ITP001 Axioms: ITP008_7.ax
%------------------------------------------------------------------------------
% File : ITP008_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 : combin.ax [Gau19]
% : HL4008_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 197 ( 93 unt; 65 typ; 0 def)
% Number of atoms : 188 ( 140 equ)
% Maximal formula atoms : 6 ( 0 avg)
% Number of connectives : 64 ( 8 ~; 4 |; 11 &)
% ( 25 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 65 ( 33 >; 32 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 63 ( 63 usr; 7 con; 0-6 aty)
% Number of variables : 670 ( 570 !; 1 ?; 670 :)
% ( 99 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ecombin_2E_3A_3E_2E0,type,
c_2Ecombin_2E_3A_3E_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)) ).
tff(c_2Ecombin_2E_3A_3E_2E2,type,
c_2Ecombin_2E_3A_3E_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27b * tyop_2Emin_2Efun(A_27b,A_27a) ) > A_27a ) ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2EASSOC_2E0,type,
c_2Ecombin_2EASSOC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool) ).
tff(c_2Ecombin_2EASSOC_2E1,type,
c_2Ecombin_2EASSOC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)) > tyop_2Emin_2Ebool ) ).
tff(c_2Emarker_2EAbbrev_2E0,type,
c_2Emarker_2EAbbrev_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ecombin_2EC_2E0,type,
c_2Ecombin_2EC_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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ecombin_2EC_2E2,type,
c_2Ecombin_2EC_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * A_27b ) > tyop_2Emin_2Efun(A_27a,A_27c) ) ).
tff(c_2Ecombin_2EC_2E3,type,
c_2Ecombin_2EC_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * A_27b * A_27a ) > A_27c ) ).
tff(c_2Ecombin_2ECOMM_2E0,type,
c_2Ecombin_2ECOMM_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool) ).
tff(c_2Ecombin_2ECOMM_2E1,type,
c_2Ecombin_2ECOMM_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)) > 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_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ecombin_2EFAIL_2E0,type,
c_2Ecombin_2EFAIL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(c_2Ecombin_2EFAIL_2E2,type,
c_2Ecombin_2EFAIL_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > A_27a ) ).
tff(c_2Ecombin_2EFCOMM_2E0,type,
c_2Ecombin_2EFCOMM_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool)) ).
tff(c_2Ecombin_2EFCOMM_2E2,type,
c_2Ecombin_2EFCOMM_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) * tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2Ecombin_2EI_2E1,type,
c_2Ecombin_2EI_2E1:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
tff(c_2Ecombin_2EK_2E0,type,
c_2Ecombin_2EK_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(c_2Ecombin_2EK_2E1,type,
c_2Ecombin_2EK_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27b,A_27a) ) ).
tff(c_2Ecombin_2EK_2E2,type,
c_2Ecombin_2EK_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > A_27a ) ).
tff(c_2Ecombin_2ELEFT__ID_2E0,type,
c_2Ecombin_2ELEFT__ID_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Ecombin_2ELEFT__ID_2E2,type,
c_2Ecombin_2ELEFT__ID_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * A_27a ) > 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_2Ecombin_2EMONOID_2E0,type,
c_2Ecombin_2EMONOID_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Ecombin_2EMONOID_2E2,type,
c_2Ecombin_2EMONOID_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2ERIGHT__ID_2E0,type,
c_2Ecombin_2ERIGHT__ID_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ).
tff(c_2Ecombin_2ERIGHT__ID_2E2,type,
c_2Ecombin_2ERIGHT__ID_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) * A_27b ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2ES_2E0,type,
c_2Ecombin_2ES_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_2Ecombin_2ES_2E2,type,
c_2Ecombin_2ES_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Efun(A_27a,A_27c) ) ).
tff(c_2Ecombin_2ES_2E3,type,
c_2Ecombin_2ES_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) * tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27c ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ecombin_2EUPDATE_2E0,type,
c_2Ecombin_2EUPDATE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))) ).
tff(c_2Ecombin_2EUPDATE_2E3,type,
c_2Ecombin_2EUPDATE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Ecombin_2EUPDATE_2E4,type,
c_2Ecombin_2EUPDATE_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Ecombin_2EW_2E0,type,
c_2Ecombin_2EW_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ecombin_2EW_2E2,type,
c_2Ecombin_2EW_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)) * A_27a ) > A_27b ) ).
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_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_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Ecombin_2Eo_2E3,type,
c_2Ecombin_2Eo_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) * A_27a ) > A_27b ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Ecombin_2E_3A_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Ecombin_2E_3A_3E_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),c_2Ecombin_2E_3A_3E_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EASSOC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] : ( c_2Ecombin_2EASSOC_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a] : ( c_2Ecombin_2EC_2E2(A_27a,A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EC_2E0(A_27a,A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0: A_27b,X2_2E0: A_27a] : ( c_2Ecombin_2EC_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = 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)),c_2Ecombin_2EC_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X1_2E0: A_27c,X2_2E0: A_27a] : ( c_2Ecombin_2EC_2E3(A_27a,A_27c,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27b,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EC_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: A_27c] : ( c_2Ecombin_2EC_2E2(A_27b,A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2EC_2E0(A_27b,A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))] : ( c_2Ecombin_2ECOMM_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E0(A_27a,A_27b),X0_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(arityeq2_2Ec_2Ecombin_2EFAIL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Ecombin_2EFAIL_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EFAIL_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EFCOMM_2E2(A_27a,A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EFCOMM_2E0(A_27a,A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EFCOMM_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EFCOMM_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Ecombin_2EI_2E1(A_27a,X0_2E0) = app_2E2(A_27a,A_27a,c_2Ecombin_2EI_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Ecombin_2EK_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EK_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27c] : ( c_2Ecombin_2EK_2E1(A_27c,A_27a,X0_2E0) = app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2EK_2E0(A_27c,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: A_27c] : ( c_2Ecombin_2EK_2E1(A_27c,A_27b,X0_2E0) = app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2EK_2E0(A_27c,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27d_20mono_2EA_27f,axiom,
! [A_27d: $tType,A_27f: $tType,X0_2E0: A_27d] : ( c_2Ecombin_2EK_2E1(A_27d,A_27f,X0_2E0) = app_2E2(A_27d,tyop_2Emin_2Efun(A_27f,A_27d),c_2Ecombin_2EK_2E0(A_27d,A_27f),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27e_20mono_2EA_27f,axiom,
! [A_27e: $tType,A_27f: $tType,X0_2E0: A_27e] : ( c_2Ecombin_2EK_2E1(A_27e,A_27f,X0_2E0) = app_2E2(A_27e,tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2EK_2E0(A_27e,A_27f),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a] : ( c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ELEFT__ID_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: A_27a] : ( c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ELEFT__ID_2E0(A_27a,A_27b),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_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: A_27b] : ( c_2Ebool_2ELET_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27a),c_2Ebool_2ELET_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: A_27b] : ( c_2Ebool_2ELET_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ebool_2ELET_2E0(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: A_27c] : ( c_2Ebool_2ELET_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27c,A_27a,app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2ELET_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: A_27c] : ( c_2Ebool_2ELET_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27b),c_2Ebool_2ELET_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a] : ( c_2Ecombin_2EMONOID_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EMONOID_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Ecombin_2EMONOID_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EMONOID_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2ERIGHT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a] : ( c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ERIGHT__ID_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2ERIGHT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: A_27b] : ( c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ecombin_2ERIGHT__ID_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0: A_27a] : ( c_2Ecombin_2ES_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = 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)),c_2Ecombin_2ES_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0: A_27a] : ( c_2Ecombin_2ES_2E3(A_27a,A_27c,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2ES_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2ES_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0_2E0,X1_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_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2ES_2E0(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2ES_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2ES_2E0(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2EUPDATE_2E3(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(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EUPDATE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0: A_27a] : ( c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_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(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EUPDATE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: A_27c,X1_2E0: A_27d,X2_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] : ( c_2Ecombin_2EUPDATE_2E3(A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),c_2Ecombin_2EUPDATE_2E0(A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: A_27c,X1_2E0: A_27d,X2_2E0: tyop_2Emin_2Efun(A_27c,A_27d),X3_2E0: A_27c] : ( c_2Ecombin_2EUPDATE_2E4(A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27c,A_27d,app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),c_2Ecombin_2EUPDATE_2E0(A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: A_27a] : ( c_2Ecombin_2EW_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EW_2E0(A_27a,A_27b),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_2Eliteral__case_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_2Eliteral__case_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_2Eliteral__case_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: A_27b] : ( c_2Ebool_2Eliteral__case_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27b,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27a),c_2Ebool_2Eliteral__case_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: A_27b] : ( c_2Ebool_2Eliteral__case_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ebool_2Eliteral__case_2E0(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: A_27c] : ( c_2Ebool_2Eliteral__case_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27c,A_27a,app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2Eliteral__case_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: A_27c] : ( c_2Ebool_2Eliteral__case_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27b),c_2Ebool_2Eliteral__case_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),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_27a),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E0(A_27a,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X2_2E0: A_27c] : ( c_2Ecombin_2Eo_2E3(A_27c,A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27d,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(A_27d,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(A_27d,A_27b)),c_2Ecombin_2Eo_2E0(A_27d,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0: A_27b] : ( c_2Ecombin_2Eo_2E3(A_27b,A_27c,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27c,app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2Eo_2E0(A_27b,A_27c,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27c,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ecombin_2Eo_2E0(A_27c,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27b,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_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E0(A_27a,A_27b,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,X0_2E0,X1_2E0) = 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)),c_2Ecombin_2Eo_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27c)] : ( c_2Ecombin_2Eo_2E2(A_27d,A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27a)),c_2Ecombin_2Eo_2E0(A_27d,A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0: A_27a] : ( c_2Ecombin_2Eo_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27c)] : ( c_2Ecombin_2Eo_2E2(A_27d,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b)),c_2Ecombin_2Eo_2E0(A_27d,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27f_20mono_2EA_27e_20mono_2EA_27d,axiom,
! [A_27d: $tType,A_27e: $tType,A_27f: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,A_27e),X1_2E0: tyop_2Emin_2Efun(A_27f,A_27d)] : ( c_2Ecombin_2Eo_2E2(A_27f,A_27e,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27e),app_2E2(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27e)),c_2Ecombin_2Eo_2E0(A_27f,A_27e,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),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_2Ecombin_2EK__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1x_27_2E0: A_27b] : ( c_2Ecombin_2EK_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) = V0x_2E0 ) ).
tff(thm_2Ecombin_2ES__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1x_27_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_27_27_2E0: A_27a] : ( c_2Ecombin_2ES_2E3(A_27a,A_27b,A_27c,V0x_2E0,V1x_27_2E0,V2x_27_27_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0x_2E0,V2x_27_27_2E0),app_2E2(A_27a,A_27b,V1x_27_2E0,V2x_27_27_2E0)) ) ).
tff(thm_2Ecombin_2EI__DEF,axiom,
! [A_27a: $tType] : ( c_2Ecombin_2EI_2E0(A_27a) = c_2Ecombin_2ES_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),A_27a,c_2Ecombin_2EK_2E0(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E0(A_27a,A_27a)) ) ).
tff(thm_2Ecombin_2EC__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1x_27_2E0: A_27b,V2x_27_27_2E0: A_27a] : ( c_2Ecombin_2EC_2E3(A_27a,A_27b,A_27c,V0x_2E0,V1x_27_2E0,V2x_27_27_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0x_2E0,V2x_27_27_2E0),V1x_27_2E0) ) ).
tff(thm_2Ecombin_2EW__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V1x_27_2E0: A_27a] : ( c_2Ecombin_2EW_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) = app_2E2(A_27a,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0,V1x_27_2E0),V1x_27_2E0) ) ).
tff(thm_2Ecombin_2Eo__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2x_2E0: A_27a] : ( c_2Ecombin_2Eo_2E3(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0) = app_2E2(A_27c,A_27b,V0f_2E0,app_2E2(A_27a,A_27c,V1g_2E0,V2x_2E0)) ) ).
tff(thm_2Ecombin_2EAPP__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Ecombin_2E_3A_3E_2E2(A_27a,A_27b,V0x_2E0,V1f_2E0) = app_2E2(A_27b,A_27a,V1f_2E0,V0x_2E0) ) ).
tff(thm_2Ecombin_2EUPDATE__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V0a_2E0: A_27a,V3x_27_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),V3x_27_2E0))
<=> ( V0a_2E0 = V3x_27_2E0 ) )
=> ! [V0a_2E0: A_27a,V1b_2E0: A_27b,V2x_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3x_27_2E0: A_27a] : ( c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,V0a_2E0,V1b_2E0,V2x_2E0,V3x_27_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),F0_2E0,V0a_2E0),V3x_27_2E0),V1b_2E0,app_2E2(A_27a,A_27b,V2x_2E0,V3x_27_2E0)) ) ) ).
tff(thm_2Ecombin_2EASSOC__DEF,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
<=> ! [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) ) ) ).
tff(thm_2Ecombin_2ECOMM__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))] :
( p(c_2Ecombin_2ECOMM_2E1(A_27a,A_27b,V0f_2E0))
<=> ! [V1x_2E0: A_27a,V2y_2E0: A_27a] : ( app_2E2(A_27a,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,V1x_2E0),V2y_2E0) = app_2E2(A_27a,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,V2y_2E0),V1x_2E0) ) ) ).
tff(thm_2Ecombin_2EFCOMM__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1g_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2EFCOMM_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0))
<=> ! [V2x_2E0: A_27c,V3y_2E0: A_27a,V4z_2E0: A_27b] : ( app_2E2(A_27a,A_27a,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0,V2x_2E0),app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,V3y_2E0),V4z_2E0)) = app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,app_2E2(A_27a,A_27a,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0,V2x_2E0),V3y_2E0)),V4z_2E0) ) ) ).
tff(thm_2Ecombin_2ERIGHT__ID__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V1e_2E0: A_27b] :
( p(c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27b,V0f_2E0,V1e_2E0))
<=> ! [V2x_2E0: A_27a] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0f_2E0,V2x_2E0),V1e_2E0) = V2x_2E0 ) ) ).
tff(thm_2Ecombin_2ELEFT__ID__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27a] :
( p(c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27b,V0f_2E0,V1e_2E0))
<=> ! [V2x_2E0: A_27b] : ( app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V1e_2E0),V2x_2E0) = V2x_2E0 ) ) ).
tff(thm_2Ecombin_2EMONOID__DEF,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V1e_2E0: A_27a] :
( p(c_2Ecombin_2EMONOID_2E2(A_27a,V0f_2E0,V1e_2E0))
<=> ( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
& p(c_2Ecombin_2ERIGHT__ID_2E2(A_27a,A_27a,V0f_2E0,V1e_2E0))
& p(c_2Ecombin_2ELEFT__ID_2E2(A_27a,A_27a,V0f_2E0,V1e_2E0)) ) ) ).
tff(thm_2Ecombin_2EFAIL__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1x_27_2E0: A_27b] : ( c_2Ecombin_2EFAIL_2E2(A_27a,A_27b,V0x_2E0,V1x_27_2E0) = V0x_2E0 ) ).
tff(thm_2Ecombin_2Eo__THM,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V2x_2E0: A_27c] : ( c_2Ecombin_2Eo_2E3(A_27c,A_27b,A_27a,V0f_2E0,V1g_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,app_2E2(A_27c,A_27a,V1g_2E0,V2x_2E0)) ) ).
tff(thm_2Ecombin_2Eo__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V2h_2E0: tyop_2Emin_2Efun(A_27d,A_27c)] : ( c_2Ecombin_2Eo_2E2(A_27d,A_27b,A_27a,V0f_2E0,c_2Ecombin_2Eo_2E2(A_27d,A_27a,A_27c,V1g_2E0,V2h_2E0)) = c_2Ecombin_2Eo_2E2(A_27d,A_27b,A_27c,c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,V0f_2E0,V1g_2E0),V2h_2E0) ) ).
tff(thm_2Ecombin_2Eo__ABS__L,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V1f_2E0),V3x_2E0) = app_2E2(A_27a,A_27c,V1f_2E0,V3x_2E0) )
=> ! [V0g_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2x_2E0: A_27b] : ( c_2Ecombin_2Eo_2E3(A_27b,A_27c,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V1f_2E0),V0g_2E0,V2x_2E0) = app_2E2(A_27a,A_27c,V1f_2E0,app_2E2(A_27b,A_27a,V0g_2E0,V2x_2E0)) ) ) ).
tff(thm_2Ecombin_2Eo__ABS__R,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c))] :
( ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V0g_2E0),V3x_2E0) = app_2E2(A_27a,A_27c,V0g_2E0,V3x_2E0) )
=> ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V2x_2E0: A_27a] : ( c_2Ecombin_2Eo_2E3(A_27a,A_27b,A_27c,V1f_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V0g_2E0),V2x_2E0) = app_2E2(A_27c,A_27b,V1f_2E0,app_2E2(A_27a,A_27c,V0g_2E0,V2x_2E0)) ) ) ).
tff(thm_2Ecombin_2EK__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( c_2Ecombin_2EK_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Ecombin_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] : ( c_2Ecombin_2ES_2E3(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(thm_2Ecombin_2ES__ABS__L,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),F0_2E0,V1f_2E0),V3x_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0,V3x_2E0) )
=> ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V2x_2E0: A_27a] : ( c_2Ecombin_2ES_2E3(A_27a,A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),F0_2E0,V1f_2E0),V0g_2E0,V2x_2E0) = app_2E2(A_27c,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0,V2x_2E0),app_2E2(A_27a,A_27c,V0g_2E0,V2x_2E0)) ) ) ).
tff(thm_2Ecombin_2ES__ABS__R,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c))] :
( ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V3x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V0g_2E0),V3x_2E0) = app_2E2(A_27a,A_27c,V0g_2E0,V3x_2E0) )
=> ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V2x_2E0: A_27a] : ( c_2Ecombin_2ES_2E3(A_27a,A_27c,A_27b,V1f_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c),F0_2E0,V0g_2E0),V2x_2E0) = app_2E2(A_27c,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0,V2x_2E0),app_2E2(A_27a,A_27c,V0g_2E0,V2x_2E0)) ) ) ).
tff(thm_2Ecombin_2EC__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)),V1x_2E0: A_27b,V2y_2E0: A_27a] : ( c_2Ecombin_2EC_2E3(A_27a,A_27b,A_27c,V0f_2E0,V1x_2E0,V2y_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2y_2E0),V1x_2E0) ) ).
tff(thm_2Ecombin_2EC__ABS__L,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),F0_2E0,V1f_2E0),V3x_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0,V3x_2E0) )
=> ! [V0y_2E0: A_27c,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V2x_2E0: A_27a] : ( c_2Ecombin_2EC_2E3(A_27a,A_27c,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),F0_2E0,V1f_2E0),V0y_2E0,V2x_2E0) = app_2E2(A_27c,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0,V2x_2E0),V0y_2E0) ) ) ).
tff(thm_2Ecombin_2EW__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V1x_2E0: A_27a] : ( c_2Ecombin_2EW_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,V1x_2E0),V1x_2E0) ) ).
tff(thm_2Ecombin_2EI__THM,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Ecombin_2EI_2E1(A_27a,V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Ecombin_2EI__o__ID,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( c_2Ecombin_2Eo_2E2(A_27a,A_27b,A_27b,c_2Ecombin_2EI_2E0(A_27b),V0f_2E0) = V0f_2E0 )
& ( c_2Ecombin_2Eo_2E2(A_27a,A_27b,A_27a,V0f_2E0,c_2Ecombin_2EI_2E0(A_27a)) = V0f_2E0 ) ) ).
tff(thm_2Ecombin_2EK__o__THM,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1v_2E0: A_27c] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,c_2Ecombin_2EK_2E1(A_27c,A_27b,V1v_2E0),V0f_2E0) = c_2Ecombin_2EK_2E1(A_27c,A_27a,V1v_2E0) )
& ! [V2f_2E0: tyop_2Emin_2Efun(A_27d,A_27e),V3v_2E0: A_27d] : ( c_2Ecombin_2Eo_2E2(A_27f,A_27e,A_27d,V2f_2E0,c_2Ecombin_2EK_2E1(A_27d,A_27f,V3v_2E0)) = c_2Ecombin_2EK_2E1(A_27e,A_27f,app_2E2(A_27d,A_27e,V2f_2E0,V3v_2E0)) ) ) ).
tff(thm_2Ecombin_2EUPDATE__APPLY,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
( ! [V0a_2E0: A_27a,V1x_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,V0a_2E0,V1x_2E0,V2f_2E0,V0a_2E0) = V1x_2E0 )
& ! [V3a_2E0: A_27c,V4b_2E0: A_27c,V5x_2E0: A_27d,V6f_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] :
( ( V3a_2E0 != V4b_2E0 )
=> ( c_2Ecombin_2EUPDATE_2E4(A_27c,A_27d,V3a_2E0,V5x_2E0,V6f_2E0,V4b_2E0) = app_2E2(A_27c,A_27d,V6f_2E0,V4b_2E0) ) ) ) ).
tff(thm_2Ecombin_2EAPPLY__UPDATE__THM,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1a_2E0: A_27a,V3c_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,V1a_2E0),V3c_2E0))
<=> ( V1a_2E0 = V3c_2E0 ) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b,V3c_2E0: A_27a] : ( c_2Ecombin_2EUPDATE_2E4(A_27a,A_27b,V1a_2E0,V2b_2E0,V0f_2E0,V3c_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),F0_2E0,V1a_2E0),V3c_2E0),V2b_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V3c_2E0)) ) ) ).
tff(thm_2Ecombin_2EUPDATE__COMMUTES,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27a,V3c_2E0: A_27b,V4d_2E0: A_27b] :
( ( V1a_2E0 != V2b_2E0 )
=> ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2b_2E0,V4d_2E0,V0f_2E0)) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2b_2E0,V4d_2E0,c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0f_2E0)) ) ) ).
tff(thm_2Ecombin_2EUPDATE__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b,V3c_2E0: A_27b] : ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V2b_2E0,V0f_2E0)) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0f_2E0) ) ).
tff(thm_2Ecombin_2EUPDATE__APPLY__ID,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b] :
( ( app_2E2(A_27a,A_27b,V0f_2E0,V1a_2E0) = V2b_2E0 )
<=> ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V2b_2E0,V0f_2E0) = V0f_2E0 ) ) ).
tff(thm_2Ecombin_2EUPDATE__APPLY__IMP__ID,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1b_2E0: A_27b,V2a_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V0f_2E0,V2a_2E0) = V1b_2E0 )
=> ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2a_2E0,V1b_2E0,V0f_2E0) = V0f_2E0 ) ) ).
tff(thm_2Ecombin_2EAPPLY__UPDATE__ID,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a] : ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V1a_2E0),V0f_2E0) = V0f_2E0 ) ).
tff(thm_2Ecombin_2EUPD11__SAME__BASE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27a,V3c_2E0: A_27b,V4d_2E0: A_27b] :
( ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0f_2E0) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2b_2E0,V4d_2E0,V0f_2E0) )
<=> ( ( ( V1a_2E0 = V2b_2E0 )
& ( V3c_2E0 = V4d_2E0 ) )
| ( ( V1a_2E0 != V2b_2E0 )
& ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0f_2E0) = V0f_2E0 )
& ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2b_2E0,V4d_2E0,V0f_2E0) = V0f_2E0 ) ) ) ) ).
tff(thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27c,A_27d),V1f1_2E0: A_27a,V2f2_2E0: A_27b,V3a_2E0: A_27c,V4b_2E0: A_27d,V5c_2E0: A_27d] :
( ( V4b_2E0 != V5c_2E0 )
=> ( c_2Ecombin_2EUPDATE_2E3(A_27c,A_27d,V3a_2E0,V4b_2E0,V0f_2E0) != c_2Ecombin_2EUPDATE_2E3(A_27c,A_27d,V3a_2E0,V5c_2E0,V0f_2E0) ) ) ).
tff(thm_2Ecombin_2EUPD11__SAME__KEY__AND__BASE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1a_2E0: A_27a,V2b_2E0: A_27b,V3c_2E0: A_27b] :
( ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V2b_2E0,V0f_2E0) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1a_2E0,V3c_2E0,V0f_2E0) )
<=> ( V2b_2E0 = V3c_2E0 ) ) ).
tff(thm_2Ecombin_2EUPD__SAME__KEY__UNWIND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2a_2E0: A_27a,V3b_2E0: A_27b,V4c_2E0: A_27b] :
( ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2a_2E0,V3b_2E0,V0f1_2E0) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2a_2E0,V4c_2E0,V1f2_2E0) )
=> ( ( V3b_2E0 = V4c_2E0 )
& ! [V5v_2E0: A_27b] : ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2a_2E0,V5v_2E0,V0f1_2E0) = c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V2a_2E0,V5v_2E0,V1f2_2E0) ) ) ) ).
tff(thm_2Ecombin_2EGEN__LET__RAND,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0v_2E0: A_27c,V1f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V2P_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( app_2E2(A_27b,A_27a,V2P_2E0,c_2Ebool_2ELET_2E2(A_27c,A_27b,V1f_2E0,V0v_2E0)) = c_2Ebool_2ELET_2E2(A_27c,A_27a,c_2Ecombin_2Eo_2E2(A_27c,A_27a,A_27b,V2P_2E0,V1f_2E0),V0v_2E0) ) ).
tff(thm_2Ecombin_2EGEN__LET__RATOR,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: A_27c,V1v_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))] : ( app_2E2(A_27c,A_27a,c_2Ebool_2ELET_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),V2f_2E0,V1v_2E0),V0x_2E0) = c_2Ebool_2ELET_2E2(A_27b,A_27a,c_2Ecombin_2EC_2E2(A_27b,A_27c,A_27a,V2f_2E0,V0x_2E0),V1v_2E0) ) ).
tff(thm_2Ecombin_2ELET__FORALL__ELIM,axiom,
! [A_27a: $tType,V0v_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ELET_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V0v_2E0) = c_2Ebool_2E_21_2E1(A_27a,c_2Ecombin_2ES_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E0,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Emarker_2EAbbrev_2E0,c_2Ecombin_2EC_2E2(A_27a,A_27a,tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E0(A_27a),V0v_2E0))),V1f_2E0)) ) ).
tff(thm_2Ecombin_2EGEN__literal__case__RAND,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0v_2E0: A_27c,V1f_2E0: tyop_2Emin_2Efun(A_27c,A_27b),V2P_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( app_2E2(A_27b,A_27a,V2P_2E0,c_2Ebool_2Eliteral__case_2E2(A_27c,A_27b,V1f_2E0,V0v_2E0)) = c_2Ebool_2Eliteral__case_2E2(A_27c,A_27a,c_2Ecombin_2Eo_2E2(A_27c,A_27a,A_27b,V2P_2E0,V1f_2E0),V0v_2E0) ) ).
tff(thm_2Ecombin_2EGEN__literal__case__RATOR,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: A_27c,V1v_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))] : ( app_2E2(A_27c,A_27a,c_2Ebool_2Eliteral__case_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),V2f_2E0,V1v_2E0),V0x_2E0) = c_2Ebool_2Eliteral__case_2E2(A_27b,A_27a,c_2Ecombin_2EC_2E2(A_27b,A_27c,A_27a,V2f_2E0,V0x_2E0),V1v_2E0) ) ).
tff(thm_2Ecombin_2Eliteral__case__FORALL__ELIM,axiom,
! [A_27a: $tType,V0v_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2Eliteral__case_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V0v_2E0) = c_2Ebool_2E_21_2E1(A_27a,c_2Ecombin_2ES_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E0,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Emarker_2EAbbrev_2E0,c_2Ecombin_2EC_2E2(A_27a,A_27a,tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E0(A_27a),V0v_2E0))),V1f_2E0)) ) ).
tff(thm_2Ecombin_2EASSOC__CONJ,axiom,
p(c_2Ecombin_2EASSOC_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E0)) ).
tff(thm_2Ecombin_2EASSOC__SYM,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] :
( p(c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0))
<=> ! [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,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) = 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)) ) ) ).
tff(thm_2Ecombin_2EASSOC__DISJ,axiom,
p(c_2Ecombin_2EASSOC_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E0)) ).
tff(thm_2Ecombin_2EFCOMM__ASSOC,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))] : ( c_2Ecombin_2EFCOMM_2E2(A_27a,A_27a,A_27a,V0f_2E0,V0f_2E0) = c_2Ecombin_2EASSOC_2E1(A_27a,V0f_2E0) ) ).
tff(thm_2Ecombin_2EMONOID__CONJ__T,axiom,
p(c_2Ecombin_2EMONOID_2E2(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E0,c_2Ebool_2ET_2E0)) ).
tff(thm_2Ecombin_2EMONOID__DISJ__F,axiom,
p(c_2Ecombin_2EMONOID_2E2(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E0,c_2Ebool_2EF_2E0)) ).
tff(thm_2Ecombin_2EFAIL__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a] : ( c_2Ecombin_2EFAIL_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0) = V1x_2E0 ) ).
%------------------------------------------------------------------------------