TPTP Problem File: ITP002_4.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ITP002_4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Eoption_2EOPTION__MAP2__THM.p, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : thm_2Eoption_2EOPTION__MAP2__THM.p [Gau20]
% : HL400501_4.p [TPAP]
% Status : Theorem
% Rating : 1.00 v8.1.0, 0.91 v7.5.0
% Syntax : Number of formulae : 2465 ( 729 unt;1079 typ; 0 def)
% Number of atoms : 3088 (1112 equ)
% Maximal formula atoms : 16 ( 1 avg)
% Number of connectives : 1882 ( 180 ~; 188 |; 425 &)
% ( 458 <=>; 631 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 18 ( 2 avg)
% Number of types : 28 ( 27 usr)
% Number of type conns : 877 ( 556 >; 321 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 429 ( 429 usr; 175 con; 0-4 aty)
% Number of variables : 4430 (4322 !; 108 ?;4430 :)
% SPC : TF0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP002_4.ax').
include('Axioms/ITP001/ITP003_4.ax').
include('Axioms/ITP001/ITP004_4.ax').
include('Axioms/ITP001/ITP005_4.ax').
include('Axioms/ITP001/ITP006_4.ax').
include('Axioms/ITP001/ITP007_4.ax').
include('Axioms/ITP001/ITP008_4.ax').
include('Axioms/ITP001/ITP009_4.ax').
include('Axioms/ITP001/ITP010_4.ax').
include('Axioms/ITP001/ITP011_4.ax').
include('Axioms/ITP001/ITP012_4.ax').
%------------------------------------------------------------------------------
tff(u,type,
u: $tType ).
tff(d,type,
d: $tType ).
tff(du,type,
du: $tType ).
tff(mono_2Etyop_2Emin_2Ebool,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(mono_2Etyop_2Eone_2Eone,type,
mono_2Etyop_2Eone_2Eone: $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( d * d ) > d ).
tff(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: d ).
tff(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: d > d ).
tff(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: ( d * d ) > d ).
tff(s,type,
s: ( d * u ) > du ).
tff(app_2E2,type,
app_2E2: ( du * du ) > u ).
tff(p,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0: u ).
tff(combin_k_2E0,type,
combin_k_2E0: u ).
tff(combin_s_2E0,type,
combin_s_2E0: u ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0: u ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1: du > u ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: u ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: ( du * du ) > u ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: u ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: du > u ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0: u ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3: ( du * du * du ) > u ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
tff(c_2Esum_2EINL_2E0,type,
c_2Esum_2EINL_2E0: u ).
tff(c_2Esum_2EINL_2E1,type,
c_2Esum_2EINL_2E1: du > u ).
tff(c_2Esum_2EINR_2E0,type,
c_2Esum_2EINR_2E0: u ).
tff(c_2Esum_2EINR_2E1,type,
c_2Esum_2EINR_2E1: du > u ).
tff(c_2Eoption_2EIS__NONE_2E0,type,
c_2Eoption_2EIS__NONE_2E0: u ).
tff(c_2Eoption_2EIS__NONE_2E1,type,
c_2Eoption_2EIS__NONE_2E1: du > u ).
tff(c_2Eoption_2EIS__SOME_2E0,type,
c_2Eoption_2EIS__SOME_2E0: u ).
tff(c_2Eoption_2EIS__SOME_2E1,type,
c_2Eoption_2EIS__SOME_2E1: du > u ).
tff(c_2Eoption_2ENONE_2E0,type,
c_2Eoption_2ENONE_2E0: u ).
tff(c_2Eoption_2EOPTION__JOIN_2E0,type,
c_2Eoption_2EOPTION__JOIN_2E0: u ).
tff(c_2Eoption_2EOPTION__JOIN_2E1,type,
c_2Eoption_2EOPTION__JOIN_2E1: du > u ).
tff(c_2Eoption_2EOPTION__MAP_2E0,type,
c_2Eoption_2EOPTION__MAP_2E0: u ).
tff(c_2Eoption_2EOPTION__MAP_2E2,type,
c_2Eoption_2EOPTION__MAP_2E2: ( du * du ) > u ).
tff(c_2Eoption_2EOPTION__MAP2_2E0,type,
c_2Eoption_2EOPTION__MAP2_2E0: u ).
tff(c_2Eoption_2EOPTION__MAP2_2E3,type,
c_2Eoption_2EOPTION__MAP2_2E3: ( du * du * du ) > u ).
tff(c_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0: u ).
tff(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1: du > u ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
tff(c_2Eoption_2ETHE_2E0,type,
c_2Eoption_2ETHE_2E0: u ).
tff(c_2Eoption_2ETHE_2E1,type,
c_2Eoption_2ETHE_2E1: du > u ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0: u ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2: ( du * du ) > u ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: u ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).
tff(c_2Eone_2Eone_2E0,type,
c_2Eone_2Eone_2E0: u ).
tff(c_2Eoption_2Eoption__ABS_2E0,type,
c_2Eoption_2Eoption__ABS_2E0: u ).
tff(c_2Eoption_2Eoption__ABS_2E1,type,
c_2Eoption_2Eoption__ABS_2E1: du > u ).
tff(c_2Eoption_2Eoption__CASE_2E0,type,
c_2Eoption_2Eoption__CASE_2E0: u ).
tff(c_2Eoption_2Eoption__CASE_2E3,type,
c_2Eoption_2Eoption__CASE_2E3: ( du * du * du ) > u ).
tff(c_2Eoption_2Eoption__REP_2E0,type,
c_2Eoption_2Eoption__REP_2E0: u ).
tff(c_2Eoption_2Eoption__REP_2E1,type,
c_2Eoption_2Eoption__REP_2E1: du > u ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: u ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: du > u ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Ec_2Ebool_2E_2F_5C_2E0,type,
mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Ec_2Ebool_2E_2F_5C_2E2,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E2,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Ebool_2EF_2E0,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Ebool_2ET_2E0,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Ebool_2E_5C_2F_2E0,type,
mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Ec_2Ebool_2E_5C_2F_2E2,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Eone_2Eone_2E0,type,
mono_2Ec_2Eone_2Eone_2E0: mono_2Etyop_2Eone_2Eone ).
tff(mono_2Ec_2Ebool_2E_7E_2E0,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Ec_2Ebool_2E_7E_2E1,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(i_mono_2Etyop_2Emin_2Ebool,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(i_mono_2Etyop_2Eone_2Eone,type,
i_mono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eone_2Eone > u ).
tff(j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(j_mono_2Etyop_2Eone_2Eone,type,
j_mono_2Etyop_2Eone_2Eone: du > mono_2Etyop_2Eone_2Eone ).
tff(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
( ! [V2x_2E0: u] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
=> ( s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ) ).
tff(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(reserved_2Eho_2Etruth,axiom,
p(mono_2Ec_2Ebool_2ET_2E0) ).
tff(reserved_2Eho_2Enotfalse,axiom,
~ p(mono_2Ec_2Ebool_2EF_2E0) ).
tff(reserved_2Eho_2Ebool__cases__ax,axiom,
! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( V0t_2E0 = mono_2Ec_2Ebool_2ET_2E0 )
| ( V0t_2E0 = mono_2Ec_2Ebool_2EF_2E0 ) ) ).
tff(reserved_2Eho_2Ei__thm,axiom,
! [A_27a: d,V0x_2E0: u] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).
tff(reserved_2Eho_2Ek__thm,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).
tff(reserved_2Eho_2Es__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(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))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).
tff(reserved_2Elogic_2E_2F_5C,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
( p(mono_2Ec_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(reserved_2Elogic_2E_5C_2F,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
( p(mono_2Ec_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(reserved_2Elogic_2E_7E,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool] :
( p(mono_2Ec_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
( p(mono_2Ec_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(reserved_2Elogic_2E_3D,axiom,
! [A_27a: d,V0_2E0: u,V1_2E0: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))
<=> ( s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ) ).
tff(reserved_2Equant_2E_21,axiom,
! [A_27a: d,V0f_2E0: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))
<=> ! [V1x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) ) ).
tff(reserved_2Equant_2E_3F,axiom,
! [A_27a: d,V0f_2E0: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))
<=> ? [V1x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) ) ).
tff(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,V0_2E0)))) = s(tyop_2Emin_2Ebool,V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0_2E0: u] : s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(j_mono_2Etyop_2Eone_2Eone(s(tyop_2Eone_2Eone,V0_2E0)))) = s(tyop_2Eone_2Eone,V0_2E0) ).
tff(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0_2E0: mono_2Etyop_2Eone_2Eone] : j_mono_2Etyop_2Eone_2Eone(s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(V0_2E0))) = V0_2E0 ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0) )
<=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))))) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) ).
tff(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27a: d,X0_2E0: u] : s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27a,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),c_2Esum_2EINL_2E0),s(A_27a,X0_2E0))) ).
tff(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27a: d,X0_2E0: mono_2Etyop_2Eone_2Eone] : s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(X0_2E0)))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),c_2Esum_2EINR_2E0),s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(X0_2E0)))) ).
tff(arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2Eoption_2EIS__NONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) ).
tff(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) ).
tff(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0)))) ).
tff(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27c),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27c),X0_2E0)))) ).
tff(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__JOIN_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) ).
tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) ).
tff(arityeq3_2Ec_2Eoption_2EOPTION__MAP2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0),s(tyop_2Eoption_2Eoption(A_27c),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2EOPTION__MAP2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27c),X2_2E0))) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0))) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] : s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(A_27b,X0_2E0))) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u] : s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2ESOME_2E0),s(A_27c,X0_2E0))) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] : s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) ).
tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) ).
tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] : s(A_27b,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),A_27b),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))) ).
tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u] : s(A_27c,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27c),X0_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),A_27c),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27c),X0_2E0))) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),X1_2E0)))) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Eoption_2Eoption__ABS_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2Eoption__ABS_2E0),s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),X0_2E0))) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) ).
tff(arityeq1_2Ec_2Eoption_2Eoption__REP_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),c_2Eoption_2Eoption__REP_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: mono_2Etyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ).
tff(thm_2Eoption_2Eoption__TY__DEF,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),V1x_2E0)))) = mono_2Ec_2Ebool_2ET_2E0
=> ? [V0rep_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),V0rep_2E0))))) ) ).
tff(thm_2Eoption_2Eoption__REP__ABS__DEF,axiom,
! [A_27a: d] :
( ! [V0a_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0a_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),V0a_2E0)
& ! [V1r_2E0: u] :
( p(mono_2Ec_2Ebool_2ET_2E0)
<=> ( s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),V1r_2E0))))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),V1r_2E0) ) ) ) ).
tff(thm_2Eoption_2ESOME__DEF,axiom,
! [A_27a: d,V0x_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27a,V0x_2E0))))) ).
tff(thm_2Eoption_2ENONE__DEF,axiom,
! [A_27a: d] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(mono_2Ec_2Eone_2Eone_2E0)))))) ).
tff(thm_2Eoption_2Eoption__case__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0v_2E0: u,V1f_2E0: u] : s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(A_27b,V0v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))) = s(A_27b,V0v_2E0)
& ! [V2x_2E0: u,V3v_2E0: u,V4f_2E0: u] : s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))),s(A_27b,V3v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(A_27a,V2x_2E0))) ) ).
tff(thm_2Eoption_2EOPTION__MAP__DEF,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0f_2E0: u,V1x_2E0: u] : s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0)))))
& ! [V2f_2E0: u] : s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) ).
tff(thm_2Eoption_2EIS__SOME__DEF,axiom,
! [A_27a: d] :
( ! [V0x_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))))) = mono_2Ec_2Ebool_2ET_2E0
& ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) = mono_2Ec_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eoption_2EIS__NONE__DEF,axiom,
! [A_27a: d] :
( ! [V0x_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))))) = mono_2Ec_2Ebool_2EF_2E0
& ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 ) ) ).
tff(thm_2Eoption_2ETHE__DEF,axiom,
! [A_27a: d,V0x_2E0: u] : s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))))) = s(A_27a,V0x_2E0) ).
tff(thm_2Eoption_2EOPTION__MAP2__DEF,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
( ! [V1x_2E0: u,V2y_2E0: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0)))))
<=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0)))))
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0))))) ) )
=> ! [V0f_2E0: u,V1x_2E0: u,V2y_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_2E0),s(A_27b,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0))))),s(A_27c,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) ) ).
tff(thm_2Eoption_2EOPTION__JOIN__DEF,axiom,
! [A_27a: d] :
( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
& ! [V0x_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0) ) ).
tff(thm_2Eoption_2Eoption__Axiom,axiom,
! [A_27a: d,A_27b: d,V0e_2E0: u,V1f_2E0: u] :
? [V2fn_2E0: u] :
( ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27b),V2fn_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(A_27b,V0e_2E0) )
& ! [V3x_2E0: u] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27b),V2fn_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0))) ) ).
tff(thm_2Eoption_2Eoption__induction,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))))
& ! [V1a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1a_2E0))))))) )
=> ! [V2x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2x_2E0))))) ) ).
tff(thm_2Eoption_2Eoption__nchotomy,axiom,
! [A_27a: d,V0opt_2E0: u] :
( ( s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
| ? [V1x_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) ) ).
tff(thm_2Eoption_2EFORALL__OPTION,axiom,
! [A_27a: d,V0P_2E0: u] :
( ! [V1opt_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt_2E0)))))
<=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))))
& ! [V2x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))))))) ) ) ).
tff(thm_2Eoption_2EEXISTS__OPTION,axiom,
! [A_27a: d,V0P_2E0: u] :
( ? [V1opt_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt_2E0)))))
<=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))))
| ? [V2x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))))))) ) ) ).
tff(thm_2Eoption_2ESOME__11,axiom,
! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1y_2E0))) )
<=> ( s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) ) ) ).
tff(thm_2Eoption_2ENOT__NONE__SOME,axiom,
! [A_27a: d,V0x_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) ).
tff(thm_2Eoption_2ENOT__SOME__NONE,axiom,
! [A_27a: d,V0x_2E0: u] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ).
tff(thm_2Eoption_2EOPTION__MAP2__THM,conjecture,
! [A_27a: d,A_27b: d,A_27c: d,V0y_2E0: u,V1x_2E0: u,V2f_2E0: u] :
( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0y_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1x_2E0))),s(A_27c,V0y_2E0))))) )
& ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
& ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0y_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
& ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).
%------------------------------------------------------------------------------