%------------------------------------------------------------------------------
% File     : ITP066_4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : lbtree.ax [Gau19]
%          : HL4066_4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  432 ( 141 unt; 229 typ;   0 def)
%            Number of atoms       :  414 ( 241 equ)
%            Maximal formula atoms :   11 (   0 avg)
%            Number of connectives :  215 (   4   ~;  20   |;  85   &)
%                                         (  39 <=>;  67  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Maximal term depth    :   18 (   3 avg)
%            Number of types       :   24 (  23 usr)
%            Number of type conns  :  203 ( 128   >;  75   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  205 ( 205 usr;  78 con; 0-4 aty)
%            Number of variables   :  753 ( 672   !;  81   ?; 753   :)
% SPC      : TF0_SAT_EQU_NAR

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

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

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

tff(mono_2Etyop_2Emin_2Ebool,type,
    mono_2Etyop_2Emin_2Ebool: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29: $tType ).

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

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

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

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

tff(tyop_2Ellist_2Ellist,type,
    tyop_2Ellist_2Ellist: d > d ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( d * d ) > d ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

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

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( d * d ) > d ).

tff(s,type,
    s: ( d * u ) > du ).

tff(app_2E2,type,
    app_2E2: ( du * du ) > u ).

tff(p,type,
    p: mono_2Etyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: u ).

tff(combin_k_2E0,type,
    combin_k_2E0: u ).

tff(combin_s_2E0,type,
    combin_s_2E0: u ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

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

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: u ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: u ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: u ).

tff(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

tff(c_2Emin_2E_3D_2E1,type,
    c_2Emin_2E_3D_2E1: du > u ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

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

tff(c_2Ebool_2E_3F_21_2E0,type,
    c_2Ebool_2E_3F_21_2E0: u ).

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

tff(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: u ).

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

tff(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: u ).

tff(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: ( du * du ) > u ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

tff(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: ( du * du ) > u ).

tff(c_2Elist_2EEL_2E0,type,
    c_2Elist_2EEL_2E0: u ).

tff(c_2Elist_2EEL_2E2,type,
    c_2Elist_2EEL_2E2: ( du * du ) > u ).

tff(c_2Elist_2EEVERY_2E0,type,
    c_2Elist_2EEVERY_2E0: u ).

tff(c_2Elist_2EEVERY_2E2,type,
    c_2Elist_2EEVERY_2E2: ( du * du ) > u ).

tff(c_2Elist_2EEXISTS_2E0,type,
    c_2Elist_2EEXISTS_2E0: u ).

tff(c_2Elist_2EEXISTS_2E2,type,
    c_2Elist_2EEXISTS_2E2: ( du * du ) > u ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

tff(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: u ).

tff(c_2Ellist_2ELCONS_2E0,type,
    c_2Ellist_2ELCONS_2E0: u ).

tff(c_2Ellist_2ELCONS_2E2,type,
    c_2Ellist_2ELCONS_2E2: ( du * du ) > u ).

tff(c_2Ewhile_2ELEAST_2E0,type,
    c_2Ewhile_2ELEAST_2E0: u ).

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

tff(c_2Elist_2ELENGTH_2E0,type,
    c_2Elist_2ELENGTH_2E0: u ).

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

tff(c_2Ellist_2ELNIL_2E0,type,
    c_2Ellist_2ELNIL_2E0: u ).

tff(c_2Elbtree_2ELf_2E0,type,
    c_2Elbtree_2ELf_2E0: u ).

tff(c_2Elbtree_2ELfrep_2E0,type,
    c_2Elbtree_2ELfrep_2E0: u ).

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

tff(c_2Earithmetic_2EMIN_2E0,type,
    c_2Earithmetic_2EMIN_2E0: u ).

tff(c_2Earithmetic_2EMIN_2E2,type,
    c_2Earithmetic_2EMIN_2E2: ( du * du ) > u ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

tff(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: u ).

tff(c_2Elbtree_2ENd_2E0,type,
    c_2Elbtree_2ENd_2E0: u ).

tff(c_2Elbtree_2ENd_2E3,type,
    c_2Elbtree_2ENd_2E3: ( du * du * du ) > u ).

tff(c_2Elbtree_2ENdrep_2E0,type,
    c_2Elbtree_2ENdrep_2E0: u ).

tff(c_2Elbtree_2ENdrep_2E3,type,
    c_2Elbtree_2ENdrep_2E3: ( du * du * du ) > u ).

tff(c_2Elbtree_2ENdrep_2E4,type,
    c_2Elbtree_2ENdrep_2E4: ( du * du * du * du ) > u ).

tff(c_2Eoption_2EOPTION__MAP_2E0,type,
    c_2Eoption_2EOPTION__MAP_2E0: u ).

tff(c_2Eoption_2EOPTION__MAP_2E2,type,
    c_2Eoption_2EOPTION__MAP_2E2: ( du * du ) > u ).

tff(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: u ).

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

tff(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: u ).

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

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: u ).

tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
    c_2Ebool_2ETYPE__DEFINITION_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).

tff(c_2Elbtree_2Ebf__flatten_2E0,type,
    c_2Elbtree_2Ebf__flatten_2E0: u ).

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

tff(c_2Elbtree_2Edepth_2E0,type,
    c_2Elbtree_2Edepth_2E0: u ).

tff(c_2Elbtree_2Edepth_2E3,type,
    c_2Elbtree_2Edepth_2E3: ( du * du * du ) > u ).

tff(c_2Ellist_2Eexists_2E0,type,
    c_2Ellist_2Eexists_2E0: u ).

tff(c_2Ellist_2Eexists_2E2,type,
    c_2Ellist_2Eexists_2E2: ( du * du ) > u ).

tff(c_2Elbtree_2Efinite_2E0,type,
    c_2Elbtree_2Efinite_2E0: u ).

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

tff(c_2Elbtree_2Eis__lbtree_2E0,type,
    c_2Elbtree_2Eis__lbtree_2E0: u ).

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

tff(c_2Elbtree_2Eis__mmindex_2E0,type,
    c_2Elbtree_2Eis__mmindex_2E0: u ).

tff(c_2Elbtree_2Eis__mmindex_2E4,type,
    c_2Elbtree_2Eis__mmindex_2E4: ( du * du * du * du ) > u ).

tff(c_2Elbtree_2Elbtree__abs_2E0,type,
    c_2Elbtree_2Elbtree__abs_2E0: u ).

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

tff(c_2Elbtree_2Elbtree__case_2E0,type,
    c_2Elbtree_2Elbtree__case_2E0: u ).

tff(c_2Elbtree_2Elbtree__case_2E3,type,
    c_2Elbtree_2Elbtree__case_2E3: ( du * du * du ) > u ).

tff(c_2Elbtree_2Elbtree__rep_2E0,type,
    c_2Elbtree_2Elbtree__rep_2E0: u ).

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

tff(c_2Elist_2Elist__CASE_2E0,type,
    c_2Elist_2Elist__CASE_2E0: u ).

tff(c_2Elist_2Elist__CASE_2E3,type,
    c_2Elist_2Elist__CASE_2E3: ( du * du * du ) > u ).

tff(c_2Elbtree_2Emap_2E0,type,
    c_2Elbtree_2Emap_2E0: u ).

tff(c_2Elbtree_2Emap_2E2,type,
    c_2Elbtree_2Emap_2E2: ( du * du ) > u ).

tff(c_2Elbtree_2Emem_2E0,type,
    c_2Elbtree_2Emem_2E0: u ).

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

tff(c_2Elbtree_2Emem_2E2,type,
    c_2Elbtree_2Emem_2E2: ( du * du ) > u ).

tff(c_2Elbtree_2Emindepth_2E0,type,
    c_2Elbtree_2Emindepth_2E0: u ).

tff(c_2Elbtree_2Emindepth_2E2,type,
    c_2Elbtree_2Emindepth_2E2: ( du * du ) > u ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: u ).

tff(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: ( du * du ) > u ).

tff(c_2Eoption_2Eoption__CASE_2E0,type,
    c_2Eoption_2Eoption__CASE_2E0: u ).

tff(c_2Eoption_2Eoption__CASE_2E3,type,
    c_2Eoption_2Eoption__CASE_2E3: ( du * du * du ) > u ).

tff(c_2Elbtree_2Eoptmin_2E0,type,
    c_2Elbtree_2Eoptmin_2E0: u ).

tff(c_2Elbtree_2Eoptmin_2E2,type,
    c_2Elbtree_2Eoptmin_2E2: ( du * du ) > u ).

tff(c_2Epair_2Epair__CASE_2E0,type,
    c_2Epair_2Epair__CASE_2E0: u ).

tff(c_2Epair_2Epair__CASE_2E2,type,
    c_2Epair_2Epair__CASE_2E2: ( du * du ) > u ).

tff(c_2Elbtree_2Epath__follow_2E0,type,
    c_2Elbtree_2Epath__follow_2E0: u ).

tff(c_2Elbtree_2Epath__follow_2E3,type,
    c_2Elbtree_2Epath__follow_2E3: ( du * du * du ) > u ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

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

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E0,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E2,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Enum_2E0_2E0,type,
    mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Eprim__rec_2E_3C_2E0,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Eprim__rec_2E_3C_2E2,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2E_3C_3D_2E0,type,
    mono_2Ec_2Earithmetic_2E_3C_3D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_3C_3D_2E2,type,
    mono_2Ec_2Earithmetic_2E_3C_3D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E2,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29 ).

tff(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2EF_2E0,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ewhile_2ELEAST_2E0,type,
    mono_2Ec_2Ewhile_2ELEAST_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Ewhile_2ELEAST_2E1,type,
    mono_2Ec_2Ewhile_2ELEAST_2E1: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2EMIN_2E0,type,
    mono_2Ec_2Earithmetic_2EMIN_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2EMIN_2E2,type,
    mono_2Ec_2Earithmetic_2EMIN_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Enum_2ESUC_2E0,type,
    mono_2Ec_2Enum_2ESUC_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Enum_2ESUC_2E1,type,
    mono_2Ec_2Enum_2ESUC_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2ET_2E0,type,
    mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E0,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E2,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Elbtree_2Eoptmin_2E0,type,
    mono_2Ec_2Elbtree_2Eoptmin_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Elbtree_2Eoptmin_2E2,type,
    mono_2Ec_2Elbtree_2Eoptmin_2E2: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Ebool_2E_7E_2E0,type,
    mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2E_7E_2E1,type,
    mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

tff(i_mono_2Etyop_2Emin_2Ebool,type,
    i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > u ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 > u ).

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

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

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

tff(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 ).

tff(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_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29 ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 ).

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

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

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

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

tff(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(reserved_2Eho_2Etruth,axiom,
    p(mono_2Ec_2Ebool_2ET_2E0) ).

tff(reserved_2Eho_2Enotfalse,axiom,
    ~ p(mono_2Ec_2Ebool_2EF_2E0) ).

tff(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = mono_2Ec_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = mono_2Ec_2Ebool_2EF_2E0 ) ) ).

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

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

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

tff(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

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

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

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

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

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

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

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

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),V0_2E0) ) ).

tff(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) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

tff(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) ) ).

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

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

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

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

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

tff(ij_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(j_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(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) ) ).

tff(ij_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

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

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))) ) ).

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

tff(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

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

tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Elbtree_2Elbtree_28A_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Ebool),X0_2E0)))) ) ).

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

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

tff(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))) ) ).

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

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,X2_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(X0_2E0,X1_2E0,X2_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(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))) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] : ( mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Ebool(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Emin_2Ebool,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)))),c_2Elist_2ECONS_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),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_2E0)))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

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

tff(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

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

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELCONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Ewhile_2ELEAST_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Ewhile_2ELEAST_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Ewhile_2ELEAST_2E0,X0_2E0) ) ).

tff(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)))) ) ).

tff(arityeq1_2Ec_2Elbtree_2ELfrep_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Elbtree_2ELfrep_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Elbtree_2ELfrep_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq2_2Ec_2Earithmetic_2EMIN_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMIN_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2EMIN_2E0,X0_2E0),X1_2E0) ) ).

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

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

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

tff(arityeq4_2Ec_2Elbtree_2ENdrep_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2ENdrep_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(X3_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))))),c_2Elbtree_2ENdrep_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X2_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(X3_2E0)))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,X1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(mono_2Ec_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27b_29_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),X1_2E0))) ) ).

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

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).

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

tff(arityeq3_2Ec_2Elbtree_2Edepth_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,X0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X2_2E0))))) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Elbtree_2Edepth_2E0),s(A_27a,X0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0)))),X2_2E0) ) ).

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

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

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

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

tff(arityeq4_2Ec_2Elbtree_2Eis__mmindex_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: mono_2Etyop_2Enum_2Enum,X3_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__mmindex_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X2_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X3_2E0))))) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Elbtree_2Eis__mmindex_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))),X2_2E0),X3_2E0) ) ).

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

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

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

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(X0_2E0)),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(X0_2E0)))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),X2_2E0))) ) ).

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

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

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

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

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

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(X0_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(X0_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ) ).

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

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

tff(arityeq2_2Ec_2Elbtree_2Eoptmin_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,X1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Elbtree_2Eoptmin_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(mono_2Ec_2Elbtree_2Eoptmin_2E0,X0_2E0),X1_2E0) ) ).

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

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

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

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

tff(arityeq3_2Ec_2Elbtree_2Epath__follow_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2Epath__follow_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(X2_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)))),c_2Elbtree_2Epath__follow_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(X2_2E0)))) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] : ( s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: 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_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,V1_2E0: 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_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V2_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V2_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Emin_2Ebool)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Elist_2ECONS_2E0) ).

tff(monoeq_2Emono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] : ( s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Emin_2Ebool)) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ENIL_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(mono_2Ec_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Eoption_2EOPTION__MAP_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2ESOME_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)))) ) ).

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

tff(thm_2Elbtree_2ENdrep__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1t1_2E0: u,V2t2_2E0: u,V4v_2E0: mono_2Etyop_2Emin_2Ebool,V5xs_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V1t1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V2t2_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V4v_2E0)))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V5xs_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V4v_2E0)),s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V1t1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V5xs_2E0)))),s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V2t2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V5xs_2E0)))))) )
     => ! [V0a_2E0: u,V1t1_2E0: u,V2t2_2E0: u,V3x_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2ENdrep_2E4(s(A_27a,V0a_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V1t1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V2t2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V3x_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V3x_2E0)),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0a_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V1t1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V2t2_2E0))))) ) ) ).

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

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

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

tff(thm_2Elbtree_2Epath__follow__def,axiom,
    ! [A_27a: d,A_27b: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V2g_2E0: u,V4h_2E0: mono_2Etyop_2Emin_2Ebool,V5t_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,V9y_2E0: u,V10z_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))))),F2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V4h_2E0)))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V5t_2E0)))),s(A_27b,V9y_2E0))),s(A_27b,V10z_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2Epath__follow_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0),s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V4h_2E0)),s(A_27b,V9y_2E0),s(A_27b,V10z_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V5t_2E0)))) )
     => ( ! [V2g_2E0: u,V4h_2E0: mono_2Etyop_2Emin_2Ebool,V5t_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,V7a_2E0: u,V8v2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a)))))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V4h_2E0)))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V5t_2E0)))),s(A_27a,V7a_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27b),V8v2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27b),V8v2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))))),F2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V4h_2E0)))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V5t_2E0)))))) )
       => ( ! [V2g_2E0: u,V4h_2E0: mono_2Etyop_2Emin_2Ebool,V5t_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,V6v_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V4h_2E0)))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V5t_2E0)))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),V6v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),V6v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a)))))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V4h_2E0)))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V5t_2E0)))))) )
         => ( ! [V0g_2E0: u,V1x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2Epath__follow_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V0g_2E0),s(A_27b,V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(mono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Emin_2Ebool)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V0g_2E0),s(A_27b,V1x_2E0))))) )
            & ! [V2g_2E0: u,V3x_2E0: u,V4h_2E0: mono_2Etyop_2Emin_2Ebool,V5t_2E0: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2Epath__follow_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0),s(A_27b,V3x_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(mono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Ebool(V4h_2E0,V5t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0),s(A_27b,V3x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V4h_2E0)))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),i_mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29(V5t_2E0)))))) ) ) ) ) ) ).

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

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

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

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

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

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

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

tff(thm_2Elbtree_2Edepth__def,axiom,
    ! [A_27a: d,V0x_2E0: u,V1x_27_2E0: u,V2x_27_27_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1x_27_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_27_27_2E0))))))
    <=> ! [V3depth_27_2E0: u] :
          ( ! [V4a0_2E0: u,V5a1_2E0: u,V6a2_2E0: mono_2Etyop_2Enum_2Enum] :
              ( ( ? [V7t1_2E0: u,V8t2_2E0: u] :
                    ( ( s(tyop_2Elbtree_2Elbtree(A_27a),V5a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V4a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0))) )
                    & ( V6a2_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
                | ? [V9m_2E0: mono_2Etyop_2Enum_2Enum,V10a_2E0: u,V11t1_2E0: u,V12t2_2E0: u] :
                    ( ( s(tyop_2Elbtree_2Elbtree(A_27a),V5a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V10a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V11t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0))) )
                    & ( V6a2_2E0 = mono_2Ec_2Enum_2ESUC_2E1(V9m_2E0) )
                    & p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V3depth_27_2E0),s(A_27a,V4a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V11t1_2E0)))),V9m_2E0)) )
                | ? [V13m_2E0: mono_2Etyop_2Enum_2Enum,V14a_2E0: u,V15t1_2E0: u,V16t2_2E0: u] :
                    ( ( s(tyop_2Elbtree_2Elbtree(A_27a),V5a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V14a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V15t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V16t2_2E0))) )
                    & ( V6a2_2E0 = mono_2Ec_2Enum_2ESUC_2E1(V13m_2E0) )
                    & p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V3depth_27_2E0),s(A_27a,V4a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V16t2_2E0)))),V13m_2E0)) ) )
             => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V3depth_27_2E0),s(A_27a,V4a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V5a1_2E0)))),V6a2_2E0)) )
         => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V3depth_27_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V1x_27_2E0)))),V2x_27_27_2E0)) ) ) ).

tff(thm_2Elbtree_2Emindepth__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0x_2E0: u,V1t_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0)))),V2n_2E0) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0))))) )
     => ! [V0x_2E0: u,V1t_2E0: u] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0)))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0)))),mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Ewhile_2ELEAST_2E1(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0)))))),mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum) ) ) ).

tff(thm_2Elbtree_2Eis__mmindex__def,axiom,
    ! [A_27a: d,V0f_2E0: u,V1l_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum,V3d_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__mmindex_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3d_2E0))))))
    <=> ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))
        & ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V3d_2E0) )
        & ! [V4i_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V4i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))
           => ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) = mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum )
              | ? [V5d_27_2E0: mono_2Etyop_2Enum_2Enum] :
                  ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V5d_27_2E0) )
                  & p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V3d_2E0,V5d_27_2E0))
                  & ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V4i_2E0,V2n_2E0))
                   => p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3d_2E0,V5d_27_2E0)) ) ) ) ) ) ) ).

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

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

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

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

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

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

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

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

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

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

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

tff(thm_2Elbtree_2Emem__thm,axiom,
    ! [A_27a: d,V0t2_2E0: u,V1t1_2E0: u,V2b_2E0: u,V3a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0)))) = mono_2Ec_2Ebool_2EF_2E0 )
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V2b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V0t2_2E0)))))))
      <=> ( ( s(A_27a,V3a_2E0) = s(A_27a,V2b_2E0) )
          | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0)))))
          | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V0t2_2E0))))) ) ) ) ).

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

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

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

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

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

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

tff(thm_2Elbtree_2Efinite__thm,axiom,
    ! [A_27a: d,A_27b: d,V0t2_2E0: u,V1t1_2E0: u,V2a_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ENd_2E3(s(A_27b,V2a_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V0t2_2E0)))))))
      <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27b),V1t1_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27b),V0t2_2E0))))) ) ) ) ).

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

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

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

tff(thm_2Elbtree_2EEXISTS__FIRST,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))
     => ? [V2l1_2E0: u,V3x_2E0: u,V4l2_2E0: u] :
          ( ( s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V4l2_2E0))))) )
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))) ) ) ).

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

tff(thm_2Elbtree_2Edepth__rules,axiom,
    ! [A_27a: d] :
      ( ! [V0x_2E0: u,V1t1_2E0: u,V2t2_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0))))))
      & ! [V3m_2E0: mono_2Etyop_2Enum_2Enum,V4x_2E0: u,V5a_2E0: u,V6t1_2E0: u,V7t2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V4x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3m_2E0))))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V4x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V5a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V3m_2E0))))))) )
      & ! [V8m_2E0: mono_2Etyop_2Enum_2Enum,V9x_2E0: u,V10a_2E0: u,V11t1_2E0: u,V12t2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V9x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V8m_2E0))))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V9x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V10a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V11t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V8m_2E0))))))) ) ) ).

tff(thm_2Elbtree_2Edepth__ind,axiom,
    ! [A_27a: d,V0depth_27_2E0: u] :
      ( ( ! [V1x_2E0: u,V2t1_2E0: u,V3t2_2E0: u] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V1x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0)))))),mono_2Ec_2Enum_2E0_2E0))
        & ! [V4m_2E0: mono_2Etyop_2Enum_2Enum,V5x_2E0: u,V6a_2E0: u,V7t1_2E0: u,V8t2_2E0: u] :
            ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V5x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0)))),V4m_2E0))
           => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V5x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V6a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0)))))),mono_2Ec_2Enum_2ESUC_2E1(V4m_2E0))) )
        & ! [V9m_2E0: mono_2Etyop_2Enum_2Enum,V10x_2E0: u,V11a_2E0: u,V12t1_2E0: u,V13t2_2E0: u] :
            ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V10x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V13t2_2E0)))),V9m_2E0))
           => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V10x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V11a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V13t2_2E0)))))),mono_2Ec_2Enum_2ESUC_2E1(V9m_2E0))) ) )
     => ! [V14a0_2E0: u,V15a1_2E0: u,V16a2_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V14a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V15a1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V16a2_2E0))))))
         => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V14a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V15a1_2E0)))),V16a2_2E0)) ) ) ).

tff(thm_2Elbtree_2Edepth__strongind,axiom,
    ! [A_27a: d,V0depth_27_2E0: u] :
      ( ( ! [V1x_2E0: u,V2t1_2E0: u,V3t2_2E0: u] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V1x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0)))))),mono_2Ec_2Enum_2E0_2E0))
        & ! [V4m_2E0: mono_2Etyop_2Enum_2Enum,V5x_2E0: u,V6a_2E0: u,V7t1_2E0: u,V8t2_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V5x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4m_2E0))))))
              & p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V5x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0)))),V4m_2E0)) )
           => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V5x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V6a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0)))))),mono_2Ec_2Enum_2ESUC_2E1(V4m_2E0))) )
        & ! [V9m_2E0: mono_2Etyop_2Enum_2Enum,V10x_2E0: u,V11a_2E0: u,V12t1_2E0: u,V13t2_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V10x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V13t2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V9m_2E0))))))
              & p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V10x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V13t2_2E0)))),V9m_2E0)) )
           => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V10x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V11a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V13t2_2E0)))))),mono_2Ec_2Enum_2ESUC_2E1(V9m_2E0))) ) )
     => ! [V14a0_2E0: u,V15a1_2E0: u,V16a2_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V14a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V15a1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V16a2_2E0))))))
         => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V14a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V15a1_2E0)))),V16a2_2E0)) ) ) ).

tff(thm_2Elbtree_2Edepth__cases,axiom,
    ! [A_27a: d,V0a0_2E0: u,V1a1_2E0: u,V2a2_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2a2_2E0))))))
    <=> ( ? [V3t1_2E0: u,V4t2_2E0: u] :
            ( ( s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V4t2_2E0))) )
            & ( V2a2_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
        | ? [V5m_2E0: mono_2Etyop_2Enum_2Enum,V6a_2E0: u,V7t1_2E0: u,V8t2_2E0: u] :
            ( ( s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V6a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0))) )
            & ( V2a2_2E0 = mono_2Ec_2Enum_2ESUC_2E1(V5m_2E0) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5m_2E0)))))) )
        | ? [V9m_2E0: mono_2Etyop_2Enum_2Enum,V10a_2E0: u,V11t1_2E0: u,V12t2_2E0: u] :
            ( ( s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V10a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V11t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0))) )
            & ( V2a2_2E0 = mono_2Ec_2Enum_2ESUC_2E1(V9m_2E0) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V9m_2E0)))))) ) ) ) ).

tff(thm_2Elbtree_2Emem__depth,axiom,
    ! [A_27a: d,V0x_2E0: u,V1t_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0)))))
     => ? [V2n_2E0: mono_2Etyop_2Enum_2Enum] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))))) ) ).

tff(thm_2Elbtree_2Edepth__mem,axiom,
    ! [A_27a: d,V0x_2E0: u,V1t_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0))))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0))))) ) ).

tff(thm_2Elbtree_2Eoptmin__ind,axiom,
    ! [V0P_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0P_2E0,mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum),mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum))
        & ! [V1x_2E0: mono_2Etyop_2Enum_2Enum] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0P_2E0,mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V1x_2E0)),mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum))
        & ! [V2y_2E0: mono_2Etyop_2Enum_2Enum] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0P_2E0,mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum),mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V2y_2E0)))
        & ! [V3x_2E0: mono_2Etyop_2Enum_2Enum,V4y_2E0: mono_2Etyop_2Enum_2Enum] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0P_2E0,mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V3x_2E0)),mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V4y_2E0))) )
     => ! [V5v_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V6v1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0P_2E0,V5v_2E0),V6v1_2E0)) ) ).

tff(thm_2Elbtree_2Eoptmin__def,axiom,
    ! [V0y_2E0: mono_2Etyop_2Enum_2Enum,V1x_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Elbtree_2Eoptmin_2E2(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum,mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum) = mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum )
      & ( mono_2Ec_2Elbtree_2Eoptmin_2E2(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V1x_2E0),mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V1x_2E0) )
      & ( mono_2Ec_2Elbtree_2Eoptmin_2E2(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum,mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V0y_2E0)) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V0y_2E0) )
      & ( mono_2Ec_2Elbtree_2Eoptmin_2E2(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V1x_2E0),mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V0y_2E0)) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EMIN_2E2(V1x_2E0,V0y_2E0)) ) ) ).

tff(thm_2Elbtree_2Emindepth__thm,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0x_2E0: u,V3a_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0x_2E0))),s(A_27a,V3a_2E0)))))
        <=> ( s(A_27a,V0x_2E0) = s(A_27a,V3a_2E0) ) )
     => ! [V0x_2E0: u,V1t2_2E0: u,V2t1_2E0: u,V3a_2E0: u] :
          ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0)))) = mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum )
          & ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t2_2E0)))))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0x_2E0))),s(A_27a,V3a_2E0)))),mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0),mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E0,mono_2Ec_2Elbtree_2Eoptmin_2E2(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0)))),j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t2_2E0))))))) ) ) ) ).

tff(thm_2Elbtree_2Emem__mindepth,axiom,
    ! [A_27a: d,V0x_2E0: u,V1t_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0)))))
     => ? [V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V2n_2E0) ) ) ).

tff(thm_2Elbtree_2Emindepth__depth,axiom,
    ! [A_27a: d,V0x_2E0: u,V1t_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V2n_2E0) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))))) ) ).

tff(thm_2Elbtree_2Emmindex__EXISTS,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1f_2E0: u,V2e_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V1f_2E0))),s(A_27a,V2e_2E0)))))
        <=> ? [V3n_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V1f_2E0),s(A_27a,V2e_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V3n_2E0) ) )
     => ! [V0l_2E0: u,V1f_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
         => ? [V4i_2E0: mono_2Etyop_2Enum_2Enum,V5m_2E0: mono_2Etyop_2Enum_2Enum] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__mmindex_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5m_2E0)))))) ) ) ).

tff(thm_2Elbtree_2Emmindex__unique,axiom,
    ! [A_27a: d,V0m_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u,V2i_2E0: mono_2Etyop_2Enum_2Enum,V3f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__mmindex_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0m_2E0))))))
     => ! [V4j_2E0: mono_2Etyop_2Enum_2Enum,V5n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__mmindex_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4j_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5n_2E0))))))
        <=> ( ( V4j_2E0 = V2i_2E0 )
            & ( V5n_2E0 = V0m_2E0 ) ) ) ) ).

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

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