TPTP Problem File: ITP014^3.p
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%------------------------------------------------------------------------------
% File : ITP014^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Ebitstring_2Eword__1comp__v2w.p, bushy 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 : thm_2Ebitstring_2Eword__1comp__v2w.p [Gau19]
% : HL406501^3.p [TPAP]
% Status : Theorem
% Rating : 1.00 v7.5.0
% Syntax : Number of formulae : 125 ( 30 unt; 49 typ; 0 def)
% Number of atoms : 305 ( 119 equ; 49 cnn)
% Maximal formula atoms : 41 ( 4 avg)
% Number of connectives : 1029 ( 49 ~; 38 |; 116 &; 717 @)
% ( 66 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 47 usr; 5 con; 0-4 aty)
% Number of variables : 237 ( 3 ^; 214 !; 1 ?; 237 :)
% ( 19 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
thf(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
thf(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: $tType > $tType > $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(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2E_2A,type,
c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2B,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2D,type,
c_2Earithmetic_2E_2D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
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_2Earithmetic_2E_3E,type,
c_2Earithmetic_2E_3E: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2E_3E_3D,type,
c_2Earithmetic_2E_3E_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $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_2EEL,type,
c_2Elist_2EEL:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > A_27a ) ).
thf(c_2Earithmetic_2EEVEN,type,
c_2Earithmetic_2EEVEN: tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2EEXP,type,
c_2Earithmetic_2EEXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2EF,type,
c_2Ebool_2EF: $o ).
thf(c_2Efcp_2EFCP,type,
c_2Efcp_2EFCP:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Enum_2Enum > A_27a ) > ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) ) ).
thf(c_2Ecombin_2EI,type,
c_2Ecombin_2EI:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
thf(c_2Elist_2ELENGTH,type,
c_2Elist_2ELENGTH:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Ebool_2ELET,type,
c_2Ebool_2ELET:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > A_27a > A_27b ) ).
thf(c_2Elist_2EMAP,type,
c_2Elist_2EMAP:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27b ) ) ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EODD,type,
c_2Earithmetic_2EODD: tyop_2Enum_2Enum > $o ).
thf(c_2Eprim__rec_2EPRE,type,
c_2Eprim__rec_2EPRE: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Enum_2ESUC,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
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_2Ebitstring_2Ebnot,type,
c_2Ebitstring_2Ebnot: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Efcp_2Edimindex,type,
c_2Efcp_2Edimindex:
!>[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_2Ebitstring_2Efixwidth,type,
c_2Ebitstring_2Efixwidth: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Enumeral_2EiZ,type,
c_2Enumeral_2EiZ: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Enumeral_2EiiSUC,type,
c_2Enumeral_2EiiSUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebitstring_2Etestbit,type,
c_2Ebitstring_2Etestbit: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) > $o ).
thf(c_2Ebool_2Ethe__value,type,
c_2Ebool_2Ethe__value:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself @ A_27a ) ).
thf(c_2Ebitstring_2Ev2w,type,
c_2Ebitstring_2Ev2w:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).
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_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_2Earithmetic_2EADD__CLAUSES,axiom,
! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2B @ c_2Enum_2E0 @ V1m )
= V1m )
& ( ( c_2Earithmetic_2E_2B @ V1m @ c_2Enum_2E0 )
= V1m )
& ( ( c_2Earithmetic_2E_2B @ ( c_2Enum_2ESUC @ V1m ) @ V0n )
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V1m @ V0n ) ) )
& ( ( c_2Earithmetic_2E_2B @ V1m @ ( c_2Enum_2ESUC @ V0n ) )
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V1m @ V0n ) ) ) ) ).
thf(thm_2Earithmetic_2EADD__SYM,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ V0m @ V1n )
= ( c_2Earithmetic_2E_2B @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2EADD__COMM,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ V0m @ V1n )
= ( c_2Earithmetic_2E_2B @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2EADD__ASSOC,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2p: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ V0m @ ( c_2Earithmetic_2E_2B @ V1n @ V2p ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2B @ V0m @ V1n ) @ V2p ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0m @ V1n )
= ( c_2Earithmetic_2E_3C_3D @ ( c_2Enum_2ESUC @ V0m ) @ V1n ) ) ).
thf(thm_2Earithmetic_2EZERO__LESS__EQ,axiom,
! [V0n: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ c_2Enum_2E0 @ V0n ) ).
thf(thm_2Earithmetic_2ENOT__LESS,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( (~) @ ( c_2Eprim__rec_2E_3C @ V0m @ V1n ) )
<=> ( c_2Earithmetic_2E_3C_3D @ V1n @ V0m ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__0,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ c_2Enum_2E0 )
<=> ( V0n = c_2Enum_2E0 ) ) ).
thf(thm_2Earithmetic_2EMULT__CLAUSES,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ c_2Enum_2E0 @ V0m )
= c_2Enum_2E0 )
& ( ( c_2Earithmetic_2E_2A @ V0m @ c_2Enum_2E0 )
= c_2Enum_2E0 )
& ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0m )
= V0m )
& ( ( c_2Earithmetic_2E_2A @ V0m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= V0m )
& ( ( c_2Earithmetic_2E_2A @ ( c_2Enum_2ESUC @ V0m ) @ V1n )
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ V0m @ V1n ) @ V1n ) )
& ( ( c_2Earithmetic_2E_2A @ V0m @ ( c_2Enum_2ESUC @ V1n ) )
= ( c_2Earithmetic_2E_2B @ V0m @ ( c_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) ) ).
thf(thm_2Earithmetic_2ELESS__EQ__TRANS,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2p: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ V0m @ V1n )
& ( c_2Earithmetic_2E_3C_3D @ V1n @ V2p ) )
=> ( c_2Earithmetic_2E_3C_3D @ V0m @ V2p ) ) ).
thf(thm_2Earithmetic_2EEQ__LESS__EQ,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( V0m = V1n )
<=> ( ( c_2Earithmetic_2E_3C_3D @ V0m @ V1n )
& ( c_2Earithmetic_2E_3C_3D @ V1n @ V0m ) ) ) ).
thf(thm_2Earithmetic_2EADD__MONO__LESS__EQ,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2p: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0m @ V1n ) @ ( c_2Earithmetic_2E_2B @ V0m @ V2p ) )
= ( c_2Earithmetic_2E_3C_3D @ V1n @ V2p ) ) ).
thf(thm_2Earithmetic_2ENOT__LEQ,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( (~) @ ( c_2Earithmetic_2E_3C_3D @ V0m @ V1n ) )
<=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Enum_2ESUC @ V1n ) @ V0m ) ) ).
thf(thm_2Earithmetic_2ENOT__NUM__EQ,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( (~) @ ( V0m = V1n ) )
<=> ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Enum_2ESUC @ V0m ) @ V1n )
| ( c_2Earithmetic_2E_3C_3D @ ( c_2Enum_2ESUC @ V1n ) @ V0m ) ) ) ).
thf(thm_2Earithmetic_2ESUC__ONE__ADD,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Enum_2ESUC @ V0n )
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0n ) ) ).
thf(thm_2Earithmetic_2ESUB__RIGHT__SUB,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2p: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2D @ V0m @ V1n ) @ V2p )
= ( c_2Earithmetic_2E_2D @ V0m @ ( c_2Earithmetic_2E_2B @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ESUB__LEFT__LESS__EQ,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2p: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Earithmetic_2E_2D @ V1n @ V2p ) )
<=> ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0m @ V2p ) @ V1n )
| ( c_2Earithmetic_2E_3C_3D @ V0m @ c_2Enum_2E0 ) ) ) ).
thf(thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2p: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ V0m @ V1n ) @ V2p )
= ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Earithmetic_2E_2B @ V1n @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ESUB__RIGHT__LESS,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2p: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ V0m @ V1n ) @ V2p )
<=> ( ( c_2Eprim__rec_2E_3C @ V0m @ ( c_2Earithmetic_2E_2B @ V1n @ V2p ) )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V2p ) ) ) ).
thf(thm_2Earithmetic_2ESUB__ELIM__THM,axiom,
! [V0b: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum,V2P: tyop_2Enum_2Enum > $o] :
( ( V2P @ ( c_2Earithmetic_2E_2D @ V1a @ V0b ) )
<=> ! [V3d: tyop_2Enum_2Enum] :
( ( ( V0b
= ( c_2Earithmetic_2E_2B @ V1a @ V3d ) )
=> ( V2P @ c_2Enum_2E0 ) )
& ( ( V1a
= ( c_2Earithmetic_2E_2B @ V0b @ V3d ) )
=> ( V2P @ V3d ) ) ) ) ).
thf(thm_2Ebitstring_2Ev2w__def,axiom,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Ev2w @ A_27a @ V0v )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V1i: tyop_2Enum_2Enum] : ( c_2Ebitstring_2Etestbit @ V1i @ V0v ) ) ) ).
thf(thm_2Ebitstring_2Ebnot__def,axiom,
( c_2Ebitstring_2Ebnot
= ( c_2Elist_2EMAP @ $o @ $o @ c_2Ebool_2E_7E ) ) ).
thf(thm_2Ebitstring_2Elength__fixwidth,axiom,
! [V0n: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Elist_2ELENGTH @ $o @ ( c_2Ebitstring_2Efixwidth @ V0n @ V1v ) )
= V0n ) ).
thf(thm_2Ebitstring_2Eel__fixwidth,axiom,
! [V0i: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2w: tyop_2Elist_2Elist @ $o] :
( ( c_2Eprim__rec_2E_3C @ V0i @ V1n )
=> ( ( c_2Elist_2EEL @ $o @ V0i @ ( c_2Ebitstring_2Efixwidth @ V1n @ V2w ) )
= ( c_2Ebool_2ECOND @ $o @ ( c_2Eprim__rec_2E_3C @ ( c_2Elist_2ELENGTH @ $o @ V2w ) @ V1n ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ V1n @ ( c_2Elist_2ELENGTH @ $o @ V2w ) ) @ V0i ) @ ( c_2Elist_2EEL @ $o @ ( c_2Earithmetic_2E_2D @ V0i @ ( c_2Earithmetic_2E_2D @ V1n @ ( c_2Elist_2ELENGTH @ $o @ V2w ) ) ) @ V2w ) ) @ ( c_2Elist_2EEL @ $o @ ( c_2Earithmetic_2E_2B @ V0i @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ $o @ V2w ) @ V1n ) ) @ V2w ) ) ) ) ).
thf(thm_2Ebitstring_2Etestbit,axiom,
! [V0b: tyop_2Enum_2Enum,V1v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Etestbit @ V0b @ V1v )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ $o
@ ^ [V2n: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Eprim__rec_2E_3C @ V0b @ V2n ) @ ( c_2Elist_2EEL @ $o @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2D @ V2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0b ) @ V1v ) )
@ ( c_2Elist_2ELENGTH @ $o @ V1v ) ) ) ).
thf(thm_2Ebool_2ETRUTH,axiom,
c_2Ebool_2ET ).
thf(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
! [V0t1: $o,V1t2: $o] :
( ( V0t1
=> V1t2 )
=> ( ( V1t2
=> V0t1 )
=> ( V0t1 = V1t2 ) ) ) ).
thf(thm_2Ebool_2EFALSITY,axiom,
! [V0t: $o] :
( c_2Ebool_2EF
=> V0t ) ).
thf(thm_2Ebool_2EEXCLUDED__MIDDLE,axiom,
! [V0t: $o] :
( V0t
| ( (~) @ V0t ) ) ).
thf(thm_2Ebool_2ELET__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b,V1x: A_27a] :
( ( c_2Ebool_2ELET @ A_27a @ A_27b @ V0f @ V1x )
= ( V0f @ V1x ) ) ).
thf(thm_2Ebool_2EFORALL__SIMP,axiom,
! [A_27a: $tType,V0t: $o] :
( ! [V1x: A_27a] : V0t
<=> V0t ) ).
thf(thm_2Ebool_2ECONJ__ASSOC,axiom,
! [V0t1: $o,V1t2: $o,V2t3: $o] :
( ( V0t1
& V1t2
& V2t3 )
<=> ( V0t1
& V1t2
& V2t3 ) ) ).
thf(thm_2Ebool_2EAND__CLAUSES,axiom,
! [V0t: $o] :
( ( ( c_2Ebool_2ET
& V0t )
<=> V0t )
& ( ( V0t
& c_2Ebool_2ET )
<=> V0t )
& ( ( c_2Ebool_2EF
& V0t )
<=> c_2Ebool_2EF )
& ( ( V0t
& c_2Ebool_2EF )
<=> c_2Ebool_2EF )
& ( ( V0t
& V0t )
<=> V0t ) ) ).
thf(thm_2Ebool_2EOR__CLAUSES,axiom,
! [V0t: $o] :
( ( ( c_2Ebool_2ET
| V0t )
<=> c_2Ebool_2ET )
& ( ( V0t
| c_2Ebool_2ET )
<=> c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
| V0t )
<=> V0t )
& ( ( V0t
| c_2Ebool_2EF )
<=> V0t )
& ( ( V0t
| V0t )
<=> V0t ) ) ).
thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t: $o] :
( ( ( c_2Ebool_2ET
=> V0t )
<=> V0t )
& ( ( V0t
=> c_2Ebool_2ET )
<=> c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> V0t )
<=> c_2Ebool_2ET )
& ( ( V0t
=> V0t )
<=> c_2Ebool_2ET )
& ( ( V0t
=> c_2Ebool_2EF )
<=> ( (~) @ V0t ) ) ) ).
thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
( ! [V0t: $o] :
( ( (~) @ ( (~) @ V0t ) )
<=> V0t )
& ( ( (~) @ c_2Ebool_2ET )
<=> c_2Ebool_2EF )
& ( ( (~) @ c_2Ebool_2EF )
<=> c_2Ebool_2ET ) ) ).
thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: $tType,V0x: A_27a] :
( ( V0x = V0x )
<=> c_2Ebool_2ET ) ).
thf(thm_2Ebool_2EEQ__SYM__EQ,axiom,
! [A_27a: $tType,V0x: A_27a,V1y: A_27a] :
( ( V0x = V1y )
<=> ( V1y = V0x ) ) ).
thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t: $o] :
( ( ( c_2Ebool_2ET = V0t )
<=> V0t )
& ( ( V0t = c_2Ebool_2ET )
<=> V0t )
& ( ( c_2Ebool_2EF = V0t )
<=> ( (~) @ V0t ) )
& ( ( V0t = c_2Ebool_2EF )
<=> ( (~) @ V0t ) ) ) ).
thf(thm_2Ebool_2ECOND__ID,axiom,
! [A_27a: $tType,V0b: $o,V1t: A_27a] :
( ( c_2Ebool_2ECOND @ A_27a @ V0b @ V1t @ V1t )
= V1t ) ).
thf(thm_2Ebool_2EDISJ__ASSOC,axiom,
! [V0A: $o,V1B: $o,V2C: $o] :
( ( V0A
| V1B
| V2C )
<=> ( V0A
| V1B
| V2C ) ) ).
thf(thm_2Ebool_2EDE__MORGAN__THM,axiom,
! [V0A: $o,V1B: $o] :
( ( ( (~)
@ ( V0A
& V1B ) )
<=> ( ( (~) @ V0A )
| ( (~) @ V1B ) ) )
& ( ( (~)
@ ( V0A
| V1B ) )
<=> ( ( (~) @ V0A )
& ( (~) @ V1B ) ) ) ) ).
thf(thm_2Ebool_2EIMP__DISJ__THM,axiom,
! [V0A: $o,V1B: $o] :
( ( V0A
=> V1B )
<=> ( ( (~) @ V0A )
| V1B ) ) ).
thf(thm_2Ebool_2EIMP__F__EQ__F,axiom,
! [V0t: $o] :
( ( V0t
=> c_2Ebool_2EF )
<=> ( V0t = c_2Ebool_2EF ) ) ).
thf(thm_2Ebool_2EAND__IMP__INTRO,axiom,
! [V0t1: $o,V1t2: $o,V2t3: $o] :
( ( V0t1
=> ( V1t2
=> V2t3 ) )
<=> ( ( V0t1
& V1t2 )
=> V2t3 ) ) ).
thf(thm_2Ebool_2EEQ__EXPAND,axiom,
! [V0t1: $o,V1t2: $o] :
( ( V0t1 = V1t2 )
<=> ( ( V0t1
& V1t2 )
| ( ( (~) @ V0t1 )
& ( (~) @ V1t2 ) ) ) ) ).
thf(thm_2Ebool_2EIMP__CONG,axiom,
! [V0x: $o,V1x_27: $o,V2y: $o,V3y_27: $o] :
( ( ( V0x = V1x_27 )
& ( V1x_27
=> ( V2y = V3y_27 ) ) )
=> ( ( V0x
=> V2y )
<=> ( V1x_27
=> V3y_27 ) ) ) ).
thf(thm_2Ebool_2ECOND__CONG,axiom,
! [A_27a: $tType,V0P: $o,V1Q: $o,V2x: A_27a,V3x_27: A_27a,V4y: A_27a,V5y_27: A_27a] :
( ( ( V0P = V1Q )
& ( V1Q
=> ( V2x = V3x_27 ) )
& ( ( (~) @ V1Q )
=> ( V4y = V5y_27 ) ) )
=> ( ( c_2Ebool_2ECOND @ A_27a @ V0P @ V2x @ V4y )
= ( c_2Ebool_2ECOND @ A_27a @ V1Q @ V3x_27 @ V5y_27 ) ) ) ).
thf(thm_2Ebool_2Ebool__case__thm,axiom,
! [A_27a: $tType] :
( ! [V0t1: A_27a,V1t2: A_27a] :
( ( c_2Ebool_2ECOND @ A_27a @ c_2Ebool_2ET @ V0t1 @ V1t2 )
= V0t1 )
& ! [V2t1: A_27a,V3t2: A_27a] :
( ( c_2Ebool_2ECOND @ A_27a @ c_2Ebool_2EF @ V2t1 @ V3t2 )
= V3t2 ) ) ).
thf(thm_2Ecombin_2EI__THM,axiom,
! [A_27a: $tType,V0x: A_27a] :
( ( c_2Ecombin_2EI @ A_27a @ V0x )
= V0x ) ).
thf(thm_2Efcp_2ECART__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0x: tyop_2Efcp_2Ecart @ A_27a @ A_27b,V1y: tyop_2Efcp_2Ecart @ A_27a @ A_27b] :
( ( V0x = V1y )
<=> ! [V2i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V2i @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
=> ( ( c_2Efcp_2Efcp__index @ A_27a @ A_27b @ V0x @ V2i )
= ( c_2Efcp_2Efcp__index @ A_27a @ A_27b @ V1y @ V2i ) ) ) ) ).
thf(thm_2Efcp_2EFCP__BETA,axiom,
! [A_27a: $tType,A_27b: $tType,V0g: tyop_2Enum_2Enum > A_27a,V1i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1i @ ( c_2Efcp_2Edimindex @ A_27b @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
=> ( ( c_2Efcp_2Efcp__index @ A_27a @ A_27b @ ( c_2Efcp_2EFCP @ A_27a @ A_27b @ V0g ) @ V1i )
= ( V0g @ V1i ) ) ) ).
thf(thm_2Elist_2ELENGTH__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1f: A_27a > A_27b] :
( ( c_2Elist_2ELENGTH @ A_27b @ ( c_2Elist_2EMAP @ A_27a @ A_27b @ V1f @ V0l ) )
= ( c_2Elist_2ELENGTH @ A_27a @ V0l ) ) ).
thf(thm_2Elist_2EEL__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2f: A_27a > A_27b] :
( ( c_2Elist_2EEL @ A_27b @ V0n @ ( c_2Elist_2EMAP @ A_27a @ A_27b @ V2f @ V1l ) )
= ( V2f @ ( c_2Elist_2EEL @ A_27a @ V0n @ V1l ) ) ) ) ).
thf(thm_2Enumeral_2Enumeral__distrib,axiom,
( ! [V0n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ c_2Enum_2E0 @ V0n )
= V0n )
& ! [V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ V1n @ c_2Enum_2E0 )
= V1n )
& ! [V2n: tyop_2Enum_2Enum,V3m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ V2n ) @ ( c_2Earithmetic_2ENUMERAL @ V3m ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Enumeral_2EiZ @ ( c_2Earithmetic_2E_2B @ V2n @ V3m ) ) ) )
& ! [V4n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ c_2Enum_2E0 @ V4n )
= c_2Enum_2E0 )
& ! [V5n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ V5n @ c_2Enum_2E0 )
= c_2Enum_2E0 )
& ! [V6n: tyop_2Enum_2Enum,V7m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ V6n ) @ ( c_2Earithmetic_2ENUMERAL @ V7m ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ V6n @ V7m ) ) )
& ! [V8n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2D @ c_2Enum_2E0 @ V8n )
= c_2Enum_2E0 )
& ! [V9n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2D @ V9n @ c_2Enum_2E0 )
= V9n )
& ! [V10n: tyop_2Enum_2Enum,V11m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ V10n ) @ ( c_2Earithmetic_2ENUMERAL @ V11m ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2D @ V10n @ V11m ) ) )
& ! [V12n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEXP @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V12n ) ) )
= c_2Enum_2E0 )
& ! [V13n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEXP @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V13n ) ) )
= c_2Enum_2E0 )
& ! [V14n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEXP @ V14n @ c_2Enum_2E0 )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
& ! [V15n: tyop_2Enum_2Enum,V16m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ V15n ) @ ( c_2Earithmetic_2ENUMERAL @ V16m ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EEXP @ V15n @ V16m ) ) )
& ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
& ! [V17n: tyop_2Enum_2Enum] :
( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ V17n ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Enum_2ESUC @ V17n ) ) )
& ( ( c_2Eprim__rec_2EPRE @ c_2Enum_2E0 )
= c_2Enum_2E0 )
& ! [V18n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2EPRE @ ( c_2Earithmetic_2ENUMERAL @ V18n ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Eprim__rec_2EPRE @ V18n ) ) )
& ! [V19n: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ V19n )
= c_2Enum_2E0 )
<=> ( V19n = c_2Earithmetic_2EZERO ) )
& ! [V20n: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0
= ( c_2Earithmetic_2ENUMERAL @ V20n ) )
<=> ( V20n = c_2Earithmetic_2EZERO ) )
& ! [V21n: tyop_2Enum_2Enum,V22m: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ V21n )
= ( c_2Earithmetic_2ENUMERAL @ V22m ) )
<=> ( V21n = V22m ) )
& ! [V23n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V23n @ c_2Enum_2E0 )
= c_2Ebool_2EF )
& ! [V24n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ V24n ) )
= ( c_2Eprim__rec_2E_3C @ c_2Earithmetic_2EZERO @ V24n ) )
& ! [V25n: tyop_2Enum_2Enum,V26m: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ V25n ) @ ( c_2Earithmetic_2ENUMERAL @ V26m ) )
= ( c_2Eprim__rec_2E_3C @ V25n @ V26m ) )
& ! [V27n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3E @ c_2Enum_2E0 @ V27n )
= c_2Ebool_2EF )
& ! [V28n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3E @ ( c_2Earithmetic_2ENUMERAL @ V28n ) @ c_2Enum_2E0 )
= ( c_2Eprim__rec_2E_3C @ c_2Earithmetic_2EZERO @ V28n ) )
& ! [V29n: tyop_2Enum_2Enum,V30m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3E @ ( c_2Earithmetic_2ENUMERAL @ V29n ) @ ( c_2Earithmetic_2ENUMERAL @ V30m ) )
= ( c_2Eprim__rec_2E_3C @ V30m @ V29n ) )
& ! [V31n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ c_2Enum_2E0 @ V31n )
= c_2Ebool_2ET )
& ! [V32n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ V32n ) @ c_2Enum_2E0 )
= ( c_2Earithmetic_2E_3C_3D @ V32n @ c_2Earithmetic_2EZERO ) )
& ! [V33n: tyop_2Enum_2Enum,V34m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ V33n ) @ ( c_2Earithmetic_2ENUMERAL @ V34m ) )
= ( c_2Earithmetic_2E_3C_3D @ V33n @ V34m ) )
& ! [V35n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3E_3D @ V35n @ c_2Enum_2E0 )
= c_2Ebool_2ET )
& ! [V36n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3E_3D @ c_2Enum_2E0 @ V36n )
<=> ( V36n = c_2Enum_2E0 ) )
& ! [V37n: tyop_2Enum_2Enum,V38m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3E_3D @ ( c_2Earithmetic_2ENUMERAL @ V37n ) @ ( c_2Earithmetic_2ENUMERAL @ V38m ) )
= ( c_2Earithmetic_2E_3C_3D @ V38m @ V37n ) )
& ! [V39n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ ( c_2Earithmetic_2ENUMERAL @ V39n ) )
= ( c_2Earithmetic_2EODD @ V39n ) )
& ! [V40n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ V40n ) )
= ( c_2Earithmetic_2EEVEN @ V40n ) )
& ( (~) @ ( c_2Earithmetic_2EODD @ c_2Enum_2E0 ) )
& ( c_2Earithmetic_2EEVEN @ c_2Enum_2E0 ) ) ).
thf(thm_2Enumeral_2Enumeral__add,axiom,
! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( ( c_2Enumeral_2EiZ @ ( c_2Earithmetic_2E_2B @ c_2Earithmetic_2EZERO @ V0n ) )
= V0n )
& ( ( c_2Enumeral_2EiZ @ ( c_2Earithmetic_2E_2B @ V0n @ c_2Earithmetic_2EZERO ) )
= V0n )
& ( ( c_2Enumeral_2EiZ @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT1 @ V0n ) @ ( c_2Earithmetic_2EBIT1 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT2 @ ( c_2Enumeral_2EiZ @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) )
& ( ( c_2Enumeral_2EiZ @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT1 @ V0n ) @ ( c_2Earithmetic_2EBIT2 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT1 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) )
& ( ( c_2Enumeral_2EiZ @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT2 @ V0n ) @ ( c_2Earithmetic_2EBIT1 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT1 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) )
& ( ( c_2Enumeral_2EiZ @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT2 @ V0n ) @ ( c_2Earithmetic_2EBIT2 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) )
& ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ c_2Earithmetic_2EZERO @ V0n ) )
= ( c_2Enum_2ESUC @ V0n ) )
& ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V0n @ c_2Earithmetic_2EZERO ) )
= ( c_2Enum_2ESUC @ V0n ) )
& ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT1 @ V0n ) @ ( c_2Earithmetic_2EBIT1 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT1 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) )
& ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT1 @ V0n ) @ ( c_2Earithmetic_2EBIT2 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) )
& ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT2 @ V0n ) @ ( c_2Earithmetic_2EBIT1 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) )
& ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT2 @ V0n ) @ ( c_2Earithmetic_2EBIT2 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT1 @ ( c_2Enumeral_2EiiSUC @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) )
& ( ( c_2Enumeral_2EiiSUC @ ( c_2Earithmetic_2E_2B @ c_2Earithmetic_2EZERO @ V0n ) )
= ( c_2Enumeral_2EiiSUC @ V0n ) )
& ( ( c_2Enumeral_2EiiSUC @ ( c_2Earithmetic_2E_2B @ V0n @ c_2Earithmetic_2EZERO ) )
= ( c_2Enumeral_2EiiSUC @ V0n ) )
& ( ( c_2Enumeral_2EiiSUC @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT1 @ V0n ) @ ( c_2Earithmetic_2EBIT1 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) )
& ( ( c_2Enumeral_2EiiSUC @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT1 @ V0n ) @ ( c_2Earithmetic_2EBIT2 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT1 @ ( c_2Enumeral_2EiiSUC @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) )
& ( ( c_2Enumeral_2EiiSUC @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT2 @ V0n ) @ ( c_2Earithmetic_2EBIT1 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT1 @ ( c_2Enumeral_2EiiSUC @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) )
& ( ( c_2Enumeral_2EiiSUC @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2EBIT2 @ V0n ) @ ( c_2Earithmetic_2EBIT2 @ V1m ) ) )
= ( c_2Earithmetic_2EBIT2 @ ( c_2Enumeral_2EiiSUC @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) ) ) ).
thf(thm_2Enumeral_2Enumeral__lte,axiom,
! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ c_2Earithmetic_2EZERO @ V0n )
= c_2Ebool_2ET )
& ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EBIT1 @ V0n ) @ c_2Earithmetic_2EZERO )
= c_2Ebool_2EF )
& ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EBIT2 @ V0n ) @ c_2Earithmetic_2EZERO )
= c_2Ebool_2EF )
& ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EBIT1 @ V0n ) @ ( c_2Earithmetic_2EBIT1 @ V1m ) )
= ( c_2Earithmetic_2E_3C_3D @ V0n @ V1m ) )
& ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EBIT1 @ V0n ) @ ( c_2Earithmetic_2EBIT2 @ V1m ) )
= ( c_2Earithmetic_2E_3C_3D @ V0n @ V1m ) )
& ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EBIT2 @ V0n ) @ ( c_2Earithmetic_2EBIT1 @ V1m ) )
<=> ( (~) @ ( c_2Earithmetic_2E_3C_3D @ V1m @ V0n ) ) )
& ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EBIT2 @ V0n ) @ ( c_2Earithmetic_2EBIT2 @ V1m ) )
= ( c_2Earithmetic_2E_3C_3D @ V0n @ V1m ) ) ) ).
thf(thm_2Esat_2ENOT__NOT,axiom,
! [V0t: $o] :
( ( (~) @ ( (~) @ V0t ) )
<=> V0t ) ).
thf(thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A: $o] :
( V0A
=> ( ( (~) @ V0A )
=> c_2Ebool_2EF ) ) ).
thf(thm_2Esat_2EOR__DUAL2,axiom,
! [V0B: $o,V1A: $o] :
( ( ( (~)
@ ( V1A
| V0B ) )
=> c_2Ebool_2EF )
<=> ( ( V1A
=> c_2Ebool_2EF )
=> ( ( (~) @ V0B )
=> c_2Ebool_2EF ) ) ) ).
thf(thm_2Esat_2EOR__DUAL3,axiom,
! [V0B: $o,V1A: $o] :
( ( ( (~)
@ ( ( (~) @ V1A )
| V0B ) )
=> c_2Ebool_2EF )
<=> ( V1A
=> ( ( (~) @ V0B )
=> c_2Ebool_2EF ) ) ) ).
thf(thm_2Esat_2EAND__INV2,axiom,
! [V0A: $o] :
( ( ( (~) @ V0A )
=> c_2Ebool_2EF )
=> ( ( V0A
=> c_2Ebool_2EF )
=> c_2Ebool_2EF ) ) ).
thf(thm_2Esat_2Edc__eq,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( V2p
<=> ( V1q = V0r ) )
<=> ( ( V2p
| V1q
| V0r )
& ( V2p
| ( (~) @ V0r )
| ( (~) @ V1q ) )
& ( V1q
| ( (~) @ V0r )
| ( (~) @ V2p ) )
& ( V0r
| ( (~) @ V1q )
| ( (~) @ V2p ) ) ) ) ).
thf(thm_2Esat_2Edc__conj,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( V2p
<=> ( V1q
& V0r ) )
<=> ( ( V2p
| ( (~) @ V1q )
| ( (~) @ V0r ) )
& ( V1q
| ( (~) @ V2p ) )
& ( V0r
| ( (~) @ V2p ) ) ) ) ).
thf(thm_2Esat_2Edc__disj,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( V2p
<=> ( V1q
| V0r ) )
<=> ( ( V2p
| ( (~) @ V1q ) )
& ( V2p
| ( (~) @ V0r ) )
& ( V1q
| V0r
| ( (~) @ V2p ) ) ) ) ).
thf(thm_2Esat_2Edc__neg,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
<=> ( (~) @ V0q ) )
<=> ( ( V1p
| V0q )
& ( ( (~) @ V0q )
| ( (~) @ V1p ) ) ) ) ).
thf(thm_2Ewords_2Eword__1comp__def,axiom,
! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
( ( c_2Ewords_2Eword__1comp @ A_27a @ V0w )
= ( c_2Efcp_2EFCP @ $o @ A_27a
@ ^ [V1i: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2Efcp_2Efcp__index @ $o @ A_27a @ V0w @ V1i ) ) ) ) ).
thf(thm_2Ewords_2EDIMINDEX__GT__0,axiom,
! [A_27a: $tType] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
thf(thm_2Ebitstring_2Eword__1comp__v2w,conjecture,
! [A_27a: $tType,V0v: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__1comp @ A_27a @ ( c_2Ebitstring_2Ev2w @ A_27a @ V0v ) )
= ( c_2Ebitstring_2Ev2w @ A_27a @ ( c_2Ebitstring_2Ebnot @ ( c_2Ebitstring_2Efixwidth @ ( c_2Efcp_2Edimindex @ A_27a @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0v ) ) ) ) ).
%------------------------------------------------------------------------------