%------------------------------------------------------------------------------
% File     : ITP102^4 : 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    : sptree.ax [Gau19]
%          : HL4102^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  974 ( 429 unt; 427 typ;   0 def)
%            Number of atoms       : 1294 ( 825 equ;  32 cnn)
%            Maximal formula atoms :   41 (   1 avg)
%            Number of connectives : 31242 (  32   ~;  13   |; 238   &;30728   @)
%                                         (  68 <=>; 163  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   42 (   6 avg;30728 nst)
%            Number of types       :    9 (   8 usr)
%            Number of type conns  : 1299 (1299   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  421 ( 419 usr; 124 con; 0-5 aty)
%            Number of variables   : 2080 (   0   ^2057   !;  23   ?;2080   :)
% 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_2Enum_2Enum_29,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: $tType ).

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

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

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

thf(mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,type,
    mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: $tType ).

thf(tyop_2Eind__type_2Erecspace,type,
    tyop_2Eind__type_2Erecspace: d > d ).

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

thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

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

thf(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

thf(tyop_2Eone_2Eone,type,
    tyop_2Eone_2Eone: d ).

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

thf(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: d > d > d ).

thf(tyop_2Esptree_2Espt,type,
    tyop_2Esptree_2Espt: 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_2Earithmetic_2E_2A_2E0,type,
    c_2Earithmetic_2E_2A_2E0: u ).

thf(c_2Earithmetic_2E_2A_2E2,type,
    c_2Earithmetic_2E_2A_2E2: du > du > u ).

thf(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: u ).

thf(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: du > du > u ).

thf(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: u ).

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

thf(c_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: u ).

thf(c_2Earithmetic_2E_2D_2E2,type,
    c_2Earithmetic_2E_2D_2E2: du > du > u ).

thf(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

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

thf(c_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_2E2,type,
    c_2Emin_2E_3D_2E2: du > du > u ).

thf(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

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

thf(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

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

thf(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: u ).

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

thf(c_2Elist_2EALL__DISTINCT_2E0,type,
    c_2Elist_2EALL__DISTINCT_2E0: u ).

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

thf(c_2Ealist_2EALOOKUP_2E0,type,
    c_2Ealist_2EALOOKUP_2E0: u ).

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

thf(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: u ).

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

thf(c_2Ebool_2EARB_2E0,type,
    c_2Ebool_2EARB_2E0: u ).

thf(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: u ).

thf(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: du > u ).

thf(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: u ).

thf(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: du > u ).

thf(c_2Esptree_2EBN_2E0,type,
    c_2Esptree_2EBN_2E0: u ).

thf(c_2Esptree_2EBN_2E2,type,
    c_2Esptree_2EBN_2E2: du > du > u ).

thf(c_2Eind__type_2EBOTTOM_2E0,type,
    c_2Eind__type_2EBOTTOM_2E0: u ).

thf(c_2Esptree_2EBS_2E0,type,
    c_2Esptree_2EBS_2E0: u ).

thf(c_2Esptree_2EBS_2E3,type,
    c_2Esptree_2EBS_2E3: du > du > du > u ).

thf(c_2Epred__set_2ECARD_2E0,type,
    c_2Epred__set_2ECARD_2E0: u ).

thf(c_2Epred__set_2ECARD_2E1,type,
    c_2Epred__set_2ECARD_2E1: du > u ).

thf(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

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

thf(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

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

thf(c_2Eind__type_2ECONSTR_2E0,type,
    c_2Eind__type_2ECONSTR_2E0: u ).

thf(c_2Eind__type_2ECONSTR_2E3,type,
    c_2Eind__type_2ECONSTR_2E3: du > du > du > u ).

thf(c_2Ebool_2EDATATYPE_2E0,type,
    c_2Ebool_2EDATATYPE_2E0: u ).

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

thf(c_2Epred__set_2EDELETE_2E0,type,
    c_2Epred__set_2EDELETE_2E0: u ).

thf(c_2Epred__set_2EDELETE_2E2,type,
    c_2Epred__set_2EDELETE_2E2: du > du > u ).

thf(c_2Epred__set_2EDIFF_2E0,type,
    c_2Epred__set_2EDIFF_2E0: u ).

thf(c_2Epred__set_2EDIFF_2E2,type,
    c_2Epred__set_2EDIFF_2E2: du > du > u ).

thf(c_2Epred__set_2EDISJOINT_2E0,type,
    c_2Epred__set_2EDISJOINT_2E0: u ).

thf(c_2Epred__set_2EDISJOINT_2E2,type,
    c_2Epred__set_2EDISJOINT_2E2: du > du > u ).

thf(c_2Earithmetic_2EDIV_2E0,type,
    c_2Earithmetic_2EDIV_2E0: u ).

thf(c_2Earithmetic_2EDIV_2E2,type,
    c_2Earithmetic_2EDIV_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_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: u ).

thf(c_2Earithmetic_2EEVEN_2E0,type,
    c_2Earithmetic_2EEVEN_2E0: u ).

thf(c_2Earithmetic_2EEVEN_2E1,type,
    c_2Earithmetic_2EEVEN_2E1: du > u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Eind__type_2EFCONS_2E0,type,
    c_2Eind__type_2EFCONS_2E0: u ).

thf(c_2Eind__type_2EFCONS_2E2,type,
    c_2Eind__type_2EFCONS_2E2: du > du > u ).

thf(c_2Epred__set_2EFINITE_2E0,type,
    c_2Epred__set_2EFINITE_2E0: u ).

thf(c_2Epred__set_2EFINITE_2E1,type,
    c_2Epred__set_2EFINITE_2E1: du > u ).

thf(c_2Elist_2EFOLDL_2E0,type,
    c_2Elist_2EFOLDL_2E0: u ).

thf(c_2Elist_2EFOLDL_2E3,type,
    c_2Elist_2EFOLDL_2E3: du > du > du > u ).

thf(c_2Elist_2EFOLDR_2E0,type,
    c_2Elist_2EFOLDR_2E0: u ).

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

thf(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: u ).

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

thf(c_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: u ).

thf(c_2Ecombin_2EI_2E1,type,
    c_2Ecombin_2EI_2E1: du > u ).

thf(c_2Epred__set_2EIMAGE_2E0,type,
    c_2Epred__set_2EIMAGE_2E0: u ).

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

thf(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: u ).

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

thf(c_2Epred__set_2EINSERT_2E0,type,
    c_2Epred__set_2EINSERT_2E0: u ).

thf(c_2Epred__set_2EINSERT_2E2,type,
    c_2Epred__set_2EINSERT_2E2: du > du > u ).

thf(c_2Epred__set_2EINTER_2E0,type,
    c_2Epred__set_2EINTER_2E0: u ).

thf(c_2Epred__set_2EINTER_2E2,type,
    c_2Epred__set_2EINTER_2E2: du > du > u ).

thf(c_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: u ).

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

thf(c_2Elist_2ELENGTH_2E0,type,
    c_2Elist_2ELENGTH_2E0: u ).

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

thf(c_2Ebool_2ELET_2E0,type,
    c_2Ebool_2ELET_2E0: u ).

thf(c_2Ebool_2ELET_2E2,type,
    c_2Ebool_2ELET_2E2: du > du > u ).

thf(c_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: u ).

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

thf(c_2Esptree_2ELN_2E0,type,
    c_2Esptree_2ELN_2E0: u ).

thf(c_2Esptree_2ELS_2E0,type,
    c_2Esptree_2ELS_2E0: u ).

thf(c_2Esptree_2ELS_2E1,type,
    c_2Esptree_2ELS_2E1: du > u ).

thf(c_2Elist_2EMAP_2E0,type,
    c_2Elist_2EMAP_2E0: u ).

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

thf(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

thf(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: u ).

thf(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: u ).

thf(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: du > u ).

thf(c_2Eoption_2EOPTION__MAP_2E0,type,
    c_2Eoption_2EOPTION__MAP_2E0: u ).

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

thf(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: u ).

thf(c_2Epair_2ESND_2E1,type,
    c_2Epair_2ESND_2E1: du > u ).

thf(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: u ).

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

thf(c_2Epred__set_2ESUBSET_2E0,type,
    c_2Epred__set_2ESUBSET_2E0: u ).

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

thf(c_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_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: u ).

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

thf(c_2Epred__set_2EUNION_2E0,type,
    c_2Epred__set_2EUNION_2E0: u ).

thf(c_2Epred__set_2EUNION_2E2,type,
    c_2Epred__set_2EUNION_2E2: du > du > u ).

thf(c_2Erelation_2EWF_2E0,type,
    c_2Erelation_2EWF_2E0: u ).

thf(c_2Erelation_2EWF_2E1,type,
    c_2Erelation_2EWF_2E1: du > u ).

thf(c_2Erelation_2EWFREC_2E0,type,
    c_2Erelation_2EWFREC_2E0: u ).

thf(c_2Erelation_2EWFREC_2E2,type,
    c_2Erelation_2EWFREC_2E2: du > du > u ).

thf(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: 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_2Epred__set_2Ecount_2E0,type,
    c_2Epred__set_2Ecount_2E0: u ).

thf(c_2Epred__set_2Ecount_2E1,type,
    c_2Epred__set_2Ecount_2E1: du > u ).

thf(c_2Esptree_2Edelete_2E0,type,
    c_2Esptree_2Edelete_2E0: u ).

thf(c_2Esptree_2Edelete_2E2,type,
    c_2Esptree_2Edelete_2E2: du > du > u ).

thf(c_2Esptree_2Edifference_2E0,type,
    c_2Esptree_2Edifference_2E0: u ).

thf(c_2Esptree_2Edifference_2E2,type,
    c_2Esptree_2Edifference_2E2: du > du > u ).

thf(c_2Esptree_2Edomain_2E0,type,
    c_2Esptree_2Edomain_2E0: u ).

thf(c_2Esptree_2Edomain_2E1,type,
    c_2Esptree_2Edomain_2E1: du > u ).

thf(c_2Esptree_2Efilter__v_2E0,type,
    c_2Esptree_2Efilter__v_2E0: u ).

thf(c_2Esptree_2Efilter__v_2E2,type,
    c_2Esptree_2Efilter__v_2E2: du > du > u ).

thf(c_2Esptree_2Efoldi_2E0,type,
    c_2Esptree_2Efoldi_2E0: u ).

thf(c_2Esptree_2Efoldi_2E3,type,
    c_2Esptree_2Efoldi_2E3: du > du > du > u ).

thf(c_2Esptree_2Efoldi_2E4,type,
    c_2Esptree_2Efoldi_2E4: du > du > du > du > u ).

thf(c_2Esptree_2EfromAList_2E0,type,
    c_2Esptree_2EfromAList_2E0: u ).

thf(c_2Esptree_2EfromAList_2E1,type,
    c_2Esptree_2EfromAList_2E1: du > u ).

thf(c_2Esptree_2EfromList_2E0,type,
    c_2Esptree_2EfromList_2E0: u ).

thf(c_2Esptree_2EfromList_2E1,type,
    c_2Esptree_2EfromList_2E1: du > u ).

thf(c_2Esptree_2Einsert_2E0,type,
    c_2Esptree_2Einsert_2E0: u ).

thf(c_2Esptree_2Einsert_2E3,type,
    c_2Esptree_2Einsert_2E3: du > du > du > u ).

thf(c_2Esptree_2Einter_2E0,type,
    c_2Esptree_2Einter_2E0: u ).

thf(c_2Esptree_2Einter_2E2,type,
    c_2Esptree_2Einter_2E2: du > du > u ).

thf(c_2Esptree_2Einter__eq_2E0,type,
    c_2Esptree_2Einter__eq_2E0: u ).

thf(c_2Esptree_2Einter__eq_2E2,type,
    c_2Esptree_2Einter__eq_2E2: du > 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_2Esptree_2Elist__insert_2E0,type,
    c_2Esptree_2Elist__insert_2E0: u ).

thf(c_2Esptree_2Elist__insert_2E2,type,
    c_2Esptree_2Elist__insert_2E2: du > du > u ).

thf(c_2Esptree_2Elist__to__num__set_2E0,type,
    c_2Esptree_2Elist__to__num__set_2E0: u ).

thf(c_2Esptree_2Elist__to__num__set_2E1,type,
    c_2Esptree_2Elist__to__num__set_2E1: du > u ).

thf(c_2Esptree_2Elookup_2E0,type,
    c_2Esptree_2Elookup_2E0: u ).

thf(c_2Esptree_2Elookup_2E2,type,
    c_2Esptree_2Elookup_2E2: du > du > u ).

thf(c_2Esptree_2Elrnext_2E0,type,
    c_2Esptree_2Elrnext_2E0: u ).

thf(c_2Esptree_2Elrnext_2E1,type,
    c_2Esptree_2Elrnext_2E1: du > u ).

thf(c_2Esptree_2Emap_2E0,type,
    c_2Esptree_2Emap_2E0: u ).

thf(c_2Esptree_2Emap_2E2,type,
    c_2Esptree_2Emap_2E2: du > du > u ).

thf(c_2Esptree_2Emapi_2E0,type,
    c_2Esptree_2Emapi_2E0: u ).

thf(c_2Esptree_2Emapi_2E2,type,
    c_2Esptree_2Emapi_2E2: du > du > u ).

thf(c_2Esptree_2Emapi0_2E0,type,
    c_2Esptree_2Emapi0_2E0: u ).

thf(c_2Esptree_2Emapi0_2E3,type,
    c_2Esptree_2Emapi0_2E3: du > du > du > u ).

thf(c_2Esptree_2Emk__BN_2E0,type,
    c_2Esptree_2Emk__BN_2E0: u ).

thf(c_2Esptree_2Emk__BN_2E2,type,
    c_2Esptree_2Emk__BN_2E2: du > du > u ).

thf(c_2Esptree_2Emk__BS_2E0,type,
    c_2Esptree_2Emk__BS_2E0: u ).

thf(c_2Esptree_2Emk__BS_2E3,type,
    c_2Esptree_2Emk__BS_2E3: du > du > du > u ).

thf(c_2Esptree_2Emk__wf_2E0,type,
    c_2Esptree_2Emk__wf_2E0: u ).

thf(c_2Esptree_2Emk__wf_2E1,type,
    c_2Esptree_2Emk__wf_2E1: du > u ).

thf(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: u ).

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

thf(c_2Eone_2Eone_2E0,type,
    c_2Eone_2Eone_2E0: u ).

thf(c_2Eoption_2Eoption__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_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_2Esptree_2Esize_2E0,type,
    c_2Esptree_2Esize_2E0: u ).

thf(c_2Esptree_2Esize_2E1,type,
    c_2Esptree_2Esize_2E1: du > u ).

thf(c_2Esptree_2Espt__CASE_2E0,type,
    c_2Esptree_2Espt__CASE_2E0: u ).

thf(c_2Esptree_2Espt__CASE_2E5,type,
    c_2Esptree_2Espt__CASE_2E5: du > du > du > du > du > u ).

thf(c_2Esptree_2Espt__acc_2E0,type,
    c_2Esptree_2Espt__acc_2E0: u ).

thf(c_2Esptree_2Espt__acc_2E2,type,
    c_2Esptree_2Espt__acc_2E2: du > du > u ).

thf(c_2Esptree_2Espt__center_2E0,type,
    c_2Esptree_2Espt__center_2E0: u ).

thf(c_2Esptree_2Espt__center_2E1,type,
    c_2Esptree_2Espt__center_2E1: du > u ).

thf(c_2Esptree_2Espt__fold_2E0,type,
    c_2Esptree_2Espt__fold_2E0: u ).

thf(c_2Esptree_2Espt__fold_2E3,type,
    c_2Esptree_2Espt__fold_2E3: du > du > du > u ).

thf(c_2Esptree_2Espt__left_2E0,type,
    c_2Esptree_2Espt__left_2E0: u ).

thf(c_2Esptree_2Espt__left_2E1,type,
    c_2Esptree_2Espt__left_2E1: du > u ).

thf(c_2Esptree_2Espt__right_2E0,type,
    c_2Esptree_2Espt__right_2E0: u ).

thf(c_2Esptree_2Espt__right_2E1,type,
    c_2Esptree_2Espt__right_2E1: du > u ).

thf(c_2Esptree_2Espt__size_2E0,type,
    c_2Esptree_2Espt__size_2E0: u ).

thf(c_2Esptree_2Espt__size_2E2,type,
    c_2Esptree_2Espt__size_2E2: du > du > u ).

thf(c_2Esptree_2Esubspt_2E0,type,
    c_2Esptree_2Esubspt_2E0: u ).

thf(c_2Esptree_2Esubspt_2E2,type,
    c_2Esptree_2Esubspt_2E2: du > du > u ).

thf(c_2Esptree_2EtoAList_2E0,type,
    c_2Esptree_2EtoAList_2E0: u ).

thf(c_2Esptree_2EtoAList_2E1,type,
    c_2Esptree_2EtoAList_2E1: du > u ).

thf(c_2Esptree_2EtoList_2E0,type,
    c_2Esptree_2EtoList_2E0: u ).

thf(c_2Esptree_2EtoList_2E1,type,
    c_2Esptree_2EtoList_2E1: du > u ).

thf(c_2Esptree_2EtoListA_2E0,type,
    c_2Esptree_2EtoListA_2E0: u ).

thf(c_2Esptree_2EtoListA_2E2,type,
    c_2Esptree_2EtoListA_2E2: du > du > u ).

thf(c_2Esptree_2Eunion_2E0,type,
    c_2Esptree_2Eunion_2E0: u ).

thf(c_2Esptree_2Eunion_2E2,type,
    c_2Esptree_2Eunion_2E2: du > du > u ).

thf(c_2Esptree_2Ewf_2E0,type,
    c_2Esptree_2Ewf_2E0: u ).

thf(c_2Esptree_2Ewf_2E1,type,
    c_2Esptree_2Ewf_2E1: du > u ).

thf(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

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

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

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

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o > $o ) > $o > $o > $o > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_20mono_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 ) > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_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 ) > ( ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

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

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_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 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

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_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

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_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

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

thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

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

thf(mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o ) > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o ) > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,type,
    mono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Earithmetic_2E_2A,type,
    mono_2Ec_2Earithmetic_2E_2A: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Earithmetic_2E_2B,type,
    mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Earithmetic_2E_2D,type,
    mono_2Ec_2Earithmetic_2E_2D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

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_2Emin_2E_40_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Ec_2Emin_2E_40_2Emono_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 ) > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Elist_2EALL__DISTINCT_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2EALL__DISTINCT_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ).

thf(mono_2Ec_2Elist_2EAPPEND_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2EAPPEND_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

thf(mono_2Ec_2Earithmetic_2EBIT1,type,
    mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Earithmetic_2EBIT2,type,
    mono_2Ec_2Earithmetic_2EBIT2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Epred__set_2ECARD_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2ECARD_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool: $o > $o > $o > $o ).

thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

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

thf(mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

thf(mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool: $o > $o ).

thf(mono_2Ec_2Epred__set_2EDELETE_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EDELETE_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Epred__set_2EDISJOINT_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EDISJOINT_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Ec_2Earithmetic_2EDIV,type,
    mono_2Ec_2Earithmetic_2EDIV: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Earithmetic_2EEVEN,type,
    mono_2Ec_2Earithmetic_2EEVEN: mono_2Etyop_2Enum_2Enum > $o ).

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

thf(mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Esptree_2ELN_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2ELN_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

thf(mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
    mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

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

thf(mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

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_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Erelation_2EWF_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Erelation_2EWF_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Ec_2Erelation_2EWFREC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Erelation_2EWFREC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( ( 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_2Ec_2Earithmetic_2EZERO,type,
    mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).

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

thf(mono_2Ec_2Epred__set_2Ecount,type,
    mono_2Ec_2Epred__set_2Ecount: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Esptree_2Edomain_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Edomain_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Esptree_2Einsert_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Einsert_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Esptree_2Elist__insert,type,
    mono_2Ec_2Esptree_2Elist__insert: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Esptree_2Elist__to__num__set,type,
    mono_2Ec_2Esptree_2Elist__to__num__set: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Esptree_2Elookup_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Elookup_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Esptree_2Elrnext,type,
    mono_2Ec_2Esptree_2Elrnext: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Eone_2Eone,type,
    mono_2Ec_2Eone_2Eone: mono_2Etyop_2Eone_2Eone ).

thf(mono_2Ec_2Esptree_2Espt__acc,type,
    mono_2Ec_2Esptree_2Espt__acc: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Esptree_2Esubspt_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Esubspt_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o ).

thf(mono_2Ec_2Esptree_2Eunion_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Eunion_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(mono_2Ec_2Esptree_2Ewf_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Esptree_2Ewf_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o ).

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

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

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

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

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: ( $o > $o > $o > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: ( $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_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 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).

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

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > 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_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > 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_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ) > u ).

thf(i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > u ).

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

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

thf(i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
    i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > u ).

thf(i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,type,
    i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > u ).

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

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

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

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: du > $o > $o > $o > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29: du > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > ( ( 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(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

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

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( ( 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(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

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_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

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_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

thf(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).

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

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

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

thf(j_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,type,
    j_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: du > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ 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_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ 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_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ).

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

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

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ 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_2Eone_2Eone,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ ( j_mono_2Etyop_2Eone_2Eone @ ( s @ tyop_2Eone_2Eone @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Eone_2Eone @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ ( j_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ).

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

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: $o > $o > $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_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 > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_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 > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_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_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_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_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_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_2Eone_2Eone,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone] :
      ( ( j_mono_2Etyop_2Eone_2Eone @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( j_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V0 ) ) )
      = V0 ) ).

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

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( ( s @ A_27a @ X0_2E0 )
        = ( s @ A_27a @ X1_2E0 ) )
    <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Emin_2E_40_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28A_27a_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28A_27a_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Emin_2E_40_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ealist_2EALOOKUP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Ealist_2EALOOKUP_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).

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_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ c_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2EBN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2EBN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2EBN_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) ) @ c_2Esptree_2EBN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Esptree_2EBS_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ c_2Esptree_2EBS_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Esptree_2EBS_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) ) ) @ c_2Esptree_2EBS_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ 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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ 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_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) ) ) @ c_2Eind__type_2ECONSTR_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X2_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_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) ) ) @ c_2Eind__type_2EFCONS_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Esptree_2Espt_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( c_2Elist_2EFOLDL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ c_2Elist_2EFOLDL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ X2 ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ c_2Elist_2EFOLDR_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ X2 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27b @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X2_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ A_27b ) ) ) @ c_2Elist_2EFOLDR_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ tyop_2Enum_2Enum ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Ecombin_2EI_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ c_2Ecombin_2EI_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) ) ).

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

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ c_2Ecombin_2EK_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) ) @ c_2Ecombin_2EK_2E0 ) @ ( s @ A_27b @ X0_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(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ A_27a @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ c_2Ebool_2ELET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Ebool_2ELET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).

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

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2ELS_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ c_2Esptree_2ELS_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2ELS_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27b ) ) @ c_2Esptree_2ELS_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) ) ).

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

thf(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ A_27b @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ A_27b ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Esptree_2Espt_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_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Esptree_2Espt_28A_27a_29_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ 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 @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2EWF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ 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 @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2EWF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ c_2Erelation_2EWFREC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Erelation_2EWFREC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Edelete_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Edelete_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Edifference_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Edifference_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Edifference_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Edifference_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2Edomain_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) )
      = ( 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_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Esptree_2Edomain_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2Edomain_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) ) )
      = ( 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_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Esptree_2Edomain_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2Edomain_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X0_2E0 ) ) ) )
      = ( 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_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Esptree_2Edomain_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Efilter__v_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Efilter__v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] :
      ( ( s @ A_27b @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ A_27b @ X2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X3_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) ) @ c_2Esptree_2Efoldi_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ A_27b @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X3_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2: mono_2Etyop_2Enum_2Enum > $o,X3_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ X2 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X3_2E0 ) ) ) )
      = ( 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_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Esptree_2Efoldi_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ X2 ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X3_2E0 ) ) ) ) ) ).

thf(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) ) @ c_2Esptree_2Efoldi_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X3_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Esptree_2Efoldi_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( c_2Esptree_2Efoldi_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) ) @ c_2Esptree_2Efoldi_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) ) @ c_2Esptree_2Efoldi_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X3_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] :
      ( ( s @ A_27a @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ A_27a @ X2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X3_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ A_27a ) ) ) ) @ c_2Esptree_2Efoldi_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X3_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2EfromAList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ c_2Esptree_2EfromAList_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2EfromAList_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) @ c_2Esptree_2EfromAList_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2EfromList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ c_2Esptree_2EfromList_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Esptree_2Einsert_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ c_2Esptree_2Einsert_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Esptree_2Einsert_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) ) ) @ c_2Esptree_2Einsert_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Einter_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Einter_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) ) @ c_2Esptree_2Einter_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ c_2Esptree_2Einter_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Einter__eq_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Einter__eq_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Elist_2Elist__CASE_2E3 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ c_2Elist_2Elist__CASE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Elookup_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Esptree_2Elookup_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Elookup_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Esptree_2Elookup_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) ) @ c_2Esptree_2Emap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ c_2Esptree_2Emap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Emap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ c_2Esptree_2Emap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) ) @ c_2Esptree_2Emap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Emapi_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Emapi_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Esptree_2Emapi0_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) ) ) @ c_2Esptree_2Emapi0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Esptree_2Emapi0_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ c_2Esptree_2Emapi0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Emk__BN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Emk__BN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Esptree_2Emk__BS_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ c_2Esptree_2Emk__BS_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2Emk__wf_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ c_2Esptree_2Emk__wf_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2Emk__wf_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27b ) ) @ c_2Esptree_2Emk__wf_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( 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_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27b_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 @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_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 @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2Esize_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Enum_2Enum ) @ c_2Esptree_2Esize_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] :
      ( ( s @ A_27b @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ X3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ X4_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) ) ) ) @ c_2Esptree_2Espt__CASE_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ X3_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ X4_2E0 ) ) ) ) ).

thf(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ X4_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) ) @ c_2Esptree_2Espt__CASE_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X3_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ X4_2E0 ) ) ) ) ).

thf(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27a_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ X4_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ c_2Esptree_2Espt__CASE_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X3_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ X4_2E0 ) ) ) ) ).

thf(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27b_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ X4_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ c_2Esptree_2Espt__CASE_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ X3_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ X4_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2Espt__center_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Espt__center_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Esptree_2Espt__center_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Esptree_2Espt__fold_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_2Esptree_2Espt__fold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ A_27a ) ) ) @ c_2Esptree_2Espt__fold_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2Espt__left_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__left_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ c_2Esptree_2Espt__left_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2Espt__right_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__right_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ c_2Esptree_2Espt__right_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Espt__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Espt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Enum_2Enum ) ) @ c_2Esptree_2Espt__size_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Esubspt_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Esptree_2Esubspt_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2EtoAList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Esptree_2EtoAList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Esptree_2EtoAList_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2EtoAList_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ ( c_2Esptree_2EtoAList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) ) @ c_2Esptree_2EtoAList_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2EtoList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Esptree_2EtoList_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2EtoList_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Esptree_2EtoList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ c_2Esptree_2EtoList_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2EtoListA_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Esptree_2EtoListA_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Eunion_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Eunion_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2Ewf_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Esptree_2Ewf_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Esptree_2Ewf_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Esptree_2Ewf_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ X0_2E0 ) ) ) ) ) ).

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

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

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o > $o,V1: $o] :
      ( ( 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 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_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_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: $o] :
      ( ( 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 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_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_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_20mono_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 ) > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o] :
      ( ( 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 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_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 > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > 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_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_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_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_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_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_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_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( 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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( 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 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_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_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( 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 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( 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 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_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 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > 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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_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_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Elist_2Elist_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_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( 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_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_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_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_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_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_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_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_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eone_2Eone] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eone_2Eone] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( 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_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Emin_2E_40_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Emin_2E_40_2E1_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 ) > $o] :
      ( ( 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 @ ( mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2EALL__DISTINCT_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Elist_2EALL__DISTINCT_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ c_2Elist_2EALL__DISTINCT_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Elist_2EALL__DISTINCT_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Elist_2EAPPEND_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ c_2Elist_2EAPPEND_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Elist_2EAPPEND_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2ECARD_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( 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 @ mono_2Ec_2Epred__set_2ECARD_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ c_2Epred__set_2ECARD_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epred__set_2ECARD_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( c_2Epred__set_2ECARD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o,V1: $o,V2: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ V0 @ V1 @ V2 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V2 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: $o,V1: mono_2Etyop_2Enum_2Enum,V2: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 @ V2 ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V2: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V0 @ V1 @ V2 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V1 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V2 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ c_2Elist_2ECONS_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ( ( 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_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2EDATATYPE_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ V0 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EDATATYPE_2E1 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EDELETE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EDELETE_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDELETE_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: 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 @ ( mono_2Ec_2Epred__set_2EDELETE_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_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_2Ec_2Epred__set_2EDIFF_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDIFF_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EDISJOINT_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Epred__set_2EDISJOINT_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EDISJOINT_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EDISJOINT_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EFINITE_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ c_2Ecombin_2EI_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( c_2Ecombin_2EI_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EIMAGE_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EIMAGE_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EIMAGE_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ 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_2Ec_2Epred__set_2EINSERT_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINSERT_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ 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_2Ec_2Epred__set_2EINTER_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINTER_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2ELN_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    ( ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ mono_2Ec_2Esptree_2ELN_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ c_2Esptree_2ELN_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ c_2Elist_2ENIL_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ c_2Eoption_2ESOME_2E0 ) ) ).

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

thf(monoeq_2Emono_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EUNION_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EUNION_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Erelation_2EWF_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Erelation_2EWF_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2EWF_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Erelation_2EWF_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( 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 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Erelation_2EWFREC_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Erelation_2EWFREC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ c_2Erelation_2EWFREC_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > 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 @ ( mono_2Ec_2Erelation_2EWFREC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Erelation_2EWFREC_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_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Edomain_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Esptree_2Edomain_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Esptree_2Edomain_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Esptree_2Edomain_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Einsert_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29_29 @ mono_2Ec_2Esptree_2Einsert_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) ) @ c_2Esptree_2Einsert_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Einsert_2E3_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Eone_2Eone,V2: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Esptree_2Einsert_2Emono_2Etyop_2Eone_2Eone @ V0 @ V1 @ V2 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V1 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V2 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Elookup_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ mono_2Ec_2Esptree_2Elookup_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ c_2Esptree_2Elookup_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Elookup_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Esptree_2Elookup_2Emono_2Etyop_2Eone_2Eone @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Esubspt_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Esptree_2Esubspt_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ c_2Esptree_2Esubspt_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Esubspt_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Esptree_2Esubspt_2Emono_2Etyop_2Eone_2Eone @ V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Eunion_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29 @ mono_2Ec_2Esptree_2Eunion_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) ) ) @ c_2Esptree_2Eunion_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Eunion_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Esptree_2Eunion_2Emono_2Etyop_2Eone_2Eone @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Ewf_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Esptree_2Ewf_2Emono_2Etyop_2Eone_2Eone ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ c_2Esptree_2Ewf_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Esptree_2Ewf_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Esptree_2Ewf_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 @ 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_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_20mono_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 ) > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_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 > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_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 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > 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_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,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_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,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_2Eone_2Eone_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eone_2Eone] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

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

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

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

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_2Ctyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,axiom,
    ! [V0: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(thm_2Esptree_2Efilter__v__def,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ! [V1f_2E0: u,V2x_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
      & ! [V3f_2E0: u,V4l_2E0: u,V5r_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4l_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4l_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5r_2E0 ) ) ) ) ) )
      & ! [V6f_2E0: u,V7l_2E0: u,V8x_2E0: u,V9r_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V6f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7l_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V6f_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V6f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7l_2E0 ) ) ) @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V6f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V6f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7l_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V6f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9r_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__center__primitive__def,axiom,
    ! [A_27a: d,F3_2E0: u,F4_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V4v7_2E0: u,V5v8_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4v7_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5v8_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     => ( ! [V6t1_2E0: u,V7x_27_2E0: u,V8t2_2E0: u] :
            ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t1_2E0 ) ) ) @ ( s @ A_27a @ V7x_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8t2_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V7x_27_2E0 ) ) ) ) ) )
       => ( ! [V3x_2E0: u] :
              ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ F2_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) )
         => ( ! [V1spt__center_2E0: u,V2a_2E0: u] :
                ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1spt__center_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2a_2E0 ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2a_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F4_2E0 ) ) ) )
           => ( ! [V0R_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
                  = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) ) )
             => ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Esptree_2Espt__center_2E0 )
                = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F1_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__right__def,axiom,
    ! [A_27a: d] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__right_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ! [V0x_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__right_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ! [V1t1_2E0: u,V2t2_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__right_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) )
      & ! [V3t1_2E0: u,V4x_2E0: u,V5t2_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__right_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ).

thf(thm_2Esptree_2Espt__left__def,axiom,
    ! [A_27a: d] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__left_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ! [V0x_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__left_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ! [V1t1_2E0: u,V2t2_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__left_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) )
      & ! [V3t1_2E0: u,V4x_2E0: u,V5t2_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__left_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) ) ) ).

thf(thm_2Esptree_2Emap__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0f_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ c_2Esptree_2ELN_2E0 ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ! [V1f_2E0: u,V2a_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27b @ V2a_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ A_27b @ V2a_2E0 ) ) ) ) ) )
      & ! [V3f_2E0: u,V4t1_2E0: u,V5t2_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V3f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V4t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V5t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V3f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V4t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V3f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V5t2_2E0 ) ) ) ) ) )
      & ! [V6f_2E0: u,V7t1_2E0: u,V8a_2E0: u,V9t2_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V6f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V7t1_2E0 ) @ ( s @ A_27b @ V8a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V9t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V6f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V7t1_2E0 ) ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V6f_2E0 ) @ ( s @ A_27b @ V8a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V6f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V9t2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2EfromAList__primitive__def,axiom,
    ! [A_27a: d,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V4fromAList_2E0: u,V7xs_2E0: u,V8x: mono_2Etyop_2Enum_2Enum,V9y_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ V4fromAList_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V7xs_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8x ) ) ) ) @ ( s @ A_27a @ V9y_2E0 ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8x ) ) @ ( s @ A_27a @ V9y_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ V4fromAList_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V7xs_2E0 ) ) ) ) ) ) ) )
     => ( ! [V4fromAList_2E0: u,V6v_2E0: u,V7xs_2E0: u] :
            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ V4fromAList_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ V6v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V7xs_2E0 ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ V6v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ V4fromAList_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V7xs_2E0 ) ) ) ) ) )
       => ( ! [V4fromAList_2E0: u,V5a_2E0: u] :
              ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ V4fromAList_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V5a_2E0 ) ) )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Elist_2Elist__CASE_2E3 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ V4fromAList_2E0 ) ) ) ) ) )
         => ( ! [V0R_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
              <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
                  & ! [V1y_2E0: u,V2x: mono_2Etyop_2Enum_2Enum,V3xs_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V3xs_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x ) ) @ ( s @ A_27a @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V3xs_2E0 ) ) ) ) ) ) ) )
           => ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ c_2Esptree_2EfromAList_2E0 )
              = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F1_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Emk__wf__def,axiom,
    ! [A_27a: d] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ! [V0x_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) )
      & ! [V1t1_2E0: u,V2t2_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) ) ) ) )
      & ! [V3t1_2E0: u,V4x_2E0: u,V5t2_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2EtoList__def,axiom,
    ! [A_27a: d,V0m_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m_2E0 ) ) ) ) ).

thf(thm_2Esptree_2EtoListA__def,axiom,
    ! [A_27a: d] :
      ( ! [V0acc_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0acc_2E0 ) )
      & ! [V1acc_2E0: u,V2a_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1acc_2E0 ) ) ) )
      & ! [V3acc_2E0: u,V4t1_2E0: u,V5t2_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) ) ) )
      & ! [V6acc_2E0: u,V7t1_2E0: u,V8a_2E0: u,V9t2_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V6acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7t1_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V6acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7t1_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2EtoAList__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0k: mono_2Etyop_2Enum_2Enum,V1v_2E0: u,V2a_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) ) ) @ ( s @ A_27a @ V1v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V2a_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ A_27a @ V1v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V2a_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Esptree_2EtoAList_2E0 )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( c_2Esptree_2Efoldi_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Emapi__def,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1pt_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1pt_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1pt_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Emapi0__def,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V5f_2E0: u,V6i: mono_2Etyop_2Enum_2Enum,V7t1_2E0: u,V8t2_2E0: u,V9inc: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V5f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6i ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V7t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V8t2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9inc ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V5f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V6i @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V9inc ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V7t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V5f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V6i @ V9inc ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V8t2_2E0 ) ) ) ) ) )
     => ( ! [V10f_2E0: u,V11i: mono_2Etyop_2Enum_2Enum,V12t1_2E0: u,V13a_2E0: u,V14t2_2E0: u,V15inc: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V10f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11i ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V12t1_2E0 ) ) ) @ ( s @ A_27b @ V13a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V14t2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V15inc ) ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V10f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11i @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V15inc ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V12t1_2E0 ) ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V10f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11i ) ) ) ) @ ( s @ A_27b @ V13a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V10f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11i @ V15inc ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V14t2_2E0 ) ) ) ) ) )
       => ( ! [V0f_2E0: u,V1i: mono_2Etyop_2Enum_2Enum] :
              ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1i ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ c_2Esptree_2ELN_2E0 ) ) )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
          & ! [V2f_2E0: u,V3i: mono_2Etyop_2Enum_2Enum,V4a_2E0: u] :
              ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V2f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3i ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27b @ V4a_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V2f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3i ) ) ) ) @ ( s @ A_27b @ V4a_2E0 ) ) ) ) ) )
          & ! [V5f_2E0: u,V6i: mono_2Etyop_2Enum_2Enum,V7t1_2E0: u,V8t2_2E0: u] :
              ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V5f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6i ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V7t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V8t2_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V5f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6i ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V7t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V8t2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Esptree_2Elrnext @ V6i ) ) ) ) ) )
          & ! [V10f_2E0: u,V11i: mono_2Etyop_2Enum_2Enum,V12t1_2E0: u,V13a_2E0: u,V14t2_2E0: u] :
              ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V10f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11i ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V12t1_2E0 ) @ ( s @ A_27b @ V13a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V14t2_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V10f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11i ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V12t1_2E0 ) ) ) @ ( s @ A_27b @ V13a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V14t2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Esptree_2Elrnext @ V11i ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Efoldi__def,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V13f_2E0: u,V14i: mono_2Etyop_2Enum_2Enum,V17a_2E0: u,V15acc_2E0: u,V16t1_2E0: u,V18t2_2E0: u,V19inc: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V13f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V14i ) ) ) ) @ ( s @ A_27b @ V17a_2E0 ) ) ) @ ( s @ A_27a @ V15acc_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V16t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V18t2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V19inc ) ) ) )
          = ( s @ A_27a @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V13f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14i @ V19inc ) ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V13f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V14i ) ) ) ) @ ( s @ A_27b @ V17a_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V13f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14i @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V19inc ) ) ) ) @ ( s @ A_27a @ V15acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V16t1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V18t2_2E0 ) ) ) )
     => ( ! [V7f_2E0: u,V8i: mono_2Etyop_2Enum_2Enum,V9acc_2E0: u,V10t1_2E0: u,V11t2_2E0: u,V12inc: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V7f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8i ) ) ) ) @ ( s @ A_27a @ V9acc_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V10t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V11t2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V12inc ) ) ) )
            = ( s @ A_27a @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V7f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V8i @ V12inc ) ) ) @ ( s @ A_27a @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V7f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V8i @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V12inc ) ) ) ) @ ( s @ A_27a @ V9acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V10t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V11t2_2E0 ) ) ) )
       => ( ! [V0f_2E0: u,V1i: mono_2Etyop_2Enum_2Enum,V2acc_2E0: u] :
              ( ( s @ A_27a @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1i ) ) @ ( s @ A_27a @ V2acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ c_2Esptree_2ELN_2E0 ) ) )
              = ( s @ A_27a @ V2acc_2E0 ) )
          & ! [V3f_2E0: u,V4i: mono_2Etyop_2Enum_2Enum,V5acc_2E0: u,V6a_2E0: u] :
              ( ( s @ A_27a @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V3f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4i ) ) @ ( s @ A_27a @ V5acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27b @ V6a_2E0 ) ) ) ) )
              = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V3f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4i ) ) ) ) @ ( s @ A_27b @ V6a_2E0 ) ) ) @ ( s @ A_27a @ V5acc_2E0 ) ) ) )
          & ! [V7f_2E0: u,V8i: mono_2Etyop_2Enum_2Enum,V9acc_2E0: u,V10t1_2E0: u,V11t2_2E0: u] :
              ( ( s @ A_27a @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V7f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8i ) ) @ ( s @ A_27a @ V9acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V10t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V11t2_2E0 ) ) ) ) )
              = ( s @ A_27a @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V7f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8i ) ) ) ) @ ( s @ A_27a @ V9acc_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V10t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V11t2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Esptree_2Elrnext @ V8i ) ) ) ) ) )
          & ! [V13f_2E0: u,V14i: mono_2Etyop_2Enum_2Enum,V15acc_2E0: u,V16t1_2E0: u,V17a_2E0: u,V18t2_2E0: u] :
              ( ( s @ A_27a @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V13f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V14i ) ) @ ( s @ A_27a @ V15acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V16t1_2E0 ) @ ( s @ A_27b @ V17a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V18t2_2E0 ) ) ) ) )
              = ( s @ A_27a @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V13f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V14i ) ) ) ) @ ( s @ A_27b @ V17a_2E0 ) ) ) @ ( s @ A_27a @ V15acc_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V16t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V18t2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Esptree_2Elrnext @ V14i ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__TY__DEF,axiom,
    ! [A_27a: d,F4_2E0: u,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V13n: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F4_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V13n ) ) ) )
          = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
     => ( ! [V9n: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F3_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9n ) ) ) )
            = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
       => ( ! [V6n: mono_2Etyop_2Enum_2Enum] :
              ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6n ) ) ) )
              = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
         => ( ! [V4n: mono_2Etyop_2Enum_2Enum] :
                ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) ) )
                = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
           => ( ! [V1a0_27_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V1a0_27_2E0 ) ) ) )
                <=> ! [V2_27spt_27_2E0: u] :
                      ( ! [V3a0_27_2E0: u] :
                          ( ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V3a0_27_2E0 )
                              = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F1_2E0 ) ) ) )
                            | ? [V5a_2E0: u] :
                                ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V3a0_27_2E0 )
                                = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F2_2E0 ) ) ) )
                            | ? [V7a0_2E0: u,V8a1_2E0: u] :
                                ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V3a0_27_2E0 )
                                  = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V7a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V8a1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F3_2E0 ) ) ) ) ) ) ) )
                                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2_27spt_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V7a0_2E0 ) ) ) )
                                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2_27spt_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V8a1_2E0 ) ) ) ) )
                            | ? [V10a0_2E0: u,V11a1_2E0: u,V12a2_2E0: u] :
                                ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V3a0_27_2E0 )
                                  = ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) ) ) @ ( s @ A_27a @ V11a1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V10a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V12a2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F4_2E0 ) ) ) ) ) ) ) )
                                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2_27spt_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V10a0_2E0 ) ) ) )
                                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2_27spt_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V12a2_2E0 ) ) ) ) ) )
                         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2_27spt_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V3a0_27_2E0 ) ) ) ) )
                     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2_27spt_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ V1a0_27_2E0 ) ) ) ) ) )
             => ? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ V0rep_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__case__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0v_2E0: u,V1f_2E0: u,V2f1_2E0: u,V3f2_2E0: u] :
          ( ( s @ A_27b @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ A_27b @ V0v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ V2f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ V3f2_2E0 ) ) )
          = ( s @ A_27b @ V0v_2E0 ) )
      & ! [V4a_2E0: u,V5v_2E0: u,V6f_2E0: u,V7f1_2E0: u,V8f2_2E0: u] :
          ( ( s @ A_27b @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ A_27b @ V5v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ V7f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ V8f2_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V6f_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) )
      & ! [V9a0_2E0: u,V10a1_2E0: u,V11v_2E0: u,V12f_2E0: u,V13f1_2E0: u,V14f2_2E0: u] :
          ( ( s @ A_27b @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9a0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10a1_2E0 ) ) ) @ ( s @ A_27b @ V11v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V12f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ V13f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ V14f2_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ V13f1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9a0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10a1_2E0 ) ) ) )
      & ! [V15a0_2E0: u,V16a1_2E0: u,V17a2_2E0: u,V18v_2E0: u,V19f_2E0: u,V20f1_2E0: u,V21f2_2E0: u] :
          ( ( s @ A_27b @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V15a0_2E0 ) @ ( s @ A_27a @ V16a1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V17a2_2E0 ) ) ) @ ( s @ A_27b @ V18v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V19f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ V20f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ V21f2_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ V21f2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V15a0_2E0 ) ) ) @ ( s @ A_27a @ V16a1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V17a2_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__size__def,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Espt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
          = mono_2Ec_2Enum_2E0 )
      & ! [V1f_2E0: u,V2a_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Espt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) ) ) ) ) )
      & ! [V3f_2E0: u,V4a0_2E0: u,V5a1_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Espt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V3f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4a0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5a1_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Espt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V3f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4a0_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Espt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V3f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5a1_2E0 ) ) ) ) ) ) )
      & ! [V6f_2E0: u,V7a0_2E0: u,V8a1_2E0: u,V9a2_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Espt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V6f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7a0_2E0 ) @ ( s @ A_27a @ V8a1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9a2_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Espt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V6f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7a0_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V6f_2E0 ) @ ( s @ A_27a @ V8a1_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Espt__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V6f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9a2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Ewf__def,axiom,
    ! [A_27a: d] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
        = mono_2Ec_2Ebool_2ET )
      & ! [V0a_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V0a_2E0 ) ) ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V1t1_2E0: u,V2t2_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) ) )
            & ( (~)
              @ ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
                & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) ) )
      & ! [V3t1_2E0: u,V4a_2E0: u,V5t2_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) )
            & ( (~)
              @ ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
                & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edelete__def,axiom,
    ! [A_27a: d,F2: mono_2Etyop_2Enum_2Enum > $o,F1: mono_2Etyop_2Enum_2Enum > $o,F0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V6k: mono_2Etyop_2Enum_2Enum] :
          ( ( F2 @ V6k )
        <=> ( V6k = mono_2Ec_2Enum_2E0 ) )
     => ( ! [V3k: mono_2Etyop_2Enum_2Enum] :
            ( ( F1 @ V3k )
          <=> ( V3k = mono_2Ec_2Enum_2E0 ) )
       => ( ! [V1k: mono_2Etyop_2Enum_2Enum] :
              ( ( F0 @ V1k )
            <=> ( V1k = mono_2Ec_2Enum_2E0 ) )
         => ( ! [V0k: mono_2Etyop_2Enum_2Enum] :
                ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
                = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
            & ! [V1k: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] :
                ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V1k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) ) ) )
            & ! [V3k: mono_2Etyop_2Enum_2Enum,V4t1_2E0: u,V5t2_2E0: u] :
                ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F1 @ V3k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V3k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V3k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V3k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) ) ) ) ) ) )
            & ! [V6k: mono_2Etyop_2Enum_2Enum,V7t1_2E0: u,V8a_2E0: u,V9t2_2E0: u] :
                ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7t1_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F2 @ V6k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V6k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V6k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7t1_2E0 ) ) ) @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7t1_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V6k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2EfromList__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1i: mono_2Etyop_2Enum_2Enum,V2t_2E0: u,V3a_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1i ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ A_27a @ V3a_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V1i @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1i ) ) @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) ) ) )
     => ! [V0l_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( c_2Elist_2EFOLDL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Esize__def,axiom,
    ! [A_27a: d] :
      ( ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
        = mono_2Ec_2Enum_2E0 )
      & ! [V0a_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V0a_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
      & ! [V1t1_2E0: u,V2t2_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) ) ) ) )
      & ! [V3t1_2E0: u,V4a_2E0: u,V5t2_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2Esptree_2Eunion__def,axiom,
    ! [A_27a: d,F4_2E0: u,F7_2E0: u,F1_2E0: u,F5_2E0: u,F8_2E0: u,F2_2E0: u,F3_2E0: u,F6_2E0: u,F0_2E0: u] :
      ( ! [V9t1_2E0: u,V10t2_2E0: u,V13t1_27_2E0: u,V14t2_27_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V14t2_27_2E0 ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V14t2_27_2E0 ) ) ) ) ) )
     => ( ! [V9t1_2E0: u,V10t2_2E0: u,V15t1_27_27_2E0: u,V16a_27_27_2E0: u,V17t2_27_27_2E0: u] :
            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F7_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V15t1_27_27_2E0 ) ) ) @ ( s @ A_27a @ V16a_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V17t2_27_27_2E0 ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V15t1_27_27_2E0 ) ) ) @ ( s @ A_27a @ V16a_27_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V17t2_27_27_2E0 ) ) ) ) ) )
       => ( ! [V9t1_2E0: u,V10t2_2E0: u,V12a_2E0: u] :
              ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ A_27a @ V12a_2E0 ) ) )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ A_27a @ V12a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) )
         => ( ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V23t1_27_2E0: u,V24t2_27_2E0: u] :
                ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V23t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V24t2_27_2E0 ) ) )
                = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V23t1_27_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V24t2_27_2E0 ) ) ) ) ) )
           => ( ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V25t1_27_27_2E0: u,V26a_27_27_27_2E0: u,V27t2_27_27_2E0: u] :
                  ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) ) @ F8_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V25t1_27_27_2E0 ) ) ) @ ( s @ A_27a @ V26a_27_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V27t2_27_27_2E0 ) ) )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V25t1_27_27_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V27t2_27_27_2E0 ) ) ) ) ) )
             => ( ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V22a_27_2E0: u] :
                    ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ A_27a @ V22a_27_2E0 ) ) )
                    = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) )
               => ( ! [V1a_2E0: u,V4t1_2E0: u,V5t2_2E0: u] :
                      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F3_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) )
                      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) )
                 => ( ! [V1a_2E0: u,V6t1_27_2E0: u,V7v4_2E0: u,V8t2_27_2E0: u] :
                        ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F6_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t1_27_2E0 ) ) ) @ ( s @ A_27a @ V7v4_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8t2_27_2E0 ) ) )
                        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t1_27_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8t2_27_2E0 ) ) ) )
                   => ( ! [V1a_2E0: u,V3b_2E0: u] :
                          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ A_27a @ V3b_2E0 ) ) )
                          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) )
                     => ( ! [V0t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) )
                        & ! [V1a_2E0: u,V2t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F3_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F6_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) ) ) )
                        & ! [V9t1_2E0: u,V10t2_2E0: u,V11t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F7_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) ) ) )
                        & ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V21t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V21t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V21t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) ) @ F8_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Einter__def,axiom,
    ! [A_27a: d,A_27b: d,F3_2E0: u,F5_2E0: u,F4_2E0: u,F7_2E0: u,F8_2E0: u,F1_2E0: u,F6_2E0: u,F2_2E0: u,F0_2E0: u] :
      ( ! [V4t1_2E0: u,V5t2_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V4t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V5t2_2E0 ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
     => ( ! [V18t1_2E0: u,V20t2_2E0: u,V23t1_27_2E0: u,V24t2_27_2E0: u] :
            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V23t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V24t2_27_2E0 ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V23t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V24t2_27_2E0 ) ) ) ) ) )
       => ( ! [V9t1_2E0: u,V10t2_2E0: u,V13t1_27_2E0: u,V14t2_27_2E0: u] :
              ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V13t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V14t2_27_2E0 ) ) )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V13t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V14t2_27_2E0 ) ) ) ) ) )
         => ( ! [V9t1_2E0: u,V10t2_2E0: u,V15t1_27_27_2E0: u,V16a_27_27_2E0: u,V17t2_27_27_2E0: u] :
                ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F7_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V15t1_27_27_2E0 ) ) ) @ ( s @ A_27b @ V16a_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V17t2_27_27_2E0 ) ) )
                = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V15t1_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V17t2_27_27_2E0 ) ) ) ) ) )
           => ( ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V25t1_27_27_2E0: u,V26a_27_27_27_2E0: u,V27t2_27_27_2E0: u] :
                  ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) ) @ F8_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V25t1_27_27_2E0 ) ) ) @ ( s @ A_27b @ V26a_27_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V27t2_27_27_2E0 ) ) )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V25t1_27_27_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V27t2_27_27_2E0 ) ) ) ) ) )
             => ( ! [V12a_2E0: u] :
                    ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ F1_2E0 ) @ ( s @ A_27b @ V12a_2E0 ) ) )
                    = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
               => ( ! [V1a_2E0: u,V6t1_27_2E0: u,V7v4_2E0: u,V8t2_27_2E0: u] :
                      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F6_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V6t1_27_2E0 ) ) ) @ ( s @ A_27b @ V7v4_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V8t2_27_2E0 ) ) )
                      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) )
                 => ( ! [V19a_2E0: u,V22a_27_2E0: u] :
                        ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ A_27b @ V22a_27_2E0 ) ) )
                        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V19a_2E0 ) ) ) )
                   => ( ! [V1a_2E0: u,V3b_2E0: u] :
                          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ A_27b @ V3b_2E0 ) ) )
                          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) )
                     => ( ! [V0t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
                        & ! [V1a_2E0: u,V2t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V2t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V2t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F6_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) ) ) )
                        & ! [V9t1_2E0: u,V10t2_2E0: u,V11t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V11t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V11t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F7_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) ) ) )
                        & ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V21t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V21t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V21t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) ) @ F8_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Einter__eq__def,axiom,
    ! [A_27a: d,F3_2E0: u,F5_2E0: u,F4_2E0: u,F7_2E0: u,F1_2E0: u,F12_2E0: u,F8_2E0: u,F11_2E0: u,F6_2E0: u,F10_2E0: u,F0_2E0: u,F9_2E0: u,F2_2E0: u] :
      ( ! [V4t1_2E0: u,V5t2_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
     => ( ! [V18t1_2E0: u,V20t2_2E0: u,V23t1_27_2E0: u,V24t2_27_2E0: u] :
            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V23t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V24t2_27_2E0 ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V23t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V24t2_27_2E0 ) ) ) ) ) )
       => ( ! [V9t1_2E0: u,V10t2_2E0: u,V13t1_27_2E0: u,V14t2_27_2E0: u] :
              ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V14t2_27_2E0 ) ) )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V14t2_27_2E0 ) ) ) ) ) )
         => ( ! [V9t1_2E0: u,V10t2_2E0: u,V15t1_27_27_2E0: u,V16a_27_27_2E0: u,V17t2_27_27_2E0: u] :
                ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F7_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V15t1_27_27_2E0 ) ) ) @ ( s @ A_27a @ V16a_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V17t2_27_27_2E0 ) ) )
                = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V15t1_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V17t2_27_27_2E0 ) ) ) ) ) )
           => ( ! [V12a_2E0: u] :
                  ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ F1_2E0 ) @ ( s @ A_27a @ V12a_2E0 ) ) )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
             => ( ! [V26a_27_27_27_2E0: u,V19a_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 ) ) @ F12_2E0 ) @ ( s @ A_27a @ V26a_27_27_27_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) )
                  <=> ( ( s @ A_27a @ V26a_27_27_27_2E0 )
                      = ( s @ A_27a @ V19a_2E0 ) ) )
               => ( ! [V19a_2E0: u,V18t1_2E0: u,V20t2_2E0: u,V25t1_27_27_2E0: u,V26a_27_27_27_2E0: u,V27t2_27_27_2E0: u] :
                      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) ) @ F8_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V25t1_27_27_2E0 ) ) ) @ ( s @ A_27a @ V26a_27_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V27t2_27_27_2E0 ) ) )
                      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F12_2E0 ) @ ( s @ A_27a @ V26a_27_27_27_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V25t1_27_27_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V27t2_27_27_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V25t1_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V27t2_27_27_2E0 ) ) ) ) ) ) ) )
                 => ( ! [V1a_2E0: u,V7b_27_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 ) ) @ F11_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ A_27a @ V7b_27_2E0 ) ) ) )
                      <=> ( ( s @ A_27a @ V1a_2E0 )
                          = ( s @ A_27a @ V7b_27_2E0 ) ) )
                   => ( ! [V1a_2E0: u,V6t1_27_2E0: u,V7b_27_2E0: u,V8t2_27_2E0: u] :
                          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F6_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t1_27_2E0 ) ) ) @ ( s @ A_27a @ V7b_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8t2_27_2E0 ) ) )
                          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F11_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ A_27a @ V7b_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
                     => ( ! [V1a_2E0: u,V3b_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 ) ) @ F10_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ A_27a @ V3b_2E0 ) ) ) )
                          <=> ( ( s @ A_27a @ V1a_2E0 )
                              = ( s @ A_27a @ V3b_2E0 ) ) )
                       => ( ! [V1a_2E0: u,V3b_2E0: u] :
                              ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ A_27a @ V3b_2E0 ) ) )
                              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F10_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ A_27a @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
                         => ( ! [V22a_27_2E0: u,V19a_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 ) ) @ F9_2E0 ) @ ( s @ A_27a @ V22a_27_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) )
                              <=> ( ( s @ A_27a @ V22a_27_2E0 )
                                  = ( s @ A_27a @ V19a_2E0 ) ) )
                           => ( ! [V19a_2E0: u,V22a_27_2E0: u] :
                                  ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ A_27a @ V22a_27_2E0 ) ) )
                                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F9_2E0 ) @ ( s @ A_27a @ V22a_27_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
                             => ( ! [V0t_2E0: u] :
                                    ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
                                    = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
                                & ! [V1a_2E0: u,V2t_2E0: u] :
                                    ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) )
                                    = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F6_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) ) ) )
                                & ! [V9t1_2E0: u,V10t2_2E0: u,V11t_2E0: u] :
                                    ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11t_2E0 ) ) )
                                    = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F7_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) ) ) )
                                & ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V21t_2E0: u] :
                                    ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V21t_2E0 ) ) )
                                    = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V21t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) ) @ F8_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edifference__def,axiom,
    ! [A_27a: d,A_27b: d,F6_2E0: u,F4_2E0: u,F8_2E0: u,F7_2E0: u,F2_2E0: u,F1_2E0: u,F5_2E0: u,F0_2E0: u,F3_2E0: u] :
      ( ! [V6t1_27_2E0: u,V7b_27_2E0: u,V8t2_27_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F6_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V6t1_27_2E0 ) ) ) @ ( s @ A_27b @ V7b_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V8t2_27_2E0 ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
     => ( ! [V9t1_2E0: u,V10t2_2E0: u,V13t1_27_2E0: u,V14t2_27_2E0: u] :
            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V13t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V14t2_27_2E0 ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V13t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V14t2_27_2E0 ) ) ) ) ) )
       => ( ! [V18t1_2E0: u,V20t2_2E0: u,V25t1_27_27_2E0: u,V26a_27_27_27_2E0: u,V27t2_27_27_2E0: u] :
              ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F8_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V25t1_27_27_2E0 ) ) ) @ ( s @ A_27b @ V26a_27_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V27t2_27_27_2E0 ) ) )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V25t1_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V27t2_27_27_2E0 ) ) ) ) ) )
         => ( ! [V9t1_2E0: u,V10t2_2E0: u,V15t1_27_27_2E0: u,V16a_27_27_2E0: u,V17t2_27_27_2E0: u] :
                ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F7_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V15t1_27_27_2E0 ) ) ) @ ( s @ A_27b @ V16a_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V17t2_27_27_2E0 ) ) )
                = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V15t1_27_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V17t2_27_27_2E0 ) ) ) ) ) )
           => ( ! [V18t1_2E0: u,V20t2_2E0: u,V22a_27_2E0: u] :
                  ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ A_27b @ V22a_27_2E0 ) ) )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) )
             => ( ! [V9t1_2E0: u,V10t2_2E0: u,V12a_2E0: u] :
                    ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ A_27b @ V12a_2E0 ) ) )
                    = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) )
               => ( ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V23t1_27_2E0: u,V24t2_27_2E0: u] :
                      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V23t1_27_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V24t2_27_2E0 ) ) )
                      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V23t1_27_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V24t2_27_2E0 ) ) ) ) ) )
                 => ( ! [V3b_2E0: u] :
                        ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ F0_2E0 ) @ ( s @ A_27b @ V3b_2E0 ) ) )
                        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
                   => ( ! [V1a_2E0: u,V4t1_2E0: u,V5t2_2E0: u] :
                          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F3_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V4t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V5t2_2E0 ) ) )
                          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) )
                     => ( ! [V0t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
                        & ! [V1a_2E0: u,V2t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V2t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V2t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F3_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F6_2E0 ) ) ) )
                        & ! [V9t1_2E0: u,V10t2_2E0: u,V11t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V11t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V11t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F7_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) ) ) )
                        & ! [V18t1_2E0: u,V19a_2E0: u,V20t2_2E0: u,V21t_2E0: u] :
                            ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V21t_2E0 ) ) )
                            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V21t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ A_27a @ V19a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) ) ) @ F8_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20t2_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elrnext__primitive__def,axiom,
    ! [F2: mono_2Etyop_2Enum_2Enum > $o,F1: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,F0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o] :
      ( ! [V3a: mono_2Etyop_2Enum_2Enum] :
          ( ( F2 @ V3a )
        <=> ( V3a = mono_2Ec_2Enum_2E0 ) )
     => ( ! [V2lrnext: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V3a: mono_2Etyop_2Enum_2Enum] :
            ( ( F1 @ V2lrnext @ V3a )
            = ( mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( F2 @ V3a ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( V2lrnext @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V3a @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
       => ( ! [V0R: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
              ( ( F0 @ V0R )
            <=> ( ( mono_2Ec_2Erelation_2EWF_2Emono_2Etyop_2Enum_2Enum @ V0R )
                & ! [V1n: mono_2Etyop_2Enum_2Enum] :
                    ( ( (~) @ ( V1n = mono_2Ec_2Enum_2E0 ) )
                   => ( V0R @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V1n ) ) ) )
         => ( mono_2Ec_2Esptree_2Elrnext
            = ( mono_2Ec_2Erelation_2EWFREC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ F0 ) @ F1 ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__def,axiom,
    ! [A_27a: d,F1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,F3: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,F2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ! [V8n: mono_2Etyop_2Enum_2Enum] :
          ( ( F1 @ V8n )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V8n ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
     => ( ! [V3n: mono_2Etyop_2Enum_2Enum] :
            ( ( F0 @ V3n )
            = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V3n ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
       => ( ! [V9n: mono_2Etyop_2Enum_2Enum] :
              ( ( F3 @ V9n )
              = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V9n ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
         => ( ! [V4n: mono_2Etyop_2Enum_2Enum] :
                ( ( F2 @ V4n )
                = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V4n ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
           => ( ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
                = mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum )
              & ! [V0v0_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V0v0_2E0 ) ) ) ) ) )
                  = ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) )
              & ! [V1t1_2E0: u,V2t2_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) ) ) ) )
                  = ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ F0 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) ) ) @ ( mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ F2 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) ) ) ) ) )
              & ! [V5t1_2E0: u,V6v1_2E0: u,V7t2_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t1_2E0 ) @ ( s @ A_27a @ V6v1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7t2_2E0 ) ) ) ) ) )
                  = ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) @ ( mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ F1 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t1_2E0 ) ) ) ) ) ) @ ( mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ F3 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7t2_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__fold__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0f_2E0: u,V1acc_2E0: u] :
          ( ( s @ A_27a @ ( c_2Esptree_2Espt__fold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V1acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ c_2Esptree_2ELN_2E0 ) ) )
          = ( s @ A_27a @ V1acc_2E0 ) )
      & ! [V2f_2E0: u,V3acc_2E0: u,V4a_2E0: u] :
          ( ( s @ A_27a @ ( c_2Esptree_2Espt__fold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f_2E0 ) @ ( s @ A_27a @ V3acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27b @ V4a_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V4a_2E0 ) ) ) @ ( s @ A_27a @ V3acc_2E0 ) ) ) )
      & ! [V5f_2E0: u,V6acc_2E0: u,V7t1_2E0: u,V8t2_2E0: u] :
          ( ( s @ A_27a @ ( c_2Esptree_2Espt__fold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V5f_2E0 ) @ ( s @ A_27a @ V6acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V7t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V8t2_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Esptree_2Espt__fold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V5f_2E0 ) @ ( s @ A_27a @ ( c_2Esptree_2Espt__fold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V5f_2E0 ) @ ( s @ A_27a @ V6acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V7t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V8t2_2E0 ) ) ) )
      & ! [V9f_2E0: u,V10acc_2E0: u,V11t1_2E0: u,V12a_2E0: u,V13t2_2E0: u] :
          ( ( s @ A_27a @ ( c_2Esptree_2Espt__fold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V9f_2E0 ) @ ( s @ A_27a @ V10acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V11t1_2E0 ) @ ( s @ A_27b @ V12a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V13t2_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Esptree_2Espt__fold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V9f_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V9f_2E0 ) @ ( s @ A_27b @ V12a_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Esptree_2Espt__fold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V9f_2E0 ) @ ( s @ A_27a @ V10acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V11t1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V13t2_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Elist__to__num__set__def,axiom,
    ( ( ( mono_2Ec_2Esptree_2Elist__to__num__set @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Enum_2Enum )
      = mono_2Ec_2Esptree_2ELN_2Emono_2Etyop_2Eone_2Eone )
    & ! [V0n: mono_2Etyop_2Enum_2Enum,V1ns: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
        ( ( mono_2Ec_2Esptree_2Elist__to__num__set @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum @ V0n @ V1ns ) )
        = ( mono_2Ec_2Esptree_2Einsert_2Emono_2Etyop_2Eone_2Eone @ V0n @ mono_2Ec_2Eone_2Eone @ ( mono_2Ec_2Esptree_2Elist__to__num__set @ V1ns ) ) ) ) ).

thf(thm_2Esptree_2Elist__insert__def,axiom,
    ( ! [V0t: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
        ( ( mono_2Ec_2Esptree_2Elist__insert @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Enum_2Enum @ V0t )
        = V0t )
    & ! [V1n: mono_2Etyop_2Enum_2Enum,V2ns: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V3t: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
        ( ( mono_2Ec_2Esptree_2Elist__insert @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum @ V1n @ V2ns ) @ V3t )
        = ( mono_2Ec_2Esptree_2Elist__insert @ V2ns @ ( mono_2Ec_2Esptree_2Einsert_2Emono_2Etyop_2Eone_2Eone @ V1n @ mono_2Ec_2Eone_2Eone @ V3t ) ) ) ) ).

thf(thm_2Esptree_2Elookup__fromList__outside,axiom,
    ! [A_27a: d,V0args_2E0: u,V1k: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0args_2E0 ) ) ) ) @ V1k )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0args_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).

thf(thm_2Esptree_2Esize__delete,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0n: mono_2Etyop_2Enum_2Enum,V1t_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) )
        <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
     => ! [V0n: mono_2Etyop_2Enum_2Enum,V1t_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2D @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edelete__fail,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1t_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) )
     => ( ( (~) @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0n @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) ) )
      <=> ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Ewf__difference,axiom,
    ! [A_27a: d,A_27b: d,V0t1_2E0: u,V1t2_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edifference__sub,axiom,
    ! [A_27a: d,A_27b: d,V0b_2E0: u,V1a_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0b_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
     => ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0b_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Eunion__num__set__sym,axiom,
    ! [V0t1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1t2: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( mono_2Ec_2Esptree_2Eunion_2Emono_2Etyop_2Eone_2Eone @ V0t1 @ V1t2 )
      = ( mono_2Ec_2Esptree_2Eunion_2Emono_2Etyop_2Eone_2Eone @ V1t2 @ V0t1 ) ) ).

thf(thm_2Esptree_2Enum__set__domain__eq,axiom,
    ! [V0t1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1t2: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( ( mono_2Ec_2Esptree_2Ewf_2Emono_2Etyop_2Eone_2Eone @ V0t1 )
        & ( mono_2Ec_2Esptree_2Ewf_2Emono_2Etyop_2Eone_2Eone @ V1t2 ) )
     => ( ( ( mono_2Ec_2Esptree_2Edomain_2Emono_2Etyop_2Eone_2Eone @ V0t1 )
          = ( mono_2Ec_2Esptree_2Edomain_2Emono_2Etyop_2Eone_2Eone @ V1t2 ) )
      <=> ( V0t1 = V1t2 ) ) ) ).

thf(thm_2Esptree_2Esize__domain,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
      = ( mono_2Ec_2Epred__set_2ECARD_2Emono_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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__mapi,axiom,
    ! [A_27a: d,A_27b: d,V0pt_2E0: u,V1f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0pt_2E0 ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0pt_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Emapi__Alist,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V1f_2E0: u,V2kv_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ V2kv_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ V2kv_2E0 ) ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ V2kv_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ V2kv_2E0 ) ) ) ) ) ) ) )
     => ! [V0pt_2E0: u,V1f_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0pt_2E0 ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ ( c_2Esptree_2EtoAList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0pt_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2EMAP__foldi,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V4k: mono_2Etyop_2Enum_2Enum,V5v_2E0: u,V6a_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4k ) ) ) ) @ ( s @ A_27a @ V5v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V6a_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4k ) ) @ ( s @ A_27a @ V5v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V6a_2E0 ) ) ) )
     => ( ! [V1f_2E0: u,V7k: mono_2Etyop_2Enum_2Enum,V8v_2E0: u,V9a_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ A_27b ) @ V1f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7k ) ) ) ) @ ( s @ A_27a @ V8v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V9a_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7k ) ) @ ( s @ A_27a @ V8v_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V9a_2E0 ) ) ) )
       => ! [V0pt_2E0: u,V1f_2E0: u,V2n: mono_2Etyop_2Enum_2Enum,V3acc_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V3acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0pt_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ A_27b ) @ V1f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V3acc_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0pt_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__mk__BN,axiom,
    ! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V2i: mono_2Etyop_2Enum_2Enum] :
          ( ( F0 @ V2i )
        <=> ( V2i = mono_2Ec_2Enum_2E0 ) )
     => ! [V0t2_2E0: u,V1t1_2E0: u,V2i: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V2i ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V2i @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V2i ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Ewf__mapi,axiom,
    ! [A_27a: d,A_27b: d,V0pt_2E0: u,V1f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0pt_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Ewf__mk__BS,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2a_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Ewf__mk__BN,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Ewf__filter__v,axiom,
    ! [A_27a: d,V0t_2E0: u,V1f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__filter__v,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V2f_2E0: u,V3v_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2f_2E0 ) ) ) @ ( s @ A_27a @ V3v_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2f_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3v_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     => ! [V0k: mono_2Etyop_2Enum_2Enum,V1t_2E0: u,V2f_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Efilter__v_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2f_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Esubspt__LN,axiom,
    ! [A_27a: d,V0sp_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0sp_2E0 ) ) ) )
        = mono_2Ec_2Ebool_2ET )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0sp_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
      <=> ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0sp_2E0 ) ) ) )
          = mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) ) ) ).

thf(thm_2Esptree_2Esubspt__trans,axiom,
    ! [A_27a: d,V0sp3_2E0: u,V1sp2_2E0: u,V2sp1_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2sp1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1sp2_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1sp2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0sp3_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2sp1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0sp3_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Esubspt__refl,axiom,
    ! [A_27a: d,V0sp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0sp_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0sp_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Esubspt__def,axiom,
    ! [A_27a: d,V0sp1_2E0: u,V1sp2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0sp1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1sp2_2E0 ) ) ) )
    <=> ! [V2k: mono_2Etyop_2Enum_2Enum] :
          ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2k @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0sp1_2E0 ) ) ) ) )
         => ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2k @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1sp2_2E0 ) ) ) ) )
            & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1sp2_2E0 ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0sp1_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__center__def,axiom,
    ! [A_27a: d,V0x_2E0: u,V1v2_2E0: u,V2v1_2E0: u,V3t2_2E0: u,V4t1_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Espt__center_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Espt__center_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Espt__center_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Espt__center_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2v1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1v2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).

thf(thm_2Esptree_2Espt__center__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) )
        & ! [V2t1_2E0: u,V3x_2E0: u,V4t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t2_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
        & ! [V5v1_2E0: u,V6v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5v1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6v2_2E0 ) ) ) ) ) ) )
     => ! [V7v_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7v_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Einsert__shadow,axiom,
    ! [A_27a: d,V0t_2E0: u,V1a: mono_2Etyop_2Enum_2Enum,V2b_2E0: u,V3c_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1a ) ) @ ( s @ A_27a @ V2b_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1a ) ) @ ( s @ A_27a @ V3c_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1a ) ) @ ( s @ A_27a @ V2b_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Einsert__insert,axiom,
    ! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V0x1: mono_2Etyop_2Enum_2Enum,V1x2: mono_2Etyop_2Enum_2Enum] :
          ( ( F0 @ V0x1 @ V1x2 )
        <=> ( V0x1 = V1x2 ) )
     => ! [V0x1: mono_2Etyop_2Enum_2Enum,V1x2: mono_2Etyop_2Enum_2Enum,V2v1_2E0: u,V3v2_2E0: u,V4t_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x1 ) ) @ ( s @ A_27a @ V2v1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x2 ) ) @ ( s @ A_27a @ V3v2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V0x1 @ V1x2 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x1 ) ) @ ( s @ A_27a @ V2v1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x2 ) ) @ ( s @ A_27a @ V3v2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x1 ) ) @ ( s @ A_27a @ V2v1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Emap__fromAList,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V1f_2E0: u,V2k: mono_2Etyop_2Enum_2Enum,V3v_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ A_27b @ V3v_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) ) ) ) )
     => ! [V0ls_2E0: u,V1f_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ V0ls_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Emap__insert,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x: mono_2Etyop_2Enum_2Enum,V2y_2E0: u,V3z_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ A_27a @ V2y_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3z_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3z_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Emap__map__o,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0t_2E0: u,V1f_2E0: u,V2g_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2g_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2g_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Ewf__map,axiom,
    ! [A_27a: d,A_27b: d,V0t_2E0: u,V1f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Emap__LN,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1t_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ c_2Esptree_2ELN_2E0 ) )
    <=> ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ).

thf(thm_2Esptree_2Elookup__map,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1s_2E0: u,V2x: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1s_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1s_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__map,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1s_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1s_2E0 ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1s_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2EtoList__map,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1s_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Esptree_2EtoList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1s_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1s_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2EfromAList__append,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V1l2_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V0l1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V1l2_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Eunion__insert__LN,axiom,
    ! [A_27a: d,V0x: mono_2Etyop_2Enum_2Enum,V1y_2E0: u,V2t2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ A_27a @ V1y_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ A_27a @ V1y_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t2_2E0 ) ) ) ) ).

thf(thm_2Esptree_2EfromAList__toAList,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Esptree_2EtoAList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ).

thf(thm_2Esptree_2Ewf__fromAList,axiom,
    ! [A_27a: d,V0ls_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V0ls_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__fromAList__toAList,axiom,
    ! [A_27a: d,V0t_2E0: u,V1x: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Esptree_2EtoAList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Edomain__fromAList,axiom,
    ! [A_27a: d,V0ls_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V0ls_2E0 ) ) ) ) ) )
      = ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Enum_2Enum ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V0ls_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__fromAList,axiom,
    ! [A_27a: d,V0ls_2E0: u,V1x: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V0ls_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V0ls_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) ) ) ) ).

thf(thm_2Esptree_2EfromAList__def,axiom,
    ! [A_27a: d] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ c_2Elist_2ENIL_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ! [V0y_2E0: u,V1xs_2E0: u,V2x: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x ) ) @ ( s @ A_27a @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V1xs_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x ) ) @ ( s @ A_27a @ V0y_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromAList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V1xs_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2EfromAList__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V1x: mono_2Etyop_2Enum_2Enum,V2y_2E0: u,V3xs_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V3xs_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ A_27a @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V3xs_2E0 ) ) ) ) ) ) ) )
     => ! [V4v_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V4v_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Edelete__compute,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2t_2E0: u,V3n: mono_2Etyop_2Enum_2Enum,V4a_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Einsert__compute,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2t_2E0: u,V3n: mono_2Etyop_2Enum_2Enum,V4a_27_2E0: u,V5a_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V3n ) ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V5a_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_27_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V5a_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V5a_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_27_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V5a_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_27_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ A_27a @ V4a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_27_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ A_27a @ V4a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) @ ( s @ A_27a @ V4a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__compute,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2t_2E0: u,V3n: mono_2Etyop_2Enum_2Enum,V4a_2E0: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Einter__assoc,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0t1_2E0: u,V1t2_2E0: u,V2t3_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V2t3_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V2t3_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Eunion__assoc,axiom,
    ! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u,V2t3_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t3_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t3_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Einter__LN,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0t_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ c_2Esptree_2ELN_2E0 ) ) ) ).

thf(thm_2Esptree_2Eunion__LN,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ).

thf(thm_2Esptree_2Edelete__mk__wf,axiom,
    ! [A_27a: d,V0x: mono_2Etyop_2Enum_2Enum,V1t_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Einsert__mk__wf,axiom,
    ! [A_27a: d,V0x: mono_2Etyop_2Enum_2Enum,V1v_2E0: u,V2t_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ A_27a @ V1v_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ A_27a @ V1v_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Einter__mk__wf,axiom,
    ! [A_27a: d,A_27b: d,V0t1_2E0: u,V1t2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Eunion__mk__wf,axiom,
    ! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t2_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t2_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Einter__eq,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0t1_2E0: u,V1t2_2E0: u,V2t3_2E0: u,V3t4_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t3_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V3t4_2E0 ) ) ) )
    <=> ! [V4x: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t3_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V3t4_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Emk__wf__eq,axiom,
    ! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t2_2E0 ) ) ) )
    <=> ! [V2x: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t2_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__mk__wf,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__mk__wf,axiom,
    ! [A_27a: d,V0x: mono_2Etyop_2Enum_2Enum,V1t_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Ewf__mk__id,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ).

thf(thm_2Esptree_2Ewf__mk__wf,axiom,
    ! [A_27a: d,V0t_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__wf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__eq__thm,axiom,
    ! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t2_2E0 ) ) ) ) )
     => ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t2_2E0 ) )
      <=> ! [V2n: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t2_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2EMEM__toList,axiom,
    ! [A_27a: d,V0x_2E0: u,V1t_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ) )
    <=> ? [V2k: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2EisEmpty__toList,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
     => ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      <=> ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ).

thf(thm_2Esptree_2EisEmpty__toListA,axiom,
    ! [A_27a: d,V0t_2E0: u,V1acc_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
     => ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      <=> ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1acc_2E0 ) ) ) ) ).

thf(thm_2Esptree_2EtoListA__append,axiom,
    ! [A_27a: d,V0t_2E0: u,V1acc_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1acc_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esptree_2EtoListA_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1acc_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Efoldi__FOLDR__toAList,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1a_2E0: u,V2t_2E0: u] :
      ( ( s @ A_27b @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ A_27b @ V1a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) )
      = ( s @ A_27b @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ V0f_2E0 ) ) ) @ ( s @ A_27b @ V1a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Esptree_2EtoAList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2EALL__DISTINCT__MAP__FST__toAList,axiom,
    ! [A_27a: d,V0t_2E0: u] : ( mono_2Ec_2Elist_2EALL__DISTINCT_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Enum_2Enum ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Esptree_2EtoAList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__empty,axiom,
    ! [A_27a: d,V0t_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
     => ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      <=> ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
          = mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) ) ) ).

thf(thm_2Esptree_2Einsert__union,axiom,
    ! [A_27a: d,V0k: mono_2Etyop_2Enum_2Enum,V1v_2E0: u,V2s_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ A_27a @ V1v_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2s_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ A_27a @ V1v_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2s_2E0 ) ) ) ) ).

thf(thm_2Esptree_2EALOOKUP__toAList,axiom,
    ! [A_27a: d,V0t_2E0: u,V1x: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ealist_2EALOOKUP_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Esptree_2EtoAList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ).

thf(thm_2Esptree_2EMEM__toAList,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2v_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2v_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Esptree_2EtoAList_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) )
    <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2v_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__mapi,axiom,
    ! [A_27a: d,A_27b: d,V0pt_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2f_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emapi_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V2f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0pt_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ V2f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0pt_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__mapi0,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V2i: mono_2Etyop_2Enum_2Enum,V3k: mono_2Etyop_2Enum_2Enum,V4v_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V0f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k ) ) ) ) @ ( s @ A_27a @ V4v_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Esptree_2Espt__acc @ V2i @ V3k ) ) ) ) ) @ ( s @ A_27a @ V4v_2E0 ) ) ) ) ) )
     => ! [V0f_2E0: u,V1pt_2E0: u,V2i: mono_2Etyop_2Enum_2Enum,V3k: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emapi0_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1pt_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1pt_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V0f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__foldi,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1k: mono_2Etyop_2Enum_2Enum,V2v_2E0: u,V3a: mono_2Etyop_2Enum_2Enum > $o] :
          ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) @ ( s @ A_27a @ V2v_2E0 ) ) ) @ V3a )
          = ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ V1k @ V3a ) )
     => ! [V0t_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Eset__foldi__keys,axiom,
    ! [A_27a: d,F1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,F0_2E0: u] :
      ( ! [V2i: mono_2Etyop_2Enum_2Enum,V6n: mono_2Etyop_2Enum_2Enum] :
          ( ( F1 @ V2i @ V6n )
          = ( mono_2Ec_2Earithmetic_2E_2B @ V2i @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Esptree_2Elrnext @ V2i ) @ V6n ) ) )
     => ( ! [V3k: mono_2Etyop_2Enum_2Enum,V4v_2E0: u,V5a: mono_2Etyop_2Enum_2Enum > $o] :
            ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k ) ) ) ) @ ( s @ A_27a @ V4v_2E0 ) ) ) @ V5a )
            = ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ V3k @ V5a ) )
       => ! [V0t_2E0: u,V1a: mono_2Etyop_2Enum_2Enum > $o,V2i: 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 ) @ ( c_2Esptree_2Efoldi_2E4 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1a ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
            = ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum @ V1a @ ( mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( F1 @ V2i ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__acc__0,axiom,
    ! [V0k: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Esptree_2Espt__acc @ mono_2Ec_2Enum_2E0 @ V0k )
      = V0k ) ).

thf(thm_2Esptree_2Espt__acc__eqn,axiom,
    ! [V0k: mono_2Etyop_2Enum_2Enum,V1i: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Esptree_2Espt__acc @ V1i @ V0k )
      = ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Esptree_2Elrnext @ V1i ) @ V0k ) @ V1i ) ) ).

thf(thm_2Esptree_2Espt__acc__thm,axiom,
    ! [F0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V0k: mono_2Etyop_2Enum_2Enum] :
          ( ( F0 @ V0k )
        <=> ( V0k = mono_2Ec_2Enum_2E0 ) )
     => ! [V0k: mono_2Etyop_2Enum_2Enum,V1i: mono_2Etyop_2Enum_2Enum] :
          ( ( mono_2Ec_2Esptree_2Espt__acc @ V1i @ V0k )
          = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( F0 @ V0k ) @ V1i @ ( mono_2Ec_2Esptree_2Espt__acc @ ( mono_2Ec_2Earithmetic_2E_2B @ V1i @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EEVEN @ V0k ) @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V1i ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V1i ) ) ) @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V0k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__acc__def__compute,axiom,
    ( ! [V0i: mono_2Etyop_2Enum_2Enum] :
        ( ( mono_2Ec_2Esptree_2Espt__acc @ V0i @ mono_2Ec_2Enum_2E0 )
        = V0i )
    & ! [V1k: mono_2Etyop_2Enum_2Enum,V2i: mono_2Etyop_2Enum_2Enum] :
        ( ( mono_2Ec_2Esptree_2Espt__acc @ V2i @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1k ) ) )
        = ( mono_2Ec_2Esptree_2Espt__acc @ ( mono_2Ec_2Earithmetic_2E_2B @ V2i @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EEVEN @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1k ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V2i ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V2i ) ) ) @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1k ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
    & ! [V3k: mono_2Etyop_2Enum_2Enum,V4i: mono_2Etyop_2Enum_2Enum] :
        ( ( mono_2Ec_2Esptree_2Espt__acc @ V4i @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3k ) ) )
        = ( mono_2Ec_2Esptree_2Espt__acc @ ( mono_2Ec_2Earithmetic_2E_2B @ V4i @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EEVEN @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3k ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V4i ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V4i ) ) ) @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3k ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__acc__def,axiom,
    ( ! [V0i: mono_2Etyop_2Enum_2Enum] :
        ( ( mono_2Ec_2Esptree_2Espt__acc @ V0i @ mono_2Ec_2Enum_2E0 )
        = V0i )
    & ! [V1k: mono_2Etyop_2Enum_2Enum,V2i: mono_2Etyop_2Enum_2Enum] :
        ( ( mono_2Ec_2Esptree_2Espt__acc @ V2i @ ( mono_2Ec_2Enum_2ESUC @ V1k ) )
        = ( mono_2Ec_2Esptree_2Espt__acc @ ( mono_2Ec_2Earithmetic_2E_2B @ V2i @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EEVEN @ ( mono_2Ec_2Enum_2ESUC @ V1k ) ) @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V2i ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V2i ) ) ) @ ( mono_2Ec_2Earithmetic_2EDIV @ V1k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__acc__ind,axiom,
    ! [V0P: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( ! [V1i: mono_2Etyop_2Enum_2Enum] : ( V0P @ V1i @ mono_2Ec_2Enum_2E0 )
        & ! [V2i: mono_2Etyop_2Enum_2Enum,V3k: mono_2Etyop_2Enum_2Enum] :
            ( ( V0P @ ( mono_2Ec_2Earithmetic_2E_2B @ V2i @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EEVEN @ ( mono_2Ec_2Enum_2ESUC @ V3k ) ) @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V2i ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V2i ) ) ) @ ( mono_2Ec_2Earithmetic_2EDIV @ V3k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
           => ( V0P @ V2i @ ( mono_2Ec_2Enum_2ESUC @ V3k ) ) ) )
     => ! [V4v: mono_2Etyop_2Enum_2Enum,V5v1: mono_2Etyop_2Enum_2Enum] : ( V0P @ V4v @ V5v1 ) ) ).

thf(thm_2Esptree_2Edomain__delete,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k: 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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) )
      = ( mono_2Ec_2Epred__set_2EDELETE_2Emono_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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) @ V1k ) ) ).

thf(thm_2Esptree_2Elookup__delete,axiom,
    ! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V1k1: mono_2Etyop_2Enum_2Enum,V2k2: mono_2Etyop_2Enum_2Enum] :
          ( ( F0 @ V1k1 @ V2k2 )
        <=> ( V1k1 = V2k2 ) )
     => ! [V0t_2E0: u,V1k1: mono_2Etyop_2Enum_2Enum,V2k2: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k1 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k2 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V1k1 @ V2k2 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k1 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__fromList,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) )
      = ( mono_2Ec_2Epred__set_2Ecount @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__sing,axiom,
    ! [A_27a: d,V0v_2E0: u,V1k: 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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V0v_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) ) )
      = ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ V1k @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) ) ).

thf(thm_2Esptree_2Edomain__difference,axiom,
    ! [A_27a: d,A_27b: d,V0t1_2E0: u,V1t2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) ) ) ) ) )
      = ( mono_2Ec_2Epred__set_2EDIFF_2Emono_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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__insert,axiom,
    ! [A_27a: d,V0v_2E0: u,V1t_2E0: u,V2k: 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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ A_27a @ V0v_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) ) )
      = ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ V2k @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__inter,axiom,
    ! [A_27a: d,A_27b: d,V0t2_2E0: u,V1t1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0t2_2E0 ) ) ) ) ) )
      = ( mono_2Ec_2Epred__set_2EINTER_2Emono_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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V0t2_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__union,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) ) )
      = ( mono_2Ec_2Epred__set_2EUNION_2Emono_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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t1_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t2_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__NONE__domain,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
    <=> ( (~) @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__inter__alt,axiom,
    ! [A_27a: d,A_27b: d,V0x: mono_2Etyop_2Enum_2Enum,V1t2_2E0: u,V2t1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0x @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1t2_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Edomain__lookup,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) )
    <=> ? [V2v_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2v_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__fromList,axiom,
    ! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Esize__insert,axiom,
    ! [A_27a: d,V0k: mono_2Etyop_2Enum_2Enum,V1v_2E0: u,V2m_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ A_27a @ V1v_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2m_2E0 ) ) ) ) ) )
      = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0k @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2m_2E0 ) ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2m_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2m_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2Esptree_2Esubspt__domain,axiom,
    ! [V0t1: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29,V1t2: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( mono_2Ec_2Esptree_2Esubspt_2Emono_2Etyop_2Eone_2Eone @ V0t1 @ V1t2 )
      = ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Esptree_2Edomain_2Emono_2Etyop_2Eone_2Eone @ V0t1 ) @ ( mono_2Ec_2Esptree_2Edomain_2Emono_2Etyop_2Eone_2Eone @ V1t2 ) ) ) ).

thf(thm_2Esptree_2Esubspt__lookup,axiom,
    ! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t2_2E0 ) ) ) )
    <=> ! [V2x: mono_2Etyop_2Enum_2Enum,V3y_2E0: u] :
          ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t1_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3y_2E0 ) ) ) )
         => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t2_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3y_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Esubspt__eq,axiom,
    ! [A_27a: d] :
      ( ! [V0t_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V1x_2E0: u,V2t_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) )
        <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Espt__center_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) ) )
      & ! [V3t1_2E0: u,V4t2_2E0: u,V5t_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__left_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t_2E0 ) ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__right_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t_2E0 ) ) ) ) ) ) ) )
      & ! [V6t1_2E0: u,V7x_2E0: u,V8t2_2E0: u,V9t_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t1_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t_2E0 ) ) ) )
        <=> ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Espt__center_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t_2E0 ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V7x_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__left_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t_2E0 ) ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Espt__right_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edatatype__spt,axiom,
    ! [A_27a: d,V0spt_2E0: u] : ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ V0spt_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esptree_2Espt @ A_27a ) ) @ c_2Esptree_2ELS_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2EBN_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) ) @ c_2Esptree_2EBS_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__11,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u,V1a_27_2E0: u] :
          ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V0a_2E0 ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_27_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V0a_2E0 )
            = ( s @ A_27a @ V1a_27_2E0 ) ) )
      & ! [V2a0_2E0: u,V3a1_2E0: u,V4a0_27_2E0: u,V5a1_27_2E0: u] :
          ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2a0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3a1_2E0 ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4a0_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5a1_27_2E0 ) ) ) )
        <=> ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2a0_2E0 )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4a0_27_2E0 ) )
            & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3a1_2E0 )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5a1_27_2E0 ) ) ) )
      & ! [V6a0_2E0: u,V7a1_2E0: u,V8a2_2E0: u,V9a0_27_2E0: u,V10a1_27_2E0: u,V11a2_27_2E0: u] :
          ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6a0_2E0 ) @ ( s @ A_27a @ V7a1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8a2_2E0 ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9a0_27_2E0 ) @ ( s @ A_27a @ V10a1_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11a2_27_2E0 ) ) ) )
        <=> ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6a0_2E0 )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9a0_27_2E0 ) )
            & ( ( s @ A_27a @ V7a1_2E0 )
              = ( s @ A_27a @ V10a1_27_2E0 ) )
            & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8a2_2E0 )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11a2_27_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__distinct,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V0a_2E0 ) ) ) ) )
      & ! [V1a1_2E0: u,V2a0_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2a0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1a1_2E0 ) ) ) ) )
      & ! [V3a2_2E0: u,V4a1_2E0: u,V5a0_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5a0_2E0 ) @ ( s @ A_27a @ V4a1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3a2_2E0 ) ) ) ) )
      & ! [V6a1_2E0: u,V7a0_2E0: u,V8a_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V8a_2E0 ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7a0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6a1_2E0 ) ) ) ) )
      & ! [V9a2_2E0: u,V10a1_2E0: u,V11a0_2E0: u,V12a_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V12a_2E0 ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11a0_2E0 ) @ ( s @ A_27a @ V10a1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9a2_2E0 ) ) ) ) )
      & ! [V13a2_2E0: u,V14a1_27_2E0: u,V15a1_2E0: u,V16a0_27_2E0: u,V17a0_2E0: u] :
          ( (~)
          @ ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V17a0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V15a1_2E0 ) ) )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V16a0_27_2E0 ) @ ( s @ A_27a @ V14a1_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13a2_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__nchotomy,axiom,
    ! [A_27a: d,V0ss_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0ss_2E0 )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      | ? [V1a_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0ss_2E0 )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) )
      | ? [V2s_2E0: u,V3s0_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0ss_2E0 )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2s_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3s0_2E0 ) ) ) )
      | ? [V4s_2E0: u,V5a_2E0: u,V6s0_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0ss_2E0 )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4s_2E0 ) @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6s0_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__Axiom,axiom,
    ! [A_27a: d,A_27b: d,V0f0_2E0: u,V1f1_2E0: u,V2f2_2E0: u,V3f3_2E0: u] :
    ? [V4fn_2E0: u] :
      ( ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ A_27b @ V0f0_2E0 ) )
      & ! [V5a_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V5a_2E0 ) ) ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f1_2E0 ) @ ( s @ A_27a @ V5a_2E0 ) ) ) )
      & ! [V6a0_2E0: u,V7a1_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6a0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7a1_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_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) @ V2f2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6a0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7a1_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6a0_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7a1_2E0 ) ) ) ) ) )
      & ! [V8a0_2E0: u,V9a1_2E0: u,V10a2_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8a0_2E0 ) @ ( s @ A_27a @ V9a1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10a2_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_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) ) @ V3f3_2E0 ) @ ( s @ A_27a @ V9a1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8a0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10a2_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8a0_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ V4fn_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10a2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
        & ! [V1a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) ) ) )
        & ! [V2s_2E0: u,V3s0_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2s_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3s0_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2s_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3s0_2E0 ) ) ) ) ) ) )
        & ! [V4s_2E0: u,V5s0_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4s_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5s0_2E0 ) ) ) ) )
           => ! [V6a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4s_2E0 ) @ ( s @ A_27a @ V6a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5s0_2E0 ) ) ) ) ) ) ) )
     => ! [V7s_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7s_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__case__cong,axiom,
    ! [A_27a: d,A_27b: d,V0v_27_2E0: u,V1f2_27_2E0: u,V2f1_27_2E0: u,V3f_27_2E0: u,V4M_2E0: u,V5M_27_2E0: u,V6v_2E0: u,V7f_2E0: u,V8f1_2E0: u,V9f2_2E0: u] :
      ( ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4M_2E0 )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5M_27_2E0 ) )
        & ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5M_27_2E0 )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
         => ( ( s @ A_27b @ V6v_2E0 )
            = ( s @ A_27b @ V0v_27_2E0 ) ) )
        & ! [V10a_2E0: u] :
            ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5M_27_2E0 )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V10a_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7f_2E0 ) @ ( s @ A_27a @ V10a_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V3f_27_2E0 ) @ ( s @ A_27a @ V10a_2E0 ) ) ) ) )
        & ! [V11a0_2E0: u,V12a1_2E0: u] :
            ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5M_27_2E0 )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11a0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12a1_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ V8f1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11a0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12a1_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ V2f1_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11a0_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12a1_2E0 ) ) ) ) )
        & ! [V13a0_2E0: u,V14a1_2E0: u,V15a2_2E0: u] :
            ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5M_27_2E0 )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13a0_2E0 ) @ ( s @ A_27a @ V14a1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V15a2_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ V9f2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13a0_2E0 ) ) ) @ ( s @ A_27a @ V14a1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V15a2_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ V1f2_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13a0_2E0 ) ) ) @ ( s @ A_27a @ V14a1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V15a2_2E0 ) ) ) ) ) )
     => ( ( s @ A_27b @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4M_2E0 ) @ ( s @ A_27b @ V6v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ V8f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ V9f2_2E0 ) ) )
        = ( s @ A_27b @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5M_27_2E0 ) @ ( s @ A_27b @ V0v_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V3f_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ V2f1_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ V1f2_27_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Espt__case__eq,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_27_2E0: u,V2v_2E0: u,V3f2_2E0: u,V4f1_2E0: u,V5f_2E0: u] :
      ( ( ( s @ A_27b @ ( c_2Esptree_2Espt__CASE_2E5 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V5f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ V4f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ V3f2_2E0 ) ) )
        = ( s @ A_27b @ V1v_27_2E0 ) )
    <=> ( ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 )
            = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
          & ( ( s @ A_27b @ V2v_2E0 )
            = ( s @ A_27b @ V1v_27_2E0 ) ) )
        | ? [V6a_2E0: u] :
            ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V6a_2E0 ) ) ) )
            & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V5f_2E0 ) @ ( s @ A_27a @ V6a_2E0 ) ) )
              = ( s @ A_27b @ V1v_27_2E0 ) ) )
        | ? [V7s_2E0: u,V8s0_2E0: u] :
            ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7s_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8s0_2E0 ) ) ) )
            & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ V4f1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7s_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8s0_2E0 ) ) )
              = ( s @ A_27b @ V1v_27_2E0 ) ) )
        | ? [V9s_2E0: u,V10a_2E0: u,V11s0_2E0: u] :
            ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 )
              = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9s_2E0 ) @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11s0_2E0 ) ) ) )
            & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ A_27b ) ) ) @ V3f2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9s_2E0 ) ) ) @ ( s @ A_27a @ V10a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11s0_2E0 ) ) )
              = ( s @ A_27b @ V1v_27_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1k: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
        & ! [V2k: mono_2Etyop_2Enum_2Enum,V3a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V3a_2E0 ) ) ) ) ) )
        & ! [V4k: mono_2Etyop_2Enum_2Enum,V5t1_2E0: u,V6t2_2E0: u] :
            ( ( ( (~) @ ( V4k = mono_2Ec_2Enum_2E0 ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V4k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V4k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t2_2E0 ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4k ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t2_2E0 ) ) ) ) ) ) )
        & ! [V7k: mono_2Etyop_2Enum_2Enum,V8t1_2E0: u,V9a_2E0: u,V10t2_2E0: u] :
            ( ( ( (~) @ ( V7k = mono_2Ec_2Enum_2E0 ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V7k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V7k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7k ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8t1_2E0 ) @ ( s @ A_27a @ V9a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t2_2E0 ) ) ) ) ) ) ) )
     => ! [V11v: mono_2Etyop_2Enum_2Enum,V12v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11v ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12v1_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__def,axiom,
    ! [A_27a: d,F2: mono_2Etyop_2Enum_2Enum > $o,F1: mono_2Etyop_2Enum_2Enum > $o,F0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V8k: mono_2Etyop_2Enum_2Enum] :
          ( ( F2 @ V8k )
        <=> ( V8k = mono_2Ec_2Enum_2E0 ) )
     => ( ! [V5k: mono_2Etyop_2Enum_2Enum] :
            ( ( F1 @ V5k )
          <=> ( V5k = mono_2Ec_2Enum_2E0 ) )
       => ( ! [V1k: mono_2Etyop_2Enum_2Enum] :
              ( ( F0 @ V1k )
            <=> ( V1k = mono_2Ec_2Enum_2E0 ) )
         => ( ! [V0k: mono_2Etyop_2Enum_2Enum] :
                ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
            & ! [V1k: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] :
                ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V1k ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
            & ! [V3t2_2E0: u,V4t1_2E0: u,V5k: mono_2Etyop_2Enum_2Enum] :
                ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t2_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F1 @ V5k ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V5k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V5k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t2_2E0 ) ) ) ) ) ) ) )
            & ! [V6t2_2E0: u,V7t1_2E0: u,V8k: mono_2Etyop_2Enum_2Enum,V9a_2E0: u] :
                ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7t1_2E0 ) @ ( s @ A_27a @ V9a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t2_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F2 @ V8k ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V9a_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V8k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V8k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t2_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Einsert__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1k: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] :
            ( ( ( ( ( (~) @ ( V1k = mono_2Ec_2Enum_2E0 ) )
                  & ( mono_2Ec_2Earithmetic_2EEVEN @ V1k ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V1k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) )
              & ( ( ( (~) @ ( V1k = mono_2Ec_2Enum_2E0 ) )
                  & ( (~) @ ( mono_2Ec_2Earithmetic_2EEVEN @ V1k ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V1k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) )
        & ! [V3k: mono_2Etyop_2Enum_2Enum,V4a_2E0: u,V5a_27_2E0: u] :
            ( ( ( ( ( (~) @ ( V3k = mono_2Ec_2Enum_2E0 ) )
                  & ( mono_2Ec_2Earithmetic_2EEVEN @ V3k ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V3k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) )
              & ( ( ( (~) @ ( V3k = mono_2Ec_2Enum_2E0 ) )
                  & ( (~) @ ( mono_2Ec_2Earithmetic_2EEVEN @ V3k ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V3k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k ) ) ) ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V5a_27_2E0 ) ) ) ) ) ) )
        & ! [V6k: mono_2Etyop_2Enum_2Enum,V7a_2E0: u,V8t1_2E0: u,V9t2_2E0: u] :
            ( ( ( ( ( (~) @ ( V6k = mono_2Ec_2Enum_2E0 ) )
                  & ( mono_2Ec_2Earithmetic_2EEVEN @ V6k ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V6k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ A_27a @ V7a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8t1_2E0 ) ) ) ) )
              & ( ( ( (~) @ ( V6k = mono_2Ec_2Enum_2E0 ) )
                  & ( (~) @ ( mono_2Ec_2Earithmetic_2EEVEN @ V6k ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V6k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ A_27a @ V7a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6k ) ) ) ) @ ( s @ A_27a @ V7a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) ) ) ) )
        & ! [V10k: mono_2Etyop_2Enum_2Enum,V11a_2E0: u,V12t1_2E0: u,V13a_27_2E0: u,V14t2_2E0: u] :
            ( ( ( ( ( (~) @ ( V10k = mono_2Ec_2Enum_2E0 ) )
                  & ( mono_2Ec_2Earithmetic_2EEVEN @ V10k ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V10k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ A_27a @ V11a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12t1_2E0 ) ) ) ) )
              & ( ( ( (~) @ ( V10k = mono_2Ec_2Enum_2E0 ) )
                  & ( (~) @ ( mono_2Ec_2Earithmetic_2EEVEN @ V10k ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V10k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ A_27a @ V11a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V14t2_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10k ) ) ) ) @ ( s @ A_27a @ V11a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12t1_2E0 ) @ ( s @ A_27a @ V13a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V14t2_2E0 ) ) ) ) ) ) ) )
     => ! [V15v: mono_2Etyop_2Enum_2Enum,V16v1_2E0: u,V17v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V15v ) ) ) ) @ ( s @ A_27a @ V16v1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V17v2_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Einsert__def,axiom,
    ! [A_27a: d,F3: mono_2Etyop_2Enum_2Enum > $o,F2: mono_2Etyop_2Enum_2Enum > $o,F1: mono_2Etyop_2Enum_2Enum > $o,F0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V11k: mono_2Etyop_2Enum_2Enum] :
          ( ( F3 @ V11k )
        <=> ( V11k = mono_2Ec_2Enum_2E0 ) )
     => ( ! [V7k: mono_2Etyop_2Enum_2Enum] :
            ( ( F2 @ V7k )
          <=> ( V7k = mono_2Ec_2Enum_2E0 ) )
       => ( ! [V2k: mono_2Etyop_2Enum_2Enum] :
              ( ( F1 @ V2k )
            <=> ( V2k = mono_2Ec_2Enum_2E0 ) )
         => ( ! [V0k: mono_2Etyop_2Enum_2Enum] :
                ( ( F0 @ V0k )
              <=> ( V0k = mono_2Ec_2Enum_2E0 ) )
           => ( ! [V0k: mono_2Etyop_2Enum_2Enum,V1a_2E0: u] :
                  ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V0k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V0k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V0k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V0k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) ) ) ) ) ) )
              & ! [V2k: mono_2Etyop_2Enum_2Enum,V3a_27_2E0: u,V4a_2E0: u] :
                  ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V3a_27_2E0 ) ) ) ) )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F1 @ V2k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V2k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V2k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ A_27a @ V3a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ A_27a @ V3a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V2k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) ) ) ) ) ) )
              & ! [V5t2_2E0: u,V6t1_2E0: u,V7k: mono_2Etyop_2Enum_2Enum,V8a_2E0: u] :
                  ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7k ) ) @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F2 @ V7k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t1_2E0 ) @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V7k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V7k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V7k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5t2_2E0 ) ) ) ) ) ) ) ) ) )
              & ! [V9t2_2E0: u,V10t1_2E0: u,V11k: mono_2Etyop_2Enum_2Enum,V12a_27_2E0: u,V13a_2E0: u] :
                  ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11k ) ) @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t1_2E0 ) @ ( s @ A_27a @ V12a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) ) )
                  = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F3 @ V11k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t1_2E0 ) @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V11k ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V11k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t1_2E0 ) ) ) @ ( s @ A_27a @ V12a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10t1_2E0 ) @ ( s @ A_27a @ V12a_27_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V11k @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9t2_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Emk__BN__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
        & ! [V1v14_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1v14_2E0 ) ) ) ) ) )
        & ! [V2v15_2E0: u,V3v16_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2v15_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3v16_2E0 ) ) ) ) ) )
        & ! [V4v17_2E0: u,V5v18_2E0: u,V6v19_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4v17_2E0 ) @ ( s @ A_27a @ V5v18_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6v19_2E0 ) ) ) ) ) )
        & ! [V7v2_2E0: u,V8t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V7v2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8t2_2E0 ) ) ) )
        & ! [V9v3_2E0: u,V10v4_2E0: u,V11t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9v3_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10v4_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11t2_2E0 ) ) ) )
        & ! [V12v5_2E0: u,V13v6_2E0: u,V14v7_2E0: u,V15t2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12v5_2E0 ) @ ( s @ A_27a @ V13v6_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V14v7_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V15t2_2E0 ) ) ) ) )
     => ! [V16v_2E0: u,V17v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V16v_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V17v1_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Emk__BN__def,axiom,
    ! [A_27a: d,V0v7_2E0: u,V1v6_2E0: u,V2v5_2E0: u,V3v4_2E0: u,V4v3_2E0: u,V5v2_2E0: u,V6v19_2E0: u,V7v18_2E0: u,V8v17_2E0: u,V9v16_2E0: u,V10v15_2E0: u,V11v14_2E0: u,V12t2_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V11v14_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V11v14_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10v15_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9v16_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10v15_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9v16_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8v17_2E0 ) @ ( s @ A_27a @ V7v18_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6v19_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V8v17_2E0 ) @ ( s @ A_27a @ V7v18_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V6v19_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V5v2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12t2_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V5v2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4v3_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3v4_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12t2_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4v3_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3v4_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12t2_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2v5_2E0 ) @ ( s @ A_27a @ V1v6_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0v7_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12t2_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2v5_2E0 ) @ ( s @ A_27a @ V1v6_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0v7_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V12t2_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Emk__BS__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
        & ! [V2v16_2E0: u,V3x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V2v16_2E0 ) ) ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
        & ! [V4v17_2E0: u,V5v18_2E0: u,V6x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4v17_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5v18_2E0 ) ) ) ) ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
        & ! [V7v19_2E0: u,V8v20_2E0: u,V9v21_2E0: u,V10x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7v19_2E0 ) @ ( s @ A_27a @ V8v20_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9v21_2E0 ) ) ) ) ) @ ( s @ A_27a @ V10x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
        & ! [V11t1_2E0: u,V12x_2E0: u,V13v4_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11t1_2E0 ) ) ) @ ( s @ A_27a @ V12x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V13v4_2E0 ) ) ) ) ) )
        & ! [V14t1_2E0: u,V15x_2E0: u,V16v5_2E0: u,V17v6_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V14t1_2E0 ) ) ) @ ( s @ A_27a @ V15x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V16v5_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V17v6_2E0 ) ) ) ) ) )
        & ! [V18t1_2E0: u,V19x_2E0: u,V20v7_2E0: u,V21v8_2E0: u,V22v9_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V18t1_2E0 ) ) ) @ ( s @ A_27a @ V19x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V20v7_2E0 ) @ ( s @ A_27a @ V21v8_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V22v9_2E0 ) ) ) ) ) ) )
     => ! [V23v_2E0: u,V24v1_2E0: u,V25v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V23v_2E0 ) ) ) @ ( s @ A_27a @ V24v1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V25v2_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Emk__BS__def,axiom,
    ! [A_27a: d,V0x_2E0: u,V1v9_2E0: u,V2v8_2E0: u,V3v7_2E0: u,V4v6_2E0: u,V5v5_2E0: u,V6v4_2E0: u,V7v21_2E0: u,V8v20_2E0: u,V9v19_2E0: u,V10v18_2E0: u,V11v17_2E0: u,V12v16_2E0: u,V13t1_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V12v16_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V12v16_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11v17_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10v18_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V11v17_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V10v18_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9v19_2E0 ) @ ( s @ A_27a @ V8v20_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7v21_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V9v19_2E0 ) @ ( s @ A_27a @ V8v20_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V7v21_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13t1_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V6v4_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13t1_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V6v4_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13t1_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5v5_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4v6_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13t1_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V5v5_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V4v6_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Emk__BS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13t1_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3v7_2E0 ) @ ( s @ A_27a @ V2v8_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1v9_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V13t1_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3v7_2E0 ) @ ( s @ A_27a @ V2v8_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1v9_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Einsert__notEmpty,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] :
      ( (~)
      @ ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ).

thf(thm_2Esptree_2Ewf__insert,axiom,
    ! [A_27a: d,V0k: mono_2Etyop_2Enum_2Enum,V1a_2E0: u,V2t_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Ewf__delete,axiom,
    ! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edelete_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__insert1,axiom,
    ! [A_27a: d,V0k: mono_2Etyop_2Enum_2Enum,V1a_2E0: u,V2t_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1a_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Elookup__insert,axiom,
    ! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V3k1: mono_2Etyop_2Enum_2Enum,V0k2: mono_2Etyop_2Enum_2Enum] :
          ( ( F0 @ V3k1 @ V0k2 )
        <=> ( V3k1 = V0k2 ) )
     => ! [V0k2: mono_2Etyop_2Enum_2Enum,V1v_2E0: u,V2t_2E0: u,V3k1: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k1 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k2 ) ) @ ( s @ A_27a @ V1v_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V3k1 @ V0k2 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1v_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k1 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2EisEmpty__union,axiom,
    ! [A_27a: d,V0m2_2E0: u,V1m1_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m2_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
    <=> ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m1_2E0 )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
        & ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m2_2E0 )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Ewf__union,axiom,
    ! [A_27a: d,V0m1_2E0: u,V1m2_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m1_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m2_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__union,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V3v_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ F0_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3v_2E0 ) ) ) )
     => ! [V0m1_2E0: u,V1m2_2E0: u,V2k: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Eunion_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ F0_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Ewf__inter,axiom,
    ! [A_27a: d,A_27b: d,V0m1_2E0: u,V1m2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Ewf_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1m2_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__inter,axiom,
    ! [A_27a: d,A_27b: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V5v_2E0: u,V6w_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_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V5v_2E0 ) ) ) @ ( s @ A_27b @ V6w_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V5v_2E0 ) ) ) )
     => ( ! [V4v4_2E0: u,V5v_2E0: u] :
            ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V4v4_2E0 ) ) ) @ ( s @ A_27a @ V5v_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V4v4_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V5v_2E0 ) ) ) ) ) )
       => ( ! [V3v3_2E0: u,V4v4_2E0: u] :
              ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V3v3_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V4v4_2E0 ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V3v3_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V4v4_2E0 ) ) ) ) ) )
         => ! [V0m1_2E0: u,V1m2_2E0: u,V2k: mono_2Etyop_2Enum_2Enum] :
              ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1m2_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1m2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F0_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__inter__eq,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V2k: mono_2Etyop_2Enum_2Enum,V1m2_2E0: u,V3v_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_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m2_2E0 ) ) ) @ ( s @ A_27a @ V3v_2E0 ) ) ) )
        <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m2_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3v_2E0 ) ) ) ) )
     => ( ! [V2k: mono_2Etyop_2Enum_2Enum,V1m2_2E0: u,V3v_2E0: u] :
            ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m2_2E0 ) ) ) @ ( s @ A_27a @ V3v_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m2_2E0 ) ) ) @ ( s @ A_27a @ V3v_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3v_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
       => ! [V0m1_2E0: u,V1m2_2E0: u,V2k: mono_2Etyop_2Enum_2Enum] :
            ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter__eq_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m2_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1m2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__inter__EQ,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1x: mono_2Etyop_2Enum_2Enum,V2t2_2E0: u,V3t1_2E0: u] :
      ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V2t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) )
      <=> ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) )
          & ( (~)
            @ ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V2t2_2E0 ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V2t2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
      <=> ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
          | ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V2t2_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__inter__assoc,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0x: mono_2Etyop_2Enum_2Enum,V1t3_2E0: u,V2t2_2E0: u,V3t1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V2t2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V1t3_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V2t2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V1t3_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elookup__difference,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V2k: mono_2Etyop_2Enum_2Enum,V1m2_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1m2_2E0 ) ) ) )
        <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1m2_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) )
     => ! [V0m1_2E0: u,V1m2_2E0: u,V2k: mono_2Etyop_2Enum_2Enum] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1m2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1m2_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0m1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2Elrnext__ind,axiom,
    ! [V0P: mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V1n: mono_2Etyop_2Enum_2Enum] :
          ( ( ( (~) @ ( V1n = mono_2Ec_2Enum_2E0 ) )
           => ( V0P @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
         => ( V0P @ V1n ) )
     => ! [V2v: mono_2Etyop_2Enum_2Enum] : ( V0P @ V2v ) ) ).

thf(thm_2Esptree_2Elrnext__def,axiom,
    ! [F0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V0n: mono_2Etyop_2Enum_2Enum] :
          ( ( F0 @ V0n )
        <=> ( V0n = mono_2Ec_2Enum_2E0 ) )
     => ! [V0n: mono_2Etyop_2Enum_2Enum] :
          ( ( mono_2Ec_2Esptree_2Elrnext @ V0n )
          = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( F0 @ V0n ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Elrnext__thm,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0a_2E0: u] :
          ( ( mono_2Ec_2Esptree_2Elrnext @ mono_2Ec_2Enum_2E0 )
          = ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
      & ! [V1n: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] :
          ( ( mono_2Ec_2Esptree_2Elrnext @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) )
          = ( mono_2Ec_2Esptree_2Elrnext @ V1n ) )
      & ( ( mono_2Ec_2Esptree_2Elrnext @ mono_2Ec_2Earithmetic_2EZERO )
        = ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
      & ! [V3n: mono_2Etyop_2Enum_2Enum] :
          ( ( mono_2Ec_2Esptree_2Elrnext @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) )
          = ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V3n ) ) )
      & ! [V4n: mono_2Etyop_2Enum_2Enum] :
          ( ( mono_2Ec_2Esptree_2Elrnext @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V4n ) )
          = ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Esptree_2Elrnext @ V4n ) ) ) ) ).

thf(thm_2Esptree_2EFINITE__domain,axiom,
    ! [A_27a: d,V0t_2E0: u] : ( mono_2Ec_2Epred__set_2EFINITE_2Emono_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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0t_2E0 ) ) ) ) ) ).

thf(thm_2Esptree_2EIN__domain,axiom,
    ! [A_27a: d,A_27b: d,V0n: mono_2Etyop_2Enum_2Enum,V1x_2E0: u,V2t1_2E0: u,V3t2_2E0: u] :
      ( ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0n @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ c_2Esptree_2ELN_2E0 ) ) ) ) )
        = mono_2Ec_2Ebool_2EF )
      & ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0n @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2ELS_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ) )
      <=> ( V0n = mono_2Ec_2Enum_2E0 ) )
      & ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0n @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBN_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t2_2E0 ) ) ) ) ) ) )
      <=> ( ( (~) @ ( V0n = mono_2Ec_2Enum_2E0 ) )
          & ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V0n ) @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t1_2E0 ) ) ) ) ) @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t2_2E0 ) ) ) ) ) ) ) )
      & ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0n @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2EBS_2E3 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t1_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t2_2E0 ) ) ) ) ) ) )
      <=> ( ( V0n = mono_2Ec_2Enum_2E0 )
          | ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2EEVEN @ V0n ) @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t1_2E0 ) ) ) ) ) @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V3t2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Emap__map__K,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1a_2E0: u,V2t_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27b @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27b @ V1a_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V2t_2E0 ) ) ) ) ).

thf(thm_2Esptree_2Elookup__map__K,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1t_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ ( c_2Esptree_2Emap_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27b @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2n @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ).

thf(thm_2Esptree_2EIMP__size__LESS__size,axiom,
    ! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esptree_2Esubspt_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1y_2E0 ) ) ) )
        & ( (~)
          @ ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 ) ) ) )
            = ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1y_2E0 ) ) ) ) ) ) )
     => ( mono_2Ec_2Eprim__rec_2E_3C @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1y_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Esize__diff__less,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0x_2E0: u,V1y_2E0: u,V2z_2E0: u,V3t: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V2z_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1y_2E0 ) ) ) ) )
        & ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V3t @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1y_2E0 ) ) ) ) )
        & ( (~) @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V3t @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V2z_2E0 ) ) ) ) ) )
        & ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V3t @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 ) ) ) ) ) )
     => ( mono_2Ec_2Eprim__rec_2E_3C @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1y_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esptree_2Esize_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Edifference_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V2z_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Esptree_2Einter__eq__LN,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Esptree_2Einter_2E2 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1y_2E0 ) ) )
        = ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ c_2Esptree_2ELN_2E0 ) )
    <=> ( mono_2Ec_2Epred__set_2EDISJOINT_2Emono_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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V0x_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27b ) @ V1y_2E0 ) ) ) ) ) ) ).

thf(thm_2Esptree_2Edomain__list__to__num__set,axiom,
    ! [V0x: mono_2Etyop_2Enum_2Enum,V1xs: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0x @ ( mono_2Ec_2Esptree_2Edomain_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Esptree_2Elist__to__num__set @ V1xs ) ) )
      = ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0x @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ V1xs ) ) ) ).

thf(thm_2Esptree_2Edomain__list__insert,axiom,
    ! [V0xs: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1x: mono_2Etyop_2Enum_2Enum,V2t: mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29] :
      ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1x @ ( mono_2Ec_2Esptree_2Edomain_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Esptree_2Elist__insert @ V0xs @ V2t ) ) )
    <=> ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1x @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ V0xs ) )
        | ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1x @ ( mono_2Ec_2Esptree_2Edomain_2Emono_2Etyop_2Eone_2Eone @ V2t ) ) ) ) ).

thf(thm_2Esptree_2Edomain__FOLDR__delete,axiom,
    ! [A_27a: d,V0ls: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1live_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27a ) @ ( tyop_2Esptree_2Espt @ A_27a ) ) ) @ c_2Esptree_2Edelete_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1live_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V0ls ) ) ) ) ) ) )
      = ( mono_2Ec_2Epred__set_2EDIFF_2Emono_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 ) @ ( c_2Esptree_2Edomain_2E1 @ ( s @ ( tyop_2Esptree_2Espt @ A_27a ) @ V1live_2E0 ) ) ) ) @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ V0ls ) ) ) ).

thf(thm_2Esptree_2Elookup__list__to__num__set,axiom,
    ! [V0x: mono_2Etyop_2Enum_2Enum,V1xs: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( mono_2Ec_2Esptree_2Elookup_2Emono_2Etyop_2Eone_2Eone @ V0x @ ( mono_2Ec_2Esptree_2Elist__to__num__set @ V1xs ) )
      = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0x @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ V1xs ) ) @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Eone_2Eone ) @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Eone_2Eone ) ) ).

thf(thm_2Esptree_2Elist__to__num__set__append,axiom,
    ! [V0l1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1l2: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
      ( ( mono_2Ec_2Esptree_2Elist__to__num__set @ ( mono_2Ec_2Elist_2EAPPEND_2Emono_2Etyop_2Enum_2Enum @ V0l1 @ V1l2 ) )
      = ( mono_2Ec_2Esptree_2Eunion_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Esptree_2Elist__to__num__set @ V0l1 ) @ ( mono_2Ec_2Esptree_2Elist__to__num__set @ V1l2 ) ) ) ).

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