TPTP Problem File: ITP007^3.p
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%------------------------------------------------------------------------------
% File : ITP007^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW.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_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW.p [Gau19]
% : HL403001^3.p [TPAP]
% Status : Theorem
% Rating : 1.00 v7.5.0
% Syntax : Number of formulae : 78 ( 14 unt; 22 typ; 0 def)
% Number of atoms : 151 ( 44 equ; 52 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 541 ( 52 ~; 45 |; 52 &; 281 @)
% ( 66 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 3 con; 0-7 aty)
% Number of variables : 189 ( 9 ^; 155 !; 5 ?; 189 :)
% ( 20 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $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_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_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2Ebool_2EF,type,
c_2Ebool_2EF: $o ).
thf(c_2Eoption_2ENONE,type,
c_2Eoption_2ENONE:
!>[A_27a: $tType] : ( tyop_2Eoption_2Eoption @ A_27a ) ).
thf(c_2Eoption_2EOPTION__MAP,type,
c_2Eoption_2EOPTION__MAP:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( tyop_2Eoption_2Eoption @ A_27a ) > ( tyop_2Eoption_2Eoption @ A_27b ) ) ).
thf(c_2EpatternMatches_2EPMATCH__FLATTEN__FUN,type,
c_2EpatternMatches_2EPMATCH__FLATTEN__FUN:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27b > A_27c ) > ( A_27b > $o ) > ( A_27b > A_27b > ( tyop_2Eoption_2Eoption @ A_27a ) ) > A_27c > ( tyop_2Eoption_2Eoption @ A_27a ) ) ).
thf(c_2EpatternMatches_2EPMATCH__ROW,type,
c_2EpatternMatches_2EPMATCH__ROW:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27b > A_27c ) > ( A_27b > $o ) > ( A_27b > A_27a ) > A_27c > ( tyop_2Eoption_2Eoption @ A_27a ) ) ).
thf(c_2EpatternMatches_2EPMATCH__ROW__COND,type,
c_2EpatternMatches_2EPMATCH__ROW__COND:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( A_27a > $o ) > A_27b > A_27a > $o ) ).
thf(c_2Eoption_2ESOME,type,
c_2Eoption_2ESOME:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Eoption_2Eoption @ A_27a ) ) ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Eoption_2Eoption__CASE,type,
c_2Eoption_2Eoption__CASE:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption @ A_27a ) > A_27b > ( A_27a > A_27b ) > A_27b ) ).
thf(c_2Eoption_2Esome,type,
c_2Eoption_2Esome:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Eoption_2Eoption @ 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_2Ebool_2EBOOL__CASES__AX,axiom,
! [V0t: $o] :
( ( V0t = c_2Ebool_2ET )
| ( V0t = c_2Ebool_2EF ) ) ).
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_2EFORALL__SIMP,axiom,
! [A_27a: $tType,V0t: $o] :
( ! [V1x: A_27a] : V0t
<=> V0t ) ).
thf(thm_2Ebool_2EIMP__F,axiom,
! [V0t: $o] :
( ( V0t
=> c_2Ebool_2EF )
=> ( (~) @ V0t ) ) ).
thf(thm_2Ebool_2EF__IMP,axiom,
! [V0t: $o] :
( ( (~) @ V0t )
=> ( V0t
=> c_2Ebool_2EF ) ) ).
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_2EFUN__EQ__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b,V1g: A_27a > A_27b] :
( ( V0f = V1g )
<=> ! [V2x: A_27a] :
( ( V0f @ V2x )
= ( V1g @ V2x ) ) ) ).
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_2ESELECT__ELIM__THM,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1Q: A_27a > $o] :
( ( ? [V2x: A_27a] : ( V0P @ V2x )
& ! [V3x: A_27a] :
( ( V0P @ V3x )
=> ( V1Q @ V3x ) ) )
=> ( V1Q @ ( c_2Emin_2E_40 @ A_27a @ V0P ) ) ) ).
thf(thm_2Ebool_2ENOT__FORALL__THM,axiom,
! [A_27a: $tType,V0P: A_27a > $o] :
( ( (~)
@ ! [V1x: A_27a] : ( V0P @ V1x ) )
<=> ? [V2x: A_27a] : ( (~) @ ( V0P @ V2x ) ) ) ).
thf(thm_2Ebool_2ENOT__EXISTS__THM,axiom,
! [A_27a: $tType,V0P: A_27a > $o] :
( ( (~)
@ ? [V1x: A_27a] : ( V0P @ V1x ) )
<=> ! [V2x: A_27a] : ( (~) @ ( V0P @ V2x ) ) ) ).
thf(thm_2Ebool_2EDISJ__ASSOC,axiom,
! [V0A: $o,V1B: $o,V2C: $o] :
( ( V0A
| V1B
| V2C )
<=> ( V0A
| V1B
| V2C ) ) ).
thf(thm_2Ebool_2EDISJ__SYM,axiom,
! [V0A: $o,V1B: $o] :
( ( V0A
| V1B )
<=> ( V1B
| V0A ) ) ).
thf(thm_2Ebool_2EDISJ__COMM,axiom,
! [V0A: $o,V1B: $o] :
( ( V0A
| V1B )
<=> ( V1B
| V0A ) ) ).
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_2EAND__IMP__INTRO,axiom,
! [V0t1: $o,V1t2: $o,V2t3: $o] :
( ( V0t1
=> ( V1t2
=> V2t3 ) )
<=> ( ( V0t1
& V1t2 )
=> V2t3 ) ) ).
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_2EAND__CONG,axiom,
! [V0P: $o,V1P_27: $o,V2Q: $o,V3Q_27: $o] :
( ( ( V2Q
=> ( V0P = V1P_27 ) )
& ( V1P_27
=> ( V2Q = V3Q_27 ) ) )
=> ( ( V0P
& V2Q )
<=> ( V1P_27
& V3Q_27 ) ) ) ).
thf(thm_2Ebool_2EUNWIND__FORALL__THM2,axiom,
! [A_27a: $tType,V0f: A_27a > $o,V1v: A_27a] :
( ! [V2x: A_27a] :
( ( V2x = V1v )
=> ( V0f @ V2x ) )
<=> ( V0f @ V1v ) ) ).
thf(thm_2Eoption_2Eoption__nchotomy,axiom,
! [A_27a: $tType,V0opt: tyop_2Eoption_2Eoption @ A_27a] :
( ( V0opt
= ( c_2Eoption_2ENONE @ A_27a ) )
| ? [V1x: A_27a] :
( V0opt
= ( c_2Eoption_2ESOME @ A_27a @ V1x ) ) ) ).
thf(thm_2Eoption_2Eoption__case__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0v: A_27b,V1f: A_27a > A_27b] :
( ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b @ ( c_2Eoption_2ENONE @ A_27a ) @ V0v @ V1f )
= V0v )
& ! [V2x: A_27a,V3v: A_27b,V4f: A_27a > A_27b] :
( ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b @ ( c_2Eoption_2ESOME @ A_27a @ V2x ) @ V3v @ V4f )
= ( V4f @ V2x ) ) ) ).
thf(thm_2Eoption_2ESOME__11,axiom,
! [A_27a: $tType,V0x: A_27a,V1y: A_27a] :
( ( ( c_2Eoption_2ESOME @ A_27a @ V0x )
= ( c_2Eoption_2ESOME @ A_27a @ V1y ) )
<=> ( V0x = V1y ) ) ).
thf(thm_2Eoption_2EOPTION__MAP__DEF,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f: A_27a > A_27b,V1x: A_27a] :
( ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b @ V0f @ ( c_2Eoption_2ESOME @ A_27a @ V1x ) )
= ( c_2Eoption_2ESOME @ A_27b @ ( V0f @ V1x ) ) )
& ! [V2f: A_27a > A_27b] :
( ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b @ V2f @ ( c_2Eoption_2ENONE @ A_27a ) )
= ( c_2Eoption_2ENONE @ A_27b ) ) ) ).
thf(thm_2Eoption_2EIF__EQUALS__OPTION,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: A_27a,V2P: $o] :
( ( ( ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V2P @ ( c_2Eoption_2ESOME @ A_27a @ V1x ) @ ( c_2Eoption_2ENONE @ A_27a ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
<=> ( (~) @ V2P ) )
& ( ( ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V2P @ ( c_2Eoption_2ENONE @ A_27a ) @ ( c_2Eoption_2ESOME @ A_27a @ V1x ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
<=> V2P )
& ( ( ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V2P @ ( c_2Eoption_2ESOME @ A_27a @ V1x ) @ ( c_2Eoption_2ENONE @ A_27a ) )
= ( c_2Eoption_2ESOME @ A_27a @ V0y ) )
<=> ( V2P
& ( V1x = V0y ) ) )
& ( ( ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V2P @ ( c_2Eoption_2ENONE @ A_27a ) @ ( c_2Eoption_2ESOME @ A_27a @ V1x ) )
= ( c_2Eoption_2ESOME @ A_27a @ V0y ) )
<=> ( ( (~) @ V2P )
& ( V1x = V0y ) ) ) ) ).
thf(thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways,axiom,
! [A_27a: $tType,A_27b: $tType,V0x: tyop_2Eoption_2Eoption @ A_27b,V1f: A_27b > A_27a] :
( ( ( ( c_2Eoption_2EOPTION__MAP @ A_27b @ A_27a @ V1f @ V0x )
= ( c_2Eoption_2ENONE @ A_27a ) )
<=> ( V0x
= ( c_2Eoption_2ENONE @ A_27b ) ) )
& ( ( ( c_2Eoption_2ENONE @ A_27a )
= ( c_2Eoption_2EOPTION__MAP @ A_27b @ A_27a @ V1f @ V0x ) )
<=> ( V0x
= ( c_2Eoption_2ENONE @ A_27b ) ) ) ) ).
thf(thm_2Eoption_2Esome__def,axiom,
! [A_27a: $tType,V0P: A_27a > $o] :
( ( c_2Eoption_2Esome @ A_27a @ V0P )
= ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ A_27a )
@ ( c_2Ebool_2E_3F @ A_27a
@ ^ [V1x: A_27a] : ( V0P @ V1x ) )
@ ( c_2Eoption_2ESOME @ A_27a
@ ( c_2Emin_2E_40 @ A_27a
@ ^ [V2x: A_27a] : ( V0P @ V2x ) ) )
@ ( c_2Eoption_2ENONE @ A_27a ) ) ) ).
thf(thm_2EpatternMatches_2EPMATCH__ROW__COND__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0pat: A_27a > A_27b,V1guard: A_27a > $o,V2inp: A_27b,V3v: A_27a] :
( ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27a @ A_27b @ V0pat @ V1guard @ V2inp @ V3v )
<=> ( ( ( V0pat @ V3v )
= V2inp )
& ( V1guard @ V3v ) ) ) ).
thf(thm_2EpatternMatches_2EPMATCH__ROW__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0pat: A_27b > A_27c,V1guard: A_27b > $o,V2rhs: A_27b > A_27a,V3i: A_27c] :
( ( c_2EpatternMatches_2EPMATCH__ROW @ A_27a @ A_27b @ A_27c @ V0pat @ V1guard @ V2rhs @ V3i )
= ( c_2Eoption_2EOPTION__MAP @ A_27b @ A_27a @ V2rhs
@ ( c_2Eoption_2Esome @ A_27b
@ ^ [V4v: A_27b] : ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27b @ A_27c @ V0pat @ V1guard @ V3i @ V4v ) ) ) ) ).
thf(thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0p: A_27b > A_27c,V1g: A_27b > $o,V2row: A_27b > A_27b > ( tyop_2Eoption_2Eoption @ A_27a ),V3v: A_27c] :
( ( c_2EpatternMatches_2EPMATCH__FLATTEN__FUN @ A_27a @ A_27b @ A_27c @ V0p @ V1g @ V2row @ V3v )
= ( c_2Eoption_2Eoption__CASE @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a )
@ ( c_2Eoption_2Esome @ A_27b
@ ^ [V4x: A_27b] : ( c_2EpatternMatches_2EPMATCH__ROW__COND @ A_27b @ A_27c @ V0p @ V1g @ V3v @ V4x ) )
@ ( c_2Eoption_2ENONE @ A_27a )
@ ^ [V5x: A_27b] : ( V2row @ V5x @ V5x ) ) ) ).
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__imp,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_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW,conjecture,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0p: A_27a > A_27b] :
( ! [V1x1: A_27a,V2x2: A_27a] :
( ( ( V0p @ V1x1 )
= ( V0p @ V2x2 ) )
=> ( V1x1 = V2x2 ) )
=> ! [V3g: A_27a > $o,V4p_27: A_27c > A_27a,V5g_27: A_27a > A_27c > $o,V6r_27: A_27a > A_27c > A_27d] :
( ( c_2EpatternMatches_2EPMATCH__FLATTEN__FUN @ A_27d @ A_27a @ A_27b @ V0p @ V3g
@ ^ [V7x: A_27a] : ( c_2EpatternMatches_2EPMATCH__ROW @ A_27d @ A_27c @ A_27a @ V4p_27 @ ( V5g_27 @ V7x ) @ ( V6r_27 @ V7x ) ) )
= ( c_2EpatternMatches_2EPMATCH__ROW @ A_27d @ A_27c @ A_27b
@ ^ [V8x: A_27c] : ( V0p @ ( V4p_27 @ V8x ) )
@ ^ [V9x: A_27c] : ( c_2Ebool_2E_2F_5C @ ( V3g @ ( V4p_27 @ V9x ) ) @ ( V5g_27 @ ( V4p_27 @ V9x ) @ V9x ) )
@ ^ [V10x: A_27c] : ( V6r_27 @ ( V4p_27 @ V10x ) @ V10x ) ) ) ) ).
%------------------------------------------------------------------------------