%------------------------------------------------------------------------------
% File     : ITP081^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : alist.ax [Gau19]
%          : HL4081^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  366 ( 152 unt; 162 typ;   0 def)
%            Number of atoms       :  328 ( 229 equ;   4 cnn)
%            Maximal formula atoms :    6 (   0 avg)
%            Number of connectives : 9672 (   4   ~;   1   |;  17   &;9582   @)
%                                         (  18 <=>;  50  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   7 avg;9582 nst)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  191 ( 191   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  160 ( 158 usr;  70 con; 0-3 aty)
%            Number of variables   :  783 (   0   ^ 781   !;   2   ?; 783   :)
% 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_2Enum_2Enum,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

thf(tyop_2Efinite__map_2Efmap,type,
    tyop_2Efinite__map_2Efmap: d > d > d ).

thf(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: d > d ).

thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

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

thf(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

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

thf(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: 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_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: u ).

thf(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: du > 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_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: u ).

thf(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_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_2Elist_2EALL__DISTINCT_2E0,type,
    c_2Elist_2EALL__DISTINCT_2E0: u ).

thf(c_2Elist_2EALL__DISTINCT_2E1,type,
    c_2Elist_2EALL__DISTINCT_2E1: du > u ).

thf(c_2Ealist_2EALOOKUP_2E0,type,
    c_2Ealist_2EALOOKUP_2E0: u ).

thf(c_2Ealist_2EALOOKUP_2E1,type,
    c_2Ealist_2EALOOKUP_2E1: du > u ).

thf(c_2Ealist_2EALOOKUP_2E2,type,
    c_2Ealist_2EALOOKUP_2E2: du > du > u ).

thf(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: u ).

thf(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: du > du > u ).

thf(c_2Epred__set_2ECARD_2E0,type,
    c_2Epred__set_2ECARD_2E0: u ).

thf(c_2Epred__set_2ECARD_2E1,type,
    c_2Epred__set_2ECARD_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_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

thf(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: du > du > u ).

thf(c_2Elist_2EEL_2E0,type,
    c_2Elist_2EEL_2E0: u ).

thf(c_2Elist_2EEL_2E2,type,
    c_2Elist_2EEL_2E2: du > du > u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Efinite__map_2EFAPPLY_2E0,type,
    c_2Efinite__map_2EFAPPLY_2E0: u ).

thf(c_2Efinite__map_2EFAPPLY_2E2,type,
    c_2Efinite__map_2EFAPPLY_2E2: du > du > u ).

thf(c_2Efinite__map_2EFDOM_2E0,type,
    c_2Efinite__map_2EFDOM_2E0: u ).

thf(c_2Efinite__map_2EFDOM_2E1,type,
    c_2Efinite__map_2EFDOM_2E1: du > u ).

thf(c_2Efinite__map_2EFEMPTY_2E0,type,
    c_2Efinite__map_2EFEMPTY_2E0: u ).

thf(c_2Elist_2EFILTER_2E0,type,
    c_2Elist_2EFILTER_2E0: u ).

thf(c_2Elist_2EFILTER_2E2,type,
    c_2Elist_2EFILTER_2E2: du > du > u ).

thf(c_2Efinite__map_2EFLOOKUP_2E0,type,
    c_2Efinite__map_2EFLOOKUP_2E0: u ).

thf(c_2Efinite__map_2EFLOOKUP_2E1,type,
    c_2Efinite__map_2EFLOOKUP_2E1: du > u ).

thf(c_2Efinite__map_2EFLOOKUP_2E2,type,
    c_2Efinite__map_2EFLOOKUP_2E2: du > du > u ).

thf(c_2Elist_2EFOLDR_2E0,type,
    c_2Elist_2EFOLDR_2E0: u ).

thf(c_2Elist_2EFOLDR_2E3,type,
    c_2Elist_2EFOLDR_2E3: du > du > du > u ).

thf(c_2Efinite__map_2EFRANGE_2E0,type,
    c_2Efinite__map_2EFRANGE_2E0: u ).

thf(c_2Efinite__map_2EFRANGE_2E1,type,
    c_2Efinite__map_2EFRANGE_2E1: du > u ).

thf(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: u ).

thf(c_2Epair_2EFST_2E1,type,
    c_2Epair_2EFST_2E1: du > u ).

thf(c_2Efinite__map_2EFUNION_2E0,type,
    c_2Efinite__map_2EFUNION_2E0: u ).

thf(c_2Efinite__map_2EFUNION_2E2,type,
    c_2Efinite__map_2EFUNION_2E2: du > du > u ).

thf(c_2Efinite__map_2EFUPDATE_2E0,type,
    c_2Efinite__map_2EFUPDATE_2E0: u ).

thf(c_2Efinite__map_2EFUPDATE_2E2,type,
    c_2Efinite__map_2EFUPDATE_2E2: du > du > u ).

thf(c_2Efinite__map_2EFUPDATE__LIST_2E0,type,
    c_2Efinite__map_2EFUPDATE__LIST_2E0: u ).

thf(c_2Efinite__map_2EFUPDATE__LIST_2E2,type,
    c_2Efinite__map_2EFUPDATE__LIST_2E2: du > du > u ).

thf(c_2Epred__set_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: u ).

thf(c_2Epred__set_2EGSPEC_2E1,type,
    c_2Epred__set_2EGSPEC_2E1: du > u ).

thf(c_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: u ).

thf(c_2Epred__set_2EIMAGE_2E0,type,
    c_2Epred__set_2EIMAGE_2E0: u ).

thf(c_2Epred__set_2EIMAGE_2E2,type,
    c_2Epred__set_2EIMAGE_2E2: du > du > u ).

thf(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: u ).

thf(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: du > du > u ).

thf(c_2Epred__set_2EINJ_2E0,type,
    c_2Epred__set_2EINJ_2E0: u ).

thf(c_2Epred__set_2EINJ_2E3,type,
    c_2Epred__set_2EINJ_2E3: du > du > du > u ).

thf(c_2Ewhile_2ELEAST_2E0,type,
    c_2Ewhile_2ELEAST_2E0: u ).

thf(c_2Ewhile_2ELEAST_2E1,type,
    c_2Ewhile_2ELEAST_2E1: du > u ).

thf(c_2Elist_2ELENGTH_2E0,type,
    c_2Elist_2ELENGTH_2E0: u ).

thf(c_2Elist_2ELENGTH_2E1,type,
    c_2Elist_2ELENGTH_2E1: du > u ).

thf(c_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: u ).

thf(c_2Elist_2ELIST__TO__SET_2E1,type,
    c_2Elist_2ELIST__TO__SET_2E1: du > u ).

thf(c_2Elist_2EMAP_2E0,type,
    c_2Elist_2EMAP_2E0: u ).

thf(c_2Elist_2EMAP_2E2,type,
    c_2Elist_2EMAP_2E2: du > du > u ).

thf(c_2Efinite__map_2EMAP__KEYS_2E0,type,
    c_2Efinite__map_2EMAP__KEYS_2E0: u ).

thf(c_2Efinite__map_2EMAP__KEYS_2E2,type,
    c_2Efinite__map_2EMAP__KEYS_2E2: du > du > u ).

thf(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

thf(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: u ).

thf(c_2Eoption_2EOPTION__MAP_2E0,type,
    c_2Eoption_2EOPTION__MAP_2E0: u ).

thf(c_2Eoption_2EOPTION__MAP_2E1,type,
    c_2Eoption_2EOPTION__MAP_2E1: du > u ).

thf(c_2Esorting_2EPERM_2E0,type,
    c_2Esorting_2EPERM_2E0: u ).

thf(c_2Esorting_2EPERM_2E2,type,
    c_2Esorting_2EPERM_2E2: du > du > u ).

thf(c_2Elist_2EREVERSE_2E0,type,
    c_2Elist_2EREVERSE_2E0: u ).

thf(c_2Elist_2EREVERSE_2E1,type,
    c_2Elist_2EREVERSE_2E1: du > u ).

thf(c_2Elist_2ESET__TO__LIST_2E0,type,
    c_2Elist_2ESET__TO__LIST_2E0: u ).

thf(c_2Elist_2ESET__TO__LIST_2E1,type,
    c_2Elist_2ESET__TO__LIST_2E1: du > u ).

thf(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: u ).

thf(c_2Epair_2ESND_2E1,type,
    c_2Epair_2ESND_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_2Esorting_2ESTABLE_2E0,type,
    c_2Esorting_2ESTABLE_2E0: u ).

thf(c_2Esorting_2ESTABLE_2E2,type,
    c_2Esorting_2ESTABLE_2E2: du > du > u ).

thf(c_2Epred__set_2ESUBSET_2E0,type,
    c_2Epred__set_2ESUBSET_2E0: u ).

thf(c_2Epred__set_2ESUBSET_2E2,type,
    c_2Epred__set_2ESUBSET_2E2: du > 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_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: u ).

thf(c_2Epair_2EUNCURRY_2E1,type,
    c_2Epair_2EUNCURRY_2E1: du > u ).

thf(c_2Epred__set_2EUNIV_2E0,type,
    c_2Epred__set_2EUNIV_2E0: u ).

thf(c_2Elist_2EZIP_2E0,type,
    c_2Elist_2EZIP_2E0: u ).

thf(c_2Elist_2EZIP_2E1,type,
    c_2Elist_2EZIP_2E1: 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_2Ealist_2Ealist__range_2E0,type,
    c_2Ealist_2Ealist__range_2E0: u ).

thf(c_2Ealist_2Ealist__range_2E1,type,
    c_2Ealist_2Ealist__range_2E1: du > u ).

thf(c_2Ealist_2Ealist__to__fmap_2E0,type,
    c_2Ealist_2Ealist__to__fmap_2E0: u ).

thf(c_2Ealist_2Ealist__to__fmap_2E1,type,
    c_2Ealist_2Ealist__to__fmap_2E1: du > u ).

thf(c_2Ealist_2Efmap__to__alist_2E0,type,
    c_2Ealist_2Efmap__to__alist_2E0: u ).

thf(c_2Ealist_2Efmap__to__alist_2E1,type,
    c_2Ealist_2Efmap__to__alist_2E1: du > u ).

thf(c_2Erelation_2Einv__image_2E0,type,
    c_2Erelation_2Einv__image_2E0: u ).

thf(c_2Erelation_2Einv__image_2E2,type,
    c_2Erelation_2Einv__image_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_2Efinite__map_2Eo__f_2E0,type,
    c_2Efinite__map_2Eo__f_2E0: u ).

thf(c_2Efinite__map_2Eo__f_2E2,type,
    c_2Efinite__map_2Eo__f_2E2: du > 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_2Erelation_2Etotal_2E0,type,
    c_2Erelation_2Etotal_2E0: u ).

thf(c_2Erelation_2Etotal_2E1,type,
    c_2Erelation_2Etotal_2E1: du > u ).

thf(c_2Erelation_2Etransitive_2E0,type,
    c_2Erelation_2Etransitive_2E0: u ).

thf(c_2Erelation_2Etransitive_2E1,type,
    c_2Erelation_2Etransitive_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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

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

thf(mono_2Ec_2Eprim__rec_2E_3C,type,
    mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

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

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

thf(mono_2Ec_2Ewhile_2ELEAST,type,
    mono_2Ec_2Ewhile_2ELEAST: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).

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_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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Enum_2Enum,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > 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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Enum_2Enum,type,
    j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).

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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Enum_2Enum @ 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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ 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_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ A_27d @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ A_27d @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ A_27d @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ A_27d @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29,axiom,
    ! [A_27a: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27d ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X1_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_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Elist_2EALL__DISTINCT_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2EALOOKUP_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Ealist_2EALOOKUP_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ealist_2EALOOKUP_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_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Ealist_2EALOOKUP_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2EALOOKUP_2E1_2Emono_2EA_27d_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27d ) ) ) @ c_2Ealist_2EALOOKUP_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ealist_2EALOOKUP_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_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Ealist_2EALOOKUP_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ealist_2EALOOKUP_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_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27c ) ) ) @ c_2Ealist_2EALOOKUP_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2EALOOKUP_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Ealist_2EALOOKUP_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2EALOOKUP_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Ealist_2EALOOKUP_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2EALOOKUP_2E1_2Emono_2EA_27d_20mono_2EA_27c,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27d ) ) ) @ c_2Ealist_2EALOOKUP_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epred__set_2ECARD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ c_2Epred__set_2ECARD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_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_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27d_29,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) ) @ c_2Elist_2EEL_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ A_27b @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ A_27b ) ) @ c_2Elist_2EEL_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Elist_2EEL_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2EFILTER_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( c_2Elist_2EFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) ) ) @ c_2Elist_2EFILTER_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFLOOKUP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Efinite__map_2EFLOOKUP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_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_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_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_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFLOOKUP_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( c_2Efinite__map_2EFLOOKUP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27d ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2EFOLDR_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFRANGE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFRANGE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ A_27a @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUNION_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EIMAGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Epred__set_2EINJ_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_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINJ_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27d ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27d_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EMAP__KEYS_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EMAP__KEYS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EMAP__KEYS_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27b: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) ) ) @ c_2Efinite__map_2EMAP__KEYS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Eoption_2EOPTION__MAP_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( 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 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( c_2Eoption_2EOPTION__MAP_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27d ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esorting_2EPERM_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2EPERM_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Esorting_2EPERM_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Esorting_2EPERM_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2EPERM_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Esorting_2EPERM_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Elist_2EREVERSE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ c_2Elist_2EREVERSE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ESET__TO__LIST_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ESET__TO__LIST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Elist_2ESET__TO__LIST_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ A_27b @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ 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 @ 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(arityeq2_2Ec_2Esorting_2ESTABLE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2ESTABLE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Esorting_2ESTABLE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_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_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ 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_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_2Ctyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27d_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27c_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Elist_2EZIP_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) ) @ ( c_2Elist_2EZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) ) ) @ c_2Elist_2EZIP_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Ealist__range_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ealist_2Ealist__range_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Ealist_2Ealist__range_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ c_2Ealist_2Ealist__to__fmap_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ c_2Ealist_2Ealist__to__fmap_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) @ c_2Ealist_2Ealist__to__fmap_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) ) @ c_2Ealist_2Ealist__to__fmap_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) ) @ c_2Ealist_2Ealist__to__fmap_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) @ c_2Ealist_2Ealist__to__fmap_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Ealist__to__fmap_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) @ c_2Ealist_2Ealist__to__fmap_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Efmap__to__alist_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Ealist_2Efmap__to__alist_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Efmap__to__alist_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ c_2Ealist_2Efmap__to__alist_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Efmap__to__alist_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ c_2Ealist_2Efmap__to__alist_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Efmap__to__alist_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ c_2Ealist_2Efmap__to__alist_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ealist_2Efmap__to__alist_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) ) @ c_2Ealist_2Efmap__to__alist_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Erelation_2Einv__image_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2Einv__image_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ 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_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Erelation_2Einv__image_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27d_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,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_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ 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 @ ( tyop_2Eoption_2Eoption @ 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_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ 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_2Efinite__map_2Eo__f_2E2_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] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [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_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( 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_27b @ ( 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_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etotal_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( 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_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2Etotal_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etransitive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( 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_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2Etransitive_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( 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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(thm_2Ealist_2Efmap__to__alist__def,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0s_2E0: u,V1k_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0s_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0s_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ) )
     => ! [V0s_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0s_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ESET__TO__LIST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0s_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2Ealist__to__fmap__def,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V1k_2E0: u,V2v_2E0: u,V3f_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27b @ V2v_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3f_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) ) ) ) ) )
     => ! [V0s_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0s_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ F0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0s_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2Ealist__range__def,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0m_2E0: u,V1v_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_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0m_2E0 ) ) ) @ ( s @ A_27a @ V1v_2E0 ) ) ) )
        <=> ? [V2k_2E0: u] :
              ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0m_2E0 ) @ ( s @ A_27b @ V2k_2E0 ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1v_2E0 ) ) ) ) )
     => ( ! [V0m_2E0: u,V1v_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0m_2E0 ) ) ) @ ( s @ A_27a @ V1v_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1v_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0m_2E0 ) ) ) @ ( s @ A_27a @ V1v_2E0 ) ) ) ) ) )
       => ! [V0m_2E0: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ealist_2Ealist__range_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0m_2E0 ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0m_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2Efmap__to__alist__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ).

thf(thm_2Ealist_2Ealist__to__fmap__thm,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0v_2E0: u,V1t_2E0: u,V2k_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) )
      & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V2k_2E0 ) @ ( s @ A_27d @ V0v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ V1t_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V2k_2E0 ) @ ( s @ A_27d @ V0v_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1q_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 @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ A_27b @ V1q_2E0 ) ) ) )
        & ! [V2x_2E0: u,V3y_2E0: u,V4t_2E0: u,V5q_2E0: u] :
            ( ( ( (~)
                @ ( ( s @ A_27b @ V2x_2E0 )
                  = ( s @ A_27b @ V5q_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 @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V4t_2E0 ) ) ) @ ( s @ A_27b @ V5q_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 @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V2x_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V4t_2E0 ) ) ) ) ) @ ( s @ A_27b @ V5q_2E0 ) ) ) ) ) )
     => ! [V6v_2E0: u,V7v1_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 @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V6v_2E0 ) ) ) @ ( s @ A_27b @ V7v1_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__def,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V2x_2E0: u,V4q_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_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27b @ V2x_2E0 ) ) ) @ ( s @ A_27b @ V4q_2E0 ) ) ) )
        <=> ( ( s @ A_27b @ V2x_2E0 )
            = ( s @ A_27b @ V4q_2E0 ) ) )
     => ( ! [V0q_2E0: u] :
            ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ A_27b @ V0q_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
        & ! [V1y_2E0: u,V2x_2E0: u,V3t_2E0: u,V4q_2E0: u] :
            ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V2x_2E0 ) @ ( s @ A_27a @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V3t_2E0 ) ) ) @ ( s @ A_27b @ V4q_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27b @ V2x_2E0 ) ) ) @ ( s @ A_27b @ V4q_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V3t_2E0 ) @ ( s @ A_27b @ V4q_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__FAILS,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1l_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V1l_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
    <=> ! [V2k_2E0: u,V3v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V2k_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V1l_2E0 ) ) ) ) ) )
         => ( (~)
            @ ( ( s @ A_27b @ V2k_2E0 )
              = ( s @ A_27b @ V0x_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__NONE,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1x_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) )
    <=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__TABULATE,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V2f_2E0: u,V3k_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) @ ( s @ A_27a @ V3k_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3k_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V3k_2E0 ) ) ) ) ) )
     => ! [V0x_2E0: u,V1l_2E0: u,V2f_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) )
         => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__EQ__FLOOKUP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0fm_2E0: u,V1al_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Efinite__map_2EFLOOKUP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1al_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1al_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V0fm_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( c_2Efinite__map_2EFLOOKUP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V0fm_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EMEM__fmap__to__alist,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: u,V2fm_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) ) ) ) ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) ) ) ) ) )
        & ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
          = ( s @ A_27b @ V0y_2E0 ) ) ) ) ).

thf(thm_2Ealist_2EMEM__fmap__to__alist__FLOOKUP,axiom,
    ! [A_27a: d,A_27b: d,V0p_2E0: u,V1fm_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V0p_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) ) ) ) ) ) ) )
    <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ A_27a @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EMEM__pair__fmap__to__alist__FLOOKUP,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u,V2fm_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) ) ) ) ) ) ) )
    <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V1y_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2ELENGTH__fmap__to__alist,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epred__set_2ECARD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2Efmap__to__alist__to__fmap,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ).

thf(thm_2Ealist_2EALOOKUP__MEM,axiom,
    ! [A_27a: d,A_27b: d,V0al_2E0: u,V1k_2E0: u,V2v_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V2v_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__SOME__FAPPLY__alist__to__fmap,axiom,
    ! [A_27a: d,A_27b: d,V0al_2E0: u,V1k_2E0: u,V2v_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V2v_2E0 ) ) ) )
     => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) )
        = ( s @ A_27b @ V2v_2E0 ) ) ) ).

thf(thm_2Ealist_2Ealist__to__fmap__FAPPLY__MEM,axiom,
    ! [A_27a: d,A_27b: d,V0al_2E0: u,V1z_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1z_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1z_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) @ ( s @ A_27a @ V1z_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__MAP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V2x_2E0: u,V3y_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ A_27c @ V2x_2E0 ) ) ) @ ( s @ A_27a @ V3y_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V2x_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) ) ) )
     => ! [V0f_2E0: u,V1al_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ V1al_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Eoption_2EOPTION__MAP_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ V1al_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EFDOM__alist__to__fmap,axiom,
    ! [A_27a: d,A_27b: d,V0al_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) ) ) ) ).

thf(thm_2Ealist_2Ealist__to__fmap__prefix,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l1_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l2_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l1_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2Ealist__to__fmap__APPEND,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__prefix,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u,V1ls_2E0: u,V2k_2E0: u,V3ls2_2E0: u] :
      ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1ls_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V0v_2E0 ) ) ) )
       => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1ls_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3ls2_2E0 ) ) ) @ ( s @ A_27a @ V2k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V0v_2E0 ) ) ) ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1ls_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) )
       => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1ls_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3ls2_2E0 ) ) ) @ ( s @ A_27a @ V2k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3ls2_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__APPEND,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V3v_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ F0_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V3v_2E0 ) ) ) )
     => ! [V0l1_2E0: u,V1l2_2E0: u,V2k_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) ) @ ( s @ A_27a @ V2k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ F0_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EFUPDATE__LIST__EQ__APPEND__REVERSE,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u,V1fm_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EFLOOKUP__FUPDATE__LIST__ALOOKUP__SOME,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u,V1ls_2E0: u,V2k_2E0: u,V3fm_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V1ls_2E0 ) @ ( s @ A_27b @ V2k_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0v_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V3fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V1ls_2E0 ) ) ) ) ) @ ( s @ A_27b @ V2k_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0v_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EFLOOKUP__FUPDATE__LIST__ALOOKUP__NONE,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u,V1k_2E0: u,V2fm_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0ls_2E0 ) @ ( s @ A_27b @ V1k_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0ls_2E0 ) ) ) ) ) @ ( s @ A_27b @ V1k_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2fm_2E0 ) @ ( s @ A_27b @ V1k_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EFUNION__alist__to__fmap,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u,V1fm_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) ) ).

thf(thm_2Ealist_2Ealist__to__fmap__MAP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F0_2E0: u] :
      ( ! [V0f1_2E0: u,V1f2_2E0: u,V3x_2E0: u,V4y_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V1f2_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27c @ V4y_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V1f2_2E0 ) @ ( s @ A_27c @ V4y_2E0 ) ) ) ) ) )
     => ! [V0f1_2E0: u,V1f2_2E0: u,V2al_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ V2al_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
         => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V1f2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ V2al_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ V2al_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2Ealist__to__fmap__to__alist,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0al_2E0: u,V1k_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ) ) ) )
     => ! [V0al_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ESET__TO__LIST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2Ealist__to__fmap__to__alist__PERM,axiom,
    ! [A_27a: d,A_27b: d,V0al_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2EPERM_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0al_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__LEAST__EL,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0ls_2E0: u,V1k_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ V2n )
        <=> ( ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) )
            = ( s @ A_27a @ V1k_2E0 ) ) )
     => ! [V0ls_2E0: u,V1k_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ewhile_2ELEAST @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__ALL__DISTINCT__MEM,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u,V1k_2E0: u,V2al_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2al_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V0v_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2al_2E0 ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2al_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V0v_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EALL__DISTINCT__fmap__to__alist__keys,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2Efmap__to__alist__inj,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u] :
      ( ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ).

thf(thm_2Ealist_2Efmap__to__alist__preserves__FDOM,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0fm1_2E0: u,V1fm2_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm1_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm2_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm1_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EPERM__fmap__to__alist,axiom,
    ! [A_27a: d,A_27b: d,V0fm2_2E0: u,V1fm1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2EPERM_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm2_2E0 ) ) ) ) ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm1_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm2_2E0 ) ) ) ).

thf(thm_2Ealist_2Ealist__to__fmap__PERM,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2EPERM_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__ALL__DISTINCT__EL,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u,V1n: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) @ ( s @ A_27a @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__ZIP__MAP__SND,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0l1_2E0: u,V1l2_2E0: u,V2k_2E0: u,V3f_2E0: u] :
      ( ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l1_2E0 ) ) ) )
        = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V1l2_2E0 ) ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) ) @ ( c_2Elist_2EZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V3f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V1l2_2E0 ) ) ) ) ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27d ) ) @ ( c_2Eoption_2EOPTION__MAP_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V3f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V1l2_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__FILTER,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0P_2E0: u,V3k_2E0: u,V4v_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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) @ ( s @ A_27a @ V3k_2E0 ) ) ) @ ( s @ A_27b @ V4v_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 @ V3k_2E0 ) ) ) ) )
     => ! [V0P_2E0: u,V1ls_2E0: u,V2x_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1ls_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1ls_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__APPEND__same,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u,V2l_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__IN__FRANGE,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u,V1k_2E0: u,V2v_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V2v_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V2v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EFRANGE__alist__to__fmap__SUBSET,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0ls_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0ls_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EIN__FRANGE__alist__to__fmap__suff,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u,V1P_2E0: u] :
      ( ! [V2v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0ls_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 @ V2v_2E0 ) ) ) ) )
     => ! [V3v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0ls_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 @ V3v_2E0 ) ) ) ) ) ) ).

thf(thm_2Ealist_2Ealist__to__fmap__MAP__matchable,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F0_2E0: u] :
      ( ! [V0f1_2E0: u,V1f2_2E0: u,V5x_2E0: u,V6y_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V1f2_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27c @ V6y_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V1f2_2E0 ) @ ( s @ A_27c @ V6y_2E0 ) ) ) ) ) )
     => ! [V0f1_2E0: u,V1f2_2E0: u,V2al_2E0: u,V3mal_2E0: u,V4v_2E0: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ V2al_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
            & ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ V3mal_2E0 )
              = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V1f2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ V2al_2E0 ) ) ) )
            & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ V4v_2E0 )
              = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ V2al_2E0 ) ) ) ) ) ) ) ) )
         => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ V3mal_2E0 ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ V4v_2E0 ) ) ) ) ).

thf(thm_2Ealist_2EMAP__values__fmap__to__alist,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V2k_2E0: u,V3v_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ A_27c @ V2k_2E0 ) ) ) @ ( s @ A_27a @ V3v_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V2k_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) ) ) )
     => ! [V0f_2E0: u,V1fm_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1fm_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1fm_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2EMAP__KEYS__I,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ c_2Ecombin_2EI_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ).

thf(thm_2Ealist_2Ealist__to__fmap__MAP__values,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V2k_2E0: u,V3v_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ A_27c @ V2k_2E0 ) ) ) @ ( s @ A_27a @ V3v_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V2k_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) ) ) )
     => ! [V0f_2E0: u,V1al_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ V1al_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Ealist_2Ealist__to__fmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ V1al_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ealist_2Eset__MAP__FST__fmap__to__alist,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ealist_2Efmap__to__alist_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ).

thf(thm_2Ealist_2Ealookup__distinct__reverse,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1k_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) ) ) ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2Eflookup__fupdate__list,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V3v_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ F0_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V3v_2E0 ) ) ) )
     => ! [V0l_2E0: u,V1k_2E0: u,V2m_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2m_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2m_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ F0_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2Efupdate__list__funion,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u,V1l_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m_2E0 ) ) ) ) ).

thf(thm_2Ealist_2Emem__to__flookup,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u,V2l_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V1y_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2Ealookup__filter,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V2x_2E0: u,V3x_27_2E0: u,V4y_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ A_27b @ V2x_2E0 ) ) ) @ ( s @ A_27b @ V3x_27_2E0 ) ) ) @ ( s @ A_27c @ V4y_2E0 ) ) ) )
        <=> ( ( s @ A_27b @ V2x_2E0 )
            = ( s @ A_27b @ V3x_27_2E0 ) ) )
     => ! [V0f_2E0: u,V1l_2E0: u,V2x_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ V1l_2E0 ) @ ( s @ A_27b @ V2x_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( c_2Elist_2EFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ A_27b @ V2x_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ V1l_2E0 ) ) ) @ ( s @ A_27b @ V2x_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2Ealookup__stable__sorted,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1sort_2E0: u,V2x_2E0: u,V3l_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etransitive_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2Etotal_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2ESTABLE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V1sort_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2Einv__image_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V1sort_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2Einv__image_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ).

thf(thm_2Ealist_2EALOOKUP__ALL__DISTINCT__PERM__same,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2EPERM_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) ) ) ) )
        & ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Ealist_2EALOOKUP_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) ) ) ) ).

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