%------------------------------------------------------------------------------
% 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    :  317 ( 126 unt; 126 typ;   0 def)
%            Number of atoms       :  421 ( 283 equ;  13 cnn)
%            Maximal formula atoms :   30 (   1 avg)
%            Number of connectives : 7315 (  13   ~;  10   |;  79   &;7126   @)
%                                         (  46 <=>;  41  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   6 avg;7126 nst)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :  183 ( 183   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  123 ( 121 usr;  48 con; 0-4 aty)
%            Number of variables   :  683 (   0   ^ 664   !;  19   ?; 683   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(u,type,
    u: $tType ).

thf(d,type,
    d: $tType ).

thf(du,type,
    du: $tType ).

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

thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: $tType ).

thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

thf(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: d > d > d ).

thf(tyop_2Eone_2Eone,type,
    tyop_2Eone_2Eone: d ).

thf(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: d > d ).

thf(tyop_2Esum_2Esum,type,
    tyop_2Esum_2Esum: d > d > d ).

thf(s,type,
    s: d > u > du ).

thf(app_2E2,type,
    app_2E2: du > du > u ).

thf(combin_i_2E0,type,
    combin_i_2E0: u ).

thf(combin_k_2E0,type,
    combin_k_2E0: u ).

thf(combin_s_2E0,type,
    combin_s_2E0: u ).

thf(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

thf(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: du > u ).

thf(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

thf(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: du > du > u ).

thf(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

thf(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: du > du > u ).

thf(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

thf(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).

thf(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

thf(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: du > u ).

thf(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: u ).

thf(c_2Emin_2E_40_2E1,type,
    c_2Emin_2E_40_2E1: du > u ).

thf(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

thf(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: du > du > du > u ).

thf(c_2Ebool_2EDATATYPE_2E0,type,
    c_2Ebool_2EDATATYPE_2E0: u ).

thf(c_2Ebool_2EDATATYPE_2E1,type,
    c_2Ebool_2EDATATYPE_2E1: du > u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Esum_2EINL_2E0,type,
    c_2Esum_2EINL_2E0: u ).

thf(c_2Esum_2EINL_2E1,type,
    c_2Esum_2EINL_2E1: du > u ).

thf(c_2Esum_2EINR_2E0,type,
    c_2Esum_2EINR_2E0: u ).

thf(c_2Esum_2EINR_2E1,type,
    c_2Esum_2EINR_2E1: du > u ).

thf(c_2Eoption_2EIS__NONE_2E0,type,
    c_2Eoption_2EIS__NONE_2E0: u ).

thf(c_2Eoption_2EIS__NONE_2E1,type,
    c_2Eoption_2EIS__NONE_2E1: du > u ).

thf(c_2Eoption_2EIS__SOME_2E0,type,
    c_2Eoption_2EIS__SOME_2E0: u ).

thf(c_2Eoption_2EIS__SOME_2E1,type,
    c_2Eoption_2EIS__SOME_2E1: du > u ).

thf(c_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: u ).

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

thf(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: u ).

thf(c_2Eoption_2EOPTION__ALL_2E0,type,
    c_2Eoption_2EOPTION__ALL_2E0: u ).

thf(c_2Eoption_2EOPTION__ALL_2E2,type,
    c_2Eoption_2EOPTION__ALL_2E2: du > du > u ).

thf(c_2Eoption_2EOPTION__APPLY_2E0,type,
    c_2Eoption_2EOPTION__APPLY_2E0: u ).

thf(c_2Eoption_2EOPTION__APPLY_2E2,type,
    c_2Eoption_2EOPTION__APPLY_2E2: du > du > u ).

thf(c_2Eoption_2EOPTION__BIND_2E0,type,
    c_2Eoption_2EOPTION__BIND_2E0: u ).

thf(c_2Eoption_2EOPTION__BIND_2E2,type,
    c_2Eoption_2EOPTION__BIND_2E2: du > du > u ).

thf(c_2Eoption_2EOPTION__CHOICE_2E0,type,
    c_2Eoption_2EOPTION__CHOICE_2E0: u ).

thf(c_2Eoption_2EOPTION__CHOICE_2E2,type,
    c_2Eoption_2EOPTION__CHOICE_2E2: du > du > u ).

thf(c_2Eoption_2EOPTION__GUARD_2E0,type,
    c_2Eoption_2EOPTION__GUARD_2E0: u ).

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

thf(c_2Eoption_2EOPTION__IGNORE__BIND_2E0,type,
    c_2Eoption_2EOPTION__IGNORE__BIND_2E0: u ).

thf(c_2Eoption_2EOPTION__IGNORE__BIND_2E2,type,
    c_2Eoption_2EOPTION__IGNORE__BIND_2E2: du > du > u ).

thf(c_2Eoption_2EOPTION__JOIN_2E0,type,
    c_2Eoption_2EOPTION__JOIN_2E0: u ).

thf(c_2Eoption_2EOPTION__JOIN_2E1,type,
    c_2Eoption_2EOPTION__JOIN_2E1: du > u ).

thf(c_2Eoption_2EOPTION__MAP_2E0,type,
    c_2Eoption_2EOPTION__MAP_2E0: u ).

thf(c_2Eoption_2EOPTION__MAP_2E2,type,
    c_2Eoption_2EOPTION__MAP_2E2: du > du > u ).

thf(c_2Eoption_2EOPTION__MAP2_2E0,type,
    c_2Eoption_2EOPTION__MAP2_2E0: u ).

thf(c_2Eoption_2EOPTION__MAP2_2E3,type,
    c_2Eoption_2EOPTION__MAP2_2E3: du > du > du > u ).

thf(c_2Eoption_2EOPTION__MCOMP_2E0,type,
    c_2Eoption_2EOPTION__MCOMP_2E0: u ).

thf(c_2Eoption_2EOPTION__MCOMP_2E2,type,
    c_2Eoption_2EOPTION__MCOMP_2E2: du > du > u ).

thf(c_2Eoption_2EOPTION__MCOMP_2E3,type,
    c_2Eoption_2EOPTION__MCOMP_2E3: du > du > du > u ).

thf(c_2Eoption_2EOPTREL_2E0,type,
    c_2Eoption_2EOPTREL_2E0: u ).

thf(c_2Eoption_2EOPTREL_2E3,type,
    c_2Eoption_2EOPTREL_2E3: du > du > du > u ).

thf(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: u ).

thf(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: du > u ).

thf(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

thf(c_2Eoption_2ETHE_2E0,type,
    c_2Eoption_2ETHE_2E0: u ).

thf(c_2Eoption_2ETHE_2E1,type,
    c_2Eoption_2ETHE_2E1: du > u ).

thf(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: u ).

thf(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
    c_2Ebool_2ETYPE__DEFINITION_2E2: du > du > u ).

thf(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

thf(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: du > du > u ).

thf(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: u ).

thf(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: du > du > u ).

thf(c_2Eone_2Eone_2E0,type,
    c_2Eone_2Eone_2E0: u ).

thf(c_2Eoption_2Eoption__ABS_2E0,type,
    c_2Eoption_2Eoption__ABS_2E0: u ).

thf(c_2Eoption_2Eoption__ABS_2E1,type,
    c_2Eoption_2Eoption__ABS_2E1: du > u ).

thf(c_2Eoption_2Eoption__CASE_2E0,type,
    c_2Eoption_2Eoption__CASE_2E0: u ).

thf(c_2Eoption_2Eoption__CASE_2E3,type,
    c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).

thf(c_2Eoption_2Eoption__REP_2E0,type,
    c_2Eoption_2Eoption__REP_2E0: u ).

thf(c_2Eoption_2Eoption__REP_2E1,type,
    c_2Eoption_2Eoption__REP_2E1: du > u ).

thf(c_2Eoption_2Esome_2E0,type,
    c_2Eoption_2Esome_2E0: u ).

thf(c_2Eoption_2Esome_2E1,type,
    c_2Eoption_2Esome_2E1: du > u ).

thf(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

thf(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: du > u ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).

thf(mono_2Eapp_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_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: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Eapp_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_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_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Ebool_2E_2F_5C,type,
    mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
    mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Ebool_2EF,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Eoption_2EOPTION__GUARD,type,
    mono_2Ec_2Eoption_2EOPTION__GUARD: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Ebool_2ET,type,
    mono_2Ec_2Ebool_2ET: $o ).

thf(mono_2Ec_2Ebool_2E_5C_2F,type,
    mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(mono_2Ec_2Eone_2Eone,type,
    mono_2Ec_2Eone_2Eone: mono_2Etyop_2Eone_2Eone ).

thf(mono_2Ec_2Ebool_2E_7E,type,
    mono_2Ec_2Ebool_2E_7E: $o > $o ).

thf(i_mono_2Etyop_2Emin_2Ebool,type,
    i_mono_2Etyop_2Emin_2Ebool: $o > u ).

thf(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: ( $o > $o ) > u ).

thf(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: ( $o > $o > $o ) > u ).

thf(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: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).

thf(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: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).

thf(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_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).

thf(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_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).

thf(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_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).

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

thf(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 ).

thf(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > $o ).

thf(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 > $o > $o ).

thf(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 > $o > $o > $o ).

thf(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 > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(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 > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(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_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(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_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(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_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

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

thf(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 ).

thf(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 ) ) ) ).

thf(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 ) ) ).

thf(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 ) ) ).

thf(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 ) ) ) ) ) ) ).

thf(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
    <=> ( V0
        & V1 ) ) ).

thf(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
    <=> ( V0
        | V1 ) ) ).

thf(reserved_2Elogic_2E_7E,axiom,
    ! [V0: $o] :
      ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
    <=> ( (~) @ V0 ) ) ).

thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
    <=> ( V0
       => V1 ) ) ).

thf(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
      ( ( 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 ) ) ) ).

thf(reserved_2Equant_2E_21,axiom,
    ! [A_27a: d,V0f_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 ) @ V0f_2E0 ) ) ) )
    <=> ! [V1x_2E0: u] : ( 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 ) ) ) ) ) ).

thf(reserved_2Equant_2E_3F,axiom,
    ! [A_27a: d,V0f_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 ) @ V0f_2E0 ) ) ) )
    <=> ? [V1x_2E0: u] : ( 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 ) ) ) ) ) ).

thf(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 ) ) ).

thf(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 ) ) ).

thf(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 ) ) ).

thf(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 ) ) ).

thf(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 ) ) ).

thf(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 ) ) ).

thf(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 ) ) ).

thf(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 ) ) ).

thf(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 ) ) ).

thf(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 ) ) ).

thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o] :
      ( ( 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 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o] :
      ( ( 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 ) ) )
      = V0 ) ).

thf(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: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_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 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_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 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_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 ) ) )
      = V0 ) ).

thf(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: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_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 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_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 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone] :
      ( ( j_mono_2Etyop_2Eone_2Eone @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: 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 ) ) )
      = V0 ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) )
    <=> ( 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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( 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 ) ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ A_27b @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0: $o,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 ) ) @ ( 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 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [A_27a: d,X0: 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 ) ) ) )
      = ( 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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o > $o,V1: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( 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 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o > $o,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( 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 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(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: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: $o] :
      ( ( 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 @ V1 ) ) )
      = ( 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 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: $o] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
      = ( 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 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eone_2Eone] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
      = ( 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 ) ) @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V1 ) ) ) ) ) ).

thf(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: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: 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 @ ( V0 @ V1 ) ) )
      = ( 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 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: 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 @ V1 ) ) )
      = ( 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 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(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_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 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V2: 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_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V0 @ V1 @ V2 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V1 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V2 ) ) ) ) ) ).

thf(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_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(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_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ c_2Eoption_2ESOME_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V0 ) ) ) ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_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: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eone_2Eone] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_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: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(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 )
     => ? [V0rep_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 ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Esum_2Esum @ A_27a @ tyop_2Eone_2Eone ) ) @ V0rep_2E0 ) ) ) ) ) ).

thf(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] :
          ( mono_2Ec_2Ebool_2ET
        <=> ( ( 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 ) ) ) ) ).

thf(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 ) ) ) ) ) ) ).

thf(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 ) ) ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ).

thf(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 )
      & ( ( 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 ) ) ).

thf(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 )
      & ( ( 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 ) ) ).

thf(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 ) ) ).

thf(thm_2Eoption_2EOPTION__MAP2__DEF,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V1x_2E0: u,V2y_2E0: u] :
          ( ( 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 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V1x_2E0 ) ) ) )
            & ( 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 ) ) ) ) ) ).

thf(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 ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ) ).

thf(thm_2Eoption_2EOPTION__GUARD__def,axiom,
    ( ( ( mono_2Ec_2Eoption_2EOPTION__GUARD @ mono_2Ec_2Ebool_2ET )
      = ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Eone_2Eone ) )
    & ( ( mono_2Ec_2Eoption_2EOPTION__GUARD @ mono_2Ec_2Ebool_2EF )
      = mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Eone_2Eone ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(thm_2Eoption_2EOPTREL__def,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1x_2E0: u,V2y_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 ) ) @ 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 ) ) ) )
            & ( 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 ) ) ) ) ) ) ) ).

thf(thm_2Eoption_2Esome__def,axiom,
    ! [A_27a: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V0P_2E0: u] :
          ( ( 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] : ( 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 ) ) ) ) ) ) ).

thf(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 )
      & ! [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 ) ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(thm_2Eoption_2Eoption__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ( 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] : ( 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] : ( 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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(thm_2Eoption_2EFORALL__OPTION,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ! [V1opt_2E0: u] : ( 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 ) ) ) )
    <=> ( ( 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] : ( 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 ) ) ) ) ) ) ) ) ).

thf(thm_2Eoption_2EEXISTS__OPTION,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ? [V1opt_2E0: u] : ( 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 ) ) ) )
    <=> ( ( 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] : ( 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 ) ) ) ) ) ) ) ) ).

thf(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 ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ).

thf(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 ) ) ) ).

thf(thm_2Eoption_2EIS__SOME__EXISTS,axiom,
    ! [A_27a: d,V0opt_2E0: u] :
      ( ( 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 ) ) ) ) ) ).

thf(thm_2Eoption_2EIS__NONE__EQ__NONE,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 ) @ V0x_2E0 ) ) ) )
    <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V0x_2E0 )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).

thf(thm_2Eoption_2ENOT__IS__SOME__EQ__NONE,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 ) @ V0x_2E0 ) ) ) ) )
    <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V0x_2E0 )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).

thf(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 ) ) ).

thf(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 ) ) ).

thf(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 )
      & ( ( 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 )
      & ! [V9x_2E0: u] :
          ( ( 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] :
          ( ( (~) @ ( 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] :
          ( ( 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] :
          ( ( 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] :
          ( ( 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] :
          ( ( 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 ) ) ) ).

thf(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 ) ) ) ) ).

thf(thm_2Eoption_2EIF__EQUALS__OPTION,axiom,
    ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2P: $o] :
      ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V2P ) ) @ ( 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 ) )
      <=> ( (~) @ V2P ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V2P ) ) @ ( 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 ) )
      <=> V2P )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V2P ) ) @ ( 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 ) ) ) )
      <=> ( V2P
          & ( ( 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 ) ) @ ( 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 ) ) ) )
      <=> ( ( (~) @ V2P )
          & ( ( s @ A_27a @ V1x_2E0 )
            = ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ).

thf(thm_2Eoption_2EIF__NONE__EQUALS__OPTION,axiom,
    ! [A_27a: d,V0x_2E0: u,V1X_2E0: u,V2P: $o] :
      ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V2P ) ) @ ( 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 ) )
      <=> ( V2P
         => ( 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 ) ) @ ( 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 ) )
      <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1X_2E0 ) ) ) )
         => V2P ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V2P ) ) @ ( 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 ) ) ) )
      <=> ( V2P
          & ( ( 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 ) ) @ ( 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 ) ) ) )
      <=> ( ( (~) @ V2P )
          & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1X_2E0 )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) ) ) ).

thf(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 ) ) ) ) ) ) ).

thf(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 ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ) ) ).

thf(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 ) ) ) ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ) ) ).

thf(thm_2Eoption_2EIS__SOME__BIND,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1g_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__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V1g_2E0 ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V0x_2E0 ) ) ) ) ) ).

thf(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 ) ) ) ).

thf(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 ) ) ) ) ) ) ) ).

thf(thm_2Eoption_2EOPTION__GUARD__COND,axiom,
    ! [V0b: $o] :
      ( ( mono_2Ec_2Eoption_2EOPTION__GUARD @ V0b )
      = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V0b @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Eone_2Eone ) @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Eone_2Eone ) ) ).

thf(thm_2Eoption_2EOPTION__GUARD__EQ__THM,axiom,
    ! [V0b: $o] :
      ( ( ( ( mono_2Ec_2Eoption_2EOPTION__GUARD @ V0b )
          = ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Eone_2Eone ) )
      <=> V0b )
      & ( ( ( mono_2Ec_2Eoption_2EOPTION__GUARD @ V0b )
          = mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Eone_2Eone )
      <=> ( (~) @ V0b ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ).

thf(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 ) ) ) ) ).

thf(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 ) ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ) ).

thf(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] :
          ( ( 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 ) ) ) )
         => ( 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 ) ) ) ) )
     => ( ( 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 ) ) ) )
       => ( 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 ) ) ) ) ) ) ).

thf(thm_2Eoption_2EOPTREL__refl,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( ! [V1x_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 @ 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] : ( 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 ) ) ) ) ) ).

thf(thm_2Eoption_2Esome__intro,axiom,
    ! [A_27a: d,V0Q_2E0: u,V1P_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 ) @ V1P_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
           => ( 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] : ( (~) @ ( 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 ) ) ) ) )
         => ( 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 ) ) ) ) ) )
     => ( 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 ) ) ) ) ) ) ) ).

thf(thm_2Eoption_2Esome__elim,axiom,
    ! [A_27a: d,V0Q_2E0: u,V1P_2E0: u] :
      ( ( 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] :
            ( ( 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 ) ) ) )
            & ( 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] : ( (~) @ ( 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 ) ) ) ) )
          & ( 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 ) ) ) ) ) ) ) ).

thf(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 )
     => ( ( 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 ) ) ) ).

thf(thm_2Eoption_2Esome__EQ,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0y_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 @ 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] :
            ( ( 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 ) ) ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(thm_2Eoption_2EOPTION__ALL__MONO,axiom,
    ! [A_27a: d,V0opt_2E0: u,V1P_27_2E0: u,V2P_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( ( 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 ) ) ) )
         => ( 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 ) ) ) ) )
     => ( ( 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 ) @ V1P_27_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V0opt_2E0 ) ) ) ) ) ) ).

thf(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 ) ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(thm_2Eoption_2Eoption__Induct,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1a_2E0: u] : ( 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 ) ) ) ) ) )
        & ( 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] : ( 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 ) ) ) ) ) ).

thf(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 ) ) ) ).

thf(thm_2Eoption_2Edatatype__option,axiom,
    ! [A_27a: d,A_27b: d,V0option_2E0: u] : ( 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 ) ) ) ) ) ) ).

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