ITP001 Axioms: ITP133^7.ax
%------------------------------------------------------------------------------
% File : ITP133^7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : HolSmt.ax [Gau19]
% : HL4133^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 433 ( 148 unt; 73 typ; 0 def)
% Number of atoms : 808 ( 284 equ; 196 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 5100 ( 196 ~; 114 |; 32 &;4497 @)
% ( 193 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg;4497 nst)
% Number of types : 6 ( 5 usr)
% Number of type conns : 123 ( 123 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 68 usr; 5 con; 0-6 aty)
% Number of variables : 1123 ( 1 ^1083 !; 1 ?;1123 :)
% ( 38 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
thf(tyop_2Efcp_2Ebit0,type,
tyop_2Efcp_2Ebit0: $tType > $tType ).
thf(tyop_2Efcp_2Ebit1,type,
tyop_2Efcp_2Ebit1: $tType > $tType ).
thf(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: $tType > $tType > $tType ).
thf(tyop_2Einteger_2Eint,type,
tyop_2Einteger_2Eint: $tType ).
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
thf(tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Enum_2E0,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Eprim__rec_2E_3C,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2E_3C_3D,type,
c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Emin_2E_40,type,
c_2Emin_2E_40:
!>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a ) ).
thf(c_2Elist_2EALL__DISTINCT,type,
c_2Elist_2EALL__DISTINCT:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EBIT2,type,
c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2Elist_2ECONS,type,
c_2Elist_2ECONS:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Ebool_2EF,type,
c_2Ebool_2EF: $o ).
thf(c_2Epred__set_2EFINITE,type,
c_2Epred__set_2EFINITE:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Ebool_2EIN,type,
c_2Ebool_2EIN:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).
thf(c_2Elist_2ELIST__TO__SET,type,
c_2Elist_2ELIST__TO__SET:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > A_27a > $o ) ).
thf(c_2Elist_2ENIL,type,
c_2Elist_2ENIL:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist @ A_27a ) ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2Epred__set_2EUNIV,type,
c_2Epred__set_2EUNIV:
!>[A_27a: $tType] : ( A_27a > $o ) ).
thf(c_2Ecombin_2EUPDATE,type,
c_2Ecombin_2EUPDATE:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( A_27a > A_27b ) > A_27a > A_27b ) ).
thf(c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2EHolSmt_2Earray__ext,type,
c_2EHolSmt_2Earray__ext:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( A_27a > A_27b ) > A_27a ) ).
thf(c_2Efcp_2Edimindex,type,
c_2Efcp_2Edimindex:
!>[A_27a: $tType] : ( ( tyop_2Ebool_2Eitself @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Ewords_2Edimword,type,
c_2Ewords_2Edimword:
!>[A_27a: $tType] : ( ( tyop_2Ebool_2Eitself @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Efcp_2Efcp__index,type,
c_2Efcp_2Efcp__index:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) > tyop_2Enum_2Enum > A_27a ) ).
thf(c_2Einteger_2Eint__add,type,
c_2Einteger_2Eint__add: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__ge,type,
c_2Einteger_2Eint__ge: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__gt,type,
c_2Einteger_2Eint__gt: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__le,type,
c_2Einteger_2Eint__le: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__lt,type,
c_2Einteger_2Eint__lt: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__mul,type,
c_2Einteger_2Eint__mul: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__neg,type,
c_2Einteger_2Eint__neg: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__of__num,type,
c_2Einteger_2Eint__of__num: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__sub,type,
c_2Einteger_2Eint__sub: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Ewords_2En2w,type,
c_2Ewords_2En2w:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Erealax_2Ereal__add,type,
c_2Erealax_2Ereal__add: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ereal_2Ereal__ge,type,
c_2Ereal_2Ereal__ge: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).
thf(c_2Ereal_2Ereal__gt,type,
c_2Ereal_2Ereal__gt: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).
thf(c_2Erealax_2Ereal__lt,type,
c_2Erealax_2Ereal__lt: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).
thf(c_2Ereal_2Ereal__lte,type,
c_2Ereal_2Ereal__lte: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).
thf(c_2Erealax_2Ereal__mul,type,
c_2Erealax_2Ereal__mul: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Erealax_2Ereal__neg,type,
c_2Erealax_2Ereal__neg: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ereal_2Ereal__of__num,type,
c_2Ereal_2Ereal__of__num: tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).
thf(c_2Ereal_2Ereal__sub,type,
c_2Ereal_2Ereal__sub: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ewords_2Esw2sw,type,
c_2Ewords_2Esw2sw:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).
thf(c_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself @ A_27a ) ).
thf(c_2Ewords_2Ew2w,type,
c_2Ewords_2Ew2w:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).
thf(c_2Ewords_2Eword__1comp,type,
c_2Ewords_2Eword__1comp:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__add,type,
c_2Ewords_2Eword__add:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__and,type,
c_2Ewords_2Eword__and:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__concat,type,
c_2Ewords_2Eword__concat:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) > ( tyop_2Efcp_2Ecart @ $o @ A_27c ) ) ).
thf(c_2Ewords_2Eword__extract,type,
c_2Ewords_2Eword__extract:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) ) ).
thf(c_2Ewords_2Eword__lo,type,
c_2Ewords_2Eword__lo:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__ls,type,
c_2Ewords_2Eword__ls:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).
thf(c_2Ewords_2Eword__mul,type,
c_2Ewords_2Eword__mul:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2Ewords_2Eword__or,type,
c_2Ewords_2Eword__or:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
thf(c_2EHolSmt_2Exor,type,
c_2EHolSmt_2Exor: $o > $o > $o ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2EHolSmt_2Exor__def,axiom,
! [V0x: $o,V1y: $o] :
( ( c_2EHolSmt_2Exor @ V0x @ V1y )
<=> ( (~) @ ( V0x = V1y ) ) ) ).
thf(thm_2EHolSmt_2Earray__ext__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0A: A_27a > A_27b,V1B: A_27a > A_27b] :
( ( c_2EHolSmt_2Earray__ext @ A_27a @ A_27b @ V0A @ V1B )
= ( c_2Emin_2E_40 @ A_27a
@ ^ [V2i: A_27a] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ A_27b @ ( V0A @ V2i ) @ ( V1B @ V2i ) ) ) ) ) ).
thf(thm_2EHolSmt_2EALL__DISTINCT__NIL,axiom,
! [A_27a: $tType] :
( ( c_2Elist_2EALL__DISTINCT @ A_27a @ ( c_2Elist_2ENIL @ A_27a ) )
= c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2EALL__DISTINCT__CONS,axiom,
! [A_27a: $tType,V0h: A_27a,V1t: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EALL__DISTINCT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V0h @ V1t ) )
<=> ( ( (~) @ ( c_2Ebool_2EIN @ A_27a @ V0h @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1t ) ) )
& ( c_2Elist_2EALL__DISTINCT @ A_27a @ V1t ) ) ) ).
thf(thm_2EHolSmt_2ENOT__MEM__NIL,axiom,
! [A_27a: $tType,V0x: A_27a] :
( ( (~) @ ( c_2Ebool_2EIN @ A_27a @ V0x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
<=> c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2ENOT__MEM__CONS,axiom,
! [A_27a: $tType,V0x: A_27a,V1h: A_27a,V2t: tyop_2Elist_2Elist @ A_27a] :
( ( (~) @ ( c_2Ebool_2EIN @ A_27a @ V0x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V1h @ V2t ) ) ) )
<=> ( ( (~) @ ( V0x = V1h ) )
& ( (~) @ ( c_2Ebool_2EIN @ A_27a @ V0x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V2t ) ) ) ) ) ).
thf(thm_2EHolSmt_2EAND__T,axiom,
! [V0p: $o] :
( ( V0p
& c_2Ebool_2ET )
<=> V0p ) ).
thf(thm_2EHolSmt_2ET__AND,axiom,
! [V0p: $o,V1q: $o] :
( ( ( c_2Ebool_2ET
& V0p )
<=> ( c_2Ebool_2ET
& V1q ) )
=> ( V0p = V1q ) ) ).
thf(thm_2EHolSmt_2EF__OR,axiom,
! [V0p: $o,V1q: $o] :
( ( ( c_2Ebool_2EF
| V0p )
<=> ( c_2Ebool_2EF
| V1q ) )
=> ( V0p = V1q ) ) ).
thf(thm_2EHolSmt_2ECONJ__CONG,axiom,
! [V0p: $o,V1q: $o,V2r: $o,V3s: $o] :
( ( V0p = V1q )
=> ( ( V2r = V3s )
=> ( ( V0p
& V2r )
<=> ( V1q
& V3s ) ) ) ) ).
thf(thm_2EHolSmt_2ENOT__NOT__ELIM,axiom,
! [V0p: $o] :
( ( (~) @ ( (~) @ V0p ) )
=> V0p ) ).
thf(thm_2EHolSmt_2ENOT__FALSE,axiom,
! [V0p: $o] :
( V0p
=> ( ( (~) @ V0p )
=> c_2Ebool_2EF ) ) ).
thf(thm_2EHolSmt_2ENNF__CONJ,axiom,
! [V0p: $o,V1q: $o,V2r: $o,V3s: $o] :
( ( ( (~) @ V0p )
<=> V2r )
=> ( ( ( (~) @ V1q )
<=> V3s )
=> ( ( (~)
@ ( V0p
& V1q ) )
<=> ( V2r
| V3s ) ) ) ) ).
thf(thm_2EHolSmt_2ENNF__DISJ,axiom,
! [V0p: $o,V1q: $o,V2r: $o,V3s: $o] :
( ( ( (~) @ V0p )
<=> V2r )
=> ( ( ( (~) @ V1q )
<=> V3s )
=> ( ( (~)
@ ( V0p
| V1q ) )
<=> ( V2r
& V3s ) ) ) ) ).
thf(thm_2EHolSmt_2ENNF__NOT__NOT,axiom,
! [V0p: $o,V1q: $o] :
( ( V0p = V1q )
=> ( ( (~) @ ( (~) @ V0p ) )
<=> V1q ) ) ).
thf(thm_2EHolSmt_2ENEG__IFF__1__1,axiom,
! [V0p: $o,V1q: $o] :
( ( V1q = V0p )
=> ( (~)
@ ( V0p
<=> ( (~) @ V1q ) ) ) ) ).
thf(thm_2EHolSmt_2ENEG__IFF__1__2,axiom,
! [V0p: $o,V1q: $o] :
( ( (~)
@ ( V0p
<=> ( (~) @ V1q ) ) )
=> ( V1q = V0p ) ) ).
thf(thm_2EHolSmt_2ENEG__IFF__2__1,axiom,
! [V0p: $o,V1q: $o] :
( ( V0p
<=> ( (~) @ V1q ) )
=> ( (~) @ ( V0p = V1q ) ) ) ).
thf(thm_2EHolSmt_2ENEG__IFF__2__2,axiom,
! [V0p: $o,V1q: $o] :
( ( (~) @ ( V0p = V1q ) )
=> ( V0p
<=> ( (~) @ V1q ) ) ) ).
thf(thm_2EHolSmt_2EDISJ__ELIM__1,axiom,
! [V0p: $o,V1q: $o,V2r: $o] :
( ( ( V0p
| V1q )
=> V2r )
=> ( V0p
=> V2r ) ) ).
thf(thm_2EHolSmt_2EDISJ__ELIM__2,axiom,
! [V0p: $o,V1q: $o,V2r: $o] :
( ( ( V0p
| V1q )
=> V2r )
=> ( V1q
=> V2r ) ) ).
thf(thm_2EHolSmt_2EIMP__DISJ__1,axiom,
! [V0p: $o,V1q: $o] :
( ( V0p
=> V1q )
=> ( ( (~) @ V0p )
| V1q ) ) ).
thf(thm_2EHolSmt_2EIMP__DISJ__2,axiom,
! [V0p: $o,V1q: $o] :
( ( ( (~) @ V0p )
=> V1q )
=> ( V0p
| V1q ) ) ).
thf(thm_2EHolSmt_2EIMP__FALSE,axiom,
! [V0p: $o] :
( ( ( (~) @ V0p )
=> c_2Ebool_2EF )
=> V0p ) ).
thf(thm_2EHolSmt_2EAND__IMP__INTRO__SYM,axiom,
! [V0p: $o,V1q: $o,V2r: $o] :
( ( ( V0p
& V1q )
=> V2r )
<=> ( V0p
=> ( V1q
=> V2r ) ) ) ).
thf(thm_2EHolSmt_2EVALID__IFF__TRUE,axiom,
! [V0p: $o] :
( V0p
=> ( V0p = c_2Ebool_2ET ) ) ).
thf(thm_2EHolSmt_2Ed001,axiom,
! [V0q: $o,V1p: $o] :
( ( (~) @ ( V1p = V0q ) )
| ( (~) @ V1p )
| V0q ) ).
thf(thm_2EHolSmt_2Ed002,axiom,
! [V0q: $o,V1p: $o] :
( ( (~) @ ( V1p = V0q ) )
| V1p
| ( (~) @ V0q ) ) ).
thf(thm_2EHolSmt_2Ed003,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
<=> ( (~) @ V0q ) )
| ( (~) @ V1p )
| V0q ) ).
thf(thm_2EHolSmt_2Ed004,axiom,
! [V0q: $o,V1p: $o] :
( ( ( (~) @ V1p )
<=> V0q )
| V1p
| ( (~) @ V0q ) ) ).
thf(thm_2EHolSmt_2Ed005,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p = V0q )
| ( (~) @ V1p )
| ( (~) @ V0q ) ) ).
thf(thm_2EHolSmt_2Ed006,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p = V0q )
| V1p
| V0q ) ).
thf(thm_2EHolSmt_2Ed007,axiom,
! [V0q: $o,V1p: $o] :
( ( (~)
@ ( ( (~) @ V1p )
<=> V0q ) )
| V1p
| V0q ) ).
thf(thm_2EHolSmt_2Ed008,axiom,
! [V0q: $o,V1p: $o] :
( ( (~)
@ ( V1p
<=> ( (~) @ V0q ) ) )
| V1p
| V0q ) ).
thf(thm_2EHolSmt_2Ed009,axiom,
! [V0q: $o,V1p: $o] :
( ( (~) @ V1p )
| V0q
| ( (~) @ ( V1p = V0q ) ) ) ).
thf(thm_2EHolSmt_2Ed010,axiom,
! [V0q: $o,V1p: $o] :
( V1p
| ( (~) @ V0q )
| ( (~) @ ( V1p = V0q ) ) ) ).
thf(thm_2EHolSmt_2Ed011,axiom,
! [V0q: $o,V1p: $o] :
( V1p
| V0q
| ( (~)
@ ( ( (~) @ V1p )
<=> V0q ) ) ) ).
thf(thm_2EHolSmt_2Ed012,axiom,
! [V0q: $o,V1p: $o] :
( V1p
| V0q
| ( (~)
@ ( V1p
<=> ( (~) @ V0q ) ) ) ) ).
thf(thm_2EHolSmt_2Ed013,axiom,
! [V0q: $o,V1p: $o] :
( ( ( (~) @ V1p )
& ( (~) @ V0q ) )
| V1p
| V0q ) ).
thf(thm_2EHolSmt_2Ed014,axiom,
! [V0q: $o,V1p: $o] :
( ( ( (~) @ V1p )
& V0q )
| V1p
| ( (~) @ V0q ) ) ).
thf(thm_2EHolSmt_2Ed015,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
& ( (~) @ V0q ) )
| ( (~) @ V1p )
| V0q ) ).
thf(thm_2EHolSmt_2Ed016,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
& V0q )
| ( (~) @ V1p )
| ( (~) @ V0q ) ) ).
thf(thm_2EHolSmt_2Ed017,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2p: $o] :
( V2p
| ( V0y
= ( c_2Ebool_2ECOND @ A_27a @ V2p @ V1x @ V0y ) ) ) ).
thf(thm_2EHolSmt_2Ed018,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2p: $o] :
( ( (~) @ V2p )
| ( V1x
= ( c_2Ebool_2ECOND @ A_27a @ V2p @ V1x @ V0y ) ) ) ).
thf(thm_2EHolSmt_2Ed019,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2p: $o] :
( V2p
| ( ( c_2Ebool_2ECOND @ A_27a @ V2p @ V1x @ V0y )
= V0y ) ) ).
thf(thm_2EHolSmt_2Ed020,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2p: $o] :
( ( (~) @ V2p )
| ( ( c_2Ebool_2ECOND @ A_27a @ V2p @ V1x @ V0y )
= V1x ) ) ).
thf(thm_2EHolSmt_2Ed021,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( V2p
| V1q
| ( (~) @ ( c_2Ebool_2ECOND @ $o @ V2p @ V0r @ V1q ) ) ) ).
thf(thm_2EHolSmt_2Ed022,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( (~) @ V2p )
| V1q
| ( (~) @ ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ V0r ) ) ) ).
thf(thm_2EHolSmt_2Ed023,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ V0r )
| ( (~) @ V2p )
| ( (~) @ V1q ) ) ).
thf(thm_2EHolSmt_2Ed024,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ V0r )
| V2p
| ( (~) @ V0r ) ) ).
thf(thm_2EHolSmt_2Ed025,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V2p @ ( c_2Ebool_2E_7E @ V1q ) @ V0r )
| ( (~) @ V2p )
| V1q ) ).
thf(thm_2EHolSmt_2Ed026,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ ( c_2Ebool_2E_7E @ V0r ) )
| V2p
| V0r ) ).
thf(thm_2EHolSmt_2Ed027,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( (~) @ ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ V0r ) )
| ( (~) @ V2p )
| V1q ) ).
thf(thm_2EHolSmt_2Ed028,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( (~) @ ( c_2Ebool_2ECOND @ $o @ V2p @ V1q @ V0r ) )
| V2p
| V0r ) ).
thf(thm_2EHolSmt_2Er001,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a] :
( ( V1x = V0y )
<=> ( V0y = V1x ) ) ).
thf(thm_2EHolSmt_2Er002,axiom,
! [A_27a: $tType,V0x: A_27a] :
( ( V0x = V0x )
<=> c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er003,axiom,
! [V0p: $o] :
( ( V0p = c_2Ebool_2ET )
<=> V0p ) ).
thf(thm_2EHolSmt_2Er004,axiom,
! [V0p: $o] :
( ( c_2Ebool_2ET = V0p )
<=> V0p ) ).
thf(thm_2EHolSmt_2Er005,axiom,
! [V0p: $o] :
( ( V0p = c_2Ebool_2EF )
<=> ( (~) @ V0p ) ) ).
thf(thm_2EHolSmt_2Er006,axiom,
! [V0p: $o] :
( ( c_2Ebool_2EF = V0p )
<=> ( (~) @ V0p ) ) ).
thf(thm_2EHolSmt_2Er007,axiom,
! [V0q: $o,V1p: $o] :
( ( ( (~) @ V1p )
<=> ( (~) @ V0q ) )
<=> ( V1p = V0q ) ) ).
thf(thm_2EHolSmt_2Er008,axiom,
! [V0q: $o,V1p: $o] :
( ( (~)
@ ( V1p
<=> ( (~) @ V0q ) ) )
<=> ( V1p = V0q ) ) ).
thf(thm_2EHolSmt_2Er009,axiom,
! [V0q: $o,V1p: $o] :
( ( (~)
@ ( ( (~) @ V1p )
<=> V0q ) )
<=> ( V1p = V0q ) ) ).
thf(thm_2EHolSmt_2Er010,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a] :
( ( c_2Ebool_2ECOND @ A_27a @ c_2Ebool_2ET @ V1x @ V0y )
= V1x ) ).
thf(thm_2EHolSmt_2Er011,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a] :
( ( c_2Ebool_2ECOND @ A_27a @ c_2Ebool_2EF @ V1x @ V0y )
= V0y ) ).
thf(thm_2EHolSmt_2Er012,axiom,
! [V0q: $o,V1p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V1p @ V0q @ c_2Ebool_2ET )
<=> ( ( (~) @ V1p )
| V0q ) ) ).
thf(thm_2EHolSmt_2Er013,axiom,
! [V0q: $o,V1p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V1p @ V0q @ c_2Ebool_2ET )
<=> ( V0q
| ( (~) @ V1p ) ) ) ).
thf(thm_2EHolSmt_2Er014,axiom,
! [V0q: $o,V1p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V1p @ V0q @ ( c_2Ebool_2E_7E @ V0q ) )
<=> ( V1p = V0q ) ) ).
thf(thm_2EHolSmt_2Er015,axiom,
! [V0q: $o,V1p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V1p @ V0q @ ( c_2Ebool_2E_7E @ V0q ) )
<=> ( V0q = V1p ) ) ).
thf(thm_2EHolSmt_2Er016,axiom,
! [V0q: $o,V1p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V1p @ ( c_2Ebool_2E_7E @ V0q ) @ V0q )
<=> ( V1p
<=> ( (~) @ V0q ) ) ) ).
thf(thm_2EHolSmt_2Er017,axiom,
! [V0q: $o,V1p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V1p @ ( c_2Ebool_2E_7E @ V0q ) @ V0q )
<=> ( ( (~) @ V0q )
<=> V1p ) ) ).
thf(thm_2EHolSmt_2Er018,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2p: $o] :
( ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_7E @ V2p ) @ V1x @ V0y )
= ( c_2Ebool_2ECOND @ A_27a @ V2p @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er019,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
( ( c_2Ebool_2ECOND @ A_27a @ V3p @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) @ V1x )
= ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_2F_5C @ V3p @ ( c_2Ebool_2E_7E @ V2q ) ) @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er020,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
( ( c_2Ebool_2ECOND @ A_27a @ V3p @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) @ V1x )
= ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ V2q ) @ V3p ) @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er021,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
( ( c_2Ebool_2ECOND @ A_27a @ V3p @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) @ V0y )
= ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_2F_5C @ V3p @ V2q ) @ V1x @ V0y ) ) ).
thf(thm_2EHolSmt_2Er022,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
( ( c_2Ebool_2ECOND @ A_27a @ V3p @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) @ V0y )
= ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_2F_5C @ V2q @ V3p ) @ V1x @ V0y ) ) ).
thf(thm_2EHolSmt_2Er023,axiom,
! [A_27a: $tType,V0z: A_27a,V1y: A_27a,V2x: A_27a,V3p: $o] :
( ( c_2Ebool_2ECOND @ A_27a @ V3p @ V2x @ ( c_2Ebool_2ECOND @ A_27a @ V3p @ V1y @ V0z ) )
= ( c_2Ebool_2ECOND @ A_27a @ V3p @ V2x @ V0z ) ) ).
thf(thm_2EHolSmt_2Er024,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
( ( c_2Ebool_2ECOND @ A_27a @ V3p @ V1x @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) )
= ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_5C_2F @ V3p @ V2q ) @ V1x @ V0y ) ) ).
thf(thm_2EHolSmt_2Er025,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2q: $o,V3p: $o] :
( ( c_2Ebool_2ECOND @ A_27a @ V3p @ V1x @ ( c_2Ebool_2ECOND @ A_27a @ V2q @ V1x @ V0y ) )
= ( c_2Ebool_2ECOND @ A_27a @ ( c_2Ebool_2E_5C_2F @ V2q @ V3p ) @ V1x @ V0y ) ) ).
thf(thm_2EHolSmt_2Er026,axiom,
! [A_27a: $tType,V0z: A_27a,V1y: A_27a,V2x: A_27a,V3p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V3p @ ( c_2Emin_2E_3D @ A_27a @ V2x @ V1y ) @ ( c_2Emin_2E_3D @ A_27a @ V2x @ V0z ) )
<=> ( V2x
= ( c_2Ebool_2ECOND @ A_27a @ V3p @ V1y @ V0z ) ) ) ).
thf(thm_2EHolSmt_2Er027,axiom,
! [A_27a: $tType,V0z: A_27a,V1y: A_27a,V2x: A_27a,V3p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V3p @ ( c_2Emin_2E_3D @ A_27a @ V2x @ V1y ) @ ( c_2Emin_2E_3D @ A_27a @ V1y @ V0z ) )
<=> ( V1y
= ( c_2Ebool_2ECOND @ A_27a @ V3p @ V2x @ V0z ) ) ) ).
thf(thm_2EHolSmt_2Er028,axiom,
! [A_27a: $tType,V0z: A_27a,V1y: A_27a,V2x: A_27a,V3p: $o] :
( ( c_2Ebool_2ECOND @ $o @ V3p @ ( c_2Emin_2E_3D @ A_27a @ V2x @ V1y ) @ ( c_2Emin_2E_3D @ A_27a @ V0z @ V1y ) )
<=> ( V1y
= ( c_2Ebool_2ECOND @ A_27a @ V3p @ V2x @ V0z ) ) ) ).
thf(thm_2EHolSmt_2Er029,axiom,
! [V0q: $o,V1p: $o] :
( ( ( (~) @ V1p )
=> V0q )
<=> ( V1p
| V0q ) ) ).
thf(thm_2EHolSmt_2Er030,axiom,
! [V0q: $o,V1p: $o] :
( ( ( (~) @ V1p )
=> V0q )
<=> ( V0q
| V1p ) ) ).
thf(thm_2EHolSmt_2Er031,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
=> V0q )
<=> ( ( (~) @ V1p )
| V0q ) ) ).
thf(thm_2EHolSmt_2Er032,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
=> V0q )
<=> ( V0q
| ( (~) @ V1p ) ) ) ).
thf(thm_2EHolSmt_2Er033,axiom,
! [V0p: $o] :
( ( c_2Ebool_2ET
=> V0p )
<=> V0p ) ).
thf(thm_2EHolSmt_2Er034,axiom,
! [V0p: $o] :
( ( V0p
=> c_2Ebool_2ET )
<=> c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er035,axiom,
! [V0p: $o] :
( ( c_2Ebool_2EF
=> V0p )
<=> c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er036,axiom,
! [V0p: $o] :
( ( V0p
=> V0p )
<=> c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er037,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( ( V2p = V1q )
=> V0r )
<=> ( V0r
| ( V1q
<=> ( (~) @ V2p ) ) ) ) ).
thf(thm_2EHolSmt_2Er038,axiom,
( ( (~) @ c_2Ebool_2ET )
<=> c_2Ebool_2EF ) ).
thf(thm_2EHolSmt_2Er039,axiom,
( ( (~) @ c_2Ebool_2EF )
<=> c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er040,axiom,
! [V0p: $o] :
( ( (~) @ ( (~) @ V0p ) )
<=> V0p ) ).
thf(thm_2EHolSmt_2Er041,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
| V0q )
<=> ( V0q
| V1p ) ) ).
thf(thm_2EHolSmt_2Er042,axiom,
! [V0p: $o] :
( ( V0p
| c_2Ebool_2ET )
<=> c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er043,axiom,
! [V0p: $o] :
( ( V0p
| ( (~) @ V0p ) )
<=> c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er044,axiom,
! [V0p: $o] :
( ( ( (~) @ V0p )
| V0p )
<=> c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er045,axiom,
! [V0p: $o] :
( ( c_2Ebool_2ET
| V0p )
<=> c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er046,axiom,
! [V0p: $o] :
( ( V0p
| c_2Ebool_2EF )
<=> V0p ) ).
thf(thm_2EHolSmt_2Er047,axiom,
! [V0p: $o] :
( ( c_2Ebool_2EF
| V0p )
<=> V0p ) ).
thf(thm_2EHolSmt_2Er048,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
& V0q )
<=> ( V0q
& V1p ) ) ).
thf(thm_2EHolSmt_2Er049,axiom,
! [V0p: $o] :
( ( V0p
& c_2Ebool_2ET )
<=> V0p ) ).
thf(thm_2EHolSmt_2Er050,axiom,
! [V0p: $o] :
( ( c_2Ebool_2ET
& V0p )
<=> V0p ) ).
thf(thm_2EHolSmt_2Er051,axiom,
! [V0p: $o] :
( ( V0p
& c_2Ebool_2EF )
<=> c_2Ebool_2EF ) ).
thf(thm_2EHolSmt_2Er052,axiom,
! [V0p: $o] :
( ( c_2Ebool_2EF
& V0p )
<=> c_2Ebool_2EF ) ).
thf(thm_2EHolSmt_2Er053,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
& V0q )
<=> ( (~)
@ ( ( (~) @ V1p )
| ( (~) @ V0q ) ) ) ) ).
thf(thm_2EHolSmt_2Er054,axiom,
! [V0q: $o,V1p: $o] :
( ( ( (~) @ V1p )
& V0q )
<=> ( (~)
@ ( V1p
| ( (~) @ V0q ) ) ) ) ).
thf(thm_2EHolSmt_2Er055,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
& ( (~) @ V0q ) )
<=> ( (~)
@ ( ( (~) @ V1p )
| V0q ) ) ) ).
thf(thm_2EHolSmt_2Er056,axiom,
! [V0q: $o,V1p: $o] :
( ( ( (~) @ V1p )
& ( (~) @ V0q ) )
<=> ( (~)
@ ( V1p
| V0q ) ) ) ).
thf(thm_2EHolSmt_2Er057,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
& V0q )
<=> ( (~)
@ ( ( (~) @ V0q )
| ( (~) @ V1p ) ) ) ) ).
thf(thm_2EHolSmt_2Er058,axiom,
! [V0q: $o,V1p: $o] :
( ( ( (~) @ V1p )
& V0q )
<=> ( (~)
@ ( ( (~) @ V0q )
| V1p ) ) ) ).
thf(thm_2EHolSmt_2Er059,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
& ( (~) @ V0q ) )
<=> ( (~)
@ ( V0q
| ( (~) @ V1p ) ) ) ) ).
thf(thm_2EHolSmt_2Er060,axiom,
! [V0q: $o,V1p: $o] :
( ( ( (~) @ V1p )
& ( (~) @ V0q ) )
<=> ( (~)
@ ( V0q
| V1p ) ) ) ).
thf(thm_2EHolSmt_2Er061,axiom,
! [A_27a: $tType,A_27b: $tType,V0x: A_27a,V1f: A_27a > A_27b] :
( ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b @ V0x @ ( V1f @ V0x ) @ V1f )
= V1f ) ).
thf(thm_2EHolSmt_2Er062,axiom,
! [A_27a: $tType,V0x: A_27a] :
( ( c_2Elist_2EALL__DISTINCT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V0x @ ( c_2Elist_2ECONS @ A_27a @ V0x @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
= c_2Ebool_2EF ) ).
thf(thm_2EHolSmt_2Er063,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a] :
( ( c_2Elist_2EALL__DISTINCT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V1x @ ( c_2Elist_2ECONS @ A_27a @ V0y @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
<=> ( (~) @ ( V1x = V0y ) ) ) ).
thf(thm_2EHolSmt_2Er064,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a] :
( ( c_2Elist_2EALL__DISTINCT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V1x @ ( c_2Elist_2ECONS @ A_27a @ V0y @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
<=> ( (~) @ ( V0y = V1x ) ) ) ).
thf(thm_2EHolSmt_2Er065,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( V1x = V0y )
<=> ( ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er066,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( V2x
= ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
<=> ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) )
= V1y ) ) ).
thf(thm_2EHolSmt_2Er067,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( V2x
= ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) )
<=> ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ V0z ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er068,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( V2x
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ V0z ) )
<=> ( ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) @ V2x ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er069,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( V2x
= ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
<=> ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er070,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( V2x
= ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
<=> ( ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er071,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( V2x
= ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
<=> ( ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ V0z ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er072,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( V2x
= ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
<=> ( ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) )
= ( c_2Einteger_2Eint__neg @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Er073,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( V2x
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1y ) @ V0z ) )
<=> ( ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) )
= V1y ) ) ).
thf(thm_2EHolSmt_2Er074,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x )
= ( c_2Einteger_2Eint__neg @ V0y ) )
<=> ( V1x = V0y ) ) ).
thf(thm_2EHolSmt_2Er075,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ V1y )
= V0z )
<=> ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) )
= ( c_2Einteger_2Eint__neg @ V0z ) ) ) ).
thf(thm_2EHolSmt_2Er076,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ V1x @ V0y )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
<=> ( V0y
= ( c_2Einteger_2Eint__neg @ V1x ) ) ) ).
thf(thm_2EHolSmt_2Er077,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ V2x @ V1y )
= V0z )
<=> ( ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) )
= ( c_2Einteger_2Eint__neg @ V2x ) ) ) ).
thf(thm_2EHolSmt_2Er078,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint,V3w: tyop_2Einteger_2Eint,V4v: tyop_2Einteger_2Eint,V5a: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ V5a @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ V4v @ V1y ) @ ( c_2Einteger_2Eint__mul @ V3w @ V0z ) ) ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
<=> ( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ V4v ) @ V1y ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ V3w ) @ V0z ) ) )
= V5a ) ) ).
thf(thm_2EHolSmt_2Er079,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V0x )
= V0x ) ).
thf(thm_2EHolSmt_2Er080,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= V0x ) ).
thf(thm_2EHolSmt_2Er081,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ V1x @ V0y )
= ( c_2Einteger_2Eint__add @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er082,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ V0x @ V0x )
= ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V0x ) ) ).
thf(thm_2EHolSmt_2Er083,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ V2x @ V1y ) @ V0z )
= ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) ) ) ).
thf(thm_2EHolSmt_2Er084,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ V2x @ V1y ) @ V0z )
= ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V0z @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Er085,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
= ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V0z @ V2x ) ) ) ).
thf(thm_2EHolSmt_2Er086,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
= ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V2x @ V0z ) ) ) ).
thf(thm_2EHolSmt_2Er087,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint,V3u: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V0z @ V3u ) ) )
= ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__add @ V3u @ V2x ) ) ) ) ).
thf(thm_2EHolSmt_2Er088,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__ge @ V0x @ V0x )
= c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er089,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__ge @ V1x @ V0y )
= ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er090,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__ge @ V1x @ V0y )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er091,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__ge @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er092,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0x ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er093,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) @ ( c_2Einteger_2Eint__neg @ V0y ) )
= ( c_2Einteger_2Eint__le @ V1x @ V0y ) ) ).
thf(thm_2EHolSmt_2Er094,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) @ V0y ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er095,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__le @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er096,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__gt @ V1x @ V0y )
<=> ( (~) @ ( c_2Einteger_2Eint__ge @ V0y @ V1x ) ) ) ).
thf(thm_2EHolSmt_2Er097,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__gt @ V1x @ V0y )
<=> ( (~) @ ( c_2Einteger_2Eint__le @ V1x @ V0y ) ) ) ).
thf(thm_2EHolSmt_2Er098,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__gt @ V1x @ V0y )
<=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Er099,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__gt @ V1x @ V0y )
<=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V0y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Er100,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__gt @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
<=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) @ ( c_2Einteger_2Eint__neg @ V1y ) ) ) ) ).
thf(thm_2EHolSmt_2Er101,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ V0x @ V0x )
= c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er102,axiom,
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= c_2Ebool_2ET ) ).
thf(thm_2EHolSmt_2Er103,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ V1x @ V0y )
= ( c_2Einteger_2Eint__ge @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er104,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1x ) @ V0y ) )
= ( c_2Einteger_2Eint__ge @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er105,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0x ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__ge @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er106,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ V1x @ V0y )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er107,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ V1x @ V0y )
= ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V0y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er108,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) @ V0y ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er109,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ V1y ) @ ( c_2Einteger_2Eint__neg @ V0z ) )
= ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) ) @ V0z ) ) ).
thf(thm_2EHolSmt_2Er110,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V2x ) @ V1y ) @ V0z )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) @ V2x ) ) ).
thf(thm_2EHolSmt_2Er111,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) ) @ V0z )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er112,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) @ V1y ) ) ).
thf(thm_2EHolSmt_2Er113,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
= ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) @ ( c_2Einteger_2Eint__neg @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Er114,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ V0z ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er115,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ V1x @ V0y )
<=> ( (~) @ ( c_2Einteger_2Eint__le @ V0y @ V1x ) ) ) ).
thf(thm_2EHolSmt_2Er116,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ V1x @ V0y )
<=> ( (~) @ ( c_2Einteger_2Eint__ge @ V1x @ V0y ) ) ) ).
thf(thm_2EHolSmt_2Er117,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ V1x @ V0y )
<=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Er118,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ V1x @ V0y )
<=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Er119,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) )
<=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) ) @ V0z ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Er120,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) )
<=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ V0z ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Er121,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1y ) @ V0z ) )
<=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Er122,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint,V3u: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1y ) @ ( c_2Einteger_2Eint__add @ V0z @ V3u ) ) )
<=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__add @ V3u @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) ) @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Er123,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint,V3v: tyop_2Einteger_2Eint,V4u: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1y ) @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__add @ V4u @ V3v ) ) ) )
<=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__add @ V4u @ ( c_2Einteger_2Eint__add @ V3v @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) ) ) ) @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Er124,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V2x ) @ V1y ) @ V0z )
<=> ( (~) @ ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) @ V2x ) ) ) ).
thf(thm_2EHolSmt_2Er125,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ V2x @ V1y ) @ V0z )
<=> ( (~) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V0z @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) ) @ V2x ) ) ) ).
thf(thm_2EHolSmt_2Er126,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V1x ) @ V0y ) )
<=> ( (~) @ ( c_2Einteger_2Eint__le @ V0y @ V1x ) ) ) ).
thf(thm_2EHolSmt_2Er127,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= V0x ) ).
thf(thm_2EHolSmt_2Er128,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V0x )
= ( c_2Einteger_2Eint__neg @ V0x ) ) ).
thf(thm_2EHolSmt_2Er129,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ V0x )
= ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0x ) ) ).
thf(thm_2EHolSmt_2Er130,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ V1x @ V0y )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ V0y ) @ V1x ) ) ).
thf(thm_2EHolSmt_2Er131,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ V1x @ V0y )
= ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) ) ).
thf(thm_2EHolSmt_2Er132,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ V1x @ V0y )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) @ V1x ) ) ).
thf(thm_2EHolSmt_2Er133,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ V0x @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0x ) ) ).
thf(thm_2EHolSmt_2Er134,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ V2x @ V1y ) @ V0z )
= ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ V1y @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) ) ) ).
thf(thm_2EHolSmt_2Er135,axiom,
! [V0z: tyop_2Einteger_2Eint,V1y: tyop_2Einteger_2Eint,V2x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ V2x @ V1y ) @ V0z )
= ( c_2Einteger_2Eint__add @ V2x @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Er136,axiom,
! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) )
<=> ( ( c_2Erealax_2Ereal__mul @ V1u @ V0x )
= ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er137,axiom,
! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal,V2a: tyop_2Erealax_2Ereal] :
( ( V2a
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) )
<=> ( ( c_2Erealax_2Ereal__mul @ V1u @ V0x )
= ( c_2Erealax_2Ereal__neg @ V2a ) ) ) ).
thf(thm_2EHolSmt_2Er138,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3a: tyop_2Erealax_2Ereal] :
( ( V3a
= ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V3a ) @ V0z ) ) )
= ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er139,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3a: tyop_2Erealax_2Ereal] :
( ( V3a
= ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__add @ V0z @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V3a ) ) ) )
= ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er140,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( V4a
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0z ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1y ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0z ) @ V4a ) )
= ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er141,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( V4a
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0z ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1y ) @ ( c_2Erealax_2Ereal__add @ V4a @ ( c_2Erealax_2Ereal__mul @ V2v @ V0z ) ) )
= ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er142,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__neg @ V4a )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) )
= V4a ) ) ).
thf(thm_2EHolSmt_2Er143,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( V6a
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) @ V6a ) ) )
= ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er144,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( V6a
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
= ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er145,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( V6a
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
= ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er146,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( V6a
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
= ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er147,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( V6a
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
= ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er148,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__neg @ V6a )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
= V6a ) ) ).
thf(thm_2EHolSmt_2Er149,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__neg @ V6a )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
= V6a ) ) ).
thf(thm_2EHolSmt_2Er150,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__neg @ V6a )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
= V6a ) ) ).
thf(thm_2EHolSmt_2Er151,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__neg @ V6a )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
= V6a ) ) ).
thf(thm_2EHolSmt_2Er152,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4u: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( V5a
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4u @ V2x ) @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
= ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ).
thf(thm_2EHolSmt_2Er153,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4u: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( V5a
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4u @ V2x ) @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
= ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ).
thf(thm_2EHolSmt_2Er154,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) )
= ( c_2Erealax_2Ereal__neg @ V4a ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) )
= V4a ) ) ).
thf(thm_2EHolSmt_2Er155,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
= ( c_2Erealax_2Ereal__neg @ V5a ) )
<=> ( ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
= V5a ) ) ).
thf(thm_2EHolSmt_2Er156,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
= ( c_2Erealax_2Ereal__neg @ V6a ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
= V6a ) ) ).
thf(thm_2EHolSmt_2Er157,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
= ( c_2Erealax_2Ereal__neg @ V6a ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
= V6a ) ) ).
thf(thm_2EHolSmt_2Er158,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) )
= ( c_2Erealax_2Ereal__neg @ V6a ) )
<=> ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) )
= V6a ) ) ).
thf(thm_2EHolSmt_2Er159,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
= ( c_2Ereal_2Ereal__lte @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er160,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__ge @ V1x @ V0y )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er161,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__gt @ V1x @ V0y )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Er162,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ V1x @ V0y )
= ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er163,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) )
= ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) @ V1y ) ) ).
thf(thm_2EHolSmt_2Er164,axiom,
! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal,V2a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) @ V2a )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__mul @ V1u @ V0x ) @ ( c_2Erealax_2Ereal__neg @ V2a ) ) ) ).
thf(thm_2EHolSmt_2Er165,axiom,
! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal,V2a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) @ ( c_2Erealax_2Ereal__neg @ V2a ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__mul @ V1u @ V0x ) @ V2a ) ) ).
thf(thm_2EHolSmt_2Er166,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er167,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ V4a )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) ) ) ).
thf(thm_2EHolSmt_2Er168,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ V4a ) ) ).
thf(thm_2EHolSmt_2Er169,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ V4a )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) ) ) ).
thf(thm_2EHolSmt_2Er170,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ V4a ) ) ).
thf(thm_2EHolSmt_2Er171,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er172,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er173,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er174,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Er175,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er176,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a ) ) ).
thf(thm_2EHolSmt_2Er177,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er178,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a ) ) ).
thf(thm_2EHolSmt_2Er179,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er180,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a ) ) ).
thf(thm_2EHolSmt_2Er181,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er182,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a ) ) ).
thf(thm_2EHolSmt_2Er183,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
= ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V5a ) ) ).
thf(thm_2EHolSmt_2Er184,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ V1x @ V0y )
<=> ( (~) @ ( c_2Ereal_2Ereal__ge @ V1x @ V0y ) ) ) ).
thf(thm_2EHolSmt_2Er185,axiom,
! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal,V2a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) @ V2a )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__mul @ V1u @ V0x ) @ ( c_2Erealax_2Ereal__neg @ V2a ) ) ) ) ).
thf(thm_2EHolSmt_2Er186,axiom,
! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal,V2a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) @ ( c_2Erealax_2Ereal__neg @ V2a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__mul @ V1u @ V0x ) @ V2a ) ) ) ).
thf(thm_2EHolSmt_2Er187,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Er188,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Er189,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ V4a )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) ) ) ) ).
thf(thm_2EHolSmt_2Er190,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ V4a ) ) ) ).
thf(thm_2EHolSmt_2Er191,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ V4a )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) ) ) ) ).
thf(thm_2EHolSmt_2Er192,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2v: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal,V4a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V1x ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2v ) @ V0y ) ) @ ( c_2Erealax_2Ereal__neg @ V4a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3u @ V1x ) @ ( c_2Erealax_2Ereal__mul @ V2v @ V0y ) ) @ V4a ) ) ) ).
thf(thm_2EHolSmt_2Er193,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ) ).
thf(thm_2EHolSmt_2Er194,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er195,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ) ).
thf(thm_2EHolSmt_2Er196,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er197,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ) ).
thf(thm_2EHolSmt_2Er198,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er199,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V6a )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) ) ) ) ).
thf(thm_2EHolSmt_2Er200,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal,V6a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V6a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V6a ) ) ) ).
thf(thm_2EHolSmt_2Er201,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Er202,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5u: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V5u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V5u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Er203,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V5a )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ) ).
thf(thm_2EHolSmt_2Er204,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V5a ) ) ) ).
thf(thm_2EHolSmt_2Er205,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V5a )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ) ).
thf(thm_2EHolSmt_2Er206,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V5a ) ) ) ).
thf(thm_2EHolSmt_2Er207,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V5a )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ) ).
thf(thm_2EHolSmt_2Er208,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V5a ) ) ) ).
thf(thm_2EHolSmt_2Er209,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ V5a )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) ) ) ) ).
thf(thm_2EHolSmt_2Er210,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4v: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4v ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V5a ) ) ) ).
thf(thm_2EHolSmt_2Er211,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3w: tyop_2Erealax_2Ereal,V4u: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3w ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4u @ V2x ) @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__mul @ V3w @ V0z ) ) ) @ V5a ) ) ) ).
thf(thm_2EHolSmt_2Er212,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3v: tyop_2Erealax_2Ereal,V4u: tyop_2Erealax_2Ereal,V5a: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V4u ) @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V3v @ V1y ) @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) ) @ ( c_2Erealax_2Ereal__neg @ V5a ) )
<=> ( (~) @ ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ V4u @ V2x ) @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3v ) @ V1y ) @ V0z ) ) @ V5a ) ) ) ).
thf(thm_2EHolSmt_2Er213,axiom,
! [V0x: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) @ V0x )
= V0x ) ).
thf(thm_2EHolSmt_2Er214,axiom,
! [V0x: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ V0x @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
= V0x ) ).
thf(thm_2EHolSmt_2Er215,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ V1x @ V0y )
= ( c_2Erealax_2Ereal__add @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er216,axiom,
! [V0x: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ V0x @ V0x )
= ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V0x ) ) ).
thf(thm_2EHolSmt_2Er217,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ V0z )
= ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) ) ) ).
thf(thm_2EHolSmt_2Er218,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ V0z )
= ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V0z @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Er219,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) )
= ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__add @ V0z @ V2x ) ) ) ).
thf(thm_2EHolSmt_2Er220,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ V0z ) )
= ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__add @ V2x @ V0z ) ) ) ).
thf(thm_2EHolSmt_2Er221,axiom,
! [V0x: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) @ V0x )
= ( c_2Erealax_2Ereal__neg @ V0x ) ) ).
thf(thm_2EHolSmt_2Er222,axiom,
! [V0x: tyop_2Erealax_2Ereal,V1u: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) @ ( c_2Erealax_2Ereal__mul @ V1u @ V0x ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V1u ) @ V0x ) ) ).
thf(thm_2EHolSmt_2Er223,axiom,
! [V0x: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ V0x @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) )
= V0x ) ).
thf(thm_2EHolSmt_2Er224,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ V1x @ V0y )
= ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) ) ).
thf(thm_2EHolSmt_2Er225,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ V1x @ V0y )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) @ V1x ) ) ).
thf(thm_2EHolSmt_2Er226,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2u: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ V1x @ ( c_2Erealax_2Ereal__mul @ V2u @ V0y ) )
= ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2u ) @ V0y ) ) ) ).
thf(thm_2EHolSmt_2Er227,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal,V2u: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ V1x @ ( c_2Erealax_2Ereal__mul @ V2u @ V0y ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V2u ) @ V0y ) @ V1x ) ) ).
thf(thm_2EHolSmt_2Er228,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ V0z )
= ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) ) ) ) ).
thf(thm_2EHolSmt_2Er229,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ V0z )
= ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0z ) @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Er230,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3u @ V0z ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V0z ) @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Er231,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3u @ V0z ) )
= ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V0z ) @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Er232,axiom,
! [V0z: tyop_2Erealax_2Ereal,V1y: tyop_2Erealax_2Ereal,V2x: tyop_2Erealax_2Ereal,V3u: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__sub @ ( c_2Erealax_2Ereal__add @ V2x @ V1y ) @ ( c_2Erealax_2Ereal__mul @ V3u @ V0z ) )
= ( c_2Erealax_2Ereal__add @ V2x @ ( c_2Erealax_2Ereal__add @ V1y @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ V3u ) @ V0z ) ) ) ) ).
thf(thm_2EHolSmt_2Er233,axiom,
! [V0x: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) @ V0x )
= ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ).
thf(thm_2EHolSmt_2Er234,axiom,
! [V0x: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0x )
= V0x ) ).
thf(thm_2EHolSmt_2Er235,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0x )
= V0x ) ).
thf(thm_2EHolSmt_2Er236,axiom,
! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ V1x @ V0y )
= ( c_2Ewords_2Eword__add @ A_27a @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er237,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0x ) )
= ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V0x ) ) ).
thf(thm_2EHolSmt_2Er238,axiom,
! [A_27a: $tType,V0z: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__add @ A_27a @ V2x @ V0z )
= ( c_2Ewords_2Eword__add @ A_27a @ V1y @ V2x ) )
<=> ( V1y = V0z ) ) ).
thf(thm_2EHolSmt_2Er239,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0x @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
=> ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
=> ( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ ( c_2Ewords_2En2w @ A_27b @ V0x ) )
= ( c_2Ewords_2En2w @ A_27c @ V0x ) ) ) ) ).
thf(thm_2EHolSmt_2Er240,axiom,
! [A_27a: $tType,A_27b: $tType,V0x: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0x @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
=> ( ( c_2Ewords_2Ew2w @ A_27a @ A_27b @ ( c_2Ewords_2En2w @ A_27a @ V0x ) )
= ( c_2Ewords_2En2w @ A_27b @ V0x ) ) ) ).
thf(thm_2EHolSmt_2Er241,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y: tyop_2Enum_2Enum,V1x: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
=> ( ( c_2Eprim__rec_2E_3C @ V0y @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
=> ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
=> ( ( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1x )
= ( c_2Ewords_2En2w @ A_27c @ V0y ) )
<=> ( V1x
= ( c_2Ewords_2En2w @ A_27b @ V0y ) ) ) ) ) ) ).
thf(thm_2EHolSmt_2Er242,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y: tyop_2Enum_2Enum,V1x: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
=> ( ( c_2Eprim__rec_2E_3C @ V0y @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
=> ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
=> ( ( ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1x )
= ( c_2Ewords_2En2w @ A_27c @ V0y ) )
<=> ( ( c_2Ewords_2En2w @ A_27b @ V0y )
= V1x ) ) ) ) ) ).
thf(thm_2EHolSmt_2Er243,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y: tyop_2Enum_2Enum,V1x: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
=> ( ( c_2Eprim__rec_2E_3C @ V0y @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
=> ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
=> ( ( ( c_2Ewords_2En2w @ A_27c @ V0y )
= ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1x ) )
<=> ( V1x
= ( c_2Ewords_2En2w @ A_27b @ V0y ) ) ) ) ) ) ).
thf(thm_2EHolSmt_2Er244,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0y: tyop_2Enum_2Enum,V1x: tyop_2Efcp_2Ecart @ $o @ A_27b] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) @ ( c_2Efcp_2Edimindex @ A_27c @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
=> ( ( c_2Eprim__rec_2E_3C @ V0y @ ( c_2Ewords_2Edimword @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
=> ( ( c_2Epred__set_2EFINITE @ A_27a @ ( c_2Epred__set_2EUNIV @ A_27a ) )
=> ( ( ( c_2Ewords_2En2w @ A_27c @ V0y )
= ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V1x ) )
<=> ( ( c_2Ewords_2En2w @ A_27b @ V0y )
= V1x ) ) ) ) ) ).
thf(thm_2EHolSmt_2Er245,axiom,
! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ V1x @ V0y )
= ( c_2Ewords_2Eword__and @ A_27a @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er246,axiom,
! [A_27a: $tType,V0z: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ V2x @ ( c_2Ewords_2Eword__and @ A_27a @ V1y @ V0z ) )
= ( c_2Ewords_2Eword__and @ A_27a @ V1y @ ( c_2Ewords_2Eword__and @ A_27a @ V2x @ V0z ) ) ) ).
thf(thm_2EHolSmt_2Er247,axiom,
! [A_27a: $tType,V0z: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ V2x @ ( c_2Ewords_2Eword__and @ A_27a @ V1y @ V0z ) )
= ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V2x @ V1y ) @ V0z ) ) ).
thf(thm_2EHolSmt_2Er248,axiom,
! [V0y: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ewords_2Eword__and @ tyop_2Eone_2Eone @ V1x @ V0y ) )
<=> ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= V1x )
& ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= V0y ) ) ) ).
thf(thm_2EHolSmt_2Er249,axiom,
! [V0y: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ewords_2Eword__and @ tyop_2Eone_2Eone @ V1x @ V0y ) )
<=> ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= V0y )
& ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= V1x ) ) ) ).
thf(thm_2EHolSmt_2Er250,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )] :
( ( c_2Ewords_2Eword__extract @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ c_2Enum_2E0 @ V0x )
= V0x ) ).
thf(thm_2EHolSmt_2Er251,axiom,
! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__lo @ A_27a @ V1x @ V0y )
<=> ( (~) @ ( c_2Ewords_2Eword__ls @ A_27a @ V0y @ V1x ) ) ) ).
thf(thm_2EHolSmt_2Er252,axiom,
! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__mul @ A_27a @ V1x @ V0y )
= ( c_2Ewords_2Eword__mul @ A_27a @ V0y @ V1x ) ) ).
thf(thm_2EHolSmt_2Er253,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
( ( c_2Ewords_2Eword__extract @ tyop_2Eone_2Eone @ tyop_2Eone_2Eone @ c_2Enum_2E0 @ c_2Enum_2E0 @ V0x )
= V0x ) ).
thf(thm_2EHolSmt_2Er254,axiom,
! [A_27a: $tType,V0z: tyop_2Efcp_2Ecart @ $o @ A_27a,V1y: tyop_2Efcp_2Ecart @ $o @ A_27a,V2x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__and @ A_27a @ ( c_2Ewords_2Eword__and @ A_27a @ V2x @ V1y ) @ V0z )
= ( c_2Ewords_2Eword__and @ A_27a @ V2x @ ( c_2Ewords_2Eword__and @ A_27a @ V1y @ V0z ) ) ) ).
thf(thm_2EHolSmt_2Er255,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__or @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ c_2Enum_2E0 ) @ V0x )
= V0x ) ).
thf(thm_2EHolSmt_2Et001,axiom,
! [A_27a: $tType,A_27b: $tType,V0z: A_27b,V1y: A_27a,V2x: A_27a,V3f: A_27a > A_27b] :
( ( V2x = V1y )
| ( ( V3f @ V2x )
= ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b @ V1y @ V0z @ V3f @ V2x ) ) ) ).
thf(thm_2EHolSmt_2Et002,axiom,
! [A_27a: $tType,A_27b: $tType,V0z: A_27b,V1y: A_27a,V2x: A_27a,V3f: A_27a > A_27b] :
( ( V2x = V1y )
| ( ( V3f @ V1y )
= ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b @ V2x @ V0z @ V3f @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Et003,axiom,
! [A_27a: $tType,A_27b: $tType,V0z: A_27b,V1y: A_27a,V2x: A_27a,V3f: A_27a > A_27b] :
( ( V2x = V1y )
| ( ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b @ V1y @ V0z @ V3f @ V2x )
= ( V3f @ V2x ) ) ) ).
thf(thm_2EHolSmt_2Et004,axiom,
! [A_27a: $tType,A_27b: $tType,V0z: A_27b,V1y: A_27a,V2x: A_27a,V3f: A_27a > A_27b] :
( ( V2x = V1y )
| ( ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b @ V2x @ V0z @ V3f @ V1y )
= ( V3f @ V1y ) ) ) ).
thf(thm_2EHolSmt_2Et005,axiom,
! [A_27a: $tType,A_27b: $tType,V0g: A_27a > A_27b,V1f: A_27a > A_27b] :
( ( V1f = V0g )
| ( (~)
@ ( ( V1f @ ( c_2EHolSmt_2Earray__ext @ A_27a @ A_27b @ V1f @ V0g ) )
= ( V0g @ ( c_2EHolSmt_2Earray__ext @ A_27a @ A_27b @ V1f @ V0g ) ) ) ) ) ).
thf(thm_2EHolSmt_2Et006,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( (~) @ ( V1x = V0y ) )
| ( c_2Einteger_2Eint__le @ V1x @ V0y ) ) ).
thf(thm_2EHolSmt_2Et007,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( (~) @ ( V1x = V0y ) )
| ( c_2Einteger_2Eint__ge @ V1x @ V0y ) ) ).
thf(thm_2EHolSmt_2Et008,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( (~) @ ( V1x = V0y ) )
| ( c_2Einteger_2Eint__ge @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Et009,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( (~) @ ( V1x = V0y ) )
| ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ V1x @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Et010,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( V1x = V0y )
| ( (~) @ ( c_2Einteger_2Eint__le @ V1x @ V0y ) )
| ( (~) @ ( c_2Einteger_2Eint__ge @ V1x @ V0y ) ) ) ).
thf(thm_2EHolSmt_2Et011,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( (~) @ ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2EHolSmt_2Et012,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( (~) @ ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
| ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Et013,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( (~) @ ( c_2Einteger_2Eint__ge @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( c_2Einteger_2Eint__ge @ V0x @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2EHolSmt_2Et014,axiom,
! [V0x: tyop_2Einteger_2Eint] :
( ( (~) @ ( c_2Einteger_2Eint__ge @ V0x @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( (~) @ ( c_2Einteger_2Eint__le @ V0x @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2EHolSmt_2Et015,axiom,
! [V0y: tyop_2Einteger_2Eint,V1x: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__ge @ V1x @ V0y )
| ( c_2Einteger_2Eint__le @ V1x @ V0y ) ) ).
thf(thm_2EHolSmt_2Et016,axiom,
! [V0y: tyop_2Erealax_2Ereal,V1x: tyop_2Erealax_2Ereal] :
( ( (~) @ ( V1x = V0y ) )
| ( c_2Ereal_2Ereal__ge @ ( c_2Erealax_2Ereal__add @ V1x @ ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__neg @ ( c_2Ereal_2Ereal__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) @ ( c_2Ereal_2Ereal__of__num @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Et017,axiom,
! [A_27a: $tType,V0x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( (~)
@ ( V0x
= ( c_2Ewords_2Eword__1comp @ A_27a @ V0x ) ) ) ).
thf(thm_2EHolSmt_2Et018,axiom,
! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a,V2i: tyop_2Enum_2Enum] :
( ( V1x = V0y )
=> ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1x @ V2i )
=> ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0y @ V2i ) ) ) ).
thf(thm_2EHolSmt_2Et019,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V0x ) )
| ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 ) ) ).
thf(thm_2EHolSmt_2Et020,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
( ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 )
=> ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 )
= ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V0x ) ) ) ).
thf(thm_2EHolSmt_2Et021,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
( ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 )
=> ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= V0x ) ) ).
thf(thm_2EHolSmt_2Et022,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
( ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 ) )
=> ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 )
= V0x ) ) ).
thf(thm_2EHolSmt_2Et023,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
( ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 ) )
=> ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V0x ) ) ) ).
thf(thm_2EHolSmt_2Et024,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 )
= ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V0x ) )
| ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0x @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Et025,axiom,
! [V0y: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ewords_2Eword__or @ tyop_2Eone_2Eone @ ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V1x ) @ ( c_2Ewords_2Eword__1comp @ tyop_2Eone_2Eone @ V0y ) ) )
| ( (~)
@ ( ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V1x @ c_2Enum_2E0 ) )
| ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ tyop_2Eone_2Eone @ V0y @ c_2Enum_2E0 ) ) ) ) ) ).
thf(thm_2EHolSmt_2Et026,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )] :
( ( ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ c_2Enum_2E0 )
= V0x )
| ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ c_2Enum_2E0 )
| ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
| ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
| ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2EHolSmt_2Et027,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1p: $o] :
( ( ( V0x
= ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
<=> V1p )
<=> ( V0x
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1p @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Et028,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1p: $o] :
( ( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= V0x )
<=> V1p )
<=> ( V0x
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1p @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Et029,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1p: $o] :
( ( V1p
<=> ( V0x
= ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
<=> ( V0x
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1p @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Et030,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone,V1p: $o] :
( ( V1p
<=> ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= V0x ) )
<=> ( V0x
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone ) @ V1p @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Et031,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )] :
( ( ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ c_2Enum_2E0 )
= ( c_2Ewords_2Eword__mul @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ewords_2Esw2sw @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ V0x ) ) )
=> ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ c_2Enum_2E0 ) ) ) ).
thf(thm_2EHolSmt_2Et032,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )] :
( ( ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ c_2Enum_2E0 )
= ( c_2Ewords_2Eword__mul @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ewords_2Esw2sw @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ V0x ) ) )
=> ( (~)
@ ( ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
<=> ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ c_2Enum_2E0 ) ) ) ) ) ).
thf(thm_2EHolSmt_2Et033,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) )] :
( ( ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ c_2Enum_2E0 )
= ( c_2Ewords_2Eword__mul @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ewords_2En2w @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( c_2Ewords_2Esw2sw @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ V0x ) ) )
=> ( (~)
@ ( ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
<=> ( ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ c_2Enum_2E0 ) )
& ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ V0x @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2EHolSmt_2Et034,axiom,
! [A_27a: $tType,V0y: tyop_2Efcp_2Ecart @ $o @ A_27a,V1x: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( ( c_2Ewords_2Eword__add @ A_27a @ ( c_2Ewords_2En2w @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1x )
= V0y )
=> ( ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V1x @ c_2Enum_2E0 )
=> ( (~) @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0y @ c_2Enum_2E0 ) ) ) ) ).
thf(thm_2EHolSmt_2Et035,axiom,
! [V0x: tyop_2Efcp_2Ecart @ $o @ tyop_2Eone_2Eone] :
( ( ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= V0x )
| ( (~)
@ ( ( c_2Ewords_2Eword__extract @ tyop_2Eone_2Eone @ tyop_2Eone_2Eone @ c_2Enum_2E0 @ c_2Enum_2E0 @ V0x )
= ( c_2Ewords_2En2w @ tyop_2Eone_2Eone @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2EHolSmt_2Ep001,axiom,
! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2EHolSmt_2Ep002,axiom,
! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Ewords_2Edimword @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2EHolSmt_2Ep003,axiom,
c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Ewords_2Edimword @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(thm_2EHolSmt_2Ep004,axiom,
c_2Epred__set_2EFINITE @ tyop_2Eone_2Eone @ ( c_2Epred__set_2EUNIV @ tyop_2Eone_2Eone ) ).
thf(thm_2EHolSmt_2Ep005,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(thm_2EHolSmt_2Ep006,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(thm_2EHolSmt_2Ep007,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(thm_2EHolSmt_2Ep008,axiom,
c_2Epred__set_2EFINITE @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ ( tyop_2Efcp_2Ebit1 @ tyop_2Eone_2Eone ) ) ) ) ) ).
thf(thm_2EHolSmt_2Ep009,axiom,
c_2Earithmetic_2E_3C_3D @ ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Efcp_2Edimindex @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ ( tyop_2Efcp_2Ebit0 @ tyop_2Eone_2Eone ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------