%------------------------------------------------------------------------------
% File     : ITP013_4 : TPTP v9.0.0. 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    : option.ax [Gau19]
%          : HL4013_4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  337 ( 123 unt; 142 typ;   0 def)
%            Number of atoms       :  381 ( 282 equ)
%            Maximal formula atoms :   27 (   1 avg)
%            Number of connectives :  201 (  15   ~;  12   |;  80   &)
%                                         (  51 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   5 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of types       :   14 (  13 usr)
%            Number of type conns  :  114 (  75   >;  39   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  128 ( 128 usr;  54 con; 0-3 aty)
%            Number of variables   :  684 ( 665   !;  19   ?; 684   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
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_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: $tType ).

tff(mono_2Etyop_2Eone_2Eone,type,
    mono_2Etyop_2Eone_2Eone: $tType ).

tff(mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: $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_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: u ).

tff(c_2Emin_2E_40_2E1,type,
    c_2Emin_2E_40_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_2EDATATYPE_2E0,type,
    c_2Ebool_2EDATATYPE_2E0: u ).

tff(c_2Ebool_2EDATATYPE_2E1,type,
    c_2Ebool_2EDATATYPE_2E1: 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_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: u ).

tff(c_2Ecombin_2EK_2E1,type,
    c_2Ecombin_2EK_2E1: du > u ).

tff(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: u ).

tff(c_2Eoption_2EOPTION__ALL_2E0,type,
    c_2Eoption_2EOPTION__ALL_2E0: u ).

tff(c_2Eoption_2EOPTION__ALL_2E2,type,
    c_2Eoption_2EOPTION__ALL_2E2: ( du * du ) > u ).

tff(c_2Eoption_2EOPTION__APPLY_2E0,type,
    c_2Eoption_2EOPTION__APPLY_2E0: u ).

tff(c_2Eoption_2EOPTION__APPLY_2E2,type,
    c_2Eoption_2EOPTION__APPLY_2E2: ( du * du ) > u ).

tff(c_2Eoption_2EOPTION__BIND_2E0,type,
    c_2Eoption_2EOPTION__BIND_2E0: u ).

tff(c_2Eoption_2EOPTION__BIND_2E2,type,
    c_2Eoption_2EOPTION__BIND_2E2: ( du * du ) > u ).

tff(c_2Eoption_2EOPTION__CHOICE_2E0,type,
    c_2Eoption_2EOPTION__CHOICE_2E0: u ).

tff(c_2Eoption_2EOPTION__CHOICE_2E2,type,
    c_2Eoption_2EOPTION__CHOICE_2E2: ( du * du ) > u ).

tff(c_2Eoption_2EOPTION__GUARD_2E0,type,
    c_2Eoption_2EOPTION__GUARD_2E0: u ).

tff(c_2Eoption_2EOPTION__GUARD_2E1,type,
    c_2Eoption_2EOPTION__GUARD_2E1: du > u ).

tff(c_2Eoption_2EOPTION__IGNORE__BIND_2E0,type,
    c_2Eoption_2EOPTION__IGNORE__BIND_2E0: u ).

tff(c_2Eoption_2EOPTION__IGNORE__BIND_2E2,type,
    c_2Eoption_2EOPTION__IGNORE__BIND_2E2: ( du * du ) > 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_2EOPTION__MCOMP_2E0,type,
    c_2Eoption_2EOPTION__MCOMP_2E0: u ).

tff(c_2Eoption_2EOPTION__MCOMP_2E2,type,
    c_2Eoption_2EOPTION__MCOMP_2E2: ( du * du ) > u ).

tff(c_2Eoption_2EOPTION__MCOMP_2E3,type,
    c_2Eoption_2EOPTION__MCOMP_2E3: ( du * du * du ) > u ).

tff(c_2Eoption_2EOPTREL_2E0,type,
    c_2Eoption_2EOPTREL_2E0: u ).

tff(c_2Eoption_2EOPTREL_2E3,type,
    c_2Eoption_2EOPTREL_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_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: u ).

tff(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_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_2Eoption_2Esome_2E0,type,
    c_2Eoption_2Esome_2E0: u ).

tff(c_2Eoption_2Esome_2E1,type,
    c_2Eoption_2Esome_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_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 * mono_2Etyop_2Eone_2Eone ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_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_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Ebool_2EF_2E0,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Eoption_2EOPTION__GUARD_2E0,type,
    mono_2Ec_2Eoption_2EOPTION__GUARD_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Ec_2Eoption_2EOPTION__GUARD_2E1,type,
    mono_2Ec_2Eoption_2EOPTION__GUARD_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

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_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 > u ).

tff(i_mono_2Etyop_2Eone_2Eone,type,
    i_mono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eone_2Eone > u ).

tff(i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > 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_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 ).

tff(j_mono_2Etyop_2Eone_2Eone,type,
    j_mono_2Etyop_2Eone_2Eone: du > mono_2Etyop_2Eone_2Eone ).

tff(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

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_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),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(ij_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),V0_2E0)))) = s(tyop_2Eoption_2Eoption(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_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_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(ji_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(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(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(A_27b,X1_2E0))),s(A_27b,X2_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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,X2_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(X0_2E0,X1_2E0,X2_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27b,X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(A_27b,X0_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_2Ecombin_2EK_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Ecombin_2EK_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__ALL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTION__ALL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_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_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27c_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27c_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_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_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__CHOICE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_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))),c_2Eoption_2EOPTION__CHOICE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2EOPTION__GUARD_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool] : ( mono_2Ec_2Eoption_2EOPTION__GUARD_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Ec_2Eoption_2EOPTION__GUARD_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__IGNORE__BIND_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__IGNORE__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__IGNORE__BIND_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_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_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_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__IGNORE__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__IGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27c),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_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_27c),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__IGNORE__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27c),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_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(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27c),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27c),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2EOPTION__MAP2_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MAP2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_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(arityeq3_2Ec_2Eoption_2EOPTION__MCOMP_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__MCOMP_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),X1_2E0),s(A_27c,X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))),s(A_27c,X2_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27c,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool))),c_2Eoption_2EOPTREL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),c_2Eoption_2EOPTREL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),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_2Emin_2Efun_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27c_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27c_29_29_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))))),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Eone_2Eone] : ( mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone,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(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_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] : ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(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))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),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(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_2Emin_2Efun(A_27a,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_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(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_2Eoption_2Esome_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2Esome_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_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_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,V1_2E0: mono_2Etyop_2Eone_2Eone] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0)),s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),c_2Ebool_2ECOND_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V2_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V1_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V2_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ENONE_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),c_2Eoption_2ESOME_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Eone_2Eone] : ( s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone(V0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME_2E1(s(tyop_2Eone_2Eone,i_mono_2Etyop_2Eone_2Eone(V0_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__BIND__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ! [V1x_2E0: u,V2f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2f_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2f_2E0),s(A_27b,V1x_2E0))) ) ) ).

tff(thm_2Eoption_2EOPTION__IGNORE__BIND__def,axiom,
    ! [A_27a: d,A_27b: d,V0m1_2E0: u,V1m2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),V0m1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),V0m1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Eoption_2Eoption(A_27a),V1m2_2E0))))) ) ).

tff(thm_2Eoption_2EOPTION__GUARD__def,axiom,
    ( ( mono_2Ec_2Eoption_2EOPTION__GUARD_2E1(mono_2Ec_2Ebool_2ET_2E0) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Eone_2Eone_2E0) )
    & ( mono_2Ec_2Eoption_2EOPTION__GUARD_2E1(mono_2Ec_2Ebool_2EF_2E0) = mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone ) ) ).

tff(thm_2Eoption_2EOPTION__CHOICE__def,axiom,
    ! [A_27a: d] :
      ( ! [V0m2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0) )
      & ! [V1x_2E0: u,V2m2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V2m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) ) ) ).

tff(thm_2Eoption_2EOPTION__MCOMP__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0g_2E0: u,V1f_2E0: u,V2m_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MCOMP_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0),s(A_27c,V2m_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0),s(A_27c,V2m_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0g_2E0))) ) ).

tff(thm_2Eoption_2EOPTION__APPLY__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ! [V1f_2E0: u,V2x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Eoption_2Eoption(A_27b),V2x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2x_2E0))) ) ) ).

tff(thm_2Eoption_2EOPTREL__def,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1x_2E0: u,V2y_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0)))))
    <=> ( ( ( s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
          & ( s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) )
        | ? [V3x0_2E0: u,V4y0_2E0: u] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x0_2E0))) )
            & ( s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V4y0_2E0))) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x0_2E0))),s(A_27b,V4y0_2E0))))) ) ) ) ).

tff(thm_2Eoption_2Esome__def,axiom,
    ! [A_27a: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V0P_2E0: u] :
          ( p(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),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_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),V0P_2E0),s(A_27a,V1x_2E0))))) )
     => ( ! [V0P_2E0: u,V2x_2E0: u] : ( 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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) )
       => ! [V0P_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) ) ) ) ).

tff(thm_2Eoption_2EOPTION__ALL__def,axiom,
    ! [A_27a: d] :
      ( ! [V0P_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ! [V1P_2E0: u,V2x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_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,axiom,
    ! [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) ) ) ).

tff(thm_2Eoption_2EIS__SOME__EXISTS,axiom,
    ! [A_27a: d,V0opt_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0opt_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_2EIS__NONE__EQ__NONE,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))
    <=> ( s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Eoption_2ENOT__IS__SOME__EQ__NONE,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))
    <=> ( s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Eoption_2Eoption__case__ID,axiom,
    ! [A_27a: d,V0x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0) ) ).

tff(thm_2Eoption_2Eoption__case__SOME__ID,axiom,
    ! [A_27a: d,V0x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0) ) ).

tff(thm_2Eoption_2Eoption__CLAUSES,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1e_2E0: u,V2e_2E0: u] :
      ( ! [V3x_2E0: u,V4y_2E0: u] :
          ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4y_2E0))) )
        <=> ( s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0) ) )
      & ! [V5x_2E0: u] : ( s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V5x_2E0))))) = s(A_27a,V5x_2E0) )
      & ! [V6x_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,V6x_2E0))) )
      & ! [V7x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7x_2E0))) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ! [V8x_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,V8x_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 )
      & ! [V9x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V9x_2E0)))))
        <=> ( s(tyop_2Eoption_2Eoption(A_27a),V9x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) )
      & ! [V10x_2E0: u] :
          ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V10x_2E0)))))
        <=> ( s(tyop_2Eoption_2Eoption(A_27a),V10x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) )
      & ! [V11x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0)))))
         => ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0) ) )
      & ! [V12x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V12x_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V12x_2E0) )
      & ! [V13x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0) )
      & ! [V14x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V14x_2E0)))))
         => ( s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V14x_2E0),s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(A_27b,V2e_2E0) ) )
      & ! [V15x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0)))))
         => ( s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0),s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0))))) ) )
      & ! [V16x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0)))))
         => ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0) ) )
      & ! [V17v_2E0: u,V18f_2E0: u] : ( s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(A_27b,V17v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V18f_2E0))) = s(A_27b,V17v_2E0) )
      & ! [V19x_2E0: u,V20v_2E0: u,V21f_2E0: u] : ( s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V19x_2E0))),s(A_27b,V20v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V21f_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V21f_2E0),s(A_27a,V19x_2E0))) )
      & ! [V22f_2E0: u,V23x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V22f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V23x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V22f_2E0),s(A_27a,V23x_2E0))))) )
      & ! [V24f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V24f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
      & ( 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) )
      & ! [V25x_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),V25x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),V25x_2E0) ) ) ).

tff(thm_2Eoption_2Eoption__case__compute,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u,V2e_2E0: u] : ( s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))))),s(A_27b,V2e_2E0))) ) ).

tff(thm_2Eoption_2EIF__EQUALS__OPTION,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2P_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V2P_2E0)),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      <=> ~ p(V2P_2E0) )
      & ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V2P_2E0)),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      <=> p(V2P_2E0) )
      & ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V2P_2E0)),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) )
      <=> ( p(V2P_2E0)
          & ( s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0) ) ) )
      & ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V2P_2E0)),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) )
      <=> ( ~ p(V2P_2E0)
          & ( s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0) ) ) ) ) ).

tff(thm_2Eoption_2EIF__NONE__EQUALS__OPTION,axiom,
    ! [A_27a: d,V0x_2E0: u,V1X_2E0: u,V2P_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V2P_2E0)),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      <=> ( p(V2P_2E0)
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0))))) ) )
      & ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V2P_2E0)),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0)))))
         => p(V2P_2E0) ) )
      & ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V2P_2E0)),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0),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))) )
      <=> ( p(V2P_2E0)
          & ( s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) ) ) )
      & ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V2P_2E0)),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) )
      <=> ( ~ p(V2P_2E0)
          & ( s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) ) ) ) ) ).

tff(thm_2Eoption_2EOPTION__MAP__EQ__SOME,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u,V2y_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),V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V2y_2E0))) )
    <=> ? [V3z_2E0: u] :
          ( ( s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3z_2E0))) )
          & ( s(A_27b,V2y_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3z_2E0))) ) ) ) ).

tff(thm_2Eoption_2EOPTION__MAP__EQ__NONE,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),V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
    <=> ( s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      <=> ( s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) )
      & ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0))) )
      <=> ( s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) ) ) ).

tff(thm_2Eoption_2EOPTION__MAP__COMPOSE,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0x_2E0: u,V1g_2E0: u,V2f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))) ) ).

tff(thm_2Eoption_2EOPTION__MAP__CONG,axiom,
    ! [A_27a: d,A_27b: d,V0opt1_2E0: u,V1opt2_2E0: u,V2f1_2E0: u,V3f2_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),V0opt1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1opt2_2E0) )
        & ! [V4x_2E0: u] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),V1opt2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) )
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f2_2E0),s(A_27a,V4x_2E0))) ) ) )
     => ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f2_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt2_2E0))) ) ) ).

tff(thm_2Eoption_2EIS__SOME__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))) ) ).

tff(thm_2Eoption_2EOPTION__JOIN__EQ__SOME,axiom,
    ! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1y_2E0))) )
    <=> ( s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),V0x_2E0) = s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1y_2E0))))) ) ) ).

tff(thm_2Eoption_2EOPTION__MAP2__SOME,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0v_2E0: u,V1o2_2E0: u,V2o1_2E0: u,V3f_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V3f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2o1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1o2_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0v_2E0))) )
    <=> ? [V4x1_2E0: u,V5x2_2E0: u] :
          ( ( s(tyop_2Eoption_2Eoption(A_27a),V2o1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x1_2E0))) )
          & ( s(tyop_2Eoption_2Eoption(A_27b),V1o2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V5x2_2E0))) )
          & ( s(A_27c,V0v_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)),V3f_2E0),s(A_27a,V4x1_2E0))),s(A_27b,V5x2_2E0))) ) ) ) ).

tff(thm_2Eoption_2EOPTION__MAP2__NONE,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0o2_2E0: u,V1o1_2E0: u,V2f_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1o1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0o2_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0) )
    <=> ( ( s(tyop_2Eoption_2Eoption(A_27a),V1o1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
        | ( s(tyop_2Eoption_2Eoption(A_27b),V0o2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) ) ) ).

tff(thm_2Eoption_2EOPTION__MAP2__cong,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0x1_2E0: u,V1x2_2E0: u,V2y1_2E0: u,V3y2_2E0: u,V4f1_2E0: u,V5f2_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),V0x1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1x2_2E0) )
        & ( s(tyop_2Eoption_2Eoption(A_27b),V2y1_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V3y2_2E0) )
        & ! [V6x_2E0: u,V7y_2E0: u] :
            ( ( ( s(tyop_2Eoption_2Eoption(A_27a),V1x2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0))) )
              & ( s(tyop_2Eoption_2Eoption(A_27b),V3y2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V7y_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)),V4f1_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_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)),V5f2_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))) ) ) )
     => ( s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V4f1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2y1_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V5f2_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x2_2E0),s(tyop_2Eoption_2Eoption(A_27b),V3y2_2E0))) ) ) ).

tff(thm_2Eoption_2EOPTION__MAP__CASE,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))))) ) ).

tff(thm_2Eoption_2EOPTION__BIND__cong,axiom,
    ! [A_27a: d,A_27b: d,V0o1_2E0: u,V1o2_2E0: u,V2f1_2E0: u,V3f2_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),V0o1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1o2_2E0) )
        & ! [V4x_2E0: u] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),V1o2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) )
           => ( s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f1_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3f2_2E0),s(A_27a,V4x_2E0))) ) ) )
     => ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V0o1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1o2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3f2_2E0))) ) ) ).

tff(thm_2Eoption_2EOPTION__BIND__EQUALS__OPTION,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1p_2E0: u,V2f_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
      <=> ( ( s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
          | ? [V3x_2E0: u] :
              ( ( s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) )
              & ( s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) ) ) )
      & ( ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) )
      <=> ? [V4x_2E0: u] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) )
            & ( s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) ) ) ) ) ).

tff(thm_2Eoption_2EIS__SOME__BIND,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1g_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1g_2E0)))))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))))) ) ).

tff(thm_2Eoption_2EOPTION__IGNORE__BIND__thm,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0v_2E0: u,V1m_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1m_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0v_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V1m_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1m_2E0) ) ) ).

tff(thm_2Eoption_2EOPTION__IGNORE__BIND__EQUALS__OPTION,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1m2_2E0: u,V2m1_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
      <=> ( ( s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
          | ( s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) ) )
      & ( ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) )
      <=> ? [V3x_2E0: u] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) )
            & ( s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) ) ) ) ) ).

tff(thm_2Eoption_2EOPTION__GUARD__COND,axiom,
    ! [V0b_2E0: mono_2Etyop_2Emin_2Ebool] : ( mono_2Ec_2Eoption_2EOPTION__GUARD_2E1(V0b_2E0) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29(V0b_2E0,mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Eone_2Eone_2E0),mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone) ) ).

tff(thm_2Eoption_2EOPTION__GUARD__EQ__THM,axiom,
    ! [V0b_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( mono_2Ec_2Eoption_2EOPTION__GUARD_2E1(V0b_2E0) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Eone_2Eone_2E0) )
      <=> p(V0b_2E0) )
      & ( ( mono_2Ec_2Eoption_2EOPTION__GUARD_2E1(V0b_2E0) = mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone )
      <=> ~ p(V0b_2E0) ) ) ).

tff(thm_2Eoption_2EOPTION__CHOICE__EQ__NONE,axiom,
    ! [A_27a: d,V0m2_2E0: u,V1m1_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1m1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
    <=> ( ( s(tyop_2Eoption_2Eoption(A_27a),V1m1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
        & ( s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ) ).

tff(thm_2Eoption_2EOPTION__CHOICE__NONE,axiom,
    ! [A_27a: d,V0m1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),V0m1_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V0m1_2E0) ) ).

tff(thm_2Eoption_2EOPTION__MCOMP__ASSOC,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0h_2E0: u,V1g_2E0: u,V2f_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),V2f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0h_2E0))) ) ).

tff(thm_2Eoption_2EOPTION__MCOMP__ID,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0g_2E0: u,V1f_2E0: u] :
      ( ( s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),V0g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),V0g_2E0) )
      & ( s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0) ) ) ).

tff(thm_2Eoption_2EOPTION__APPLY__MAP2,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0y_2E0: u,V1x_2E0: u,V2f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0))) ) ).

tff(thm_2Eoption_2ESOME__SOME__APPLY,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V0x_2E0))))) ) ).

tff(thm_2Eoption_2ESOME__APPLY__PERMUTE,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0x_2E0: u,V2f_2E0: u] : ( 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_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V0x_2E0))) )
     => ! [V0x_2E0: u,V1f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),F0_2E0),s(A_27a,V0x_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1f_2E0))) ) ) ).

tff(thm_2Eoption_2EOPTION__APPLY__o,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0x_2E0: u,V1g_2E0: u,V2f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1g_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1g_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))))) ) ).

tff(thm_2Eoption_2EOPTREL__MONO,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: u,V2Q_2E0: u,V3P_2E0: u] :
      ( ! [V4x_2E0: u,V5y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0))))) ) ) ).

tff(thm_2Eoption_2EOPTREL__refl,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( ! [V1x_2E0: u] : 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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0)))))
     => ! [V2x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2x_2E0))))) ) ).

tff(thm_2Eoption_2Esome__intro,axiom,
    ! [A_27a: d,V0Q_2E0: u,V1P_2E0: u] :
      ( ( ! [V2x_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_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),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))))))) )
        & ( ! [V3x_2E0: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_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),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_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),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))))) ) ).

tff(thm_2Eoption_2Esome__elim,axiom,
    ! [A_27a: d,V0Q_2E0: u,V1P_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),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))))))
     => ( ? [V2x_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_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),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))))))) )
        | ( ! [V3x_2E0: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_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),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))))) ) ) ) ).

tff(thm_2Eoption_2Esome__F,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0),s(A_27a,V0x_2E0)))) = mono_2Ec_2Ebool_2EF_2E0 )
     => ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Eoption_2Esome__EQ,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0y_2E0: u,V2x_2E0: u] :
          ( 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)),F1_2E0),s(A_27a,V0y_2E0))),s(A_27a,V2x_2E0)))))
        <=> ( s(A_27a,V0y_2E0) = s(A_27a,V2x_2E0) ) )
     => ( ! [V0y_2E0: u,V1x_2E0: u] :
            ( 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)),F0_2E0),s(A_27a,V0y_2E0))),s(A_27a,V1x_2E0)))))
          <=> ( s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0) ) )
       => ! [V0y_2E0: u] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(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)),F0_2E0),s(A_27a,V0y_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) )
            & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(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)),F1_2E0),s(A_27a,V0y_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) ) ) ) ) ).

tff(thm_2Eoption_2Eoption__case__cong,axiom,
    ! [A_27a: d,A_27b: d,V0v_27_2E0: u,V1f_27_2E0: u,V2M_2E0: u,V3M_27_2E0: u,V4v_2E0: u,V5f_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),V2M_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0) )
        & ( ( s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
         => ( s(A_27b,V4v_2E0) = s(A_27b,V0v_27_2E0) ) )
        & ! [V6x_2E0: u] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0))) )
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0),s(A_27a,V6x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_27_2E0),s(A_27a,V6x_2E0))) ) ) )
     => ( s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V2M_2E0),s(A_27b,V4v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0))) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0),s(A_27b,V0v_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_27_2E0))) ) ) ).

tff(thm_2Eoption_2EOPTION__ALL__MONO,axiom,
    ! [A_27a: d,V0opt_2E0: u,V1P_27_2E0: u,V2P_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_27_2E0),s(A_27a,V3x_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_27_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0))))) ) ) ).

tff(thm_2Eoption_2EOPTION__ALL__CONG,axiom,
    ! [A_27a: d,V0opt_2E0: u,V1opt_27_2E0: u,V2P_2E0: u,V3P_27_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1opt_27_2E0) )
        & ! [V4x_2E0: u] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),V1opt_27_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) )
           => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V4x_2E0)))) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt_27_2E0)))) ) ) ).

tff(thm_2Eoption_2Eoption__case__eq,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u,V1sc_2E0: u,V2opt_2E0: u,V3nc_2E0: u] :
      ( ( s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V2opt_2E0),s(A_27b,V3nc_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1sc_2E0))) = s(A_27b,V0v_2E0) )
    <=> ( ( ( s(tyop_2Eoption_2Eoption(A_27a),V2opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
          & ( s(A_27b,V3nc_2E0) = s(A_27b,V0v_2E0) ) )
        | ? [V4x_2E0: u] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),V2opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) )
            & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1sc_2E0),s(A_27a,V4x_2E0))) = s(A_27b,V0v_2E0) ) ) ) ) ).

tff(thm_2Eoption_2Eoption__Induct,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [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)))))))
        & 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),V2x_2E0))))) ) ).

tff(thm_2Eoption_2Eoption__CASES,axiom,
    ! [A_27a: d,V0opt_2E0: u] :
      ( ? [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))) )
      | ( s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Eoption_2Edatatype__option,axiom,
    ! [A_27a: d,A_27b: d,V0option_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),A_27b)),V0option_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))))))) ).

%------------------------------------------------------------------------------