ITP001 Axioms: ITP003_7.ax
%------------------------------------------------------------------------------
% File : ITP003_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : bool.ax [Gau19]
% : HL4003_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 300 ( 65 unt; 63 typ; 0 def)
% Number of atoms : 790 ( 211 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 603 ( 50 ~; 65 |; 138 &)
% ( 148 <=>; 202 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 50 ( 30 >; 20 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 60 ( 60 usr; 7 con; 0-5 aty)
% Number of variables : 995 ( 871 !; 59 ?; 995 :)
% ( 65 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Emin_2Eind,type,
tyop_2Emin_2Eind: $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_2E1,type,
c_2Emin_2E_3D_2E1:
!>[A_27a: $tType] : ( 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_2Ebool_2E_3F_21_2E0,type,
c_2Ebool_2E_3F_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_21_2E1,type,
c_2Ebool_2E_3F_21_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_2EARB_2E0,type,
c_2Ebool_2EARB_2E0:
!>[A_27a: $tType] : A_27a ).
tff(c_2Ebool_2EBOUNDED_2E0,type,
c_2Ebool_2EBOUNDED_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EBOUNDED_2E1,type,
c_2Ebool_2EBOUNDED_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
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_2EDATATYPE_2E0,type,
c_2Ebool_2EDATATYPE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EDATATYPE_2E1,type,
c_2Ebool_2EDATATYPE_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ELET_2E0,type,
c_2Ebool_2ELET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ebool_2ELET_2E2,type,
c_2Ebool_2ELET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Ebool_2EONE__ONE_2E0,type,
c_2Ebool_2EONE__ONE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EONE__ONE_2E1,type,
c_2Ebool_2EONE__ONE_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2EONTO_2E0,type,
c_2Ebool_2EONTO_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EONTO_2E1,type,
c_2Ebool_2EONTO_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ERES__ABSTRACT_2E0,type,
c_2Ebool_2ERES__ABSTRACT_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Ebool_2ERES__ABSTRACT_2E2,type,
c_2Ebool_2ERES__ABSTRACT_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Ebool_2ERES__ABSTRACT_2E3,type,
c_2Ebool_2ERES__ABSTRACT_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Ebool_2ERES__EXISTS_2E0,type,
c_2Ebool_2ERES__EXISTS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ERES__EXISTS_2E2,type,
c_2Ebool_2ERES__EXISTS_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ERES__EXISTS__UNIQUE_2E0,type,
c_2Ebool_2ERES__EXISTS__UNIQUE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ERES__EXISTS__UNIQUE_2E2,type,
c_2Ebool_2ERES__EXISTS__UNIQUE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ERES__FORALL_2E0,type,
c_2Ebool_2ERES__FORALL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ERES__FORALL_2E2,type,
c_2Ebool_2ERES__FORALL_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ERES__SELECT_2E0,type,
c_2Ebool_2ERES__SELECT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a)) ).
tff(c_2Ebool_2ERES__SELECT_2E2,type,
c_2Ebool_2ERES__SELECT_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > A_27a ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > 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_2Ebool_2Eitself__case_2E0,type,
c_2Ebool_2Eitself__case_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)) ).
tff(c_2Ebool_2Eitself__case_2E2,type,
c_2Ebool_2Eitself__case_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Ebool_2Eitself(A_27a) * A_27b ) > A_27b ) ).
tff(c_2Ebool_2Eliteral__case_2E0,type,
c_2Ebool_2Eliteral__case_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ebool_2Eliteral__case_2E2,type,
c_2Ebool_2Eliteral__case_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Ebool_2Ethe__value_2E0,type,
c_2Ebool_2Ethe__value_2E0:
!>[A_27a: $tType] : tyop_2Ebool_2Eitself(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(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Emin_2E_3D_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_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_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_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(arityeq1_2Ec_2Ebool_2EBOUNDED_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EBOUNDED_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2EBOUNDED_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ebool_2ECOND_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27b,X2_2E0: A_27b] : ( c_2Ebool_2ECOND_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ebool_2ECOND_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Ebool_2EDATATYPE_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_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: A_27a] : ( c_2Ebool_2ELET_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ELET_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: A_27a] : ( c_2Ebool_2ELET_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),c_2Ebool_2ELET_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Ebool_2ELET_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = 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),c_2Ebool_2ELET_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0: A_27a] : ( c_2Ebool_2ELET_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ebool_2ELET_2E0(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ebool_2EONE__ONE_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind)] : ( c_2Ebool_2EONE__ONE_2E1(tyop_2Emin_2Eind,tyop_2Emin_2Eind,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E0(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EONTO_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ebool_2EONTO_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EONTO_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind)] : ( c_2Ebool_2EONTO_2E1(tyop_2Emin_2Eind,tyop_2Emin_2Eind,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E0(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ERES__ABSTRACT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ebool_2ERES__ABSTRACT_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ebool_2ERES__ABSTRACT_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ERES__ABSTRACT_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0: A_27a] : ( c_2Ebool_2ERES__ABSTRACT_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ebool_2ERES__ABSTRACT_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ERES__EXISTS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2ERES__EXISTS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ERES__EXISTS__UNIQUE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2ERES__EXISTS__UNIQUE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ERES__FORALL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2ERES__FORALL_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ERES__SELECT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ERES__SELECT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Ebool_2ERES__SELECT_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebool_2Eitself_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a)] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(A_27a,tyop_2Ebool_2Eitself(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(A_27a,tyop_2Ebool_2Eitself(A_27a)),X0_2E0),X1_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(arityeq2_2Ec_2Ebool_2Eitself__case_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27a),X1_2E0: A_27b] : ( c_2Ebool_2Eitself__case_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27b,app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Efun(A_27b,A_27b),c_2Ebool_2Eitself__case_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2Eliteral__case_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: A_27a] : ( c_2Ebool_2Eliteral__case_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2Eliteral__case_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: A_27a] : ( c_2Ebool_2Eliteral__case_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),c_2Ebool_2Eliteral__case_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0: A_27a] : ( c_2Ebool_2Eliteral__case_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ebool_2Eliteral__case_2E0(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),X1_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_2EETA__AX,axiom,
! [A_27a: $tType,A_27b: $tType,V0M_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0M_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,V0M_2E0,V1x_2E0) ) ).
tff(thm_2Ebool_2ESELECT__AX,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))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Emin_2E_40_2E1(A_27a,V0P_2E0))) ) ).
tff(thm_2Ebool_2EINFINITY__AX,axiom,
? [V0f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind)] :
( p(c_2Ebool_2EONE__ONE_2E1(tyop_2Emin_2Eind,tyop_2Emin_2Eind,V0f_2E0))
& ~ p(c_2Ebool_2EONTO_2E1(tyop_2Emin_2Eind,tyop_2Emin_2Eind,V0f_2E0)) ) ).
tff(thm_2Ebool_2ET__DEF,axiom,
( p(c_2Ebool_2ET_2E0)
<=> ! [V0x_2E0: tyop_2Emin_2Ebool] : ( V0x_2E0 = V0x_2E0 ) ) ).
tff(thm_2Ebool_2EFORALL__DEF,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0x_2E0))
<=> ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,V0x_2E0,V1x_2E0) = c_2Ebool_2ET_2E0 ) ) ).
tff(thm_2Ebool_2EEXISTS__DEF,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,V0x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0x_2E0,c_2Emin_2E_40_2E1(A_27a,V0x_2E0)) ) ).
tff(thm_2Ebool_2EAND__DEF,axiom,
! [V0x_2E0: tyop_2Emin_2Ebool,V1x_27_2E0: tyop_2Emin_2Ebool] :
( ( p(V0x_2E0)
& p(V1x_27_2E0) )
<=> ! [V2t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0x_2E0)
=> ( p(V1x_27_2E0)
=> p(V2t_2E0) ) )
=> p(V2t_2E0) ) ) ).
tff(thm_2Ebool_2EOR__DEF,axiom,
! [V0x_2E0: tyop_2Emin_2Ebool,V1x_27_2E0: tyop_2Emin_2Ebool] :
( ( p(V0x_2E0)
| p(V1x_27_2E0) )
<=> ! [V2t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0x_2E0)
=> p(V2t_2E0) )
=> ( ( p(V1x_27_2E0)
=> p(V2t_2E0) )
=> p(V2t_2E0) ) ) ) ).
tff(thm_2Ebool_2EF__DEF,axiom,
( p(c_2Ebool_2EF_2E0)
<=> ! [V0t_2E0: tyop_2Emin_2Ebool] : p(V0t_2E0) ) ).
tff(thm_2Ebool_2ENOT__DEF,axiom,
! [V0x_2E0: tyop_2Emin_2Ebool] :
( ~ p(V0x_2E0)
<=> ( p(V0x_2E0)
=> p(c_2Ebool_2EF_2E0) ) ) ).
tff(thm_2Ebool_2EEXISTS__UNIQUE__DEF,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_21_2E1(A_27a,V0x_2E0))
<=> ( p(c_2Ebool_2E_3F_2E1(A_27a,V0x_2E0))
& ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0x_2E0,V1x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0x_2E0,V2y_2E0)) )
=> ( V1x_2E0 = V2y_2E0 ) ) ) ) ).
tff(thm_2Ebool_2ELET__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_27_2E0: A_27a] : ( c_2Ebool_2ELET_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) = app_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) ) ).
tff(thm_2Ebool_2ECOND__DEF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V0x_2E0: tyop_2Emin_2Ebool,V1x_27_2E0: A_27a,V2x_27_27_2E0: A_27a,V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V1x_27_2E0),V2x_27_27_2E0),V3x_2E0))
<=> ( ( ( V0x_2E0 = c_2Ebool_2ET_2E0 )
=> ( V3x_2E0 = V1x_27_2E0 ) )
& ( ( V0x_2E0 = c_2Ebool_2EF_2E0 )
=> ( V3x_2E0 = V2x_27_27_2E0 ) ) ) )
=> ! [V0x_2E0: tyop_2Emin_2Ebool,V1x_27_2E0: A_27a,V2x_27_27_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,V0x_2E0,V1x_27_2E0,V2x_27_27_2E0) = c_2Emin_2E_40_2E1(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V1x_27_2E0),V2x_27_27_2E0)) ) ) ).
tff(thm_2Ebool_2EONE__ONE__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Ebool_2EONE__ONE_2E1(A_27a,A_27b,V0x_2E0))
<=> ! [V1x1_2E0: A_27a,V2x2_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V0x_2E0,V1x1_2E0) = app_2E2(A_27a,A_27b,V0x_2E0,V2x2_2E0) )
=> ( V1x1_2E0 = V2x2_2E0 ) ) ) ).
tff(thm_2Ebool_2EONTO__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Ebool_2EONTO_2E1(A_27a,A_27b,V0x_2E0))
<=> ! [V1y_2E0: A_27b] :
? [V2x_2E0: A_27a] : ( V1y_2E0 = app_2E2(A_27a,A_27b,V0x_2E0,V2x_2E0) ) ) ).
tff(thm_2Ebool_2ETYPE__DEFINITION,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Ebool_2ETYPE__DEFINITION_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0))
<=> ( ! [V2x_27_2E0: A_27b,V3x_27_27_2E0: A_27b] :
( ( app_2E2(A_27b,A_27a,V1x_27_2E0,V2x_27_2E0) = app_2E2(A_27b,A_27a,V1x_27_2E0,V3x_27_27_2E0) )
=> ( V2x_27_2E0 = V3x_27_27_2E0 ) )
& ! [V4x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0x_2E0,V4x_2E0))
<=> ? [V5x_27_2E0: A_27b] : ( V4x_2E0 = app_2E2(A_27b,A_27a,V1x_27_2E0,V5x_27_2E0) ) ) ) ) ).
tff(thm_2Ebool_2Eliteral__case__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_27_2E0: A_27a] : ( c_2Ebool_2Eliteral__case_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) = app_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) ) ).
tff(thm_2Ebool_2EIN__DEF,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1x_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1x_27_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V1x_27_2E0,V0x_2E0) ) ).
tff(thm_2Ebool_2ERES__FORALL__DEF,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2ERES__FORALL_2E2(A_27a,V0x_2E0,V1x_27_2E0))
<=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1x_27_2E0,V2x_2E0)) ) ) ).
tff(thm_2Ebool_2ERES__EXISTS__DEF,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2ERES__EXISTS_2E2(A_27a,V0x_2E0,V1x_27_2E0))
<=> ? [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1x_27_2E0,V2x_2E0)) ) ) ).
tff(thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1x_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: A_27a,V4y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V1x_27_2E0),V3x_2E0),V4y_2E0))
<=> ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1x_27_2E0,V3x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1x_27_2E0,V4y_2E0)) )
=> ( V3x_2E0 = V4y_2E0 ) ) )
=> ( ! [V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0x_2E0),V1x_27_2E0),V3x_2E0) = c_2Ebool_2ERES__FORALL_2E2(A_27a,V0x_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V1x_27_2E0),V3x_2E0)) )
=> ( ! [V1x_27_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),F0_2E0,V1x_27_2E0),V2x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V1x_27_2E0,V2x_2E0) )
=> ! [V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(A_27a,V0x_2E0,V1x_27_2E0))
<=> ( p(c_2Ebool_2ERES__EXISTS_2E2(A_27a,V0x_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1x_27_2E0)))
& p(c_2Ebool_2ERES__FORALL_2E2(A_27a,V0x_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0x_2E0),V1x_27_2E0))) ) ) ) ) ) ).
tff(thm_2Ebool_2ERES__SELECT__DEF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0x_2E0),V1x_27_2E0),V2x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1x_27_2E0,V2x_2E0)) ) )
=> ! [V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ERES__SELECT_2E2(A_27a,V0x_2E0,V1x_27_2E0) = 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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0x_2E0),V1x_27_2E0)) ) ) ).
tff(thm_2Ebool_2EBOUNDED__DEF,axiom,
! [V0x_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EBOUNDED_2E1(V0x_2E0) = c_2Ebool_2ET_2E0 ) ).
tff(thm_2Ebool_2EDATATYPE__TAG__DEF,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Ebool_2EDATATYPE_2E1(A_27a,V0x_2E0) = c_2Ebool_2ET_2E0 ) ).
tff(thm_2Ebool_2ERES__ABSTRACT__DEF,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0p_2E0))
=> ( c_2Ebool_2ERES__ABSTRACT_2E3(A_27a,A_27b,V0p_2E0,V1m_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1m_2E0,V2x_2E0) ) )
& ! [V3p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4m1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V5m2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V6x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V3p_2E0))
=> ( app_2E2(A_27a,A_27b,V4m1_2E0,V6x_2E0) = app_2E2(A_27a,A_27b,V5m2_2E0,V6x_2E0) ) )
=> ( c_2Ebool_2ERES__ABSTRACT_2E2(A_27a,A_27b,V3p_2E0,V4m1_2E0) = c_2Ebool_2ERES__ABSTRACT_2E2(A_27a,A_27b,V3p_2E0,V5m2_2E0) ) ) ) ).
tff(thm_2Ebool_2Eitself__TY__DEF,axiom,
! [A_27a: $tType] :
? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a)] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(A_27a,tyop_2Ebool_2Eitself(A_27a),c_2Emin_2E_3D_2E1(A_27a,c_2Ebool_2EARB_2E0(A_27a)),V0rep_2E0)) ).
tff(thm_2Ebool_2Eitself__case__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0b_2E0: A_27b] : ( c_2Ebool_2Eitself__case_2E2(A_27a,A_27b,c_2Ebool_2Ethe__value_2E0(A_27a),V0b_2E0) = V0b_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_2EETA__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0M_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0M_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,V0M_2E0,V1x_2E0) ) ).
tff(thm_2Ebool_2EEXCLUDED__MIDDLE,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( p(V0t_2E0)
| ~ p(V0t_2E0) ) ).
tff(thm_2Ebool_2EBETA__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1y_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V1y_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V1y_2E0) ) ).
tff(thm_2Ebool_2ELET__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: A_27a] : ( c_2Ebool_2ELET_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) ) ).
tff(thm_2Ebool_2EFORALL__THM,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(thm_2Ebool_2EEXISTS__THM,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(thm_2Ebool_2EABS__SIMP,axiom,
! [A_27a: $tType,A_27b: $tType,V0t1_2E0: A_27a,V1t2_2E0: A_27b] : ( V0t1_2E0 = V0t1_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_2EEXISTS__SIMP,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Ebool] :
( ? [V1x_2E0: A_27a] : p(V0t_2E0)
<=> p(V0t_2E0) ) ).
tff(thm_2Ebool_2EAND__INTRO__THM,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( p(V0t1_2E0)
=> ( p(V1t2_2E0)
=> ( p(V0t1_2E0)
& p(V1t2_2E0) ) ) ) ).
tff(thm_2Ebool_2EAND1__THM,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
& p(V1t2_2E0) )
=> p(V0t1_2E0) ) ).
tff(thm_2Ebool_2EAND2__THM,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
& p(V1t2_2E0) )
=> p(V1t2_2E0) ) ).
tff(thm_2Ebool_2ECONJ__SYM,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
& p(V1t2_2E0) )
<=> ( p(V1t2_2E0)
& p(V0t1_2E0) ) ) ).
tff(thm_2Ebool_2ECONJ__COMM,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
& p(V1t2_2E0) )
<=> ( p(V1t2_2E0)
& p(V0t1_2E0) ) ) ).
tff(thm_2Ebool_2ECONJ__ASSOC,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_2EOR__INTRO__THM1,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( p(V0t1_2E0)
=> ( p(V0t1_2E0)
| p(V1t2_2E0) ) ) ).
tff(thm_2Ebool_2EOR__INTRO__THM2,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( p(V1t2_2E0)
=> ( p(V0t1_2E0)
| p(V1t2_2E0) ) ) ).
tff(thm_2Ebool_2EOR__ELIM__THM,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool,V1t1_2E0: tyop_2Emin_2Ebool,V2t2_2E0: tyop_2Emin_2Ebool] :
( ( p(V1t1_2E0)
| p(V2t2_2E0) )
=> ( ( p(V1t1_2E0)
=> p(V0t_2E0) )
=> ( ( p(V2t2_2E0)
=> 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_2ENOT__F,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ~ p(V0t_2E0)
=> ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Ebool_2ENOT__AND,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
~ ( p(V0t_2E0)
& ~ p(V0t_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_2EEQ__REFL,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( V0x_2E0 = V0x_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,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
( ( V0x_2E0 = V1y_2E0 )
=> ( V1y_2E0 = V0x_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_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_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__TRANS,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a,V2z_2E0: A_27a] :
( ( ( V0x_2E0 = V1y_2E0 )
& ( V1y_2E0 = V2z_2E0 ) )
=> ( V0x_2E0 = V2z_2E0 ) ) ).
tff(thm_2Ebool_2EBOOL__EQ__DISTINCT,axiom,
( ( c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0 )
& ( c_2Ebool_2EF_2E0 != c_2Ebool_2ET_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_2ECOND__CLAUSES,axiom,
! [A_27a: $tType,V0t1_2E0: A_27a,V1t2_2E0: A_27a] :
( ( c_2Ebool_2ECOND_2E3(A_27a,c_2Ebool_2ET_2E0,V0t1_2E0,V1t2_2E0) = V0t1_2E0 )
& ( c_2Ebool_2ECOND_2E3(A_27a,c_2Ebool_2EF_2E0,V0t1_2E0,V1t2_2E0) = V1t2_2E0 ) ) ).
tff(thm_2Ebool_2ECOND__ID,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Ebool,V1t_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,V0b_2E0,V1t_2E0,V1t_2E0) = V1t_2E0 ) ).
tff(thm_2Ebool_2ESELECT__THM,axiom,
! [A_27a: $tType,F0_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),V1x_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),F0_2E0,V0P_2E0),V1x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,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),F0_2E0,V0P_2E0))))
<=> ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) ) ) ).
tff(thm_2Ebool_2ESELECT__REFL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V0x_2E0: A_27a,V1y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0),V1y_2E0))
<=> ( V1y_2E0 = V0x_2E0 ) )
=> ! [V0x_2E0: A_27a] : ( c_2Emin_2E_40_2E1(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0)) = V0x_2E0 ) ) ).
tff(thm_2Ebool_2ESELECT__REFL__2,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V0x_2E0: A_27a,V1y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0),V1y_2E0))
<=> ( V0x_2E0 = V1y_2E0 ) )
=> ! [V0x_2E0: A_27a] : ( c_2Emin_2E_40_2E1(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0)) = V0x_2E0 ) ) ).
tff(thm_2Ebool_2ESELECT__UNIQUE,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] :
( ! [V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2y_2E0))
<=> ( V2y_2E0 = V1x_2E0 ) )
=> ( c_2Emin_2E_40_2E1(A_27a,V0P_2E0) = V1x_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_2EFORALL__AND__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))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
<=> ( ! [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
& ! [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V4x_2E0)) ) ) ).
tff(thm_2Ebool_2ELEFT__AND__FORALL__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
( ( ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
& p(V1Q_2E0) )
<=> ! [V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
& p(V1Q_2E0) ) ) ).
tff(thm_2Ebool_2ERIGHT__AND__FORALL__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(V0P_2E0)
& ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
<=> ! [V3x_2E0: A_27a] :
( p(V0P_2E0)
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) ) ).
tff(thm_2Ebool_2EEXISTS__OR__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))
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
<=> ( ? [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
| ? [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V4x_2E0)) ) ) ).
tff(thm_2Ebool_2ELEFT__OR__EXISTS__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
( ( ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
| p(V1Q_2E0) )
<=> ? [V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
| p(V1Q_2E0) ) ) ).
tff(thm_2Ebool_2ERIGHT__OR__EXISTS__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(V0P_2E0)
| ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
<=> ? [V3x_2E0: A_27a] :
( p(V0P_2E0)
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) ) ).
tff(thm_2Ebool_2EBOTH__EXISTS__AND__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Ebool] :
( ? [V2x_2E0: A_27a] :
( p(V0P_2E0)
& p(V1Q_2E0) )
<=> ( ? [V3x_2E0: A_27a] : p(V0P_2E0)
& ? [V4x_2E0: A_27a] : p(V1Q_2E0) ) ) ).
tff(thm_2Ebool_2ELEFT__EXISTS__AND__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
( ? [V2x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
& p(V1Q_2E0) )
<=> ( ? [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
& p(V1Q_2E0) ) ) ).
tff(thm_2Ebool_2ERIGHT__EXISTS__AND__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ? [V2x_2E0: A_27a] :
( p(V0P_2E0)
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
<=> ( p(V0P_2E0)
& ? [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) ) ).
tff(thm_2Ebool_2EBOTH__FORALL__OR__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Ebool] :
( ! [V2x_2E0: A_27a] :
( p(V0P_2E0)
| p(V1Q_2E0) )
<=> ( ! [V3x_2E0: A_27a] : p(V0P_2E0)
| ! [V4x_2E0: A_27a] : p(V1Q_2E0) ) ) ).
tff(thm_2Ebool_2ELEFT__FORALL__OR__THM,axiom,
! [A_27a: $tType,V0Q_2E0: tyop_2Emin_2Ebool,V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0))
| p(V0Q_2E0) )
<=> ( ! [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3x_2E0))
| p(V0Q_2E0) ) ) ).
tff(thm_2Ebool_2ERIGHT__FORALL__OR__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( p(V0P_2E0)
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
<=> ( p(V0P_2E0)
| ! [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) ) ).
tff(thm_2Ebool_2EBOTH__FORALL__IMP__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Ebool] :
( ! [V2x_2E0: A_27a] :
( p(V0P_2E0)
=> p(V1Q_2E0) )
<=> ( ? [V3x_2E0: A_27a] : p(V0P_2E0)
=> ! [V4x_2E0: A_27a] : p(V1Q_2E0) ) ) ).
tff(thm_2Ebool_2ELEFT__FORALL__IMP__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
( ! [V2x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
=> p(V1Q_2E0) )
<=> ( ? [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
=> p(V1Q_2E0) ) ) ).
tff(thm_2Ebool_2ERIGHT__FORALL__IMP__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( p(V0P_2E0)
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
<=> ( p(V0P_2E0)
=> ! [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) ) ).
tff(thm_2Ebool_2EBOTH__EXISTS__IMP__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Ebool] :
( ? [V2x_2E0: A_27a] :
( p(V0P_2E0)
=> p(V1Q_2E0) )
<=> ( ! [V3x_2E0: A_27a] : p(V0P_2E0)
=> ? [V4x_2E0: A_27a] : p(V1Q_2E0) ) ) ).
tff(thm_2Ebool_2ELEFT__EXISTS__IMP__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
( ? [V2x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
=> p(V1Q_2E0) )
<=> ( ! [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
=> p(V1Q_2E0) ) ) ).
tff(thm_2Ebool_2ERIGHT__EXISTS__IMP__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ? [V2x_2E0: A_27a] :
( p(V0P_2E0)
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
<=> ( p(V0P_2E0)
=> ? [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) ) ).
tff(thm_2Ebool_2EOR__IMP__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) ) ) ).
tff(thm_2Ebool_2ENOT__IMP,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_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_2ELEFT__AND__OVER__OR,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(V0A_2E0)
& p(V2C_2E0) ) ) ) ).
tff(thm_2Ebool_2ERIGHT__AND__OVER__OR,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool,V2C_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V1B_2E0)
| p(V2C_2E0) )
& p(V0A_2E0) )
<=> ( ( p(V1B_2E0)
& p(V0A_2E0) )
| ( p(V2C_2E0)
& p(V0A_2E0) ) ) ) ).
tff(thm_2Ebool_2ELEFT__OR__OVER__AND,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(V0A_2E0)
| p(V2C_2E0) ) ) ) ).
tff(thm_2Ebool_2ERIGHT__OR__OVER__AND,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool,V2C_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V1B_2E0)
& p(V2C_2E0) )
| p(V0A_2E0) )
<=> ( ( p(V1B_2E0)
| p(V0A_2E0) )
& ( p(V2C_2E0)
| p(V0A_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_2EDISJ__IMP__THM,axiom,
! [V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Ebool,V2R_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V0P_2E0)
| p(V1Q_2E0) )
=> p(V2R_2E0) )
<=> ( ( p(V0P_2E0)
=> p(V2R_2E0) )
& ( p(V1Q_2E0)
=> p(V2R_2E0) ) ) ) ).
tff(thm_2Ebool_2EIMP__CONJ__THM,axiom,
! [V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Ebool,V2R_2E0: tyop_2Emin_2Ebool] :
( ( p(V0P_2E0)
=> ( p(V1Q_2E0)
& p(V2R_2E0) ) )
<=> ( ( p(V0P_2E0)
=> p(V1Q_2E0) )
& ( p(V0P_2E0)
=> p(V2R_2E0) ) ) ) ).
tff(thm_2Ebool_2EIMP__F__EQ__F,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t_2E0)
=> p(c_2Ebool_2EF_2E0) )
<=> ( V0t_2E0 = c_2Ebool_2EF_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_2EEQ__IMP__THM,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( ( V0t1_2E0 = V1t2_2E0 )
<=> ( ( p(V0t1_2E0)
=> p(V1t2_2E0) )
& ( p(V1t2_2E0)
=> p(V0t1_2E0) ) ) ) ).
tff(thm_2Ebool_2EEQ__EXPAND,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool] :
( ( V0t1_2E0 = V1t2_2E0 )
<=> ( ( p(V0t1_2E0)
& p(V1t2_2E0) )
| ( ~ p(V0t1_2E0)
& ~ p(V1t2_2E0) ) ) ) ).
tff(thm_2Ebool_2ECOND__RATOR,axiom,
! [A_27a: $tType,A_27b: $tType,V0b_2E0: tyop_2Emin_2Ebool,V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,A_27b),V0b_2E0,V1f_2E0,V2g_2E0),V3x_2E0) = c_2Ebool_2ECOND_2E3(A_27b,V0b_2E0,app_2E2(A_27a,A_27b,V1f_2E0,V3x_2E0),app_2E2(A_27a,A_27b,V2g_2E0,V3x_2E0)) ) ).
tff(thm_2Ebool_2ECOND__RAND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1b_2E0: tyop_2Emin_2Ebool,V2x_2E0: A_27a,V3y_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,c_2Ebool_2ECOND_2E3(A_27a,V1b_2E0,V2x_2E0,V3y_2E0)) = c_2Ebool_2ECOND_2E3(A_27b,V1b_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0)) ) ).
tff(thm_2Ebool_2ECOND__ABS,axiom,
! [A_27a: $tType,A_27b: $tType,V0b_2E0: tyop_2Emin_2Ebool,V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3x_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27b,V0b_2E0,app_2E2(A_27a,A_27b,V1f_2E0,V3x_2E0),app_2E2(A_27a,A_27b,V2g_2E0,V3x_2E0)) = app_2E2(A_27a,A_27b,c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,A_27b),V0b_2E0,V1f_2E0,V2g_2E0),V3x_2E0) ) ).
tff(thm_2Ebool_2ECOND__EXPAND,axiom,
! [V0b_2E0: tyop_2Emin_2Ebool,V1t1_2E0: tyop_2Emin_2Ebool,V2t2_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V0b_2E0,V1t1_2E0,V2t2_2E0))
<=> ( ( ~ p(V0b_2E0)
| p(V1t1_2E0) )
& ( p(V0b_2E0)
| p(V2t2_2E0) ) ) ) ).
tff(thm_2Ebool_2ECOND__EXPAND__IMP,axiom,
! [V0b_2E0: tyop_2Emin_2Ebool,V1t1_2E0: tyop_2Emin_2Ebool,V2t2_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V0b_2E0,V1t1_2E0,V2t2_2E0))
<=> ( ( p(V0b_2E0)
=> p(V1t1_2E0) )
& ( ~ p(V0b_2E0)
=> p(V2t2_2E0) ) ) ) ).
tff(thm_2Ebool_2ECOND__EXPAND__OR,axiom,
! [V0b_2E0: tyop_2Emin_2Ebool,V1t1_2E0: tyop_2Emin_2Ebool,V2t2_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V0b_2E0,V1t1_2E0,V2t2_2E0))
<=> ( ( p(V0b_2E0)
& p(V1t1_2E0) )
| ( ~ p(V0b_2E0)
& p(V2t2_2E0) ) ) ) ).
tff(thm_2Ebool_2ETYPE__DEFINITION__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Ebool_2ETYPE__DEFINITION_2E2(A_27a,A_27b,V0P_2E0,V1rep_2E0))
<=> ( ! [V2x_27_2E0: A_27b,V3x_27_27_2E0: A_27b] :
( ( app_2E2(A_27b,A_27a,V1rep_2E0,V2x_27_2E0) = app_2E2(A_27b,A_27a,V1rep_2E0,V3x_27_27_2E0) )
=> ( V2x_27_2E0 = V3x_27_27_2E0 ) )
& ! [V4x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0))
<=> ? [V5x_27_2E0: A_27b] : ( V4x_2E0 = app_2E2(A_27b,A_27a,V1rep_2E0,V5x_27_2E0) ) ) ) ) ).
tff(thm_2Ebool_2EONTO__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Ebool_2EONTO_2E1(A_27a,A_27b,V0f_2E0))
<=> ! [V1y_2E0: A_27b] :
? [V2x_2E0: A_27a] : ( V1y_2E0 = app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) ) ) ).
tff(thm_2Ebool_2EONE__ONE__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Ebool_2EONE__ONE_2E1(A_27a,A_27b,V0f_2E0))
<=> ! [V1x1_2E0: A_27a,V2x2_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V0f_2E0,V1x1_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V2x2_2E0) )
=> ( V1x1_2E0 = V2x2_2E0 ) ) ) ).
tff(thm_2Ebool_2EABS__REP__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ? [V1rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(A_27a,A_27b,V0P_2E0,V1rep_2E0))
=> ? [V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V3abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V4a_2E0: A_27b] : ( app_2E2(A_27a,A_27b,V3abs_2E0,app_2E2(A_27b,A_27a,V2rep_2E0,V4a_2E0)) = V4a_2E0 )
& ! [V5r_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V5r_2E0))
<=> ( app_2E2(A_27b,A_27a,V2rep_2E0,app_2E2(A_27a,A_27b,V3abs_2E0,V5r_2E0)) = V5r_2E0 ) ) ) ) ).
tff(thm_2Ebool_2ELET__RAND,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1N_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0P_2E0),V1N_2E0),V4x_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,V0P_2E0,app_2E2(A_27a,A_27b,V1N_2E0,V4x_2E0)) )
=> ( ! [V1N_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),F0_2E0,V1N_2E0),V3x_2E0) = app_2E2(A_27a,A_27b,V1N_2E0,V3x_2E0) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1N_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2M_2E0: A_27a] : ( app_2E2(A_27b,tyop_2Emin_2Ebool,V0P_2E0,c_2Ebool_2ELET_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),F0_2E0,V1N_2E0),V2M_2E0)) = c_2Ebool_2ELET_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0P_2E0),V1N_2E0),V2M_2E0) ) ) ) ).
tff(thm_2Ebool_2ELET__RATOR,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))] :
( ! [V1N_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0b_2E0: A_27b,V4x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),F1_2E0,V1N_2E0),V0b_2E0),V4x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V1N_2E0,V4x_2E0),V0b_2E0) )
=> ( ! [V1N_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),F0_2E0,V1N_2E0),V3x_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V1N_2E0,V3x_2E0) )
=> ! [V0b_2E0: A_27b,V1N_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2M_2E0: A_27a] : ( app_2E2(A_27b,A_27c,c_2Ebool_2ELET_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),F0_2E0,V1N_2E0),V2M_2E0),V0b_2E0) = c_2Ebool_2ELET_2E2(A_27a,A_27c,app_2E2(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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),F1_2E0,V1N_2E0),V0b_2E0),V2M_2E0) ) ) ) ).
tff(thm_2Ebool_2ESWAP__FORALL__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V1x_2E0),V2y_2E0))
<=> ! [V3y_2E0: A_27b,V4x_2E0: A_27a] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V4x_2E0),V3y_2E0)) ) ).
tff(thm_2Ebool_2ESWAP__EXISTS__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ? [V1x_2E0: A_27a,V2y_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V1x_2E0),V2y_2E0))
<=> ? [V3y_2E0: A_27b,V4x_2E0: A_27a] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V4x_2E0),V3y_2E0)) ) ).
tff(thm_2Ebool_2EEXISTS__UNIQUE__THM,axiom,
! [A_27a: $tType,F0_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),V1x_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),F0_2E0,V0P_2E0),V1x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0P_2E0)))
<=> ( ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4y_2E0)) )
=> ( V3x_2E0 = V4y_2E0 ) ) ) ) ) ).
tff(thm_2Ebool_2ELET__CONG,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),V2M_2E0: A_27a,V3N_2E0: A_27a] :
( ( ( V2M_2E0 = V3N_2E0 )
& ! [V4x_2E0: A_27a] :
( ( V4x_2E0 = V3N_2E0 )
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V4x_2E0) ) ) )
=> ( c_2Ebool_2ELET_2E2(A_27a,A_27b,V0f_2E0,V2M_2E0) = c_2Ebool_2ELET_2E2(A_27a,A_27b,V1g_2E0,V3N_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_2ELEFT__AND__CONG,axiom,
! [V0P_2E0: tyop_2Emin_2Ebool,V1P_27_2E0: tyop_2Emin_2Ebool,V2Q_2E0: tyop_2Emin_2Ebool,V3Q_27_2E0: tyop_2Emin_2Ebool] :
( ( ( 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_2EOR__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_2ELEFT__OR__CONG,axiom,
! [V0P_2E0: tyop_2Emin_2Ebool,V1P_27_2E0: tyop_2Emin_2Ebool,V2Q_2E0: tyop_2Emin_2Ebool,V3Q_27_2E0: tyop_2Emin_2Ebool] :
( ( ( 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_2ECOND__CONG,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Ebool,V2x_2E0: A_27a,V3x_27_2E0: A_27a,V4y_2E0: A_27a,V5y_27_2E0: A_27a] :
( ( ( V0P_2E0 = V1Q_2E0 )
& ( p(V1Q_2E0)
=> ( V2x_2E0 = V3x_27_2E0 ) )
& ( ~ p(V1Q_2E0)
=> ( V4y_2E0 = V5y_27_2E0 ) ) )
=> ( c_2Ebool_2ECOND_2E3(A_27a,V0P_2E0,V2x_2E0,V4y_2E0) = c_2Ebool_2ECOND_2E3(A_27a,V1Q_2E0,V3x_27_2E0,V5y_27_2E0) ) ) ).
tff(thm_2Ebool_2ERES__FORALL__CONG,axiom,
! [A_27a: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V3P_2E0 = V2Q_2E0 )
=> ( ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V2Q_2E0))
=> ( app_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V4x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0g_2E0,V4x_2E0) ) )
=> ( c_2Ebool_2ERES__FORALL_2E2(A_27a,V3P_2E0,V1f_2E0) = c_2Ebool_2ERES__FORALL_2E2(A_27a,V2Q_2E0,V0g_2E0) ) ) ) ).
tff(thm_2Ebool_2ERES__EXISTS__CONG,axiom,
! [A_27a: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V3P_2E0 = V2Q_2E0 )
=> ( ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V2Q_2E0))
=> ( app_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V4x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0g_2E0,V4x_2E0) ) )
=> ( c_2Ebool_2ERES__EXISTS_2E2(A_27a,V3P_2E0,V1f_2E0) = c_2Ebool_2ERES__EXISTS_2E2(A_27a,V2Q_2E0,V0g_2E0) ) ) ) ).
tff(thm_2Ebool_2EMONO__AND,axiom,
! [V0z_2E0: tyop_2Emin_2Ebool,V1y_2E0: tyop_2Emin_2Ebool,V2x_2E0: tyop_2Emin_2Ebool,V3w_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V2x_2E0)
=> p(V1y_2E0) )
& ( p(V0z_2E0)
=> p(V3w_2E0) ) )
=> ( ( p(V2x_2E0)
& p(V0z_2E0) )
=> ( p(V1y_2E0)
& p(V3w_2E0) ) ) ) ).
tff(thm_2Ebool_2EMONO__OR,axiom,
! [V0z_2E0: tyop_2Emin_2Ebool,V1y_2E0: tyop_2Emin_2Ebool,V2x_2E0: tyop_2Emin_2Ebool,V3w_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V2x_2E0)
=> p(V1y_2E0) )
& ( p(V0z_2E0)
=> p(V3w_2E0) ) )
=> ( ( p(V2x_2E0)
| p(V0z_2E0) )
=> ( p(V1y_2E0)
| p(V3w_2E0) ) ) ) ).
tff(thm_2Ebool_2EMONO__IMP,axiom,
! [V0z_2E0: tyop_2Emin_2Ebool,V1y_2E0: tyop_2Emin_2Ebool,V2x_2E0: tyop_2Emin_2Ebool,V3w_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V1y_2E0)
=> p(V2x_2E0) )
& ( p(V0z_2E0)
=> p(V3w_2E0) ) )
=> ( ( p(V2x_2E0)
=> p(V0z_2E0) )
=> ( p(V1y_2E0)
=> p(V3w_2E0) ) ) ) ).
tff(thm_2Ebool_2EMONO__NOT,axiom,
! [V0y_2E0: tyop_2Emin_2Ebool,V1x_2E0: tyop_2Emin_2Ebool] :
( ( p(V0y_2E0)
=> p(V1x_2E0) )
=> ( ~ p(V1x_2E0)
=> ~ p(V0y_2E0) ) ) ).
tff(thm_2Ebool_2EMONO__NOT__EQ,axiom,
! [V0y_2E0: tyop_2Emin_2Ebool,V1x_2E0: tyop_2Emin_2Ebool] :
( ( p(V0y_2E0)
=> p(V1x_2E0) )
<=> ( ~ p(V1x_2E0)
=> ~ p(V0y_2E0) ) ) ).
tff(thm_2Ebool_2EMONO__ALL,axiom,
! [A_27a: $tType,V0Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0Q_2E0,V2x_2E0)) )
=> ( ! [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3x_2E0))
=> ! [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0Q_2E0,V4x_2E0)) ) ) ).
tff(thm_2Ebool_2EMONO__EXISTS,axiom,
! [A_27a: $tType,V0Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0Q_2E0,V2x_2E0)) )
=> ( ? [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V3x_2E0))
=> ? [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0Q_2E0,V4x_2E0)) ) ) ).
tff(thm_2Ebool_2EMONO__COND,axiom,
! [V0z_2E0: tyop_2Emin_2Ebool,V1y_2E0: tyop_2Emin_2Ebool,V2x_2E0: tyop_2Emin_2Ebool,V3w_2E0: tyop_2Emin_2Ebool,V4b_2E0: tyop_2Emin_2Ebool] :
( ( p(V2x_2E0)
=> p(V1y_2E0) )
=> ( ( p(V0z_2E0)
=> p(V3w_2E0) )
=> ( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V4b_2E0,V2x_2E0,V0z_2E0))
=> p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,V4b_2E0,V1y_2E0,V3w_2E0)) ) ) ) ).
tff(thm_2Ebool_2EEXISTS__REFL,axiom,
! [A_27a: $tType,V0a_2E0: A_27a] :
? [V1x_2E0: A_27a] : ( V1x_2E0 = V0a_2E0 ) ).
tff(thm_2Ebool_2EEXISTS__UNIQUE__REFL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V0a_2E0: A_27a,V1x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0a_2E0),V1x_2E0))
<=> ( V1x_2E0 = V0a_2E0 ) )
=> ! [V0a_2E0: A_27a] : p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0a_2E0))) ) ).
tff(thm_2Ebool_2EUNWIND__THM1,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: A_27a] :
( ? [V2x_2E0: A_27a] :
( ( V1a_2E0 = V2x_2E0 )
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1a_2E0)) ) ).
tff(thm_2Ebool_2EUNWIND__THM2,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: A_27a] :
( ? [V2x_2E0: A_27a] :
( ( V2x_2E0 = V1a_2E0 )
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1a_2E0)) ) ).
tff(thm_2Ebool_2EUNWIND__FORALL__THM1,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1v_2E0: A_27a] :
( ! [V2x_2E0: A_27a] :
( ( V1v_2E0 = V2x_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_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_2Ebool_2ESKOLEM__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a] :
? [V2y_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V1x_2E0),V2y_2E0))
<=> ? [V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
! [V4x_2E0: A_27a] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V4x_2E0),app_2E2(A_27a,A_27b,V3f_2E0,V4x_2E0))) ) ).
tff(thm_2Ebool_2Ebool__case__thm,axiom,
! [A_27a: $tType] :
( ! [V0t1_2E0: A_27a,V1t2_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,c_2Ebool_2ET_2E0,V0t1_2E0,V1t2_2E0) = V0t1_2E0 )
& ! [V2t1_2E0: A_27a,V3t2_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,c_2Ebool_2EF_2E0,V2t1_2E0,V3t2_2E0) = V3t2_2E0 ) ) ).
tff(thm_2Ebool_2Ebool__case__ID,axiom,
! [A_27a: $tType,V0b_2E0: tyop_2Emin_2Ebool,V1t_2E0: A_27a] : ( c_2Ebool_2ECOND_2E3(A_27a,V0b_2E0,V1t_2E0,V1t_2E0) = V1t_2E0 ) ).
tff(thm_2Ebool_2EboolAxiom,axiom,
! [A_27a: $tType,V0t1_2E0: A_27a,V1t2_2E0: A_27a] :
? [V2fn_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)] :
( ( app_2E2(tyop_2Emin_2Ebool,A_27a,V2fn_2E0,c_2Ebool_2ET_2E0) = V0t1_2E0 )
& ( app_2E2(tyop_2Emin_2Ebool,A_27a,V2fn_2E0,c_2Ebool_2EF_2E0) = V1t2_2E0 ) ) ).
tff(thm_2Ebool_2Ebool__INDUCT,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0P_2E0,c_2Ebool_2ET_2E0))
& p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0P_2E0,c_2Ebool_2EF_2E0)) )
=> ! [V1b_2E0: tyop_2Emin_2Ebool] : p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0P_2E0,V1b_2E0)) ) ).
tff(thm_2Ebool_2Ebool__case__CONG,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Ebool,V2x_2E0: A_27a,V3x_27_2E0: A_27a,V4y_2E0: A_27a,V5y_27_2E0: A_27a] :
( ( ( V0P_2E0 = V1Q_2E0 )
& ( p(V1Q_2E0)
=> ( V2x_2E0 = V3x_27_2E0 ) )
& ( ~ p(V1Q_2E0)
=> ( V4y_2E0 = V5y_27_2E0 ) ) )
=> ( c_2Ebool_2ECOND_2E3(A_27a,V0P_2E0,V2x_2E0,V4y_2E0) = c_2Ebool_2ECOND_2E3(A_27a,V1Q_2E0,V3x_27_2E0,V5y_27_2E0) ) ) ).
tff(thm_2Ebool_2EFORALL__BOOL,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V1b_2E0: tyop_2Emin_2Ebool] : p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0P_2E0,V1b_2E0))
<=> ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0P_2E0,c_2Ebool_2ET_2E0))
& p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0P_2E0,c_2Ebool_2EF_2E0)) ) ) ).
tff(thm_2Ebool_2EUEXISTS__OR__THM,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,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),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1Q_2E0),V2x_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) ) )
=> ( ! [V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4x_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),F2_2E0,V1Q_2E0),V4x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V4x_2E0) )
=> ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_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),V3x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1Q_2E0)))
=> ( p(c_2Ebool_2E_3F_21_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)))
| p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F2_2E0,V1Q_2E0))) ) ) ) ) ) ).
tff(thm_2Ebool_2EUEXISTS__SIMP,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V0t_2E0: tyop_2Emin_2Ebool,V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0t_2E0),V1x_2E0) = V0t_2E0 )
=> ! [V0t_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0t_2E0)))
<=> ( p(V0t_2E0)
& ! [V2x_2E0: A_27a,V3y_2E0: A_27a] : ( V2x_2E0 = V3y_2E0 ) ) ) ) ).
tff(thm_2Ebool_2ERES__FORALL__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2ERES__FORALL_2E2(A_27a,V0P_2E0,V1f_2E0))
<=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0P_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V2x_2E0)) ) ) ).
tff(thm_2Ebool_2ERES__EXISTS__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2ERES__EXISTS_2E2(A_27a,V0P_2E0,V1f_2E0))
<=> ? [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0P_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V2x_2E0)) ) ) ).
tff(thm_2Ebool_2ERES__EXISTS__UNIQUE__THM,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: A_27a,V4y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V1f_2E0),V3x_2E0),V4y_2E0))
<=> ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V3x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V4y_2E0)) )
=> ( V3x_2E0 = V4y_2E0 ) ) )
=> ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0P_2E0),V1f_2E0),V3x_2E0) = c_2Ebool_2ERES__FORALL_2E2(A_27a,V0P_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V1f_2E0),V3x_2E0)) )
=> ( ! [V1f_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),F0_2E0,V1f_2E0),V2x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V2x_2E0) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(A_27a,V0P_2E0,V1f_2E0))
<=> ( p(c_2Ebool_2ERES__EXISTS_2E2(A_27a,V0P_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1f_2E0)))
& p(c_2Ebool_2ERES__FORALL_2E2(A_27a,V0P_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0P_2E0),V1f_2E0))) ) ) ) ) ) ).
tff(thm_2Ebool_2ERES__SELECT__THM,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1f_2E0),V2x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0P_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V2x_2E0)) ) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ERES__SELECT_2E2(A_27a,V0P_2E0,V1f_2E0) = 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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1f_2E0)) ) ) ).
tff(thm_2Ebool_2ERES__FORALL__TRUE,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,F0_2E0,V1x_2E0) = c_2Ebool_2ET_2E0 )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ERES__FORALL_2E2(A_27a,V0P_2E0,F0_2E0) = c_2Ebool_2ET_2E0 ) ) ).
tff(thm_2Ebool_2ERES__EXISTS__FALSE,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,F0_2E0,V1x_2E0) = c_2Ebool_2EF_2E0 )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ERES__EXISTS_2E2(A_27a,V0P_2E0,F0_2E0) = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Ebool_2EBOOL__FUN__CASES__THM,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V1x_2E0: tyop_2Emin_2Ebool] : ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0) = c_2Ebool_2ET_2E0 )
| ! [V2x_2E0: tyop_2Emin_2Ebool] : ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0f_2E0,V2x_2E0) = c_2Ebool_2EF_2E0 )
| ! [V3x_2E0: tyop_2Emin_2Ebool] : ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0f_2E0,V3x_2E0) = V3x_2E0 )
| ! [V4x_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0f_2E0,V4x_2E0))
<=> ~ p(V4x_2E0) ) ) ).
tff(thm_2Ebool_2EBOOL__FUN__INDUCT,axiom,
! [F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ! [V4b_2E0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F3_2E0,V4b_2E0))
<=> ~ p(V4b_2E0) )
=> ( ! [V1b_2E0: tyop_2Emin_2Ebool] : ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F0_2E0,V1b_2E0) = c_2Ebool_2ET_2E0 )
=> ( ! [V2b_2E0: tyop_2Emin_2Ebool] : ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F1_2E0,V2b_2E0) = c_2Ebool_2EF_2E0 )
=> ( ! [V3b_2E0: tyop_2Emin_2Ebool] : ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,F2_2E0,V3b_2E0) = V3b_2E0 )
=> ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,F0_2E0))
& p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,F1_2E0))
& p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,F2_2E0))
& p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,F3_2E0)) )
=> ! [V5f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V5f_2E0)) ) ) ) ) ) ).
tff(thm_2Ebool_2Eliteral__case__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: A_27a] : ( c_2Ebool_2Eliteral__case_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) ) ).
tff(thm_2Ebool_2Eliteral__case__RAND,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1N_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4x_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_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),F1_2E0,V0P_2E0),V1N_2E0),V4x_2E0) = app_2E2(A_27b,A_27c,V0P_2E0,app_2E2(A_27a,A_27b,V1N_2E0,V4x_2E0)) )
=> ( ! [V1N_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),F0_2E0,V1N_2E0),V3x_2E0) = app_2E2(A_27a,A_27b,V1N_2E0,V3x_2E0) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1N_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2M_2E0: A_27a] : ( app_2E2(A_27b,A_27c,V0P_2E0,c_2Ebool_2Eliteral__case_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),F0_2E0,V1N_2E0),V2M_2E0)) = c_2Ebool_2Eliteral__case_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_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),F1_2E0,V0P_2E0),V1N_2E0),V2M_2E0) ) ) ) ).
tff(thm_2Ebool_2Eliteral__case__RATOR,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))] :
( ! [V1N_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0b_2E0: A_27b,V4x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),F1_2E0,V1N_2E0),V0b_2E0),V4x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V1N_2E0,V4x_2E0),V0b_2E0) )
=> ( ! [V1N_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),F0_2E0,V1N_2E0),V3x_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V1N_2E0,V3x_2E0) )
=> ! [V0b_2E0: A_27b,V1N_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2M_2E0: A_27a] : ( app_2E2(A_27b,A_27c,c_2Ebool_2Eliteral__case_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),F0_2E0,V1N_2E0),V2M_2E0),V0b_2E0) = c_2Ebool_2Eliteral__case_2E2(A_27a,A_27c,app_2E2(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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),F1_2E0,V1N_2E0),V0b_2E0),V2M_2E0) ) ) ) ).
tff(thm_2Ebool_2Eliteral__case__CONG,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),V2M_2E0: A_27a,V3N_2E0: A_27a] :
( ( ( V2M_2E0 = V3N_2E0 )
& ! [V4x_2E0: A_27a] :
( ( V4x_2E0 = V3N_2E0 )
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V4x_2E0) ) ) )
=> ( c_2Ebool_2Eliteral__case_2E2(A_27a,A_27b,V0f_2E0,V2M_2E0) = c_2Ebool_2Eliteral__case_2E2(A_27a,A_27b,V1g_2E0,V3N_2E0) ) ) ).
tff(thm_2Ebool_2Eliteral__case__id,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))))] :
( ! [V3x_2E0: A_27a,V2a_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V3x_2E0),V2a_2E0))
<=> ( V3x_2E0 = V2a_2E0 ) )
=> ( ! [V2a_2E0: A_27a,V1t_2E0: A_27b,V0u_2E0: A_27b,V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),F0_2E0,V2a_2E0),V1t_2E0),V0u_2E0),V3x_2E0) = c_2Ebool_2ECOND_2E3(A_27b,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V3x_2E0),V2a_2E0),V1t_2E0,V0u_2E0) )
=> ! [V0u_2E0: A_27b,V1t_2E0: A_27b,V2a_2E0: A_27a] : ( c_2Ebool_2Eliteral__case_2E2(A_27a,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),F0_2E0,V2a_2E0),V1t_2E0),V0u_2E0),V2a_2E0) = V1t_2E0 ) ) ) ).
tff(thm_2Ebool_2EBOUNDED__THM,axiom,
! [V0v_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EBOUNDED_2E1(V0v_2E0) = c_2Ebool_2ET_2E0 ) ).
tff(thm_2Ebool_2ELCOMM__THM,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27a,V3z_2E0: A_27a] : ( app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V1x_2E0),app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V2y_2E0),V3z_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V1x_2E0),V2y_2E0)),V3z_2E0) )
=> ( ! [V4x_2E0: A_27a,V5y_2E0: A_27a] : ( app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V4x_2E0),V5y_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V5y_2E0),V4x_2E0) )
=> ! [V6x_2E0: A_27a,V7y_2E0: A_27a,V8z_2E0: A_27a] : ( app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V6x_2E0),app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V7y_2E0),V8z_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V7y_2E0),app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,V6x_2E0),V8z_2E0)) ) ) ) ).
tff(thm_2Ebool_2EDATATYPE__TAG__THM,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Ebool_2EDATATYPE_2E1(A_27a,V0x_2E0) = c_2Ebool_2ET_2E0 ) ).
tff(thm_2Ebool_2EDATATYPE__BOOL,axiom,
! [V0bool_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] : ( c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0bool_2E0,c_2Ebool_2ET_2E0),c_2Ebool_2EF_2E0)) = c_2Ebool_2ET_2E0 ) ).
tff(thm_2Ebool_2EITSELF__UNIQUE,axiom,
! [A_27a: $tType,V0i_2E0: tyop_2Ebool_2Eitself(A_27a)] : ( V0i_2E0 = c_2Ebool_2Ethe__value_2E0(A_27a) ) ).
tff(thm_2Ebool_2Eitself__Axiom,axiom,
! [A_27a: $tType,A_27b: $tType,V0e_2E0: A_27b] :
? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27b)] : ( app_2E2(tyop_2Ebool_2Eitself(A_27a),A_27b,V1f_2E0,c_2Ebool_2Ethe__value_2E0(A_27a)) = V0e_2E0 ) ).
tff(thm_2Ebool_2Eitself__induction,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Ebool_2Ethe__value_2E0(A_27a)))
=> ! [V1i_2E0: tyop_2Ebool_2Eitself(A_27a)] : p(app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1i_2E0)) ) ).
tff(thm_2Ebool_2EFORALL__itself,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool)] :
( ! [V1x_2E0: tyop_2Ebool_2Eitself(A_27a)] : p(app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0))
<=> p(app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Ebool_2Ethe__value_2E0(A_27a))) ) ).
tff(thm_2Ebool_2EEXISTS__itself,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool)] :
( ? [V1x_2E0: tyop_2Ebool_2Eitself(A_27a)] : p(app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0))
<=> p(app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Ebool_2Ethe__value_2E0(A_27a))) ) ).
tff(thm_2Ebool_2EPULL__EXISTS,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
( ( ( ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
=> p(V1Q_2E0) )
<=> ! [V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
=> p(V1Q_2E0) ) )
& ( ( ? [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0))
& p(V1Q_2E0) )
<=> ? [V5x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V5x_2E0))
& p(V1Q_2E0) ) )
& ( ( p(V1Q_2E0)
& ? [V6x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V6x_2E0)) )
<=> ? [V7x_2E0: A_27a] :
( p(V1Q_2E0)
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V7x_2E0)) ) ) ) ).
tff(thm_2Ebool_2EPULL__FORALL,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V1Q_2E0)
=> ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
<=> ! [V3x_2E0: A_27a] :
( p(V1Q_2E0)
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0)) ) )
& ( ( ! [V4x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0))
& p(V1Q_2E0) )
<=> ! [V5x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V5x_2E0))
& p(V1Q_2E0) ) )
& ( ( p(V1Q_2E0)
& ! [V6x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V6x_2E0)) )
<=> ! [V7x_2E0: A_27a] :
( p(V1Q_2E0)
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V7x_2E0)) ) ) ) ).
tff(thm_2Ebool_2EPEIRCE,axiom,
! [V0Q_2E0: tyop_2Emin_2Ebool,V1P_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V1P_2E0)
=> p(V0Q_2E0) )
=> p(V1P_2E0) )
=> p(V1P_2E0) ) ).
tff(thm_2Ebool_2EJRH__INDUCT__UTIL,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: A_27a] :
( ! [V2x_2E0: A_27a] :
( ( V2x_2E0 = V1t_2E0 )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
=> p(c_2Ebool_2E_3F_2E1(A_27a,V0P_2E0)) ) ).
tff(thm_2Ebool_2EDISJ__EQ__IMP,axiom,
! [V0A_2E0: tyop_2Emin_2Ebool,V1B_2E0: tyop_2Emin_2Ebool] :
( ( p(V0A_2E0)
| p(V1B_2E0) )
<=> ( ~ p(V0A_2E0)
=> p(V1B_2E0) ) ) ).
%------------------------------------------------------------------------------