TPTP Problem File: ITP007_3.p
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- Solve Problem
%------------------------------------------------------------------------------
% 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 : 133 ( 25 unt; 45 typ; 0 def)
% Number of atoms : 320 ( 79 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 286 ( 54 ~; 47 |; 54 &)
% ( 74 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 46 ( 22 >; 24 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 43 ( 43 usr; 6 con; 0-7 aty)
% Number of variables : 360 ( 301 !; 6 ?; 360 :)
% ( 53 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Eoption_2ENONE_2E0,type,
c_2Eoption_2ENONE_2E0:
!>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).
tff(c_2Eoption_2EOPTION__MAP_2E0,type,
c_2Eoption_2EOPTION__MAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))) ).
tff(c_2Eoption_2EOPTION__MAP_2E2,type,
c_2Eoption_2EOPTION__MAP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Eoption_2Eoption(A_27a) ) > tyop_2Eoption_2Eoption(A_27b) ) ).
tff(c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0,type,
c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))))) ).
tff(c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3,type,
c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,A_27c) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))) ) > tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)) ) ).
tff(c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4,type,
c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,A_27c) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))) * A_27c ) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2EpatternMatches_2EPMATCH__ROW_2E0,type,
c_2EpatternMatches_2EPMATCH__ROW_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))))) ).
tff(c_2EpatternMatches_2EPMATCH__ROW_2E3,type,
c_2EpatternMatches_2EPMATCH__ROW_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,A_27c) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)) ) ).
tff(c_2EpatternMatches_2EPMATCH__ROW_2E4,type,
c_2EpatternMatches_2EPMATCH__ROW_2E4:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,A_27c) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) * A_27c ) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2EpatternMatches_2EPMATCH__ROW__COND_2E0,type,
c_2EpatternMatches_2EPMATCH__ROW__COND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2EpatternMatches_2EPMATCH__ROW__COND_2E4,type,
c_2EpatternMatches_2EPMATCH__ROW__COND_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27b * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Eoption_2Eoption__CASE_2E0,type,
c_2Eoption_2Eoption__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))) ).
tff(c_2Eoption_2Eoption__CASE_2E3,type,
c_2Eoption_2Eoption__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > A_27b ) ).
tff(c_2Eoption_2Esome_2E0,type,
c_2Eoption_2Esome_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2Eoption_2Esome_2E1,type,
c_2Eoption_2Esome_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Emin_2E_40_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Emin_2E_40_2E0(A_27a),X0_2E0) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Eoption_2Eoption(A_27a)] : c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Eoption_2Eoption(A_27a)] : c_2Eoption_2EOPTION__MAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Eoption_2Eoption(A_27b)] : c_2Eoption_2EOPTION__MAP_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq3_2Ec_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))] : c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3(A_27d,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)))),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0(A_27d,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq4_2Ec_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X3_2E0: A_27c] : c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27c,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)))),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ).
tff(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X3_2E0: A_27c] : c_2EpatternMatches_2EPMATCH__ROW_2E4(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27c,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)))),c_2EpatternMatches_2EPMATCH__ROW_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ).
tff(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] : c_2EpatternMatches_2EPMATCH__ROW_2E3(A_27d,A_27c,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))),c_2EpatternMatches_2EPMATCH__ROW_2E0(A_27d,A_27c,A_27a),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] : c_2EpatternMatches_2EPMATCH__ROW_2E3(A_27d,A_27c,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d))),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)))),c_2EpatternMatches_2EPMATCH__ROW_2E0(A_27d,A_27c,A_27b),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW__COND_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: A_27b,X3_2E0: A_27a] : c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2EpatternMatches_2EPMATCH__ROW__COND_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ).
tff(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW__COND_2E4_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: A_27c,X3_2E0: A_27b] : c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2EpatternMatches_2EPMATCH__ROW__COND_2E0(A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : c_2Eoption_2ESOME_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b] : c_2Eoption_2ESOME_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E0(A_27b),X0_2E0) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : c_2Eoption_2Eoption__CASE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),c_2Eoption_2Eoption__CASE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27b),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))] : c_2Eoption_2Eoption__CASE_2E3(A_27b,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2Eoption__CASE_2E0(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Eoption_2Esome_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Eoption_2Esome_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Esome_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Ebool_2EBOOL__CASES__AX,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Ebool_2ETRUTH,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
=> p(V1t2_2E0) )
=> ( ( p(V1t2_2E0)
=> p(V0t1_2E0) )
=> ( V0t1_2E0 = V1t2_2E0 ) ) ) ).
tff(thm_2Ebool_2EFALSITY,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2EF_2E0)
=> p(V0t_2E0) ) ).
tff(thm_2Ebool_2EEXCLUDED__MIDDLE,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( p(V0t_2E0)
| ~ p(V0t_2E0) ) ).
tff(thm_2Ebool_2EFORALL__SIMP,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Ebool] :
( ! [V1x_2E0: A_27a] : p(V0t_2E0)
<=> p(V0t_2E0) ) ).
tff(thm_2Ebool_2EIMP__F,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t_2E0)
=> p(c_2Ebool_2EF_2E0) )
=> ~ p(V0t_2E0) ) ).
tff(thm_2Ebool_2EF__IMP,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ~ p(V0t_2E0)
=> ( p(V0t_2E0)
=> p(c_2Ebool_2EF_2E0) ) ) ).
tff(thm_2Ebool_2EAND__CLAUSES,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( ( p(c_2Ebool_2ET_2E0)
& p(V0t_2E0) )
<=> p(V0t_2E0) )
& ( ( p(V0t_2E0)
& p(c_2Ebool_2ET_2E0) )
<=> p(V0t_2E0) )
& ( ( p(c_2Ebool_2EF_2E0)
& p(V0t_2E0) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ( p(V0t_2E0)
& p(c_2Ebool_2EF_2E0) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ( p(V0t_2E0)
& p(V0t_2E0) )
<=> p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2EOR__CLAUSES,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( ( p(c_2Ebool_2ET_2E0)
| p(V0t_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(V0t_2E0)
| p(c_2Ebool_2ET_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(c_2Ebool_2EF_2E0)
| p(V0t_2E0) )
<=> p(V0t_2E0) )
& ( ( p(V0t_2E0)
| p(c_2Ebool_2EF_2E0) )
<=> p(V0t_2E0) )
& ( ( p(V0t_2E0)
| p(V0t_2E0) )
<=> p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( ( p(c_2Ebool_2ET_2E0)
=> p(V0t_2E0) )
<=> p(V0t_2E0) )
& ( ( p(V0t_2E0)
=> p(c_2Ebool_2ET_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(c_2Ebool_2EF_2E0)
=> p(V0t_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(V0t_2E0)
=> p(V0t_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(V0t_2E0)
=> p(c_2Ebool_2EF_2E0) )
<=> ~ p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2ENOT__CLAUSES,axiom,
( ! [V0t_2E0: tyop_2Emin_2Ebool] :
( ~ ~ p(V0t_2E0)
<=> p(V0t_2E0) )
& ( ~ p(c_2Ebool_2ET_2E0)
<=> p(c_2Ebool_2EF_2E0) )
& ( ~ p(c_2Ebool_2EF_2E0)
<=> p(c_2Ebool_2ET_2E0) ) ) ).
tff(thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] :
( ( V0x_2E0 = V0x_2E0 )
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2Ebool_2EEQ__SYM__EQ,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
( ( V0x_2E0 = V1y_2E0 )
<=> ( V1y_2E0 = V0x_2E0 ) ) ).
tff(thm_2Ebool_2EFUN__EQ__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( V0f_2E0 = V1g_2E0 )
<=> ! [V2x_2E0: A_27a] : app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) ) ).
tff(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = V0t_2E0 )
<=> p(V0t_2E0) )
& ( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
<=> p(V0t_2E0) )
& ( ( c_2Ebool_2EF_2E0 = V0t_2E0 )
<=> ~ p(V0t_2E0) )
& ( ( V0t_2E0 = c_2Ebool_2EF_2E0 )
<=> ~ p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2ESELECT__ELIM__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
& ! [V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,c_2Emin_2E_40_2E1(A_27a,V0P_2E0))) ) ).
tff(thm_2Ebool_2ENOT__FORALL__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0))
<=> ? [V2x_2E0: A_27a] : ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) ) ).
tff(thm_2Ebool_2ENOT__EXISTS__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0))
<=> ! [V2x_2E0: A_27a] : ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) ) ).
tff(thm_2Ebool_2EDISJ__ASSOC,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool,V2C_2E0: tyop_2Emin_2Ebool] :
( ( p(V0A_2E0)
| p(V1B_2E0)
| p(V2C_2E0) )
<=> ( p(V0A_2E0)
| p(V1B_2E0)
| p(V2C_2E0) ) ) ).
tff(thm_2Ebool_2EDISJ__SYM,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool] :
( ( p(V0A_2E0)
| p(V1B_2E0) )
<=> ( p(V1B_2E0)
| p(V0A_2E0) ) ) ).
tff(thm_2Ebool_2EDISJ__COMM,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool] :
( ( p(V0A_2E0)
| p(V1B_2E0) )
<=> ( p(V1B_2E0)
| p(V0A_2E0) ) ) ).
tff(thm_2Ebool_2EDE__MORGAN__THM,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool] :
( ( ~ ( p(V0A_2E0)
& p(V1B_2E0) )
<=> ( ~ p(V0A_2E0)
| ~ p(V1B_2E0) ) )
& ( ~ ( p(V0A_2E0)
| p(V1B_2E0) )
<=> ( ~ p(V0A_2E0)
& ~ p(V1B_2E0) ) ) ) ).
tff(thm_2Ebool_2EIMP__DISJ__THM,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool] :
( ( p(V0A_2E0)
=> p(V1B_2E0) )
<=> ( ~ p(V0A_2E0)
| p(V1B_2E0) ) ) ).
tff(thm_2Ebool_2EAND__IMP__INTRO,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool,V2t3_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
=> ( p(V1t2_2E0)
=> p(V2t3_2E0) ) )
<=> ( ( p(V0t1_2E0)
& p(V1t2_2E0) )
=> p(V2t3_2E0) ) ) ).
tff(thm_2Ebool_2EIMP__CONG,axiom,
! [V0x_2E0: tyop_2Emin_2Ebool,V1x_27_2E0: tyop_2Emin_2Ebool,V2y_2E0: tyop_2Emin_2Ebool,V3y_27_2E0: tyop_2Emin_2Ebool] :
( ( ( V0x_2E0 = V1x_27_2E0 )
& ( p(V1x_27_2E0)
=> ( V2y_2E0 = V3y_27_2E0 ) ) )
=> ( ( p(V0x_2E0)
=> p(V2y_2E0) )
<=> ( p(V1x_27_2E0)
=> p(V3y_27_2E0) ) ) ) ).
tff(thm_2Ebool_2EAND__CONG,axiom,
! [V0P_2E0: tyop_2Emin_2Ebool,V1P_27_2E0: tyop_2Emin_2Ebool,V2Q_2E0: tyop_2Emin_2Ebool,V3Q_27_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V2Q_2E0)
=> ( V0P_2E0 = V1P_27_2E0 ) )
& ( p(V1P_27_2E0)
=> ( V2Q_2E0 = V3Q_27_2E0 ) ) )
=> ( ( p(V0P_2E0)
& p(V2Q_2E0) )
<=> ( p(V1P_27_2E0)
& p(V3Q_27_2E0) ) ) ) ).
tff(thm_2Ebool_2EUNWIND__FORALL__THM2,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1v_2E0: A_27a] :
( ! [V2x_2E0: A_27a] :
( ( V2x_2E0 = V1v_2E0 )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V2x_2E0)) )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1v_2E0)) ) ).
tff(thm_2Eoption_2Eoption__nchotomy,axiom,
! [A_27a: $tType,V0opt_2E0: tyop_2Eoption_2Eoption(A_27a)] :
( ( V0opt_2E0 = c_2Eoption_2ENONE_2E0(A_27a) )
| ? [V1x_2E0: A_27a] : V0opt_2E0 = c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0) ) ).
tff(thm_2Eoption_2Eoption__case__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0v_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : c_2Eoption_2Eoption__CASE_2E3(A_27a,A_27b,c_2Eoption_2ENONE_2E0(A_27a),V0v_2E0,V1f_2E0) = V0v_2E0
& ! [V2x_2E0: A_27a,V3v_2E0: A_27b,V4f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : c_2Eoption_2Eoption__CASE_2E3(A_27a,A_27b,c_2Eoption_2ESOME_2E1(A_27a,V2x_2E0),V3v_2E0,V4f_2E0) = app_2E2(A_27a,A_27b,V4f_2E0,V2x_2E0) ) ).
tff(thm_2Eoption_2ESOME__11,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
( ( c_2Eoption_2ESOME_2E1(A_27a,V0x_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V1y_2E0) )
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Eoption_2EOPTION__MAP__DEF,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: A_27a] : c_2Eoption_2EOPTION__MAP_2E2(A_27a,A_27b,V0f_2E0,c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0)) = c_2Eoption_2ESOME_2E1(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0))
& ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : c_2Eoption_2EOPTION__MAP_2E2(A_27a,A_27b,V2f_2E0,c_2Eoption_2ENONE_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27b) ) ).
tff(thm_2Eoption_2EIF__EQUALS__OPTION,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2P_2E0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),V2P_2E0,c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0),c_2Eoption_2ENONE_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27a) )
<=> ~ p(V2P_2E0) )
& ( ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),V2P_2E0,c_2Eoption_2ENONE_2E0(A_27a),c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0)) = c_2Eoption_2ENONE_2E0(A_27a) )
<=> p(V2P_2E0) )
& ( ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),V2P_2E0,c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0),c_2Eoption_2ENONE_2E0(A_27a)) = c_2Eoption_2ESOME_2E1(A_27a,V0y_2E0) )
<=> ( p(V2P_2E0)
& ( V1x_2E0 = V0y_2E0 ) ) )
& ( ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),V2P_2E0,c_2Eoption_2ENONE_2E0(A_27a),c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V0y_2E0) )
<=> ( ~ p(V2P_2E0)
& ( V1x_2E0 = V0y_2E0 ) ) ) ) ).
tff(thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Eoption_2Eoption(A_27b),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( ( ( c_2Eoption_2EOPTION__MAP_2E2(A_27b,A_27a,V1f_2E0,V0x_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
<=> ( V0x_2E0 = c_2Eoption_2ENONE_2E0(A_27b) ) )
& ( ( c_2Eoption_2ENONE_2E0(A_27a) = c_2Eoption_2EOPTION__MAP_2E2(A_27b,A_27a,V1f_2E0,V0x_2E0) )
<=> ( V0x_2E0 = c_2Eoption_2ENONE_2E0(A_27b) ) ) ) ).
tff(thm_2Eoption_2Esome__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0P_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0)) )
=> ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0P_2E0),V2x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Eoption_2Esome_2E1(A_27a,V0P_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0P_2E0),c_2Eoption_2ESOME_2E1(A_27a,c_2Emin_2E_40_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0P_2E0))),c_2Eoption_2ENONE_2E0(A_27a)) ) ) ).
tff(thm_2EpatternMatches_2EPMATCH__ROW__COND__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0pat_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1guard_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2inp_2E0: A_27b,V3v_2E0: A_27a] :
( p(c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(A_27a,A_27b,V0pat_2E0,V1guard_2E0,V2inp_2E0,V3v_2E0))
<=> ( ( app_2E2(A_27a,A_27b,V0pat_2E0,V3v_2E0) = V2inp_2E0 )
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1guard_2E0,V3v_2E0)) ) ) ).
tff(thm_2EpatternMatches_2EPMATCH__ROW__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))] :
( ! [V0pat_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1guard_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3i_2E0: A_27c,V4v_2E0: A_27b] : app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0pat_2E0),V1guard_2E0),V3i_2E0),V4v_2E0) = c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(A_27b,A_27c,V0pat_2E0,V1guard_2E0,V3i_2E0,V4v_2E0)
=> ! [V0pat_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1guard_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2rhs_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V3i_2E0: A_27c] : c_2EpatternMatches_2EPMATCH__ROW_2E4(A_27a,A_27b,A_27c,V0pat_2E0,V1guard_2E0,V2rhs_2E0,V3i_2E0) = c_2Eoption_2EOPTION__MAP_2E2(A_27b,A_27a,V2rhs_2E0,c_2Eoption_2Esome_2E1(A_27b,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0pat_2E0),V1guard_2E0),V3i_2E0))) ) ).
tff(thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))] :
( ! [V2row_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V5x_2E0: A_27b] : app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),F1_2E0,V2row_2E0),V5x_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2row_2E0,V5x_2E0),V5x_2E0)
=> ( ! [V0p_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3v_2E0: A_27c,V4x_2E0: A_27b] : app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0p_2E0),V1g_2E0),V3v_2E0),V4x_2E0) = c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(A_27b,A_27c,V0p_2E0,V1g_2E0,V3v_2E0,V4x_2E0)
=> ! [V0p_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2row_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V3v_2E0: A_27c] : c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4(A_27a,A_27b,A_27c,V0p_2E0,V1g_2E0,V2row_2E0,V3v_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27b,tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(A_27b,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0p_2E0),V1g_2E0),V3v_2E0)),c_2Eoption_2ENONE_2E0(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),F1_2E0,V2row_2E0)) ) ) ).
tff(thm_2Esat_2ENOT__NOT,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ~ ~ p(V0t_2E0)
<=> p(V0t_2E0) ) ).
tff(thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool] :
( p(V0A_2E0)
=> ( ~ p(V0A_2E0)
=> p(c_2Ebool_2EF_2E0) ) ) ).
tff(thm_2Esat_2EOR__DUAL2,axiom,
! [V0B_2E0: tyop_2Emin_2Ebool,V1A_2E0: tyop_2Emin_2Ebool] :
( ( ~ ( p(V1A_2E0)
| p(V0B_2E0) )
=> p(c_2Ebool_2EF_2E0) )
<=> ( ( p(V1A_2E0)
=> p(c_2Ebool_2EF_2E0) )
=> ( ~ p(V0B_2E0)
=> p(c_2Ebool_2EF_2E0) ) ) ) ).
tff(thm_2Esat_2EOR__DUAL3,axiom,
! [V0B_2E0: tyop_2Emin_2Ebool,V1A_2E0: tyop_2Emin_2Ebool] :
( ( ~ ( ~ p(V1A_2E0)
| p(V0B_2E0) )
=> p(c_2Ebool_2EF_2E0) )
<=> ( p(V1A_2E0)
=> ( ~ p(V0B_2E0)
=> p(c_2Ebool_2EF_2E0) ) ) ) ).
tff(thm_2Esat_2EAND__INV2,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool] :
( ( ~ p(V0A_2E0)
=> p(c_2Ebool_2EF_2E0) )
=> ( ( p(V0A_2E0)
=> p(c_2Ebool_2EF_2E0) )
=> p(c_2Ebool_2EF_2E0) ) ) ).
tff(thm_2Esat_2Edc__eq,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( ( p(V2p_2E0)
<=> ( V1q_2E0 = V0r_2E0 ) )
<=> ( ( p(V2p_2E0)
| p(V1q_2E0)
| p(V0r_2E0) )
& ( p(V2p_2E0)
| ~ p(V0r_2E0)
| ~ p(V1q_2E0) )
& ( p(V1q_2E0)
| ~ p(V0r_2E0)
| ~ p(V2p_2E0) )
& ( p(V0r_2E0)
| ~ p(V1q_2E0)
| ~ p(V2p_2E0) ) ) ) ).
tff(thm_2Esat_2Edc__conj,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( ( p(V2p_2E0)
<=> ( p(V1q_2E0)
& p(V0r_2E0) ) )
<=> ( ( p(V2p_2E0)
| ~ p(V1q_2E0)
| ~ p(V0r_2E0) )
& ( p(V1q_2E0)
| ~ p(V2p_2E0) )
& ( p(V0r_2E0)
| ~ p(V2p_2E0) ) ) ) ).
tff(thm_2Esat_2Edc__disj,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( ( p(V2p_2E0)
<=> ( p(V1q_2E0)
| p(V0r_2E0) ) )
<=> ( ( p(V2p_2E0)
| ~ p(V1q_2E0) )
& ( p(V2p_2E0)
| ~ p(V0r_2E0) )
& ( p(V1q_2E0)
| p(V0r_2E0)
| ~ p(V2p_2E0) ) ) ) ).
tff(thm_2Esat_2Edc__imp,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1q_2E0: tyop_2Emin_2Ebool,V2p_2E0: tyop_2Emin_2Ebool] :
( ( p(V2p_2E0)
<=> ( p(V1q_2E0)
=> p(V0r_2E0) ) )
<=> ( ( p(V2p_2E0)
| p(V1q_2E0) )
& ( p(V2p_2E0)
| ~ p(V0r_2E0) )
& ( ~ p(V1q_2E0)
| p(V0r_2E0)
| ~ p(V2p_2E0) ) ) ) ).
tff(thm_2Esat_2Edc__neg,axiom,
! [V0q_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
<=> ~ p(V0q_2E0) )
<=> ( ( p(V1p_2E0)
| p(V0q_2E0) )
& ( ~ p(V0q_2E0)
| ~ p(V1p_2E0) ) ) ) ).
tff(thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW,conjecture,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))))),F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27d))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)))] :
( ! [V4p_27_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V5g_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V6r_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),V7x_2E0: A_27a] : app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))))),F0_2E0,V4p_27_2E0),V5g_27_2E0),V6r_27_2E0),V7x_2E0) = c_2EpatternMatches_2EPMATCH__ROW_2E3(A_27d,A_27c,A_27a,V4p_27_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V5g_27_2E0,V7x_2E0),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27d),V6r_27_2E0,V7x_2E0))
=> ( ! [V6r_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),V4p_27_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V10x_2E0: A_27c] : app_2E2(A_27c,A_27d,app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27d)),F3_2E0,V6r_27_2E0),V4p_27_2E0),V10x_2E0) = app_2E2(A_27c,A_27d,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27d),V6r_27_2E0,app_2E2(A_27c,A_27a,V4p_27_2E0,V10x_2E0)),V10x_2E0)
=> ( ! [V3g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4p_27_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V5g_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V9x_2E0: A_27c] :
( p(app_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F2_2E0,V3g_2E0),V4p_27_2E0),V5g_27_2E0),V9x_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3g_2E0,app_2E2(A_27c,A_27a,V4p_27_2E0,V9x_2E0)))
& p(app_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V5g_27_2E0,app_2E2(A_27c,A_27a,V4p_27_2E0,V9x_2E0)),V9x_2E0)) ) )
=> ( ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4p_27_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V8x_2E0: A_27c] : app_2E2(A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),F1_2E0,V0p_2E0),V4p_27_2E0),V8x_2E0) = app_2E2(A_27a,A_27b,V0p_2E0,app_2E2(A_27c,A_27a,V4p_27_2E0,V8x_2E0))
=> ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V1x1_2E0: A_27a,V2x2_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V0p_2E0,V1x1_2E0) = app_2E2(A_27a,A_27b,V0p_2E0,V2x2_2E0) )
=> ( V1x1_2E0 = V2x2_2E0 ) )
=> ! [V3g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4p_27_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V5g_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V6r_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d))] : c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3(A_27d,A_27a,A_27b,V0p_2E0,V3g_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))))),F0_2E0,V4p_27_2E0),V5g_27_2E0),V6r_27_2E0)) = c_2EpatternMatches_2EPMATCH__ROW_2E3(A_27d,A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),F1_2E0,V0p_2E0),V4p_27_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F2_2E0,V3g_2E0),V4p_27_2E0),V5g_27_2E0),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27d)),F3_2E0,V6r_27_2E0),V4p_27_2E0)) ) ) ) ) ) ).
%------------------------------------------------------------------------------