%------------------------------------------------------------------------------
% File     : ITP066^4 : 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    : lbtree.ax [Gau19]
%          : HL4066^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  398 ( 147 unt; 197 typ;   0 def)
%            Number of atoms       :  450 ( 244 equ;   2 cnn)
%            Maximal formula atoms :   11 (   1 avg)
%            Number of connectives : 9540 (   2   ~;  18   |;  84   &;9337   @)
%                                         (  34 <=>;  65  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   34 (   7 avg;9337 nst)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :  385 ( 385   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  193 ( 191 usr;  65 con; 0-4 aty)
%            Number of variables   :  757 (   0   ^ 676   !;  81   ?; 757   :)
% 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_2Elist_2Elist_28tyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Enum_2Enum,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: $tType ).

thf(tyop_2Elbtree_2Elbtree,type,
    tyop_2Elbtree_2Elbtree: d > d ).

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

thf(tyop_2Ellist_2Ellist,type,
    tyop_2Ellist_2Ellist: 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_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_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: 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_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: u ).

thf(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: du > du > u ).

thf(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

thf(c_2Emin_2E_3D_2E1,type,
    c_2Emin_2E_3D_2E1: du > 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_2Ebool_2E_3F_21_2E0,type,
    c_2Ebool_2E_3F_21_2E0: u ).

thf(c_2Ebool_2E_3F_21_2E1,type,
    c_2Ebool_2E_3F_21_2E1: du > u ).

thf(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: u ).

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

thf(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: u ).

thf(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: du > 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_2Elist_2EEVERY_2E0,type,
    c_2Elist_2EEVERY_2E0: u ).

thf(c_2Elist_2EEVERY_2E2,type,
    c_2Elist_2EEVERY_2E2: du > du > u ).

thf(c_2Elist_2EEXISTS_2E0,type,
    c_2Elist_2EEXISTS_2E0: u ).

thf(c_2Elist_2EEXISTS_2E2,type,
    c_2Elist_2EEXISTS_2E2: du > du > u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: u ).

thf(c_2Ellist_2ELCONS_2E0,type,
    c_2Ellist_2ELCONS_2E0: u ).

thf(c_2Ellist_2ELCONS_2E2,type,
    c_2Ellist_2ELCONS_2E2: 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_2Ellist_2ELNIL_2E0,type,
    c_2Ellist_2ELNIL_2E0: u ).

thf(c_2Elbtree_2ELf_2E0,type,
    c_2Elbtree_2ELf_2E0: u ).

thf(c_2Elbtree_2ELfrep_2E0,type,
    c_2Elbtree_2ELfrep_2E0: u ).

thf(c_2Elbtree_2ELfrep_2E1,type,
    c_2Elbtree_2ELfrep_2E1: du > u ).

thf(c_2Earithmetic_2EMIN_2E0,type,
    c_2Earithmetic_2EMIN_2E0: u ).

thf(c_2Earithmetic_2EMIN_2E2,type,
    c_2Earithmetic_2EMIN_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_2Elbtree_2ENd_2E0,type,
    c_2Elbtree_2ENd_2E0: u ).

thf(c_2Elbtree_2ENd_2E3,type,
    c_2Elbtree_2ENd_2E3: du > du > du > u ).

thf(c_2Elbtree_2ENdrep_2E0,type,
    c_2Elbtree_2ENdrep_2E0: u ).

thf(c_2Elbtree_2ENdrep_2E3,type,
    c_2Elbtree_2ENdrep_2E3: du > du > du > u ).

thf(c_2Elbtree_2ENdrep_2E4,type,
    c_2Elbtree_2ENdrep_2E4: du > du > du > du > u ).

thf(c_2Eoption_2EOPTION__MAP_2E0,type,
    c_2Eoption_2EOPTION__MAP_2E0: u ).

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

thf(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: u ).

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

thf(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: u ).

thf(c_2Enum_2ESUC_2E1,type,
    c_2Enum_2ESUC_2E1: du > u ).

thf(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

thf(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: u ).

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

thf(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

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

thf(c_2Elbtree_2Ebf__flatten_2E0,type,
    c_2Elbtree_2Ebf__flatten_2E0: u ).

thf(c_2Elbtree_2Ebf__flatten_2E1,type,
    c_2Elbtree_2Ebf__flatten_2E1: du > u ).

thf(c_2Elbtree_2Edepth_2E0,type,
    c_2Elbtree_2Edepth_2E0: u ).

thf(c_2Elbtree_2Edepth_2E3,type,
    c_2Elbtree_2Edepth_2E3: du > du > du > u ).

thf(c_2Ellist_2Eexists_2E0,type,
    c_2Ellist_2Eexists_2E0: u ).

thf(c_2Ellist_2Eexists_2E2,type,
    c_2Ellist_2Eexists_2E2: du > du > u ).

thf(c_2Elbtree_2Efinite_2E0,type,
    c_2Elbtree_2Efinite_2E0: u ).

thf(c_2Elbtree_2Efinite_2E1,type,
    c_2Elbtree_2Efinite_2E1: du > u ).

thf(c_2Elbtree_2Eis__lbtree_2E0,type,
    c_2Elbtree_2Eis__lbtree_2E0: u ).

thf(c_2Elbtree_2Eis__lbtree_2E1,type,
    c_2Elbtree_2Eis__lbtree_2E1: du > u ).

thf(c_2Elbtree_2Eis__mmindex_2E0,type,
    c_2Elbtree_2Eis__mmindex_2E0: u ).

thf(c_2Elbtree_2Eis__mmindex_2E4,type,
    c_2Elbtree_2Eis__mmindex_2E4: du > du > du > du > u ).

thf(c_2Elbtree_2Elbtree__abs_2E0,type,
    c_2Elbtree_2Elbtree__abs_2E0: u ).

thf(c_2Elbtree_2Elbtree__abs_2E1,type,
    c_2Elbtree_2Elbtree__abs_2E1: du > u ).

thf(c_2Elbtree_2Elbtree__case_2E0,type,
    c_2Elbtree_2Elbtree__case_2E0: u ).

thf(c_2Elbtree_2Elbtree__case_2E3,type,
    c_2Elbtree_2Elbtree__case_2E3: du > du > du > u ).

thf(c_2Elbtree_2Elbtree__rep_2E0,type,
    c_2Elbtree_2Elbtree__rep_2E0: u ).

thf(c_2Elbtree_2Elbtree__rep_2E1,type,
    c_2Elbtree_2Elbtree__rep_2E1: du > u ).

thf(c_2Elist_2Elist__CASE_2E0,type,
    c_2Elist_2Elist__CASE_2E0: u ).

thf(c_2Elist_2Elist__CASE_2E3,type,
    c_2Elist_2Elist__CASE_2E3: du > du > du > u ).

thf(c_2Elbtree_2Emap_2E0,type,
    c_2Elbtree_2Emap_2E0: u ).

thf(c_2Elbtree_2Emap_2E2,type,
    c_2Elbtree_2Emap_2E2: du > du > u ).

thf(c_2Elbtree_2Emem_2E0,type,
    c_2Elbtree_2Emem_2E0: u ).

thf(c_2Elbtree_2Emem_2E1,type,
    c_2Elbtree_2Emem_2E1: du > u ).

thf(c_2Elbtree_2Emem_2E2,type,
    c_2Elbtree_2Emem_2E2: du > du > u ).

thf(c_2Elbtree_2Emindepth_2E0,type,
    c_2Elbtree_2Emindepth_2E0: u ).

thf(c_2Elbtree_2Emindepth_2E2,type,
    c_2Elbtree_2Emindepth_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_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_2Elbtree_2Eoptmin_2E0,type,
    c_2Elbtree_2Eoptmin_2E0: u ).

thf(c_2Elbtree_2Eoptmin_2E2,type,
    c_2Elbtree_2Eoptmin_2E2: du > du > u ).

thf(c_2Epair_2Epair__CASE_2E0,type,
    c_2Epair_2Epair__CASE_2E0: u ).

thf(c_2Epair_2Epair__CASE_2E2,type,
    c_2Epair_2Epair__CASE_2E2: du > du > u ).

thf(c_2Elbtree_2Epath__follow_2E0,type,
    c_2Elbtree_2Epath__follow_2E0: u ).

thf(c_2Elbtree_2Epath__follow_2E3,type,
    c_2Elbtree_2Epath__follow_2E3: du > du > du > u ).

thf(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

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

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

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

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: ( $o > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ) > $o > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ).

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_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

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

thf(mono_2Ec_2Enum_2E0,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

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_2Earithmetic_2E_3C_3D,type,
    mono_2Ec_2Earithmetic_2E_3C_3D: 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_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Emin_2Ebool: $o > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ).

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_2Earithmetic_2EMIN,type,
    mono_2Ec_2Earithmetic_2EMIN: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ).

thf(mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(mono_2Ec_2Enum_2ESUC,type,
    mono_2Ec_2Enum_2ESUC: mono_2Etyop_2Enum_2Enum > 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_2Elbtree_2Eoptmin,type,
    mono_2Ec_2Elbtree_2Eoptmin: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

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

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

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: ( $o > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ) > 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > u ).

thf(i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > u ).

thf(i_mono_2Etyop_2Enum_2Enum,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).

thf(i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > u ).

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

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: du > $o > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: du > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ).

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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(j_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ).

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

thf(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

thf(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ! [V2x_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).

thf(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
      = ( s @ A_27a @ V0x_2E0 ) ) ).

thf(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
      = ( s @ A_27a @ V0x_2E0 ) ) ).

thf(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
      ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
      = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).

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

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

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

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

thf(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
    <=> ( ( s @ A_27a @ V0_2E0 )
        = ( s @ A_27a @ V1_2E0 ) ) ) ).

thf(reserved_2Equant_2E_21,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
    <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).

thf(reserved_2Equant_2E_3F,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
    <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ 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(ij_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ 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_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_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(ji_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0 ) ) )
      = V0 ) ).

thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
      = ( 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 ) ) ) ) ).

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_2Emin_2E_3D_2E1_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X0_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_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Elbtree_2Elbtree_28A_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ A_27b @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ A_27b ) @ c_2Emin_2E_40_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27b_29,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ c_2Emin_2E_40_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) ) ) @ c_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ A_27b @ X2_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ A_27b @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ 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_2EEVERY_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ 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_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2EEVERY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2EEVERY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ 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_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2EEXISTS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2EEXISTS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELCONS_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_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_2Elbtree_2ELfrep_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Elbtree_2ELfrep_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ c_2Elbtree_2ELfrep_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elbtree_2ENd_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) ) ) @ c_2Elbtree_2ENd_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elbtree_2ENd_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) ) @ c_2Elbtree_2ENd_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elbtree_2ENdrep_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Elbtree_2ENdrep_2E3 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ c_2Elbtree_2ENdrep_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Elbtree_2ENdrep_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Elbtree_2ENdrep_2E4 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ X3 ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ c_2Elbtree_2ENdrep_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ X3 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27b_29_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) @ X1_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(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elbtree_2Ebf__flatten_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Elbtree_2Ebf__flatten_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Elbtree_2Ebf__flatten_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elbtree_2Edepth_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X2 ) ) ) ) )
      = ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Elbtree_2Edepth_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X1_2E0 ) ) ) @ X2 ) ) ).

thf(arityeq2_2Ec_2Ellist_2Eexists_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Ellist_2Eexists_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elbtree_2Efinite_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Elbtree_2Efinite_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elbtree_2Efinite_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Elbtree_2Efinite_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elbtree_2Eis__lbtree_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Eis__lbtree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ c_2Elbtree_2Eis__lbtree_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq4_2Ec_2Elbtree_2Eis__mmindex_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2: mono_2Etyop_2Enum_2Enum,X3: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Eis__mmindex_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X2 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X3 ) ) ) ) )
      = ( 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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Elbtree_2Eis__mmindex_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ X2 @ X3 ) ) ).

thf(arityeq1_2Ec_2Elbtree_2Elbtree__abs_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Elbtree__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ c_2Elbtree_2Elbtree__abs_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elbtree_2Elbtree__case_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27a @ ( c_2Elbtree_2Elbtree__case_2E3 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) ) @ c_2Elbtree_2Elbtree__case_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elbtree_2Elbtree__rep_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Elbtree_2Elbtree__rep_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Elbtree_2Elbtree__rep_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Elist_2Elist__CASE_2E3 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Elist_2Elist__CASE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elbtree_2Emap_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ c_2Elbtree_2Emap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elbtree_2Emap_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) ) @ c_2Elbtree_2Emap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elbtree_2Emem_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Elbtree_2Emem_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Elbtree_2Emem_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elbtree_2Emem_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Elbtree_2Emem_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Elbtree_2Emindepth_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Elbtree_2Emindepth_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ c_2Elbtree_2Emindepth_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0: $o > $o,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ X0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ 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 @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ X0 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27b_29_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2Ctyop_2Epair_2Eprod_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Elbtree_2Elbtree_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27b_29_20mono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27b_29_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elbtree_2Epath__follow_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Elbtree_2Epath__follow_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ X2 ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Elbtree_2Epath__follow_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ X2 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o > $o,V1: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o > $o,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
      ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_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(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0: $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V2: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0 @ V1 @ V2 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V2 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ c_2Elist_2ECONS_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
      ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Emin_2Ebool @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ c_2Elist_2ENIL_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ c_2Eoption_2ESOME_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) ) ) ) ).

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

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

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
      ( ( 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(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(thm_2Elbtree_2ELfrep__def,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Elbtree_2ELfrep_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(thm_2Elbtree_2ENdrep__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1t1_2E0: u,V2t2_2E0: u,V4v: $o,V5xs: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1t1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2t2_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V4v ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V5xs ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V4v ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V5xs ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2t2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V5xs ) ) ) ) ) ) )
     => ! [V0a_2E0: u,V1t1_2E0: u,V2t2_2E0: u,V3x: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Elbtree_2ENdrep_2E4 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2t2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V3x ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Elist_2Elist__CASE_2E3 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V3x ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1t1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2t2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Eis__lbtree__def,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Eis__lbtree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0t_2E0 ) ) ) )
    <=> ? [V1P_2E0: u] :
          ( ! [V2t_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2t_2E0 ) ) ) )
             => ( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2t_2E0 )
                  = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Elbtree_2ELfrep_2E0 ) )
                | ? [V3a_2E0: u,V4t1_2E0: u,V5t2_2E0: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V4t1_2E0 ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V5t2_2E0 ) ) ) )
                    & ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2t_2E0 )
                      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Elbtree_2ENdrep_2E3 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V4t1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V5t2_2E0 ) ) ) ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0t_2E0 ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Elbtree__TY__DEF,axiom,
    ! [A_27a: d] :
    ? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ c_2Elbtree_2Eis__lbtree_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V0rep_2E0 ) ) ) ) ).

thf(thm_2Elbtree_2Elbtree__absrep,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u] :
          ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Elbtree__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Elbtree_2Elbtree__rep_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0a_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0a_2E0 ) )
      & ! [V1r_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Eis__lbtree_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1r_2E0 ) ) ) )
        <=> ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Elbtree_2Elbtree__rep_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Elbtree__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1r_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1r_2E0 ) ) ) ) ).

thf(thm_2Elbtree_2Epath__follow__def,axiom,
    ! [A_27a: d,A_27b: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V2g_2E0: u,V4h: $o,V5t: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,V9y_2E0: u,V10z_2E0: u] :
          ( ( 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 @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ V2g_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V4h ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V5t ) ) ) ) @ ( s @ A_27b @ V9y_2E0 ) ) ) @ ( s @ A_27b @ V10z_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Elbtree_2Epath__follow_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ V2g_2E0 ) @ ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V4h ) ) @ ( s @ A_27b @ V9y_2E0 ) @ ( s @ A_27b @ V10z_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V5t ) ) ) ) )
     => ( ! [V2g_2E0: u,V4h: $o,V5t: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,V7a_2E0: u,V8v2_2E0: u] :
            ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ V2g_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V4h ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V5t ) ) ) ) @ ( s @ A_27a @ V7a_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ V8v2_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ V8v2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ V2g_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V4h ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V5t ) ) ) ) ) ) )
       => ( ! [V2g_2E0: u,V4h: $o,V5t: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,V6v_2E0: u] :
              ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ V2g_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V4h ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V5t ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ V6v_2E0 ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ V6v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ V2g_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V4h ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V5t ) ) ) ) ) ) )
         => ( ! [V0g_2E0: u,V1x_2E0: u] :
                ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Elbtree_2Epath__follow_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ V0g_2E0 ) @ ( s @ A_27b @ V1x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Emin_2Ebool ) ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ V0g_2E0 ) @ ( s @ A_27b @ V1x_2E0 ) ) ) ) ) )
            & ! [V2g_2E0: u,V3x_2E0: u,V4h: $o,V5t: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
                ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Elbtree_2Epath__follow_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ V2g_2E0 ) @ ( s @ A_27b @ V3x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Emin_2Ebool @ V4h @ V5t ) ) ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ V2g_2E0 ) @ ( s @ A_27b @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) ) @ V2g_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V4h ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 @ V5t ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2ELf__def,axiom,
    ! [A_27a: d] :
      ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 )
      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Elbtree__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Elbtree_2ELfrep_2E0 ) ) ) ) ).

thf(thm_2Elbtree_2ENd__def,axiom,
    ! [A_27a: d,V0a_2E0: u,V1t1_2E0: u,V2t2_2E0: u] :
      ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t2_2E0 ) ) )
      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Elbtree__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Elbtree_2ENdrep_2E3 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Elbtree_2Elbtree__rep_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Elbtree_2Elbtree__rep_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Elbtree__case__def,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F2_2E0: u,F3_2E0: u,F1_2E0: u] :
      ( ! [V2t_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 ) ) ) )
        <=> ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 )
            = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ c_2Elbtree_2ELf_2E0 ) ) )
     => ( ! [V2t_2E0: u,V6t1_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V6t1_2E0 ) ) ) )
          <=> ? [V7a_2E0: u,V8t2_2E0: u] :
                ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 )
                = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27b @ V7a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V6t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V8t2_2E0 ) ) ) ) )
       => ( ! [V2t_2E0: u,V9t2_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V9t2_2E0 ) ) ) )
            <=> ? [V10a_2E0: u,V11t1_2E0: u] :
                  ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 )
                  = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27b @ V10a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V11t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V9t2_2E0 ) ) ) ) )
         => ( ! [V2t_2E0: u,V3a_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_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 ) ) ) @ ( s @ A_27b @ V3a_2E0 ) ) ) )
              <=> ? [V4t1_2E0: u,V5t2_2E0: u] :
                    ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 )
                    = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27b @ V3a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V4t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V5t2_2E0 ) ) ) ) )
           => ! [V0e_2E0: u,V1f_2E0: u,V2t_2E0: u] :
                ( ( s @ A_27a @ ( c_2Elbtree_2Elbtree__case_2E3 @ ( s @ A_27a @ V0e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 ) ) )
                = ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 ) ) ) @ ( s @ A_27a @ V0e_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emem__def,axiom,
    ! [A_27a: d,V0x_2E0: u,V1x_27_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1x_27_2E0 ) ) ) )
    <=> ! [V2mem_27_2E0: u] :
          ( ! [V3a0_2E0: u,V4a1_2E0: u] :
              ( ( ? [V5t1_2E0: u,V6t2_2E0: u] :
                    ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4a1_2E0 )
                    = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V3a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V5t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t2_2E0 ) ) ) )
                | ? [V7b_2E0: u,V8t1_2E0: u,V9t2_2E0: u] :
                    ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4a1_2E0 )
                      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V7b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V8t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V9t2_2E0 ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2mem_27_2E0 ) @ ( s @ A_27a @ V3a0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V8t1_2E0 ) ) ) ) )
                | ? [V10b_2E0: u,V11t1_2E0: u,V12t2_2E0: u] :
                    ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4a1_2E0 )
                      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V10b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V11t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V12t2_2E0 ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2mem_27_2E0 ) @ ( s @ A_27a @ V3a0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V12t2_2E0 ) ) ) ) ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2mem_27_2E0 ) @ ( s @ A_27a @ V3a0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4a1_2E0 ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2mem_27_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1x_27_2E0 ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emap__def,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) ) )
        = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ c_2Elbtree_2ELf_2E0 ) )
      & ! [V1a_2E0: u,V2t1_2E0: u,V3t2_2E0: u] :
          ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Efinite__def,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0x_2E0 ) ) ) )
    <=> ! [V1finite_27_2E0: u] :
          ( ! [V2a0_2E0: u] :
              ( ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2a0_2E0 )
                  = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) )
                | ? [V3a_2E0: u,V4t1_2E0: u,V5t2_2E0: u] :
                    ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2a0_2E0 )
                      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V5t2_2E0 ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4t1_2E0 ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V5t2_2E0 ) ) ) ) ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2a0_2E0 ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0x_2E0 ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Ebf__flatten__def,axiom,
    ! [A_27a: d] :
      ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Elbtree_2Ebf__flatten_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ c_2Elist_2ENIL_2E0 ) ) )
        = ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
      & ! [V0ts_2E0: u] :
          ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Elbtree_2Ebf__flatten_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V0ts_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Elbtree_2Ebf__flatten_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V0ts_2E0 ) ) ) )
      & ! [V1a_2E0: u,V2t1_2E0: u,V3t2_2E0: u,V4ts_2E0: u] :
          ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Elbtree_2Ebf__flatten_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V4ts_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Elbtree_2Ebf__flatten_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V4ts_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Edepth__def,axiom,
    ! [A_27a: d,V0x_2E0: u,V1x_27_2E0: u,V2x_27_27: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1x_27_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x_27_27 ) ) ) ) )
    <=> ! [V3depth_27_2E0: u] :
          ( ! [V4a0_2E0: u,V5a1_2E0: u,V6a2: mono_2Etyop_2Enum_2Enum] :
              ( ( ? [V7t1_2E0: u,V8t2_2E0: u] :
                    ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V5a1_2E0 )
                      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V4a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V8t2_2E0 ) ) ) )
                    & ( V6a2 = mono_2Ec_2Enum_2E0 ) )
                | ? [V9m: mono_2Etyop_2Enum_2Enum,V10a_2E0: u,V11t1_2E0: u,V12t2_2E0: u] :
                    ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V5a1_2E0 )
                      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V11t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V12t2_2E0 ) ) ) )
                    & ( V6a2
                      = ( mono_2Ec_2Enum_2ESUC @ V9m ) )
                    & ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V3depth_27_2E0 ) @ ( s @ A_27a @ V4a0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V11t1_2E0 ) ) ) @ V9m ) )
                | ? [V13m: mono_2Etyop_2Enum_2Enum,V14a_2E0: u,V15t1_2E0: u,V16t2_2E0: u] :
                    ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V5a1_2E0 )
                      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V14a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V15t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V16t2_2E0 ) ) ) )
                    & ( V6a2
                      = ( mono_2Ec_2Enum_2ESUC @ V13m ) )
                    & ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V3depth_27_2E0 ) @ ( s @ A_27a @ V4a0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V16t2_2E0 ) ) ) @ V13m ) ) )
             => ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V3depth_27_2E0 ) @ ( s @ A_27a @ V4a0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V5a1_2E0 ) ) ) @ V6a2 ) )
         => ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V3depth_27_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1x_27_2E0 ) ) ) @ V2x_27_27 ) ) ) ).

thf(thm_2Elbtree_2Emindepth__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0x_2E0: u,V1t_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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) ) ) @ V2n )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) ) )
     => ! [V0x_2E0: u,V1t_2E0: u] :
          ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Elbtree_2Emindepth_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) ) ) )
          = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) ) ) ) @ ( mono_2Ec_2Eoption_2ESOME_2Emono_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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) ).

thf(thm_2Elbtree_2Eis__mmindex__def,axiom,
    ! [A_27a: d,V0f_2E0: u,V1l_2E0: u,V2n: mono_2Etyop_2Enum_2Enum,V3d: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Eis__mmindex_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3d ) ) ) ) )
    <=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V2n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) )
        & ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0f_2E0 ) @ ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V3d ) )
        & ! [V4i: mono_2Etyop_2Enum_2Enum] :
            ( ( mono_2Ec_2Eprim__rec_2E_3C @ V4i @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) )
           => ( ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0f_2E0 ) @ ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4i ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) )
                = mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum )
              | ? [V5d_27: mono_2Etyop_2Enum_2Enum] :
                  ( ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0f_2E0 ) @ ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4i ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) )
                    = ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V5d_27 ) )
                  & ( mono_2Ec_2Earithmetic_2E_3C_3D @ V3d @ V5d_27 )
                  & ( ( mono_2Ec_2Eprim__rec_2E_3C @ V4i @ V2n )
                   => ( mono_2Ec_2Eprim__rec_2E_3C @ V3d @ V5d_27 ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Elbtree__cases,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0t_2E0 )
        = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) )
      | ? [V1a_2E0: u,V2t1_2E0: u,V3t2_2E0: u] :
          ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0t_2E0 )
          = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) ) ).

thf(thm_2Elbtree_2ELf__NOT__Nd,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2a_2E0: u] :
      ( (~)
      @ ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 )
        = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0t2_2E0 ) ) ) ) ) ).

thf(thm_2Elbtree_2ENd__11,axiom,
    ! [A_27a: d,V0u2_2E0: u,V1u1_2E0: u,V2t2_2E0: u,V3t1_2E0: u,V4a2_2E0: u,V5a1_2E0: u] :
      ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V5a1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1u1_2E0 ) ) )
        = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V4a2_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t2_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0u2_2E0 ) ) ) )
    <=> ( ( ( s @ A_27a @ V5a1_2E0 )
          = ( s @ A_27a @ V4a2_2E0 ) )
        & ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t1_2E0 )
          = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t2_2E0 ) )
        & ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1u1_2E0 )
          = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0u2_2E0 ) ) ) ) ).

thf(thm_2Elbtree_2Elbtree__ue__Axiom,axiom,
    ! [A_27a: d,A_27b: d,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V4b_2E0: u,V1g_2E0: u,V6y_2E0: u,V7z_2E0: u] :
          ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) ) ) @ F3_2E0 ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V6y_2E0 ) ) ) @ ( s @ A_27a @ V7z_2E0 ) ) )
          = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27b @ V4b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V6y_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V7z_2E0 ) ) ) ) ) )
     => ( ! [V1g_2E0: u,V4b_2E0: u,V5v2_2E0: u] :
            ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ V1g_2E0 ) ) ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ V5v2_2E0 ) ) )
            = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ V5v2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) ) ) @ F3_2E0 ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ V1g_2E0 ) ) ) ) ) )
       => ( ! [V1g_2E0: u,V3v_2E0: u] :
              ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V3v_2E0 ) ) )
              = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ V1g_2E0 ) ) ) ) ) )
         => ( ! [V0f_2E0: u,V1g_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ V1g_2E0 ) ) ) )
              <=> ! [V2x_2E0: u] :
                    ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
                    = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ c_2Elbtree_2ELf_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ V1g_2E0 ) ) ) ) ) ) )
           => ! [V0f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elbtree_2Elbtree @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) ) @ V0f_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Elbtree__case__thm,axiom,
    ! [A_27a: d,A_27b: d,V0t2_2E0: u,V1t1_2E0: u,V2f_2E0: u,V3e_2E0: u,V4a_2E0: u] :
      ( ( ( s @ A_27a @ ( c_2Elbtree_2Elbtree__case_2E3 @ ( s @ A_27a @ V3e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ c_2Elbtree_2ELf_2E0 ) ) )
        = ( s @ A_27a @ V3e_2E0 ) )
      & ( ( s @ A_27a @ ( c_2Elbtree_2Elbtree__case_2E3 @ ( s @ A_27a @ V3e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27b @ V4a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V4a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V1t1_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V0t2_2E0 ) ) ) ) ) ).

thf(thm_2Elbtree_2Elbtree__bisimulation,axiom,
    ! [A_27a: d,V0t_2E0: u,V1u_2E0: u] :
      ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0t_2E0 )
        = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1u_2E0 ) )
    <=> ? [V2R_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0t_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1u_2E0 ) ) ) )
          & ! [V3t_2E0: u,V4u_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4u_2E0 ) ) ) )
             => ( ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t_2E0 )
                    = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) )
                  & ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4u_2E0 )
                    = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) ) )
                | ? [V5a_2E0: u,V6t1_2E0: u,V7u1_2E0: u,V8t2_2E0: u,V9u2_2E0: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t1_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7u1_2E0 ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V8t2_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V9u2_2E0 ) ) ) )
                    & ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t_2E0 )
                      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V8t2_2E0 ) ) ) )
                    & ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4u_2E0 )
                      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7u1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V9u2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Elbtree__strong__bisimulation,axiom,
    ! [A_27a: d,V0t_2E0: u,V1u_2E0: u] :
      ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0t_2E0 )
        = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1u_2E0 ) )
    <=> ? [V2R_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0t_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1u_2E0 ) ) ) )
          & ! [V3t_2E0: u,V4u_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4u_2E0 ) ) ) )
             => ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t_2E0 )
                  = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4u_2E0 ) )
                | ? [V5a_2E0: u,V6t1_2E0: u,V7u1_2E0: u,V8t2_2E0: u,V9u2_2E0: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t1_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7u1_2E0 ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V8t2_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V9u2_2E0 ) ) ) )
                    & ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t_2E0 )
                      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V8t2_2E0 ) ) ) )
                    & ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4u_2E0 )
                      = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7u1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V9u2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emem__rules,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u,V1t1_2E0: u,V2t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t2_2E0 ) ) ) ) ) )
      & ! [V3a_2E0: u,V4b_2E0: u,V5t1_2E0: u,V6t2_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V5t1_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V4b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V5t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t2_2E0 ) ) ) ) ) ) )
      & ! [V7a_2E0: u,V8b_2E0: u,V9t1_2E0: u,V10t2_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V7a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V10t2_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V7a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V8b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V10t2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emem__ind,axiom,
    ! [A_27a: d,V0mem_27_2E0: u] :
      ( ( ! [V1a_2E0: u,V2t1_2E0: u,V3t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) ) )
        & ! [V4a_2E0: u,V5b_2E0: u,V6t1_2E0: u,V7t2_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t1_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V5b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7t2_2E0 ) ) ) ) ) ) )
        & ! [V8a_2E0: u,V9b_2E0: u,V10t1_2E0: u,V11t2_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V11t2_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V9b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V10t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V11t2_2E0 ) ) ) ) ) ) ) )
     => ! [V12a0_2E0: u,V13a1_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V12a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V13a1_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V12a0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V13a1_2E0 ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emem__strongind,axiom,
    ! [A_27a: d,V0mem_27_2E0: u] :
      ( ( ! [V1a_2E0: u,V2t1_2E0: u,V3t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) ) )
        & ! [V4a_2E0: u,V5b_2E0: u,V6t1_2E0: u,V7t2_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t1_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t1_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V5b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7t2_2E0 ) ) ) ) ) ) )
        & ! [V8a_2E0: u,V9b_2E0: u,V10t1_2E0: u,V11t2_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V11t2_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V11t2_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V9b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V10t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V11t2_2E0 ) ) ) ) ) ) ) )
     => ! [V12a0_2E0: u,V13a1_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V12a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V13a1_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0mem_27_2E0 ) @ ( s @ A_27a @ V12a0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V13a1_2E0 ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emem__cases,axiom,
    ! [A_27a: d,V0a0_2E0: u,V1a1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V0a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1a1_2E0 ) ) ) )
    <=> ( ? [V2t1_2E0: u,V3t2_2E0: u] :
            ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1a1_2E0 )
            = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V0a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) )
        | ? [V4b_2E0: u,V5t1_2E0: u,V6t2_2E0: u] :
            ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1a1_2E0 )
              = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V4b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V5t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t2_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V0a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V5t1_2E0 ) ) ) ) )
        | ? [V7b_2E0: u,V8t1_2E0: u,V9t2_2E0: u] :
            ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1a1_2E0 )
              = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V7b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V8t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V9t2_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V0a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V9t2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emem__thm,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2b_2E0: u,V3a_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) ) ) )
        = mono_2Ec_2Ebool_2EF )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V2b_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0t2_2E0 ) ) ) ) ) )
      <=> ( ( ( s @ A_27a @ V3a_2E0 )
            = ( s @ A_27a @ V2b_2E0 ) )
          | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t1_2E0 ) ) ) )
          | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0t2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emap__eq__Lf,axiom,
    ! [A_27a: d,A_27b: d,V0t_2E0: u,V1f_2E0: u] :
      ( ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V0t_2E0 ) ) )
          = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) )
      <=> ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V0t_2E0 )
          = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ c_2Elbtree_2ELf_2E0 ) ) )
      & ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 )
          = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V0t_2E0 ) ) ) )
      <=> ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V0t_2E0 )
          = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ c_2Elbtree_2ELf_2E0 ) ) ) ) ).

thf(thm_2Elbtree_2Emap__eq__Nd,axiom,
    ! [A_27a: d,A_27b: d,V0t2_2E0: u,V1t1_2E0: u,V2t_2E0: u,V3f_2E0: u,V4a_2E0: u] :
      ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V3f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 ) ) )
        = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0t2_2E0 ) ) ) )
    <=> ? [V5a_27_2E0: u,V6t1_27_2E0: u,V7t2_27_2E0: u] :
          ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V2t_2E0 )
            = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27b @ V5a_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V6t1_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V7t2_27_2E0 ) ) ) )
          & ( ( s @ A_27a @ V4a_2E0 )
            = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V3f_2E0 ) @ ( s @ A_27b @ V5a_27_2E0 ) ) ) )
          & ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t1_2E0 )
            = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V3f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V6t1_27_2E0 ) ) ) )
          & ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0t2_2E0 )
            = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V3f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V7t2_27_2E0 ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Efinite__rules,axiom,
    ! [A_27a: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) ) ) )
      & ! [V0a_2E0: u,V1t1_2E0: u,V2t2_2E0: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t1_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t2_2E0 ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Efinite__ind,axiom,
    ! [A_27a: d,V0finite_27_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) ) ) )
        & ! [V1a_2E0: u,V2t1_2E0: u,V3t2_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) ) ) ) )
     => ! [V4a0_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4a0_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4a0_2E0 ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Efinite__strongind,axiom,
    ! [A_27a: d,V0finite_27_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) ) ) )
        & ! [V1a_2E0: u,V2t1_2E0: u,V3t2_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) ) ) ) )
     => ! [V4a0_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4a0_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0finite_27_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4a0_2E0 ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Efinite__cases,axiom,
    ! [A_27a: d,V0a0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0a0_2E0 ) ) ) )
    <=> ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0a0_2E0 )
          = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) )
        | ? [V1a_2E0: u,V2t1_2E0: u,V3t2_2E0: u] :
            ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V0a0_2E0 )
              = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Efinite__thm,axiom,
    ! [A_27a: d,A_27b: d,V0t2_2E0: u,V1t1_2E0: u,V2a_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) ) ) )
        = mono_2Ec_2Ebool_2ET )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27b @ V2a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V0t2_2E0 ) ) ) ) ) )
      <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V1t1_2E0 ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V0t2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Efinite__map,axiom,
    ! [A_27a: d,A_27b: d,V0t_2E0: u,V1f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V0t_2E0 ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Efinite_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27b ) @ V0t_2E0 ) ) ) ) ) ).

thf(thm_2Elbtree_2Ebf__flatten__eq__lnil,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Elbtree_2Ebf__flatten_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V0l_2E0 ) ) )
        = ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
    <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V0l_2E0 ) ) ) ) ) ).

thf(thm_2Elbtree_2Ebf__flatten__append,axiom,
    ! [A_27a: d,V0l2_2E0: u,V1l1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E1 @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V1l1_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Elbtree_2Ebf__flatten_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V0l2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Elbtree_2Ebf__flatten_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V0l2_2E0 ) ) ) ) ) ).

thf(thm_2Elbtree_2EEXISTS__FIRST,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) )
     => ? [V2l1_2E0: u,V3x_2E0: u,V4l2_2E0: u] :
          ( ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l2_2E0 ) ) ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_7E ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l1_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 @ V3x_2E0 ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Eexists__bf__flatten,axiom,
    ! [A_27a: d,V0x_2E0: u,V1tlist_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Elbtree_2Ebf__flatten_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V1tlist_2E0 ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Elbtree_2Emem_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V1tlist_2E0 ) ) ) ) ) ).

thf(thm_2Elbtree_2Edepth__rules,axiom,
    ! [A_27a: d] :
      ( ! [V0x_2E0: u,V1t1_2E0: u,V2t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) )
      & ! [V3m: mono_2Etyop_2Enum_2Enum,V4x_2E0: u,V5a_2E0: u,V6t1_2E0: u,V7t2_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V6t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7t2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V3m ) ) ) ) ) ) )
      & ! [V8m: mono_2Etyop_2Enum_2Enum,V9x_2E0: u,V10a_2E0: u,V11t1_2E0: u,V12t2_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V12t2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8m ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V11t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V12t2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V8m ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Edepth__ind,axiom,
    ! [A_27a: d,V0depth_27_2E0: u] :
      ( ( ! [V1x_2E0: u,V2t1_2E0: u,V3t2_2E0: u] : ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) ) @ mono_2Ec_2Enum_2E0 )
        & ! [V4m: mono_2Etyop_2Enum_2Enum,V5x_2E0: u,V6a_2E0: u,V7t1_2E0: u,V8t2_2E0: u] :
            ( ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7t1_2E0 ) ) ) @ V4m )
           => ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V6a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V8t2_2E0 ) ) ) ) ) @ ( mono_2Ec_2Enum_2ESUC @ V4m ) ) )
        & ! [V9m: mono_2Etyop_2Enum_2Enum,V10x_2E0: u,V11a_2E0: u,V12t1_2E0: u,V13t2_2E0: u] :
            ( ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V10x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V13t2_2E0 ) ) ) @ V9m )
           => ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V10x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V11a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V12t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V13t2_2E0 ) ) ) ) ) @ ( mono_2Ec_2Enum_2ESUC @ V9m ) ) ) )
     => ! [V14a0_2E0: u,V15a1_2E0: u,V16a2: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V14a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V15a1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V16a2 ) ) ) ) )
         => ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V14a0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V15a1_2E0 ) ) ) @ V16a2 ) ) ) ).

thf(thm_2Elbtree_2Edepth__strongind,axiom,
    ! [A_27a: d,V0depth_27_2E0: u] :
      ( ( ! [V1x_2E0: u,V2t1_2E0: u,V3t2_2E0: u] : ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t2_2E0 ) ) ) ) ) @ mono_2Ec_2Enum_2E0 )
        & ! [V4m: mono_2Etyop_2Enum_2Enum,V5x_2E0: u,V6a_2E0: u,V7t1_2E0: u,V8t2_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7t1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4m ) ) ) ) )
              & ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7t1_2E0 ) ) ) @ V4m ) )
           => ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V6a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V8t2_2E0 ) ) ) ) ) @ ( mono_2Ec_2Enum_2ESUC @ V4m ) ) )
        & ! [V9m: mono_2Etyop_2Enum_2Enum,V10x_2E0: u,V11a_2E0: u,V12t1_2E0: u,V13t2_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V10x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V13t2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9m ) ) ) ) )
              & ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V10x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V13t2_2E0 ) ) ) @ V9m ) )
           => ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V10x_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V11a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V12t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V13t2_2E0 ) ) ) ) ) @ ( mono_2Ec_2Enum_2ESUC @ V9m ) ) ) )
     => ! [V14a0_2E0: u,V15a1_2E0: u,V16a2: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V14a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V15a1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V16a2 ) ) ) ) )
         => ( 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 @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0depth_27_2E0 ) @ ( s @ A_27a @ V14a0_2E0 ) ) ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V15a1_2E0 ) ) ) @ V16a2 ) ) ) ).

thf(thm_2Elbtree_2Edepth__cases,axiom,
    ! [A_27a: d,V0a0_2E0: u,V1a1_2E0: u,V2a2: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V0a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1a1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2a2 ) ) ) ) )
    <=> ( ? [V3t1_2E0: u,V4t2_2E0: u] :
            ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1a1_2E0 )
              = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V0a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V3t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V4t2_2E0 ) ) ) )
            & ( V2a2 = mono_2Ec_2Enum_2E0 ) )
        | ? [V5m: mono_2Etyop_2Enum_2Enum,V6a_2E0: u,V7t1_2E0: u,V8t2_2E0: u] :
            ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1a1_2E0 )
              = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V6a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V8t2_2E0 ) ) ) )
            & ( V2a2
              = ( mono_2Ec_2Enum_2ESUC @ V5m ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V0a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V7t1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) ) )
        | ? [V9m: mono_2Etyop_2Enum_2Enum,V10a_2E0: u,V11t1_2E0: u,V12t2_2E0: u] :
            ( ( ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1a1_2E0 )
              = ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V11t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V12t2_2E0 ) ) ) )
            & ( V2a2
              = ( mono_2Ec_2Enum_2ESUC @ V9m ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V0a0_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V12t2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9m ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emem__depth,axiom,
    ! [A_27a: d,V0x_2E0: u,V1t_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) ) ) )
     => ? [V2n: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Edepth__mem,axiom,
    ! [A_27a: d,V0x_2E0: u,V1t_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) ) ) ) ) ).

thf(thm_2Elbtree_2Eoptmin__ind,axiom,
    ! [V0P: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o] :
      ( ( ( V0P @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum )
        & ! [V1x: mono_2Etyop_2Enum_2Enum] : ( V0P @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V1x ) @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum )
        & ! [V2y: mono_2Etyop_2Enum_2Enum] : ( V0P @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V2y ) )
        & ! [V3x: mono_2Etyop_2Enum_2Enum,V4y: mono_2Etyop_2Enum_2Enum] : ( V0P @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V3x ) @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V4y ) ) )
     => ! [V5v: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V6v1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( V0P @ V5v @ V6v1 ) ) ).

thf(thm_2Elbtree_2Eoptmin__def,axiom,
    ! [V0y: mono_2Etyop_2Enum_2Enum,V1x: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Elbtree_2Eoptmin @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum )
        = mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum )
      & ( ( mono_2Ec_2Elbtree_2Eoptmin @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V1x ) @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum )
        = ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V1x ) )
      & ( ( mono_2Ec_2Elbtree_2Eoptmin @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V0y ) )
        = ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V0y ) )
      & ( ( mono_2Ec_2Elbtree_2Eoptmin @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V1x ) @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V0y ) )
        = ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EMIN @ V1x @ V0y ) ) ) ) ).

thf(thm_2Elbtree_2Emindepth__thm,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0x_2E0: u,V3a_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27a @ V3a_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V0x_2E0 )
            = ( s @ A_27a @ V3a_2E0 ) ) )
     => ! [V0x_2E0: u,V1t2_2E0: u,V2t1_2E0: u,V3a_2E0: u] :
          ( ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Elbtree_2Emindepth_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ c_2Elbtree_2ELf_2E0 ) ) ) )
            = mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum )
          & ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Elbtree_2Emindepth_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ ( c_2Elbtree_2ENd_2E3 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t2_2E0 ) ) ) ) ) )
            = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27a @ V3a_2E0 ) ) ) ) @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Elbtree_2Eoptmin @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Elbtree_2Emindepth_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V2t1_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Elbtree_2Emindepth_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t2_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emem__mindepth,axiom,
    ! [A_27a: d,V0x_2E0: u,V1t_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Emem_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) ) ) )
     => ? [V2n: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Elbtree_2Emindepth_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) ) ) )
          = ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V2n ) ) ) ).

thf(thm_2Elbtree_2Emindepth__depth,axiom,
    ! [A_27a: d,V0x_2E0: u,V1t_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
      ( ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Elbtree_2Emindepth_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) ) ) )
        = ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V2n ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Edepth_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ V1t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emmindex__EXISTS,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1f_2E0: u,V2e_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V1f_2E0 ) ) ) @ ( s @ A_27a @ V2e_2E0 ) ) ) )
        <=> ? [V3n: mono_2Etyop_2Enum_2Enum] :
              ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V2e_2E0 ) ) ) )
              = ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V3n ) ) )
     => ! [V0l_2E0: u,V1f_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) )
         => ? [V4i: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Eis__mmindex_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4i ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) ) ) ) ).

thf(thm_2Elbtree_2Emmindex__unique,axiom,
    ! [A_27a: d,V0m: mono_2Etyop_2Enum_2Enum,V1l_2E0: u,V2i: mono_2Etyop_2Enum_2Enum,V3f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Eis__mmindex_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0m ) ) ) ) )
     => ! [V4j: mono_2Etyop_2Enum_2Enum,V5n: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elbtree_2Eis__mmindex_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4j ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5n ) ) ) ) )
        <=> ( ( V4j = V2i )
            & ( V5n = V0m ) ) ) ) ).

thf(thm_2Elbtree_2Emem__bf__flatten,axiom,
    ! [A_27a: d,V0x_2E0: u,V1tlist_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Elbtree_2Ebf__flatten_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V1tlist_2E0 ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elbtree_2Elbtree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Elbtree_2Emem_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Elbtree_2Elbtree @ A_27a ) ) @ V1tlist_2E0 ) ) ) ) ) ).

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