiom,
c_24__type__1105___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__5671___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.BFormula',axiom,
c_24__type__470___24t(cCoq_2emicromega_2eTauto_2eBFormula) ).
fof('$_typeof_Coq.micromega.Tauto.Cj',axiom,
c_24__type__10085___24t(cCoq_2emicromega_2eTauto_2eCj) ).
fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
c_24__type__26753___24t(cCoq_2emicromega_2eTauto_2eFF) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__5267___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.I',axiom,
c_24__type__5694___24t(cCoq_2emicromega_2eTauto_2eI) ).
fof('$_typeof_Coq.micromega.Tauto.N',axiom,
c_24__type__26765___24t(cCoq_2emicromega_2eTauto_2eN) ).
fof('$_typeof_Coq.micromega.Tauto.X',axiom,
c_24__type__10068___24t(cCoq_2emicromega_2eTauto_2eX) ).
fof('$_typeof_Coq.micromega.VarMap.Branch',axiom,
c_24__type__5743___24t(cCoq_2emicromega_2eVarMap_2eBranch) ).
fof('$_typeof_Coq.micromega.VarMap.Elt',axiom,
c_24__type__5735___24t(cCoq_2emicromega_2eVarMap_2eElt) ).
fof('$_typeof_Coq.micromega.VarMap.Empty',axiom,
c_24__type__10087___24t(cCoq_2emicromega_2eVarMap_2eEmpty) ).
fof('$_typeof_Coq.micromega.VarMap.find',axiom,
c_24__type__5774___24t(cCoq_2emicromega_2eVarMap_2efind) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__470___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__3432___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__3437___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__3429___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__3437___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__3699___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__6052___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__3437___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__6052___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEpow',axiom,
c_24__type__6058___24t(cCoq_2esetoid__ring_2eField__theory_2eFEpow) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__3437___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__470___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__4258___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons2',axiom,
c_24__type__4385___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons2) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__3997___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__3778___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__3758___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__470___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__3747___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__3758___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.get_signZ',axiom,
c_24__type__534___24t(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__1446___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__1451___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__1443___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__1647___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__1451___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__8356___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__1451___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__470___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__1197___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__1184___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__5104___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__1189___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__470___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__2467___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__2067___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__1887___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_RTopology.RTop',axiom,
cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(cRTopology_2eRTop) ).
fof('$_typeof_RTopology.R_metric',axiom,
c_24__type__294___24t(cRTopology_2eR__metric) ).
fof('$_typeof_Topology.Compactness.compact',axiom,
c_24__type__63481___24t(cTopology_2eCompactness_2ecompact) ).
fof('$_typeof_Topology.Completeness.cauchy',axiom,
c_24__type__20___24t(cTopology_2eCompleteness_2ecauchy) ).
fof('$_typeof_Topology.Continuity.continuous_at',axiom,
c_24__type__5948___24t(cTopology_2eContinuity_2econtinuous__at) ).
fof('$_typeof_Topology.CountabilityAxioms.first_countable',axiom,
c_24__type__63481___24t(cTopology_2eCountabilityAxioms_2efirst__countable) ).
fof('$_typeof_Topology.DirectedSets.Build_DirectedSet',axiom,
c_24__type__68131___24t(cTopology_2eDirectedSets_2eBuild__DirectedSet) ).
fof('$_typeof_Topology.DirectedSets.DS_ord',axiom,
c_24__type__2912___24t(cTopology_2eDirectedSets_2eDS__ord) ).
fof('$_typeof_Topology.DirectedSets.DS_set',axiom,
c_24__type__2882___24t(cTopology_2eDirectedSets_2eDS__set) ).
fof('$_typeof_Topology.DirectedSets.DirectedSet',axiom,
cType___24t(cTopology_2eDirectedSets_2eDirectedSet) ).
fof('$_typeof_Topology.DirectedSets.eventually',axiom,
c_24__type__2916___24t(cTopology_2eDirectedSets_2eeventually) ).
fof('$_typeof_Topology.DirectedSets.exists_arbitrarily_large',axiom,
c_24__type__2916___24t(cTopology_2eDirectedSets_2eexists__arbitrarily__large) ).
fof('$_typeof_Topology.FilterLimits.filter_cluster_point',axiom,
c_24__type__68257___24t(cTopology_2eFilterLimits_2efilter__cluster__point) ).
fof('$_typeof_Topology.FilterLimits.filter_limit',axiom,
c_24__type__68257___24t(cTopology_2eFilterLimits_2efilter__limit) ).
fof('$_typeof_Topology.Filters.Filter',axiom,
c_24__type__470___24t(cTopology_2eFilters_2eFilter) ).
fof('$_typeof_Topology.Filters.filter_family',axiom,
c_24__type__64905___24t(cTopology_2eFilters_2efilter__family) ).
fof('$_typeof_Topology.FiltersAndNets.Build_filter_to_net_DS_set',axiom,
c_24__type__68519___24t(cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set) ).
fof('$_typeof_Topology.FiltersAndNets.filter_to_net',axiom,
c_24__type__78754___24t(cTopology_2eFiltersAndNets_2efilter__to__net) ).
fof('$_typeof_Topology.FiltersAndNets.filter_to_net_DS_set',axiom,
c_24__type__68490___24t(cTopology_2eFiltersAndNets_2efilter__to__net__DS__set) ).
fof('$_typeof_Topology.FiltersAndNets.net_tail',axiom,
c_24__type__68449___24t(cTopology_2eFiltersAndNets_2enet__tail) ).
fof('$_typeof_Topology.FiltersAndNets.tail_filter_basis',axiom,
c_24__type__68454___24t(cTopology_2eFiltersAndNets_2etail__filter__basis) ).
fof('$_typeof_Topology.InteriorsClosures.closure',axiom,
c_24__type__897___24t(cTopology_2eInteriorsClosures_2eclosure) ).
fof('$_typeof_Topology.MetricSpaces.metrizes',axiom,
c_24__type__217___24t(cTopology_2eMetricSpaces_2emetrizes) ).
fof('$_typeof_Topology.MetricSpaces.open_ball',axiom,
c_24__type__558___24t(cTopology_2eMetricSpaces_2eopen__ball) ).
fof('$_typeof_Topology.Neighborhoods.neighborhood',axiom,
c_24__type__948___24t(cTopology_2eNeighborhoods_2eneighborhood) ).
fof('$_typeof_Topology.Neighborhoods.open_neighborhood',axiom,
c_24__type__948___24t(cTopology_2eNeighborhoods_2eopen__neighborhood) ).
fof('$_typeof_Topology.Nets.Build_cluster_point_subnet_DS_set',axiom,
c_24__type__69516___24t(cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set) ).
fof('$_typeof_Topology.Nets.Net',axiom,
c_24__type__4475___24t(cTopology_2eNets_2eNet) ).
fof('$_typeof_Topology.Nets.cluster_point_subnet',axiom,
c_24__type__78747___24t(cTopology_2eNets_2ecluster__point__subnet) ).
fof('$_typeof_Topology.Nets.cluster_point_subnet_DS',axiom,
c_24__type__69615___24t(cTopology_2eNets_2ecluster__point__subnet__DS) ).
fof('$_typeof_Topology.Nets.cluster_point_subnet_DS_ord',axiom,
c_24__type__69601___24t(cTopology_2eNets_2ecluster__point__subnet__DS__ord) ).
fof('$_typeof_Topology.Nets.cluster_point_subnet_DS_set',axiom,
c_24__type__69470___24t(cTopology_2eNets_2ecluster__point__subnet__DS__set) ).
fof('$_typeof_Topology.Nets.cps_U',axiom,
c_24__type__69584___24t(cTopology_2eNets_2ecps__U) ).
fof('$_typeof_Topology.Nets.cps_i',axiom,
c_24__type__69554___24t(cTopology_2eNets_2ecps__i) ).
fof('$_typeof_Topology.Nets.intro_neighborhood_net_DS',axiom,
c_24__type__69026___24t(cTopology_2eNets_2eintro__neighborhood__net__DS) ).
fof('$_typeof_Topology.Nets.neighborhood_net',axiom,
c_24__type__69278___24t(cTopology_2eNets_2eneighborhood__net) ).
fof('$_typeof_Topology.Nets.neighborhood_net_DS_ord',axiom,
c_24__type__69236___24t(cTopology_2eNets_2eneighborhood__net__DS__ord) ).
fof('$_typeof_Topology.Nets.neighborhood_net_DS_set',axiom,
c_24__type__68989___24t(cTopology_2eNets_2eneighborhood__net__DS__set) ).
fof('$_typeof_Topology.Nets.net_cluster_point',axiom,
c_24__type__291___24t(cTopology_2eNets_2enet__cluster__point) ).
fof('$_typeof_Topology.Nets.net_limit',axiom,
c_24__type__291___24t(cTopology_2eNets_2enet__limit) ).
fof('$_typeof_Topology.SeparatednessAxioms.Hausdorff',axiom,
c_24__type__63481___24t(cTopology_2eSeparatednessAxioms_2eHausdorff) ).
fof('$_typeof_Topology.SupInf.is_glb',axiom,
c_24__type__330___24t(cTopology_2eSupInf_2eis__glb) ).
fof('$_typeof_Topology.SupInf.is_lower_bound',axiom,
c_24__type__330___24t(cTopology_2eSupInf_2eis__lower__bound) ).
fof('$_typeof_Topology.TopologicalSpaces.TopologicalSpace',axiom,
cType___24t(cTopology_2eTopologicalSpaces_2eTopologicalSpace) ).
fof('$_typeof_Topology.TopologicalSpaces.closed',axiom,
c_24__type__2615___24t(cTopology_2eTopologicalSpaces_2eclosed) ).
fof('$_typeof_Topology.TopologicalSpaces.open',axiom,
c_24__type__2615___24t(cTopology_2eTopologicalSpaces_2eopen) ).
fof('$_typeof_Topology.TopologicalSpaces.point_set',axiom,
c_24__type__462___24t(cTopology_2eTopologicalSpaces_2epoint__set) ).
fof('$_typeof_Topology.WeakTopology.WeakTopology',axiom,
c_24__type__64738___24t(cTopology_2eWeakTopology_2eWeakTopology) ).
fof('$_typeof_ZornsLemma.CountableTypes.Countable',axiom,
c_24__type__63488___24t(cZornsLemma_2eCountableTypes_2eCountable) ).
fof('$_typeof_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble',axiom,
c_24__type__880___24t(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble) ).
fof('$_typeof_ZornsLemma.Families.Family',axiom,
c_24__type__470___24t(cZornsLemma_2eFamilies_2eFamily) ).
fof('$_typeof_ZornsLemma.FunctionProperties.injective',axiom,
c_24__type__13083___24t(cZornsLemma_2eFunctionProperties_2einjective) ).
fof('$_typeof_ZornsLemma.InverseImage.inverse_image',axiom,
c_24__type__6391___24t(cZornsLemma_2eInverseImage_2einverse__image) ).
fof('Coq.Arith.Compare_dec.dec_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.dec_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> 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))
=> cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Factorial.fact_neq_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eArith_2eFactorial_2efact___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.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.Le.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Le.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Lt.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.Lt.lt_n_Sm_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_pred_n_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eNat_2epred___24a1(V0__n),V0__n)) ) ) ).
fof('Coq.Arith.Lt.neq_0_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eInit_2eDatatypes_2eO != V0__n
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)) ) ) ).
fof('Coq.Arith.Max.le_max_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m))) ) ) ).
fof('Coq.Arith.Max.le_max_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m))) ) ) ).
fof('Coq.Arith.Minus.le_plus_minus',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))
=> V1__m = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eNat_2esub___24a2(V1__m,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.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.Mult.mult_le_compat_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2emul___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2emul___24a2(V2__p,V1__m))) ) ) ) ) ).
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.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_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(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.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO)) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.nlt_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO)) ) ).
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.diff_false_true',axiom,
cCoq_2eInit_2eDatatypes_2efalse != cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__5979___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__28___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_ind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__5979___24t(V1__P)
=> ( p(happ(V1__P,V0__n))
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V3__m))
=> ( p(happ(V1__P,V3__m))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m))) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V4__n))
=> p(happ(V1__P,V4__n)) ) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.Init.Specif.proj2_sig',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__327___24t(V0__A,V1__P)
=> ! [V2__e] :
( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> p(happ(V1__P,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e))) ) ) ) ).
fof('Coq.Init.Specif.sigT_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__10022___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__63274___24t(V0__A,V1__P,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__p] :
( t(V4__p,happ(V1__P,V3__x))
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,V3__x,V4__p))) ) )
=> ! [V4__s] :
( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V4__s)
=> p(happ(V2__P,V4__s)) ) ) ) ) ) ).
fof('Coq.Init.Specif.sig_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__327___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__9957___24t(V0__A,V1__P,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,V3__x))) ) )
=> ! [V4__s] :
( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V4__s)
=> p(happ(V2__P,V4__s)) ) ) ) ) ) ).
fof('Coq.Init.Specif.sumbool_ind',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__63280___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Init.Tactics.decide_left',axiom,
! [V0__C] :
( cProp___24t(V0__C)
=> ! [V1__decide] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__C,c_24__prop__10051___24a1(V0__C),V1__decide)
=> ( p(V0__C)
=> ! [V3__P] :
( c_24__type__10053___24t(V0__C,V3__P)
=> ( ( p(V0__C)
=> p(happ(V3__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__C,c_24__prop__10056___24a1(V0__C)))) )
=> p(happ(V3__P,V1__decide)) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalChoice.choice',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__10517___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,V1__B)
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__91___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_all_ex_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__327___24t(V0__U,V1__P)
=> ( ~ ! [V2__n] :
( t(V2__n,V0__U)
=> p(happ(V1__P,V2__n)) )
=> ? [V3__n] :
( t(V3__n,V0__U)
& ~ p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_ex_all_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__327___24t(V0__U,V1__P)
=> ( ~ ? [V2__n] :
( t(V2__n,V0__U)
& p(happ(V1__P,V2__n)) )
=> ! [V3__n] :
( t(V3__n,V0__U)
=> ~ p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.NNPP',axiom,
! [V0__p] :
( cProp___24t(V0__p)
=> ( ~ ~ p(V0__p)
=> p(V0__p) ) ) ).
fof('Coq.Logic.Classical_Prop.classic',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_to_and',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> ( p(V0__P)
& ~ p(V1__Q) ) ) ) ) ).
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.Reals.ArithProp.tech8',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__i))) ) ) ).
fof('Coq.Reals.DiscrR.Rlt_R0_R2',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ).
fof('Coq.Reals.MVT.IAF',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__k] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__k)
=> ! [V4__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(V0__f,V4__pr)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V2__b))
=> ( ! [V6__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__c)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V6__c))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__c,V2__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V6__c,happ(V4__pr,V6__c)),V3__k)) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V0__f,V2__b),happ(V0__f,V1__a)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V3__k,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V2__b,V1__a)))) ) ) ) ) ) ) ) ).
fof('Coq.Reals.MVT.IAF_var',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__g] :
( c_24__type__795___24t(V1__g)
=> ! [V2__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__a)
=> ! [V3__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__b)
=> ! [V4__pr1] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(V0__f,V4__pr1)
=> ! [V5__pr2] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(V1__g,V5__pr2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V3__b))
=> ( ! [V7__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__c)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V7__c))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V7__c,V3__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V1__g,V7__c,happ(V5__pr2,V7__c)),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V7__c,happ(V4__pr1,V7__c)))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V1__g,V3__b),happ(V1__g,V2__a)),cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V0__f,V3__b),happ(V0__f,V2__a)))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.MVT.antiderivative_Ucte',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__g1] :
( c_24__type__795___24t(V1__g1)
=> ! [V2__g2] :
( c_24__type__795___24t(V2__g2)
=> ! [V3__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__a)
=> ! [V4__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__b)
=> ( cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(V0__f,V1__g1,V3__a,V4__b)
=> ( cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(V0__f,V2__g2,V3__a,V4__b)
=> ? [V7__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__c)
& ! [V8__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V3__a,V8__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__x,V4__b)) )
=> happ(V1__g1,V8__x) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(V2__g2,V8__x),V7__c) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.MVT.derive_increasing_interv',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ! [V2__f] :
( c_24__type__795___24t(V2__f)
=> ! [V3__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(V2__f,V3__pr)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V1__b))
=> ( ! [V5__t] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__t)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V5__t))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V5__t,V1__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V2__f,V5__t,happ(V3__pr,V5__t)))) ) )
=> ! [V6__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__x)
=> ! [V7__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V6__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__x,V1__b)) )
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V7__y))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V7__y,V1__b)) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V6__x,V7__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V2__f,V6__x),happ(V2__f,V7__y))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.MVT.derive_increasing_interv_ax',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ! [V2__f] :
( c_24__type__795___24t(V2__f)
=> ! [V3__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(V2__f,V3__pr)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V1__b))
=> ( ( ! [V5__t] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__t)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V5__t))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V5__t,V1__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V2__f,V5__t,happ(V3__pr,V5__t)))) ) )
=> ! [V6__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__x)
=> ! [V7__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V6__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__x,V1__b)) )
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V7__y))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V7__y,V1__b)) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V6__x,V7__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V2__f,V6__x),happ(V2__f,V7__y))) ) ) ) ) ) )
& ( ! [V5__t] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__t)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V5__t))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V5__t,V1__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V2__f,V5__t,happ(V3__pr,V5__t)))) ) )
=> ! [V6__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__x)
=> ! [V7__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V6__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__x,V1__b)) )
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V7__y))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V7__y,V1__b)) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V6__x,V7__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V2__f,V6__x),happ(V2__f,V7__y))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.MVT.derive_increasing_interv_var',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ! [V2__f] :
( c_24__type__795___24t(V2__f)
=> ! [V3__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(V2__f,V3__pr)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V1__b))
=> ( ! [V5__t] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__t)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V5__t))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V5__t,V1__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V2__f,V5__t,happ(V3__pr,V5__t)))) ) )
=> ! [V6__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__x)
=> ! [V7__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V6__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__x,V1__b)) )
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V7__y))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V7__y,V1__b)) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V6__x,V7__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V2__f,V6__x),happ(V2__f,V7__y))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.PSeries_reg.Boule_convex',axiom,
! [V0__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__c)
=> ! [V1__d] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V1__d)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__y)
=> ! [V4__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__z)
=> ( cCoq_2eReals_2ePSeries__reg_2eBoule___24a3(V0__c,V1__d,V2__x)
=> ( cCoq_2eReals_2ePSeries__reg_2eBoule___24a3(V0__c,V1__d,V3__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__x,V4__z))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V4__z,V3__y)) )
=> cCoq_2eReals_2ePSeries__reg_2eBoule___24a3(V0__c,V1__d,V4__z) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.PartSum.cauchy_abs',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ( cCoq_2eReals_2ePartSum_2eCauchy__crit__series___24a1(c_24__lam__63257___24a1(V0__An))
=> cCoq_2eReals_2ePartSum_2eCauchy__crit__series___24a1(V0__An) ) ) ).
fof('Coq.Reals.PartSum.cond_pos_sum',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(V0__An,V2__n))) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V1__N))) ) ) ) ).
fof('Coq.Reals.PartSum.scal_sum',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__x,cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V1__N)) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__6593___24a2(V0__An,V2__x),V1__N) ) ) ) ).
fof('Coq.Reals.PartSum.sum_Rle',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__Bn] :
( c_24__type__5115___24t(V1__Bn)
=> ! [V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V3__n,V2__N))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__An,V3__n),happ(V1__Bn,V3__n))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V2__N),cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__Bn,V2__N))) ) ) ) ) ).
fof('Coq.Reals.PartSum.sum_cv_maj',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__fn] :
( c_24__type__6580___24t(V1__fn)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ! [V3__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__l2)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__61712___24a2(V1__fn,V2__x),V3__l1)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__14596___24a1(V0__An),V4__l2)
=> ( ! [V7__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V7__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(happ(happ(V1__fn,V7__n),V2__x)),happ(V0__An,V7__n))) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V3__l1),V4__l2)) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.PartSum.sum_eq',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__Bn] :
( c_24__type__5115___24t(V1__Bn)
=> ! [V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ! [V3__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__i)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V3__i,V2__N))
=> happ(V0__An,V3__i) = happ(V1__Bn,V3__i) ) )
=> cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V2__N) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__Bn,V2__N) ) ) ) ) ).
fof('Coq.Reals.PartSum.sum_growing',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__Bn] :
( c_24__type__5115___24t(V1__Bn)
=> ! [V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__An,V3__n),happ(V1__Bn,V3__n))) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V2__N),cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__Bn,V2__N))) ) ) ) ) ).
fof('Coq.Reals.PartSum.sum_incr',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ! [V2__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__14596___24a1(V0__An),V2__l)
=> ( ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(V0__An,V4__n))) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V1__N),V2__l)) ) ) ) ) ) ).
fof('Coq.Reals.PartSum.tech4',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__k] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__k)
=> ! [V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__k))
=> ( ! [V4__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__i)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__An,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__i)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__k,happ(V0__An,V4__i)))) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__An,V2__N),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(V0__An,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eReals_2eRpow__def_2epow___24a2(V1__k,V2__N)))) ) ) ) ) ) ).
fof('Coq.Reals.PartSum.tech5',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__N)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V1__N),happ(V0__An,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__N))) ) ) ).
fof('Coq.Reals.RIneq.INR_IZR_INZ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n)) ) ).
fof('Coq.Reals.RIneq.INR_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) = cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Reals.RIneq.INR_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Reals.RIneq.IZR_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.IZR_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.IZR_neq',axiom,
! [V0__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z1)
=> ! [V1__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z2)
=> ( V0__z1 != V1__z2
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_dec',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
| V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Req_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Req_ge_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V1__r2 = V0__r1
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Req_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Req_le_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V1__r2 = V0__r1
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_not_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_refl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,V0__r)) ) ).
fof('Coq.Reals.RIneq.Rge_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_not_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_0_lt_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Rinv_1',axiom,
cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.RIneq.Rinv_1_lt_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_involutive',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) = V0__r ) ) ).
fof('Coq.Reals.RIneq.Rinv_l_sym',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r),V0__r) ) ) ).
fof('Coq.Reals.RIneq.Rinv_le_contravar',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__y),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__x))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_lt_0_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.Reals.RIneq.Rinv_lt_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_mult_distr',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_neq_0_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.Rinv_r_simpl_m',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1)) = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_r_sym',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) ) ) ).
fof('Coq.Reals.RIneq.Rle_0_sqr',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r))) ) ).
fof('Coq.Reals.RIneq.Rle_Rinv',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__y),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__x))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_antisym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1))
=> V0__r1 = V1__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_le_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)) )
<=> V0__r1 = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rle_lt_0_plus_1',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ) ) ).
fof('Coq.Reals.RIneq.Rle_lt_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_not_gt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_not_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_or_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
| p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_refl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,V0__r)) ) ).
fof('Coq.Reals.RIneq.Rle_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_0_1',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('Coq.Reals.RIneq.Rlt_Rminus',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V1__b))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__b,V0__a))) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_dichotomy_converse',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) )
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_eq_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( V0__r1 = V1__r2
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V3__r4))
=> ( V3__r4 = V2__r3
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_gt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_irrefl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,V0__r)) ) ).
fof('Coq.Reals.RIneq.Rlt_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_le_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_or_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rminus_diag_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_diag_uniq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_diag_uniq_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_eq_contra',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_not_eq_right',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_0_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.Rmult_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.Rmult_1_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = V0__r ) ).
fof('Coq.Reals.RIneq.Rmult_eq_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_eq_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V1__r1 = V2__r2 ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_gt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_gt_0_lt_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V2__r3,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_0_lt_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__r3))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__r3))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_compat_neg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_ge_compat_neg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_pos',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_reg_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_gt_compat_neg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_reg_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_minus_distr_l',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V2__r3)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3)) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_opp_opp',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) ) ) ).
fof('Coq.Reals.RIneq.Rmult_plus_distr_r',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V2__r3)) ) ) ) ).
fof('Coq.Reals.RIneq.Rnot_gt_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ~ p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rnot_le_gt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rnot_le_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rnot_lt_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_0',axiom,
cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.RIneq.Ropp_0_ge_le_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_0_gt_lt_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_0_le_ge_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_eq_0_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.Ropp_eq_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_ge_le_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_gt_lt_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_involutive',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) = V0__r ) ).
fof('Coq.Reals.RIneq.Ropp_le_cancel',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_le_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_le_ge_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_lt_cancel',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_lt_gt_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_minus_distr',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.RIneq.Ropp_minus_distr\'',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) ) ) ).
fof('Coq.Reals.RIneq.Ropp_mult_distr_l_reverse',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),V1__r2) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)) ) ) ).
fof('Coq.Reals.RIneq.Ropp_mult_distr_r_reverse',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)) ) ) ).
fof('Coq.Reals.RIneq.Ropp_plus_distr',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ) ) ).
fof('Coq.Reals.RIneq.Rplus_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rplus_0_r_uniq',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1) = V0__r
=> V1__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_0_l',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_R0',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V1__r2 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)
=> V1__r1 = V2__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_le_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_lt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_lt_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_reg_pos_r',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_reg_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_le_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_le_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_reg_pos_r',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_opp_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r),V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.Rsqr_0',axiom,
cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.RIneq.Rtotal_order',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| V0__r1 = V1__r2
| p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.S_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ).
fof('Coq.Reals.RIneq.cond_pos',axiom,
! [V0__p] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V0__p)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2epos___24a1(V0__p))) ) ).
fof('Coq.Reals.RIneq.double',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V0__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V0__r1) ) ).
fof('Coq.Reals.RIneq.double_var',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> V0__r1 = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ) ).
fof('Coq.Reals.RIneq.f_equal_R',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__4509___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.le_INR',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_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.le_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)))
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Reals.RIneq.le_epsilon',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ! [V2__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__eps))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V2__eps))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.lt_0_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n))) ) ) ).
fof('Coq.Reals.RIneq.lt_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.lt_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)))
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Reals.RIneq.mult_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.plus_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.plus_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.pos_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n))) ) ).
fof('Coq.Reals.RIneq.sum_inequa_Rle_lt',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__c)
=> ! [V4__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__y)
=> ! [V5__d] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__d)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__x,V2__b))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V3__c,V4__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V4__y,V5__d))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__a,V3__c),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__x,V4__y)))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__x,V4__y),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__b,V5__d))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.tech_Rplus',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__s] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__s)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__s))
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__s) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.RList.RList_P14',axiom,
! [V0__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V0__l)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> cCoq_2eReals_2eRList_2eRlength___24a1(cCoq_2eReals_2eRList_2emid__Rlist___24a2(V0__l,V1__a)) = cCoq_2eReals_2eRList_2eRlength___24a1(V0__l) ) ) ).
fof('Coq.Reals.RList.RList_P2',axiom,
! [V0__l1] :
( cCoq_2eReals_2eRList_2eRlist___24t(V0__l1)
=> ! [V1__l2] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l2)
=> ( cCoq_2eReals_2eRList_2eordered__Rlist___24a1(V1__l2)
=> cCoq_2eReals_2eRList_2eordered__Rlist___24a1(cCoq_2eReals_2eRList_2econs__ORlist___24a2(V0__l1,V1__l2)) ) ) ) ).
fof('Coq.Reals.RList.RList_P4',axiom,
! [V0__l1] :
( cCoq_2eReals_2eRList_2eRlist___24t(V0__l1)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ( cCoq_2eReals_2eRList_2eordered__Rlist___24a1(cCoq_2eReals_2eRList_2econs___24a2(V1__a,V0__l1))
=> cCoq_2eReals_2eRList_2eordered__Rlist___24a1(V0__l1) ) ) ) ).
fof('Coq.Reals.RList.RList_P5',axiom,
! [V0__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V0__l)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ( cCoq_2eReals_2eRList_2eordered__Rlist___24a1(V0__l)
=> ( cCoq_2eReals_2eRList_2eIn___24a2(V1__x,V0__l)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRList_2epos__Rl___24a2(V0__l,cCoq_2eInit_2eDatatypes_2eO),V1__x)) ) ) ) ) ).
fof('Coq.Reals.RList.RList_P7',axiom,
! [V0__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V0__l)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ( cCoq_2eReals_2eRList_2eordered__Rlist___24a1(V0__l)
=> ( cCoq_2eReals_2eRList_2eIn___24a2(V1__x,V0__l)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__x,cCoq_2eReals_2eRList_2epos__Rl___24a2(V0__l,cCoq_2eInit_2eNat_2epred___24a1(cCoq_2eReals_2eRList_2eRlength___24a1(V0__l))))) ) ) ) ) ).
fof('Coq.Reals.RList.RList_P9',axiom,
! [V0__l1] :
( cCoq_2eReals_2eRList_2eRlist___24t(V0__l1)
=> ! [V1__l2] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l2)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ( cCoq_2eReals_2eRList_2eIn___24a2(V2__x,cCoq_2eReals_2eRList_2econs__ORlist___24a2(V0__l1,V1__l2))
<=> ( cCoq_2eReals_2eRList_2eIn___24a2(V2__x,V0__l1)
| cCoq_2eReals_2eRList_2eIn___24a2(V2__x,V1__l2) ) ) ) ) ) ).
fof('Coq.Reals.RList.Rlist_ind',axiom,
! [V0__P] :
( c_24__type__6691___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eReals_2eRList_2enil))
=> ( ! [V2__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r)
=> ! [V3__r] :
( cCoq_2eReals_2eRList_2eRlist___24t(V3__r)
=> ( p(happ(V0__P,V3__r))
=> p(happ(V0__P,cCoq_2eReals_2eRList_2econs___24a2(V2__r,V3__r))) ) ) )
=> ! [V3__r] :
( cCoq_2eReals_2eRList_2eRlist___24t(V3__r)
=> p(happ(V0__P,V3__r)) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_1',axiom,
cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.R_sqr.Rsqr_incr_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_incr_0_var',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_incr_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_incrst_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y)) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_incrst_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_inj',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)
=> V0__x = V1__y ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_mult',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_neg',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x)) ) ).
fof('Coq.Reals.R_sqr.Rsqr_neg_pos_le_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__y),V0__x)) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_neg_pos_le_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__y),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_pos_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x))) ) ) ).
fof('Coq.Reals.R_sqr.neg_pos_Rsqr_le',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__y),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y))) ) ) ) ) ).
fof('Coq.Reals.R_sqr.triangle_rectangle',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__z))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V2__z)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V2__z),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V2__z))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V2__z),V1__y))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,V2__z)) ) ) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.Rle_mult_inv_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__y)))) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.Rsqr_sqrt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x)) = V0__x ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_0',axiom,
cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.R_sqrt.sqrt_Rsqr',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x)) = V0__x ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_def',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x)) = V0__x ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_div',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y)) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_eq_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__x = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_inj',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x) = cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y)
=> V0__x = V1__y ) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_le_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_le_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_le_1_alt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y))) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_lem_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x) = V1__y
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__y,V1__y) = V0__x ) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_lem_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__y,V1__y) = V0__x
=> cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x) = V1__y ) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_less',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),V0__x)) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_lt_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y)) ) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_lt_0_alt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_lt_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_lt_1_alt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y))) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_mult',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y)) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_mult_alt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y)) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x))) ) ).
fof('Coq.Reals.R_sqrt.sqrt_positivity',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x))) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_pow2',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))) = V0__x ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_sqrt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x)) = V0__x ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_square',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,V0__x)) = V0__x ) ) ).
fof('Coq.Reals.Ranalysis1.continuity_comp',axiom,
! [V0__f1] :
( c_24__type__795___24t(V0__f1)
=> ! [V1__f2] :
( c_24__type__795___24t(V1__f2)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V0__f1)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V1__f2)
=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(cCoq_2eReals_2eRanalysis1_2ecomp___24a2(V1__f2,V0__f1)) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.continuity_minus',axiom,
! [V0__f1] :
( c_24__type__795___24t(V0__f1)
=> ! [V1__f2] :
( c_24__type__795___24t(V1__f2)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V0__f1)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V1__f2)
=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(cCoq_2eReals_2eRanalysis1_2eminus__fct___24a2(V0__f1,V1__f2)) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.continuity_mult',axiom,
! [V0__f1] :
( c_24__type__795___24t(V0__f1)
=> ! [V1__f2] :
( c_24__type__795___24t(V1__f2)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V0__f1)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V1__f2)
=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(cCoq_2eReals_2eRanalysis1_2emult__fct___24a2(V0__f1,V1__f2)) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.continuity_opp',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V0__f)
=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(cCoq_2eReals_2eRanalysis1_2eopp__fct___24a1(V0__f)) ) ) ).
fof('Coq.Reals.Ranalysis1.continuity_pt_opp',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__x0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x0)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V1__x0)
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(cCoq_2eReals_2eRanalysis1_2eopp__fct___24a1(V0__f),V1__x0) ) ) ) ).
fof('Coq.Reals.Ranalysis1.deriv_maximum',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__c)
=> ! [V4__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V3__c,V4__pr)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V3__c))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V3__c,V2__b))
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V2__b))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V7__x),happ(V0__f,V3__c))) ) ) )
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V3__c,V4__pr) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.deriv_minimum',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__c)
=> ! [V4__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V3__c,V4__pr)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V3__c))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V3__c,V2__b))
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V2__b))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V3__c),happ(V0__f,V7__x))) ) ) )
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V3__c,V4__pr) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derivable_continuous',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1___24Anonymous] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(V0__f,V1___24Anonymous)
=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V0__f) ) ) ).
fof('Coq.Reals.Ranalysis1.derivable_continuous_pt',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2___24Anonymous] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V2___24Anonymous)
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V1__x) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derivable_derive',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V2__pr)
=> ? [V3__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l)
& cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V2__pr) = V3__l ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derivable_pt_lim_const',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(V0__a),V1__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.Reals.Ranalysis1.derivable_pt_lim_id',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRanalysis1_2eid,V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ).
fof('Coq.Reals.Ranalysis1.derivable_pt_lim_minus',axiom,
! [V0__f1] :
( c_24__type__795___24t(V0__f1)
=> ! [V1__f2] :
( c_24__type__795___24t(V1__f2)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ! [V3__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__l2)
=> ( cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f1,V2__x,V3__l1)
=> ( cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V1__f2,V2__x,V4__l2)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRanalysis1_2eminus__fct___24a2(V0__f1,V1__f2),V2__x,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V3__l1,V4__l2)) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derivable_pt_lim_plus',axiom,
! [V0__f1] :
( c_24__type__795___24t(V0__f1)
=> ! [V1__f2] :
( c_24__type__795___24t(V1__f2)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ! [V3__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__l2)
=> ( cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f1,V2__x,V3__l1)
=> ( cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V1__f2,V2__x,V4__l2)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRanalysis1_2eplus__fct___24a2(V0__f1,V1__f2),V2__x,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V3__l1,V4__l2)) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derive_pt_eq_0',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l)
=> ! [V3__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V3__pr)
=> ( cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f,V1__x,V2__l)
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V3__pr) = V2__l ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derive_pt_eq_1',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l)
=> ! [V3__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V3__pr)
=> ( cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V3__pr) = V2__l
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f,V1__x,V2__l) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.pr_nu',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__pr1] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V2__pr1)
=> ! [V3__pr2] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V3__pr2)
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V2__pr1) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V3__pr2) ) ) ) ) ).
fof('Coq.Reals.Ranalysis4.Rcontinuity_abs',axiom,
cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(cCoq_2eReals_2eRbasic__fun_2eRabs) ).
fof('Coq.Reals.Ranalysis4.continuity_finite_sum',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(c_24__lam__7048___24a2(V0__An,V1__N)) ) ) ).
fof('Coq.Reals.Ranalysis5.continuity_pt_recip_interv',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__g] :
( c_24__type__795___24t(V1__g)
=> ! [V2__lb] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__lb)
=> ! [V3__ub] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__ub)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V3__ub))
=> ( ! [V5__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__x)
=> ! [V6__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,V5__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V5__x,V6__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__y,V3__ub))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V5__x),happ(V0__f,V6__y))) ) ) ) ) )
=> ( ! [V6__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V6__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__x,happ(V0__f,V3__ub)))
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f,V1__g,V6__x) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V6__x) ) ) )
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V7__x,happ(V0__f,V3__ub)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,happ(V1__g,V7__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V7__x),V3__ub)) ) ) ) )
=> ( ! [V8__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__a)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,V8__a))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__a,V3__ub)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V8__a) ) )
=> ! [V9__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V9__b)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V2__lb),V9__b))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V9__b,happ(V0__f,V3__ub))) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V1__g,V9__b) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis5.derive_pt_recip_interv_prelim1_0',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__g] :
( c_24__type__795___24t(V1__g)
=> ! [V2__lb] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__lb)
=> ! [V3__ub] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__ub)
=> ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V3__ub))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V2__lb),V4__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V4__x,happ(V0__f,V3__ub))) )
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ! [V8__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V8__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__y,V3__ub))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V7__x),happ(V0__f,V8__y))) ) ) ) ) )
=> ( ! [V8__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V8__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__x,happ(V0__f,V3__ub)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,happ(V1__g,V8__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V8__x),V3__ub)) ) ) ) )
=> ( ! [V9__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V9__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V9__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V9__x,happ(V0__f,V3__ub)))
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f,V1__g,V9__x) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V9__x) ) ) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,happ(V1__g,V4__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V1__g,V4__x),V3__ub)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis5.derive_pt_recip_interv_prelim1_1',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__g] :
( c_24__type__795___24t(V1__g)
=> ! [V2__lb] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__lb)
=> ! [V3__ub] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__ub)
=> ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V3__ub))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V2__lb),V4__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V4__x,happ(V0__f,V3__ub))) )
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ! [V8__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V8__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__y,V3__ub))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V7__x),happ(V0__f,V8__y))) ) ) ) ) )
=> ( ! [V8__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V8__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__x,happ(V0__f,V3__ub)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,happ(V1__g,V8__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V8__x),V3__ub)) ) ) ) )
=> ( ! [V9__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V9__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V9__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V9__x,happ(V0__f,V3__ub)))
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f,V1__g,V9__x) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V9__x) ) ) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,happ(V1__g,V4__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V4__x),V3__ub)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis5.f_incr_implies_g_incr_interv',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__g] :
( c_24__type__795___24t(V1__g)
=> ! [V2__lb] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__lb)
=> ! [V3__ub] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__ub)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V3__ub))
=> ( ! [V5__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__x)
=> ! [V6__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,V5__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V5__x,V6__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__y,V3__ub))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V5__x),happ(V0__f,V6__y))) ) ) ) ) )
=> ( ! [V6__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V6__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__x,happ(V0__f,V3__ub)))
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f,V1__g,V6__x) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V6__x) ) ) )
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V7__x,happ(V0__f,V3__ub)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,happ(V1__g,V7__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V7__x),V3__ub)) ) ) ) )
=> ! [V8__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__x)
=> ! [V9__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V9__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V8__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V8__x,V9__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V9__y,happ(V0__f,V3__ub)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V1__g,V8__x),happ(V1__g,V9__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis5.leftinv_is_rightinv_interv',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__g] :
( c_24__type__795___24t(V1__g)
=> ! [V2__lb] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__lb)
=> ! [V3__ub] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__ub)
=> ( ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> ! [V5__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,V4__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V4__x,V5__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V5__y,V3__ub))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V4__x),happ(V0__f,V5__y))) ) ) ) ) )
=> ( ! [V5__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V5__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V5__y,happ(V0__f,V3__ub)))
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f,V1__g,V5__y) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V5__y) ) ) )
=> ( ! [V6__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V6__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__x,happ(V0__f,V3__ub)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,happ(V1__g,V6__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V6__x),V3__ub)) ) ) ) )
=> ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,V7__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V7__x,V3__ub)) )
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V1__g,V0__f,V7__x) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V7__x) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis5.pr_nu_var2_interv',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__g] :
( c_24__type__795___24t(V1__g)
=> ! [V2__lb] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__lb)
=> ! [V3__ub] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__ub)
=> ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> ! [V5__pr1] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V4__x,V5__pr1)
=> ! [V6__pr2] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V1__g,V4__x,V6__pr2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V3__ub))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V4__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V4__x,V3__ub)) )
=> ( ! [V9__h] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V9__h)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V9__h))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V9__h,V3__ub)) )
=> happ(V0__f,V9__h) = happ(V1__g,V9__h) ) )
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V4__x,V5__pr1) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V1__g,V4__x,V6__pr2) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ratan.Datan_seq_increasing',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V2__n,cCoq_2eInit_2eDatatypes_2eO))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRatan_2eDatan__seq___24a2(V0__x,V2__n),cCoq_2eReals_2eRatan_2eDatan__seq___24a2(V1__y,V2__n))) ) ) ) ) ) ).
fof('Coq.Reals.Ratan.Ratan_seq_converging',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(cCoq_2eReals_2eRatan_2eRatan__seq___24a1(V0__x),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.Reals.Ratan.Ratan_seq_decreasing',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(cCoq_2eReals_2eRatan_2eRatan__seq___24a1(V0__x)) ) ) ).
fof('Coq.Reals.Ratan.Ropp_div',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x),V1__y) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.Reals.Ratan.Un_cv_ext',axiom,
! [V0__un] :
( c_24__type__5115___24t(V0__un)
=> ! [V1__vn] :
( c_24__type__5115___24t(V1__vn)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__un,V2__n) = happ(V1__vn,V2__n) )
=> ! [V3__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__un,V3__l)
=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(V1__vn,V3__l) ) ) ) ) ) ).
fof('Coq.Reals.Ratan.atan_increasing',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRatan_2eatan___24a1(V0__x),cCoq_2eReals_2eRatan_2eatan___24a1(V1__y))) ) ) ) ).
fof('Coq.Reals.Ratan.ps_atanSeq_continuity_pt_1',axiom,
! [V0__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__N)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(c_24__lam__7248___24a1(V0__N),V1__x) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rlt_asym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rlt_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_1_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__r) = V0__r ) ).
fof('Coq.Reals.Raxioms.Rmult_assoc',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),V2__r3) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V2__r3)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_lt_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_plus_distr_l',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V2__r3)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_0_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r) = V0__r ) ).
fof('Coq.Reals.Raxioms.Rplus_assoc',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V2__r3)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_lt_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2))) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_opp_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.Raxioms.archimed',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r)),V0__r))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r)),V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('Coq.Reals.Rbasic_fun.RRle_abs',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x))) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_R0',axiom,
cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rbasic_fun.Rabs_Rabsolu',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x)) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_Ropp',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x)) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_def1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__a))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__a),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),V1__a)) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_def2',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),V1__a))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__a))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__a),V0__x)) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_le',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__b),V0__a))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__a),V1__b)) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_left',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_left1',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__a) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__a) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_mult',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__y)) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_no_R0',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x))) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_pos_eq',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) = V0__x ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_pos_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x))) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_right',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = V0__r ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_triang',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__a,V1__b)),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__a),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__b)))) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_triang_inv2',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__a),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__b))),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__a,V1__b)))) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rle_abs',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x))) ) ).
fof('Coq.Reals.Rbasic_fun.Rle_max_compat_l',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V2__z,V0__x),cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V2__z,V1__y))) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rle_max_compat_r',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V2__z),cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V1__y,V2__z))) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rle_min_compat_l',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V2__z,V0__x),cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V2__z,V1__y))) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rle_min_compat_r',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V2__z),cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V1__y,V2__z))) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.RmaxAbs',axiom,
! [V0__p] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__p,V1__q))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__q,V2__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__q),cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__p),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V2__r)))) ) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.RmaxRmult',axiom,
! [V0__p] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__r))
=> cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r,V0__p),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r,V1__q)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r,cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__p,V1__q)) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmax_l',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y))) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmax_left',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,V0__x))
=> cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V0__x ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmax_lub',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V2__z))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,V2__z))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y),V2__z)) ) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmax_r',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y))) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmax_right',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V1__y ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_Rgt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__r1,V1__r2),V2__r))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V2__r))
& p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,V2__r)) ) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_glb',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__z,V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__z,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__z,cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_l',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y),V0__x)) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_left',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V0__x ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_r',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y),V1__y)) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_right',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,V0__x))
=> cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V1__y ) ) ) ).
fof('Coq.Reals.Rfunctions.INR_fact_neq_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(V0__n)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.Rfunctions.R_dist_eq',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V0__x,V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.Rfunctions.Rle_pow',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__n))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__m),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__n))) ) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.fact_simpl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eArith_2eFactorial_2efact___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eArith_2eFactorial_2efact___24a1(V0__n)) ) ).
fof('Coq.Reals.Rfunctions.pow1',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.pow_R1_Rle',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__k))) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_Rabs',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n),cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),V1__n))) ) ) ).
fof('Coq.Reals.Rfunctions.pow_add',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__m)) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_incr',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V1__y,V2__n))) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_le',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__a))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__a,V1__n))) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n))) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_maj_Rabs',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__y),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V1__y,V2__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__n))) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_mult',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n1)
=> ! [V2__n2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n2)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eNat_2emul___24a2(V1__n1,V2__n2)) = cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n1),V2__n2) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_nonzero',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_P17',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__pr1] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V1__a,V2__b,V3__pr1)
=> ! [V4__pr2] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(c_24__lam__63032___24a3(V0__f,V1__a,V2__b),V1__a,V2__b,V4__pr2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V2__b))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V2__b,V3__pr1)),cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(c_24__lam__63032___24a3(V0__f,V1__a,V2__b),V1__a,V2__b,V4__pr2))) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_P18',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__g] :
( c_24__type__795___24t(V1__g)
=> ! [V2__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__a)
=> ! [V3__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__b)
=> ! [V4__pr1] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V2__a,V3__b,V4__pr1)
=> ! [V5__pr2] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V1__g,V2__a,V3__b,V5__pr2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V3__b))
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__a,V7__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V3__b)) )
=> happ(V0__f,V7__x) = happ(V1__g,V7__x) ) )
=> cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V2__a,V3__b,V4__pr1) = cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V1__g,V2__a,V3__b,V5__pr2) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_P19',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__g] :
( c_24__type__795___24t(V1__g)
=> ! [V2__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__a)
=> ! [V3__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__b)
=> ! [V4__pr1] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V2__a,V3__b,V4__pr1)
=> ! [V5__pr2] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V1__g,V2__a,V3__b,V5__pr2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V3__b))
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__a,V7__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V3__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V7__x),happ(V1__g,V7__x))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V2__a,V3__b,V4__pr1),cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V1__g,V2__a,V3__b,V5__pr2))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_P20',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V2__b))
=> ! [V4__pr] :
( c_24__type__79371___24t(V0__f,V1__a,V2__b,V4__pr)
=> ! [V5__pr0] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V1__a,V2__b,V5__pr0)
=> cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V2__b,V5__pr0) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRiemannInt_2eprimitive___24a5(V0__f,V1__a,V2__b,V4__pr,V2__b),cCoq_2eReals_2eRiemannInt_2eprimitive___24a5(V0__f,V1__a,V2__b,V4__pr,V1__a)) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_P25',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__c)
=> ! [V4__pr1] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V1__a,V2__b,V4__pr1)
=> ! [V5__pr2] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V2__b,V3__c,V5__pr2)
=> ! [V6__pr3] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V1__a,V3__c,V6__pr3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V2__b))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__b,V3__c))
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V2__b,V4__pr1),cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V2__b,V3__c,V5__pr2)) = cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V3__c,V6__pr3) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_P26',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__c)
=> ! [V4__pr1] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V1__a,V2__b,V4__pr1)
=> ! [V5__pr2] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V2__b,V3__c,V5__pr2)
=> ! [V6__pr3] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V1__a,V3__c,V6__pr3)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V2__b,V4__pr1),cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V2__b,V3__c,V5__pr2)) = cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V3__c,V6__pr3) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_P28',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V2__b))
=> ( ! [V5__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V5__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V5__x,V2__b)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V5__x) ) )
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V3__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V3__x,V2__b)) )
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRiemannInt_2eprimitive___24a4(V0__f,V1__a,V2__b,cCoq_2eReals_2eRiemannInt_2eFTC__P1___24a3(V0__f,V1__a,V2__b)),V3__x,happ(V0__f,V3__x)) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_P29',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V2__b))
=> ( ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V4__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V4__x,V2__b)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V4__x) ) )
=> cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(V0__f,cCoq_2eReals_2eRiemannInt_2eprimitive___24a4(V0__f,V1__a,V2__b,cCoq_2eReals_2eRiemannInt_2eFTC__P1___24a3(V0__f,V1__a,V2__b)),V1__a,V2__b) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_P5',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__pr1] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V1__a,V2__b,V3__pr1)
=> ! [V4__pr2] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V1__a,V2__b,V4__pr2)
=> cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V2__b,V3__pr1) = cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V2__b,V4__pr2) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_P9',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__pr] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V1__a,V1__a,V2__pr)
=> cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V1__a,V2__pr) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_const_bound',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l)
=> ! [V4__u] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__u)
=> ! [V5__h] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V1__a,V2__b,V5__h)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V2__b))
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V7__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V2__b)) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V3__l,happ(V0__f,V7__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V7__x),V4__u)) ) ) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V3__l,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V2__b,V1__a)),cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V2__b,V5__h)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V2__b,V5__h),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V4__u,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V2__b,V1__a)))) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt.RinvN_cv',axiom,
cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__7680,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ).
fof('Coq.Reals.RiemannInt.Rle_cv_lim',axiom,
! [V0__Un] :
( c_24__type__5115___24t(V0__Un)
=> ! [V1__Vn] :
( c_24__type__5115___24t(V1__Vn)
=> ! [V2__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l2)
=> ( ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,V4__n),happ(V1__Vn,V4__n))) )
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V2__l1)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V1__Vn,V3__l2)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__l1,V3__l2)) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt_SF.StepFun_P10',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ! [V2__lf] :
( cCoq_2eReals_2eRList_2eRlist___24t(V2__lf)
=> ! [V3__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__a)
=> ! [V4__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V3__a,V4__b))
=> ( cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple___24a5(V0__f,V3__a,V4__b,V1__l,V2__lf)
=> ? [V7__l_27] :
( cCoq_2eReals_2eRList_2eRlist___24t(V7__l_27)
& ? [V8__lf_27] :
( cCoq_2eReals_2eRList_2eRlist___24t(V8__lf_27)
& cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple__opt___24a5(V0__f,V3__a,V4__b,V7__l_27,V8__lf_27) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt_SF.StepFun_P14',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__l1] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eReals_2eRList_2eRlist___24t(V2__l2)
=> ! [V3__lf1] :
( cCoq_2eReals_2eRList_2eRlist___24t(V3__lf1)
=> ! [V4__lf2] :
( cCoq_2eReals_2eRList_2eRlist___24t(V4__lf2)
=> ! [V5__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__a)
=> ! [V6__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V5__a,V6__b))
=> ( cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple___24a5(V0__f,V5__a,V6__b,V1__l1,V3__lf1)
=> ( cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple__opt___24a5(V0__f,V5__a,V6__b,V2__l2,V4__lf2)
=> cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V3__lf1,V1__l1) = cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V4__lf2,V2__l2) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt_SF.StepFun_P17',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__l1] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eReals_2eRList_2eRlist___24t(V2__l2)
=> ! [V3__lf1] :
( cCoq_2eReals_2eRList_2eRlist___24t(V3__lf1)
=> ! [V4__lf2] :
( cCoq_2eReals_2eRList_2eRlist___24t(V4__lf2)
=> ! [V5__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__a)
=> ! [V6__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__b)
=> ( cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple___24a5(V0__f,V5__a,V6__b,V1__l1,V3__lf1)
=> ( cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple___24a5(V0__f,V5__a,V6__b,V2__l2,V4__lf2)
=> cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V3__lf1,V1__l1) = cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V4__lf2,V2__l2) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt_SF.StepFun_P2',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ! [V2__f] :
( c_24__type__795___24t(V2__f)
=> ! [V3__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V3__l)
=> ! [V4__lf] :
( cCoq_2eReals_2eRList_2eRlist___24t(V4__lf)
=> ( cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple___24a5(V2__f,V0__a,V1__b,V3__l,V4__lf)
=> cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple___24a5(V2__f,V1__b,V0__a,V3__l,V4__lf) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt_SF.StepFun_P3',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__c)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b))
=> cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple___24a5(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(V2__c),V0__a,V1__b,cCoq_2eReals_2eRList_2econs___24a2(V0__a,cCoq_2eReals_2eRList_2econs___24a2(V1__b,cCoq_2eReals_2eRList_2enil)),cCoq_2eReals_2eRList_2econs___24a2(V2__c,cCoq_2eReals_2eRList_2enil)) ) ) ) ) ).
fof('Coq.Reals.RiemannInt_SF.StepFun_P37',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ! [V2__f] :
( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(V0__a,V1__b,V2__f)
=> ! [V3__g] :
( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(V0__a,V1__b,V3__g)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b))
=> ( ! [V5__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V5__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V5__x,V1__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRiemannInt__SF_2efe___24a4(V0__a,V1__b,V2__f,V5__x),cCoq_2eReals_2eRiemannInt__SF_2efe___24a4(V0__a,V1__b,V3__g,V5__x))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRiemannInt__SF_2eRiemannInt__SF___24a3(V0__a,V1__b,V2__f),cCoq_2eReals_2eRiemannInt__SF_2eRiemannInt__SF___24a3(V0__a,V1__b,V3__g))) ) ) ) ) ) ) ).
fof('Coq.Reals.RiemannInt_SF.StepFun_P7',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ! [V2__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r1)
=> ! [V3__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r2)
=> ! [V4__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__r3)
=> ! [V5__f] :
( c_24__type__795___24t(V5__f)
=> ! [V6__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V6__l)
=> ! [V7__lf] :
( cCoq_2eReals_2eRList_2eRlist___24t(V7__lf)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b))
=> ( cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple___24a5(V5__f,V0__a,V1__b,cCoq_2eReals_2eRList_2econs___24a2(V2__r1,cCoq_2eReals_2eRList_2econs___24a2(V3__r2,V6__l)),cCoq_2eReals_2eRList_2econs___24a2(V4__r3,V7__lf))
=> cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple___24a5(V5__f,V3__r2,V1__b,cCoq_2eReals_2eRList_2econs___24a2(V3__r2,V6__l),V7__lf) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Rpower.Rle_Rpower',axiom,
! [V0__e] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__e)
=> ! [V1__n] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__e))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__n,V2__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpower_2eRpower___24a2(V0__e,V1__n),cCoq_2eReals_2eRpower_2eRpower___24a2(V0__e,V2__m))) ) ) ) ) ) ).
fof('Coq.Reals.Rpower.Rle_Rpower_l',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__c)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__c))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__a))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpower_2eRpower___24a2(V0__a,V2__c),cCoq_2eReals_2eRpower_2eRpower___24a2(V1__b,V2__c))) ) ) ) ) ) ).
fof('Coq.Reals.Rpower.Rlt_Rpower_l',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__c)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__c))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__a))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V1__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRpower_2eRpower___24a2(V0__a,V2__c),cCoq_2eReals_2eRpower_2eRpower___24a2(V1__b,V2__c))) ) ) ) ) ) ).
fof('Coq.Reals.Rpower.arcsinh_le',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpower_2earcsinh___24a1(V0__x),cCoq_2eReals_2eRpower_2earcsinh___24a1(V1__y))) ) ) ) ).
fof('Coq.Reals.Rpower.arcsinh_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRpower_2earcsinh___24a1(V0__x),cCoq_2eReals_2eRpower_2earcsinh___24a1(V1__y))) ) ) ) ).
fof('Coq.Reals.Rprod.le_n_2n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V0__n))) ) ).
fof('Coq.Reals.Rprod.prod_SO_Rle',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__Bn] :
( c_24__type__5115___24t(V1__Bn)
=> ! [V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V3__n,V2__N))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(V0__An,V3__n)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__An,V3__n),happ(V1__Bn,V3__n))) ) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V0__An,V2__N),cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V1__Bn,V2__N))) ) ) ) ) ).
fof('Coq.Reals.Rprod.prod_SO_pos',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V2__n,V1__N))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(V0__An,V2__n))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V0__An,V1__N))) ) ) ) ).
fof('Coq.Reals.Rseries.Un_bound_imp',axiom,
! [V0__Un] :
( c_24__type__5115___24t(V0__Un)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,V2__n),V1__x)) )
=> cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(cCoq_2eReals_2eRseries_2eEUn___24a1(V0__Un),V1__x) ) ) ) ).
fof('Coq.Reals.Rseries.finite_greater',axiom,
! [V0__Un] :
( c_24__type__5115___24t(V0__Un)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ? [V2__M] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__M)
& ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V3__n,V1__N))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,V3__n),V2__M)) ) ) ) ) ) ).
fof('Coq.Reals.Rseries.growing_prop',axiom,
! [V0__Un] :
( c_24__type__5115___24t(V0__Un)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( cCoq_2eReals_2eRseries_2eUn__growing___24a1(V0__Un)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V1__n,V2__m)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(V0__Un,V1__n),happ(V0__Un,V2__m))) ) ) ) ) ) ).
fof('Coq.Reals.Rsqrt_def.Rsqrt_positivity',axiom,
! [V0__x] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRsqrt__def_2eRsqrt___24a1(V0__x))) ) ).
fof('Coq.Reals.Rsqrt_def.continuity_seq',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__Un] :
( c_24__type__5115___24t(V1__Un)
=> ! [V2__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V2__l)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V1__Un,V2__l)
=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__26270___24a2(V0__f,V1__Un),happ(V0__f,V2__l)) ) ) ) ) ) ).
fof('Coq.Reals.Rsqrt_def.cv_dicho',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l2)
=> ! [V4__P] :
( c_24__type__9400___24t(V4__P)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(cCoq_2eReals_2eRsqrt__def_2edicho__lb___24a3(V0__x,V1__y,V4__P),V2__l1)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(cCoq_2eReals_2eRsqrt__def_2edicho__up___24a3(V0__x,V1__y,V4__P),V3__l2)
=> V2__l1 = V3__l2 ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Rsqrt_def.dicho_comp',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__P] :
( c_24__type__9400___24t(V2__P)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRsqrt__def_2edicho__lb___24a4(V0__x,V1__y,V2__P,V3__n),cCoq_2eReals_2eRsqrt__def_2edicho__up___24a4(V0__x,V1__y,V2__P,V3__n))) ) ) ) ) ) ).
fof('Coq.Reals.Rsqrt_def.dicho_lb_growing',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__P] :
( c_24__type__9400___24t(V2__P)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> cCoq_2eReals_2eRseries_2eUn__growing___24a1(cCoq_2eReals_2eRsqrt__def_2edicho__lb___24a3(V0__x,V1__y,V2__P)) ) ) ) ) ).
fof('Coq.Reals.Rsqrt_def.dicho_lb_maj',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__P] :
( c_24__type__9400___24t(V2__P)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> cCoq_2eReals_2eSeqProp_2ehas__ub___24a1(cCoq_2eReals_2eRsqrt__def_2edicho__lb___24a3(V0__x,V1__y,V2__P)) ) ) ) ) ).
fof('Coq.Reals.Rsqrt_def.dicho_lb_maj_y',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__P] :
( c_24__type__9400___24t(V2__P)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRsqrt__def_2edicho__lb___24a4(V0__x,V1__y,V2__P,V4__n),V1__y)) ) ) ) ) ) ).
fof('Coq.Reals.Rsqrt_def.dicho_up_decreasing',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__P] :
( c_24__type__9400___24t(V2__P)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(cCoq_2eReals_2eRsqrt__def_2edicho__up___24a3(V0__x,V1__y,V2__P)) ) ) ) ) ).
fof('Coq.Reals.Rsqrt_def.dicho_up_min',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__P] :
( c_24__type__9400___24t(V2__P)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> cCoq_2eReals_2eSeqProp_2ehas__lb___24a1(cCoq_2eReals_2eRsqrt__def_2edicho__up___24a3(V0__x,V1__y,V2__P)) ) ) ) ) ).
fof('Coq.Reals.Rsqrt_def.dicho_up_min_x',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__P] :
( c_24__type__9400___24t(V2__P)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRsqrt__def_2edicho__up___24a4(V0__x,V1__y,V2__P,V4__n))) ) ) ) ) ) ).
fof('Coq.Reals.Rsqrt_def.pow_2_n_infty',axiom,
cCoq_2eReals_2eSeqProp_2ecv__infty___24a1(cCoq_2eReals_2eRsqrt__def_2epow__2__n) ).
fof('Coq.Reals.Rtopology.Heine',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__X] :
( c_24__type__332___24t(V1__X)
=> ( cCoq_2eReals_2eRtopology_2ecompact___24a1(V1__X)
=> ( ! [V3__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__x)
=> ( p(happ(V1__X,V3__x))
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V3__x) ) )
=> cCoq_2eReals_2eRtopology_2euniform__continuity___24a2(V0__f,V1__X) ) ) ) ) ).
fof('Coq.Reals.Rtopology.compact_P1',axiom,
! [V0__X] :
( c_24__type__332___24t(V0__X)
=> ( cCoq_2eReals_2eRtopology_2ecompact___24a1(V0__X)
=> cCoq_2eReals_2eRtopology_2ebounded___24a1(V0__X) ) ) ).
fof('Coq.Reals.Rtopology.compact_P2',axiom,
! [V0__X] :
( c_24__type__332___24t(V0__X)
=> ( cCoq_2eReals_2eRtopology_2ecompact___24a1(V0__X)
=> cCoq_2eReals_2eRtopology_2eclosed__set___24a1(V0__X) ) ) ).
fof('Coq.Reals.Rtopology.compact_P3',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> cCoq_2eReals_2eRtopology_2ecompact___24a1(c_24__lam__26274___24a2(V0__a,V1__b)) ) ) ).
fof('Coq.Reals.Rtopology.continuity_ab_maj',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V2__b))
=> ( ! [V4__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__c)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V4__c))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V4__c,V2__b)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V4__c) ) )
=> ? [V5__Mx] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__Mx)
& ! [V6__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__c)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V6__c))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__c,V2__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V6__c),happ(V0__f,V5__Mx))) ) )
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V5__Mx))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V5__Mx,V2__b)) ) ) ) ) ) ) ).
fof('Coq.Reals.Rtopology.continuity_ab_min',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V2__b))
=> ( ! [V4__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__c)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V4__c))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V4__c,V2__b)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V4__c) ) )
=> ? [V5__mx] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__mx)
& ! [V6__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__c)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V6__c))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__c,V2__b)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V5__mx),happ(V0__f,V6__c))) ) )
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V5__mx))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V5__mx,V2__b)) ) ) ) ) ) ) ).
fof('Coq.Reals.Rtopology.neighbourhood_P1',axiom,
! [V0__D1] :
( c_24__type__332___24t(V0__D1)
=> ! [V1__D2] :
( c_24__type__332___24t(V1__D2)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ( cCoq_2eReals_2eRtopology_2eincluded___24a2(V0__D1,V1__D2)
=> ( cCoq_2eReals_2eRtopology_2eneighbourhood___24a2(V0__D1,V2__x)
=> cCoq_2eReals_2eRtopology_2eneighbourhood___24a2(V1__D2,V2__x) ) ) ) ) ) ).
fof('Coq.Reals.Rtopology.prolongement_C0',axiom,
! [V0__f] :
( c_24__type__795___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V2__b))
=> ( ! [V4__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__c)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V4__c))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V4__c,V2__b)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V4__c) ) )
=> ? [V5__g] :
( c_24__type__795___24t(V5__g)
& cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V5__g)
& ! [V6__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__c)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V6__c))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V6__c,V2__b)) )
=> happ(V5__g,V6__c) = happ(V0__f,V6__c) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Rtrigo1.PI_4',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) ).
fof('Coq.Reals.Rtrigo1.PI_RGT_0',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ).
fof('Coq.Reals.Rtrigo1.cos_decr_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRtrigo1_2ePI))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,cCoq_2eReals_2eRtrigo1_2ePI))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V1__y)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,V0__x)) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Rtrigo1.cos_decr_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRtrigo1_2ePI))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,cCoq_2eReals_2eRtrigo1_2ePI))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V1__y),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x))) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Rtrigo1.cos_decreasing_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRtrigo1_2ePI))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,cCoq_2eReals_2eRtrigo1_2ePI))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V1__y)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__y,V0__x)) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Rtrigo1.cos_decreasing_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRtrigo1_2ePI))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,cCoq_2eReals_2eRtrigo1_2ePI))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V1__y),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x))) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Rtrigo1.cos_neg',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2ecos___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x)) = cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x) ) ).
fof('Coq.Reals.Rtrigo1.sin_PI',axiom,
cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRtrigo1_2ePI) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rtrigo1.sin_PI_x',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRtrigo1_2ePI,V0__x)) = cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x) ) ).
fof('Coq.Reals.Rtrigo1.sin_ge_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRtrigo1_2ePI))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x))) ) ) ) ).
fof('Coq.Reals.Rtrigo1.sin_gt_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRtrigo1_2ePI))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x))) ) ) ) ).
fof('Coq.Reals.Rtrigo1.sin_neg',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x)) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x)) ) ).
fof('Coq.Reals.Rtrigo_def.cos_sym',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x) = cCoq_2eReals_2eRtrigo__def_2ecos___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x)) ) ).
fof('Coq.Reals.Rtrigo_def.exp_0',axiom,
cCoq_2eReals_2eRtrigo__def_2eexp___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.Rtrigo_def.pow_i',axiom,
! [V0__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__i)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__i))
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__i) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Rtrigo_def.sin_0',axiom,
cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.SeqProp.CV_minus',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__Bn] :
( c_24__type__5115___24t(V1__Bn)
=> ! [V2__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l2)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__An,V2__l1)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V1__Bn,V3__l2)
=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__9949___24a2(V0__An,V1__Bn),cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V2__l1,V3__l2)) ) ) ) ) ) ) ).
fof('Coq.Reals.SeqProp.CV_mult',axiom,
! [V0__An] :
( c_24__type__5115___24t(V0__An)
=> ! [V1__Bn] :
( c_24__type__5115___24t(V1__Bn)
=> ! [V2__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l2)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__An,V2__l1)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V1__Bn,V3__l2)
=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__9942___24a2(V0__An,V1__Bn),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__l1,V3__l2)) ) ) ) ) ) ) ).
fof('Coq.Reals.SeqProp.UL_sequence',axiom,
! [V0__Un] :
( c_24__type__5115___24t(V0__Un)
=> ! [V1__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l2)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V1__l1)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V2__l2)
=> V1__l1 = V2__l2 ) ) ) ) ) ).
fof('Coq.Reals.SeqProp.decreasing_ineq',axiom,
! [V0__Un] :
( c_24__type__5115___24t(V0__Un)
=> ! [V1__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__l)
=> ( cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(V0__Un)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V1__l)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__l,happ(V0__Un,V4__n))) ) ) ) ) ) ).
fof('Coq.Reals.SeqProp.decreasing_prop',axiom,
! [V0__Un] :
( c_24__type__5115___24t(V0__Un)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(V0__Un)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__n))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,V2__n),happ(V0__Un,V1__m))) ) ) ) ) ) ).
fof('Coq.Reals.SeqProp.growing_ineq',axiom,
! [V0__Un] :
( c_24__type__5115___24t(V0__Un)
=> ! [V1__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__l)
=> ( cCoq_2eReals_2eRseries_2eUn__growing___24a1(V0__Un)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V1__l)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,V4__n),V1__l)) ) ) ) ) ) ).
fof('Coq.Reals.SeqProp.tech9',axiom,
! [V0__Un] :
( c_24__type__5115___24t(V0__Un)
=> ( cCoq_2eReals_2eRseries_2eUn__growing___24a1(V0__Un)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V2__m,V3__n))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,V2__m),happ(V0__Un,V3__n))) ) ) ) ) ) ).
fof('Coq.Reals.Sqrt_reg.continuity_pt_sqrt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(cCoq_2eReals_2eR__sqrt_2esqrt,V0__x) ) ) ).
fof('Coq.Reals.Sqrt_reg.sqrt_continuity_pt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(cCoq_2eReals_2eR__sqrt_2esqrt,V0__x) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_preorder',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Sets.Classical_sets.Complement_Complement',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__U,V1__A)) = V1__A ) ) ).
fof('Coq.Sets.Ensembles.Extensionality_Ensembles',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ( cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V0__U,V1__A,V2__B)
=> V1__A = V2__B ) ) ) ) ).
fof('Coq.Sets.Ensembles.Full_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__U),V1__x) ) ) ).
fof('Coq.Sets.Ensembles.Inhabited_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V2__x)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__B) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Intersection_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__B,V2__C),V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Image.Im_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__V] :
( cType___24t(V1__V)
=> ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ! [V3__f] :
( c_24__type__91___24t(V0__U,V1__V,V3__f)
=> ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__X,V4__x)
=> ! [V6__y] :
( t(V6__y,V1__V)
=> ( V6__y = happ(V3__f,V4__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__V,cCoq_2eSets_2eImage_2eIm___24a4(V0__U,V1__V,V2__X,V3__f),V6__y) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Empty_set_minimal',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__X) ) ) ).
fof('Coq.Sets.Powerset.Intersection_decreases_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__a,V2__b),V1__a) ) ) ) ).
fof('Coq.Sets.Powerset.Intersection_decreases_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__a,V2__b),V2__b) ) ) ) ).
fof('Coq.ZArith.Zbool.Zle_bool_imp_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.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_mul',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_2emul___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n)) ) ).
fof('Coq.ZArith.Znat.inj_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_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.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)
=> 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)
=> 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.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zmult_le_approx',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n),V2__p))
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m) ) ) ) ) ) ) ).
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.Fourier_util.Rle_mult_inv_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__y)))) ) ) ) ) ).
fof('Coq.micromega.Fourier_util.Rle_zero_pos_plus1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))) ) ) ).
fof('Coq.micromega.RMicromega.RTautoChecker_sound',axiom,
! [V0__f] :
( cCoq_2emicromega_2eTauto_2eBFormula___24t(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),V0__f)
=> ! [V1__w] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eRMicromega_2eRWitness,V1__w)
=> ( cCoq_2emicromega_2eRMicromega_2eRTautoChecker___24a2(V0__f,V1__w) = cCoq_2eInit_2eDatatypes_2etrue
=> ! [V3__env] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(cCoq_2eReals_2eRdefinitions_2eR,V3__env)
=> cCoq_2emicromega_2eTauto_2eeval__bf___24a3(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),cCoq_2emicromega_2eRMicromega_2eReval__formula___24a1(V3__env),V0__f) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA13',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__6562___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_Zmult_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__6562___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V0__x)))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y))) ) ) ) ) ).
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__6562___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_plus_distr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__6562___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__6562___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__6562___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__6562___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__6562___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__6562___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__6562___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__6562___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
& cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.setoid_ring.RealField.Rlt_0_2',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ).
fof('RTopology.RTop_metrizable',axiom,
cTopology_2eMetricSpaces_2emetrizable___24a1(cRTopology_2eRTop) ).
fof('RTopology.RTop_metrization',axiom,
cTopology_2eMetricSpaces_2emetrizes___24a2(cRTopology_2eRTop,cRTopology_2eR__metric) ).
fof('RTopology.RTop_neighborhood_is_neighbourhood',axiom,
! [V0__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cCoq_2eReals_2eRdefinitions_2eR,V0__U)
=> ! [V1__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r)
=> ( cTopology_2eNeighborhoods_2eneighborhood___24a3(cRTopology_2eRTop,V0__U,V1__r)
<=> cCoq_2eReals_2eRtopology_2eneighbourhood___24a2(V0__U,V1__r) ) ) ) ).
fof('RTopology.R_interval_open',axiom,
! [V0__p] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__q)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(cRTopology_2eRTop,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__73344___24a2(V0__p,V1__q))) ) ) ).
fof('RTopology.R_lower_beam_open',axiom,
! [V0__p] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__p)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(cRTopology_2eRTop,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__72851___24a1(V0__p))) ) ).
fof('RTopology.R_metric_is_metric',axiom,
cTopology_2eMetricSpaces_2emetric___24a2(cCoq_2eReals_2eRdefinitions_2eR,cRTopology_2eR__metric) ).
fof('RTopology.R_upper_beam_open',axiom,
! [V0__p] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__p)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(cRTopology_2eRTop,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__72876___24a1(V0__p))) ) ).
fof('Topology.Compactness.compact_impl_filter_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eCompactness_2ecompact___24a1(V0__X)
=> ! [V2__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ? [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
& cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V2__F,V3__x0) ) ) ) ) ).
fof('Topology.Compactness.compact_impl_net_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eCompactness_2ecompact___24a1(V0__X)
=> ! [V2__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V2__I)
=> ! [V3__x] :
( cTopology_2eNets_2eNet___24t(V2__I,V0__X,V3__x)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V2__I))
=> ? [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
& cTopology_2eNets_2enet__cluster__point___24a4(V2__I,V0__X,V3__x,V5__x0) ) ) ) ) ) ) ).
fof('Topology.Compactness.filter_cluster_point_impl_compact',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ? [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
& cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V1__F,V2__x0) ) )
=> cTopology_2eCompactness_2ecompact___24a1(V0__X) ) ) ).
fof('Topology.Compactness.net_cluster_point_impl_compact',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__I))
=> ? [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x0)
& cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V4__x0) ) ) ) )
=> cTopology_2eCompactness_2ecompact___24a1(V0__X) ) ) ).
fof('Topology.Completeness.cauchy_sequence_with_cluster_point_converges',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__25___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__x] :
( cTopology_2eNets_2eNet___24t(cTopology_2eDirectedSets_2enat__DS,cTopology_2eMetricSpaces_2eMetricTopology___24a2(V0__X,V1__d),V3__x)
=> ! [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(cTopology_2eMetricSpaces_2eMetricTopology___24a2(V0__X,V1__d),V4__x0)
=> ( cTopology_2eCompleteness_2ecauchy___24a3(V0__X,V1__d,V3__x)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(cTopology_2eDirectedSets_2enat__DS,cTopology_2eMetricSpaces_2eMetricTopology___24a2(V0__X,V1__d),V3__x,V4__x0)
=> cTopology_2eNets_2enet__limit___24a4(cTopology_2eDirectedSets_2enat__DS,cTopology_2eMetricSpaces_2eMetricTopology___24a2(V0__X,V1__d),V3__x,V4__x0) ) ) ) ) ) ) ) ).
fof('Topology.Continuity.continuous_at_open_neighborhoods',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__5952___24t(V0__X,V1__Y,V2__f)
=> ! [V3__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x)
=> ( ! [V4__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V4__V)
=> ( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V1__Y,V4__V,happ(V2__f,V3__x))
=> cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f,V4__V),V3__x) ) )
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x) ) ) ) ) ) ).
fof('Topology.Continuity.continuous_func_continuous_everywhere',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__5952___24t(V0__X,V1__Y,V2__f)
=> ( cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V2__f)
=> ! [V4__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x)
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V4__x) ) ) ) ) ) ).
fof('Topology.DirectedSets.DS_join_cond',axiom,
! [V0__d] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__d)
=> ! [V1__i] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__d,V1__i)
=> ! [V2__j] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__d,V2__j)
=> ? [V3__k] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__d,V3__k)
& cTopology_2eDirectedSets_2eDS__ord___24a3(V0__d,V1__i,V3__k)
& cTopology_2eDirectedSets_2eDS__ord___24a3(V0__d,V2__j,V3__k) ) ) ) ) ).
fof('Topology.DirectedSets.DS_ord_cond',axiom,
! [V0__d] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__d)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(cTopology_2eDirectedSets_2eDS__set___24a1(V0__d),cTopology_2eDirectedSets_2eDS__ord___24a1(V0__d)) ) ).
fof('Topology.DirectedSets.eventually_and',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__P] :
( c_24__type__2919___24t(V0__I,V1__P)
=> ! [V2__Q] :
( c_24__type__2919___24t(V0__I,V2__Q)
=> ( cTopology_2eDirectedSets_2eeventually___24a2(V0__I,V1__P)
=> ( cTopology_2eDirectedSets_2eeventually___24a2(V0__I,V2__Q)
=> cTopology_2eDirectedSets_2eeventually___24a2(V0__I,c_24__lam__78771___24a3(V0__I,V1__P,V2__Q)) ) ) ) ) ) ).
fof('Topology.DirectedSets.eventually_impl',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__P] :
( c_24__type__2919___24t(V0__I,V1__P)
=> ! [V2__Q] :
( c_24__type__2919___24t(V0__I,V2__Q)
=> ( cTopology_2eDirectedSets_2eeventually___24a2(V0__I,V1__P)
=> ( cTopology_2eDirectedSets_2eeventually___24a2(V0__I,c_24__lam__78784___24a3(V0__I,V1__P,V2__Q))
=> cTopology_2eDirectedSets_2eeventually___24a2(V0__I,V2__Q) ) ) ) ) ) ).
fof('Topology.DirectedSets.eventually_impl_base',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__P] :
( c_24__type__2919___24t(V0__I,V1__P)
=> ! [V2__Q] :
( c_24__type__2919___24t(V0__I,V2__Q)
=> ( ! [V3__i] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__I,V3__i)
=> ( p(happ(V1__P,V3__i))
=> p(happ(V2__Q,V3__i)) ) )
=> ( cTopology_2eDirectedSets_2eeventually___24a2(V0__I,V1__P)
=> cTopology_2eDirectedSets_2eeventually___24a2(V0__I,V2__Q) ) ) ) ) ) ).
fof('Topology.DirectedSets.not_eal_eventually_not',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__P] :
( c_24__type__2919___24t(V0__I,V1__P)
=> ( ~ cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V0__I,V1__P)
=> cTopology_2eDirectedSets_2eeventually___24a2(V0__I,c_24__lam__78791___24a2(V0__I,V1__P)) ) ) ) ).
fof('Topology.DirectedSets.not_eventually_eal_not',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__P] :
( c_24__type__2919___24t(V0__I,V1__P)
=> ( ~ cTopology_2eDirectedSets_2eeventually___24a2(V0__I,V1__P)
=> cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V0__I,c_24__lam__78796___24a2(V0__I,V1__P)) ) ) ) ).
fof('Topology.Filters.filter_empty',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__f] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__f)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f),cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__X)) ) ) ).
fof('Topology.Filters.filter_full',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__f] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__f)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f),cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X)) ) ) ).
fof('Topology.Filters.filter_upward_closed',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__f] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__f)
=> ! [V2__S1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__S1)
=> ! [V3__S2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S2)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f),V2__S1)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V2__S1,V3__S2)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f),V3__S2) ) ) ) ) ) ) ).
fof('Topology.FiltersAndNets.filter_cluster_point_impl_filter_to_net_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ( cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V1__F,V2__x0)
=> cTopology_2eNets_2enet__cluster__point___24a4(cTopology_2eFiltersAndNets_2efilter__to__net__DS___24a2(V0__X,V1__F),V0__X,cTopology_2eFiltersAndNets_2efilter__to__net___24a2(V0__X,V1__F),V2__x0) ) ) ) ) ).
fof('Topology.FiltersAndNets.filter_to_net_cluster_point_impl_filter_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(cTopology_2eFiltersAndNets_2efilter__to__net__DS___24a2(V0__X,V1__F),V0__X,cTopology_2eFiltersAndNets_2efilter__to__net___24a2(V0__X,V1__F),V2__x0)
=> cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V1__F,V2__x0) ) ) ) ) ).
fof('Topology.FiltersAndNets.net_cluster_point_impl_tail_filter_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__J)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__J,V0__X,V2__x)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J))
=> ! [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V1__J,V0__X,V2__x,V4__x0)
=> cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,cTopology_2eFiltersAndNets_2etail__filter___24a3(V0__X,V1__J,V2__x),V4__x0) ) ) ) ) ) ) ).
fof('Topology.FiltersAndNets.net_limit_impl_tail_filter_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__J)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__J,V0__X,V2__x)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J))
=> ! [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x0)
=> ( cTopology_2eNets_2enet__limit___24a4(V1__J,V0__X,V2__x,V4__x0)
=> cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,cTopology_2eFiltersAndNets_2etail__filter___24a3(V0__X,V1__J,V2__x),V4__x0) ) ) ) ) ) ) ).
fof('Topology.FiltersAndNets.tail_filter_cluster_point_impl_net_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__J)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__J,V0__X,V2__x)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J))
=> ! [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x0)
=> ( cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,cTopology_2eFiltersAndNets_2etail__filter___24a3(V0__X,V1__J,V2__x),V4__x0)
=> cTopology_2eNets_2enet__cluster__point___24a4(V1__J,V0__X,V2__x,V4__x0) ) ) ) ) ) ) ).
fof('Topology.FiltersAndNets.tail_filter_limit_impl_net_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__J)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__J,V0__X,V2__x)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J))
=> ! [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x0)
=> ( cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,cTopology_2eFiltersAndNets_2etail__filter___24a3(V0__X,V1__J,V2__x),V4__x0)
=> cTopology_2eNets_2enet__limit___24a4(V1__J,V0__X,V2__x,V4__x0) ) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.closure_closed',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S)) ) ) ).
fof('Topology.InteriorsClosures.closure_impl_meets_every_open_neighborhood',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),V2__x)
=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V2__x)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V4__U)) ) ) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.closure_inflationary',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S)) ) ) ).
fof('Topology.InteriorsClosures.closure_minimal',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__F)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V2__F)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),V2__F) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.meets_every_open_neighborhood_impl_closure',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V3__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U,V2__x)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V3__U)) ) ) )
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),V2__x) ) ) ) ) ).
fof('Topology.MetricSpaces.Build_metric',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__25___24t(V0__X,V1__d)
=> ( ! [V2__x] :
( t(V2__x,V0__X)
=> ! [V3__y] :
( t(V3__y,V0__X)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(V1__d,V2__x),V3__y),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
=> ( ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__y] :
( t(V4__y,V0__X)
=> happ(happ(V1__d,V3__x),V4__y) = happ(happ(V1__d,V4__y),V3__x) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__X)
=> ! [V5__y] :
( t(V5__y,V0__X)
=> ! [V6__z] :
( t(V6__z,V0__X)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(V1__d,V4__x),V6__z),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(V1__d,V4__x),V5__y),happ(happ(V1__d,V5__y),V6__z)))) ) ) )
=> ( ! [V5__x] :
( t(V5__x,V0__X)
=> happ(happ(V1__d,V5__x),V5__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
=> ( ! [V6__x] :
( t(V6__x,V0__X)
=> ! [V7__y] :
( t(V7__y,V0__X)
=> ( happ(happ(V1__d,V6__x),V7__y) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V6__x = V7__y ) ) )
=> cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.MetricTopology_metrizable',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__25___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> cTopology_2eMetricSpaces_2emetrizes___24a2(cTopology_2eMetricSpaces_2eMetricTopology___24a2(V0__X,V1__d),V1__d) ) ) ) ).
fof('Topology.MetricSpaces.intro_metrizable',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__222___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> cTopology_2eMetricSpaces_2emetrizable___24a1(V0__X) ) ) ) ) ).
fof('Topology.MetricSpaces.intro_open_ball',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__25___24t(V0__X,V1__d)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> ! [V3__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V3__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis___24a3(V0__X,V1__d,V2__x),cTopology_2eMetricSpaces_2eopen__ball___24a4(V0__X,V1__d,V2__x,V3__r)) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_nonneg',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__25___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__y] :
( t(V4__y,V0__X)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(V1__d,V3__x),V4__y),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_space_net_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__222___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> ! [V3__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__I)
=> ! [V4__x] :
( cTopology_2eNets_2eNet___24t(V3__I,V0__X,V4__x)
=> ! [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
=> ( ! [V6__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V6__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V3__I,c_24__lam__6461___24a6(V0__X,V1__d,V3__I,V4__x,V5__x0,V6__eps)) ) )
=> cTopology_2eNets_2enet__cluster__point___24a4(V3__I,V0__X,V4__x,V5__x0) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_space_net_cluster_point_converse',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__222___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> ! [V3__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__I)
=> ! [V4__x] :
( cTopology_2eNets_2eNet___24t(V3__I,V0__X,V4__x)
=> ! [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V3__I,V0__X,V4__x,V5__x0)
=> ! [V7__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V7__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V3__I,c_24__lam__41709___24a6(V0__X,V1__d,V3__I,V4__x,V5__x0,V7__eps)) ) ) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_space_net_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__222___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> ! [V3__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__I)
=> ! [V4__x] :
( cTopology_2eNets_2eNet___24t(V3__I,V0__X,V4__x)
=> ! [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
=> ( ! [V6__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V6__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cTopology_2eDirectedSets_2eeventually___24a2(V3__I,c_24__lam__4420___24a6(V0__X,V1__d,V3__I,V4__x,V5__x0,V6__eps)) ) )
=> cTopology_2eNets_2enet__limit___24a4(V3__I,V0__X,V4__x,V5__x0) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_space_net_limit_converse',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__222___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> ! [V3__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__I)
=> ! [V4__x] :
( cTopology_2eNets_2eNet___24t(V3__I,V0__X,V4__x)
=> ! [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
=> ( cTopology_2eNets_2enet__limit___24a4(V3__I,V0__X,V4__x,V5__x0)
=> ! [V7__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V7__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cTopology_2eDirectedSets_2eeventually___24a2(V3__I,c_24__lam__4435___24a6(V0__X,V1__d,V3__I,V4__x,V5__x0,V7__eps)) ) ) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_sym',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__25___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__y] :
( t(V4__y,V0__X)
=> happ(happ(V1__d,V3__x),V4__y) = happ(happ(V1__d,V4__y),V3__x) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_zero',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__25___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> happ(happ(V1__d,V3__x),V3__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Topology.MetricSpaces.triangle_inequality',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__25___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__y] :
( t(V4__y,V0__X)
=> ! [V5__z] :
( t(V5__z,V0__X)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(V1__d,V3__x),V5__z),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(V1__d,V3__x),V4__y),happ(happ(V1__d,V4__y),V5__z)))) ) ) ) ) ) ) ).
fof('Topology.NeighborhoodBases.open_neighborhood_basis_elements',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__NB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__NB)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V0__X,V1__NB,V2__x)
=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__NB,V4__U)
=> cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,V4__U,V2__x) ) ) ) ) ) ) ).
fof('Topology.Neighborhoods.open_neighborhood_is_neighborhood',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,V1__U,V2__x)
=> cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,V1__U,V2__x) ) ) ) ) ).
fof('Topology.Nets.Subnet_ind',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__J)
=> ! [V4__P] :
( c_24__type__78800___24t(V0__X,V1__I,V3__J,V4__P)
=> ( ! [V5__h] :
( c_24__type__69406___24t(V0__X,V1__I,V3__J,V5__h)
=> ( ! [V6__j1] :
( cTopology_2eDirectedSets_2eDS__set___24t(V3__J,V6__j1)
=> ! [V7__j2] :
( cTopology_2eDirectedSets_2eDS__set___24t(V3__J,V7__j2)
=> ( cTopology_2eDirectedSets_2eDS__ord___24a3(V3__J,V6__j1,V7__j2)
=> cTopology_2eDirectedSets_2eDS__ord___24a3(V1__I,happ(V5__h,V6__j1),happ(V5__h,V7__j2)) ) ) )
=> ( cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V1__I,c_24__lam__78820___24a4(V0__X,V1__I,V3__J,V5__h))
=> p(happ(V4__P,c_24__lam__78832___24a5(V0__X,V1__I,V2__x,V3__J,V5__h))) ) ) )
=> ! [V6__n] :
( cTopology_2eNets_2eNet___24t(V3__J,V0__X,V6__n)
=> ( cTopology_2eNets_2eSubnet___24a5(V0__X,V1__I,V2__x,V3__J,V6__n)
=> p(happ(V4__P,V6__n)) ) ) ) ) ) ) ) ) ).
fof('Topology.Nets.cluster_point_subnet_converges',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V3__x0)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__I))
=> cTopology_2eNets_2enet__limit___24a4(cTopology_2eNets_2ecluster__point__subnet__DS___24a4(V0__X,V1__I,V2__x,V3__x0),V0__X,cTopology_2eNets_2ecluster__point__subnet___24a4(V0__X,V1__I,V2__x,V3__x0),V3__x0) ) ) ) ) ) ) ).
fof('Topology.Nets.cluster_point_subnet_is_subnet',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V3__x0)
=> cTopology_2eNets_2eSubnet___24a5(V0__X,V1__I,V2__x,cTopology_2eNets_2ecluster__point__subnet__DS___24a4(V0__X,V1__I,V2__x,V3__x0),cTopology_2eNets_2ecluster__point__subnet___24a4(V0__X,V1__I,V2__x,V3__x0)) ) ) ) ) ) ).
fof('Topology.Nets.continuous_func_preserves_net_limits',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__5952___24t(V0__X,V1__Y,V2__f)
=> ! [V3__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__I)
=> ! [V4__x] :
( cTopology_2eNets_2eNet___24t(V3__I,V0__X,V4__x)
=> ! [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
=> ( cTopology_2eNets_2enet__limit___24a4(V3__I,V0__X,V4__x,V5__x0)
=> ( cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V5__x0)
=> cTopology_2eNets_2enet__limit___24a4(V3__I,V1__Y,c_24__lam__69289___24a5(V0__X,V1__Y,V2__f,V3__I,V4__x),happ(V2__f,V5__x0)) ) ) ) ) ) ) ) ) ).
fof('Topology.Nets.cps_U_open_neigh',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ! [V4__c] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(V0__X,V1__I,V2__x,V3__x0,V4__c)
=> cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,cTopology_2eNets_2ecps__U___24a5(V0__X,V1__I,V2__x,V3__x0,V4__c),V3__x0) ) ) ) ) ) ).
fof('Topology.Nets.cps_xi_in_U',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ! [V4__c] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(V0__X,V1__I,V2__x,V3__x0,V4__c)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eNets_2ecps__U___24a5(V0__X,V1__I,V2__x,V3__x0,V4__c),happ(V2__x,cTopology_2eNets_2ecps__i___24a5(V0__X,V1__I,V2__x,V3__x0,V4__c))) ) ) ) ) ) ).
fof('Topology.Nets.func_preserving_net_limits_is_continuous',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__5952___24t(V0__X,V1__Y,V2__f)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( ! [V4__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V4__I)
=> ! [V5__x] :
( cTopology_2eNets_2eNet___24t(V4__I,V0__X,V5__x)
=> ( cTopology_2eNets_2enet__limit___24a4(V4__I,V0__X,V5__x,V3__x0)
=> cTopology_2eNets_2enet__limit___24a4(V4__I,V1__Y,c_24__lam__79168___24a5(V0__X,V1__Y,V2__f,V4__I,V5__x),happ(V2__f,V3__x0)) ) ) )
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x0) ) ) ) ) ) ).
fof('Topology.Nets.intro_subnet',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__J)
=> ! [V4__h] :
( c_24__type__69406___24t(V0__X,V1__I,V3__J,V4__h)
=> ( ! [V5__j1] :
( cTopology_2eDirectedSets_2eDS__set___24t(V3__J,V5__j1)
=> ! [V6__j2] :
( cTopology_2eDirectedSets_2eDS__set___24t(V3__J,V6__j2)
=> ( cTopology_2eDirectedSets_2eDS__ord___24a3(V3__J,V5__j1,V6__j2)
=> cTopology_2eDirectedSets_2eDS__ord___24a3(V1__I,happ(V4__h,V5__j1),happ(V4__h,V6__j2)) ) ) )
=> ( cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V1__I,c_24__lam__69423___24a4(V0__X,V1__I,V3__J,V4__h))
=> cTopology_2eNets_2eSubnet___24a5(V0__X,V1__I,V2__x,V3__J,c_24__lam__69435___24a5(V0__X,V1__I,V2__x,V3__J,V4__h)) ) ) ) ) ) ) ) ).
fof('Topology.Nets.neighborhood_net_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> cTopology_2eNets_2enet__limit___24a4(cTopology_2eNets_2eneighborhood__net__DS___24a2(V0__X,V1__x),V0__X,cTopology_2eNets_2eneighborhood__net___24a2(V0__X,V1__x),V1__x) ) ) ).
fof('Topology.Nets.net_cluster_point_impl_subnet_converges',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V3__x0)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__I))
=> ? [V6__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V6__J)
& ? [V7__y] :
( cTopology_2eNets_2eNet___24t(V6__J,V0__X,V7__y)
& cTopology_2eNets_2eSubnet___24a5(V0__X,V1__I,V2__x,V6__J,V7__y)
& cTopology_2eNets_2enet__limit___24a4(V6__J,V0__X,V7__y,V3__x0) ) ) ) ) ) ) ) ) ).
fof('Topology.Nets.net_cluster_point_in_closure',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__X)
=> ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V2__S)
=> ! [V3__x] :
( cTopology_2eNets_2eNet___24t(V0__I,V1__X,V3__x)
=> ! [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V1__X,V4__x0)
=> ( cTopology_2eDirectedSets_2eeventually___24a2(V0__I,c_24__lam__4491___24a4(V0__I,V1__X,V2__S,V3__x))
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V0__I,V1__X,V3__x,V4__x0)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V1__X,V2__S),V4__x0) ) ) ) ) ) ) ) ).
fof('Topology.Nets.net_limit_in_closure',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__X)
=> ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V2__S)
=> ! [V3__x] :
( cTopology_2eNets_2eNet___24t(V0__I,V1__X,V3__x)
=> ! [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V1__X,V4__x0)
=> ( cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V0__I,c_24__lam__4491___24a4(V0__I,V1__X,V2__S,V3__x))
=> ( cTopology_2eNets_2enet__limit___24a4(V0__I,V1__X,V3__x,V4__x0)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V1__X,V2__S),V4__x0) ) ) ) ) ) ) ) ).
fof('Topology.Nets.net_limit_is_cluster_point',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__X)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V0__I,V1__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V1__X,V3__x0)
=> ( cTopology_2eNets_2enet__limit___24a4(V0__I,V1__X,V2__x,V3__x0)
=> cTopology_2eNets_2enet__cluster__point___24a4(V0__I,V1__X,V2__x,V3__x0) ) ) ) ) ) ).
fof('Topology.Nets.net_limits_determine_topology',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),V2__x0)
=> ? [V4__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V4__I)
& ? [V5__x] :
( cTopology_2eNets_2eNet___24t(V4__I,V0__X,V5__x)
& ! [V6__i] :
( cTopology_2eDirectedSets_2eDS__set___24t(V4__I,V6__i)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,happ(V5__x,V6__i)) )
& cTopology_2eNets_2enet__limit___24a4(V4__I,V0__X,V5__x,V2__x0) ) ) ) ) ) ) ).
fof('Topology.Nets.subnet_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ! [V4__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V4__J)
=> ! [V5__y] :
( cTopology_2eNets_2eNet___24t(V4__J,V0__X,V5__y)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V4__J,V0__X,V5__y,V3__x0)
=> ( cTopology_2eNets_2eSubnet___24a5(V0__X,V1__I,V2__x,V4__J,V5__y)
=> cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V3__x0) ) ) ) ) ) ) ) ) ).
fof('Topology.Nets.subnet_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ! [V4__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V4__J)
=> ! [V5__y] :
( cTopology_2eNets_2eNet___24t(V4__J,V0__X,V5__y)
=> ( cTopology_2eNets_2enet__limit___24a4(V1__I,V0__X,V2__x,V3__x0)
=> ( cTopology_2eNets_2eSubnet___24a5(V0__X,V1__I,V2__x,V4__J,V5__y)
=> cTopology_2eNets_2enet__limit___24a4(V4__J,V0__X,V5__y,V3__x0) ) ) ) ) ) ) ) ) ).
fof('Topology.OpenBases.Build_TopologicalSpace_from_open_basis_basis',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__B)
=> ( cTopology_2eOpenBases_2eopen__basis__cond___24a2(V0__X,V1__B)
=> ( cTopology_2eOpenBases_2eopen__basis__cover__cond___24a2(V0__X,V1__B)
=> cTopology_2eOpenBases_2eopen__basis___24a2(cTopology_2eOpenBases_2eBuild__TopologicalSpace__from__open__basis___24a2(V0__X,V1__B),V1__B) ) ) ) ) ).
fof('Topology.OpenBases.open_basis_cover',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__B)
=> ( cTopology_2eOpenBases_2eopen__basis___24a2(V0__X,V1__B)
=> ! [V3__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x)
=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V3__x)
=> ? [V7__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V7__V)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__B,V7__V)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V7__V,V4__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V7__V,V3__x) ) ) ) ) ) ) ) ) ).
fof('Topology.SeparatednessAxioms.Hausdorff_impl_net_limit_is_unique_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X)
=> ( cTopology_2eNets_2enet__limit___24a4(V1__I,V0__X,V2__x,V3__x0)
=> ! [V6__y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V6__y)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V6__y)
=> V6__y = V3__x0 ) ) ) ) ) ) ) ) ).
fof('Topology.SeparatednessAxioms.Hausdorff_impl_net_limit_unique',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ( cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X)
=> cCoq_2eInit_2eLogic_2euniqueness___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eNets_2enet__limit___24a3(V1__I,V0__X,V2__x)) ) ) ) ) ).
fof('Topology.SeparatednessAxioms.net_limit_is_unique_cluster_point_impl_Hausdorff',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ! [V4__y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__y)
=> ( cTopology_2eNets_2enet__limit___24a4(V1__I,V0__X,V2__x,V3__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V4__y)
=> V4__y = V3__x0 ) ) ) ) ) )
=> cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X) ) ) ).
fof('Topology.SeparatednessAxioms.net_limit_uniqueness_impl_Hausdorff',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> cCoq_2eInit_2eLogic_2euniqueness___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eNets_2enet__limit___24a3(V1__I,V0__X,V2__x)) ) )
=> cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X) ) ) ).
fof('Topology.SupInf.lt_plus_epsilon_le',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ! [V2__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V2__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__y,V2__eps))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ) ) ).
fof('Topology.TopologicalSpaces.open_full',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t))) ) ).
fof('Topology.TopologicalSpaces.open_intersection2',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> ! [V1__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V1__U)
=> ! [V2__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V2__V)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,V1__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,V2__V)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V1__U,V2__V)) ) ) ) ) ) ).
fof('Topology.WeakTopology.net_limit_in_projections_impl_net_limit_in_weak_topology',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__Y] :
( c_24__type__64707___24t(V1__A,V2__Y)
=> ! [V3__f] :
( c_24__type__78923___24t(V0__X,V1__A,V2__Y,V3__f)
=> ! [V4__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V4__I)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V4__I))
=> ! [V6__x] :
( cTopology_2eNets_2eNet___24t(V4__I,cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,V1__A,V2__Y,V3__f),V6__x)
=> ! [V7__x0] :
( t(V7__x0,V0__X)
=> ( ! [V8__a] :
( t(V8__a,V1__A)
=> cTopology_2eNets_2enet__limit___24a4(V4__I,happ(V2__Y,V8__a),c_24__lam__78940___24a7(V0__X,V1__A,V2__Y,V3__f,V4__I,V6__x,V8__a),happ(happ(V3__f,V8__a),V7__x0)) )
=> cTopology_2eNets_2enet__limit___24a4(V4__I,cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,V1__A,V2__Y,V3__f),V6__x,V7__x0) ) ) ) ) ) ) ) ) ) ).
fof('Topology.WeakTopology.net_limit_in_weak_topology_impl_net_limit_in_projections',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__Y] :
( c_24__type__64707___24t(V1__A,V2__Y)
=> ! [V3__f] :
( c_24__type__78880___24t(V0__X,V1__A,V2__Y,V3__f)
=> ! [V4__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V4__I)
=> ! [V5__x] :
( cTopology_2eNets_2eNet___24t(V4__I,cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,V1__A,V2__Y,V3__f),V5__x)
=> ! [V6__x0] :
( t(V6__x0,V0__X)
=> ( cTopology_2eNets_2enet__limit___24a4(V4__I,cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,V1__A,V2__Y,V3__f),V5__x,V6__x0)
=> ! [V8__a] :
( t(V8__a,V1__A)
=> cTopology_2eNets_2enet__limit___24a4(V4__I,happ(V2__Y,V8__a),c_24__lam__78897___24a7(V0__X,V1__A,V2__Y,V3__f,V4__I,V5__x,V8__a),happ(happ(V3__f,V8__a),V6__x0)) ) ) ) ) ) ) ) ) ) ).
fof('Topology.WeakTopology.weak_topology_makes_continuous_funcs',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__Y] :
( c_24__type__64707___24t(V1__A,V2__Y)
=> ! [V3__f] :
( c_24__type__78868___24t(V0__X,V1__A,V2__Y,V3__f)
=> ! [V4__a] :
( t(V4__a,V1__A)
=> cTopology_2eContinuity_2econtinuous___24a3(cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,V1__A,V2__Y,V3__f),happ(V2__Y,V4__a),happ(V3__f,V4__a)) ) ) ) ) ) ).
fof('ZornsLemma.EnsemblesSpec.intro_characteristic_sat',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__P] :
( c_24__type__327___24t(V0__X,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> ( p(happ(V1__P,V2__x))
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__X,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V0__X,V1__P),V2__x) ) ) ) ) ).
fof('ZornsLemma.Families.family_union_intro',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__T,V2__S)
=> ! [V3__x] :
( t(V3__x,V0__T)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V2__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V2__S,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,V1__F),V3__x) ) ) ) ) ) ) ).
fof('ZornsLemma.FiniteIntersections.finite_intersections_ind',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__S] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__S)
=> ! [V2__P] :
( c_24__type__375___24t(V0__X,V2__P)
=> ( p(happ(V2__P,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X)))
=> ( ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__S,V4__U)
=> p(happ(V2__P,V4__U)) ) )
=> ( ! [V5__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V5__U)
=> ! [V6__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V6__V)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),V5__U)
=> ( p(happ(V2__P,V5__U))
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),V6__V)
=> ( p(happ(V2__P,V6__V))
=> p(happ(V2__P,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V5__U,V6__V))) ) ) ) ) ) )
=> ! [V6__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V6__e)
=> ( cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a3(V0__X,V1__S,V6__e)
=> p(happ(V2__P,V6__e)) ) ) ) ) ) ) ) ) ).
fof('ZornsLemma.FiniteIntersections.intro_full',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__S] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__S)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X)) ) ) ).
fof('ZornsLemma.FiniteIntersections.intro_intersection',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__S] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__S)
=> ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__U)
=> ! [V3__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__V)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),V3__V)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V2__U,V3__V)) ) ) ) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.indexed_intersection_intro',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V0__A,V1__T,V2__F)
=> ! [V3__x] :
( t(V3__x,V1__T)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__T,happ(V2__F,V4__a),V3__x) )
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__T,cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V0__A,V1__T,V2__F),V3__x) ) ) ) ) ) ).
fof('ZornsLemma.InfiniteTypes.finite_nat_initial_segment',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2enat,c_24__lam__68792___24a1(V0__n))) ) ).
fof('ZornsLemma.Proj1SigInjective.subset_eq_compatT',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__327___24t(V0__U,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( p(happ(V1__P,V2__x))
=> ( p(happ(V1__P,V3__y))
=> ( V2__x = V3__y
=> cCoq_2eInit_2eSpecif_2eexist___24a3(V0__U,V1__P,V2__x) = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__U,V1__P,V3__y) ) ) ) ) ) ) ) ).
fof('$adef_Coq.Reals.Raxioms.bound_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRaxioms_2ebound,V_24X1))
<=> cCoq_2eReals_2eRaxioms_2ebound___24a1(V_24X1) ) ).
fof('$adef_Topology.OpenBases.open_basis_cover_cond_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eOpenBases_2eopen__basis__cover__cond,V_24X1),V_24X2))
<=> cTopology_2eOpenBases_2eopen__basis__cover__cond___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_9584_$a1',axiom,
! [V_24X1] : happ(c_24__lam__9584,V_24X1) = c_24__lam__9584___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ranalysis1.constant_D_eq_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2econstant__D__eq,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRanalysis1_2econstant__D__eq___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rsqrt_def.dicho_up_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRsqrt__def_2edicho__up,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRsqrt__def_2edicho__up___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Ranalysis1.id_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRanalysis1_2eid,V_24X1) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V_24X1) ).
fof('$adef_$_lam_70066_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__70066,V_24X1),V_24X2),V_24X3) = c_24__lam__70066___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_69373_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__69373,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__69373___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Sets.Ensembles.Singleton_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSingleton,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eSingleton___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.Subbases.Build_TopologicalSpace_from_subbasis_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eSubbases_2eBuild__TopologicalSpace__from__subbasis,V_24X1),V_24X2) = cTopology_2eSubbases_2eBuild__TopologicalSpace__from__subbasis___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rlimit.Build_Metric_Space_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRlimit_2eBuild__Metric__Space,V_24X1),V_24X2) = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.preorder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2epreorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_ZornsLemma.Families.FamilyUnion_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eFamilies_2eFamilyUnion,V_24X1),V_24X2) = cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RiemannInt.primitive_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRiemannInt_2eprimitive,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRiemannInt_2eprimitive___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.Reals.Rfunctions.R_dist_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eR__dist,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_61735_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__61735,V_24X1),V_24X2),V_24X3) = c_24__prop__61735___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_14642_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__14642,V_24X1),V_24X2) = c_24__prop__14642___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1),V_24X2) = cCoq_2eReals_2eRIneq_2emkposreal___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rsqrt_def.dicho_lb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRsqrt__def_2edicho__lb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRsqrt__def_2edicho__lb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
fof('$adef_$_lam_79311_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__79311,V_24X1),V_24X2))
<=> c_24__lam__79311___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RiemannInt_SF.IsStepFun_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Ranalysis1.plus_fct_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2eplus__fct,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2eplus__fct___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mk_monpol_list_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Reals.Ranalysis1.derive_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2ederive,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2ederive___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sig_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_64547_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__64547,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> c_24__lam__64547___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.map_Formula_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__Formula,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2emap__Formula___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_63257_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__63257,V_24X1),V_24X2) = c_24__lam__63257___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRanalysis1_2ederivable,V_24X1) = cCoq_2eReals_2eRanalysis1_2ederivable___24a1(V_24X1) ).
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('$adef_$_lam_9949_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__9949,V_24X1),V_24X2),V_24X3) = c_24__lam__9949___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_6873_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__6873,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__6873___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_$_case_Coq.Init.Datatypes.bool$9466_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_249466,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249466___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_9826_$a1',axiom,
! [V_24X1] : happ(c_24__lam__9826,V_24X1) = c_24__lam__9826___24a1(V_24X1) ).
fof('$adef_Topology.Continuity.continuous_at_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTopology_2eContinuity_2econtinuous__at,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTopology_2eContinuity_2econtinuous__at___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Reals.Rlimit.limit_in_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eReals_2eRlimit_2elimit__in,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eReals_2eRlimit_2elimit__in___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1755_$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__1755,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__1755___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_pt_lim_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___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('$adef_Coq.Reals.RList.Rtail_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRList_2eRtail,V_24X1) = cCoq_2eReals_2eRList_2eRtail___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_78940_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__78940,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__78940___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_ZornsLemma.FiniteTypes.FiniteT_$a1',axiom,
! [V_24X1] :
( p(happ(cZornsLemma_2eFiniteTypes_2eFiniteT,V_24X1))
<=> cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtopology.included_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtopology_2eincluded,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtopology_2eincluded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_6382_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__6382,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__6382___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_9820_$a1',axiom,
! [V_24X1] : happ(c_24__lam__9820,V_24X1) = c_24__lam__9820___24a1(V_24X1) ).
fof('$adef_$_lam_6509_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__6509,V_24X1),V_24X2),V_24X3) = c_24__lam__6509___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_6461_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(c_24__lam__6461,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> c_24__lam__6461___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_ZornsLemma.FiniteIntersections.finite_intersections_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eFiniteIntersections_2efinite__intersections,V_24X1),V_24X2) = cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RList.Rlist_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRList_2eRlist__rect,V_24X1) = cCoq_2eReals_2eRList_2eRlist__rect___24a1(V_24X1) ).
fof('$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_$_prop_7285_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__7285,V_24X1),V_24X2) = c_24__prop__7285___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.Families.FamilyIntersection_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eFamilies_2eFamilyIntersection,V_24X1),V_24X2) = cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_$_lam_7275_$a1',axiom,
! [V_24X1] : happ(c_24__lam__7275,V_24X1) = c_24__lam__7275___24a1(V_24X1) ).
fof('$adef_$_lam_9366_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__9366,V_24X1),V_24X2) = c_24__lam__9366___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_70066_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__70066,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__70066___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Topology.FiltersAndNets.filter_to_net_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFiltersAndNets_2efilter__to__net,V_24X1),V_24X2) = cTopology_2eFiltersAndNets_2efilter__to__net___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Topology.Nets.neighborhood_net_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eNets_2eneighborhood__net,V_24X1),V_24X2) = cTopology_2eNets_2eneighborhood__net___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_6593_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__6593,V_24X1),V_24X2),V_24X3) = c_24__lam__6593___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_6593_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__6593,V_24X1),V_24X2) = c_24__lam__6593___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_69387_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__69387,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__69387___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Sets.Ensembles.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.RList.In_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRList_2eIn,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRList_2eIn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Specif.projT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_78791_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__78791,V_24X1),V_24X2) = c_24__lam__78791___24a2(V_24X1,V_24X2) ).
fof('$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_$_let_var_8_up_9375_9391_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__8__up__9375__9391,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__8__up__9375__9391___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.RIneq.Rle_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRIneq_2eRle__dec,V_24X1),V_24X2) = cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.comp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ecomp,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_14634_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__14634,V_24X1),V_24X2) = c_24__prop__14634___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_624_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__624,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__624___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_lam_7051_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__7051,V_24X1),V_24X2) = c_24__lam__7051___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.TopologicalSpaces.open_$a1',axiom,
! [V_24X1] : happ(cTopology_2eTopologicalSpaces_2eopen,V_24X1) = cTopology_2eTopologicalSpaces_2eopen___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_61722_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__61722,V_24X1),V_24X2) = c_24__prop__61722___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.SeqProp.opp_seq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eSeqProp_2eopp__seq,V_24X1),V_24X2) = cCoq_2eReals_2eSeqProp_2eopp__seq___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.TopologicalSpaces.closed_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eTopologicalSpaces_2eclosed,V_24X1),V_24X2))
<=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_7140_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__7140,V_24X1),V_24X2) = c_24__lam__7140___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Empty_set_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eEmpty__set,V_24X1) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Complement_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eEnsembles_2eComplement,V_24X1),V_24X2) = cCoq_2eSets_2eEnsembles_2eComplement___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.derive_pt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederive__pt,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_41709_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(c_24__lam__41709,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> c_24__lam__41709___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
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('$adef_Topology.Neighborhoods.neighborhood_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eNeighborhoods_2eneighborhood,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eNeighborhoods_2eneighborhood___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Ranalysis1.fct_cte_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2efct__cte,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2efct__cte___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.InverseImage.inverse_image_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cZornsLemma_2eInverseImage_2einverse__image,V_24X1),V_24X2),V_24X3),V_24X4) = cZornsLemma_2eInverseImage_2einverse__image___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rtrigo1.cos_lb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo1_2ecos__lb,V_24X1) = cCoq_2eReals_2eRtrigo1_2ecos__lb___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.nonneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2enonneg,V_24X1) = cCoq_2eReals_2eRIneq_2enonneg___24a1(V_24X1) ).
fof('$adef_$_lam_1755_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__1755,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__1755___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.Reals.RiemannInt_SF.pre_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2epre,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRiemannInt__SF_2epre___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.Nets.Subnet_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cTopology_2eNets_2eSubnet,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cTopology_2eNets_2eSubnet___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.Rtopology.mkfamily_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRtopology_2emkfamily,V_24X1),V_24X2) = cCoq_2eReals_2eRtopology_2emkfamily___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RList.pos_Rl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRList_2epos__Rl,V_24X1),V_24X2) = cCoq_2eReals_2eRList_2epos__Rl___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_4420_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__4420,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__4420___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_6382_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__6382,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__6382___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_let_var_9_z_9376_9392_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__9__z__9376__9392,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__9__z__9376__9392___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.RiemannInt_SF.mkStepFun_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2emkStepFun,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRiemannInt__SF_2emkStepFun___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Raxioms.INR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRaxioms_2eINR,V_24X1) = cCoq_2eReals_2eRaxioms_2eINR___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RList.insert_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRList_2einsert,V_24X1),V_24X2) = cCoq_2eReals_2eRList_2einsert___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_9584_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__9584,V_24X1),V_24X2))
<=> c_24__lam__9584___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtopology.neighbourhood_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtopology_2eneighbourhood,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtopology_2eneighbourhood___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.Nets.cluster_point_subnet_DS_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet__DS,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eNets_2ecluster__point__subnet__DS___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.MetricSpaces.metric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eMetricSpaces_2emetric,V_24X1),V_24X2))
<=> cTopology_2eMetricSpaces_2emetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.SeqProp.Un_decreasing_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eSeqProp_2eUn__decreasing,V_24X1))
<=> cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(V_24X1) ) ).
fof('$adef_Topology.Nets.neighborhood_net_DS_set_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eNets_2eneighborhood__net__DS__set,V_24X1),V_24X2) = cTopology_2eNets_2eneighborhood__net__DS__set___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rtrigo_def.cos_in_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtrigo__def_2ecos__in,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtrigo__def_2ecos__in___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_79320_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__79320,V_24X1),V_24X2) = c_24__lam__79320___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_9869_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__9869,V_24X1),V_24X2))
<=> c_24__lam__9869___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_7104_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__7104,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__7104___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.Rdefinitions.up_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eup,V_24X1) = cCoq_2eReals_2eRdefinitions_2eup___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rtrigo_def.exist_exp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2eexist__exp,V_24X1) = cCoq_2eReals_2eRtrigo__def_2eexist__exp___24a1(V_24X1) ).
fof('$adef_$_lam_79168_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__79168,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__79168___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Reals.Rfunctions.sum_f_R0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2esum__f__R0,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RiemannInt_SF.adapted_couple_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Complement_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eComplement,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eComplement___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.Reals.Rtrigo_alt.sin_approx_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRtrigo__alt_2esin__approx,V_24X1),V_24X2) = cCoq_2eReals_2eRtrigo__alt_2esin__approx___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.SeqProp.cv_infty_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eSeqProp_2ecv__infty,V_24X1))
<=> cCoq_2eReals_2eSeqProp_2ecv__infty___24a1(V_24X1) ) ).
fof('$adef_$_prop_10056_$a1',axiom,
! [V_24X1] : happ(c_24__prop__10056,V_24X1) = c_24__prop__10056___24a1(V_24X1) ).
fof('$adef_ZornsLemma.CountableTypes.Countable_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cZornsLemma_2eCountableTypes_2eCountable,V_24X1),V_24X2))
<=> cZornsLemma_2eCountableTypes_2eCountable___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_7275_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__7275,V_24X1),V_24X2))
<=> c_24__lam__7275___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rtopology.disc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRtopology_2edisc,V_24X1),V_24X2) = cCoq_2eReals_2eRtopology_2edisc___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.DirectedSets.exists_arbitrarily_large_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eDirectedSets_2eexists__arbitrarily__large,V_24X1),V_24X2))
<=> cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_63032_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__63032,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__63032___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_4697_$a1',axiom,
! [V_24X1] : happ(c_24__lam__4697,V_24X1) = c_24__lam__4697___24a1(V_24X1) ).
fof('$adef_Coq.Reals.PartSum.Cauchy_crit_series_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2ePartSum_2eCauchy__crit__series,V_24X1))
<=> cCoq_2eReals_2ePartSum_2eCauchy__crit__series___24a1(V_24X1) ) ).
fof('$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_$_lam_78791_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__78791,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__78791___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RList.app_Rlist_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRList_2eapp__Rlist,V_24X1),V_24X2) = cCoq_2eReals_2eRList_2eapp__Rlist___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_72851_$a1',axiom,
! [V_24X1] : happ(c_24__lam__72851,V_24X1) = c_24__lam__72851___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sigT_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.MetricSpaces.metric_topology_neighborhood_basis_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.Rtopology.covering_finite_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtopology_2ecovering__finite,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtopology_2ecovering__finite___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rtopology.open_set_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRtopology_2eopen__set,V_24X1))
<=> cCoq_2eReals_2eRtopology_2eopen__set___24a1(V_24X1) ) ).
fof('$adef_$_lam_6461_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__6461,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__6461___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Reals.Rtopology.adherence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtopology_2eadherence,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtopology_2eadherence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_var_9_z_9443_9459_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__9__z__9443__9459,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__9__z__9443__9459___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rtrigo_def.sin_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2esin,V_24X1) = cCoq_2eReals_2eRtrigo__def_2esin___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rtrigo_alt.sin_term_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__alt_2esin__term,V_24X1) = cCoq_2eReals_2eRtrigo__alt_2esin__term___24a1(V_24X1) ).
fof('$adef_$_lam_72876_$a1',axiom,
! [V_24X1] : happ(c_24__lam__72876,V_24X1) = c_24__lam__72876___24a1(V_24X1) ).
fof('$adef_Topology.FiltersAndNets.tail_filter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eFiltersAndNets_2etail__filter,V_24X1),V_24X2),V_24X3) = cTopology_2eFiltersAndNets_2etail__filter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.SeqProp.has_ub_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eSeqProp_2ehas__ub,V_24X1))
<=> cCoq_2eReals_2eSeqProp_2ehas__ub___24a1(V_24X1) ) ).
fof('$adef_$_lam_78796_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__78796,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__78796___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.Nets.cluster_point_subnet_DS_set_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet__DS__set,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eNets_2ecluster__point__subnet__DS__set___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RMicromega.Reval_formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eReval__formula,V_24X1) = cCoq_2emicromega_2eRMicromega_2eReval__formula___24a1(V_24X1) ).
fof('$adef_$_lam_15052_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__15052,V_24X1),V_24X2),V_24X3) = c_24__lam__15052___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_8087_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__8087,V_24X1),V_24X2) = c_24__prop__8087___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons2_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Topology.NeighborhoodBases.neighborhood_basis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eNeighborhoodBases_2eneighborhood__basis,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eNeighborhoodBases_2eneighborhood__basis___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_69289_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__69289,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__69289___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_let_var_7_down_9403_9419_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__7__down__9403__9419,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__7__down__9403__9419___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_9854_$a1',axiom,
! [V_24X1] : happ(c_24__lam__9854,V_24X1) = c_24__lam__9854___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_824_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__824,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__824___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_78832_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__78832,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__78832___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_ZornsLemma.Families.FamilyUnion_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFamilies_2eFamilyUnion,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFamilies_2eFamilyUnion___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_$_lam_78897_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__78897,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__78897___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_lam_63032_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__63032,V_24X1),V_24X2),V_24X3) = c_24__lam__63032___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_6987_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__6987,V_24X1),V_24X2) = c_24__lam__6987___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rpower.ln_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRpower_2eln,V_24X1) = cCoq_2eReals_2eRpower_2eln___24a1(V_24X1) ).
fof('$adef_$_lam_548_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__548,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__548___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.Rtrigo_def.sin_in_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtrigo__def_2esin__in,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtrigo__def_2esin__in___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RiemannInt_SF.is_subdivision_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.setoid_ring.Field_theory.PEsimp_$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_2eField__theory_2ePEsimp,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons1_$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_2eField__theory_2eFcons1,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_2eField__theory_2eFcons1___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Topology.Subbases.subbasis_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eSubbases_2esubbasis,V_24X1),V_24X2))
<=> cTopology_2eSubbases_2esubbasis___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RList.cons_Rlist_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRList_2econs__Rlist,V_24X1),V_24X2) = cCoq_2eReals_2eRList_2econs__Rlist___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtrigo1.tan_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo1_2etan,V_24X1) = cCoq_2eReals_2eRtrigo1_2etan___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RiemannInt.primitive_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eReals_2eRiemannInt_2eprimitive,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eReals_2eRiemannInt_2eprimitive___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.Rtrigo_def.exp_in_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtrigo__def_2eexp__in,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtrigo__def_2eexp__in___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_7048_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7048,V_24X1),V_24X2),V_24X3) = c_24__lam__7048___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.Nets.net_limit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTopology_2eNets_2enet__limit,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTopology_2eNets_2enet__limit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_$_prop_14643_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__14643,V_24X1),V_24X2) = c_24__prop__14643___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_10055_$a1',axiom,
! [V_24X1] : happ(c_24__prop__10055,V_24X1) = c_24__prop__10055___24a1(V_24X1) ).
fof('$adef_Topology.TopologicalSpaces.open_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eTopologicalSpaces_2eopen,V_24X1),V_24X2))
<=> cTopology_2eTopologicalSpaces_2eopen___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rtopology.covering_open_set_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtopology_2ecovering__open__set,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtopology_2ecovering__open__set___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.AltSeries.tg_alt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eAltSeries_2etg__alt,V_24X1),V_24X2) = cCoq_2eReals_2eAltSeries_2etg__alt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_5815_$a1',axiom,
! [V_24X1] : happ(c_24__lam__5815,V_24X1) = c_24__lam__5815___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.condition_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2econdition,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_791_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__791,V_24X1),V_24X2) = c_24__prop__791___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_9_z_9405_9421_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__9__z__9405__9421,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__9__z__9405__9421___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.MetricSpaces.open_ball_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eMetricSpaces_2eopen__ball,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eMetricSpaces_2eopen__ball___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Ranalysis1.minus_fct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2eminus__fct,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2eminus__fct___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_8_up_9404_9420_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__8__up__9404__9420,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__8__up__9404__9420___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.Reals.Ranalysis1.opp_fct_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRanalysis1_2eopp__fct,V_24X1) = cCoq_2eReals_2eRanalysis1_2eopp__fct___24a1(V_24X1) ).
fof('$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_$_lam_68442_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__68442,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__68442___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_$_lam_9818_$a1',axiom,
! [V_24X1] : happ(c_24__lam__9818,V_24X1) = c_24__lam__9818___24a1(V_24X1) ).
fof('$adef_Topology.OpenBases.open_basis_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eOpenBases_2eopen__basis,V_24X1),V_24X2))
<=> cTopology_2eOpenBases_2eopen__basis___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Ranalysis1.opp_fct_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2eopp__fct,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2eopp__fct___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_9942_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__9942,V_24X1),V_24X2),V_24X3) = c_24__lam__9942___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('$adef_Coq.Reals.Rfunctions.infinite_sum_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRfunctions_2einfinite__sum,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Ranalysis1.continuity_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRanalysis1_2econtinuity,V_24X1))
<=> cCoq_2eReals_2eRanalysis1_2econtinuity___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('$adef_Coq.Sets.Ensembles.Inhabited_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eEnsembles_2eInhabited,V_24X1),V_24X2))
<=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_61736_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__61736,V_24X1),V_24X2),V_24X3) = c_24__prop__61736___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.AltSeries.tg_alt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eAltSeries_2etg__alt,V_24X1) = cCoq_2eReals_2eAltSeries_2etg__alt___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_9551_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__9551,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__9551___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.RList.mid_Rlist_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRList_2emid__Rlist,V_24X1),V_24X2) = cCoq_2eReals_2eRList_2emid__Rlist___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RList.ordered_Rlist_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRList_2eordered__Rlist,V_24X1))
<=> cCoq_2eReals_2eRList_2eordered__Rlist___24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRminus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_7944_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7944,V_24X1),V_24X2),V_24X3) = c_24__lam__7944___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rtrigo1.sin_ub_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo1_2esin__ub,V_24X1) = cCoq_2eReals_2eRtrigo1_2esin__ub___24a1(V_24X1) ).
fof('$adef_$_prop_10051_$a1',axiom,
! [V_24X1] : happ(c_24__prop__10051,V_24X1) = c_24__prop__10051___24a1(V_24X1) ).
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('$adef_Coq.Reals.Raxioms.is_lub_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRaxioms_2eis__lub,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRaxioms_2eis__lub___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_9839_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__9839,V_24X1),V_24X2))
<=> c_24__lam__9839___24a2(V_24X1,V_24X2) ) ).
fof('$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.Reals.Rseries.Un_cv_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRseries_2eUn__cv,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Nets.net_cluster_point_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTopology_2eNets_2enet__cluster__point,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTopology_2eNets_2enet__cluster__point___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Specif.sig_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RMicromega.Rnegate_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eRnegate,V_24X1) = cCoq_2emicromega_2eRMicromega_2eRnegate___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rtopology.subfamily_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRtopology_2esubfamily,V_24X1),V_24X2) = cCoq_2eReals_2eRtopology_2esubfamily___24a2(V_24X1,V_24X2) ).
fof('$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.Reals.RiemannInt.RinvN_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRiemannInt_2eRinvN__pos,V_24X1) = cCoq_2eReals_2eRiemannInt_2eRinvN__pos___24a1(V_24X1) ).
fof('$adef_$_lam_6873_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__6873,V_24X1),V_24X2) = c_24__lam__6873___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_69435_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__69435,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__69435___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_5813_$a1',axiom,
! [V_24X1] : happ(c_24__lam__5813,V_24X1) = c_24__lam__5813___24a1(V_24X1) ).
fof('$adef_$_lam_61712_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__61712,V_24X1),V_24X2) = c_24__lam__61712___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtrigo_def.cos_n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2ecos__n,V_24X1) = cCoq_2eReals_2eRtrigo__def_2ecos__n___24a1(V_24X1) ).
fof('$adef_Coq.Reals.NewtonInt.Newton_integrable_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eNewtonInt_2eNewton__integrable,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eNewtonInt_2eNewton__integrable___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.micromega.Tauto.map_bformula_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2emap__bformula,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2emap__bformula___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Reals.RiemannInt.mkC1_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRiemannInt_2emkC1,V_24X1),V_24X2) = cCoq_2eReals_2eRiemannInt_2emkC1___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ratan.Datan_seq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRatan_2eDatan__seq,V_24X1),V_24X2) = cCoq_2eReals_2eRatan_2eDatan__seq___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.OpenBases.open_basis_cond_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eOpenBases_2eopen__basis__cond,V_24X1),V_24X2))
<=> cTopology_2eOpenBases_2eopen__basis__cond___24a2(V_24X1,V_24X2) ) ).
fof('$adef_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction,V_24X1),V_24X2) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_4491_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__4491,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__4491___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Topology.MetricSpaces.metrizes_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eMetricSpaces_2emetrizes,V_24X1),V_24X2))
<=> cTopology_2eMetricSpaces_2emetrizes___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.DirectedSets.eventually_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eDirectedSets_2eeventually,V_24X1),V_24X2))
<=> cTopology_2eDirectedSets_2eeventually___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_18_mkmult_pow_2189_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__2189,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__2189___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Reals.RiemannInt.c1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRiemannInt_2ec1,V_24X1) = cCoq_2eReals_2eRiemannInt_2ec1___24a1(V_24X1) ).
fof('$adef_Coq.Reals.PartSum.SP_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2ePartSum_2eSP,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2ePartSum_2eSP___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_78771_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__78771,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__78771___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_$_prop_4704_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4704,V_24X1),V_24X2) = c_24__prop__4704___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_7248_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__7248,V_24X1),V_24X2) = c_24__lam__7248___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Nets.cluster_point_subnet_DS_ord_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet__DS__ord,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cTopology_2eNets_2ecluster__point__subnet__DS__ord___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Sets.Ensembles.Included_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIncluded,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_$_lam_79320_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__79320,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__79320___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_case_Topology.TopologicalSpaces.TopologicalSpace$64651_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Topology_2eTopologicalSpaces_2eTopologicalSpace_2464651,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Topology_2eTopologicalSpaces_2eTopologicalSpace_2464651___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_7680_$a1',axiom,
! [V_24X1] : happ(c_24__lam__7680,V_24X1) = c_24__lam__7680___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rsqrt_def.pow_2_n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRsqrt__def_2epow__2__n,V_24X1) = cCoq_2eReals_2eRsqrt__def_2epow__2__n___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rlimit.Build_Metric_Space_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eReals_2eRlimit_2eBuild__Metric__Space,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Reals.RiemannInt_SF.fe_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2efe,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRiemannInt__SF_2efe___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_72876_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__72876,V_24X1),V_24X2))
<=> c_24__lam__72876___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Reals.Rtopology.ind_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtopology_2eind,V_24X1) = cCoq_2eReals_2eRtopology_2eind___24a1(V_24X1) ).
fof('$adef_$_let_17_mkopp_pow_2188_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__2188,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__2188___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Topology.DirectedSets.Build_DirectedSet_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eDirectedSets_2eBuild__DirectedSet,V_24X1),V_24X2) = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rseries.Un_growing_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRseries_2eUn__growing,V_24X1))
<=> cCoq_2eReals_2eRseries_2eUn__growing___24a1(V_24X1) ) ).
fof('$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.Reals.RList.cons_ORlist_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRList_2econs__ORlist,V_24X1),V_24X2) = cCoq_2eReals_2eRList_2econs__ORlist___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rsigma.sigma_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRsigma_2esigma,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRsigma_2esigma___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.OrderTopology.order_topology_subbasis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eOrderTopology_2eorder__topology__subbasis,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eOrderTopology_2eorder__topology__subbasis___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_RTopology.R_metric_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cRTopology_2eR__metric,V_24X1),V_24X2) = cRTopology_2eR__metric___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_$_lam_7140_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7140,V_24X1),V_24X2),V_24X3) = c_24__lam__7140___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_17_mkopp_pow_2188_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__2188,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__2188___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_4491_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__4491,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__4491___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Topology.Filters.Build_Filter_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFilters_2eBuild__Filter,V_24X1),V_24X2) = cTopology_2eFilters_2eBuild__Filter___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.Rnormalise_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eRnormalise,V_24X1) = cCoq_2emicromega_2eRMicromega_2eRnormalise___24a1(V_24X1) ).
fof('$adef_$_lam_78771_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__78771,V_24X1),V_24X2),V_24X3) = c_24__lam__78771___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_ZornsLemma.Families.Family_$a1',axiom,
! [V_24X1] : happ(cZornsLemma_2eFamilies_2eFamily,V_24X1) = cZornsLemma_2eFamilies_2eFamily___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V_24X1) ).
fof('$adef_Topology.FiltersAndNets.Build_filter_to_net_DS_set_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_79311_$a1',axiom,
! [V_24X1] : happ(c_24__lam__79311,V_24X1) = c_24__lam__79311___24a1(V_24X1) ).
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('$adef_Coq.Reals.Rbasic_fun.Rmin_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRbasic__fun_2eRmin,V_24X1),V_24X2) = cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Raxioms.is_upper_bound_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRaxioms_2eis__upper__bound,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRaxioms_2eis__upper__bound___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('$adef_Topology.FiltersAndNets.filter_to_net_DS_set_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFiltersAndNets_2efilter__to__net__DS__set,V_24X1),V_24X2) = cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rlimit.limit1_in_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eReals_2eRlimit_2elimit1__in,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eReals_2eRlimit_2elimit1__in___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_284_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__284,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__284___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.RiemannInt.RiemannInt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRiemannInt_2eRiemannInt,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Ranalysis1.plus_fct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2eplus__fct,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2eplus__fct___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.fst_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2efst___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_9818_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__9818,V_24X1),V_24X2))
<=> c_24__lam__9818___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('$adef_Topology.Nets.cps_i_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cTopology_2eNets_2ecps__i,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cTopology_2eNets_2ecps__i___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_fix_9372_1_Dichotomy_ub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__fix__9372__1__Dichotomy__ub,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__fix__9372__1__Dichotomy__ub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Sets.Ensembles.Intersection_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIntersection,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eIntersection___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_69707_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__69707,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__69707___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_$_lam_79426_$a1',axiom,
! [V_24X1] : happ(c_24__lam__79426,V_24X1) = c_24__lam__79426___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_$_lam_7248_$a1',axiom,
! [V_24X1] : happ(c_24__lam__7248,V_24X1) = c_24__lam__7248___24a1(V_24X1) ).
fof('$adef_$_lam_548_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__548,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__548___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.FilterLimits.filter_cluster_point_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eFilterLimits_2efilter__cluster__point,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rtopology.point_adherent_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtopology_2epoint__adherent,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtopology_2epoint__adherent___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_7051_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7051,V_24X1),V_24X2),V_24X3) = c_24__lam__7051___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_4420_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(c_24__lam__4420,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> c_24__lam__4420___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_ZornsLemma.IndexedFamilies.IndexedIntersection_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedIntersection,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rmax_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRbasic__fun_2eRmax,V_24X1),V_24X2) = cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V_24X1,V_24X2) ).
fof('$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.Reals.Ranalysis1.derive_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederive,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2ederive___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_26274_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__26274,V_24X1),V_24X2) = c_24__lam__26274___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Intersection_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIntersection,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_69435_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__69435,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__69435___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_let_var_8_up_9442_9458_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__8__up__9442__9458,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__8__up__9442__9458___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Reals.RiemannInt_SF.open_interval_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eopen__interval,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRiemannInt__SF_2eopen__interval___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.OpenBases.Build_TopologicalSpace_from_open_basis_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eOpenBases_2eBuild__TopologicalSpace__from__open__basis,V_24X1),V_24X2) = cTopology_2eOpenBases_2eBuild__TopologicalSpace__from__open__basis___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_16_mkpow_2187_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__2187,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__2187___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Topology.TopologicalSpaces.point_set_$a1',axiom,
! [V_24X1] : happ(cTopology_2eTopologicalSpaces_2epoint__set,V_24X1) = cTopology_2eTopologicalSpaces_2epoint__set___24a1(V_24X1) ).
fof('$adef_$_lam_7932_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7932,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7932___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Reals.Rtrigo_def.exist_cos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2eexist__cos,V_24X1) = cCoq_2eReals_2eRtrigo__def_2eexist__cos___24a1(V_24X1) ).
fof('$adef_$_let_var_7_down_9374_9390_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__7__down__9374__9390,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__7__down__9374__9390___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.RiemannInt_SF.fe_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2efe,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRiemannInt__SF_2efe___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.RiemannInt_SF.adapted_couple_opt_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple__opt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eReals_2eRiemannInt__SF_2eadapted__couple__opt___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.Rtrigo1.sin_lb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo1_2esin__lb,V_24X1) = cCoq_2eReals_2eRtrigo1_2esin__lb___24a1(V_24X1) ).
fof('$adef_$_lam_78897_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__78897,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__78897___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_$_lam_624_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__624,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__624___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Reals.Ranalysis1.mkDifferential_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2emkDifferential,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2emkDifferential___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_9942_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__9942,V_24X1),V_24X2) = c_24__lam__9942___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtopology.image_dir_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRtopology_2eimage__dir,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRtopology_2eimage__dir___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.AltSeries.positivity_seq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eAltSeries_2epositivity__seq,V_24X1))
<=> cCoq_2eReals_2eAltSeries_2epositivity__seq___24a1(V_24X1) ) ).
fof('$adef_$_lam_69373_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(c_24__lam__69373,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> c_24__lam__69373___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.micromega.Tauto.tauto_checker_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2etauto__checker,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2emicromega_2eTauto_2etauto__checker___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.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.RList.Rlength_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRList_2eRlength,V_24X1) = cCoq_2eReals_2eRList_2eRlength___24a1(V_24X1) ).
fof('$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_$_lam_69700_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__69700,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__69700___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Sets.Ensembles.Full_set_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eEnsembles_2eFull__set,V_24X1),V_24X2))
<=> cCoq_2eSets_2eEnsembles_2eFull__set___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.FiltersAndNets.ftn_x_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFiltersAndNets_2eftn__x,V_24X1),V_24X2) = cTopology_2eFiltersAndNets_2eftn__x___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_15052_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__15052,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__15052___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.WeakTopology.weak_topology_subbasis_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cTopology_2eWeakTopology_2eweak__topology__subbasis,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cTopology_2eWeakTopology_2eweak__topology__subbasis___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.Rsqrt_def.dicho_lb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRsqrt__def_2edicho__lb,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRsqrt__def_2edicho__lb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_lam_9949_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__9949,V_24X1),V_24X2) = c_24__lam__9949___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_78820_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__78820,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__78820___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.RiemannInt.RinvN_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRiemannInt_2eRinvN,V_24X1) = cCoq_2eReals_2eRiemannInt_2eRinvN___24a1(V_24X1) ).
fof('$adef_$_lam_69707_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__69707,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__69707___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Topology.TopologicalSpaces.Build_TopologicalSpace_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace,V_24X1),V_24X2) = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_7856_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__7856,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__7856___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_8348_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__8348,V_24X1),V_24X2),V_24X3) = c_24__lam__8348___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_7944_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7944,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7944___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Ranalysis1.mult_fct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2emult__fct,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2emult__fct___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.Continuity.continuous_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eContinuity_2econtinuous,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eContinuity_2econtinuous___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_8348_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__8348,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__8348___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.d1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRanalysis1_2ed1,V_24X1) = cCoq_2eReals_2eRanalysis1_2ed1___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rseries.Cauchy_crit_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRseries_2eCauchy__crit,V_24X1))
<=> cCoq_2eReals_2eRseries_2eCauchy__crit___24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.Rtopology.disc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRtopology_2edisc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRtopology_2edisc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$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('$adef_Coq.Reals.Rderiv.continue_in_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRderiv_2econtinue__in,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRderiv_2econtinue__in___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_73344_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__73344,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__73344___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.Nets.neighborhood_net_DS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eNets_2eneighborhood__net__DS,V_24X1),V_24X2) = cTopology_2eNets_2eneighborhood__net__DS___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eSpecif_2esigT__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_9826_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__9826,V_24X1),V_24X2))
<=> c_24__lam__9826___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rtrigo_def.cos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2ecos,V_24X1) = cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V_24X1) ).
fof('$adef_$_lam_26274_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__26274,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__26274___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.OrderTopology.OrderTopology_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eOrderTopology_2eOrderTopology,V_24X1),V_24X2) = cTopology_2eOrderTopology_2eOrderTopology___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.pow_fct_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2epow__fct,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2epow__fct___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_7104_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7104,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7104___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_7932_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__7932,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__7932___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Reals.Rtrigo_def.exp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2eexp,V_24X1) = cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V_24X1) ).
fof('$adef_$_lam_78820_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__78820,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__78820___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Ranalysis1.minus_fct_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2eminus__fct,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2eminus__fct___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_7856_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__7856,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__7856___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Topology.FiltersAndNets.filter_to_net_DS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFiltersAndNets_2efilter__to__net__DS,V_24X1),V_24X2) = cTopology_2eFiltersAndNets_2efilter__to__net__DS___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_9839_$a1',axiom,
! [V_24X1] : happ(c_24__lam__9839,V_24X1) = c_24__lam__9839___24a1(V_24X1) ).
fof('$adef_$_lam_78784_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__78784,V_24X1),V_24X2),V_24X3) = c_24__lam__78784___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_79168_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__79168,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__79168___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rcase_abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRbasic__fun_2eRcase__abs,V_24X1) = cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rtrigo_def.exist_sin_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2eexist__sin,V_24X1) = cCoq_2eReals_2eRtrigo__def_2eexist__sin___24a1(V_24X1) ).
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] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Compare_dec.le_lt_dec_$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('$adef_Topology.WeakTopology.WeakTopology_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eWeakTopology_2eWeakTopology,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eWeakTopology_2eWeakTopology___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.SupInf.is_lower_bound_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eSupInf_2eis__lower__bound,V_24X1),V_24X2))
<=> cTopology_2eSupInf_2eis__lower__bound___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_9366_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__9366,V_24X1),V_24X2),V_24X3) = c_24__lam__9366___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_78940_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__78940,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__78940___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Reals.Ranalysis1.continuity_pt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRanalysis1_2econtinuity__pt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rlimit.dist_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRlimit_2edist,V_24X1) = cCoq_2eReals_2eRlimit_2edist___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('$adef_$_lam_64547_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__64547,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__64547___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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.Reals.Ranalysis1.increasing_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRanalysis1_2eincreasing,V_24X1))
<=> cCoq_2eReals_2eRanalysis1_2eincreasing___24a1(V_24X1) ) ).
fof('$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_Coq.Reals.RiemannInt_SF.Int_SF_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eInt__SF,V_24X1),V_24X2) = cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_lam_9869_$a1',axiom,
! [V_24X1] : happ(c_24__lam__9869,V_24X1) = c_24__lam__9869___24a1(V_24X1) ).
fof('$adef_ZornsLemma.IndexedFamilies.IndexedIntersection_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedIntersection,V_24X1),V_24X2),V_24X3) = cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.Nets.cluster_point_subnet_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cTopology_2eNets_2ecluster__point__subnet___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.PSeries_reg.Boule_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2ePSeries__reg_2eBoule,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2ePSeries__reg_2eBoule___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RMicromega.RTautoChecker_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eRTautoChecker,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eRTautoChecker___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.DirectedSets.DS_ord_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eDirectedSets_2eDS__ord,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eDirectedSets_2eDS__ord___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rsqrt_def.Rsqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRsqrt__def_2eRsqrt,V_24X1) = cCoq_2eReals_2eRsqrt__def_2eRsqrt___24a1(V_24X1) ).
fof('$adef_Topology.MetricSpaces.metric_topology_neighborhood_basis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis,V_24X1),V_24X2),V_24X3) = cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.NeighborhoodBases.open_neighborhood_basis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_6509_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__6509,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__6509___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Finite_sets.Finite_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eFinite__sets_2eFinite,V_24X1),V_24X2))
<=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rderiv.D_x_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRderiv_2eD__x,V_24X1),V_24X2) = cCoq_2eReals_2eRderiv_2eD__x___24a2(V_24X1,V_24X2) ).
fof('$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_Topology.DirectedSets.DS_set_$a1',axiom,
! [V_24X1] : happ(cTopology_2eDirectedSets_2eDS__set,V_24X1) = cTopology_2eDirectedSets_2eDS__set___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_pt_abs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_ZornsLemma.FunctionProperties.injective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFunctionProperties_2einjective,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFunctionProperties_2einjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.Nets.cluster_point_subnet_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eNets_2ecluster__point__subnet___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_79419_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__79419,V_24X1),V_24X2),V_24X3) = c_24__lam__79419___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rtopology.eq_Dom_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtopology_2eeq__Dom,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtopology_2eeq__Dom___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_26270_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__26270,V_24X1),V_24X2),V_24X3) = c_24__lam__26270___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Image.Im_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eSets_2eImage_2eIm,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eSets_2eImage_2eIm___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Nets.net_limit_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eNets_2enet__limit,V_24X1),V_24X2),V_24X3) = cTopology_2eNets_2enet__limit___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_69387_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__69387,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__69387___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Reals.Rtopology.complementary_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtopology_2ecomplementary,V_24X1) = cCoq_2eReals_2eRtopology_2ecomplementary___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('$adef_Coq.Reals.Ranalysis1.antiderivative_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2eantiderivative,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.Ranalysis1.comp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2ecomp,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2ecomp___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_63142_$a1',axiom,
! [V_24X1] : happ(c_24__lam__63142,V_24X1) = c_24__lam__63142___24a1(V_24X1) ).
fof('$adef_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.FiltersAndNets.tail_filter_basis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eFiltersAndNets_2etail__filter__basis,V_24X1),V_24X2),V_24X3) = cTopology_2eFiltersAndNets_2etail__filter__basis___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_14596_$a1',axiom,
! [V_24X1] : happ(c_24__lam__14596,V_24X1) = c_24__lam__14596___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eneg,V_24X1) = cCoq_2eReals_2eRIneq_2eneg___24a1(V_24X1) ).
fof('$adef_$_prop_7284_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__7284,V_24X1),V_24X2) = c_24__prop__7284___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_79426_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__79426,V_24X1),V_24X2) = c_24__lam__79426___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_69423_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__69423,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__69423___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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.Reals.SeqProp.opp_seq_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eSeqProp_2eopp__seq,V_24X1) = cCoq_2eReals_2eSeqProp_2eopp__seq___24a1(V_24X1) ).
fof('$adef_$_lam_70086_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__70086,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__70086___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Specif.sumbool_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.FF_$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('$adef_$_lam_9336_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__9336,V_24X1),V_24X2))
<=> c_24__lam__9336___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rtopology.intersection_domain_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRtopology_2eintersection__domain,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRtopology_2eintersection__domain___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rpower.arcsinh_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRpower_2earcsinh,V_24X1) = cCoq_2eReals_2eRpower_2earcsinh___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rsqrt_def.dicho_up_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRsqrt__def_2edicho__up,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRsqrt__def_2edicho__up___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_824_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__824,V_24X1),V_24X2) = c_24__lam__824___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rlimit.Base_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRlimit_2eBase,V_24X1) = cCoq_2eReals_2eRlimit_2eBase___24a1(V_24X1) ).
fof('$adef_$_lam_26270_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__26270,V_24X1),V_24X2) = c_24__lam__26270___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_70086_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__70086,V_24X1),V_24X2),V_24X3) = c_24__lam__70086___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.RIneq.pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2epos,V_24X1) = cCoq_2eReals_2eRIneq_2epos___24a1(V_24X1) ).
fof('$adef_$_lam_9820_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__9820,V_24X1),V_24X2) = c_24__lam__9820___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_69423_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__69423,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__69423___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.FilterLimits.neighborhood_filter_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFilterLimits_2eneighborhood__filter,V_24X1),V_24X2) = cTopology_2eFilterLimits_2eneighborhood__filter___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.InteriorsClosures.closure_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eInteriorsClosures_2eclosure,V_24X1),V_24X2) = cTopology_2eInteriorsClosures_2eclosure___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.SupInf.is_glb_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eSupInf_2eis__glb,V_24X1),V_24X2))
<=> cTopology_2eSupInf_2eis__glb___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RiemannInt_SF.RiemannInt_SF_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eRiemannInt__SF,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRiemannInt__SF_2eRiemannInt__SF___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rprod.prod_f_R0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRprod_2eprod__f__R0,V_24X1),V_24X2) = cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_5813_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__5813,V_24X1),V_24X2))
<=> c_24__lam__5813___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.RMicromega.RWeakChecker_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eRWeakChecker,V_24X1) = cCoq_2emicromega_2eRMicromega_2eRWeakChecker___24a1(V_24X1) ).
fof('$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_$_lam_9854_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__9854,V_24X1),V_24X2))
<=> c_24__lam__9854___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.MetricSpaces.MetricTopology_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eMetricSpaces_2eMetricTopology,V_24X1),V_24X2) = cTopology_2eMetricSpaces_2eMetricTopology___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_41709_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__41709,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__41709___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_let_18_mkmult_pow_2189_$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__2189,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__2189___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.Init.Logic.uniqueness_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eLogic_2euniqueness,V_24X1),V_24X2))
<=> cCoq_2eInit_2eLogic_2euniqueness___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.Nets.Build_cluster_point_subnet_DS_set_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Reals.R_sqrt.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eR__sqrt_2esqrt,V_24X1) = cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_68442_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__68442,V_24X1),V_24X2),V_24X3) = c_24__lam__68442___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.RiemannInt.FTC_P1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRiemannInt_2eFTC__P1,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRiemannInt_2eFTC__P1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Logic.inhabited_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eLogic_2einhabited,V_24X1))
<=> cCoq_2eInit_2eLogic_2einhabited___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_4435_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(c_24__lam__4435,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> c_24__lam__4435___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Completeness.cauchy_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eCompleteness_2ecauchy,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eCompleteness_2ecauchy___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.Compactness.compact_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eCompactness_2ecompact,V_24X1))
<=> cTopology_2eCompactness_2ecompact___24a1(V_24X1) ) ).
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('$adef_Coq.Reals.RIneq.mknonnegreal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1),V_24X2) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_901_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__901,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__901___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Ensembles.Same_set_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSame__set,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.Nets.cps_U_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cTopology_2eNets_2ecps__U,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cTopology_2eNets_2ecps__U___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.Reals.RList.FF_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRList_2eFF,V_24X1),V_24X2) = cCoq_2eReals_2eRList_2eFF___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Nets.neighborhood_net_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eNets_2eneighborhood__net,V_24X1),V_24X2),V_24X3) = cTopology_2eNets_2eneighborhood__net___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Specif.projT1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT1,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_79419_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__79419,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__79419___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.Rpow_def.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRpow__def_2epow,V_24X1),V_24X2) = cCoq_2eReals_2eRpow__def_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rtopology.uniform_continuity_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtopology_2euniform__continuity,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtopology_2euniform__continuity___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_72851_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__72851,V_24X1),V_24X2))
<=> c_24__lam__72851___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR__2,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RList.Rlist_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRList_2eRlist__rec,V_24X1) = cCoq_2eReals_2eRList_2eRlist__rec___24a1(V_24X1) ).
fof('$adef_$_lam_284_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__284,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__284___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.micromega.RingMicromega.PsatzSquare_$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_792_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__792,V_24X1),V_24X2) = c_24__prop__792___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Nets.intro_neighborhood_net_DS_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eNets_2eintro__neighborhood__net__DS,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_7048_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__7048,V_24X1),V_24X2) = c_24__lam__7048___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Full_set_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eFull__set,V_24X1) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ratan.Ratan_seq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRatan_2eRatan__seq,V_24X1),V_24X2) = cCoq_2eReals_2eRatan_2eRatan__seq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rseries.EUn_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRseries_2eEUn,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRseries_2eEUn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_8088_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__8088,V_24X1),V_24X2) = c_24__prop__8088___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_14596_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__14596,V_24X1),V_24X2) = c_24__lam__14596___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rseries.EUn_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRseries_2eEUn,V_24X1) = cCoq_2eReals_2eRseries_2eEUn___24a1(V_24X1) ).
fof('$adef_$_lam_73344_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__73344,V_24X1),V_24X2) = c_24__lam__73344___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ratan.atan_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2eatan,V_24X1) = cCoq_2eReals_2eRatan_2eatan___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RiemannInt_SF.subdivision_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2esubdivision,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRiemannInt__SF_2esubdivision___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.VarMap.find_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2efind,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2efind___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rsqrt_def.Dichotomy_lb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_901_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__901,V_24X1),V_24X2) = c_24__lam__901___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.FiltersAndNets.net_tail_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eFiltersAndNets_2enet__tail,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eFiltersAndNets_2enet__tail___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.RiemannInt_SF.co_interval_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eco__interval,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRiemannInt__SF_2eco__interval___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.RList.cons_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRList_2econs,V_24X1),V_24X2) = cCoq_2eReals_2eRList_2econs___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_78832_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__78832,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__78832___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.Ranalysis1.decreasing_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRanalysis1_2edecreasing,V_24X1))
<=> cCoq_2eReals_2eRanalysis1_2edecreasing___24a1(V_24X1) ) ).
fof('$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.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_7_down_9441_9457_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__7__down__9441__9457,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__7__down__9441__9457___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_79313_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__79313,V_24X1),V_24X2) = c_24__lam__79313___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_68792_$a1',axiom,
! [V_24X1] : happ(c_24__lam__68792,V_24X1) = c_24__lam__68792___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rsqrt_def.Dichotomy_ub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRsqrt__def_2eDichotomy__ub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__ub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.Filters.filter_family_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFilters_2efilter__family,V_24X1),V_24X2) = cTopology_2eFilters_2efilter__family___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtopology.compact_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRtopology_2ecompact,V_24X1))
<=> cCoq_2eReals_2eRtopology_2ecompact___24a1(V_24X1) ) ).
fof('$adef_Topology.Nets.neighborhood_net_DS_ord_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTopology_2eNets_2eneighborhood__net__DS__ord,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTopology_2eNets_2eneighborhood__net__DS__ord___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_6987_$a1',axiom,
! [V_24X1] : happ(c_24__lam__6987,V_24X1) = c_24__lam__6987___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rpower.Rpower_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRpower_2eRpower,V_24X1),V_24X2) = cCoq_2eReals_2eRpower_2eRpower___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ratan.Ratan_seq_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2eRatan__seq,V_24X1) = cCoq_2eReals_2eRatan_2eRatan__seq___24a1(V_24X1) ).
fof('$adef_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble,V_24X1),V_24X2) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_9336_$a1',axiom,
! [V_24X1] : happ(c_24__lam__9336,V_24X1) = c_24__lam__9336___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ranalysis1.mult_fct_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2emult__fct,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2emult__fct___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.Rge_le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRIneq_2eRge__le,V_24X1),V_24X2) = cCoq_2eReals_2eRIneq_2eRge__le___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rabs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRbasic__fun_2eRabs,V_24X1) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V_24X1) ).
fof('$adef_Topology.CountabilityAxioms.first_countable_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eCountabilityAxioms_2efirst__countable,V_24X1))
<=> cTopology_2eCountabilityAxioms_2efirst__countable___24a1(V_24X1) ) ).
fof('$adef_$_fix_9439_0_Dichotomy_lb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__fix__9439__0__Dichotomy__lb,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__fix__9439__0__Dichotomy__lb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_Topology.WeakTopology.weak_topology_subbasis_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eWeakTopology_2eweak__topology__subbasis,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eWeakTopology_2eweak__topology__subbasis___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_79313_$a1',axiom,
! [V_24X1] : happ(c_24__lam__79313,V_24X1) = c_24__lam__79313___24a1(V_24X1) ).
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('$adef_Coq.Reals.Rtrigo_alt.cos_approx_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRtrigo__alt_2ecos__approx,V_24X1),V_24X2) = cCoq_2eReals_2eRtrigo__alt_2ecos__approx___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Topology.SeparatednessAxioms.Hausdorff_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eSeparatednessAxioms_2eHausdorff,V_24X1))
<=> cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V_24X1) ) ).
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('$adef_Topology.Neighborhoods.open_neighborhood_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eNeighborhoods_2eopen__neighborhood,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rtrigo_alt.cos_term_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__alt_2ecos__term,V_24X1) = cCoq_2eReals_2eRtrigo__alt_2ecos__term___24a1(V_24X1) ).
fof('$adef_$_lam_5815_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__5815,V_24X1),V_24X2) = c_24__lam__5815___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_78784_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__78784,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__78784___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).
fof('$adef_$_lam_78796_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__78796,V_24X1),V_24X2) = c_24__lam__78796___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Nets.Net_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eNets_2eNet,V_24X1),V_24X2) = cTopology_2eNets_2eNet___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$9399_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_249399,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249399___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rtrigo1.cos_ub_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo1_2ecos__ub,V_24X1) = cCoq_2eReals_2eRtrigo1_2ecos__ub___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rtopology.f_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtopology_2ef,V_24X1) = cCoq_2eReals_2eRtopology_2ef___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.eval_bf_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__bf,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eTauto_2eeval__bf___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_let_11_subst_l_1683_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__1683,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__1683___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_Topology.DirectedSets.DS_ord_$a1',axiom,
! [V_24X1] : happ(cTopology_2eDirectedSets_2eDS__ord,V_24X1) = cTopology_2eDirectedSets_2eDS__ord___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ranalysis1.fct_cte_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRanalysis1_2efct__cte,V_24X1) = cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(V_24X1) ).
fof('$adef_$_lam_69700_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__69700,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__69700___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_ZornsLemma.CountableTypes.CountableT_$a1',axiom,
! [V_24X1] :
( p(happ(cZornsLemma_2eCountableTypes_2eCountableT,V_24X1))
<=> cZornsLemma_2eCountableTypes_2eCountableT___24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_pt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2ederivable__pt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_61712_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__61712,V_24X1),V_24X2),V_24X3) = c_24__lam__61712___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rtopology.closed_set_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRtopology_2eclosed__set,V_24X1))
<=> cCoq_2eReals_2eRtopology_2eclosed__set___24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.RiemannInt_SF.Nbound_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRiemannInt__SF_2eNbound,V_24X1))
<=> cCoq_2eReals_2eRiemannInt__SF_2eNbound___24a1(V_24X1) ) ).
fof('$adef_$_lam_69289_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__69289,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__69289___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$9428_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_249428,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_249428___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.Filters.Filter_$a1',axiom,
! [V_24X1] : happ(cTopology_2eFilters_2eFilter,V_24X1) = cTopology_2eFilters_2eFilter___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.FiltersAndNets.net_tail_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eFiltersAndNets_2enet__tail,V_24X1),V_24X2),V_24X3) = cTopology_2eFiltersAndNets_2enet__tail___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_16_mkpow_2187_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__2187,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__2187___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_Topology.Nets.cluster_point_subnet_DS_ord_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet__DS__ord,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eNets_2ecluster__point__subnet__DS__ord___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.RiemannInt_SF.subdivision_val_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2esubdivision__val,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRiemannInt__SF_2esubdivision__val___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.Factorial.fact_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2eFactorial_2efact,V_24X1) = cCoq_2eArith_2eFactorial_2efact___24a1(V_24X1) ).
fof('$adef_Coq.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_Topology.OpenBases.B_open_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eOpenBases_2eB__open,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eOpenBases_2eB__open___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).
fof('$adef_$_prop_6638_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__6638,V_24X1),V_24X2) = c_24__prop__6638___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtopology.bounded_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRtopology_2ebounded,V_24X1))
<=> cCoq_2eReals_2eRtopology_2ebounded___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$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('$adef_ZornsLemma.FiniteIntersections.finite_intersections_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFiniteIntersections_2efinite__intersections,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Image.Im_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eSets_2eImage_2eIm,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eSets_2eImage_2eIm___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_9551_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__9551,V_24X1),V_24X2),V_24X3) = c_24__lam__9551___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_Topology.MetricSpaces.metrizable_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eMetricSpaces_2emetrizable,V_24X1))
<=> cTopology_2eMetricSpaces_2emetrizable___24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.RiemannInt_SF.StepFun_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eStepFun,V_24X1),V_24X2) = cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rderiv.D_x_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRderiv_2eD__x,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRderiv_2eD__x___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.denum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2edenum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_68792_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__68792,V_24X1),V_24X2))
<=> c_24__lam__68792___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sets.Ensembles.Ensemble_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eEnsemble,V_24X1) = cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V_24X1) ).
fof('$adef_$_lam_4435_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__4435,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__4435___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_63257_$a1',axiom,
! [V_24X1] : happ(c_24__lam__63257,V_24X1) = c_24__lam__63257___24a1(V_24X1) ).
fof('$adef_Topology.FilterLimits.filter_limit_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eFilterLimits_2efilter__limit,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eFilterLimits_2efilter__limit___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$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('$adef_Coq.Reals.SeqProp.has_lb_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eSeqProp_2ehas__lb,V_24X1))
<=> cCoq_2eReals_2eSeqProp_2ehas__lb___24a1(V_24X1) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.no_cond_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRanalysis1_2eno__cond,V_24X1))
<=> cCoq_2eReals_2eRanalysis1_2eno__cond___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('$adef_Coq.Reals.Rtrigo_def.sin_n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2esin__n,V_24X1) = cCoq_2eReals_2eRtrigo__def_2esin__n___24a1(V_24X1) ).
fof('$adef_$_lam_63142_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__63142,V_24X1),V_24X2))
<=> c_24__lam__63142___24a2(V_24X1,V_24X2) ) ).
fof('$tdef_$_type_897',axiom,
! [V_24Y] :
( c_24__type__897___24t(V_24Y)
<=> t(V_24Y,c_24__type__897) ) ).
fof('$tdef_$_type_6740',axiom,
! [V_24Y] :
( c_24__type__6740___24t(V_24Y)
<=> t(V_24Y,c_24__type__6740) ) ).
fof('$tdef_Coq.Reals.Rlimit.Metric_Space',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRlimit_2eMetric__Space) ) ).
fof('$tdef_$_type_79274',axiom,
! [V_24Y] :
( c_24__type__79274___24t(V_24Y)
<=> t(V_24Y,c_24__type__79274) ) ).
fof('$tdef_$_type_6691',axiom,
! [V_24Y] :
( c_24__type__6691___24t(V_24Y)
<=> t(V_24Y,c_24__type__6691) ) ).
fof('$tdef_$_type_26727',axiom,
! [V_24Y] :
( c_24__type__26727___24t(V_24Y)
<=> t(V_24Y,c_24__type__26727) ) ).
fof('$tdef_$_type_3747',axiom,
! [V_24Y] :
( c_24__type__3747___24t(V_24Y)
<=> t(V_24Y,c_24__type__3747) ) ).
fof('$tdef_$_type_69236',axiom,
! [V_24Y] :
( c_24__type__69236___24t(V_24Y)
<=> t(V_24Y,c_24__type__69236) ) ).
fof('$tdef_$_type_6875',axiom,
! [V_24Y] :
( c_24__type__6875___24t(V_24Y)
<=> t(V_24Y,c_24__type__6875) ) ).
fof('$tdef_$_type_4475',axiom,
! [V_24Y] :
( c_24__type__4475___24t(V_24Y)
<=> t(V_24Y,c_24__type__4475) ) ).
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_$_type_64711',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__64711___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__64711___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9706',axiom,
! [V_24Y] :
( c_24__type__9706___24t(V_24Y)
<=> t(V_24Y,c_24__type__9706) ) ).
fof('$tdef_$_type_14645',axiom,
! [V_24Y] :
( c_24__type__14645___24t(V_24Y)
<=> t(V_24Y,c_24__type__14645) ) ).
fof('$tdef_$_type_529',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__529___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__529___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_327',axiom,
! [V_24X1,V_24Y] :
( c_24__type__327___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__327___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1665',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1665___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1665___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_63312',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__63312___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__63312___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_61740',axiom,
! [V_24Y] :
( c_24__type__61740___24t(V_24Y)
<=> t(V_24Y,c_24__type__61740) ) ).
fof('$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_7537',axiom,
! [V_24Y] :
( c_24__type__7537___24t(V_24Y)
<=> t(V_24Y,c_24__type__7537) ) ).
fof('$tdef_Coq.Reals.RiemannInt_SF.StepFun',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8077',axiom,
! [V_24Y] :
( c_24__type__8077___24t(V_24Y)
<=> t(V_24Y,c_24__type__8077) ) ).
fof('$tdef_$_type_297',axiom,
! [V_24Y] :
( c_24__type__297___24t(V_24Y)
<=> t(V_24Y,c_24__type__297) ) ).
fof('$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_63274',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__63274___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__63274___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_10713',axiom,
! [V_24Y] :
( c_24__type__10713___24t(V_24Y)
<=> t(V_24Y,c_24__type__10713) ) ).
fof('$tdef_$_type_876',axiom,
! [V_24Y] :
( c_24__type__876___24t(V_24Y)
<=> t(V_24Y,c_24__type__876) ) ).
fof('$tdef_Topology.Nets.neighborhood_net_DS_set',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cTopology_2eNets_2eneighborhood__net__DS__set___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cTopology_2eNets_2eneighborhood__net__DS__set___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_79198',axiom,
! [V_24Y] :
( c_24__type__79198___24t(V_24Y)
<=> t(V_24Y,c_24__type__79198) ) ).
fof('$tdef_$_type_15009',axiom,
! [V_24Y] :
( c_24__type__15009___24t(V_24Y)
<=> t(V_24Y,c_24__type__15009) ) ).
fof('$tdef_$_type_7980',axiom,
! [V_24Y] :
( c_24__type__7980___24t(V_24Y)
<=> t(V_24Y,c_24__type__7980) ) ).
fof('$tdef_$_type_70044',axiom,
! [V_24Y] :
( c_24__type__70044___24t(V_24Y)
<=> t(V_24Y,c_24__type__70044) ) ).
fof('$tdef_$_type_68519',axiom,
! [V_24Y] :
( c_24__type__68519___24t(V_24Y)
<=> t(V_24Y,c_24__type__68519) ) ).
fof('$tdef_$_type_14632',axiom,
! [V_24Y] :
( c_24__type__14632___24t(V_24Y)
<=> t(V_24Y,c_24__type__14632) ) ).
fof('$tdef_$_type_63481',axiom,
! [V_24Y] :
( c_24__type__63481___24t(V_24Y)
<=> t(V_24Y,c_24__type__63481) ) ).
fof('$tdef_$_type_64365',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__64365___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__64365___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_$_type_1907',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1907___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1907___24a1(V_24X1)) ) ).
fof('$tdef_$_type_69615',axiom,
! [V_24Y] :
( c_24__type__69615___24t(V_24Y)
<=> t(V_24Y,c_24__type__69615) ) ).
fof('$tdef_$_type_6636',axiom,
! [V_24Y] :
( c_24__type__6636___24t(V_24Y)
<=> t(V_24Y,c_24__type__6636) ) ).
fof('$tdef_$_type_7271',axiom,
! [V_24Y] :
( c_24__type__7271___24t(V_24Y)
<=> t(V_24Y,c_24__type__7271) ) ).
fof('$tdef_$_type_2522',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2522___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2522___24a2(V_24X1,V_24X2)) ) ).
fof('$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_8343',axiom,
! [V_24Y] :
( c_24__type__8343___24t(V_24Y)
<=> t(V_24Y,c_24__type__8343) ) ).
fof('$tdef_$_type_69989',axiom,
! [V_24Y] :
( c_24__type__69989___24t(V_24Y)
<=> t(V_24Y,c_24__type__69989) ) ).
fof('$tdef_$_type_1134',axiom,
! [V_24Y] :
( c_24__type__1134___24t(V_24Y)
<=> t(V_24Y,c_24__type__1134) ) ).
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_$_type_6391',axiom,
! [V_24Y] :
( c_24__type__6391___24t(V_24Y)
<=> t(V_24Y,c_24__type__6391) ) ).
fof('$tdef_Topology.Nets.Net',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cTopology_2eNets_2eNet___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cTopology_2eNets_2eNet___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_162',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__162___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__162___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5817',axiom,
! [V_24Y] :
( c_24__type__5817___24t(V_24Y)
<=> t(V_24Y,c_24__type__5817) ) ).
fof('$tdef_$_type_1902',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1902___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1902___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8137',axiom,
! [V_24Y] :
( c_24__type__8137___24t(V_24Y)
<=> t(V_24Y,c_24__type__8137) ) ).
fof('$tdef_$_type_68989',axiom,
! [V_24Y] :
( c_24__type__68989___24t(V_24Y)
<=> t(V_24Y,c_24__type__68989) ) ).
fof('$tdef_$_type_4702',axiom,
! [V_24Y] :
( c_24__type__4702___24t(V_24Y)
<=> t(V_24Y,c_24__type__4702) ) ).
fof('$tdef_$_type_7322',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__7322___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__7322___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_5735',axiom,
! [V_24Y] :
( c_24__type__5735___24t(V_24Y)
<=> t(V_24Y,c_24__type__5735) ) ).
fof('$tdef_$_type_26692',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__26692___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__26692___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1887',axiom,
! [V_24Y] :
( c_24__type__1887___24t(V_24Y)
<=> t(V_24Y,c_24__type__1887) ) ).
fof('$tdef_$_type_8097',axiom,
! [V_24Y] :
( c_24__type__8097___24t(V_24Y)
<=> t(V_24Y,c_24__type__8097) ) ).
fof('$tdef_$_type_4258',axiom,
! [V_24Y] :
( c_24__type__4258___24t(V_24Y)
<=> t(V_24Y,c_24__type__4258) ) ).
fof('$tdef_$_type_64707',axiom,
! [V_24X1,V_24Y] :
( c_24__type__64707___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__64707___24a1(V_24X1)) ) ).
fof('$tdef_$_type_5948',axiom,
! [V_24Y] :
( c_24__type__5948___24t(V_24Y)
<=> t(V_24Y,c_24__type__5948) ) ).
fof('$tdef_$_type_7999',axiom,
! [V_24Y] :
( c_24__type__7999___24t(V_24Y)
<=> t(V_24Y,c_24__type__7999) ) ).
fof('$tdef_$_type_5671',axiom,
! [V_24Y] :
( c_24__type__5671___24t(V_24Y)
<=> t(V_24Y,c_24__type__5671) ) ).
fof('$tdef_$_type_78923',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__78923___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__78923___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_3699',axiom,
! [V_24Y] :
( c_24__type__3699___24t(V_24Y)
<=> t(V_24Y,c_24__type__3699) ) ).
fof('$tdef_$_type_3432',axiom,
! [V_24Y] :
( c_24__type__3432___24t(V_24Y)
<=> t(V_24Y,c_24__type__3432) ) ).
fof('$tdef_Topology.TopologicalSpaces.TopologicalSpace',axiom,
! [V_24Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V_24Y)
<=> t(V_24Y,cTopology_2eTopologicalSpaces_2eTopologicalSpace) ) ).
fof('$tdef_$_type_8356',axiom,
! [V_24Y] :
( c_24__type__8356___24t(V_24Y)
<=> t(V_24Y,c_24__type__8356) ) ).
fof('$tdef_$_type_7336',axiom,
! [V_24Y] :
( c_24__type__7336___24t(V_24Y)
<=> t(V_24Y,c_24__type__7336) ) ).
fof('$tdef_$_type_69278',axiom,
! [V_24Y] :
( c_24__type__69278___24t(V_24Y)
<=> t(V_24Y,c_24__type__69278) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_14798',axiom,
! [V_24Y] :
( c_24__type__14798___24t(V_24Y)
<=> t(V_24Y,c_24__type__14798) ) ).
fof('$tdef_$_type_6901',axiom,
! [V_24Y] :
( c_24__type__6901___24t(V_24Y)
<=> t(V_24Y,c_24__type__6901) ) ).
fof('$tdef_$_type_2506',axiom,
! [V_24Y] :
( c_24__type__2506___24t(V_24Y)
<=> t(V_24Y,c_24__type__2506) ) ).
fof('$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_3429',axiom,
! [V_24Y] :
( c_24__type__3429___24t(V_24Y)
<=> t(V_24Y,c_24__type__3429) ) ).
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_$_type_5743',axiom,
! [V_24Y] :
( c_24__type__5743___24t(V_24Y)
<=> t(V_24Y,c_24__type__5743) ) ).
fof('$tdef_$_type_9987',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__9987___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__9987___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_73179',axiom,
! [V_24Y] :
( c_24__type__73179___24t(V_24Y)
<=> t(V_24Y,c_24__type__73179) ) ).
fof('$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_14748',axiom,
! [V_24Y] :
( c_24__type__14748___24t(V_24Y)
<=> t(V_24Y,c_24__type__14748) ) ).
fof('$tdef_$_type_26721',axiom,
! [V_24Y] :
( c_24__type__26721___24t(V_24Y)
<=> t(V_24Y,c_24__type__26721) ) ).
fof('$tdef_Topology.Nets.cluster_point_subnet_DS_set',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cTopology_2eNets_2ecluster__point__subnet__DS__set___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_324',axiom,
! [V_24Y] :
( c_24__type__324___24t(V_24Y)
<=> t(V_24Y,c_24__type__324) ) ).
fof('$tdef_$_type_6567',axiom,
! [V_24Y] :
( c_24__type__6567___24t(V_24Y)
<=> t(V_24Y,c_24__type__6567) ) ).
fof('$tdef_$_type_291',axiom,
! [V_24Y] :
( c_24__type__291___24t(V_24Y)
<=> t(V_24Y,c_24__type__291) ) ).
fof('$tdef_$_type_63416',axiom,
! [V_24Y] :
( c_24__type__63416___24t(V_24Y)
<=> t(V_24Y,c_24__type__63416) ) ).
fof('$tdef_$_type_62162',axiom,
! [V_24Y] :
( c_24__type__62162___24t(V_24Y)
<=> t(V_24Y,c_24__type__62162) ) ).
fof('$tdef_$_type_6866',axiom,
! [V_24Y] :
( c_24__type__6866___24t(V_24Y)
<=> t(V_24Y,c_24__type__6866) ) ).
fof('$tdef_$_type_6821',axiom,
! [V_24Y] :
( c_24__type__6821___24t(V_24Y)
<=> t(V_24Y,c_24__type__6821) ) ).
fof('$tdef_$_type_5163',axiom,
! [V_24Y] :
( c_24__type__5163___24t(V_24Y)
<=> t(V_24Y,c_24__type__5163) ) ).
fof('$tdef_$_type_5267',axiom,
! [V_24Y] :
( c_24__type__5267___24t(V_24Y)
<=> t(V_24Y,c_24__type__5267) ) ).
fof('$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_9400',axiom,
! [V_24Y] :
( c_24__type__9400___24t(V_24Y)
<=> t(V_24Y,c_24__type__9400) ) ).
fof('$tdef_$_type_78880',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__78880___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__78880___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_63157',axiom,
! [V_24Y] :
( c_24__type__63157___24t(V_24Y)
<=> t(V_24Y,c_24__type__63157) ) ).
fof('$tdef_$_type_558',axiom,
! [V_24Y] :
( c_24__type__558___24t(V_24Y)
<=> t(V_24Y,c_24__type__558) ) ).
fof('$tdef_$_type_70166',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__70166___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__70166___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_3096',axiom,
! [V_24Y] :
( c_24__type__3096___24t(V_24Y)
<=> t(V_24Y,c_24__type__3096) ) ).
fof('$tdef_$_type_7306',axiom,
! [V_24Y] :
( c_24__type__7306___24t(V_24Y)
<=> t(V_24Y,c_24__type__7306) ) ).
fof('$tdef_$_type_79352',axiom,
! [V_24Y] :
( c_24__type__79352___24t(V_24Y)
<=> t(V_24Y,c_24__type__79352) ) ).
fof('$tdef_$_type_6965',axiom,
! [V_24Y] :
( c_24__type__6965___24t(V_24Y)
<=> t(V_24Y,c_24__type__6965) ) ).
fof('$tdef_$_type_2852',axiom,
! [V_24Y] :
( c_24__type__2852___24t(V_24Y)
<=> t(V_24Y,c_24__type__2852) ) ).
fof('$tdef_$_type_2615',axiom,
! [V_24Y] :
( c_24__type__2615___24t(V_24Y)
<=> t(V_24Y,c_24__type__2615) ) ).
fof('$tdef_$_type_9602',axiom,
! [V_24Y] :
( c_24__type__9602___24t(V_24Y)
<=> t(V_24Y,c_24__type__9602) ) ).
fof('$tdef_$_type_5104',axiom,
! [V_24Y] :
( c_24__type__5104___24t(V_24Y)
<=> t(V_24Y,c_24__type__5104) ) ).
fof('$tdef_$_type_68131',axiom,
! [V_24Y] :
( c_24__type__68131___24t(V_24Y)
<=> t(V_24Y,c_24__type__68131) ) ).
fof('$tdef_$_type_2671',axiom,
! [V_24Y] :
( c_24__type__2671___24t(V_24Y)
<=> t(V_24Y,c_24__type__2671) ) ).
fof('$tdef_$_type_69406',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__69406___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__69406___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_6722',axiom,
! [V_24Y] :
( c_24__type__6722___24t(V_24Y)
<=> t(V_24Y,c_24__type__6722) ) ).
fof('$tdef_$_type_6562',axiom,
! [V_24Y] :
( c_24__type__6562___24t(V_24Y)
<=> t(V_24Y,c_24__type__6562) ) ).
fof('$tdef_$_type_79221',axiom,
! [V_24Y] :
( c_24__type__79221___24t(V_24Y)
<=> t(V_24Y,c_24__type__79221) ) ).
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_$_type_63385',axiom,
! [V_24Y] :
( c_24__type__63385___24t(V_24Y)
<=> t(V_24Y,c_24__type__63385) ) ).
fof('$tdef_$_type_495',axiom,
! [V_24Y] :
( c_24__type__495___24t(V_24Y)
<=> t(V_24Y,c_24__type__495) ) ).
fof('$tdef_$_type_15091',axiom,
! [V_24Y] :
( c_24__type__15091___24t(V_24Y)
<=> t(V_24Y,c_24__type__15091) ) ).
fof('$tdef_$_type_14603',axiom,
! [V_24Y] :
( c_24__type__14603___24t(V_24Y)
<=> t(V_24Y,c_24__type__14603) ) ).
fof('$tdef_$_type_10068',axiom,
! [V_24Y] :
( c_24__type__10068___24t(V_24Y)
<=> t(V_24Y,c_24__type__10068) ) ).
fof('$tdef_$_type_10657',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10657___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10657___24a1(V_24X1)) ) ).
fof('$tdef_$_type_9573',axiom,
! [V_24Y] :
( c_24__type__9573___24t(V_24Y)
<=> t(V_24Y,c_24__type__9573) ) ).
fof('$tdef_$_type_69601',axiom,
! [V_24Y] :
( c_24__type__69601___24t(V_24Y)
<=> t(V_24Y,c_24__type__69601) ) ).
fof('$tdef_$_type_294',axiom,
! [V_24Y] :
( c_24__type__294___24t(V_24Y)
<=> t(V_24Y,c_24__type__294) ) ).
fof('$tdef_$_type_7939',axiom,
! [V_24Y] :
( c_24__type__7939___24t(V_24Y)
<=> t(V_24Y,c_24__type__7939) ) ).
fof('$tdef_$_type_15289',axiom,
! [V_24Y] :
( c_24__type__15289___24t(V_24Y)
<=> t(V_24Y,c_24__type__15289) ) ).
fof('$tdef_$_type_15033',axiom,
! [V_24Y] :
( c_24__type__15033___24t(V_24Y)
<=> t(V_24Y,c_24__type__15033) ) ).
fof('$tdef_$_type_1446',axiom,
! [V_24Y] :
( c_24__type__1446___24t(V_24Y)
<=> t(V_24Y,c_24__type__1446) ) ).
fof('$tdef_$_type_78747',axiom,
! [V_24Y] :
( c_24__type__78747___24t(V_24Y)
<=> t(V_24Y,c_24__type__78747) ) ).
fof('$tdef_$_type_6730',axiom,
! [V_24Y] :
( c_24__type__6730___24t(V_24Y)
<=> t(V_24Y,c_24__type__6730) ) ).
fof('$tdef_$_type_3088',axiom,
! [V_24Y] :
( c_24__type__3088___24t(V_24Y)
<=> t(V_24Y,c_24__type__3088) ) ).
fof('$tdef_$_type_1451',axiom,
! [V_24Y] :
( c_24__type__1451___24t(V_24Y)
<=> t(V_24Y,c_24__type__1451) ) ).
fof('$tdef_Coq.Reals.RiemannInt.C1_fun',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRiemannInt_2eC1__fun___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRiemannInt_2eC1__fun) ) ).
fof('$tdef_$_type_810',axiom,
! [V_24Y] :
( c_24__type__810___24t(V_24Y)
<=> t(V_24Y,c_24__type__810) ) ).
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_$_type_20',axiom,
! [V_24Y] :
( c_24__type__20___24t(V_24Y)
<=> t(V_24Y,c_24__type__20) ) ).
fof('$tdef_$_type_9581',axiom,
! [V_24Y] :
( c_24__type__9581___24t(V_24Y)
<=> t(V_24Y,c_24__type__9581) ) ).
fof('$tdef_$_type_63739',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__63739___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__63739___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_375',axiom,
! [V_24X1,V_24Y] :
( c_24__type__375___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__375___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6860',axiom,
! [V_24Y] :
( c_24__type__6860___24t(V_24Y)
<=> t(V_24Y,c_24__type__6860) ) ).
fof('$tdef_$_type_63488',axiom,
! [V_24Y] :
( c_24__type__63488___24t(V_24Y)
<=> t(V_24Y,c_24__type__63488) ) ).
fof('$tdef_$_type_318',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__318___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__318___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_79371',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__79371___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__79371___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_601',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__601___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__601___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_ZornsLemma.Families.Family',axiom,
! [V_24X1,V_24Y] :
( cZornsLemma_2eFamilies_2eFamily___24t(V_24X1,V_24Y)
<=> t(V_24Y,cZornsLemma_2eFamilies_2eFamily___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26620',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__26620___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__26620___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_10019',axiom,
! [V_24Y] :
( c_24__type__10019___24t(V_24Y)
<=> t(V_24Y,c_24__type__10019) ) ).
fof('$tdef_$_type_6038',axiom,
! [V_24Y] :
( c_24__type__6038___24t(V_24Y)
<=> t(V_24Y,c_24__type__6038) ) ).
fof('$tdef_$_type_64750',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__64750___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__64750___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_4494',axiom,
! [V_24Y] :
( c_24__type__4494___24t(V_24Y)
<=> t(V_24Y,c_24__type__4494) ) ).
fof('$tdef_$_type_6794',axiom,
! [V_24Y] :
( c_24__type__6794___24t(V_24Y)
<=> t(V_24Y,c_24__type__6794) ) ).
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_$_type_79409',axiom,
! [V_24Y] :
( c_24__type__79409___24t(V_24Y)
<=> t(V_24Y,c_24__type__79409) ) ).
fof('$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_812',axiom,
! [V_24Y] :
( c_24__type__812___24t(V_24Y)
<=> t(V_24Y,c_24__type__812) ) ).
fof('$tdef_$_type_63319',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__63319___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__63319___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_2544',axiom,
! [V_24Y] :
( c_24__type__2544___24t(V_24Y)
<=> t(V_24Y,c_24__type__2544) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_6580',axiom,
! [V_24Y] :
( c_24__type__6580___24t(V_24Y)
<=> t(V_24Y,c_24__type__6580) ) ).
fof('$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_302',axiom,
! [V_24Y] :
( c_24__type__302___24t(V_24Y)
<=> t(V_24Y,c_24__type__302) ) ).
fof('$tdef_$_type_69026',axiom,
! [V_24Y] :
( c_24__type__69026___24t(V_24Y)
<=> t(V_24Y,c_24__type__69026) ) ).
fof('$tdef_$_type_15225',axiom,
! [V_24Y] :
( c_24__type__15225___24t(V_24Y)
<=> t(V_24Y,c_24__type__15225) ) ).
fof('$tdef_$_type_6989',axiom,
! [V_24Y] :
( c_24__type__6989___24t(V_24Y)
<=> t(V_24Y,c_24__type__6989) ) ).
fof('$tdef_Topology.Filters.Filter',axiom,
! [V_24X1,V_24Y] :
( cTopology_2eFilters_2eFilter___24t(V_24X1,V_24Y)
<=> t(V_24Y,cTopology_2eFilters_2eFilter___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1443',axiom,
! [V_24Y] :
( c_24__type__1443___24t(V_24Y)
<=> t(V_24Y,c_24__type__1443) ) ).
fof('$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('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).
fof('$tdef_ZornsLemma.IndexedFamilies.IndexedFamily',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9613',axiom,
! [V_24Y] :
( c_24__type__9613___24t(V_24Y)
<=> t(V_24Y,c_24__type__9613) ) ).
fof('$tdef_$_type_462',axiom,
! [V_24Y] :
( c_24__type__462___24t(V_24Y)
<=> t(V_24Y,c_24__type__462) ) ).
fof('$tdef_$_type_87',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__87___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__87___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_9668',axiom,
! [V_24Y] :
( c_24__type__9668___24t(V_24Y)
<=> t(V_24Y,c_24__type__9668) ) ).
fof('$tdef_$_type_4012',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4012___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4012___24a1(V_24X1)) ) ).
fof('$tdef_Topology.DirectedSets.DirectedSet',axiom,
! [V_24Y] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V_24Y)
<=> t(V_24Y,cTopology_2eDirectedSets_2eDirectedSet) ) ).
fof('$tdef_$_type_6662',axiom,
! [V_24Y] :
( c_24__type__6662___24t(V_24Y)
<=> t(V_24Y,c_24__type__6662) ) ).
fof('$tdef_$_type_864',axiom,
! [V_24Y] :
( c_24__type__864___24t(V_24Y)
<=> t(V_24Y,c_24__type__864) ) ).
fof('$tdef_$_type_484',axiom,
! [V_24Y] :
( c_24__type__484___24t(V_24Y)
<=> t(V_24Y,c_24__type__484) ) ).
fof('$tdef_$_type_3091',axiom,
! [V_24Y] :
( c_24__type__3091___24t(V_24Y)
<=> t(V_24Y,c_24__type__3091) ) ).
fof('$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_$_type_6962',axiom,
! [V_24Y] :
( c_24__type__6962___24t(V_24Y)
<=> t(V_24Y,c_24__type__6962) ) ).
fof('$tdef_$_type_1647',axiom,
! [V_24Y] :
( c_24__type__1647___24t(V_24Y)
<=> t(V_24Y,c_24__type__1647) ) ).
fof('$tdef_$_type_6704',axiom,
! [V_24Y] :
( c_24__type__6704___24t(V_24Y)
<=> t(V_24Y,c_24__type__6704) ) ).
fof('$tdef_$_type_10731',axiom,
! [V_24Y] :
( c_24__type__10731___24t(V_24Y)
<=> t(V_24Y,c_24__type__10731) ) ).
fof('$tdef_Coq.Reals.Ranalysis1.derivable_pt',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRanalysis1_2ederivable__pt___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2738',axiom,
! [V_24Y] :
( c_24__type__2738___24t(V_24Y)
<=> t(V_24Y,c_24__type__2738) ) ).
fof('$tdef_$_type_7315',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__7315___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__7315___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1679',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1679___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1679___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Topology.FiltersAndNets.filter_to_net_DS_set',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7962',axiom,
! [V_24Y] :
( c_24__type__7962___24t(V_24Y)
<=> t(V_24Y,c_24__type__7962) ) ).
fof('$tdef_$_type_73136',axiom,
! [V_24Y] :
( c_24__type__73136___24t(V_24Y)
<=> t(V_24Y,c_24__type__73136) ) ).
fof('$tdef_$_type_70059',axiom,
! [V_24Y] :
( c_24__type__70059___24t(V_24Y)
<=> t(V_24Y,c_24__type__70059) ) ).
fof('$tdef_$_type_10124',axiom,
! [V_24Y] :
( c_24__type__10124___24t(V_24Y)
<=> t(V_24Y,c_24__type__10124) ) ).
fof('$tdef_$_type_6818',axiom,
! [V_24Y] :
( c_24__type__6818___24t(V_24Y)
<=> t(V_24Y,c_24__type__6818) ) ).
fof('$tdef_$_type_5774',axiom,
! [V_24Y] :
( c_24__type__5774___24t(V_24Y)
<=> t(V_24Y,c_24__type__5774) ) ).
fof('$tdef_$_type_26715',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__26715___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__26715___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_612',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__612___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__612___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_63326',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__63326___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__63326___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_69516',axiom,
! [V_24Y] :
( c_24__type__69516___24t(V_24Y)
<=> t(V_24Y,c_24__type__69516) ) ).
fof('$tdef_$_type_7923',axiom,
! [V_24Y] :
( c_24__type__7923___24t(V_24Y)
<=> t(V_24Y,c_24__type__7923) ) ).
fof('$tdef_$_type_68449',axiom,
! [V_24Y] :
( c_24__type__68449___24t(V_24Y)
<=> t(V_24Y,c_24__type__68449) ) ).
fof('$tdef_$_type_470',axiom,
! [V_24Y] :
( c_24__type__470___24t(V_24Y)
<=> t(V_24Y,c_24__type__470) ) ).
fof('$tdef_$_type_64346',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__64346___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__64346___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_9283',axiom,
! [V_24Y] :
( c_24__type__9283___24t(V_24Y)
<=> t(V_24Y,c_24__type__9283) ) ).
fof('$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_10100',axiom,
! [V_24Y] :
( c_24__type__10100___24t(V_24Y)
<=> t(V_24Y,c_24__type__10100) ) ).
fof('$tdef_$_type_6880',axiom,
! [V_24Y] :
( c_24__type__6880___24t(V_24Y)
<=> t(V_24Y,c_24__type__6880) ) ).
fof('$tdef_$_type_15123',axiom,
! [V_24Y] :
( c_24__type__15123___24t(V_24Y)
<=> t(V_24Y,c_24__type__15123) ) ).
fof('$tdef_$_type_6944',axiom,
! [V_24Y] :
( c_24__type__6944___24t(V_24Y)
<=> t(V_24Y,c_24__type__6944) ) ).
fof('$tdef_$_type_1670',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1670___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1670___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_61790',axiom,
! [V_24Y] :
( c_24__type__61790___24t(V_24Y)
<=> t(V_24Y,c_24__type__61790) ) ).
fof('$tdef_Topology.DirectedSets.DS_set',axiom,
! [V_24X1,V_24Y] :
( cTopology_2eDirectedSets_2eDS__set___24t(V_24X1,V_24Y)
<=> t(V_24Y,cTopology_2eDirectedSets_2eDS__set___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4543',axiom,
! [V_24Y] :
( c_24__type__4543___24t(V_24Y)
<=> t(V_24Y,c_24__type__4543) ) ).
fof('$tdef_$_type_4505',axiom,
! [V_24Y] :
( c_24__type__4505___24t(V_24Y)
<=> t(V_24Y,c_24__type__4505) ) ).
fof('$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_2640',axiom,
! [V_24Y] :
( c_24__type__2640___24t(V_24Y)
<=> t(V_24Y,c_24__type__2640) ) ).
fof('$tdef_$_type_15157',axiom,
! [V_24Y] :
( c_24__type__15157___24t(V_24Y)
<=> t(V_24Y,c_24__type__15157) ) ).
fof('$tdef_$_type_6851',axiom,
! [V_24Y] :
( c_24__type__6851___24t(V_24Y)
<=> t(V_24Y,c_24__type__6851) ) ).
fof('$tdef_$_type_1100',axiom,
! [V_24Y] :
( c_24__type__1100___24t(V_24Y)
<=> t(V_24Y,c_24__type__1100) ) ).
fof('$tdef_$_type_10015',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10015___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10015___24a2(V_24X1,V_24X2)) ) ).
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_$_type_2840',axiom,
! [V_24Y] :
( c_24__type__2840___24t(V_24Y)
<=> t(V_24Y,c_24__type__2840) ) ).
fof('$tdef_$_type_11029',axiom,
! [V_24Y] :
( c_24__type__11029___24t(V_24Y)
<=> t(V_24Y,c_24__type__11029) ) ).
fof('$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_14657',axiom,
! [V_24Y] :
( c_24__type__14657___24t(V_24Y)
<=> t(V_24Y,c_24__type__14657) ) ).
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_$_type_26602',axiom,
! [V_24Y] :
( c_24__type__26602___24t(V_24Y)
<=> t(V_24Y,c_24__type__26602) ) ).
fof('$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_9823',axiom,
! [V_24Y] :
( c_24__type__9823___24t(V_24Y)
<=> t(V_24Y,c_24__type__9823) ) ).
fof('$tdef_$_type_91',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__91___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__91___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Reals.Ranalysis1.derivable',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRanalysis1_2ederivable___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1105',axiom,
! [V_24Y] :
( c_24__type__1105___24t(V_24Y)
<=> t(V_24Y,c_24__type__1105) ) ).
fof('$tdef_$_type_10039',axiom,
! [V_24Y] :
( c_24__type__10039___24t(V_24Y)
<=> t(V_24Y,c_24__type__10039) ) ).
fof('$tdef_$_type_5113',axiom,
! [V_24Y] :
( c_24__type__5113___24t(V_24Y)
<=> t(V_24Y,c_24__type__5113) ) ).
fof('$tdef_$_type_2916',axiom,
! [V_24Y] :
( c_24__type__2916___24t(V_24Y)
<=> t(V_24Y,c_24__type__2916) ) ).
fof('$tdef_$_type_10517',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10517___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10517___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6640',axiom,
! [V_24Y] :
( c_24__type__6640___24t(V_24Y)
<=> t(V_24Y,c_24__type__6640) ) ).
fof('$tdef_$_type_14805',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14805___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14805___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_7959',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__7959___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__7959___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14727',axiom,
! [V_24Y] :
( c_24__type__14727___24t(V_24Y)
<=> t(V_24Y,c_24__type__14727) ) ).
fof('$tdef_$_type_6975',axiom,
! [V_24Y] :
( c_24__type__6975___24t(V_24Y)
<=> t(V_24Y,c_24__type__6975) ) ).
fof('$tdef_$_type_68490',axiom,
! [V_24Y] :
( c_24__type__68490___24t(V_24Y)
<=> t(V_24Y,c_24__type__68490) ) ).
fof('$tdef_$_type_222',axiom,
! [V_24X1,V_24Y] :
( c_24__type__222___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__222___24a1(V_24X1)) ) ).
fof('$tdef_$_type_68454',axiom,
! [V_24Y] :
( c_24__type__68454___24t(V_24Y)
<=> t(V_24Y,c_24__type__68454) ) ).
fof('$tdef_$_type_10134',axiom,
! [V_24Y] :
( c_24__type__10134___24t(V_24Y)
<=> t(V_24Y,c_24__type__10134) ) ).
fof('$tdef_$_type_3758',axiom,
! [V_24Y] :
( c_24__type__3758___24t(V_24Y)
<=> t(V_24Y,c_24__type__3758) ) ).
fof('$tdef_Coq.Sets.Ensembles.Ensemble',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V_24X1)) ) ).
fof('$tdef_$_type_534',axiom,
! [V_24Y] :
( c_24__type__534___24t(V_24Y)
<=> t(V_24Y,c_24__type__534) ) ).
fof('$tdef_$_type_2882',axiom,
! [V_24Y] :
( c_24__type__2882___24t(V_24Y)
<=> t(V_24Y,c_24__type__2882) ) ).
fof('$tdef_$_type_7341',axiom,
! [V_24Y] :
( c_24__type__7341___24t(V_24Y)
<=> t(V_24Y,c_24__type__7341) ) ).
fof('$tdef_$_type_6887',axiom,
! [V_24Y] :
( c_24__type__6887___24t(V_24Y)
<=> t(V_24Y,c_24__type__6887) ) ).
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_$_type_4531',axiom,
! [V_24Y] :
( c_24__type__4531___24t(V_24Y)
<=> t(V_24Y,c_24__type__4531) ) ).
fof('$tdef_$_type_14636',axiom,
! [V_24Y] :
( c_24__type__14636___24t(V_24Y)
<=> t(V_24Y,c_24__type__14636) ) ).
fof('$tdef_$_type_79305',axiom,
! [V_24Y] :
( c_24__type__79305___24t(V_24Y)
<=> t(V_24Y,c_24__type__79305) ) ).
fof('$tdef_$_type_61768',axiom,
! [V_24Y] :
( c_24__type__61768___24t(V_24Y)
<=> t(V_24Y,c_24__type__61768) ) ).
fof('$tdef_$_type_332',axiom,
! [V_24Y] :
( c_24__type__332___24t(V_24Y)
<=> t(V_24Y,c_24__type__332) ) ).
fof('$tdef_$_type_79223',axiom,
! [V_24Y] :
( c_24__type__79223___24t(V_24Y)
<=> t(V_24Y,c_24__type__79223) ) ).
fof('$tdef_$_type_9188',axiom,
! [V_24Y] :
( c_24__type__9188___24t(V_24Y)
<=> t(V_24Y,c_24__type__9188) ) ).
fof('$tdef_$_type_62182',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__62182___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__62182___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$tdef_Coq.micromega.Tauto.BFormula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eTauto_2eBFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eBFormula___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.Ranalysis1.Differential',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRanalysis1_2eDifferential___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRanalysis1_2eDifferential) ) ).
fof('$tdef_$_type_9084',axiom,
! [V_24Y] :
( c_24__type__9084___24t(V_24Y)
<=> t(V_24Y,c_24__type__9084) ) ).
fof('$tdef_Coq.Reals.Rtopology.family',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRtopology_2efamily___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRtopology_2efamily) ) ).
fof('$tdef_$_type_64321',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__64321___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__64321___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2467',axiom,
! [V_24Y] :
( c_24__type__2467___24t(V_24Y)
<=> t(V_24Y,c_24__type__2467) ) ).
fof('$tdef_$_type_26608',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__26608___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__26608___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_78800',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__78800___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__78800___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_5952',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5952___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5952___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15203',axiom,
! [V_24Y] :
( c_24__type__15203___24t(V_24Y)
<=> t(V_24Y,c_24__type__15203) ) ).
fof('$tdef_$_type_14812',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14812___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14812___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_880',axiom,
! [V_24Y] :
( c_24__type__880___24t(V_24Y)
<=> t(V_24Y,c_24__type__880) ) ).
fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_$_type_69470',axiom,
! [V_24Y] :
( c_24__type__69470___24t(V_24Y)
<=> t(V_24Y,c_24__type__69470) ) ).
fof('$tdef_$_type_69350',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__69350___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__69350___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2484',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2484___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2484___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_217',axiom,
! [V_24Y] :
( c_24__type__217___24t(V_24Y)
<=> t(V_24Y,c_24__type__217) ) ).
fof('$tdef_Topology.TopologicalSpaces.point_set',axiom,
! [V_24X1,V_24Y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V_24X1,V_24Y)
<=> t(V_24Y,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V_24X1)) ) ).
fof('$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_9981',axiom,
! [V_24Y] :
( c_24__type__9981___24t(V_24Y)
<=> t(V_24Y,c_24__type__9981) ) ).
fof('$tdef_$_type_6058',axiom,
! [V_24Y] :
( c_24__type__6058___24t(V_24Y)
<=> t(V_24Y,c_24__type__6058) ) ).
fof('$tdef_$_type_500',axiom,
! [V_24Y] :
( c_24__type__500___24t(V_24Y)
<=> t(V_24Y,c_24__type__500) ) ).
fof('$tdef_$_type_7848',axiom,
! [V_24Y] :
( c_24__type__7848___24t(V_24Y)
<=> t(V_24Y,c_24__type__7848) ) ).
fof('$tdef_$_type_26572',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__26572___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__26572___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_2824',axiom,
! [V_24Y] :
( c_24__type__2824___24t(V_24Y)
<=> t(V_24Y,c_24__type__2824) ) ).
fof('$tdef_$_type_2526',axiom,
! [V_24Y] :
( c_24__type__2526___24t(V_24Y)
<=> t(V_24Y,c_24__type__2526) ) ).
fof('$tdef_$_type_79231',axiom,
! [V_24X1,V_24Y] :
( c_24__type__79231___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__79231___24a1(V_24X1)) ) ).
fof('$tdef_$_type_64738',axiom,
! [V_24Y] :
( c_24__type__64738___24t(V_24Y)
<=> t(V_24Y,c_24__type__64738) ) ).
fof('$tdef_$_type_5193',axiom,
! [V_24Y] :
( c_24__type__5193___24t(V_24Y)
<=> t(V_24Y,c_24__type__5193) ) ).
fof('$tdef_$_type_26765',axiom,
! [V_24Y] :
( c_24__type__26765___24t(V_24Y)
<=> t(V_24Y,c_24__type__26765) ) ).
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_$_type_8172',axiom,
! [V_24Y] :
( c_24__type__8172___24t(V_24Y)
<=> t(V_24Y,c_24__type__8172) ) ).
fof('$tdef_Coq.Reals.Rlimit.Base',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRlimit_2eBase___24a1(V_24X1)) ) ).
fof('$tdef_$_type_10085',axiom,
! [V_24Y] :
( c_24__type__10085___24t(V_24Y)
<=> t(V_24Y,c_24__type__10085) ) ).
fof('$tdef_Coq.Reals.RList.Rlist',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRList_2eRlist___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRList_2eRlist) ) ).
fof('$tdef_$_type_6489',axiom,
! [V_24Y] :
( c_24__type__6489___24t(V_24Y)
<=> t(V_24Y,c_24__type__6489) ) ).
fof('$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_9866',axiom,
! [V_24Y] :
( c_24__type__9866___24t(V_24Y)
<=> t(V_24Y,c_24__type__9866) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_7308',axiom,
! [V_24Y] :
( c_24__type__7308___24t(V_24Y)
<=> t(V_24Y,c_24__type__7308) ) ).
fof('$tdef_$_type_10121',axiom,
! [V_24Y] :
( c_24__type__10121___24t(V_24Y)
<=> t(V_24Y,c_24__type__10121) ) ).
fof('$tdef_$_type_9546',axiom,
! [V_24Y] :
( c_24__type__9546___24t(V_24Y)
<=> t(V_24Y,c_24__type__9546) ) ).
fof('$tdef_$_type_4690',axiom,
! [V_24Y] :
( c_24__type__4690___24t(V_24Y)
<=> t(V_24Y,c_24__type__4690) ) ).
fof('$tdef_$_type_27271',axiom,
! [V_24Y] :
( c_24__type__27271___24t(V_24Y)
<=> t(V_24Y,c_24__type__27271) ) ).
fof('$tdef_$_type_7096',axiom,
! [V_24Y] :
( c_24__type__7096___24t(V_24Y)
<=> t(V_24Y,c_24__type__7096) ) ).
fof('$tdef_$_type_26698',axiom,
! [V_24Y] :
( c_24__type__26698___24t(V_24Y)
<=> t(V_24Y,c_24__type__26698) ) ).
fof('$tdef_Coq.Reals.RiemannInt_SF.is_subdivision',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRiemannInt__SF_2eis__subdivision___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_5694',axiom,
! [V_24Y] :
( c_24__type__5694___24t(V_24Y)
<=> t(V_24Y,c_24__type__5694) ) ).
fof('$tdef_$_type_489',axiom,
! [V_24Y] :
( c_24__type__489___24t(V_24Y)
<=> t(V_24Y,c_24__type__489) ) ).
fof('$tdef_$_type_10053',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10053___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10053___24a1(V_24X1)) ) ).
fof('$tdef_$_type_948',axiom,
! [V_24Y] :
( c_24__type__948___24t(V_24Y)
<=> t(V_24Y,c_24__type__948) ) ).
fof('$tdef_$_type_69584',axiom,
! [V_24Y] :
( c_24__type__69584___24t(V_24Y)
<=> t(V_24Y,c_24__type__69584) ) ).
fof('$tdef_$_type_15047',axiom,
! [V_24Y] :
( c_24__type__15047___24t(V_24Y)
<=> t(V_24Y,c_24__type__15047) ) ).
fof('$tdef_$_type_330',axiom,
! [V_24Y] :
( c_24__type__330___24t(V_24Y)
<=> t(V_24Y,c_24__type__330) ) ).
fof('$tdef_$_type_6052',axiom,
! [V_24Y] :
( c_24__type__6052___24t(V_24Y)
<=> t(V_24Y,c_24__type__6052) ) ).
fof('$tdef_$_type_4472',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4472___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4472___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5117',axiom,
! [V_24Y] :
( c_24__type__5117___24t(V_24Y)
<=> t(V_24Y,c_24__type__5117) ) ).
fof('$tdef_$_type_4699',axiom,
! [V_24Y] :
( c_24__type__4699___24t(V_24Y)
<=> t(V_24Y,c_24__type__4699) ) ).
fof('$tdef_$_type_2501',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2501___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2501___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1652',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1652___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1652___24a1(V_24X1)) ) ).
fof('$tdef_$_type_5864',axiom,
! [V_24Y] :
( c_24__type__5864___24t(V_24Y)
<=> t(V_24Y,c_24__type__5864) ) ).
fof('$tdef_$_type_9322',axiom,
! [V_24Y] :
( c_24__type__9322___24t(V_24Y)
<=> t(V_24Y,c_24__type__9322) ) ).
fof('$tdef_$_type_69554',axiom,
! [V_24Y] :
( c_24__type__69554___24t(V_24Y)
<=> t(V_24Y,c_24__type__69554) ) ).
fof('$tdef_$_type_6750',axiom,
! [V_24Y] :
( c_24__type__6750___24t(V_24Y)
<=> t(V_24Y,c_24__type__6750) ) ).
fof('$tdef_$_type_6667',axiom,
! [V_24Y] :
( c_24__type__6667___24t(V_24Y)
<=> t(V_24Y,c_24__type__6667) ) ).
fof('$tdef_$_type_5851',axiom,
! [V_24Y] :
( c_24__type__5851___24t(V_24Y)
<=> t(V_24Y,c_24__type__5851) ) ).
fof('$tdef_$_type_15255',axiom,
! [V_24Y] :
( c_24__type__15255___24t(V_24Y)
<=> t(V_24Y,c_24__type__15255) ) ).
fof('$tdef_$_type_15140',axiom,
! [V_24Y] :
( c_24__type__15140___24t(V_24Y)
<=> t(V_24Y,c_24__type__15140) ) ).
fof('$tdef_$_type_14640',axiom,
! [V_24Y] :
( c_24__type__14640___24t(V_24Y)
<=> t(V_24Y,c_24__type__14640) ) ).
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_$_type_6652',axiom,
! [V_24Y] :
( c_24__type__6652___24t(V_24Y)
<=> t(V_24Y,c_24__type__6652) ) ).
fof('$tdef_$_type_62517',axiom,
! [V_24Y] :
( c_24__type__62517___24t(V_24Y)
<=> t(V_24Y,c_24__type__62517) ) ).
fof('$tdef_$_type_1189',axiom,
! [V_24Y] :
( c_24__type__1189___24t(V_24Y)
<=> t(V_24Y,c_24__type__1189) ) ).
fof('$tdef_$_type_15272',axiom,
! [V_24Y] :
( c_24__type__15272___24t(V_24Y)
<=> t(V_24Y,c_24__type__15272) ) ).
fof('$tdef_$_type_61720',axiom,
! [V_24Y] :
( c_24__type__61720___24t(V_24Y)
<=> t(V_24Y,c_24__type__61720) ) ).
fof('$tdef_$_type_68257',axiom,
! [V_24Y] :
( c_24__type__68257___24t(V_24Y)
<=> t(V_24Y,c_24__type__68257) ) ).
fof('$tdef_$_type_6513',axiom,
! [V_24Y] :
( c_24__type__6513___24t(V_24Y)
<=> t(V_24Y,c_24__type__6513) ) ).
fof('$tdef_$_type_1661',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1661___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1661___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4692',axiom,
! [V_24Y] :
( c_24__type__4692___24t(V_24Y)
<=> t(V_24Y,c_24__type__4692) ) ).
fof('$tdef_$_type_7324',axiom,
! [V_24Y] :
( c_24__type__7324___24t(V_24Y)
<=> t(V_24Y,c_24__type__7324) ) ).
fof('$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_63133',axiom,
! [V_24Y] :
( c_24__type__63133___24t(V_24Y)
<=> t(V_24Y,c_24__type__63133) ) ).
fof('$tdef_$_type_795',axiom,
! [V_24Y] :
( c_24__type__795___24t(V_24Y)
<=> t(V_24Y,c_24__type__795) ) ).
fof('$tdef_$_type_2067',axiom,
! [V_24Y] :
( c_24__type__2067___24t(V_24Y)
<=> t(V_24Y,c_24__type__2067) ) ).
fof('$tdef_$_type_1111',axiom,
! [V_24Y] :
( c_24__type__1111___24t(V_24Y)
<=> t(V_24Y,c_24__type__1111) ) ).
fof('$tdef_$_type_10087',axiom,
! [V_24Y] :
( c_24__type__10087___24t(V_24Y)
<=> t(V_24Y,c_24__type__10087) ) ).
fof('$tdef_$_type_61733',axiom,
! [V_24Y] :
( c_24__type__61733___24t(V_24Y)
<=> t(V_24Y,c_24__type__61733) ) ).
fof('$tdef_$_type_78868',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__78868___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__78868___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_61844',axiom,
! [V_24Y] :
( c_24__type__61844___24t(V_24Y)
<=> t(V_24Y,c_24__type__61844) ) ).
fof('$tdef_$_type_2621',axiom,
! [V_24Y] :
( c_24__type__2621___24t(V_24Y)
<=> t(V_24Y,c_24__type__2621) ) ).
fof('$tdef_$_type_10114',axiom,
! [V_24Y] :
( c_24__type__10114___24t(V_24Y)
<=> t(V_24Y,c_24__type__10114) ) ).
fof('$tdef_$_type_1197',axiom,
! [V_24Y] :
( c_24__type__1197___24t(V_24Y)
<=> t(V_24Y,c_24__type__1197) ) ).
fof('$tdef_$_type_8092',axiom,
! [V_24Y] :
( c_24__type__8092___24t(V_24Y)
<=> t(V_24Y,c_24__type__8092) ) ).
fof('$tdef_$_type_6857',axiom,
! [V_24Y] :
( c_24__type__6857___24t(V_24Y)
<=> t(V_24Y,c_24__type__6857) ) ).
fof('$tdef_$_type_3437',axiom,
! [V_24Y] :
( c_24__type__3437___24t(V_24Y)
<=> t(V_24Y,c_24__type__3437) ) ).
fof('$tdef_$_type_4385',axiom,
! [V_24Y] :
( c_24__type__4385___24t(V_24Y)
<=> t(V_24Y,c_24__type__4385) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_10126',axiom,
! [V_24Y] :
( c_24__type__10126___24t(V_24Y)
<=> t(V_24Y,c_24__type__10126) ) ).
fof('$tdef_$_type_26580',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__26580___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__26580___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_4263',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4263___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4263___24a1(V_24X1)) ) ).
fof('$tdef_$_type_9999',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9999___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9999___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_26732',axiom,
! [V_24Y] :
( c_24__type__26732___24t(V_24Y)
<=> t(V_24Y,c_24__type__26732) ) ).
fof('$tdef_$_type_15012',axiom,
! [V_24Y] :
( c_24__type__15012___24t(V_24Y)
<=> t(V_24Y,c_24__type__15012) ) ).
fof('$tdef_$_type_9437',axiom,
! [V_24Y] :
( c_24__type__9437___24t(V_24Y)
<=> t(V_24Y,c_24__type__9437) ) ).
fof('$tdef_Coq.Reals.RiemannInt_SF.IsStepFun',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_5115',axiom,
! [V_24Y] :
( c_24__type__5115___24t(V_24Y)
<=> t(V_24Y,c_24__type__5115) ) ).
fof('$tdef_$_type_10022',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10022___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10022___24a1(V_24X1)) ) ).
fof('$tdef_$_type_64905',axiom,
! [V_24Y] :
( c_24__type__64905___24t(V_24Y)
<=> t(V_24Y,c_24__type__64905) ) ).
fof('$tdef_$_type_14744',axiom,
! [V_24Y] :
( c_24__type__14744___24t(V_24Y)
<=> t(V_24Y,c_24__type__14744) ) ).
fof('$tdef_$_type_78754',axiom,
! [V_24Y] :
( c_24__type__78754___24t(V_24Y)
<=> t(V_24Y,c_24__type__78754) ) ).
fof('$tdef_$_type_7896',axiom,
! [V_24Y] :
( c_24__type__7896___24t(V_24Y)
<=> t(V_24Y,c_24__type__7896) ) ).
fof('$tdef_$_type_3997',axiom,
! [V_24Y] :
( c_24__type__3997___24t(V_24Y)
<=> t(V_24Y,c_24__type__3997) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_70079',axiom,
! [V_24Y] :
( c_24__type__70079___24t(V_24Y)
<=> t(V_24Y,c_24__type__70079) ) ).
fof('$tdef_$_type_2636',axiom,
! [V_24Y] :
( c_24__type__2636___24t(V_24Y)
<=> t(V_24Y,c_24__type__2636) ) ).
fof('$tdef_$_type_5979',axiom,
! [V_24Y] :
( c_24__type__5979___24t(V_24Y)
<=> t(V_24Y,c_24__type__5979) ) ).
fof('$tdef_$_type_63308',axiom,
! [V_24Y] :
( c_24__type__63308___24t(V_24Y)
<=> t(V_24Y,c_24__type__63308) ) ).
fof('$tdef_$_type_2912',axiom,
! [V_24Y] :
( c_24__type__2912___24t(V_24Y)
<=> t(V_24Y,c_24__type__2912) ) ).
fof('$tdef_$_type_2919',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2919___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2919___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2618',axiom,
! [V_24Y] :
( c_24__type__2618___24t(V_24Y)
<=> t(V_24Y,c_24__type__2618) ) ).
fof('$tdef_$_type_6949',axiom,
! [V_24Y] :
( c_24__type__6949___24t(V_24Y)
<=> t(V_24Y,c_24__type__6949) ) ).
fof('$tdef_$_type_6689',axiom,
! [V_24Y] :
( c_24__type__6689___24t(V_24Y)
<=> t(V_24Y,c_24__type__6689) ) ).
fof('$tdef_$_type_9370',axiom,
! [V_24Y] :
( c_24__type__9370___24t(V_24Y)
<=> t(V_24Y,c_24__type__9370) ) ).
fof('$tdef_$_type_9741',axiom,
! [V_24Y] :
( c_24__type__9741___24t(V_24Y)
<=> t(V_24Y,c_24__type__9741) ) ).
fof('$tdef_$_type_6892',axiom,
! [V_24Y] :
( c_24__type__6892___24t(V_24Y)
<=> t(V_24Y,c_24__type__6892) ) ).
fof('$tdef_$_type_25',axiom,
! [V_24X1,V_24Y] :
( c_24__type__25___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__25___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13083',axiom,
! [V_24Y] :
( c_24__type__13083___24t(V_24Y)
<=> t(V_24Y,c_24__type__13083) ) ).
fof('$tdef_$_type_15306',axiom,
! [V_24Y] :
( c_24__type__15306___24t(V_24Y)
<=> t(V_24Y,c_24__type__15306) ) ).
fof('$tdef_$_type_69692',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__69692___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__69692___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Reals.RiemannInt.Riemann_integrable',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_9957',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__9957___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__9957___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6878',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6878___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6878___24a1(V_24X1)) ) ).
fof('$tdef_$_type_334',axiom,
! [V_24Y] :
( c_24__type__334___24t(V_24Y)
<=> t(V_24Y,c_24__type__334) ) ).
fof('$tdef_$_type_26753',axiom,
! [V_24Y] :
( c_24__type__26753___24t(V_24Y)
<=> t(V_24Y,c_24__type__26753) ) ).
fof('$tdef_$_type_3778',axiom,
! [V_24Y] :
( c_24__type__3778___24t(V_24Y)
<=> t(V_24Y,c_24__type__3778) ) ).
fof('$tdef_$_type_1184',axiom,
! [V_24Y] :
( c_24__type__1184___24t(V_24Y)
<=> t(V_24Y,c_24__type__1184) ) ).
fof('$tdef_$_type_4509',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4509___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4509___24a1(V_24X1)) ) ).
fof('$tdef_$_type_63280',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__63280___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__63280___24a2(V_24X1,V_24X2)) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__x] :
( cTopology_2eNets_2eNet___24t(V0__I,cRTopology_2eRTop,V1__x)
=> ! [V2__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__a)
=> ! [V3__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__b)
=> ( ! [V4__i] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__I,V4__i)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,happ(V1__x,V4__i)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__x,V4__i),V3__b)) ) )
=> ? [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(cRTopology_2eRTop,V5__x0)
& cTopology_2eNets_2enet__cluster__point___24a4(V0__I,cRTopology_2eRTop,V1__x,V5__x0) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------