%------------------------------------------------------------------------------
% File     : ITP108^4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : fmsp.ax [Gau19]
%          : HL4108^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  147 (  50 unt;  85 typ;   0 def)
%            Number of atoms       :  118 (  51 equ;   1 cnn)
%            Maximal formula atoms :    6 (   0 avg)
%            Number of connectives : 3553 (   1   ~;   1   |;   5   &;3528   @)
%                                         (   9 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   7 avg;3528 nst)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  107 ( 107   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   83 (  81 usr;  37 con; 0-4 aty)
%            Number of variables   :  218 (   0   ^ 217   !;   1   ?; 218   :)
% SPC      : TH0_SAT_EQU_NAR

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

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

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

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

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

thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

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

thf(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

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

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

thf(tyop_2Esptree_2Espt,type,
    tyop_2Esptree_2Espt: d > d ).

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

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

thf(combin_i_2E0,type,
    combin_i_2E0: u ).

thf(combin_k_2E0,type,
    combin_k_2E0: u ).

thf(combin_s_2E0,type,
    combin_s_2E0: u ).

thf(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

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

thf(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

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

thf(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

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

thf(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

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

thf(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

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

thf(c_2Ecombin_2EC_2E0,type,
    c_2Ecombin_2EC_2E0: u ).

thf(c_2Ecombin_2EC_2E1,type,
    c_2Ecombin_2EC_2E1: du > u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Efinite__map_2EFDOM_2E0,type,
    c_2Efinite__map_2EFDOM_2E0: u ).

thf(c_2Efinite__map_2EFEMPTY_2E0,type,
    c_2Efinite__map_2EFEMPTY_2E0: u ).

thf(c_2Efinite__map_2EFLOOKUP_2E0,type,
    c_2Efinite__map_2EFLOOKUP_2E0: u ).

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

thf(c_2Efmsp_2EFMSP_2E0,type,
    c_2Efmsp_2EFMSP_2E0: u ).

thf(c_2Efmsp_2EFMSP_2E2,type,
    c_2Efmsp_2EFMSP_2E2: du > du > u ).

thf(c_2Efmsp_2EFMSP_2E4,type,
    c_2Efmsp_2EFMSP_2E4: du > du > du > du > u ).

thf(c_2Efinite__map_2EFUNION_2E0,type,
    c_2Efinite__map_2EFUNION_2E0: u ).

thf(c_2Etransfer_2EFUN__REL_2E0,type,
    c_2Etransfer_2EFUN__REL_2E0: u ).

thf(c_2Etransfer_2EFUN__REL_2E2,type,
    c_2Etransfer_2EFUN__REL_2E2: du > du > u ).

thf(c_2Etransfer_2EFUN__REL_2E4,type,
    c_2Etransfer_2EFUN__REL_2E4: du > du > du > du > u ).

thf(c_2Efinite__map_2EFUPDATE_2E0,type,
    c_2Efinite__map_2EFUPDATE_2E0: u ).

thf(c_2Esptree_2ELN_2E0,type,
    c_2Esptree_2ELN_2E0: u ).

thf(c_2Eoption_2EOPTREL_2E0,type,
    c_2Eoption_2EOPTREL_2E0: u ).

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

thf(c_2Etransfer_2EPAIR__REL_2E0,type,
    c_2Etransfer_2EPAIR__REL_2E0: u ).

thf(c_2Etransfer_2EPAIR__REL_2E2,type,
    c_2Etransfer_2EPAIR__REL_2E2: du > du > u ).

thf(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

thf(c_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: u ).

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

thf(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

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

thf(c_2Etransfer_2Ebi__unique_2E0,type,
    c_2Etransfer_2Ebi__unique_2E0: u ).

thf(c_2Etransfer_2Ebi__unique_2E1,type,
    c_2Etransfer_2Ebi__unique_2E1: du > u ).

thf(c_2Etransfer_2Ebitotal_2E0,type,
    c_2Etransfer_2Ebitotal_2E0: u ).

thf(c_2Etransfer_2Ebitotal_2E1,type,
    c_2Etransfer_2Ebitotal_2E1: du > u ).

thf(c_2Esptree_2Edelete_2E0,type,
    c_2Esptree_2Edelete_2E0: u ).

thf(c_2Esptree_2Edomain_2E0,type,
    c_2Esptree_2Edomain_2E0: u ).

thf(c_2Efinite__map_2Efdomsub_2E0,type,
    c_2Efinite__map_2Efdomsub_2E0: u ).

thf(c_2Esptree_2Einsert_2E0,type,
    c_2Esptree_2Einsert_2E0: u ).

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

thf(c_2Esptree_2Elookup_2E0,type,
    c_2Esptree_2Elookup_2E0: u ).

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

thf(c_2Esptree_2Eunion_2E0,type,
    c_2Esptree_2Eunion_2E0: u ).

thf(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

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

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

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

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

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

thf(mono_2Ec_2Emin_2E_3D_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Emin_2E_3D_2Emono_2Etyop_2Emin_2Ebool: $o > $o > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).

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

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

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

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

thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
      = V0 ) ).

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

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

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

thf(arityeq1_2Ec_2Ecombin_2EC_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27c_29_20mono_2Etyop_2Esptree_2Espt_28A_27c_29,axiom,
    ! [A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ ( c_2Ecombin_2EC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) ) @ c_2Ecombin_2EC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmsp_2EFMSP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Efmsp_2EFMSP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Efmsp_2EFMSP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Efmsp_2EFMSP_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmsp_2EFMSP_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Efmsp_2EFMSP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X3_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Etransfer_2EFUN__REL_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1: $o > $o > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EFUN__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( 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 @ X1 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Etransfer_2EFUN__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( 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 @ X1 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Etransfer_2EFUN__REL_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Esptree_2Espt_28A_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EFUN__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Etransfer_2EFUN__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Etransfer_2EFUN__REL_2E2_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Esptree_2Espt_28A_27c_29_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1: $o > $o > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EFUN__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( 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 @ X1 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Etransfer_2EFUN__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( 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 @ X1 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Etransfer_2EFUN__REL_2E2_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Esptree_2Espt_28A_27c_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Esptree_2Espt_28A_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EFUN__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Etransfer_2EFUN__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Etransfer_2EFUN__REL_2E4_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Esptree_2Espt_28A_27c_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EFUN__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Etransfer_2EFUN__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X3_2E0 ) ) ) ) ) ).

thf(arityeq4_2Ec_2Etransfer_2EFUN__REL_2E4_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Esptree_2Espt_28A_27c_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Esptree_2Espt_28A_27c_29_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EFUN__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Etransfer_2EFUN__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ X3_2E0 ) ) ) ) ) ).

thf(arityeq4_2Ec_2Etransfer_2EFUN__REL_2E4_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Esptree_2Espt_28A_27c_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_2Ctyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28A_27c_29_2Ctyop_2Esptree_2Espt_28A_27c_29_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EFUN__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Etransfer_2EFUN__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ X3_2E0 ) ) ) ) ) ).

thf(arityeq4_2Ec_2Etransfer_2EFUN__REL_2E4_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Esptree_2Espt_28A_27c_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27c_29_2Ctyop_2Esptree_2Espt_28A_27c_29_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EFUN__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Etransfer_2EFUN__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ X3_2E0 ) ) ) ) ) ).

thf(arityeq4_2Ec_2Etransfer_2EFUN__REL_2E4_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28A_27c_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1: $o > $o > $o,X2_2E0: u,X3_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EFUN__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( 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 @ X1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Etransfer_2EFUN__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( 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 @ X1 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ X3_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Etransfer_2EFUN__REL_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27c_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Esptree_2Espt_28A_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EFUN__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Etransfer_2EFUN__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Etransfer_2EPAIR__REL_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EPAIR__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Etransfer_2EPAIR__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27c_20mono_2Etyop_2Esptree_2Espt_28A_27c_29,axiom,
    ! [A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Etransfer_2Ebi__unique_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebi__unique_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Etransfer_2Ebi__unique_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Etransfer_2Ebitotal_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebitotal_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Etransfer_2Ebitotal_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Etransfer_2Ebitotal_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebitotal_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Etransfer_2Ebitotal_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Etransfer_2Ebitotal_2E1_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Esptree_2Espt_28A_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebitotal_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Etransfer_2Ebitotal_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Esptree_2Einsert_2E3_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27c @ X1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) ) @ c_2Esptree_2Einsert_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esptree_2Elookup_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Eoption_2Eoption @ A_27c ) ) ) @ c_2Esptree_2Elookup_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ X1_2E0 ) ) ) ) ).

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

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

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

thf(monoeq_2Emono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ( ( 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 @ mono_2Ec_2Emin_2E_3D_2Emono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) ) ).

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

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

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

thf(thm_2Efmsp_2EFMSP__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0AN_2E0: u,V1BC_2E0: u,V2fm_2E0: u,V3sp_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmsp_2EFMSP_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V1BC_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V3sp_2E0 ) ) ) )
    <=> ! [V4a_2E0: u,V5n: mono_2Etyop_2Enum_2Enum] :
          ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0AN_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ V5n )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V1BC_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Esptree_2Elookup_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5n ) ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V3sp_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efmsp_2EFMSP__FDOM,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0BC_2E0: u,V1AN_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EFUN__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Efmsp_2EFMSP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EFUN__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( 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 @ mono_2Ec_2Emin_2E_3D_2Emono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Esptree_2Edomain_2E0 ) ) ) ) ).

thf(thm_2Efmsp_2EFMSP__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0BC_2E0: u,V1AN_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmsp_2EFMSP_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ c_2Esptree_2ELN_2E0 ) ) ) ) ).

thf(thm_2Efmsp_2EFMSP__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V2sp_2E0: u,V3n: mono_2Etyop_2Enum_2Enum,V4v_2E0: u] :
          ( ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V2sp_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) ) ) @ ( s @ A_27c @ V4v_2E0 ) ) )
          = ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Esptree_2Einsert_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ A_27c @ V4v_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V2sp_2E0 ) ) ) )
     => ( ! [V2sp_2E0: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V2sp_2E0 ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Esptree_2Espt @ A_27c ) @ V2sp_2E0 ) ) ) ) ) )
       => ! [V0BC_2E0: u,V1AN_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebi__unique_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EFUN__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Efmsp_2EFMSP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EFUN__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EPAIR__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Efmsp_2EFMSP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ F0_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmsp_2EFMSP__bitotal,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0BC_2E0: u,V1AN_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebitotal_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebitotal_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebi__unique_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebitotal_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Efmsp_2EFMSP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmsp_2EFMSP__FORALL,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0BC_2E0: u,V1AN_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebitotal_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebitotal_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebi__unique_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EFUN__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EFUN__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Efmsp_2EFMSP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) @ ( 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 @ mono_2Ec_2Emin_2E_3D_2Emono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( 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 @ mono_2Ec_2Emin_2E_3D_2Emono_2Etyop_2Emin_2Ebool ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) ) ) ) ) ).

thf(thm_2Efmsp_2EFMSP__FUNION,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0BC_2E0: u,V1AN_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EFUN__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Efmsp_2EFMSP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EFUN__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Efmsp_2EFMSP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Efmsp_2EFMSP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUNION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ c_2Esptree_2Eunion_2E0 ) ) ) ) ).

thf(thm_2Efmsp_2EFMSP__FDOMSUB,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0BC_2E0: u,V1AN_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2Ebi__unique_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EFUN__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Efmsp_2EFMSP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Etransfer_2EFUN__REL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Efmsp_2EFMSP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V1AN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V0BC_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2Efdomsub_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ ( c_2Ecombin_2EC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) @ c_2Esptree_2Edelete_2E0 ) ) ) ) ) ) ) ).

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