%------------------------------------------------------------------------------
% File     : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Archive of Formal Proofs
% Problem  :
% Version  : Especial.
% English  :

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : Separation_Logic_Unbounded/0001_Combinability/prob_00134_005566__6584380_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 2231 ( 299 unt; 954 typ;   0 def)
%            Number of atoms       : 4930 (1044 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives : 19783 ( 546   ~;  58   |; 325   &;16174   @)
%                                         (   0 <=>;2680  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (  10 avg)
%            Number of types       :  191 ( 190 usr)
%            Number of type conns  : 2441 (2441   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  767 ( 764 usr; 138 con; 0-7 aty)
%            Number of variables   : 4787 (  77   ^;4554   !; 156   ?;4787   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 16:04:41.164
%------------------------------------------------------------------------------
% Could-be-implicit typings (190)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J_J,type,
    set_Pr4654484256145968327at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
    produc5052769453400272615at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J_J,type,
    set_Pr1064757066610246855at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
    produc1903999119065525479at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_J_J,type,
    set_Pr6429226126823767239od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_J,type,
    produc467843052564343527od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr4375867511396588897at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J_J,type,
    set_Pr8186174039193902343od_a_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc8039618346972058113at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
    produc8300268311522786087od_a_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr6894797015334228705at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J_J,type,
    set_Pr3075999220293227143od_a_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc3003658523197049473at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
    produc4846567752052077479od_a_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr8072821036331221345at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_J_J,type,
    set_Pr3057449061824239751od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
    set_Pr7459493094073627847at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J_J,type,
    set_Pr4049313843747668231od_a_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc3355805666032155649at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    set_Pr1292856356524837895od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_J,type,
    produc7738053905463721127od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    produc1319942482725812455at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
    produc2232466541489530151od_a_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc1960492347614157607od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr5564308138774400199at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
    set_Pr4391781608169641287at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc1906917888121415911at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    produc5306847434115292263at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr5297940549829899463at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    set_Pr2036461669354544199od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr4427867301352232263at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_J,type,
    set_Pr5368513128717298887od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc6487378988399798503at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr6357112501083536723at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr2070915713504248735at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr8921550766394648263at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    produc684523539999456103od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc266773502759220327at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    produc8963987812249958119od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc7900197031719409907at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc8421973624431248703at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_J_J,type,
    set_Pr2690992919715838407_nat_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr6149578361169461959_o_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr8788114079658965319at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc6206612473762214375at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr6274769524298744783_o_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr6710357650329316159at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr3469353857373938623at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    set_Pr1013884327308616903od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_J,type,
    produc7457699637131276519_nat_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    produc7379504648073755111_o_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc743030839026790503at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_J_J,type,
    set_Pr6689048260218027963_nat_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr2083485662371163247_o_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    produc1534263882305827951_o_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc2213792681670464479at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc4017409457303293023at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J_J,type,
    set_Pr9196163270038067219um_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_J_J,type,
    set_Pr7959180466389761223_nat_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr6004696033780540487_o_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_J_J,type,
    set_Pr7661140670241666375_nat_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr5706656237632445639_o_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr4168889959610442875at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    produc2245965095621756647od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_J,type,
    produc1771412367706247771_nat_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    produc3814013152794810639_o_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    set_Pr8269993260027997383od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J,type,
    produc6322778544207219763um_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_J,type,
    produc6880771863443770087_nat_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    produc2801964973402174055_o_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_J,type,
    produc3198298408749073255_nat_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    produc8342863555562253031_o_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc5153585639972752539at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J_J,type,
    set_Pr4885524344002532491um_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J_J,type,
    set_Pr6890301357480955147um_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_J_J,type,
    set_Pr1345543789004997635_nat_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr8614431393250552707_o_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    produc6176228915706226407od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J,type,
    produc5291834824148674091um_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J,type,
    produc5855907259854397099um_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_J,type,
    produc4474022258528981411_nat_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    produc395215368487385379_o_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J_J,type,
    set_Pr9037604441019230663um_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr1627845231345427177at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr8695894162071895333at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J,type,
    produc5974065977577044711um_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc8434689566910009353at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc3770297804798658629at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    set_Pr2990377294110839183od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr8020157162464038753at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr2243238557815556065at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc6629909188158935855od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc8156772699570739713at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc299292417334301313at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    set_Pr6419213211702811143od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    set_Pr5192616823003386503od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr308927743835700381at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr8044876533244767088at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mtf__a_J_J,type,
    set_Pr7219508552201550942_nat_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr1604112560894399303at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc696920298598856999od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc5450868540414226855od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc6319085873323607741at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    set_Pr5465339146700379459od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_op989438649584373901at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc656436880464960016at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mtf__a_J,type,
    produc6627350631851327998_nat_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr1968968238647823434at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mtf__a_J_J,type,
    set_Pr5256879730163711364_nat_a: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_se5479201105039950375at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc7299876168958306407at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc3217940817873794019od_o_o: $tType ).

thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    option8699557107911914541at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_op7555165197759865831at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc3842678439083338090at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mtf__a_J,type,
    produc6136831119191938980_nat_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    set_Pr5975447109543910128od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr4329608150637261639at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mtf__a_J_J,type,
    set_Pr6196119011418371550_o_o_a: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_se5885513654436145793at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    set_Pr7077720281583819975od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_J_J,type,
    set_Pr1275464188344874039_a_c_d: $tType ).

thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    option7754883786268931591at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr4231629511564852513at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J_J,type,
    set_Pr9037244641242167277od_a_a: $tType ).

thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    set_op3605315081486705933od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    produc931656912218737808od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc3843707927480180839at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mtf__a_J,type,
    produc6136140800252116606_o_o_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    set_Pr8055703017043224813od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr457366540195662369at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    set_se9147984907235033255od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    produc7004997421203748071od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_J,type,
    produc5278197477302038359_a_c_d: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J_J,type,
    set_Pr5931134355633282247od_a_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc2304671794888584641at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
    produc721097834699853453od_a_a: $tType ).

thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    option8293164206536526765od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    set_Pr4819730946363549639od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_Pr8693737435421807431at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc7898102162437433997od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc732395585841259969at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    set_Pr1932065953672099015od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_Pr1076074158304066111at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
    produc7983190928304305895od_a_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc5781518669219163367od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc859450856879609959at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J,type,
    set_Pr1799381062826258619_nat_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J,type,
    set_Pr6607724941775425903_o_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc2934264451710624999od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J,type,
    set_Pr5101254089914283719_nat_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J,type,
    set_Pr63822404152778311_o_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    set_Pr7011910401827753159od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J,type,
    set_Pr2429666174773179787um_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    produc4465838814804890855od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_se5158245632345848097at_nat: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    option8963830502488799655at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__a_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    set_Pr5845495582615845127_set_a: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_se7855581050983116737at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    set_se5342866143169225671od_o_o: $tType ).

thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
    option6413918287372586467_a_c_d: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    option956769437226787789od_o_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_Mt__Set__Oset_Itf__a_J_J,type,
    produc1703568184450464039_set_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_Pr1261947904930325089at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    set_se491199571785101031od_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_Sum_sum_nat_nat: $tType ).

thf(ty_n_t__UnboundedLogic__Oassertion_Itf__a_Mtf__b_Mtf__d_Mtf__c_J,type,
    assertion_a_b_d_c: $tType ).

thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J,type,
    set_Sum_sum_nat_o: $tType ).

thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J,type,
    set_Sum_sum_o_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
    set_Product_prod_a_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
    product_prod_a_c_d: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    product_prod_nat_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    set_Product_prod_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Nat__Onat_J_J,type,
    set_option_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_I_Eo_M_Eo_J_J,type,
    set_Sum_sum_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
    set_option_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
    product_prod_a_a: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
    set_set_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    product_prod_o_o: $tType ).

thf(ty_n_t__Option__Ooption_It__Nat__Onat_J,type,
    option_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
    set_nat: $tType ).

thf(ty_n_t__Option__Ooption_Itf__a_J,type,
    option_a: $tType ).

thf(ty_n_t__Set__Oset_Itf__c_J,type,
    set_c: $tType ).

thf(ty_n_t__Set__Oset_Itf__a_J,type,
    set_a: $tType ).

thf(ty_n_t__Set__Oset_I_Eo_J,type,
    set_o: $tType ).

thf(ty_n_t__Nat__Onat,type,
    nat: $tType ).

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

thf(ty_n_tf__c,type,
    c: $tType ).

thf(ty_n_tf__b,type,
    b: $tType ).

thf(ty_n_tf__a,type,
    a: $tType ).

% Explicit typings (764)
thf(sy_c_BNF__Cardinal__Arithmetic_Ocprod_001_Eo_001_Eo,type,
    bNF_Ca8659498892590988930od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Pr7011910401827753159od_o_o ).

thf(sy_c_BNF__Cardinal__Arithmetic_Ocprod_001_Eo_001t__Nat__Onat,type,
    bNF_Ca669077093115854694_o_nat: set_Product_prod_o_o > set_Pr1261947904930325089at_nat > set_Pr6607724941775425903_o_nat ).

thf(sy_c_BNF__Cardinal__Arithmetic_Ocprod_001t__Nat__Onat_001_Eo,type,
    bNF_Ca3771748454224040004_nat_o: set_Pr1261947904930325089at_nat > set_Product_prod_o_o > set_Pr1799381062826258619_nat_o ).

thf(sy_c_BNF__Cardinal__Arithmetic_Ocprod_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_Ca5918273672090100260at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).

thf(sy_c_BNF__Cardinal__Arithmetic_Octwo,type,
    bNF_Cardinal_ctwo: set_Product_prod_o_o ).

thf(sy_c_BNF__Cardinal__Arithmetic_Oczero_001_Eo,type,
    bNF_Cardinal_czero_o: set_Product_prod_o_o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001_Eo,type,
    bNF_Ca3172636760949973492d_of_o: set_o > set_Product_prod_o_o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Nat__Onat,type,
    bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    bNF_Ca6121500631330824515od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_Ca8664924986033767453at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_Ca9194600574093320387at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Sum____Type__Osum_I_Eo_M_Eo_J,type,
    bNF_Ca5391278176305430217um_o_o: set_Sum_sum_o_o > set_Pr2429666174773179787um_o_o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J,type,
    bNF_Ca1325121287712659829_o_nat: set_Sum_sum_o_nat > set_Pr63822404152778311_o_nat ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J,type,
    bNF_Ca4833655811768152859_nat_o: set_Sum_sum_nat_o > set_Pr5101254089914283719_nat_o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_Ca786952496063569315at_nat: set_Sum_sum_nat_nat > set_Pr1076074158304066111at_nat ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001tf__a,type,
    bNF_Ca1104715389982341978d_of_a: set_a > set_Product_prod_a_a ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001_Eo,type,
    bNF_Ca8331644756375544342r_on_o: set_o > set_Product_prod_o_o > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001t__Nat__Onat,type,
    bNF_Ca1281551314933786834on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    bNF_Ca4198200952365436517od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_Ca7438713789483989055at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_Ca8230877790521596901at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_Ca4526578624105657733od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_Ca4062989147270679263at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001tf__a,type,
    bNF_Ca453948448923306620r_on_a: set_a > set_Product_prod_a_a > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocofinal_001_Eo,type,
    bNF_Ca4363140458462388713inal_o: set_o > set_Product_prod_o_o > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocofinal_001t__Nat__Onat,type,
    bNF_Ca5159621140400407487al_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocofinal_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_Ca3407573850950408152od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_Ocofinal_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_Ca8448034394003515314at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_BNF__Cardinal__Order__Relation_OnatLeq,type,
    bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OfromCard_001_Eo_001_Eo,type,
    bNF_Gr5731841836078664636rd_o_o: set_o > set_Product_prod_o_o > $o > $o ).

thf(sy_c_BNF__Greatest__Fixpoint_OfromCard_001_Eo_001t__Nat__Onat,type,
    bNF_Gr6736587135095141548_o_nat: set_o > set_Pr1261947904930325089at_nat > nat > $o ).

thf(sy_c_BNF__Greatest__Fixpoint_OfromCard_001t__Nat__Onat_001_Eo,type,
    bNF_Gr615886459348551050_nat_o: set_nat > set_Product_prod_o_o > $o > nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OfromCard_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_Gr6953169559552526942at_nat: set_nat > set_Pr1261947904930325089at_nat > nat > nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OfromCard_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001_Eo,type,
    bNF_Gr3541370040355373357_o_o_o: set_Pr1932065953672099015od_o_o > set_Product_prod_o_o > $o > produc2934264451710624999od_o_o ).

thf(sy_c_BNF__Greatest__Fixpoint_OfromCard_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Nat__Onat,type,
    bNF_Gr6179234852794809723_o_nat: set_Pr1932065953672099015od_o_o > set_Pr1261947904930325089at_nat > nat > produc2934264451710624999od_o_o ).

thf(sy_c_BNF__Greatest__Fixpoint_OfromCard_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
    bNF_Gr6550272361737169109at_nat: set_Pr457366540195662369at_nat > set_Pr1261947904930325089at_nat > nat > produc732395585841259969at_nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OfromCard_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
    bNF_Gr2810406598121987579at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > nat > produc3843707927480180839at_nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OfromCard_001tf__a_001_Eo,type,
    bNF_Gr1283079227033720918rd_a_o: set_a > set_Product_prod_o_o > $o > a ).

thf(sy_c_BNF__Greatest__Fixpoint_OfromCard_001tf__a_001t__Nat__Onat,type,
    bNF_Gr4132913802490790546_a_nat: set_a > set_Pr1261947904930325089at_nat > nat > a ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_Gr1939940824387609677od_o_o: set_Pr1932065953672099015od_o_o > ( produc2934264451710624999od_o_o > set_Product_prod_o_o ) > ( produc2934264451710624999od_o_o > set_Product_prod_o_o ) > set_Pr1932065953672099015od_o_o ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_Gr9251090155517351at_nat: set_Pr1932065953672099015od_o_o > ( produc2934264451710624999od_o_o > set_Product_prod_o_o ) > ( produc2934264451710624999od_o_o > set_Pr1261947904930325089at_nat ) > set_Pr457366540195662369at_nat ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_Gr3579140021203399117at_nat: set_Pr1932065953672099015od_o_o > ( produc2934264451710624999od_o_o > set_Pr1261947904930325089at_nat ) > ( produc2934264451710624999od_o_o > set_Pr1261947904930325089at_nat ) > set_Pr4329608150637261639at_nat ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_Gr4234126200300082471od_o_o: set_Pr457366540195662369at_nat > ( produc732395585841259969at_nat > set_Product_prod_o_o ) > ( produc732395585841259969at_nat > set_Product_prod_o_o ) > set_Pr1932065953672099015od_o_o ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_Gr3107587960415891841at_nat: set_Pr457366540195662369at_nat > ( produc732395585841259969at_nat > set_Product_prod_o_o ) > ( produc732395585841259969at_nat > set_Pr1261947904930325089at_nat ) > set_Pr457366540195662369at_nat ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_Gr325834636694211021od_o_o: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_Product_prod_o_o ) > ( produc3843707927480180839at_nat > set_Product_prod_o_o ) > set_Pr1932065953672099015od_o_o ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_Gr6396972118715063079at_nat: set_Pr4329608150637261639at_nat > ( produc3843707927480180839at_nat > set_Product_prod_o_o ) > ( produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ) > set_Pr457366540195662369at_nat ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001tf__a_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_Gr7634195438189357284od_o_o: set_a > ( a > set_Product_prod_o_o ) > ( a > set_Product_prod_o_o ) > set_Pr1932065953672099015od_o_o ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001tf__a_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_Gr4130978120127398590at_nat: set_a > ( a > set_Product_prod_o_o ) > ( a > set_Pr1261947904930325089at_nat ) > set_Pr457366540195662369at_nat ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001tf__a_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_Gr3725372617274885988at_nat: set_a > ( a > set_Pr1261947904930325089at_nat ) > ( a > set_Pr1261947904930325089at_nat ) > set_Pr4329608150637261639at_nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard_001_Eo_001_Eo,type,
    bNF_Gr748490023993654765rd_o_o: set_o > set_Product_prod_o_o > $o > $o ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard_001_Eo_001t__Nat__Onat,type,
    bNF_Gr1235702096034787515_o_nat: set_o > set_Pr1261947904930325089at_nat > $o > nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard_001t__Nat__Onat_001_Eo,type,
    bNF_Gr4338373457142972825_nat_o: set_nat > set_Product_prod_o_o > nat > $o ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_Gr5321390424033619983at_nat: set_nat > set_Pr1261947904930325089at_nat > nat > nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001_Eo,type,
    bNF_Gr1716226591470254558_o_o_o: set_Pr1932065953672099015od_o_o > set_Product_prod_o_o > produc2934264451710624999od_o_o > $o ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Nat__Onat,type,
    bNF_Gr2687907518133588746_o_nat: set_Pr1932065953672099015od_o_o > set_Pr1261947904930325089at_nat > produc2934264451710624999od_o_o > nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
    bNF_Gr859799933468256996at_nat: set_Pr457366540195662369at_nat > set_Pr1261947904930325089at_nat > produc732395585841259969at_nat > nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
    bNF_Gr8319706499545975946at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat > nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard_001tf__a_001_Eo,type,
    bNF_Gr3684918198958735879rd_a_o: set_a > set_Product_prod_o_o > a > $o ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard_001tf__a_001t__Nat__Onat,type,
    bNF_Gr1543889757740115745_a_nat: set_a > set_Pr1261947904930325089at_nat > a > nat ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard__pred_001_Eo_001_Eo,type,
    bNF_Gr3194703283472089838ed_o_o: set_o > set_Product_prod_o_o > ( $o > $o ) > $o ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard__pred_001_Eo_001t__Nat__Onat,type,
    bNF_Gr988296774780055034_o_nat: set_o > set_Pr1261947904930325089at_nat > ( $o > nat ) > $o ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard__pred_001t__Nat__Onat_001_Eo,type,
    bNF_Gr4090968135888240344_nat_o: set_nat > set_Product_prod_o_o > ( nat > $o ) > $o ).

thf(sy_c_BNF__Greatest__Fixpoint_OtoCard__pred_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_Gr4367463400984379536at_nat: set_nat > set_Pr1261947904930325089at_nat > ( nat > nat ) > $o ).

thf(sy_c_BNF__Wellorder__Constructions_Obsqr_001_Eo,type,
    bNF_Wellorder_bsqr_o: set_Product_prod_o_o > set_Pr7011910401827753159od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_Obsqr_001t__Nat__Onat,type,
    bNF_We1732890022510290291qr_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_Obsqr_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_We3935152771354962724od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_Obsqr_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_We6127972852007642366at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001_Eo_001_Eo,type,
    bNF_We2654380646378065620so_o_o: set_Pr1932065953672099015od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001_Eo_001t__Nat__Onat,type,
    bNF_We4116350175183677332_o_nat: set_Pr457366540195662369at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Nat__Onat_001_Eo,type,
    bNF_We7219021536291862642_nat_o: set_Pr8055703017043224813od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    bNF_We3478797130297825300od_o_o: set_Pr8269993260027997383od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
    bNF_We2927691233937746154_o_nat: set_Pr2083485662371163247_o_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
    bNF_We6436225757993239184_nat_o: set_Pr6689048260218027963_nat_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We4425979316902024558at_nat: set_Pr8788114079658965319at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
    bNF_We2916028399495512580_o_nat: set_Pr6149578361169461959_o_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We5155846448255121108at_nat: set_Pr2070915713504248735at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
    bNF_We2682271528455076432_nat_o: set_Pr2690992919715838407_nat_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We7873800260583935406at_nat: set_Pr6357112501083536723at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We4319090096570846868at_nat: set_Pr5297940549829899463at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Sum____Type__Osum_I_Eo_M_Eo_J_001_Eo,type,
    bNF_We5455623833347018717_o_o_o: set_Pr5465339146700379459od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_001_Eo,type,
    bNF_We8455499808419870611_nat_o: set_Pr5192616823003386503od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    bNF_We1461007947729398933at_nat: set_Pr2243238557815556065at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_001_Eo,type,
    bNF_We7828181885127712877at_o_o: set_Pr6419213211702811143od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_001t__Nat__Onat,type,
    bNF_We5202279374879649339_o_nat: set_Pr8020157162464038753at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    bNF_We4717344193235055909at_nat: set_Pr1627845231345427177at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We3455965832816432340at_nat: set_Pr8921550766394648263at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001_Eo_001_Eo,type,
    bNF_We8115293805659342695eq_o_o: set_Pr1932065953672099015od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001_Eo_001t__Nat__Onat,type,
    bNF_We3435943820185352641_o_nat: set_Pr457366540195662369at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Nat__Onat_001_Eo,type,
    bNF_We6538615181293537951_nat_o: set_Pr8055703017043224813od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_We2031159114419172489at_nat: set_Pr4329608150637261639at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Nat__Onat_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We4444846861891280440at_nat: set_Pr8695894162071895333at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Nat__Onat_001tf__a,type,
    bNF_We8703263850440670853_nat_a: set_Pr9037244641242167277od_a_a ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    bNF_We5263191010062085543od_o_o: set_Pr8269993260027997383od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
    bNF_We5526594851599572503_o_nat: set_Pr2083485662371163247_o_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
    bNF_We9035129375655065533_nat_o: set_Pr6689048260218027963_nat_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We7027591586743403905at_nat: set_Pr8788114079658965319at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
    bNF_We5517640669336891927_o_nat: set_Pr6149578361169461959_o_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We1398974386449396097at_nat: set_Pr2070915713504248735at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
    bNF_We5283883798296455779_nat_o: set_Pr2690992919715838407_nat_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We4116928198778210395at_nat: set_Pr6357112501083536723at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We145940432564263207at_nat: set_Pr5297940549829899463at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001_Eo,type,
    bNF_We5212295730361461848_o_o_o: set_Pr1292856356524837895od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Nat__Onat,type,
    bNF_We7173072801150825232_o_nat: set_Pr8072821036331221345at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001tf__a,type,
    bNF_We8478588574694708158_o_o_a: set_Pr4049313843747668231od_a_a ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
    bNF_We8470213457150283754at_nat: set_Pr6894797015334228705at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    bNF_We6709918416631134564_nat_a: set_Pr3075999220293227143od_a_a ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
    bNF_We8384597595354199696at_nat: set_Pr4375867511396588897at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    bNF_We3386010043725180990_nat_a: set_Pr8186174039193902343od_a_a ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_M_Eo_J_001_Eo,type,
    bNF_We3513324756044439818_o_o_o: set_Pr5465339146700379459od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_M_Eo_J_001t__Nat__Onat,type,
    bNF_We3900823710022635230_o_nat: set_Pr308927743835700381at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_M_Eo_J_001t__Sum____Type__Osum_I_Eo_M_Eo_J,type,
    bNF_We8987810345020088115um_o_o: set_Pr9037604441019230663um_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_M_Eo_J_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J,type,
    bNF_We3854041083340105611_o_nat: set_Pr8614431393250552707_o_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_M_Eo_J_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J,type,
    bNF_We7362575607395598641_nat_o: set_Pr1345543789004997635_nat_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_M_Eo_J_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We1329699954732187917at_nat: set_Pr4168889959610442875at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_001_Eo,type,
    bNF_We8188024427803757478_nat_o: set_Pr5192616823003386503od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    bNF_We7395407223230661442at_nat: set_Pr2243238557815556065at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_001t__Sum____Type__Osum_I_Eo_M_Eo_J,type,
    bNF_We8976728017661452183um_o_o: set_Pr6890301357480955147um_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J,type,
    bNF_We8273322497166968871_o_nat: set_Pr5706656237632445639_o_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J,type,
    bNF_We2558484984367686093_nat_o: set_Pr7661140670241666375_nat_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We7431878391334027121at_nat: set_Pr3469353857373938623at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_001_Eo,type,
    bNF_We7560706504511599744at_o_o: set_Pr6419213211702811143od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_001t__Nat__Onat,type,
    bNF_We1913306613526136040_o_nat: set_Pr8020157162464038753at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_001t__Sum____Type__Osum_I_Eo_M_Eo_J,type,
    bNF_We1079009337437905725um_o_o: set_Pr4885524344002532491um_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J,type,
    bNF_We2094493454282013185_o_nat: set_Pr6004696033780540487_o_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J,type,
    bNF_We5603027978337506215_nat_o: set_Pr7959180466389761223_nat_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We295405470918883351at_nat: set_Pr6710357650329316159at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
    bNF_We6200507331307258288_nat_o: set_Pr2990377294110839183od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    bNF_We5086521355153908664at_nat: set_Pr1627845231345427177at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_001t__Sum____Type__Osum_I_Eo_M_Eo_J,type,
    bNF_We7217180388603359757um_o_o: set_Pr9196163270038067219um_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J,type,
    bNF_We7239028013353664305_o_nat: set_Pr6274769524298744783_o_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_We5082115074515246823at_nat: set_Pr8921550766394648263at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001tf__a_001_Eo,type,
    bNF_We2079833050348105345eq_a_o: set_Pr4819730946363549639od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001tf__a_001t__Nat__Onat,type,
    bNF_We4671332349262384423_a_nat: set_Pr4231629511564852513at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001tf__a_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    bNF_We9207374611879307856od_o_o: set_Pr3057449061824239751od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001tf__a_001tf__a,type,
    bNF_We6465643273610285415eq_a_a: set_Pr5931134355633282247od_a_a ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001_Eo_001_Eo,type,
    bNF_We2568191115274586186ss_o_o: set_Pr1932065953672099015od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001_Eo_001t__Nat__Onat,type,
    bNF_We8182288985678559134_o_nat: set_Pr457366540195662369at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Nat__Onat_001_Eo,type,
    bNF_We2061588309931968636_nat_o: set_Pr8055703017043224813od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_We3448473429330749420at_nat: set_Pr4329608150637261639at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    bNF_We9142809693765176714od_o_o: set_Pr6429226126823767239od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We1318246335796365322at_nat: set_Pr1064757066610246855at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We2594139806602030986at_nat: set_Pr4654484256145968327at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Sum____Type__Osum_I_Eo_M_Eo_J_001_Eo,type,
    bNF_We7847786823715778023_o_o_o: set_Pr5465339146700379459od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Sum____Type__Osum_I_Eo_M_Eo_J_001t__Nat__Onat,type,
    bNF_We7066948511106741057_o_nat: set_Pr308927743835700381at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_001_Eo,type,
    bNF_We2130777192033087497_nat_o: set_Pr5192616823003386503od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    bNF_We1194315142955236767at_nat: set_Pr2243238557815556065at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_001_Eo,type,
    bNF_We1503459268740929763at_o_o: set_Pr6419213211702811143od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_001t__Nat__Onat,type,
    bNF_We4935586570105487173_o_nat: set_Pr8020157162464038753at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
    bNF_We9222787287886609421_nat_o: set_Pr2990377294110839183od_o_o ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    bNF_We7041958966232365723at_nat: set_Pr1627845231345427177at_nat ).

thf(sy_c_BNF__Wellorder__Constructions_OordLess_001tf__a_001tf__a,type,
    bNF_We3281422121813167946ss_a_a: set_Pr5931134355633282247od_a_a ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001_Eo,type,
    bNF_We6437023980930612612_rel_o: set_Product_prod_o_o > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Nat__Onat,type,
    bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    bNF_We8581212502267700435od_o_o: set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We1688423684019388333at_nat: set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We4027175587370390611at_nat: set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_We6243063140137587187od_o_o: set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_We5602466822260561997at_nat: set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001tf__a,type,
    bNF_We1162827675446709994_rel_a: set_Product_prod_a_a > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    bNF_We6886001019485585053od_o_o: set_Pr1013884327308616903od_o_o > set_Pr1932065953672099015od_o_o > produc2934264451710624999od_o_o > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We6170040095471856759at_nat: set_Pr4427867301352232263at_nat > set_Pr457366540195662369at_nat > produc732395585841259969at_nat > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We2939539520719410205at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_We794377122088811965od_o_o: set_Pr1932065953672099015od_o_o > set_se491199571785101031od_o_o > set_Product_prod_o_o > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_We943883530777384727at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001tf__a,type,
    bNF_We6697304935525757620inim_a: set_Product_prod_a_a > set_a > a > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001_Eo,type,
    bNF_We3104086342435940326max2_o: set_Product_prod_o_o > $o > $o > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001t__Nat__Onat,type,
    bNF_We2380939065524664066x2_nat: set_Pr1261947904930325089at_nat > nat > nat > nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    bNF_We5307229915971165237od_o_o: set_Pr1013884327308616903od_o_o > produc2934264451710624999od_o_o > produc2934264451710624999od_o_o > produc2934264451710624999od_o_o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We7253295970193759759at_nat: set_Pr4427867301352232263at_nat > produc732395585841259969at_nat > produc732395585841259969at_nat > produc732395585841259969at_nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We1807050579049552309at_nat: set_Pr5564308138774400199at_nat > produc3843707927480180839at_nat > produc3843707927480180839at_nat > produc3843707927480180839at_nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_We9141258785624724309od_o_o: set_Pr1932065953672099015od_o_o > set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_We6094461251688579247at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001tf__a,type,
    bNF_We3763454674811381836max2_a: set_Product_prod_a_a > a > a > a ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001_Eo,type,
    bNF_We537455116209922916inim_o: set_Product_prod_o_o > set_o > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001t__Nat__Onat,type,
    bNF_We3275124272252294916im_nat: set_Pr1261947904930325089at_nat > set_nat > nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    bNF_We4719373430050929331od_o_o: set_Pr1013884327308616903od_o_o > set_Pr1932065953672099015od_o_o > produc2934264451710624999od_o_o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We6249471513304245645at_nat: set_Pr4427867301352232263at_nat > set_Pr457366540195662369at_nat > produc732395585841259969at_nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We7473068394052389427at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_We6151898823597705171od_o_o: set_Pr1932065953672099015od_o_o > set_se491199571785101031od_o_o > set_Product_prod_o_o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_We6832956061294468653at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001tf__a,type,
    bNF_We5615626441682584778inim_a: set_Product_prod_a_a > set_a > a ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osuc_001_Eo,type,
    bNF_We8594000642646999417_suc_o: set_Product_prod_o_o > set_o > $o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osuc_001t__Nat__Onat,type,
    bNF_We6243639482952820783uc_nat: set_Pr1261947904930325089at_nat > set_nat > nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osuc_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    bNF_We7386194254115604808od_o_o: set_Pr1013884327308616903od_o_o > set_Pr1932065953672099015od_o_o > produc2934264451710624999od_o_o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osuc_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We5419384366696408482at_nat: set_Pr4427867301352232263at_nat > set_Pr457366540195662369at_nat > produc732395585841259969at_nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osuc_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bNF_We2397293392365222856at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osuc_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bNF_We1257987224342916968od_o_o: set_Pr1932065953672099015od_o_o > set_se491199571785101031od_o_o > set_Product_prod_o_o ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osuc_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_We3445218718054152002at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osuc_001tf__a,type,
    bNF_We6154283375207884895_suc_a: set_Product_prod_a_a > set_a > a ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    basic_3307925540671692871od_o_o: produc2934264451710624999od_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    basic_3533134110227475617at_nat: produc732395585841259969at_nat > set_se491199571785101031od_o_o ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    basic_3661821009137050567at_nat: produc3843707927480180839at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Basic__BNFs_Osnds_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    basic_2174982398181630341od_o_o: produc2934264451710624999od_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Basic__BNFs_Osnds_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    basic_7607750056555722463at_nat: produc732395585841259969at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Basic__BNFs_Osnds_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    basic_484852565060450053at_nat: produc3843707927480180839at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Combinability_Ologic_Ocombinable_001tf__a_001tf__b_001tf__c_001tf__d,type,
    combinable_a_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( b > b > b ) > ( a > $o ) > ( ( c > d ) > set_a ) > assertion_a_b_d_c > $o ).

thf(sy_c_Equiv__Relations_Oequiv_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    equiv_3398664326906728093od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_Equiv__Relations_Oequiv_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    equiv_2520666332425567351at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_Equiv__Relations_Oequiv_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    equiv_4443766944827089949at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_Equiv__Relations_Oequiv_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    equiv_4332955795722587581od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Equiv__Relations_Oequiv_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    equiv_6458487239543531287at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Equiv__Relations_Oequiv_001tf__a,type,
    equiv_equiv_a: set_a > set_Product_prod_a_a > $o ).

thf(sy_c_Equiv__Relations_Oproj_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    equiv_6719278489894859850od_o_o: set_Pr1932065953672099015od_o_o > set_Product_prod_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Equiv__Relations_Oproj_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    equiv_4785085088318667978at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Equiv__Relations_Oquotient_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    equiv_1831625524721748142od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o > set_se9147984907235033255od_o_o ).

thf(sy_c_Equiv__Relations_Oquotient_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    equiv_2323626691971332616at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat > set_se5885513654436145793at_nat ).

thf(sy_c_Equiv__Relations_Oquotient_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    equiv_8408515162552411438at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > set_se5479201105039950375at_nat ).

thf(sy_c_Equiv__Relations_Oquotient_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    equiv_3134926782319234254od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > set_se5342866143169225671od_o_o ).

thf(sy_c_Equiv__Relations_Oquotient_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    equiv_7923377459618294184at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > set_se5158245632345848097at_nat ).

thf(sy_c_Equiv__Relations_Oquotient_001tf__a,type,
    equiv_quotient_a: set_a > set_Product_prod_a_a > set_set_a ).

thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
    finite_finite_o: set_o > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
    finite_finite_nat: set_nat > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Nat__Onat_J,type,
    finite5523153139673422903on_nat: set_option_nat > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__a_J,type,
    finite1674126218327898605tion_a: set_option_a > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    finite6120865539452801872od_o_o: set_Product_prod_o_o > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    finite820925532130942480od_o_o: set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    finite8072506237346428522at_nat: set_Pr457366540195662369at_nat > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    finite4343798906461161616at_nat: set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    finite9011636195296603184od_o_o: set_se491199571785101031od_o_o > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    finite9047747110432174090at_nat: set_se7855581050983116737at_nat > $o ).

thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
    finite_finite_a: set_a > $o ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_Itf__a_J_001tf__a_001tf__a,type,
    comp_option_a_a_a: ( option_a > a ) > ( a > option_a ) > a > a ).

thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_Itf__a_J,type,
    fun_upd_nat_option_a: ( nat > option_a ) > nat > option_a > nat > option_a ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Option__Ooption_Itf__a_J,type,
    fun_up7252388491999432090tion_a: ( produc2934264451710624999od_o_o > option_a ) > produc2934264451710624999od_o_o > option_a > produc2934264451710624999od_o_o > option_a ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_Itf__a_J,type,
    fun_up564627978254483264tion_a: ( produc732395585841259969at_nat > option_a ) > produc732395585841259969at_nat > option_a > produc732395585841259969at_nat > option_a ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_Itf__a_J,type,
    fun_up7579534627831735322tion_a: ( produc3843707927480180839at_nat > option_a ) > produc3843707927480180839at_nat > option_a > produc3843707927480180839at_nat > option_a ).

thf(sy_c_Fun_Ofun__upd_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    fun_up3230021793924660483od_o_o: ( set_Product_prod_o_o > option956769437226787789od_o_o ) > set_Product_prod_o_o > option956769437226787789od_o_o > set_Product_prod_o_o > option956769437226787789od_o_o ).

thf(sy_c_Fun_Ofun__upd_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_up3688893386320429021at_nat: ( set_Product_prod_o_o > option8963830502488799655at_nat ) > set_Product_prod_o_o > option8963830502488799655at_nat > set_Product_prod_o_o > option8963830502488799655at_nat ).

thf(sy_c_Fun_Ofun__upd_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_up1071884767227745027at_nat: ( set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ) > set_Pr1261947904930325089at_nat > option8963830502488799655at_nat > set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).

thf(sy_c_Fun_Ofun__upd_001tf__a_001t__Option__Ooption_Itf__a_J,type,
    fun_upd_a_option_a: ( a > option_a ) > a > option_a > a > option_a ).

thf(sy_c_Fun_Ofun__upd_001tf__c_001tf__d,type,
    fun_upd_c_d: ( c > d ) > c > d > c > d ).

thf(sy_c_Fun_Oid_001tf__a,type,
    id_a: a > a ).

thf(sy_c_Fun_Oinj__on_001_Eo_001_Eo,type,
    inj_on_o_o: ( $o > $o ) > set_o > $o ).

thf(sy_c_Fun_Oinj__on_001_Eo_001t__Nat__Onat,type,
    inj_on_o_nat: ( $o > nat ) > set_o > $o ).

thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001_Eo,type,
    inj_on_nat_o: ( nat > $o ) > set_nat > $o ).

thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
    inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).

thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001tf__a,type,
    inj_on_nat_a: ( nat > a ) > set_nat > $o ).

thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001tf__a,type,
    inj_on8505222220193863496_o_o_a: ( produc2934264451710624999od_o_o > a ) > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    inj_on258112795223470062_nat_a: ( produc732395585841259969at_nat > a ) > set_Pr457366540195662369at_nat > $o ).

thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    inj_on258414713793403336_nat_a: ( produc3843707927480180839at_nat > a ) > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Fun_Oinj__on_001tf__a_001t__Nat__Onat,type,
    inj_on_a_nat: ( a > nat ) > set_a > $o ).

thf(sy_c_Fun_Oinj__on_001tf__a_001t__Option__Ooption_Itf__a_J,type,
    inj_on_a_option_a: ( a > option_a ) > set_a > $o ).

thf(sy_c_Fun_Oinj__on_001tf__a_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    inj_on10636220523687386od_o_o: ( a > produc2934264451710624999od_o_o ) > set_a > $o ).

thf(sy_c_Fun_Oinj__on_001tf__a_001tf__a,type,
    inj_on_a_a: ( a > a ) > set_a > $o ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    minus_7052513330764642158od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    minus_5063024033727795502od_o_o: set_Pr1013884327308616903od_o_o > set_Pr1013884327308616903od_o_o > set_Pr1013884327308616903od_o_o ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    minus_2318593706003940014at_nat: set_Pr4427867301352232263at_nat > set_Pr4427867301352232263at_nat > set_Pr4427867301352232263at_nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    minus_8235382265540049710at_nat: set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    minus_5704166846132356910od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    minus_1608234471674494216at_nat: set_Pr457366540195662369at_nat > set_Pr457366540195662369at_nat > set_Pr457366540195662369at_nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    minus_3314409938677909166at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
    minus_6817036919807184750od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J,type,
    minus_minus_set_a: set_a > set_a > set_a ).

thf(sy_c_If_001t__Option__Ooption_Itf__a_J,type,
    if_option_a: $o > option_a > option_a > option_a ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    inf_in6630186493572433077od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    inf_in3075509010647812879at_nat: set_Pr457366540195662369at_nat > set_Pr457366540195662369at_nat > set_Pr457366540195662369at_nat ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    inf_in8747346010413679829od_o_o: set_se491199571785101031od_o_o > set_se491199571785101031od_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    inf_in767997467307849391at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
    inf_inf_set_a: set_a > set_a > set_a ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_Eo_J,type,
    sup_sup_set_o: set_o > set_o > set_o ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
    sup_sup_set_nat: set_nat > set_nat > set_nat ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    sup_su5769328420594410459od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    sup_su4078869789063261851od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    sup_su1477959037604056251od_o_o: set_se491199571785101031od_o_o > set_se491199571785101031od_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    sup_su3642409539654194069at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Map_Odom_001t__Nat__Onat_001tf__a,type,
    dom_nat_a: ( nat > option_a ) > set_nat ).

thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001tf__a,type,
    dom_Pr3509670420972068777_o_o_a: ( produc2934264451710624999od_o_o > option_a ) > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    dom_Pr8042991038213739471_nat_a: ( produc732395585841259969at_nat > option_a ) > set_Pr457366540195662369at_nat ).

thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    dom_Pr1957410074072848681_nat_a: ( produc3843707927480180839at_nat > option_a ) > set_Pr4329608150637261639at_nat ).

thf(sy_c_Map_Odom_001tf__a_001tf__a,type,
    dom_a_a: ( a > option_a ) > set_a ).

thf(sy_c_Map_Ograph_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    graph_5719763352399009470od_o_o: ( set_Product_prod_o_o > option956769437226787789od_o_o ) > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Map_Ograph_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    graph_2163970799110208408at_nat: ( set_Product_prod_o_o > option8963830502488799655at_nat ) > set_Pr457366540195662369at_nat ).

thf(sy_c_Map_Ograph_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    graph_2380648924068268862at_nat: ( set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ) > set_Pr4329608150637261639at_nat ).

thf(sy_c_Map_Omap__add_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001tf__a,type,
    map_ad9054432547132481292_o_o_a: ( produc2934264451710624999od_o_o > option_a ) > ( produc2934264451710624999od_o_o > option_a ) > produc2934264451710624999od_o_o > option_a ).

thf(sy_c_Map_Omap__add_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    map_ad4947507604491699634_nat_a: ( produc732395585841259969at_nat > option_a ) > ( produc732395585841259969at_nat > option_a ) > produc732395585841259969at_nat > option_a ).

thf(sy_c_Map_Omap__add_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    map_ad6003791139528408460_nat_a: ( produc3843707927480180839at_nat > option_a ) > ( produc3843707927480180839at_nat > option_a ) > produc3843707927480180839at_nat > option_a ).

thf(sy_c_Map_Omap__add_001tf__a_001tf__a,type,
    map_add_a_a: ( a > option_a ) > ( a > option_a ) > a > option_a ).

thf(sy_c_Map_Orestrict__map_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001tf__a,type,
    restri4233077244345833607_o_o_a: ( produc2934264451710624999od_o_o > option_a ) > set_Pr1932065953672099015od_o_o > produc2934264451710624999od_o_o > option_a ).

thf(sy_c_Map_Orestrict__map_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    restri896928924502181293_nat_a: ( produc732395585841259969at_nat > option_a ) > set_Pr457366540195662369at_nat > produc732395585841259969at_nat > option_a ).

thf(sy_c_Map_Orestrict__map_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    restri4040463761431659527_nat_a: ( produc3843707927480180839at_nat > option_a ) > set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat > option_a ).

thf(sy_c_Map_Orestrict__map_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    restri2278710580326071152od_o_o: ( set_Product_prod_o_o > option956769437226787789od_o_o ) > set_se491199571785101031od_o_o > set_Product_prod_o_o > option956769437226787789od_o_o ).

thf(sy_c_Map_Orestrict__map_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    restri2174721201111129930at_nat: ( set_Product_prod_o_o > option8963830502488799655at_nat ) > set_se491199571785101031od_o_o > set_Product_prod_o_o > option8963830502488799655at_nat ).

thf(sy_c_Map_Orestrict__map_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    restri512981303736921584at_nat: ( set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ) > set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).

thf(sy_c_Map_Orestrict__map_001tf__a_001tf__a,type,
    restrict_map_a_a: ( a > option_a ) > set_a > a > option_a ).

thf(sy_c_Option_Obind_001tf__a_001tf__a,type,
    bind_a_a: option_a > ( a > option_a ) > option_a ).

thf(sy_c_Option_Ois__none_001tf__a,type,
    is_none_a: option_a > $o ).

thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
    none_nat: option_nat ).

thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    none_P8254367833036352840od_o_o: option8293164206536526765od_o_o ).

thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    none_P5828533823149705634at_nat: option7754883786268931591at_nat ).

thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    none_P5811896708078067656at_nat: option8699557107911914541at_nat ).

thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    none_s7246968996079588200od_o_o: option956769437226787789od_o_o ).

thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    none_s625347054029921090at_nat: option8963830502488799655at_nat ).

thf(sy_c_Option_Ooption_ONone_001tf__a,type,
    none_a: option_a ).

thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
    some_nat: nat > option_nat ).

thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    some_P7068320699308846284od_o_o: produc2934264451710624999od_o_o > option8293164206536526765od_o_o ).

thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    some_P123625206269196070at_nat: produc732395585841259969at_nat > option7754883786268931591at_nat ).

thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    some_P131194445498448716at_nat: produc3843707927480180839at_nat > option8699557107911914541at_nat ).

thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J,type,
    some_P1084500821511757806_a_c_d: product_prod_a_c_d > option6413918287372586467_a_c_d ).

thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    some_s1360601300120069868od_o_o: set_Product_prod_o_o > option956769437226787789od_o_o ).

thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    some_s147305329494351046at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).

thf(sy_c_Option_Ooption_OSome_001tf__a,type,
    some_a: a > option_a ).

thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    map_op2750206784353119307od_o_o: ( produc2934264451710624999od_o_o > produc2934264451710624999od_o_o ) > option8293164206536526765od_o_o > option8293164206536526765od_o_o ).

thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    map_op8542782130795478475at_nat: ( produc732395585841259969at_nat > produc732395585841259969at_nat ) > option7754883786268931591at_nat > option7754883786268931591at_nat ).

thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    map_op4646528093940530251at_nat: ( produc3843707927480180839at_nat > produc3843707927480180839at_nat ) > option8699557107911914541at_nat > option8699557107911914541at_nat ).

thf(sy_c_Option_Ooption_Omap__option_001tf__a_001tf__a,type,
    map_option_a_a: ( a > a ) > option_a > option_a ).

thf(sy_c_Option_Ooption_Oset__option_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    set_op3337521775309186165od_o_o: option8293164206536526765od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Option_Ooption_Oset__option_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_op8338180575893423695at_nat: option7754883786268931591at_nat > set_Pr457366540195662369at_nat ).

thf(sy_c_Option_Ooption_Oset__option_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_op5866586666149159413at_nat: option8699557107911914541at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Option_Ooption_Oset__option_001tf__a,type,
    set_option_a2: option_a > set_a ).

thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    the_Pr7254245475272632699od_o_o: option8293164206536526765od_o_o > produc2934264451710624999od_o_o ).

thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    the_Pr9097376869753557077at_nat: option7754883786268931591at_nat > produc732395585841259969at_nat ).

thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    the_Pr6298817542474494203at_nat: option8699557107911914541at_nat > produc3843707927480180839at_nat ).

thf(sy_c_Option_Ooption_Othe_001tf__a,type,
    the_a: option_a > a ).

thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    these_2277756779245414180od_o_o: set_op3605315081486705933od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    these_663420305483081086at_nat: set_op7555165197759865831at_nat > set_Pr457366540195662369at_nat ).

thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    these_1872268174106123684at_nat: set_op989438649584373901at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Option_Othese_001tf__a,type,
    these_a: set_option_a > set_a ).

thf(sy_c_Order__Relation_OAboveS_001_Eo,type,
    order_AboveS_o: set_Product_prod_o_o > set_o > set_o ).

thf(sy_c_Order__Relation_OAboveS_001t__Nat__Onat,type,
    order_AboveS_nat: set_Pr1261947904930325089at_nat > set_nat > set_nat ).

thf(sy_c_Order__Relation_OAboveS_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    order_909087248044410034od_o_o: set_Pr1013884327308616903od_o_o > set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Order__Relation_OAboveS_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_3539579856470909964at_nat: set_Pr4427867301352232263at_nat > set_Pr457366540195662369at_nat > set_Pr457366540195662369at_nat ).

thf(sy_c_Order__Relation_OAboveS_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_5334716200017444146at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Order__Relation_OAboveS_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    order_5655281162628242642od_o_o: set_Pr1932065953672099015od_o_o > set_se491199571785101031od_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Order__Relation_OAboveS_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    order_9095727932502173612at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Order__Relation_OAboveS_001tf__a,type,
    order_AboveS_a: set_Product_prod_a_a > set_a > set_a ).

thf(sy_c_Order__Relation_Olinear__order__on_001_Eo,type,
    order_6238756238976269133r_on_o: set_o > set_Product_prod_o_o > $o ).

thf(sy_c_Order__Relation_Olinear__order__on_001t__Nat__Onat,type,
    order_4473980167227706203on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Order__Relation_Olinear__order__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    order_91209724698019100od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_Order__Relation_Olinear__order__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_9086815480479278966at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_Order__Relation_Olinear__order__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_2711500226769404828at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_Order__Relation_Olinear__order__on_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    order_2625247082195685180od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Order__Relation_Olinear__order__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    order_5942792088423767318at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Order__Relation_Olinear__order__on_001tf__a,type,
    order_8768733634509060147r_on_a: set_a > set_Product_prod_a_a > $o ).

thf(sy_c_Order__Relation_Oofilter_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    order_543634532542674813od_o_o: set_Pr1013884327308616903od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Order__Relation_Oofilter_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_3205064739578148183at_nat: set_Pr4427867301352232263at_nat > set_Pr457366540195662369at_nat > $o ).

thf(sy_c_Order__Relation_Oofilter_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_3142731893281451261at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Order__Relation_Oofilter_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    order_136921456694023837od_o_o: set_Pr1932065953672099015od_o_o > set_se491199571785101031od_o_o > $o ).

thf(sy_c_Order__Relation_Oofilter_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    order_6860593127430111223at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > $o ).

thf(sy_c_Order__Relation_Oofilter_001tf__a,type,
    order_ofilter_a: set_Product_prod_a_a > set_a > $o ).

thf(sy_c_Order__Relation_Opreorder__on_001_Eo,type,
    order_preorder_on_o: set_o > set_Product_prod_o_o > $o ).

thf(sy_c_Order__Relation_Opreorder__on_001t__Nat__Onat,type,
    order_4861654808422542329on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Order__Relation_Opreorder__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    order_3482285145583873534od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_Order__Relation_Opreorder__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_8058285401901086552at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_Order__Relation_Opreorder__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_4077073789452270206at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_Order__Relation_Opreorder__on_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    order_6208692358724846110od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Order__Relation_Opreorder__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    order_7173764778206869240at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Order__Relation_Opreorder__on_001tf__a,type,
    order_preorder_on_a: set_a > set_Product_prod_a_a > $o ).

thf(sy_c_Order__Relation_OunderS_001_Eo,type,
    order_underS_o: set_Product_prod_o_o > $o > set_o ).

thf(sy_c_Order__Relation_OunderS_001t__Nat__Onat,type,
    order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).

thf(sy_c_Order__Relation_OunderS_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    order_1929855754104155309od_o_o: set_Pr1013884327308616903od_o_o > produc2934264451710624999od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Order__Relation_OunderS_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_6745690092771398279at_nat: set_Pr4427867301352232263at_nat > produc732395585841259969at_nat > set_Pr457366540195662369at_nat ).

thf(sy_c_Order__Relation_OunderS_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_3736018788886245933at_nat: set_Pr5564308138774400199at_nat > produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Order__Relation_OunderS_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    order_3915675016455977933od_o_o: set_Pr1932065953672099015od_o_o > set_Product_prod_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Order__Relation_OunderS_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    order_2644262826035875111at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Order__Relation_OunderS_001tf__a,type,
    order_underS_a: set_Product_prod_a_a > a > set_a ).

thf(sy_c_Order__Relation_Ounder_001t__Nat__Onat,type,
    order_under_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).

thf(sy_c_Order__Relation_Ounder_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    order_8825441150112336748od_o_o: set_Pr1932065953672099015od_o_o > set_Product_prod_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Order__Relation_Ounder_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    order_8557040927991152966at_nat: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Order__Relation_Owell__order__on_001_Eo,type,
    order_2615775362358406454r_on_o: set_o > set_Product_prod_o_o > $o ).

thf(sy_c_Order__Relation_Owell__order__on_001t__Nat__Onat,type,
    order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Order__Relation_Owell__order__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    order_2783320356396525957od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_Order__Relation_Owell__order__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_1951249980326167391at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_Order__Relation_Owell__order__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    order_2339240034117818117at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_Order__Relation_Owell__order__on_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    order_3767514495197212837od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Order__Relation_Owell__order__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    order_1968183844437341695at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Order__Relation_Owell__order__on_001tf__a,type,
    order_6972113574731384220r_on_a: set_a > set_Product_prod_a_a > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_Eo_J,type,
    bot_bot_set_o: set_o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
    bot_bot_set_nat: set_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
    bot_bot_set_option_a: set_option_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bot_bo7073875226086086771od_o_o: set_Product_prod_o_o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    bot_bo498831808395348787od_o_o: set_Pr1932065953672099015od_o_o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    bot_bo1676454896636820109at_nat: set_Pr457366540195662369at_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    bot_bo228742789529271731at_nat: set_Pr4329608150637261639at_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    bot_bo8006819982598807891od_o_o: set_se491199571785101031od_o_o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bot_bo3083307316010499117at_nat: set_se7855581050983116737at_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
    bot_bot_set_a: set_a ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
    ord_less_nat: nat > nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    ord_le3253702748690112691od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    ord_le7866589430770878221at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
    ord_less_eq_set_o: set_o > set_o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    ord_le192195778054999463od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    ord_le7586318239878589543od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    ord_le4841768313324958145at_nat: set_Pr457366540195662369at_nat > set_Pr457366540195662369at_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    ord_le1268244103169919719at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    ord_le2654036014095304327od_o_o: set_se491199571785101031od_o_o > set_se491199571785101031od_o_o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    ord_le2077887516847798113at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
    ord_less_eq_set_a: set_a > set_a > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
    top_top_set_nat: set_nat ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Nat__Onat_J_J,type,
    top_to8920198386146353926on_nat: set_option_nat ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
    top_top_set_option_a: set_option_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    top_to1478448522960722999od_o_o: set_se491199571785101031od_o_o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    top_to7629004291339433233at_nat: set_se7855581050983116737at_nat ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
    top_top_set_a: set_a ).

thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
    product_Pair_o_o: $o > $o > product_prod_o_o ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    produc3331439552374987607od_o_o: product_prod_o_o > product_prod_o_o > produc4465838814804890855od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc6658621592305443671od_o_o: produc2934264451710624999od_o_o > produc2934264451710624999od_o_o > produc2245965095621756647od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001tf__a,type,
    produc6642224045558206830_o_o_a: produc2934264451710624999od_o_o > a > produc6136140800252116606_o_o_a ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc4785852428192286935at_nat: produc732395585841259969at_nat > produc732395585841259969at_nat > produc266773502759220327at_nat ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    produc538889887490039572_nat_a: produc732395585841259969at_nat > a > produc6136831119191938980_nat_a ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc4770972565181134295od_o_o: produc7898102162437433997od_o_o > produc7898102162437433997od_o_o > produc684523539999456103od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc2335810615602371415at_nat: produc3843707927480180839at_nat > produc3843707927480180839at_nat > produc1906917888121415911at_nat ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    produc517308312889114094_nat_a: produc3843707927480180839at_nat > a > produc6627350631851327998_nat_a ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J,type,
    produc8093790510458973071_a_c_d: product_prod_a_c_d > option6413918287372586467_a_c_d > produc5278197477302038359_a_c_d ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    produc763777882069021527od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > produc2934264451710624999od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc8517790099723286449at_nat: set_Product_prod_o_o > set_Pr1261947904930325089at_nat > produc732395585841259969at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    produc2070086378307464573od_o_o: set_Pr1261947904930325089at_nat > set_Product_prod_o_o > produc7898102162437433997od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc7668796723872103605at_nat: set_Pr1261947904930325089at_nat > set_Pr1076074158304066111at_nat > produc3770297804798658629at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
    produc6016498021161588349od_a_a: set_Pr1261947904930325089at_nat > set_Product_prod_a_a > produc721097834699853453od_a_a ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc189021232855538519od_o_o: set_Pr7011910401827753159od_o_o > set_Pr7011910401827753159od_o_o > produc6176228915706226407od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J,type,
    produc8026554252588472319_o_nat: set_Pr7011910401827753159od_o_o > set_Pr6607724941775425903_o_nat > produc3814013152794810639_o_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J,type,
    produc3218210373639305035_nat_o: set_Pr7011910401827753159od_o_o > set_Pr1799381062826258619_nat_o > produc1771412367706247771_nat_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc6996284652319478231at_nat: set_Pr7011910401827753159od_o_o > set_Pr8693737435421807431at_nat > produc743030839026790503at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J,type,
    produc5910034646884183383_o_nat: set_Pr6607724941775425903_o_nat > set_Pr6607724941775425903_o_nat > produc7379504648073755111_o_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc6295173111627586351at_nat: set_Pr6607724941775425903_o_nat > set_Pr8693737435421807431at_nat > produc8421973624431248703at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J,type,
    produc3222486542081100375_nat_o: set_Pr1799381062826258619_nat_o > set_Pr1799381062826258619_nat_o > produc7457699637131276519_nat_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc5773396518915747555at_nat: set_Pr1799381062826258619_nat_o > set_Pr8693737435421807431at_nat > produc7900197031719409907at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc3236233026405413719at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > produc6487378988399798503at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    produc8369371535328480407od_o_o: set_Pr1013884327308616903od_o_o > set_Product_prod_o_o > produc1960492347614157607od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc1598809612926693617at_nat: set_Pr1013884327308616903od_o_o > set_Pr1261947904930325089at_nat > produc3355805666032155649at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    produc23025780167396183od_o_o: set_Pr1013884327308616903od_o_o > set_Pr1013884327308616903od_o_o > produc467843052564343527od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
    produc6706904248712485783od_a_a: set_Pr1013884327308616903od_o_o > set_Product_prod_a_a > produc2232466541489530151od_a_a ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc4982878492540823665at_nat: set_Pr4427867301352232263at_nat > set_Pr1261947904930325089at_nat > produc3003658523197049473at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    produc8612946581105484631at_nat: set_Pr4427867301352232263at_nat > set_Pr4427867301352232263at_nat > produc1903999119065525479at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
    produc6483374742268400407od_a_a: set_Pr4427867301352232263at_nat > set_Product_prod_a_a > produc4846567752052077479od_a_a ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc5407148829662812401at_nat: set_Pr5564308138774400199at_nat > set_Pr1261947904930325089at_nat > produc8039618346972058113at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    produc7545183385222921047at_nat: set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat > produc5052769453400272615at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
    produc4160138634059301783od_a_a: set_Pr5564308138774400199at_nat > set_Product_prod_a_a > produc8300268311522786087od_a_a ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    produc2282539314773629783od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o > produc8963987812249958119od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc4325049062531119319at_nat: set_Pr457366540195662369at_nat > set_Pr457366540195662369at_nat > produc5306847434115292263at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    produc5317466613051064531od_o_o: set_Pr2429666174773179787um_o_o > set_Product_prod_o_o > produc3217940817873794019od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc4966347635449911085at_nat: set_Pr2429666174773179787um_o_o > set_Pr1261947904930325089at_nat > produc6319085873323607741at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J,type,
    produc1030987845608174167um_o_o: set_Pr2429666174773179787um_o_o > set_Pr2429666174773179787um_o_o > produc5974065977577044711um_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J,type,
    produc3782849074957862163_o_nat: set_Pr2429666174773179787um_o_o > set_Pr63822404152778311_o_nat > produc395215368487385379_o_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J,type,
    produc8820280760719367571_nat_o: set_Pr2429666174773179787um_o_o > set_Pr5101254089914283719_nat_o > produc4474022258528981411_nat_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc6767169964153735947at_nat: set_Pr2429666174773179787um_o_o > set_Pr1076074158304066111at_nat > produc5153585639972752539at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    produc8931464078238085911od_o_o: set_Pr63822404152778311_o_nat > set_Product_prod_o_o > produc5450868540414226855od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc7234148943500302193at_nat: set_Pr63822404152778311_o_nat > set_Pr1261947904930325089at_nat > produc299292417334301313at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J,type,
    produc5149556716212013723um_o_o: set_Pr63822404152778311_o_nat > set_Pr2429666174773179787um_o_o > produc5855907259854397099um_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J,type,
    produc728317944619019095_o_nat: set_Pr63822404152778311_o_nat > set_Pr63822404152778311_o_nat > produc8342863555562253031_o_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J,type,
    produc5765749630380524503_nat_o: set_Pr63822404152778311_o_nat > set_Pr5101254089914283719_nat_o > produc3198298408749073255_nat_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc5352410120312684367at_nat: set_Pr63822404152778311_o_nat > set_Pr1076074158304066111at_nat > produc4017409457303293023at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    produc4177515836422716055od_o_o: set_Pr5101254089914283719_nat_o > set_Product_prod_o_o > produc696920298598856999od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc5868257188881964785at_nat: set_Pr5101254089914283719_nat_o > set_Pr1261947904930325089at_nat > produc8156772699570739713at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J,type,
    produc4585484280506290715um_o_o: set_Pr5101254089914283719_nat_o > set_Pr2429666174773179787um_o_o > produc5291834824148674091um_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J,type,
    produc4410791399313715927_o_nat: set_Pr5101254089914283719_nat_o > set_Pr63822404152778311_o_nat > produc2801964973402174055_o_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J,type,
    produc224851048220445527_nat_o: set_Pr5101254089914283719_nat_o > set_Pr5101254089914283719_nat_o > produc6880771863443770087_nat_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc3548793344679855823at_nat: set_Pr5101254089914283719_nat_o > set_Pr1076074158304066111at_nat > produc2213792681670464479at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    produc9174727453167716639od_o_o: set_Pr1076074158304066111at_nat > set_Product_prod_o_o > produc6629909188158935855od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc6460772959230282105at_nat: set_Pr1076074158304066111at_nat > set_Pr1261947904930325089at_nat > produc8434689566910009353at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J,type,
    produc3837620720005901475um_o_o: set_Pr1076074158304066111at_nat > set_Pr2429666174773179787um_o_o > produc6322778544207219763um_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J,type,
    produc2864506647045777759_o_nat: set_Pr1076074158304066111at_nat > set_Pr63822404152778311_o_nat > produc1534263882305827951_o_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc2112825387572549975at_nat: set_Pr1076074158304066111at_nat > set_Pr1076074158304066111at_nat > produc6206612473762214375at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    produc1574450146682772567od_o_o: set_Product_prod_a_a > set_Product_prod_o_o > produc5781518669219163367od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc2553196175173902513at_nat: set_Product_prod_a_a > set_Pr1261947904930325089at_nat > produc2304671794888584641at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    produc5353641014327778071od_o_o: set_Product_prod_a_a > set_Pr1013884327308616903od_o_o > produc7738053905463721127od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
    produc3372137660326521687od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > produc7983190928304305895od_a_a ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc4478624491032480599od_o_o: set_se491199571785101031od_o_o > set_se491199571785101031od_o_o > produc7004997421203748071od_o_o ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc7462898802507495127at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > produc7299876168958306407at_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__a_J_001t__Set__Oset_Itf__a_J,type,
    produc9088192753505129239_set_a: set_a > set_a > produc1703568184450464039_set_a ).

thf(sy_c_Product__Type_OPair_001tf__a_001_062_Itf__c_Mtf__d_J,type,
    product_Pair_a_c_d: a > ( c > d ) > product_prod_a_c_d ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc7371010082742806528od_o_o: a > produc2934264451710624999od_o_o > produc931656912218737808od_o_o ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc7802126073954666586at_nat: a > produc732395585841259969at_nat > produc3842678439083338090at_nat ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc3162473886009270912at_nat: a > produc3843707927480180839at_nat > produc656436880464960016at_nat ).

thf(sy_c_Product__Type_OPair_001tf__a_001tf__a,type,
    product_Pair_a_a: a > a > product_prod_a_a ).

thf(sy_c_Product__Type_Ocurry_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001_Eo,type,
    produc4861507100678042957_o_o_o: ( produc2934264451710624999od_o_o > $o ) > set_Product_prod_o_o > set_Product_prod_o_o > $o ).

thf(sy_c_Product__Type_Ocurry_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_Eo,type,
    produc5440495499350717427_nat_o: ( produc732395585841259969at_nat > $o ) > set_Product_prod_o_o > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Product__Type_Ocurry_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_Eo,type,
    produc7820828192191229133_nat_o: ( produc3843707927480180839at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Relation_ODomain_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    domain2187190646820045772od_o_o: set_Pr1013884327308616903od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Relation_ODomain_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    domain8659765193365367884at_nat: set_Pr4427867301352232263at_nat > set_Pr457366540195662369at_nat ).

thf(sy_c_Relation_ODomain_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    domain1102310642530566604at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Relation_ODomain_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    domain8908270702770587084od_o_o: set_Pr1932065953672099015od_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Relation_ODomain_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    domain8494901049294654374at_nat: set_Pr457366540195662369at_nat > set_se491199571785101031od_o_o ).

thf(sy_c_Relation_ODomain_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    domain8802589944165416012at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Relation_ODomain_001tf__a_001tf__a,type,
    domain_a_a: set_Product_prod_a_a > set_a ).

thf(sy_c_Relation_OField_001_Eo,type,
    field_o: set_Product_prod_o_o > set_o ).

thf(sy_c_Relation_OField_001t__Nat__Onat,type,
    field_nat: set_Pr1261947904930325089at_nat > set_nat ).

thf(sy_c_Relation_OField_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    field_5121862139100741428od_o_o: set_Pr1013884327308616903od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Relation_OField_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    field_7361900449976055182at_nat: set_Pr4427867301352232263at_nat > set_Pr457366540195662369at_nat ).

thf(sy_c_Relation_OField_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    field_2862844103579723188at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Relation_OField_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    field_6101175518749917524od_o_o: set_Pr1932065953672099015od_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Relation_OField_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    field_3145993188331922222at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Relation_OField_001tf__a,type,
    field_a: set_Product_prod_a_a > set_a ).

thf(sy_c_Relation_OId_001_Eo,type,
    id_o: set_Product_prod_o_o ).

thf(sy_c_Relation_OId_001t__Nat__Onat,type,
    id_nat: set_Pr1261947904930325089at_nat ).

thf(sy_c_Relation_OId_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    id_Pro5927853813057311299od_o_o: set_Pr1013884327308616903od_o_o ).

thf(sy_c_Relation_OId_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    id_Pro6320881530060322077at_nat: set_Pr4427867301352232263at_nat ).

thf(sy_c_Relation_OId_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    id_Pro5428700290092274115at_nat: set_Pr5564308138774400199at_nat ).

thf(sy_c_Relation_OId_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    id_set2647307015711338339od_o_o: set_Pr1932065953672099015od_o_o ).

thf(sy_c_Relation_OId_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    id_set1796276052702428605at_nat: set_Pr4329608150637261639at_nat ).

thf(sy_c_Relation_OId_001tf__a,type,
    id_a2: set_Product_prod_a_a ).

thf(sy_c_Relation_OImage_001_Eo_001_Eo,type,
    image_o_o: set_Product_prod_o_o > set_o > set_o ).

thf(sy_c_Relation_OImage_001t__Nat__Onat_001t__Nat__Onat,type,
    image_nat_nat: set_Pr1261947904930325089at_nat > set_nat > set_nat ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    image_1313870842500862867od_o_o: set_Pr1013884327308616903od_o_o > set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001tf__a,type,
    image_7612288785953357226_o_o_a: set_Pr6196119011418371550_o_o_a > set_Pr1932065953672099015od_o_o > set_a ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    image_1966035174115581203at_nat: set_Pr4427867301352232263at_nat > set_Pr457366540195662369at_nat > set_Pr457366540195662369at_nat ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    image_3924149183600524624_nat_a: set_Pr5256879730163711364_nat_a > set_Pr457366540195662369at_nat > set_a ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    image_3736809421353964435at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001tf__a,type,
    image_8821586633200209450_nat_a: set_Pr7219508552201550942_nat_a > set_Pr4329608150637261639at_nat > set_a ).

thf(sy_c_Relation_OImage_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    image_3256184292080368531od_o_o: set_Pr1932065953672099015od_o_o > set_se491199571785101031od_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Relation_OImage_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    image_2461788823225053677at_nat: set_Pr457366540195662369at_nat > set_se491199571785101031od_o_o > set_se7855581050983116737at_nat ).

thf(sy_c_Relation_OImage_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    image_3892192845344445203at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Relation_OImage_001tf__a_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    image_8341074823137956924od_o_o: set_Pr5975447109543910128od_o_o > set_a > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Relation_OImage_001tf__a_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    image_1964013333210375830at_nat: set_Pr1968968238647823434at_nat > set_a > set_Pr457366540195662369at_nat ).

thf(sy_c_Relation_OImage_001tf__a_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    image_2243380169465590460at_nat: set_Pr8044876533244767088at_nat > set_a > set_Pr4329608150637261639at_nat ).

thf(sy_c_Relation_OImage_001tf__a_001tf__a,type,
    image_a_a: set_Product_prod_a_a > set_a > set_a ).

thf(sy_c_Relation_ORange_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    range_1318165146934585909od_o_o: set_Pr1932065953672099015od_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Relation_ORange_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    range_8412904782085253007at_nat: set_Pr457366540195662369at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Relation_ORange_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    range_880292732526890933at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Relation_Oantisym__on_001t__Nat__Onat,type,
    antisym_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Relation_Oantisym__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    antisy2259881126919591626od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_Relation_Oantisym__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    antisy1857962754316978724at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_Relation_Oantisym__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    antisy6856624793204979530at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_Relation_Oantisym__on_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    antisy777991898044409578od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Relation_Oantisym__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    antisy1130263102092445124at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Relation_Oantisym__on_001tf__a,type,
    antisym_on_a: set_a > set_Product_prod_a_a > $o ).

thf(sy_c_Relation_Oasym__on_001t__Nat__Onat,type,
    asym_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Relation_Oasym__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    asym_o7797749731265203737od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_Relation_Oasym__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    asym_o194845430079802867at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_Relation_Oasym__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    asym_o9101232109321078681at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_Relation_Oasym__on_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    asym_o8381145231034218809od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Relation_Oasym__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    asym_o5033339280856310931at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Relation_Oasym__on_001tf__a,type,
    asym_on_a: set_a > set_Product_prod_a_a > $o ).

thf(sy_c_Relation_Orefl__on_001t__Nat__Onat,type,
    refl_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Relation_Orefl__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    refl_o8365827894042769382od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_Relation_Orefl__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    refl_o3078925143892389184at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_Relation_Orefl__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    refl_o7446464703481863270at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_Relation_Orefl__on_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    refl_o935183656833700870od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Relation_Orefl__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    refl_o6955724340487615712at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Relation_Orefl__on_001tf__a,type,
    refl_on_a: set_a > set_Product_prod_a_a > $o ).

thf(sy_c_Relation_Osingle__valued_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    single7370670047157432131od_o_o: set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Relation_Osingle__valued_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    single7212042597521132957at_nat: set_Pr457366540195662369at_nat > $o ).

thf(sy_c_Relation_Osingle__valued_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    single6503460853754975939at_nat: set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Relation_Ototal__on_001_Eo,type,
    total_on_o: set_o > set_Product_prod_o_o > $o ).

thf(sy_c_Relation_Ototal__on_001t__Nat__Onat,type,
    total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    total_3055748755304958059od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    total_8996415722781341509at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    total_1513685709984341995at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_Relation_Ototal__on_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    total_5784220159268842891od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Relation_Ototal__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    total_7212417256332265445at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Relation_Ototal__on_001tf__a,type,
    total_on_a: set_a > set_Product_prod_a_a > $o ).

thf(sy_c_Relation_Otrans__on_001t__Nat__Onat,type,
    trans_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Relation_Otrans__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    trans_2549647969203962503od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_Relation_Otrans__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    trans_3798871764278489953at_nat: set_Pr457366540195662369at_nat > set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_Relation_Otrans__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    trans_4802246114490097159at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_Relation_Otrans__on_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    trans_7029024365671003047od_o_o: set_se491199571785101031od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Relation_Otrans__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    trans_3732288485672914945at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Relation_Otrans__on_001tf__a,type,
    trans_on_a: set_a > set_Product_prod_a_a > $o ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    collec3302784863738620242od_o_o: ( produc2934264451710624999od_o_o > $o ) > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    collec1729919521702017196at_nat: ( produc732395585841259969at_nat > $o ) > set_Pr457366540195662369at_nat ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    collec6321179662152712658at_nat: ( produc3843707927480180839at_nat > $o ) > set_Pr4329608150637261639at_nat ).

thf(sy_c_Set_OCollect_001tf__a,type,
    collect_a: ( a > $o ) > set_a ).

thf(sy_c_Set_Odisjnt_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    disjnt556417628418099406od_o_o: set_se491199571785101031od_o_o > set_se491199571785101031od_o_o > $o ).

thf(sy_c_Set_Odisjnt_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    disjnt2544082741087298984at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > $o ).

thf(sy_c_Set_Oimage_001_Eo_001_Eo,type,
    image_o_o2: ( $o > $o ) > set_o > set_o ).

thf(sy_c_Set_Oimage_001_Eo_001t__Nat__Onat,type,
    image_o_nat: ( $o > nat ) > set_o > set_nat ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001_Eo,type,
    image_nat_o: ( nat > $o ) > set_nat > set_o ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
    image_nat_nat2: ( nat > nat ) > set_nat > set_nat ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Option__Ooption_It__Nat__Onat_J,type,
    image_nat_option_nat: ( nat > option_nat ) > set_nat > set_option_nat ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Option__Ooption_Itf__a_J,type,
    image_nat_option_a: ( nat > option_a ) > set_nat > set_option_a ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_001t__Option__Ooption_Itf__a_J,type,
    image_1441591353514620194tion_a: ( produc2934264451710624999od_o_o > option_a ) > set_Pr1932065953672099015od_o_o > set_option_a ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_Itf__a_J,type,
    image_6589722576923083464tion_a: ( produc732395585841259969at_nat > option_a ) > set_Pr457366540195662369at_nat > set_option_a ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_Itf__a_J,type,
    image_7626837539197272994tion_a: ( produc3843707927480180839at_nat > option_a ) > set_Pr4329608150637261639at_nat > set_option_a ).

thf(sy_c_Set_Oimage_001tf__a_001t__Option__Ooption_Itf__a_J,type,
    image_a_option_a: ( a > option_a ) > set_a > set_option_a ).

thf(sy_c_Set_Oinsert_001_Eo,type,
    insert_o: $o > set_o > set_o ).

thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
    insert_nat: nat > set_nat > set_nat ).

thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Nat__Onat_J,type,
    insert_option_nat: option_nat > set_option_nat > set_option_nat ).

thf(sy_c_Set_Oinsert_001t__Option__Ooption_Itf__a_J,type,
    insert_option_a: option_a > set_option_a > set_option_a ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    insert6201435330877294327od_o_o: product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    insert3855699742481506999od_o_o: produc2934264451710624999od_o_o > set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    insert8109617542356073361at_nat: produc732395585841259969at_nat > set_Pr457366540195662369at_nat > set_Pr457366540195662369at_nat ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    insert3817420688681518039od_o_o: set_Product_prod_o_o > set_se491199571785101031od_o_o > set_se491199571785101031od_o_o ).

thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    insert9200635055090092081at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).

thf(sy_c_Set_Oinsert_001tf__a,type,
    insert_a: a > set_a > set_a ).

thf(sy_c_Sum__Type_OPlus_001_Eo_001_Eo,type,
    sum_Plus_o_o: set_o > set_o > set_Sum_sum_o_o ).

thf(sy_c_Sum__Type_OPlus_001_Eo_001t__Nat__Onat,type,
    sum_Plus_o_nat: set_o > set_nat > set_Sum_sum_o_nat ).

thf(sy_c_Sum__Type_OPlus_001t__Nat__Onat_001_Eo,type,
    sum_Plus_nat_o: set_nat > set_o > set_Sum_sum_nat_o ).

thf(sy_c_Sum__Type_OPlus_001t__Nat__Onat_001t__Nat__Onat,type,
    sum_Plus_nat_nat: set_nat > set_nat > set_Sum_sum_nat_nat ).

thf(sy_c_Transitive__Closure_Oacyclic_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    transi6732886088652640214od_o_o: set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Transitive__Closure_Oacyclic_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    transi5940216143853766832at_nat: set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    transi3610599525415160810od_o_o: set_Pr1013884327308616903od_o_o > set_Pr1013884327308616903od_o_o ).

thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    transi4536970581772660548at_nat: set_Pr4427867301352232263at_nat > set_Pr4427867301352232263at_nat ).

thf(sy_c_Transitive__Closure_Ortrancl_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    transi5049001397978532970at_nat: set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat ).

thf(sy_c_Transitive__Closure_Ortrancl_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    transi8975321201238539274od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Transitive__Closure_Ortrancl_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    transi6170703685534862052at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Transitive__Closure_Ortrancl_001tf__a,type,
    transitive_rtrancl_a: set_Product_prod_a_a > set_Product_prod_a_a ).

thf(sy_c_UnboundedLogic_Oassertion_OAnd_001tf__a_001tf__b_001tf__d_001tf__c,type,
    and_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Oassertion_OBounded_001tf__a_001tf__b_001tf__d_001tf__c,type,
    bounded_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Oassertion_OExists_001tf__c_001tf__a_001tf__b_001tf__d,type,
    exists_c_a_b_d: c > assertion_a_b_d_c > assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Oassertion_OForall_001tf__c_001tf__a_001tf__b_001tf__d,type,
    forall_c_a_b_d: c > assertion_a_b_d_c > assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Oassertion_OImp_001tf__a_001tf__b_001tf__d_001tf__c,type,
    imp_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Oassertion_OMult_001tf__b_001tf__a_001tf__d_001tf__c,type,
    mult_b_a_d_c: b > assertion_a_b_d_c > assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Oassertion_OOr_001tf__a_001tf__b_001tf__d_001tf__c,type,
    or_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Oassertion_OPred_001tf__a_001tf__b_001tf__d_001tf__c,type,
    pred_a_b_d_c: assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Oassertion_OSem_001tf__c_001tf__d_001tf__a_001tf__b,type,
    sem_c_d_a_b: ( ( c > d ) > a > $o ) > assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Oassertion_OStar_001tf__a_001tf__b_001tf__d_001tf__c,type,
    star_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Oassertion_OWand_001tf__a_001tf__b_001tf__d_001tf__c,type,
    wand_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c > assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Oassertion_OWildcard_001tf__a_001tf__b_001tf__d_001tf__c,type,
    wildcard_a_b_d_c: assertion_a_b_d_c > assertion_a_b_d_c ).

thf(sy_c_UnboundedLogic_Ologic_001tf__a_001tf__b,type,
    logic_a_b: ( a > a > option_a ) > ( b > a > a ) > ( b > b > b ) > ( b > b > b ) > ( b > b ) > b > ( a > $o ) > $o ).

thf(sy_c_UnboundedLogic_Ologic_Oentails_001tf__a_001tf__b_001tf__d_001tf__c,type,
    entails_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > ( ( c > d ) > set_a ) > assertion_a_b_d_c > $o ).

thf(sy_c_UnboundedLogic_Ologic_Oequal__outside_001tf__c_001tf__d,type,
    equal_outside_c_d: ( c > d ) > ( c > d ) > set_c > $o ).

thf(sy_c_UnboundedLogic_Ologic_Oequivalent_001tf__a_001tf__b_001tf__d_001tf__c,type,
    equivalent_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > ( ( c > d ) > set_a ) > assertion_a_b_d_c > $o ).

thf(sy_c_UnboundedLogic_Ologic_Ointuitionistic_001tf__a_001tf__b_001tf__c_001tf__d,type,
    intuit7508411120625971703_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > ( c > d ) > ( ( c > d ) > set_a ) > assertion_a_b_d_c > $o ).

thf(sy_c_UnboundedLogic_Ologic_Omodified_001tf__a_001tf__c_001tf__d,type,
    modified_a_c_d: set_Pr1275464188344874039_a_c_d > set_c ).

thf(sy_c_UnboundedLogic_Ologic_Onot__in__fv_001tf__a_001tf__b_001tf__d_001tf__c,type,
    not_in_fv_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > set_c > $o ).

thf(sy_c_UnboundedLogic_Ologic_Opure_001tf__a_001tf__b_001tf__d_001tf__c,type,
    pure_a_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > $o ).

thf(sy_c_UnboundedLogic_Ologic_Osafe_001tf__a_001tf__c_001tf__d,type,
    safe_a_c_d: set_Pr1275464188344874039_a_c_d > product_prod_a_c_d > $o ).

thf(sy_c_UnboundedLogic_Ologic_Osat_001tf__a_001tf__b_001tf__c_001tf__d,type,
    sat_a_b_c_d: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > a > ( c > d ) > ( ( c > d ) > set_a ) > assertion_a_b_d_c > $o ).

thf(sy_c_UnboundedLogic_Ologic_Ovalid__hoare__triple_001tf__a_001tf__b_001tf__d_001tf__c,type,
    valid_6037315502795721655_b_d_c: ( a > a > option_a ) > ( b > a > a ) > ( a > $o ) > assertion_a_b_d_c > set_Pr1275464188344874039_a_c_d > assertion_a_b_d_c > ( ( c > d ) > set_a ) > $o ).

thf(sy_c_UnboundedLogic_Opre__logic_Ocompatible_001tf__a,type,
    pre_compatible_a: ( a > a > option_a ) > a > a > $o ).

thf(sy_c_UnboundedLogic_Opre__logic_Olarger_001tf__a,type,
    pre_larger_a: ( a > a > option_a ) > a > a > $o ).

thf(sy_c_Wellfounded_Ofinite__psubset_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    finite1053609180499918954od_o_o: set_Pr1932065953672099015od_o_o ).

thf(sy_c_Wellfounded_Ofinite__psubset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    finite469560695537375940at_nat: set_Pr4329608150637261639at_nat ).

thf(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    lex_pr2209867684007004015od_o_o: set_Pr1932065953672099015od_o_o > set_Pr1932065953672099015od_o_o > set_Pr1013884327308616903od_o_o ).

thf(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    lex_pr568118237913915337at_nat: set_Pr1932065953672099015od_o_o > set_Pr4329608150637261639at_nat > set_Pr4427867301352232263at_nat ).

thf(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    lex_pr3343786553352869269od_o_o: set_Pr4329608150637261639at_nat > set_Pr1932065953672099015od_o_o > set_Pr2036461669354544199od_o_o ).

thf(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    lex_pr8000699672184251119at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat ).

thf(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    max_ex7572203241849361634od_o_o: set_Pr7011910401827753159od_o_o > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).

thf(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    max_ex9141845325704764834od_o_o: set_Pr1013884327308616903od_o_o > set_Pr5368513128717298887od_o_o ).

thf(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    max_ex1111939896555521276at_nat: set_Pr4427867301352232263at_nat > set_Pr4391781608169641287at_nat ).

thf(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    max_ex8833738776070432290at_nat: set_Pr5564308138774400199at_nat > set_Pr7459493094073627847at_nat ).

thf(sy_c_Wellfounded_Omax__ext_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    max_ex5401630698724402626od_o_o: set_Pr1932065953672099015od_o_o > set_Pr7077720281583819975od_o_o ).

thf(sy_c_Wellfounded_Omax__ext_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    max_ex4535816423174879388at_nat: set_Pr4329608150637261639at_nat > set_Pr1604112560894399303at_nat ).

thf(sy_c_Wellfounded_Omax__ext_001tf__a,type,
    max_ext_a: set_Product_prod_a_a > set_Pr5845495582615845127_set_a ).

thf(sy_c_Wellfounded_Omeasure_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    measur5705974739304014543od_o_o: ( set_Product_prod_o_o > nat ) > set_Pr1932065953672099015od_o_o ).

thf(sy_c_Wellfounded_Omeasure_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    measur1827424007717751593at_nat: ( set_Pr1261947904930325089at_nat > nat ) > set_Pr4329608150637261639at_nat ).

thf(sy_c_Wellfounded_Owf_001_Eo,type,
    wf_o: set_Product_prod_o_o > $o ).

thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
    wf_nat: set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Wellfounded_Owf_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    wf_Pro3213319136295691984od_o_o: set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_Wellfounded_Owf_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    wf_Pro661967360799104810at_nat: set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_Wellfounded_Owf_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    wf_Pro2357547232388600144at_nat: set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_Wellfounded_Owf_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    wf_set2384217916178216176od_o_o: set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_Wellfounded_Owf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    wf_set7675013139414177994at_nat: set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_Wellfounded_Owf_001tf__a,type,
    wf_a: set_Product_prod_a_a > $o ).

thf(sy_c_Wfrec_Osame__fst_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    same_f884114232143252012od_o_o: ( set_Product_prod_o_o > $o ) > ( set_Product_prod_o_o > set_Pr1932065953672099015od_o_o ) > set_Pr1013884327308616903od_o_o ).

thf(sy_c_Wfrec_Osame__fst_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    same_f6937299433074352134at_nat: ( set_Product_prod_o_o > $o ) > ( set_Product_prod_o_o > set_Pr4329608150637261639at_nat ) > set_Pr4427867301352232263at_nat ).

thf(sy_c_Wfrec_Osame__fst_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    same_f1460074399991292076at_nat: ( set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat ) > set_Pr5564308138774400199at_nat ).

thf(sy_c_member_001_Eo,type,
    member_o: $o > set_o > $o ).

thf(sy_c_member_001t__Nat__Onat,type,
    member_nat: nat > set_nat > $o ).

thf(sy_c_member_001t__Option__Ooption_It__Nat__Onat_J,type,
    member_option_nat: option_nat > set_option_nat > $o ).

thf(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    member3623239300863961174od_o_o: option8293164206536526765od_o_o > set_op3605315081486705933od_o_o > $o ).

thf(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member8056002749114821168at_nat: option7754883786268931591at_nat > set_op7555165197759865831at_nat > $o ).

thf(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member4288423094740844502at_nat: option8699557107911914541at_nat > set_op989438649584373901at_nat > $o ).

thf(sy_c_member_001t__Option__Ooption_Itf__a_J,type,
    member_option_a: option_a > set_option_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    member7466972457876170832od_o_o: product_prod_o_o > set_Product_prod_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    member3169104723136097040od_o_o: produc4465838814804890855od_o_o > set_Pr7011910401827753159od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    member5560047953027865360od_o_o: produc2245965095621756647od_o_o > set_Pr1013884327308616903od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mtf__a_J,type,
    member1826218620961749927_o_o_a: produc6136140800252116606_o_o_a > set_Pr6196119011418371550_o_o_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member208136763105818512at_nat: produc266773502759220327at_nat > set_Pr4427867301352232263at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mtf__a_J,type,
    member9163085975106382925_nat_a: produc6136831119191938980_nat_a > set_Pr5256879730163711364_nat_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    member625886800346054288od_o_o: produc684523539999456103od_o_o > set_Pr2036461669354544199od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member6009668390874684176at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mtf__a_J,type,
    member1060612044916223527_nat_a: produc6627350631851327998_nat_a > set_Pr7219508552201550942_nat_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_Itf__a_M_062_Itf__c_Mtf__d_J_J_J_J,type,
    member1180172933830803072_a_c_d: produc5278197477302038359_a_c_d > set_Pr1275464188344874039_a_c_d > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    member444158400953824016od_o_o: produc2934264451710624999od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member4095101504841534314at_nat: produc732395585841259969at_nat > set_Pr457366540195662369at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    member2037436044582932534od_o_o: produc7898102162437433997od_o_o > set_Pr8055703017043224813od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member7606898804734335598at_nat: produc3770297804798658629at_nat > set_Pr8695894162071895333at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
    member5274544965882063670od_a_a: produc721097834699853453od_a_a > set_Pr9037244641242167277od_a_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    member7930742895388902160od_o_o: produc6176228915706226407od_o_o > set_Pr8269993260027997383od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    member1643650677906951352_o_nat: produc3814013152794810639_o_nat > set_Pr2083485662371163247_o_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_J,type,
    member8824421929673164292_nat_o: produc1771412367706247771_nat_o > set_Pr6689048260218027963_nat_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member8717407822839053200at_nat: produc743030839026790503at_nat > set_Pr8788114079658965319at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    member6130509595031242000_o_nat: produc7379504648073755111_o_nat > set_Pr6149578361169461959_o_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member2414491960730527720at_nat: produc8421973624431248703at_nat > set_Pr2070915713504248735at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_J,type,
    member6208704584088763408_nat_o: produc7457699637131276519_nat_o > set_Pr2690992919715838407_nat_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member1892715368018688924at_nat: produc7900197031719409907at_nat > set_Pr6357112501083536723at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member5855424355840516880at_nat: produc6487378988399798503at_nat > set_Pr5297940549829899463at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    member5998968164356017744od_o_o: produc1960492347614157607od_o_o > set_Pr1292856356524837895od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member7927422385807836842at_nat: produc3355805666032155649at_nat > set_Pr8072821036331221345at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_J,type,
    member2182030262393914128od_o_o: produc467843052564343527od_o_o > set_Pr6429226126823767239od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
    member2379278310075879248od_a_a: produc2232466541489530151od_a_a > set_Pr4049313843747668231od_a_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member8415039729195402282at_nat: produc3003658523197049473at_nat > set_Pr6894797015334228705at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
    member4079835277323035408at_nat: produc1903999119065525479at_nat > set_Pr1064757066610246855at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
    member7043285137284140240od_a_a: produc4846567752052077479od_a_a > set_Pr3075999220293227143od_a_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member7359442244455152298at_nat: produc8039618346972058113at_nat > set_Pr4375867511396588897at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
    member2845199937591886608at_nat: produc5052769453400272615at_nat > set_Pr4654484256145968327at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
    member6195182203977450320od_a_a: produc8300268311522786087od_a_a > set_Pr8186174039193902343od_a_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J,type,
    member3740103928775426832od_o_o: produc8963987812249958119od_o_o > set_Pr5368513128717298887od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    member7768518508883498896at_nat: produc5306847434115292263at_nat > set_Pr4391781608169641287at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    member1466754251312161552at_nat: produc1319942482725812455at_nat > set_Pr7459493094073627847at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    member8030178841557499788od_o_o: produc3217940817873794019od_o_o > set_Pr5465339146700379459od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member989342599902505446at_nat: produc6319085873323607741at_nat > set_Pr308927743835700381at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J,type,
    member3483138326940501008um_o_o: produc5974065977577044711um_o_o > set_Pr9037604441019230663um_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    member3365704633057040844_o_nat: produc395215368487385379_o_nat > set_Pr8614431393250552707_o_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_J,type,
    member7444511523098636876_nat_o: produc4474022258528981411_nat_o > set_Pr1345543789004997635_nat_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member9006821182645044420at_nat: produc5153585639972752539at_nat > set_Pr4168889959610442875at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    member121125266993124560od_o_o: produc5450868540414226855od_o_o > set_Pr5192616823003386503od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member6178483945413987626at_nat: produc299292417334301313at_nat > set_Pr2243238557815556065at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J,type,
    member8826396524424052564um_o_o: produc5855907259854397099um_o_o > set_Pr6890301357480955147um_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    member2972727061379769104_o_nat: produc8342863555562253031_o_nat > set_Pr5706656237632445639_o_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_J,type,
    member7051533951421365136_nat_o: produc3198298408749073255_nat_o > set_Pr7661140670241666375_nat_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member234890756356643848at_nat: produc4017409457303293023at_nat > set_Pr3469353857373938623at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    member4590549062032530512od_o_o: produc696920298598856999od_o_o > set_Pr6419213211702811143od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member4812592190795650218at_nat: produc8156772699570739713at_nat > set_Pr8020157162464038753at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J,type,
    member8262324088718329556um_o_o: produc5291834824148674091um_o_o > set_Pr4885524344002532491um_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    member6655200516074465936_o_nat: produc2801964973402174055_o_nat > set_Pr6004696033780540487_o_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_J,type,
    member1510635369261286160_nat_o: produc6880771863443770087_nat_o > set_Pr7959180466389761223_nat_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_Mt__Sum____Type__Osum_It__Nat__Onat_M_Eo_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member7654646017578591112at_nat: produc2213792681670464479at_nat > set_Pr6710357650329316159at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    member3285728679383846360od_o_o: produc6629909188158935855od_o_o > set_Pr2990377294110839183od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member3047918529990910514at_nat: produc8434689566910009353at_nat > set_Pr1627845231345427177at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_M_Eo_J_Mt__Sum____Type__Osum_I_Eo_M_Eo_J_J_J_J,type,
    member952642050024735836um_o_o: produc6322778544207219763um_o_o > set_Pr9196163270038067219um_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_I_Eo_Mt__Nat__Onat_J_J_J_J,type,
    member6975117218213954584_o_nat: produc1534263882305827951_o_nat > set_Pr6274769524298744783_o_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member3674313732307032336at_nat: produc6206612473762214375at_nat > set_Pr8921550766394648263at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    member3905523654690943504od_o_o: produc5781518669219163367od_o_o > set_Pr4819730946363549639od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member6858118926070794858at_nat: produc2304671794888584641at_nat > set_Pr4231629511564852513at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J_J_J,type,
    member7884865674050070224od_o_o: produc7738053905463721127od_o_o > set_Pr3057449061824239751od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
    member4903802553882211088od_a_a: produc7983190928304305895od_a_a > set_Pr5931134355633282247od_a_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    member9169340693537962768od_o_o: produc7004997421203748071od_o_o > set_Pr7077720281583819975od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member4300370950623927696at_nat: produc7299876168958306407at_nat > set_Pr1604112560894399303at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_Itf__a_J_Mt__Set__Oset_Itf__a_J_J,type,
    member7983343339038529360_set_a: produc1703568184450464039_set_a > set_Pr5845495582615845127_set_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    member5845106769783146937od_o_o: produc931656912218737808od_o_o > set_Pr5975447109543910128od_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member6868933294997782035at_nat: produc3842678439083338090at_nat > set_Pr1968968238647823434at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member4313070330384631353at_nat: produc656436880464960016at_nat > set_Pr8044876533244767088at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
    member1426531477525435216od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    member3157015407008874800od_o_o: set_Product_prod_o_o > set_se491199571785101031od_o_o > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    member4387393612980313840od_o_o: set_Pr1932065953672099015od_o_o > set_se9147984907235033255od_o_o > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member3243375828287704010at_nat: set_Pr457366540195662369at_nat > set_se5885513654436145793at_nat > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member6273874620674182256at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat > $o ).

thf(sy_c_member_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    member2239101972932892176od_o_o: set_se491199571785101031od_o_o > set_se5342866143169225671od_o_o > $o ).

thf(sy_c_member_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member8313122109188517482at_nat: set_se7855581050983116737at_nat > set_se5158245632345848097at_nat > $o ).

thf(sy_c_member_001t__Set__Oset_Itf__a_J,type,
    member_set_a: set_a > set_set_a > $o ).

thf(sy_c_member_001tf__a,type,
    member_a: a > set_a > $o ).

thf(sy_v_A,type,
    a2: assertion_a_b_d_c ).

thf(sy_v_B,type,
    b2: assertion_a_b_d_c ).

thf(sy_v__092_060Delta_062,type,
    delta: ( c > d ) > set_a ).

thf(sy_v__092_060sigma_062_H____,type,
    sigma: a ).

thf(sy_v__092_060sigma_062____,type,
    sigma2: a ).

thf(sy_v_a____,type,
    a3: a ).

thf(sy_v_aa____,type,
    aa: a ).

thf(sy_v_aaa____,type,
    aaa: a ).

thf(sy_v_b____,type,
    b3: a ).

thf(sy_v_baa____,type,
    baa: a ).

thf(sy_v_mult,type,
    mult: b > a > a ).

thf(sy_v_one,type,
    one: b ).

thf(sy_v_p____,type,
    p: b ).

thf(sy_v_plus,type,
    plus: a > a > option_a ).

thf(sy_v_q____,type,
    q: b ).

thf(sy_v_s____,type,
    s: c > d ).

thf(sy_v_sadd,type,
    sadd: b > b > b ).

thf(sy_v_sinv,type,
    sinv: b > b ).

thf(sy_v_smult,type,
    smult: b > b > b ).

thf(sy_v_valid,type,
    valid: a > $o ).

thf(sy_v_x____,type,
    x: a ).

% Relevant facts (1273)
thf(fact_0_commutative,axiom,
    ! [A: a,B: a] :
      ( ( plus @ A @ B )
      = ( plus @ B @ A ) ) ).

% commutative
thf(fact_1_can__divide,axiom,
    ! [P: b,A: a,B: a] :
      ( ( ( mult @ P @ A )
        = ( mult @ P @ B ) )
     => ( A = B ) ) ).

% can_divide
thf(fact_2_unique__inv,axiom,
    ! [A: a,P: b,B: a] :
      ( ( A
        = ( mult @ P @ B ) )
      = ( B
        = ( mult @ ( sinv @ P ) @ A ) ) ) ).

% unique_inv
thf(fact_3_pure__def,axiom,
    ! [A2: assertion_a_b_d_c] :
      ( ( pure_a_b_d_c @ plus @ mult @ valid @ A2 )
      = ( ! [Sigma: a,Sigma2: a,S: c > d,Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
            ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta @ A2 )
            = ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S @ Delta2 @ A2 ) ) ) ) ).

% pure_def
thf(fact_4_equivalentI,axiom,
    ! [Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ! [Sigma3: a,S2: c > d] :
          ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta3 @ A2 )
         => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta3 @ B2 ) )
     => ( ! [Sigma3: a,S2: c > d] :
            ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta3 @ B2 )
           => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta3 @ A2 ) )
       => ( equivalent_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta3 @ B2 ) ) ) ).

% equivalentI
thf(fact_5_entailsI,axiom,
    ! [Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ! [Sigma3: a,S2: c > d] :
          ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta3 @ A2 )
         => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta3 @ B2 ) )
     => ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta3 @ B2 ) ) ).

% entailsI
thf(fact_6_entails__def,axiom,
    ! [A2: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
      ( ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta3 @ B2 )
      = ( ! [Sigma: a,S: c > d] :
            ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta3 @ A2 )
           => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta3 @ B2 ) ) ) ) ).

% entails_def
thf(fact_7_one__neutral,axiom,
    ! [A: a] :
      ( ( mult @ one @ A )
      = A ) ).

% one_neutral
thf(fact_8_sat_Osimps_I10_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ pred_a_b_d_c )
      = ( member_a @ Sigma4 @ ( Delta3 @ S3 ) ) ) ).

% sat.simps(10)
thf(fact_9_not__in__fv__def,axiom,
    ! [A2: assertion_a_b_d_c,S4: set_c] :
      ( ( not_in_fv_a_b_d_c @ plus @ mult @ valid @ A2 @ S4 )
      = ( ! [Sigma: a,S: c > d,Delta: ( c > d ) > set_a,S5: c > d] :
            ( ( equal_outside_c_d @ S @ S5 @ S4 )
           => ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta @ A2 )
              = ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S5 @ Delta @ A2 ) ) ) ) ) ).

% not_in_fv_def
thf(fact_10_sat_Osimps_I12_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( wildcard_a_b_d_c @ A2 ) )
      = ( ? [A3: a,P2: b] :
            ( ( Sigma4
              = ( mult @ P2 @ A3 ) )
            & ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S3 @ Delta3 @ A2 ) ) ) ) ).

% sat.simps(12)
thf(fact_11_sat_Osimps_I7_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( and_a_b_d_c @ A2 @ B2 ) )
      = ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ A2 )
        & ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ B2 ) ) ) ).

% sat.simps(7)
thf(fact_12_sat_Osimps_I6_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( or_a_b_d_c @ A2 @ B2 ) )
      = ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ A2 )
        | ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ B2 ) ) ) ).

% sat.simps(6)
thf(fact_13_sat_Osimps_I5_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( imp_a_b_d_c @ A2 @ B2 ) )
      = ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ A2 )
       => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ B2 ) ) ) ).

% sat.simps(5)
thf(fact_14_sat__imp,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ A2 )
       => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ B2 ) )
     => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ).

% sat_imp
thf(fact_15_sat_Osimps_I11_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( bounded_a_b_d_c @ A2 ) )
      = ( ( valid @ Sigma4 )
       => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ A2 ) ) ) ).

% sat.simps(11)
thf(fact_16_sat_Osimps_I1_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,P: b,A2: assertion_a_b_d_c] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( mult_b_a_d_c @ P @ A2 ) )
      = ( ? [A3: a] :
            ( ( Sigma4
              = ( mult @ P @ A3 ) )
            & ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S3 @ Delta3 @ A2 ) ) ) ) ).

% sat.simps(1)
thf(fact_17_sat__mult,axiom,
    ! [Sigma4: a,P: b,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ! [A4: a] :
          ( ( Sigma4
            = ( mult @ P @ A4 ) )
         => ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S3 @ Delta3 @ A2 ) )
     => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ).

% sat_mult
thf(fact_18_equivalent__def,axiom,
    ! [A2: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
      ( ( equivalent_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta3 @ B2 )
      = ( ( entails_a_b_d_c @ plus @ mult @ valid @ A2 @ Delta3 @ B2 )
        & ( entails_a_b_d_c @ plus @ mult @ valid @ B2 @ Delta3 @ A2 ) ) ) ).

% equivalent_def
thf(fact_19_sinv__inverse,axiom,
    ! [P: b] :
      ( ( smult @ P @ ( sinv @ P ) )
      = one ) ).

% sinv_inverse
thf(fact_20_assms,axiom,
    combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ delta @ b2 ).

% assms
thf(fact_21_sat_Osimps_I4_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,B: ( c > d ) > a > $o] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( sem_c_d_a_b @ B ) )
      = ( B @ S3 @ Sigma4 ) ) ).

% sat.simps(4)
thf(fact_22_valid__mono,axiom,
    ! [A: a,B: a] :
      ( ( ( valid @ A )
        & ( pre_larger_a @ plus @ A @ B ) )
     => ( valid @ B ) ) ).

% valid_mono
thf(fact_23_larger__same,axiom,
    ! [A: a,B: a,P: b] :
      ( ( pre_larger_a @ plus @ A @ B )
      = ( pre_larger_a @ plus @ ( mult @ P @ A ) @ ( mult @ P @ B ) ) ) ).

% larger_same
thf(fact_24_compatible__multiples,axiom,
    ! [P: b,A: a,Q: b,B: a] :
      ( ( pre_compatible_a @ plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) )
     => ( pre_compatible_a @ plus @ A @ B ) ) ).

% compatible_multiples
thf(fact_25_compatible__imp,axiom,
    ! [A: a,B: a,P: b] :
      ( ( pre_compatible_a @ plus @ A @ B )
     => ( pre_compatible_a @ plus @ ( mult @ P @ A ) @ ( mult @ P @ B ) ) ) ).

% compatible_imp
thf(fact_26_compatible__iff,axiom,
    ! [A: a,B: a,P: b] :
      ( ( pre_compatible_a @ plus @ A @ B )
      = ( pre_compatible_a @ plus @ ( mult @ P @ A ) @ ( mult @ P @ B ) ) ) ).

% compatible_iff
thf(fact_27_sadd__comm,axiom,
    ! [P: b,Q: b] :
      ( ( sadd @ P @ Q )
      = ( sadd @ Q @ P ) ) ).

% sadd_comm
thf(fact_28_smult__asso,axiom,
    ! [P: b,Q: b,R: b] :
      ( ( smult @ ( smult @ P @ Q ) @ R )
      = ( smult @ P @ ( smult @ Q @ R ) ) ) ).

% smult_asso
thf(fact_29_smult__comm,axiom,
    ! [P: b,Q: b] :
      ( ( smult @ P @ Q )
      = ( smult @ Q @ P ) ) ).

% smult_comm
thf(fact_30_double__mult,axiom,
    ! [P: b,Q: b,A: a] :
      ( ( mult @ P @ ( mult @ Q @ A ) )
      = ( mult @ ( smult @ P @ Q ) @ A ) ) ).

% double_mult
thf(fact_31_smult__distrib,axiom,
    ! [P: b,Q: b,R: b] :
      ( ( smult @ P @ ( sadd @ Q @ R ) )
      = ( sadd @ ( smult @ P @ Q ) @ ( smult @ P @ R ) ) ) ).

% smult_distrib
thf(fact_32_compatible__smaller,axiom,
    ! [A: a,B: a,X: a] :
      ( ( pre_larger_a @ plus @ A @ B )
     => ( ( pre_compatible_a @ plus @ X @ A )
       => ( pre_compatible_a @ plus @ X @ B ) ) ) ).

% compatible_smaller
thf(fact_33_larger__implies__compatible,axiom,
    ! [X: a,Y: a] :
      ( ( pre_larger_a @ plus @ X @ Y )
     => ( pre_compatible_a @ plus @ X @ Y ) ) ).

% larger_implies_compatible
thf(fact_34_sone__neutral,axiom,
    ! [P: b] :
      ( ( smult @ one @ P )
      = P ) ).

% sone_neutral
thf(fact_35_intuitionisticI,axiom,
    ! [S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ! [A4: a,B3: a] :
          ( ( ( pre_larger_a @ plus @ A4 @ B3 )
            & ( sat_a_b_c_d @ plus @ mult @ valid @ B3 @ S3 @ Delta3 @ A2 ) )
         => ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S3 @ Delta3 @ A2 ) )
     => ( intuit7508411120625971703_b_c_d @ plus @ mult @ valid @ S3 @ Delta3 @ A2 ) ) ).

% intuitionisticI
thf(fact_36_mem__Collect__eq,axiom,
    ! [A: produc2934264451710624999od_o_o,P3: produc2934264451710624999od_o_o > $o] :
      ( ( member444158400953824016od_o_o @ A @ ( collec3302784863738620242od_o_o @ P3 ) )
      = ( P3 @ A ) ) ).

% mem_Collect_eq
thf(fact_37_mem__Collect__eq,axiom,
    ! [A: produc732395585841259969at_nat,P3: produc732395585841259969at_nat > $o] :
      ( ( member4095101504841534314at_nat @ A @ ( collec1729919521702017196at_nat @ P3 ) )
      = ( P3 @ A ) ) ).

% mem_Collect_eq
thf(fact_38_mem__Collect__eq,axiom,
    ! [A: produc3843707927480180839at_nat,P3: produc3843707927480180839at_nat > $o] :
      ( ( member8757157785044589968at_nat @ A @ ( collec6321179662152712658at_nat @ P3 ) )
      = ( P3 @ A ) ) ).

% mem_Collect_eq
thf(fact_39_mem__Collect__eq,axiom,
    ! [A: a,P3: a > $o] :
      ( ( member_a @ A @ ( collect_a @ P3 ) )
      = ( P3 @ A ) ) ).

% mem_Collect_eq
thf(fact_40_Collect__mem__eq,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o] :
      ( ( collec3302784863738620242od_o_o
        @ ^ [X2: produc2934264451710624999od_o_o] : ( member444158400953824016od_o_o @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_41_Collect__mem__eq,axiom,
    ! [A2: set_Pr457366540195662369at_nat] :
      ( ( collec1729919521702017196at_nat
        @ ^ [X2: produc732395585841259969at_nat] : ( member4095101504841534314at_nat @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_42_Collect__mem__eq,axiom,
    ! [A2: set_Pr4329608150637261639at_nat] :
      ( ( collec6321179662152712658at_nat
        @ ^ [X2: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_43_Collect__mem__eq,axiom,
    ! [A2: set_a] :
      ( ( collect_a
        @ ^ [X2: a] : ( member_a @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_44_intuitionistic__def,axiom,
    ! [S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( intuit7508411120625971703_b_c_d @ plus @ mult @ valid @ S3 @ Delta3 @ A2 )
      = ( ! [A3: a,B4: a] :
            ( ( ( pre_larger_a @ plus @ A3 @ B4 )
              & ( sat_a_b_c_d @ plus @ mult @ valid @ B4 @ S3 @ Delta3 @ A2 ) )
           => ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S3 @ Delta3 @ A2 ) ) ) ) ).

% intuitionistic_def
thf(fact_45_logic__axioms,axiom,
    logic_a_b @ plus @ mult @ smult @ sadd @ sinv @ one @ valid ).

% logic_axioms
thf(fact_46_pre__logic_Ocompatible_Ocong,axiom,
    pre_compatible_a = pre_compatible_a ).

% pre_logic.compatible.cong
thf(fact_47_pre__logic_Olarger_Ocong,axiom,
    pre_larger_a = pre_larger_a ).

% pre_logic.larger.cong
thf(fact_48_logic_Ocombinable_Ocong,axiom,
    combinable_a_b_c_d = combinable_a_b_c_d ).

% logic.combinable.cong
thf(fact_49_assertion_Odistinct_I17_J,axiom,
    ! [X1: ( c > d ) > a > $o] :
      ( ( sem_c_d_a_b @ X1 )
     != pred_a_b_d_c ) ).

% assertion.distinct(17)
thf(fact_50_logic_Osat_Ocong,axiom,
    sat_a_b_c_d = sat_a_b_c_d ).

% logic.sat.cong
thf(fact_51_logic_Oentails_Ocong,axiom,
    entails_a_b_d_c = entails_a_b_d_c ).

% logic.entails.cong
thf(fact_52_logic_Oequivalent_Ocong,axiom,
    equivalent_a_b_d_c = equivalent_a_b_d_c ).

% logic.equivalent.cong
thf(fact_53_logic_Opure_Ocong,axiom,
    pure_a_b_d_c = pure_a_b_d_c ).

% logic.pure.cong
thf(fact_54_assertion_Odistinct_I37_J,axiom,
    ! [X21: b,X22: assertion_a_b_d_c] :
      ( ( mult_b_a_d_c @ X21 @ X22 )
     != pred_a_b_d_c ) ).

% assertion.distinct(37)
thf(fact_55_assertion_Odistinct_I127_J,axiom,
    ! [X11: assertion_a_b_d_c] :
      ( pred_a_b_d_c
     != ( bounded_a_b_d_c @ X11 ) ) ).

% assertion.distinct(127)
thf(fact_56_assertion_Odistinct_I107_J,axiom,
    ! [X71: assertion_a_b_d_c,X72: assertion_a_b_d_c] :
      ( ( imp_a_b_d_c @ X71 @ X72 )
     != pred_a_b_d_c ) ).

% assertion.distinct(107)
thf(fact_57_assertion_Odistinct_I85_J,axiom,
    ! [X51: assertion_a_b_d_c,X52: assertion_a_b_d_c] :
      ( ( or_a_b_d_c @ X51 @ X52 )
     != pred_a_b_d_c ) ).

% assertion.distinct(85)
thf(fact_58_assertion_Odistinct_I97_J,axiom,
    ! [X61: assertion_a_b_d_c,X62: assertion_a_b_d_c] :
      ( ( and_a_b_d_c @ X61 @ X62 )
     != pred_a_b_d_c ) ).

% assertion.distinct(97)
thf(fact_59_assertion_Odistinct_I129_J,axiom,
    ! [X12: assertion_a_b_d_c] :
      ( pred_a_b_d_c
     != ( wildcard_a_b_d_c @ X12 ) ) ).

% assertion.distinct(129)
thf(fact_60_combinable__def,axiom,
    ! [Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A2 )
      = ( ! [P2: b,Q2: b] : ( entails_a_b_d_c @ plus @ mult @ valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P2 @ A2 ) @ ( mult_b_a_d_c @ Q2 @ A2 ) ) @ Delta3 @ ( mult_b_a_d_c @ ( sadd @ P2 @ Q2 ) @ A2 ) ) ) ) ).

% combinable_def
thf(fact_61_combinable__instantiate__one,axiom,
    ! [Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S3: c > d,B: a,X: a,P: b,Q: b] :
      ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A2 )
     => ( ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S3 @ Delta3 @ A2 )
       => ( ( sat_a_b_c_d @ plus @ mult @ valid @ B @ S3 @ Delta3 @ A2 )
         => ( ( ( some_a @ X )
              = ( plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) ) )
           => ( ( ( sadd @ P @ Q )
                = one )
             => ( sat_a_b_c_d @ plus @ mult @ valid @ X @ S3 @ Delta3 @ A2 ) ) ) ) ) ) ).

% combinable_instantiate_one
thf(fact_62_combinable__instantiate,axiom,
    ! [Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S3: c > d,B: a,X: a,P: b,Q: b] :
      ( ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A2 )
     => ( ( sat_a_b_c_d @ plus @ mult @ valid @ A @ S3 @ Delta3 @ A2 )
       => ( ( sat_a_b_c_d @ plus @ mult @ valid @ B @ S3 @ Delta3 @ A2 )
         => ( ( ( some_a @ X )
              = ( plus @ ( mult @ P @ A ) @ ( mult @ Q @ B ) ) )
           => ( sat_a_b_c_d @ plus @ mult @ valid @ X @ S3 @ Delta3 @ ( mult_b_a_d_c @ ( sadd @ P @ Q ) @ A2 ) ) ) ) ) ) ).

% combinable_instantiate
thf(fact_63_combinableI__old,axiom,
    ! [Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ! [A4: a,B3: a,P4: b,Q3: b,X3: a,Sigma3: a,S2: c > d] :
          ( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S2 @ Delta3 @ A2 )
            & ( sat_a_b_c_d @ plus @ mult @ valid @ B3 @ S2 @ Delta3 @ A2 )
            & ( ( some_a @ Sigma3 )
              = ( plus @ ( mult @ P4 @ A4 ) @ ( mult @ Q3 @ B3 ) ) )
            & ( Sigma3
              = ( mult @ ( sadd @ P4 @ Q3 ) @ X3 ) ) )
         => ( sat_a_b_c_d @ plus @ mult @ valid @ X3 @ S2 @ Delta3 @ A2 ) )
     => ( combinable_a_b_c_d @ plus @ mult @ sadd @ valid @ Delta3 @ A2 ) ) ).

% combinableI_old
thf(fact_64_distrib__mult,axiom,
    ! [P: b,Q: b,X: a] :
      ( ( some_a @ ( mult @ ( sadd @ P @ Q ) @ X ) )
      = ( plus @ ( mult @ P @ X ) @ ( mult @ Q @ X ) ) ) ).

% distrib_mult
thf(fact_65_compatible__def,axiom,
    ! [A: a,B: a] :
      ( ( pre_compatible_a @ plus @ A @ B )
      = ( ( plus @ A @ B )
       != none_a ) ) ).

% compatible_def
thf(fact_66_plus__mult,axiom,
    ! [A: a,B: a,C: a,P: b] :
      ( ( ( some_a @ A )
        = ( plus @ B @ C ) )
     => ( ( some_a @ ( mult @ P @ A ) )
        = ( plus @ ( mult @ P @ B ) @ ( mult @ P @ C ) ) ) ) ).

% plus_mult
thf(fact_67_larger__def,axiom,
    ! [A: a,B: a] :
      ( ( pre_larger_a @ plus @ A @ B )
      = ( ? [C2: a] :
            ( ( some_a @ A )
            = ( plus @ B @ C2 ) ) ) ) ).

% larger_def
thf(fact_68_larger__first__sum,axiom,
    ! [Y: a,A: a,B: a,X: a] :
      ( ( ( some_a @ Y )
        = ( plus @ A @ B ) )
     => ( ( pre_larger_a @ plus @ X @ Y )
       => ? [A5: a] :
            ( ( ( some_a @ X )
              = ( plus @ A5 @ B ) )
            & ( pre_larger_a @ plus @ A5 @ A ) ) ) ) ).

% larger_first_sum
thf(fact_69_sum__both__larger,axiom,
    ! [X4: a,A6: a,B5: a,X: a,A: a,B: a] :
      ( ( ( some_a @ X4 )
        = ( plus @ A6 @ B5 ) )
     => ( ( ( some_a @ X )
          = ( plus @ A @ B ) )
       => ( ( pre_larger_a @ plus @ A6 @ A )
         => ( ( pre_larger_a @ plus @ B5 @ B )
           => ( pre_larger_a @ plus @ X4 @ X ) ) ) ) ) ).

% sum_both_larger
thf(fact_70_move__sum,axiom,
    ! [A: a,A1: a,A22: a,B: a,B1: a,B22: a,X: a,X1: a,X23: a] :
      ( ( ( some_a @ A )
        = ( plus @ A1 @ A22 ) )
     => ( ( ( some_a @ B )
          = ( plus @ B1 @ B22 ) )
       => ( ( ( some_a @ X )
            = ( plus @ A @ B ) )
         => ( ( ( some_a @ X1 )
              = ( plus @ A1 @ B1 ) )
           => ( ( ( some_a @ X23 )
                = ( plus @ A22 @ B22 ) )
             => ( ( some_a @ X )
                = ( plus @ X1 @ X23 ) ) ) ) ) ) ) ).

% move_sum
thf(fact_71_asso1,axiom,
    ! [A: a,B: a,Ab: a,C: a,Bc: a] :
      ( ( ( ( plus @ A @ B )
          = ( some_a @ Ab ) )
        & ( ( plus @ B @ C )
          = ( some_a @ Bc ) ) )
     => ( ( plus @ Ab @ C )
        = ( plus @ A @ Bc ) ) ) ).

% asso1
thf(fact_72_asso3,axiom,
    ! [A: a,B: a,C: a,Bc: a] :
      ( ~ ( pre_compatible_a @ plus @ A @ B )
     => ( ( ( plus @ B @ C )
          = ( some_a @ Bc ) )
       => ~ ( pre_compatible_a @ plus @ A @ Bc ) ) ) ).

% asso3
thf(fact_73_asso2,axiom,
    ! [A: a,B: a,Ab: a,C: a] :
      ( ( ( ( plus @ A @ B )
          = ( some_a @ Ab ) )
        & ~ ( pre_compatible_a @ plus @ B @ C ) )
     => ~ ( pre_compatible_a @ plus @ Ab @ C ) ) ).

% asso2
thf(fact_74_sat_Osimps_I2_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( star_a_b_d_c @ A2 @ B2 ) )
      = ( ? [A3: a,B4: a] :
            ( ( ( some_a @ Sigma4 )
              = ( plus @ A3 @ B4 ) )
            & ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S3 @ Delta3 @ A2 )
            & ( sat_a_b_c_d @ plus @ mult @ valid @ B4 @ S3 @ Delta3 @ B2 ) ) ) ) ).

% sat.simps(2)
thf(fact_75_logic_Osat_Osimps_I2_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( star_a_b_d_c @ A2 @ B2 ) )
        = ( ? [A3: a,B4: a] :
              ( ( ( some_a @ Sigma4 )
                = ( Plus @ A3 @ B4 ) )
              & ( sat_a_b_c_d @ Plus @ Mult @ Valid @ A3 @ S3 @ Delta3 @ A2 )
              & ( sat_a_b_c_d @ Plus @ Mult @ Valid @ B4 @ S3 @ Delta3 @ B2 ) ) ) ) ) ).

% logic.sat.simps(2)
thf(fact_76_logic_Osmult__distrib,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,R: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( Smult @ P @ ( Sadd @ Q @ R ) )
        = ( Sadd @ ( Smult @ P @ Q ) @ ( Smult @ P @ R ) ) ) ) ).

% logic.smult_distrib
thf(fact_77_logic_Osone__neutral,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( Smult @ One @ P )
        = P ) ) ).

% logic.sone_neutral
thf(fact_78_logic_Osinv__inverse,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( Smult @ P @ ( Sinv @ P ) )
        = One ) ) ).

% logic.sinv_inverse
thf(fact_79_logic_Odistrib__mult,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,X: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( some_a @ ( Mult @ ( Sadd @ P @ Q ) @ X ) )
        = ( Plus @ ( Mult @ P @ X ) @ ( Mult @ Q @ X ) ) ) ) ).

% logic.distrib_mult
thf(fact_80_logic_Oone__neutral,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( Mult @ One @ A )
        = A ) ) ).

% logic.one_neutral
thf(fact_81_logic_Odouble__mult,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,A: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( Mult @ P @ ( Mult @ Q @ A ) )
        = ( Mult @ ( Smult @ P @ Q ) @ A ) ) ) ).

% logic.double_mult
thf(fact_82_logic_Ocommutative,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( Plus @ A @ B )
        = ( Plus @ B @ A ) ) ) ).

% logic.commutative
thf(fact_83_logic_Ounique__inv,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,P: b,B: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( A
          = ( Mult @ P @ B ) )
        = ( B
          = ( Mult @ ( Sinv @ P ) @ A ) ) ) ) ).

% logic.unique_inv
thf(fact_84_logic_Osmult__comm,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( Smult @ P @ Q )
        = ( Smult @ Q @ P ) ) ) ).

% logic.smult_comm
thf(fact_85_logic_Osmult__asso,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b,R: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( Smult @ ( Smult @ P @ Q ) @ R )
        = ( Smult @ P @ ( Smult @ Q @ R ) ) ) ) ).

% logic.smult_asso
thf(fact_86_logic_Ocan__divide,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A: a,B: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( ( Mult @ P @ A )
          = ( Mult @ P @ B ) )
       => ( A = B ) ) ) ).

% logic.can_divide
thf(fact_87_logic_Osadd__comm,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,Q: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( Sadd @ P @ Q )
        = ( Sadd @ Q @ P ) ) ) ).

% logic.sadd_comm
thf(fact_88_logic_Oplus__mult,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,C: a,P: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( ( some_a @ A )
          = ( Plus @ B @ C ) )
       => ( ( some_a @ ( Mult @ P @ A ) )
          = ( Plus @ ( Mult @ P @ B ) @ ( Mult @ P @ C ) ) ) ) ) ).

% logic.plus_mult
thf(fact_89_logic_Omove__sum,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,A1: a,A22: a,B: a,B1: a,B22: a,X: a,X1: a,X23: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( ( some_a @ A )
          = ( Plus @ A1 @ A22 ) )
       => ( ( ( some_a @ B )
            = ( Plus @ B1 @ B22 ) )
         => ( ( ( some_a @ X )
              = ( Plus @ A @ B ) )
           => ( ( ( some_a @ X1 )
                = ( Plus @ A1 @ B1 ) )
             => ( ( ( some_a @ X23 )
                  = ( Plus @ A22 @ B22 ) )
               => ( ( some_a @ X )
                  = ( Plus @ X1 @ X23 ) ) ) ) ) ) ) ) ).

% logic.move_sum
thf(fact_90_logic_Oasso1,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,Ab: a,C: a,Bc: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( ( ( Plus @ A @ B )
            = ( some_a @ Ab ) )
          & ( ( Plus @ B @ C )
            = ( some_a @ Bc ) ) )
       => ( ( Plus @ Ab @ C )
          = ( Plus @ A @ Bc ) ) ) ) ).

% logic.asso1
thf(fact_91_logic_Oasso2,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,Ab: a,C: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( ( ( Plus @ A @ B )
            = ( some_a @ Ab ) )
          & ~ ( pre_compatible_a @ Plus @ B @ C ) )
       => ~ ( pre_compatible_a @ Plus @ Ab @ C ) ) ) ).

% logic.asso2
thf(fact_92_logic_Oasso3,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,C: a,Bc: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ~ ( pre_compatible_a @ Plus @ A @ B )
       => ( ( ( Plus @ B @ C )
            = ( some_a @ Bc ) )
         => ~ ( pre_compatible_a @ Plus @ A @ Bc ) ) ) ) ).

% logic.asso3
thf(fact_93_logic_Osum__both__larger,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X4: a,A6: a,B5: a,X: a,A: a,B: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( ( some_a @ X4 )
          = ( Plus @ A6 @ B5 ) )
       => ( ( ( some_a @ X )
            = ( Plus @ A @ B ) )
         => ( ( pre_larger_a @ Plus @ A6 @ A )
           => ( ( pre_larger_a @ Plus @ B5 @ B )
             => ( pre_larger_a @ Plus @ X4 @ X ) ) ) ) ) ) ).

% logic.sum_both_larger
thf(fact_94_logic_Olarger__first__sum,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Y: a,A: a,B: a,X: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( ( some_a @ Y )
          = ( Plus @ A @ B ) )
       => ( ( pre_larger_a @ Plus @ X @ Y )
         => ? [A5: a] :
              ( ( ( some_a @ X )
                = ( Plus @ A5 @ B ) )
              & ( pre_larger_a @ Plus @ A5 @ A ) ) ) ) ) ).

% logic.larger_first_sum
thf(fact_95_logic__def,axiom,
    ( logic_a_b
    = ( ^ [Plus2: a > a > option_a,Mult2: b > a > a,Smult2: b > b > b,Sadd2: b > b > b,Sinv2: b > b,One2: b,Valid2: a > $o] :
          ( ! [A3: a,B4: a] :
              ( ( Plus2 @ A3 @ B4 )
              = ( Plus2 @ B4 @ A3 ) )
          & ! [A3: a,B4: a,Ab2: a,C2: a,Bc2: a] :
              ( ( ( ( Plus2 @ A3 @ B4 )
                  = ( some_a @ Ab2 ) )
                & ( ( Plus2 @ B4 @ C2 )
                  = ( some_a @ Bc2 ) ) )
             => ( ( Plus2 @ Ab2 @ C2 )
                = ( Plus2 @ A3 @ Bc2 ) ) )
          & ! [A3: a,B4: a,Ab2: a,C2: a] :
              ( ( ( ( Plus2 @ A3 @ B4 )
                  = ( some_a @ Ab2 ) )
                & ~ ( pre_compatible_a @ Plus2 @ B4 @ C2 ) )
             => ~ ( pre_compatible_a @ Plus2 @ Ab2 @ C2 ) )
          & ! [P2: b] :
              ( ( Smult2 @ P2 @ ( Sinv2 @ P2 ) )
              = One2 )
          & ! [P2: b] :
              ( ( Smult2 @ One2 @ P2 )
              = P2 )
          & ! [P2: b,Q2: b] :
              ( ( Sadd2 @ P2 @ Q2 )
              = ( Sadd2 @ Q2 @ P2 ) )
          & ! [P2: b,Q2: b] :
              ( ( Smult2 @ P2 @ Q2 )
              = ( Smult2 @ Q2 @ P2 ) )
          & ! [P2: b,Q2: b,R2: b] :
              ( ( Smult2 @ P2 @ ( Sadd2 @ Q2 @ R2 ) )
              = ( Sadd2 @ ( Smult2 @ P2 @ Q2 ) @ ( Smult2 @ P2 @ R2 ) ) )
          & ! [P2: b,Q2: b,R2: b] :
              ( ( Smult2 @ ( Smult2 @ P2 @ Q2 ) @ R2 )
              = ( Smult2 @ P2 @ ( Smult2 @ Q2 @ R2 ) ) )
          & ! [P2: b,Q2: b,A3: a] :
              ( ( Mult2 @ P2 @ ( Mult2 @ Q2 @ A3 ) )
              = ( Mult2 @ ( Smult2 @ P2 @ Q2 ) @ A3 ) )
          & ! [A3: a,B4: a,C2: a,P2: b] :
              ( ( ( some_a @ A3 )
                = ( Plus2 @ B4 @ C2 ) )
             => ( ( some_a @ ( Mult2 @ P2 @ A3 ) )
                = ( Plus2 @ ( Mult2 @ P2 @ B4 ) @ ( Mult2 @ P2 @ C2 ) ) ) )
          & ! [P2: b,Q2: b,X2: a] :
              ( ( some_a @ ( Mult2 @ ( Sadd2 @ P2 @ Q2 ) @ X2 ) )
              = ( Plus2 @ ( Mult2 @ P2 @ X2 ) @ ( Mult2 @ Q2 @ X2 ) ) )
          & ! [A3: a] :
              ( ( Mult2 @ One2 @ A3 )
              = A3 )
          & ! [A3: a,B4: a] :
              ( ( ( Valid2 @ A3 )
                & ( pre_larger_a @ Plus2 @ A3 @ B4 ) )
             => ( Valid2 @ B4 ) ) ) ) ) ).

% logic_def
thf(fact_96_logic_Ocombinable__instantiate__one,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S3: c > d,B: a,X: a,P: b,Q: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( combinable_a_b_c_d @ Plus @ Mult @ Sadd @ Valid @ Delta3 @ A2 )
       => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ A @ S3 @ Delta3 @ A2 )
         => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ B @ S3 @ Delta3 @ A2 )
           => ( ( ( some_a @ X )
                = ( Plus @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) ) )
             => ( ( ( Sadd @ P @ Q )
                  = One )
               => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ X @ S3 @ Delta3 @ A2 ) ) ) ) ) ) ) ).

% logic.combinable_instantiate_one
thf(fact_97_logic_OcombinableI__old,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ! [A4: a,B3: a,P4: b,Q3: b,X3: a,Sigma3: a,S2: c > d] :
            ( ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ A4 @ S2 @ Delta3 @ A2 )
              & ( sat_a_b_c_d @ Plus @ Mult @ Valid @ B3 @ S2 @ Delta3 @ A2 )
              & ( ( some_a @ Sigma3 )
                = ( Plus @ ( Mult @ P4 @ A4 ) @ ( Mult @ Q3 @ B3 ) ) )
              & ( Sigma3
                = ( Mult @ ( Sadd @ P4 @ Q3 ) @ X3 ) ) )
           => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ X3 @ S2 @ Delta3 @ A2 ) )
       => ( combinable_a_b_c_d @ Plus @ Mult @ Sadd @ Valid @ Delta3 @ A2 ) ) ) ).

% logic.combinableI_old
thf(fact_98_logic_Ocompatible__iff,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,P: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( pre_compatible_a @ Plus @ A @ B )
        = ( pre_compatible_a @ Plus @ ( Mult @ P @ A ) @ ( Mult @ P @ B ) ) ) ) ).

% logic.compatible_iff
thf(fact_99_logic_Ocompatible__imp,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,P: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( pre_compatible_a @ Plus @ A @ B )
       => ( pre_compatible_a @ Plus @ ( Mult @ P @ A ) @ ( Mult @ P @ B ) ) ) ) ).

% logic.compatible_imp
thf(fact_100_logic_Ocompatible__multiples,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P: b,A: a,Q: b,B: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( pre_compatible_a @ Plus @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) )
       => ( pre_compatible_a @ Plus @ A @ B ) ) ) ).

% logic.compatible_multiples
thf(fact_101_logic_Ovalid__mono,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( ( Valid @ A )
          & ( pre_larger_a @ Plus @ A @ B ) )
       => ( Valid @ B ) ) ) ).

% logic.valid_mono
thf(fact_102_logic_Olarger__same,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,P: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( pre_larger_a @ Plus @ A @ B )
        = ( pre_larger_a @ Plus @ ( Mult @ P @ A ) @ ( Mult @ P @ B ) ) ) ) ).

% logic.larger_same
thf(fact_103_pre__logic_Olarger__def,axiom,
    ( pre_larger_a
    = ( ^ [Plus2: a > a > option_a,A3: a,B4: a] :
        ? [C2: a] :
          ( ( some_a @ A3 )
          = ( Plus2 @ B4 @ C2 ) ) ) ) ).

% pre_logic.larger_def
thf(fact_104_pre__logic_Ocompatible__def,axiom,
    ( pre_compatible_a
    = ( ^ [Plus2: a > a > option_a,A3: a,B4: a] :
          ( ( Plus2 @ A3 @ B4 )
         != none_a ) ) ) ).

% pre_logic.compatible_def
thf(fact_105_assertion_Odistinct_I55_J,axiom,
    ! [X31: assertion_a_b_d_c,X32: assertion_a_b_d_c] :
      ( ( star_a_b_d_c @ X31 @ X32 )
     != pred_a_b_d_c ) ).

% assertion.distinct(55)
thf(fact_106_logic_Ointuitionistic__def,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( intuit7508411120625971703_b_c_d @ Plus @ Mult @ Valid @ S3 @ Delta3 @ A2 )
        = ( ! [A3: a,B4: a] :
              ( ( ( pre_larger_a @ Plus @ A3 @ B4 )
                & ( sat_a_b_c_d @ Plus @ Mult @ Valid @ B4 @ S3 @ Delta3 @ A2 ) )
             => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ A3 @ S3 @ Delta3 @ A2 ) ) ) ) ) ).

% logic.intuitionistic_def
thf(fact_107_logic_OintuitionisticI,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ! [A4: a,B3: a] :
            ( ( ( pre_larger_a @ Plus @ A4 @ B3 )
              & ( sat_a_b_c_d @ Plus @ Mult @ Valid @ B3 @ S3 @ Delta3 @ A2 ) )
           => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ A4 @ S3 @ Delta3 @ A2 ) )
       => ( intuit7508411120625971703_b_c_d @ Plus @ Mult @ Valid @ S3 @ Delta3 @ A2 ) ) ) ).

% logic.intuitionisticI
thf(fact_108_logic_Ocombinable__instantiate,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,A: a,S3: c > d,B: a,X: a,P: b,Q: b] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( combinable_a_b_c_d @ Plus @ Mult @ Sadd @ Valid @ Delta3 @ A2 )
       => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ A @ S3 @ Delta3 @ A2 )
         => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ B @ S3 @ Delta3 @ A2 )
           => ( ( ( some_a @ X )
                = ( Plus @ ( Mult @ P @ A ) @ ( Mult @ Q @ B ) ) )
             => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ X @ S3 @ Delta3 @ ( mult_b_a_d_c @ ( Sadd @ P @ Q ) @ A2 ) ) ) ) ) ) ) ).

% logic.combinable_instantiate
thf(fact_109_logic_Ocombinable__def,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( combinable_a_b_c_d @ Plus @ Mult @ Sadd @ Valid @ Delta3 @ A2 )
        = ( ! [P2: b,Q2: b] : ( entails_a_b_d_c @ Plus @ Mult @ Valid @ ( star_a_b_d_c @ ( mult_b_a_d_c @ P2 @ A2 ) @ ( mult_b_a_d_c @ Q2 @ A2 ) ) @ Delta3 @ ( mult_b_a_d_c @ ( Sadd @ P2 @ Q2 ) @ A2 ) ) ) ) ) ).

% logic.combinable_def
thf(fact_110_logic_Osat_Osimps_I1_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,P: b,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( mult_b_a_d_c @ P @ A2 ) )
        = ( ? [A3: a] :
              ( ( Sigma4
                = ( Mult @ P @ A3 ) )
              & ( sat_a_b_c_d @ Plus @ Mult @ Valid @ A3 @ S3 @ Delta3 @ A2 ) ) ) ) ) ).

% logic.sat.simps(1)
thf(fact_111_logic_Osat__mult,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,P: b,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ! [A4: a] :
            ( ( Sigma4
              = ( Mult @ P @ A4 ) )
           => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ A4 @ S3 @ Delta3 @ A2 ) )
       => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( mult_b_a_d_c @ P @ A2 ) ) ) ) ).

% logic.sat_mult
thf(fact_112_logic_Osat_Osimps_I11_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( bounded_a_b_d_c @ A2 ) )
        = ( ( Valid @ Sigma4 )
         => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ A2 ) ) ) ) ).

% logic.sat.simps(11)
thf(fact_113_logic_Osat_Osimps_I5_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( imp_a_b_d_c @ A2 @ B2 ) )
        = ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ A2 )
         => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ B2 ) ) ) ) ).

% logic.sat.simps(5)
thf(fact_114_logic_Osat__imp,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ A2 )
         => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ B2 ) )
       => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( imp_a_b_d_c @ A2 @ B2 ) ) ) ) ).

% logic.sat_imp
thf(fact_115_logic_Osat_Osimps_I7_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( and_a_b_d_c @ A2 @ B2 ) )
        = ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ A2 )
          & ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ B2 ) ) ) ) ).

% logic.sat.simps(7)
thf(fact_116_logic_Osat_Osimps_I6_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( or_a_b_d_c @ A2 @ B2 ) )
        = ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ A2 )
          | ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ B2 ) ) ) ) ).

% logic.sat.simps(6)
thf(fact_117_logic_Osat_Osimps_I12_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( wildcard_a_b_d_c @ A2 ) )
        = ( ? [A3: a,P2: b] :
              ( ( Sigma4
                = ( Mult @ P2 @ A3 ) )
              & ( sat_a_b_c_d @ Plus @ Mult @ Valid @ A3 @ S3 @ Delta3 @ A2 ) ) ) ) ) ).

% logic.sat.simps(12)
thf(fact_118_logic_Osat_Osimps_I4_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,B: ( c > d ) > a > $o] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( sem_c_d_a_b @ B ) )
        = ( B @ S3 @ Sigma4 ) ) ) ).

% logic.sat.simps(4)
thf(fact_119_logic_Osat_Osimps_I10_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ pred_a_b_d_c )
        = ( member_a @ Sigma4 @ ( Delta3 @ S3 ) ) ) ) ).

% logic.sat.simps(10)
thf(fact_120_logic_Ocompatible__smaller,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A: a,B: a,X: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( pre_larger_a @ Plus @ A @ B )
       => ( ( pre_compatible_a @ Plus @ X @ A )
         => ( pre_compatible_a @ Plus @ X @ B ) ) ) ) ).

% logic.compatible_smaller
thf(fact_121_logic_Olarger__implies__compatible,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,X: a,Y: a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( pre_larger_a @ Plus @ X @ Y )
       => ( pre_compatible_a @ Plus @ X @ Y ) ) ) ).

% logic.larger_implies_compatible
thf(fact_122_logic_OentailsI,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ! [Sigma3: a,S2: c > d] :
            ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma3 @ S2 @ Delta3 @ A2 )
           => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma3 @ S2 @ Delta3 @ B2 ) )
       => ( entails_a_b_d_c @ Plus @ Mult @ Valid @ A2 @ Delta3 @ B2 ) ) ) ).

% logic.entailsI
thf(fact_123_logic_Oentails__def,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( entails_a_b_d_c @ Plus @ Mult @ Valid @ A2 @ Delta3 @ B2 )
        = ( ! [Sigma: a,S: c > d] :
              ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma @ S @ Delta3 @ A2 )
             => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma @ S @ Delta3 @ B2 ) ) ) ) ) ).

% logic.entails_def
thf(fact_124_logic_OequivalentI,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ! [Sigma3: a,S2: c > d] :
            ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma3 @ S2 @ Delta3 @ A2 )
           => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma3 @ S2 @ Delta3 @ B2 ) )
       => ( ! [Sigma3: a,S2: c > d] :
              ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma3 @ S2 @ Delta3 @ B2 )
             => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma3 @ S2 @ Delta3 @ A2 ) )
         => ( equivalent_a_b_d_c @ Plus @ Mult @ Valid @ A2 @ Delta3 @ B2 ) ) ) ) ).

% logic.equivalentI
thf(fact_125_logic_Opure__def,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( pure_a_b_d_c @ Plus @ Mult @ Valid @ A2 )
        = ( ! [Sigma: a,Sigma2: a,S: c > d,Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
              ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma @ S @ Delta @ A2 )
              = ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma2 @ S @ Delta2 @ A2 ) ) ) ) ) ).

% logic.pure_def
thf(fact_126_logic_Oequivalent__def,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,Delta3: ( c > d ) > set_a,B2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( equivalent_a_b_d_c @ Plus @ Mult @ Valid @ A2 @ Delta3 @ B2 )
        = ( ( entails_a_b_d_c @ Plus @ Mult @ Valid @ A2 @ Delta3 @ B2 )
          & ( entails_a_b_d_c @ Plus @ Mult @ Valid @ B2 @ Delta3 @ A2 ) ) ) ) ).

% logic.equivalent_def
thf(fact_127_logic_Onot__in__fv__def,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,S4: set_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( not_in_fv_a_b_d_c @ Plus @ Mult @ Valid @ A2 @ S4 )
        = ( ! [Sigma: a,S: c > d,Delta: ( c > d ) > set_a,S5: c > d] :
              ( ( equal_outside_c_d @ S @ S5 @ S4 )
             => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma @ S @ Delta @ A2 )
                = ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma @ S5 @ Delta @ A2 ) ) ) ) ) ) ).

% logic.not_in_fv_def
thf(fact_128_sat__wand,axiom,
    ! [S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,Sigma4: a,B2: assertion_a_b_d_c] :
      ( ! [A4: a,Sigma5: a] :
          ( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A4 @ S3 @ Delta3 @ A2 )
            & ( ( some_a @ Sigma5 )
              = ( plus @ Sigma4 @ A4 ) ) )
         => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma5 @ S3 @ Delta3 @ B2 ) )
     => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ).

% sat_wand
thf(fact_129_sat_Osimps_I3_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( wand_a_b_d_c @ A2 @ B2 ) )
      = ( ! [A3: a,Sigma2: a] :
            ( ( ( sat_a_b_c_d @ plus @ mult @ valid @ A3 @ S3 @ Delta3 @ A2 )
              & ( ( some_a @ Sigma2 )
                = ( plus @ Sigma4 @ A3 ) ) )
           => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S3 @ Delta3 @ B2 ) ) ) ) ).

% sat.simps(3)
thf(fact_130__092_060open_062Some_Abaa_A_061_Ab_A_092_060oplus_062_Aaa_092_060close_062,axiom,
    ( ( some_a @ baa )
    = ( plus @ b3 @ aa ) ) ).

% \<open>Some baa = b \<oplus> aa\<close>
thf(fact_131__092_060open_062Some_Aaaa_A_061_Aa_A_092_060oplus_062_Aaa_092_060close_062,axiom,
    ( ( some_a @ aaa )
    = ( plus @ a3 @ aa ) ) ).

% \<open>Some aaa = a \<oplus> aa\<close>
thf(fact_132_not__None__eq,axiom,
    ! [X: option_a] :
      ( ( X != none_a )
      = ( ? [Y2: a] :
            ( X
            = ( some_a @ Y2 ) ) ) ) ).

% not_None_eq
thf(fact_133_not__Some__eq,axiom,
    ! [X: option_a] :
      ( ( ! [Y2: a] :
            ( X
           != ( some_a @ Y2 ) ) )
      = ( X = none_a ) ) ).

% not_Some_eq
thf(fact_134__092_060open_062aa_M_As_M_A_092_060Delta_062_A_092_060Turnstile_062_AA_A_092_060and_062_ASome_A_092_060sigma_062_H_A_061_Ax_A_092_060oplus_062_Aaa_092_060close_062,axiom,
    ( ( sat_a_b_c_d @ plus @ mult @ valid @ aa @ s @ delta @ a2 )
    & ( ( some_a @ sigma )
      = ( plus @ x @ aa ) ) ) ).

% \<open>aa, s, \<Delta> \<Turnstile> A \<and> Some \<sigma>' = x \<oplus> aa\<close>
thf(fact_135_calculation,axiom,
    ( ( some_a @ ( mult @ ( sadd @ p @ q ) @ sigma ) )
    = ( plus @ ( mult @ p @ aaa ) @ ( mult @ q @ baa ) ) ) ).

% calculation
thf(fact_136_option_Oinject,axiom,
    ! [X23: a,Y22: a] :
      ( ( ( some_a @ X23 )
        = ( some_a @ Y22 ) )
      = ( X23 = Y22 ) ) ).

% option.inject
thf(fact_137_assertion_Oinject_I4_J,axiom,
    ! [X41: assertion_a_b_d_c,X42: assertion_a_b_d_c,Y41: assertion_a_b_d_c,Y42: assertion_a_b_d_c] :
      ( ( ( wand_a_b_d_c @ X41 @ X42 )
        = ( wand_a_b_d_c @ Y41 @ Y42 ) )
      = ( ( X41 = Y41 )
        & ( X42 = Y42 ) ) ) ).

% assertion.inject(4)
thf(fact_138__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062aaa_O_ASome_Aaaa_A_061_Aa_A_092_060oplus_062_Aaa_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [Aaa: a] :
        ( ( some_a @ Aaa )
       != ( plus @ a3 @ aa ) ) ).

% \<open>\<And>thesis. (\<And>aaa. Some aaa = a \<oplus> aa \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_139__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062baa_O_ASome_Abaa_A_061_Ab_A_092_060oplus_062_Aaa_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [Baa: a] :
        ( ( some_a @ Baa )
       != ( plus @ b3 @ aa ) ) ).

% \<open>\<And>thesis. (\<And>baa. Some baa = b \<oplus> aa \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_140__092_060open_062a_A_D_D_Aaa_092_060close_062,axiom,
    pre_compatible_a @ plus @ a3 @ aa ).

% \<open>a ## aa\<close>
thf(fact_141__092_060open_062b_A_D_D_Aaa_092_060close_062,axiom,
    pre_compatible_a @ plus @ b3 @ aa ).

% \<open>b ## aa\<close>
thf(fact_142__092_060open_062Some_A_Isadd_Ap_Aq_A_092_060odot_062_Aaa_J_A_061_Ap_A_092_060odot_062_Aaa_A_092_060oplus_062_Aq_A_092_060odot_062_Aaa_092_060close_062,axiom,
    ( ( some_a @ ( mult @ ( sadd @ p @ q ) @ aa ) )
    = ( plus @ ( mult @ p @ aa ) @ ( mult @ q @ aa ) ) ) ).

% \<open>Some (sadd p q \<odot> aa) = p \<odot> aa \<oplus> q \<odot> aa\<close>
thf(fact_143__092_060open_062a_M_As_M_A_092_060Delta_062_A_092_060Turnstile_062_AWand_AA_AB_A_092_060and_062_Ab_M_As_M_A_092_060Delta_062_A_092_060Turnstile_062_AWand_AA_AB_A_092_060and_062_ASome_A_092_060sigma_062_A_061_Ap_A_092_060odot_062_Aa_A_092_060oplus_062_Aq_A_092_060odot_062_Ab_A_092_060and_062_A_092_060sigma_062_A_061_Asadd_Ap_Aq_A_092_060odot_062_Ax_092_060close_062,axiom,
    ( ( sat_a_b_c_d @ plus @ mult @ valid @ a3 @ s @ delta @ ( wand_a_b_d_c @ a2 @ b2 ) )
    & ( sat_a_b_c_d @ plus @ mult @ valid @ b3 @ s @ delta @ ( wand_a_b_d_c @ a2 @ b2 ) )
    & ( ( some_a @ sigma2 )
      = ( plus @ ( mult @ p @ a3 ) @ ( mult @ q @ b3 ) ) )
    & ( sigma2
      = ( mult @ ( sadd @ p @ q ) @ x ) ) ) ).

% \<open>a, s, \<Delta> \<Turnstile> Wand A B \<and> b, s, \<Delta> \<Turnstile> Wand A B \<and> Some \<sigma> = p \<odot> a \<oplus> q \<odot> b \<and> \<sigma> = sadd p q \<odot> x\<close>
thf(fact_144__092_060open_062Some_A_Isadd_Ap_Aq_A_092_060odot_062_A_092_060sigma_062_H_J_A_061_A_092_060sigma_062_A_092_060oplus_062_Asadd_Ap_Aq_A_092_060odot_062_Aaa_092_060close_062,axiom,
    ( ( some_a @ ( mult @ ( sadd @ p @ q ) @ sigma ) )
    = ( plus @ sigma2 @ ( mult @ ( sadd @ p @ q ) @ aa ) ) ) ).

% \<open>Some (sadd p q \<odot> \<sigma>') = \<sigma> \<oplus> sadd p q \<odot> aa\<close>
thf(fact_145_assertion_Odistinct_I25_J,axiom,
    ! [X21: b,X22: assertion_a_b_d_c,X41: assertion_a_b_d_c,X42: assertion_a_b_d_c] :
      ( ( mult_b_a_d_c @ X21 @ X22 )
     != ( wand_a_b_d_c @ X41 @ X42 ) ) ).

% assertion.distinct(25)
thf(fact_146_assertion_Odistinct_I43_J,axiom,
    ! [X31: assertion_a_b_d_c,X32: assertion_a_b_d_c,X41: assertion_a_b_d_c,X42: assertion_a_b_d_c] :
      ( ( star_a_b_d_c @ X31 @ X32 )
     != ( wand_a_b_d_c @ X41 @ X42 ) ) ).

% assertion.distinct(43)
thf(fact_147_assertion_Odistinct_I73_J,axiom,
    ! [X41: assertion_a_b_d_c,X42: assertion_a_b_d_c,X11: assertion_a_b_d_c] :
      ( ( wand_a_b_d_c @ X41 @ X42 )
     != ( bounded_a_b_d_c @ X11 ) ) ).

% assertion.distinct(73)
thf(fact_148_assertion_Odistinct_I65_J,axiom,
    ! [X41: assertion_a_b_d_c,X42: assertion_a_b_d_c,X71: assertion_a_b_d_c,X72: assertion_a_b_d_c] :
      ( ( wand_a_b_d_c @ X41 @ X42 )
     != ( imp_a_b_d_c @ X71 @ X72 ) ) ).

% assertion.distinct(65)
thf(fact_149_assertion_Odistinct_I61_J,axiom,
    ! [X41: assertion_a_b_d_c,X42: assertion_a_b_d_c,X51: assertion_a_b_d_c,X52: assertion_a_b_d_c] :
      ( ( wand_a_b_d_c @ X41 @ X42 )
     != ( or_a_b_d_c @ X51 @ X52 ) ) ).

% assertion.distinct(61)
thf(fact_150_assertion_Odistinct_I63_J,axiom,
    ! [X41: assertion_a_b_d_c,X42: assertion_a_b_d_c,X61: assertion_a_b_d_c,X62: assertion_a_b_d_c] :
      ( ( wand_a_b_d_c @ X41 @ X42 )
     != ( and_a_b_d_c @ X61 @ X62 ) ) ).

% assertion.distinct(63)
thf(fact_151_assertion_Odistinct_I75_J,axiom,
    ! [X41: assertion_a_b_d_c,X42: assertion_a_b_d_c,X12: assertion_a_b_d_c] :
      ( ( wand_a_b_d_c @ X41 @ X42 )
     != ( wildcard_a_b_d_c @ X12 ) ) ).

% assertion.distinct(75)
thf(fact_152_assertion_Odistinct_I5_J,axiom,
    ! [X1: ( c > d ) > a > $o,X41: assertion_a_b_d_c,X42: assertion_a_b_d_c] :
      ( ( sem_c_d_a_b @ X1 )
     != ( wand_a_b_d_c @ X41 @ X42 ) ) ).

% assertion.distinct(5)
thf(fact_153_assertion_Odistinct_I71_J,axiom,
    ! [X41: assertion_a_b_d_c,X42: assertion_a_b_d_c] :
      ( ( wand_a_b_d_c @ X41 @ X42 )
     != pred_a_b_d_c ) ).

% assertion.distinct(71)
thf(fact_154_logic_Osat__wand,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,Sigma4: a,B2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ! [A4: a,Sigma5: a] :
            ( ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ A4 @ S3 @ Delta3 @ A2 )
              & ( ( some_a @ Sigma5 )
                = ( Plus @ Sigma4 @ A4 ) ) )
           => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma5 @ S3 @ Delta3 @ B2 ) )
       => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( wand_a_b_d_c @ A2 @ B2 ) ) ) ) ).

% logic.sat_wand
thf(fact_155_logic_Osat_Osimps_I3_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c,B2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( wand_a_b_d_c @ A2 @ B2 ) )
        = ( ! [A3: a,Sigma2: a] :
              ( ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ A3 @ S3 @ Delta3 @ A2 )
                & ( ( some_a @ Sigma2 )
                  = ( Plus @ Sigma4 @ A3 ) ) )
             => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma2 @ S3 @ Delta3 @ B2 ) ) ) ) ) ).

% logic.sat.simps(3)
thf(fact_156_combine__options__cases,axiom,
    ! [X: option_a,P3: option_a > option_a > $o,Y: option_a] :
      ( ( ( X = none_a )
       => ( P3 @ X @ Y ) )
     => ( ( ( Y = none_a )
         => ( P3 @ X @ Y ) )
       => ( ! [A4: a,B3: a] :
              ( ( X
                = ( some_a @ A4 ) )
             => ( ( Y
                  = ( some_a @ B3 ) )
               => ( P3 @ X @ Y ) ) )
         => ( P3 @ X @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_157_split__option__all,axiom,
    ( ( ^ [P5: option_a > $o] :
        ! [X5: option_a] : ( P5 @ X5 ) )
    = ( ^ [P6: option_a > $o] :
          ( ( P6 @ none_a )
          & ! [X2: a] : ( P6 @ ( some_a @ X2 ) ) ) ) ) ).

% split_option_all
thf(fact_158_split__option__ex,axiom,
    ( ( ^ [P5: option_a > $o] :
        ? [X5: option_a] : ( P5 @ X5 ) )
    = ( ^ [P6: option_a > $o] :
          ( ( P6 @ none_a )
          | ? [X2: a] : ( P6 @ ( some_a @ X2 ) ) ) ) ) ).

% split_option_ex
thf(fact_159_option_Oexhaust,axiom,
    ! [Y: option_a] :
      ( ( Y != none_a )
     => ~ ! [X24: a] :
            ( Y
           != ( some_a @ X24 ) ) ) ).

% option.exhaust
thf(fact_160_option_OdiscI,axiom,
    ! [Option: option_a,X23: a] :
      ( ( Option
        = ( some_a @ X23 ) )
     => ( Option != none_a ) ) ).

% option.discI
thf(fact_161_option_Odistinct_I1_J,axiom,
    ! [X23: a] :
      ( none_a
     != ( some_a @ X23 ) ) ).

% option.distinct(1)
thf(fact_162_not__in__fv__mod,axiom,
    ! [A2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Sigma4: a,S3: c > d,Sigma6: a,S6: c > d,X: a,Delta3: ( c > d ) > set_a] :
      ( ( not_in_fv_a_b_d_c @ plus @ mult @ valid @ A2 @ ( modified_a_c_d @ C ) )
     => ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma4 @ S3 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma6 @ S6 ) ) ) @ C )
       => ( ( sat_a_b_c_d @ plus @ mult @ valid @ X @ S3 @ Delta3 @ A2 )
          = ( sat_a_b_c_d @ plus @ mult @ valid @ X @ S6 @ Delta3 @ A2 ) ) ) ) ).

% not_in_fv_mod
thf(fact_163_assertion_Oexhaust,axiom,
    ! [Y: assertion_a_b_d_c] :
      ( ! [X13: ( c > d ) > a > $o] :
          ( Y
         != ( sem_c_d_a_b @ X13 ) )
     => ( ! [X212: b,X222: assertion_a_b_d_c] :
            ( Y
           != ( mult_b_a_d_c @ X212 @ X222 ) )
       => ( ! [X312: assertion_a_b_d_c,X322: assertion_a_b_d_c] :
              ( Y
             != ( star_a_b_d_c @ X312 @ X322 ) )
         => ( ! [X412: assertion_a_b_d_c,X422: assertion_a_b_d_c] :
                ( Y
               != ( wand_a_b_d_c @ X412 @ X422 ) )
           => ( ! [X512: assertion_a_b_d_c,X522: assertion_a_b_d_c] :
                  ( Y
                 != ( or_a_b_d_c @ X512 @ X522 ) )
             => ( ! [X612: assertion_a_b_d_c,X622: assertion_a_b_d_c] :
                    ( Y
                   != ( and_a_b_d_c @ X612 @ X622 ) )
               => ( ! [X712: assertion_a_b_d_c,X722: assertion_a_b_d_c] :
                      ( Y
                     != ( imp_a_b_d_c @ X712 @ X722 ) )
                 => ( ! [X81: c,X82: assertion_a_b_d_c] :
                        ( Y
                       != ( exists_c_a_b_d @ X81 @ X82 ) )
                   => ( ! [X91: c,X92: assertion_a_b_d_c] :
                          ( Y
                         != ( forall_c_a_b_d @ X91 @ X92 ) )
                     => ( ( Y != pred_a_b_d_c )
                       => ( ! [X112: assertion_a_b_d_c] :
                              ( Y
                             != ( bounded_a_b_d_c @ X112 ) )
                         => ~ ! [X122: assertion_a_b_d_c] :
                                ( Y
                               != ( wildcard_a_b_d_c @ X122 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% assertion.exhaust
thf(fact_164_sat_Osimps_I8_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,X: c,A2: assertion_a_b_d_c] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( exists_c_a_b_d @ X @ A2 ) )
      = ( ? [V: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ ( fun_upd_c_d @ S3 @ X @ V ) @ Delta3 @ A2 ) ) ) ).

% sat.simps(8)
thf(fact_165_sat_Osimps_I9_J,axiom,
    ! [Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,X: c,A2: assertion_a_b_d_c] :
      ( ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( forall_c_a_b_d @ X @ A2 ) )
      = ( ! [V: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ ( fun_upd_c_d @ S3 @ X @ V ) @ Delta3 @ A2 ) ) ) ).

% sat.simps(9)
thf(fact_166_sat__forall,axiom,
    ! [Sigma4: a,S3: c > d,X: c,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ! [V2: d] : ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ ( fun_upd_c_d @ S3 @ X @ V2 ) @ Delta3 @ A2 )
     => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma4 @ S3 @ Delta3 @ ( forall_c_a_b_d @ X @ A2 ) ) ) ).

% sat_forall
thf(fact_167_valid__hoare__tripleI,axiom,
    ! [Delta3: ( c > d ) > set_a,P3: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q4: assertion_a_b_d_c] :
      ( ! [Sigma3: a,S2: c > d] :
          ( ( ( valid @ Sigma3 )
            & ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta3 @ P3 ) )
         => ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma3 @ S2 ) ) )
     => ( ! [Sigma3: a,S2: c > d,Sigma5: a,S7: c > d] :
            ( ( ( valid @ Sigma3 )
              & ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma3 @ S2 @ Delta3 @ P3 ) )
           => ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma3 @ S2 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma5 @ S7 ) ) ) @ C )
             => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma5 @ S7 @ Delta3 @ Q4 ) ) )
       => ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P3 @ C @ Q4 @ Delta3 ) ) ) ).

% valid_hoare_tripleI
thf(fact_168_valid__hoare__triple__def,axiom,
    ! [P3: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q4: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
      ( ( valid_6037315502795721655_b_d_c @ plus @ mult @ valid @ P3 @ C @ Q4 @ Delta3 )
      = ( ! [Sigma: a,S: c > d] :
            ( ( ( valid @ Sigma )
              & ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma @ S @ Delta3 @ P3 ) )
           => ( ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma @ S ) )
              & ! [Sigma2: a,S5: c > d] :
                  ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma @ S ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma2 @ S5 ) ) ) @ C )
                 => ( sat_a_b_c_d @ plus @ mult @ valid @ Sigma2 @ S5 @ Delta3 @ Q4 ) ) ) ) ) ) ).

% valid_hoare_triple_def
thf(fact_169_logic_Osat_Osimps_I9_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,X: c,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( forall_c_a_b_d @ X @ A2 ) )
        = ( ! [V: d] : ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ ( fun_upd_c_d @ S3 @ X @ V ) @ Delta3 @ A2 ) ) ) ) ).

% logic.sat.simps(9)
thf(fact_170_logic_Osat__forall,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,X: c,Delta3: ( c > d ) > set_a,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ! [V2: d] : ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ ( fun_upd_c_d @ S3 @ X @ V2 ) @ Delta3 @ A2 )
       => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( forall_c_a_b_d @ X @ A2 ) ) ) ) ).

% logic.sat_forall
thf(fact_171_logic_Osat_Osimps_I8_J,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Sigma4: a,S3: c > d,Delta3: ( c > d ) > set_a,X: c,A2: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ S3 @ Delta3 @ ( exists_c_a_b_d @ X @ A2 ) )
        = ( ? [V: d] : ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma4 @ ( fun_upd_c_d @ S3 @ X @ V ) @ Delta3 @ A2 ) ) ) ) ).

% logic.sat.simps(8)
thf(fact_172_logic_Ovalid__hoare__tripleI,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,Delta3: ( c > d ) > set_a,P3: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q4: assertion_a_b_d_c] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ! [Sigma3: a,S2: c > d] :
            ( ( ( Valid @ Sigma3 )
              & ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma3 @ S2 @ Delta3 @ P3 ) )
           => ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma3 @ S2 ) ) )
       => ( ! [Sigma3: a,S2: c > d,Sigma5: a,S7: c > d] :
              ( ( ( Valid @ Sigma3 )
                & ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma3 @ S2 @ Delta3 @ P3 ) )
             => ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma3 @ S2 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma5 @ S7 ) ) ) @ C )
               => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma5 @ S7 @ Delta3 @ Q4 ) ) )
         => ( valid_6037315502795721655_b_d_c @ Plus @ Mult @ Valid @ P3 @ C @ Q4 @ Delta3 ) ) ) ) ).

% logic.valid_hoare_tripleI
thf(fact_173_logic_Ovalid__hoare__triple__def,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,P3: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Q4: assertion_a_b_d_c,Delta3: ( c > d ) > set_a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( valid_6037315502795721655_b_d_c @ Plus @ Mult @ Valid @ P3 @ C @ Q4 @ Delta3 )
        = ( ! [Sigma: a,S: c > d] :
              ( ( ( Valid @ Sigma )
                & ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma @ S @ Delta3 @ P3 ) )
             => ( ( safe_a_c_d @ C @ ( product_Pair_a_c_d @ Sigma @ S ) )
                & ! [Sigma2: a,S5: c > d] :
                    ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma @ S ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma2 @ S5 ) ) ) @ C )
                   => ( sat_a_b_c_d @ Plus @ Mult @ Valid @ Sigma2 @ S5 @ Delta3 @ Q4 ) ) ) ) ) ) ) ).

% logic.valid_hoare_triple_def
thf(fact_174_assertion_Odistinct_I69_J,axiom,
    ! [X41: assertion_a_b_d_c,X42: assertion_a_b_d_c,X912: c,X922: assertion_a_b_d_c] :
      ( ( wand_a_b_d_c @ X41 @ X42 )
     != ( forall_c_a_b_d @ X912 @ X922 ) ) ).

% assertion.distinct(69)
thf(fact_175_assertion_Odistinct_I67_J,axiom,
    ! [X41: assertion_a_b_d_c,X42: assertion_a_b_d_c,X812: c,X822: assertion_a_b_d_c] :
      ( ( wand_a_b_d_c @ X41 @ X42 )
     != ( exists_c_a_b_d @ X812 @ X822 ) ) ).

% assertion.distinct(67)
thf(fact_176_assertion_Odistinct_I121_J,axiom,
    ! [X912: c,X922: assertion_a_b_d_c] :
      ( ( forall_c_a_b_d @ X912 @ X922 )
     != pred_a_b_d_c ) ).

% assertion.distinct(121)
thf(fact_177_assertion_Odistinct_I115_J,axiom,
    ! [X812: c,X822: assertion_a_b_d_c] :
      ( ( exists_c_a_b_d @ X812 @ X822 )
     != pred_a_b_d_c ) ).

% assertion.distinct(115)
thf(fact_178_logic_Onot__in__fv__mod,axiom,
    ! [Plus: a > a > option_a,Mult: b > a > a,Smult: b > b > b,Sadd: b > b > b,Sinv: b > b,One: b,Valid: a > $o,A2: assertion_a_b_d_c,C: set_Pr1275464188344874039_a_c_d,Sigma4: a,S3: c > d,Sigma6: a,S6: c > d,X: a,Delta3: ( c > d ) > set_a] :
      ( ( logic_a_b @ Plus @ Mult @ Smult @ Sadd @ Sinv @ One @ Valid )
     => ( ( not_in_fv_a_b_d_c @ Plus @ Mult @ Valid @ A2 @ ( modified_a_c_d @ C ) )
       => ( ( member1180172933830803072_a_c_d @ ( produc8093790510458973071_a_c_d @ ( product_Pair_a_c_d @ Sigma4 @ S3 ) @ ( some_P1084500821511757806_a_c_d @ ( product_Pair_a_c_d @ Sigma6 @ S6 ) ) ) @ C )
         => ( ( sat_a_b_c_d @ Plus @ Mult @ Valid @ X @ S3 @ Delta3 @ A2 )
            = ( sat_a_b_c_d @ Plus @ Mult @ Valid @ X @ S6 @ Delta3 @ A2 ) ) ) ) ) ).

% logic.not_in_fv_mod
thf(fact_179_prod_Oinject,axiom,
    ! [X1: set_Product_prod_o_o,X23: set_Product_prod_o_o,Y1: set_Product_prod_o_o,Y22: set_Product_prod_o_o] :
      ( ( ( produc763777882069021527od_o_o @ X1 @ X23 )
        = ( produc763777882069021527od_o_o @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X23 = Y22 ) ) ) ).

% prod.inject
thf(fact_180_prod_Oinject,axiom,
    ! [X1: set_Product_prod_o_o,X23: set_Pr1261947904930325089at_nat,Y1: set_Product_prod_o_o,Y22: set_Pr1261947904930325089at_nat] :
      ( ( ( produc8517790099723286449at_nat @ X1 @ X23 )
        = ( produc8517790099723286449at_nat @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X23 = Y22 ) ) ) ).

% prod.inject
thf(fact_181_prod_Oinject,axiom,
    ! [X1: set_Pr1261947904930325089at_nat,X23: set_Pr1261947904930325089at_nat,Y1: set_Pr1261947904930325089at_nat,Y22: set_Pr1261947904930325089at_nat] :
      ( ( ( produc2922128104949294807at_nat @ X1 @ X23 )
        = ( produc2922128104949294807at_nat @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X23 = Y22 ) ) ) ).

% prod.inject
thf(fact_182_old_Oprod_Oinject,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,A6: set_Product_prod_o_o,B5: set_Product_prod_o_o] :
      ( ( ( produc763777882069021527od_o_o @ A @ B )
        = ( produc763777882069021527od_o_o @ A6 @ B5 ) )
      = ( ( A = A6 )
        & ( B = B5 ) ) ) ).

% old.prod.inject
thf(fact_183_old_Oprod_Oinject,axiom,
    ! [A: set_Product_prod_o_o,B: set_Pr1261947904930325089at_nat,A6: set_Product_prod_o_o,B5: set_Pr1261947904930325089at_nat] :
      ( ( ( produc8517790099723286449at_nat @ A @ B )
        = ( produc8517790099723286449at_nat @ A6 @ B5 ) )
      = ( ( A = A6 )
        & ( B = B5 ) ) ) ).

% old.prod.inject
thf(fact_184_old_Oprod_Oinject,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A6: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
      ( ( ( produc2922128104949294807at_nat @ A @ B )
        = ( produc2922128104949294807at_nat @ A6 @ B5 ) )
      = ( ( A = A6 )
        & ( B = B5 ) ) ) ).

% old.prod.inject
thf(fact_185_Pair__inject,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,A6: set_Product_prod_o_o,B5: set_Product_prod_o_o] :
      ( ( ( produc763777882069021527od_o_o @ A @ B )
        = ( produc763777882069021527od_o_o @ A6 @ B5 ) )
     => ~ ( ( A = A6 )
         => ( B != B5 ) ) ) ).

% Pair_inject
thf(fact_186_Pair__inject,axiom,
    ! [A: set_Product_prod_o_o,B: set_Pr1261947904930325089at_nat,A6: set_Product_prod_o_o,B5: set_Pr1261947904930325089at_nat] :
      ( ( ( produc8517790099723286449at_nat @ A @ B )
        = ( produc8517790099723286449at_nat @ A6 @ B5 ) )
     => ~ ( ( A = A6 )
         => ( B != B5 ) ) ) ).

% Pair_inject
thf(fact_187_Pair__inject,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A6: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
      ( ( ( produc2922128104949294807at_nat @ A @ B )
        = ( produc2922128104949294807at_nat @ A6 @ B5 ) )
     => ~ ( ( A = A6 )
         => ( B != B5 ) ) ) ).

% Pair_inject
thf(fact_188_prod__cases,axiom,
    ! [P3: produc2934264451710624999od_o_o > $o,P: produc2934264451710624999od_o_o] :
      ( ! [A4: set_Product_prod_o_o,B3: set_Product_prod_o_o] : ( P3 @ ( produc763777882069021527od_o_o @ A4 @ B3 ) )
     => ( P3 @ P ) ) ).

% prod_cases
thf(fact_189_prod__cases,axiom,
    ! [P3: produc732395585841259969at_nat > $o,P: produc732395585841259969at_nat] :
      ( ! [A4: set_Product_prod_o_o,B3: set_Pr1261947904930325089at_nat] : ( P3 @ ( produc8517790099723286449at_nat @ A4 @ B3 ) )
     => ( P3 @ P ) ) ).

% prod_cases
thf(fact_190_prod__cases,axiom,
    ! [P3: produc3843707927480180839at_nat > $o,P: produc3843707927480180839at_nat] :
      ( ! [A4: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( P3 @ ( produc2922128104949294807at_nat @ A4 @ B3 ) )
     => ( P3 @ P ) ) ).

% prod_cases
thf(fact_191_surj__pair,axiom,
    ! [P: produc2934264451710624999od_o_o] :
    ? [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
      ( P
      = ( produc763777882069021527od_o_o @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_192_surj__pair,axiom,
    ! [P: produc732395585841259969at_nat] :
    ? [X3: set_Product_prod_o_o,Y3: set_Pr1261947904930325089at_nat] :
      ( P
      = ( produc8517790099723286449at_nat @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_193_surj__pair,axiom,
    ! [P: produc3843707927480180839at_nat] :
    ? [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
      ( P
      = ( produc2922128104949294807at_nat @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_194_old_Oprod_Oexhaust,axiom,
    ! [Y: produc2934264451710624999od_o_o] :
      ~ ! [A4: set_Product_prod_o_o,B3: set_Product_prod_o_o] :
          ( Y
         != ( produc763777882069021527od_o_o @ A4 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_195_old_Oprod_Oexhaust,axiom,
    ! [Y: produc732395585841259969at_nat] :
      ~ ! [A4: set_Product_prod_o_o,B3: set_Pr1261947904930325089at_nat] :
          ( Y
         != ( produc8517790099723286449at_nat @ A4 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_196_old_Oprod_Oexhaust,axiom,
    ! [Y: produc3843707927480180839at_nat] :
      ~ ! [A4: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
          ( Y
         != ( produc2922128104949294807at_nat @ A4 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_197_ssubst__Pair__rhs,axiom,
    ! [R: set_Product_prod_o_o,S3: set_Product_prod_o_o,R3: set_Pr1932065953672099015od_o_o,S6: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ S3 ) @ R3 )
     => ( ( S6 = S3 )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ S6 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_198_ssubst__Pair__rhs,axiom,
    ! [R: set_Product_prod_o_o,S3: set_Pr1261947904930325089at_nat,R3: set_Pr457366540195662369at_nat,S6: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ S3 ) @ R3 )
     => ( ( S6 = S3 )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ S6 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_199_ssubst__Pair__rhs,axiom,
    ! [R: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat,S6: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ S3 ) @ R3 )
     => ( ( S6 = S3 )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ S6 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_200_option_Ocollapse,axiom,
    ! [Option: option_a] :
      ( ( Option != none_a )
     => ( ( some_a @ ( the_a @ Option ) )
        = Option ) ) ).

% option.collapse
thf(fact_201_curryI,axiom,
    ! [F: produc2934264451710624999od_o_o > $o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( F @ ( produc763777882069021527od_o_o @ A @ B ) )
     => ( produc4861507100678042957_o_o_o @ F @ A @ B ) ) ).

% curryI
thf(fact_202_curryI,axiom,
    ! [F: produc732395585841259969at_nat > $o,A: set_Product_prod_o_o,B: set_Pr1261947904930325089at_nat] :
      ( ( F @ ( produc8517790099723286449at_nat @ A @ B ) )
     => ( produc5440495499350717427_nat_o @ F @ A @ B ) ) ).

% curryI
thf(fact_203_curryI,axiom,
    ! [F: produc3843707927480180839at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( F @ ( produc2922128104949294807at_nat @ A @ B ) )
     => ( produc7820828192191229133_nat_o @ F @ A @ B ) ) ).

% curryI
thf(fact_204_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc2934264451710624999od_o_o,M: produc2934264451710624999od_o_o > option_a] :
      ( ~ ( member444158400953824016od_o_o @ K @ ( dom_Pr3509670420972068777_o_o_a @ M ) )
     => ( ( fun_up7252388491999432090tion_a @ M @ K @ none_a )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_205_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc732395585841259969at_nat,M: produc732395585841259969at_nat > option_a] :
      ( ~ ( member4095101504841534314at_nat @ K @ ( dom_Pr8042991038213739471_nat_a @ M ) )
     => ( ( fun_up564627978254483264tion_a @ M @ K @ none_a )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_206_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc3843707927480180839at_nat,M: produc3843707927480180839at_nat > option_a] :
      ( ~ ( member8757157785044589968at_nat @ K @ ( dom_Pr1957410074072848681_nat_a @ M ) )
     => ( ( fun_up7579534627831735322tion_a @ M @ K @ none_a )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_207_fun__upd__None__if__notin__dom,axiom,
    ! [K: a,M: a > option_a] :
      ( ~ ( member_a @ K @ ( dom_a_a @ M ) )
     => ( ( fun_upd_a_option_a @ M @ K @ none_a )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_208_map__add__upd__left,axiom,
    ! [M: produc2934264451710624999od_o_o,E2: produc2934264451710624999od_o_o > option_a,E1: produc2934264451710624999od_o_o > option_a,U1: a] :
      ( ~ ( member444158400953824016od_o_o @ M @ ( dom_Pr3509670420972068777_o_o_a @ E2 ) )
     => ( ( map_ad9054432547132481292_o_o_a @ ( fun_up7252388491999432090tion_a @ E1 @ M @ ( some_a @ U1 ) ) @ E2 )
        = ( fun_up7252388491999432090tion_a @ ( map_ad9054432547132481292_o_o_a @ E1 @ E2 ) @ M @ ( some_a @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_209_map__add__upd__left,axiom,
    ! [M: produc732395585841259969at_nat,E2: produc732395585841259969at_nat > option_a,E1: produc732395585841259969at_nat > option_a,U1: a] :
      ( ~ ( member4095101504841534314at_nat @ M @ ( dom_Pr8042991038213739471_nat_a @ E2 ) )
     => ( ( map_ad4947507604491699634_nat_a @ ( fun_up564627978254483264tion_a @ E1 @ M @ ( some_a @ U1 ) ) @ E2 )
        = ( fun_up564627978254483264tion_a @ ( map_ad4947507604491699634_nat_a @ E1 @ E2 ) @ M @ ( some_a @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_210_map__add__upd__left,axiom,
    ! [M: produc3843707927480180839at_nat,E2: produc3843707927480180839at_nat > option_a,E1: produc3843707927480180839at_nat > option_a,U1: a] :
      ( ~ ( member8757157785044589968at_nat @ M @ ( dom_Pr1957410074072848681_nat_a @ E2 ) )
     => ( ( map_ad6003791139528408460_nat_a @ ( fun_up7579534627831735322tion_a @ E1 @ M @ ( some_a @ U1 ) ) @ E2 )
        = ( fun_up7579534627831735322tion_a @ ( map_ad6003791139528408460_nat_a @ E1 @ E2 ) @ M @ ( some_a @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_211_map__add__upd__left,axiom,
    ! [M: a,E2: a > option_a,E1: a > option_a,U1: a] :
      ( ~ ( member_a @ M @ ( dom_a_a @ E2 ) )
     => ( ( map_add_a_a @ ( fun_upd_a_option_a @ E1 @ M @ ( some_a @ U1 ) ) @ E2 )
        = ( fun_upd_a_option_a @ ( map_add_a_a @ E1 @ E2 ) @ M @ ( some_a @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_212_domI,axiom,
    ! [M: produc2934264451710624999od_o_o > option_a,A: produc2934264451710624999od_o_o,B: a] :
      ( ( ( M @ A )
        = ( some_a @ B ) )
     => ( member444158400953824016od_o_o @ A @ ( dom_Pr3509670420972068777_o_o_a @ M ) ) ) ).

% domI
thf(fact_213_domI,axiom,
    ! [M: produc732395585841259969at_nat > option_a,A: produc732395585841259969at_nat,B: a] :
      ( ( ( M @ A )
        = ( some_a @ B ) )
     => ( member4095101504841534314at_nat @ A @ ( dom_Pr8042991038213739471_nat_a @ M ) ) ) ).

% domI
thf(fact_214_domI,axiom,
    ! [M: produc3843707927480180839at_nat > option_a,A: produc3843707927480180839at_nat,B: a] :
      ( ( ( M @ A )
        = ( some_a @ B ) )
     => ( member8757157785044589968at_nat @ A @ ( dom_Pr1957410074072848681_nat_a @ M ) ) ) ).

% domI
thf(fact_215_domI,axiom,
    ! [M: a > option_a,A: a,B: a] :
      ( ( ( M @ A )
        = ( some_a @ B ) )
     => ( member_a @ A @ ( dom_a_a @ M ) ) ) ).

% domI
thf(fact_216_domD,axiom,
    ! [A: produc2934264451710624999od_o_o,M: produc2934264451710624999od_o_o > option_a] :
      ( ( member444158400953824016od_o_o @ A @ ( dom_Pr3509670420972068777_o_o_a @ M ) )
     => ? [B3: a] :
          ( ( M @ A )
          = ( some_a @ B3 ) ) ) ).

% domD
thf(fact_217_domD,axiom,
    ! [A: produc732395585841259969at_nat,M: produc732395585841259969at_nat > option_a] :
      ( ( member4095101504841534314at_nat @ A @ ( dom_Pr8042991038213739471_nat_a @ M ) )
     => ? [B3: a] :
          ( ( M @ A )
          = ( some_a @ B3 ) ) ) ).

% domD
thf(fact_218_domD,axiom,
    ! [A: produc3843707927480180839at_nat,M: produc3843707927480180839at_nat > option_a] :
      ( ( member8757157785044589968at_nat @ A @ ( dom_Pr1957410074072848681_nat_a @ M ) )
     => ? [B3: a] :
          ( ( M @ A )
          = ( some_a @ B3 ) ) ) ).

% domD
thf(fact_219_domD,axiom,
    ! [A: a,M: a > option_a] :
      ( ( member_a @ A @ ( dom_a_a @ M ) )
     => ? [B3: a] :
          ( ( M @ A )
          = ( some_a @ B3 ) ) ) ).

% domD
thf(fact_220_domIff,axiom,
    ! [A: produc2934264451710624999od_o_o,M: produc2934264451710624999od_o_o > option_a] :
      ( ( member444158400953824016od_o_o @ A @ ( dom_Pr3509670420972068777_o_o_a @ M ) )
      = ( ( M @ A )
       != none_a ) ) ).

% domIff
thf(fact_221_domIff,axiom,
    ! [A: produc732395585841259969at_nat,M: produc732395585841259969at_nat > option_a] :
      ( ( member4095101504841534314at_nat @ A @ ( dom_Pr8042991038213739471_nat_a @ M ) )
      = ( ( M @ A )
       != none_a ) ) ).

% domIff
thf(fact_222_domIff,axiom,
    ! [A: produc3843707927480180839at_nat,M: produc3843707927480180839at_nat > option_a] :
      ( ( member8757157785044589968at_nat @ A @ ( dom_Pr1957410074072848681_nat_a @ M ) )
      = ( ( M @ A )
       != none_a ) ) ).

% domIff
thf(fact_223_domIff,axiom,
    ! [A: a,M: a > option_a] :
      ( ( member_a @ A @ ( dom_a_a @ M ) )
      = ( ( M @ A )
       != none_a ) ) ).

% domIff
thf(fact_224_option_Osel,axiom,
    ! [X23: a] :
      ( ( the_a @ ( some_a @ X23 ) )
      = X23 ) ).

% option.sel
thf(fact_225_option_Oexpand,axiom,
    ! [Option: option_a,Option2: option_a] :
      ( ( ( Option = none_a )
        = ( Option2 = none_a ) )
     => ( ( ( Option != none_a )
         => ( ( Option2 != none_a )
           => ( ( the_a @ Option )
              = ( the_a @ Option2 ) ) ) )
       => ( Option = Option2 ) ) ) ).

% option.expand
thf(fact_226_curryE,axiom,
    ! [F: produc2934264451710624999od_o_o > $o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( produc4861507100678042957_o_o_o @ F @ A @ B )
     => ( F @ ( produc763777882069021527od_o_o @ A @ B ) ) ) ).

% curryE
thf(fact_227_curryE,axiom,
    ! [F: produc732395585841259969at_nat > $o,A: set_Product_prod_o_o,B: set_Pr1261947904930325089at_nat] :
      ( ( produc5440495499350717427_nat_o @ F @ A @ B )
     => ( F @ ( produc8517790099723286449at_nat @ A @ B ) ) ) ).

% curryE
thf(fact_228_curryE,axiom,
    ! [F: produc3843707927480180839at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( produc7820828192191229133_nat_o @ F @ A @ B )
     => ( F @ ( produc2922128104949294807at_nat @ A @ B ) ) ) ).

% curryE
thf(fact_229_curryD,axiom,
    ! [F: produc2934264451710624999od_o_o > $o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( produc4861507100678042957_o_o_o @ F @ A @ B )
     => ( F @ ( produc763777882069021527od_o_o @ A @ B ) ) ) ).

% curryD
thf(fact_230_curryD,axiom,
    ! [F: produc732395585841259969at_nat > $o,A: set_Product_prod_o_o,B: set_Pr1261947904930325089at_nat] :
      ( ( produc5440495499350717427_nat_o @ F @ A @ B )
     => ( F @ ( produc8517790099723286449at_nat @ A @ B ) ) ) ).

% curryD
thf(fact_231_curryD,axiom,
    ! [F: produc3843707927480180839at_nat > $o,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( produc7820828192191229133_nat_o @ F @ A @ B )
     => ( F @ ( produc2922128104949294807at_nat @ A @ B ) ) ) ).

% curryD
thf(fact_232_option_Oexhaust__sel,axiom,
    ! [Option: option_a] :
      ( ( Option != none_a )
     => ( Option
        = ( some_a @ ( the_a @ Option ) ) ) ) ).

% option.exhaust_sel
thf(fact_233_option_Oset__sel,axiom,
    ! [A: option8293164206536526765od_o_o] :
      ( ( A != none_P8254367833036352840od_o_o )
     => ( member444158400953824016od_o_o @ ( the_Pr7254245475272632699od_o_o @ A ) @ ( set_op3337521775309186165od_o_o @ A ) ) ) ).

% option.set_sel
thf(fact_234_option_Oset__sel,axiom,
    ! [A: option7754883786268931591at_nat] :
      ( ( A != none_P5828533823149705634at_nat )
     => ( member4095101504841534314at_nat @ ( the_Pr9097376869753557077at_nat @ A ) @ ( set_op8338180575893423695at_nat @ A ) ) ) ).

% option.set_sel
thf(fact_235_option_Oset__sel,axiom,
    ! [A: option8699557107911914541at_nat] :
      ( ( A != none_P5811896708078067656at_nat )
     => ( member8757157785044589968at_nat @ ( the_Pr6298817542474494203at_nat @ A ) @ ( set_op5866586666149159413at_nat @ A ) ) ) ).

% option.set_sel
thf(fact_236_option_Oset__sel,axiom,
    ! [A: option_a] :
      ( ( A != none_a )
     => ( member_a @ ( the_a @ A ) @ ( set_option_a2 @ A ) ) ) ).

% option.set_sel
thf(fact_237_bind__eq__None__conv,axiom,
    ! [A: option_a,F: a > option_a] :
      ( ( ( bind_a_a @ A @ F )
        = none_a )
      = ( ( A = none_a )
        | ( ( F @ ( the_a @ A ) )
          = none_a ) ) ) ).

% bind_eq_None_conv
thf(fact_238_elem__set,axiom,
    ! [X: produc2934264451710624999od_o_o,Xo: option8293164206536526765od_o_o] :
      ( ( member444158400953824016od_o_o @ X @ ( set_op3337521775309186165od_o_o @ Xo ) )
      = ( Xo
        = ( some_P7068320699308846284od_o_o @ X ) ) ) ).

% elem_set
thf(fact_239_elem__set,axiom,
    ! [X: produc732395585841259969at_nat,Xo: option7754883786268931591at_nat] :
      ( ( member4095101504841534314at_nat @ X @ ( set_op8338180575893423695at_nat @ Xo ) )
      = ( Xo
        = ( some_P123625206269196070at_nat @ X ) ) ) ).

% elem_set
thf(fact_240_elem__set,axiom,
    ! [X: produc3843707927480180839at_nat,Xo: option8699557107911914541at_nat] :
      ( ( member8757157785044589968at_nat @ X @ ( set_op5866586666149159413at_nat @ Xo ) )
      = ( Xo
        = ( some_P131194445498448716at_nat @ X ) ) ) ).

% elem_set
thf(fact_241_elem__set,axiom,
    ! [X: a,Xo: option_a] :
      ( ( member_a @ X @ ( set_option_a2 @ Xo ) )
      = ( Xo
        = ( some_a @ X ) ) ) ).

% elem_set
thf(fact_242_bind__runit,axiom,
    ! [X: option_a] :
      ( ( bind_a_a @ X @ some_a )
      = X ) ).

% bind_runit
thf(fact_243_set__empty__eq,axiom,
    ! [Xo: option_a] :
      ( ( ( set_option_a2 @ Xo )
        = bot_bot_set_a )
      = ( Xo = none_a ) ) ).

% set_empty_eq
thf(fact_244_option_Osimps_I14_J,axiom,
    ( ( set_option_a2 @ none_a )
    = bot_bot_set_a ) ).

% option.simps(14)
thf(fact_245_bind__eq__Some__conv,axiom,
    ! [F: option_a,G: a > option_a,X: a] :
      ( ( ( bind_a_a @ F @ G )
        = ( some_a @ X ) )
      = ( ? [Y2: a] :
            ( ( F
              = ( some_a @ Y2 ) )
            & ( ( G @ Y2 )
              = ( some_a @ X ) ) ) ) ) ).

% bind_eq_Some_conv
thf(fact_246_bind_Obind__lzero,axiom,
    ! [F: a > option_a] :
      ( ( bind_a_a @ none_a @ F )
      = none_a ) ).

% bind.bind_lzero
thf(fact_247_option_Oset__cases,axiom,
    ! [E: produc2934264451710624999od_o_o,A: option8293164206536526765od_o_o] :
      ( ( member444158400953824016od_o_o @ E @ ( set_op3337521775309186165od_o_o @ A ) )
     => ( A
        = ( some_P7068320699308846284od_o_o @ E ) ) ) ).

% option.set_cases
thf(fact_248_option_Oset__cases,axiom,
    ! [E: produc732395585841259969at_nat,A: option7754883786268931591at_nat] :
      ( ( member4095101504841534314at_nat @ E @ ( set_op8338180575893423695at_nat @ A ) )
     => ( A
        = ( some_P123625206269196070at_nat @ E ) ) ) ).

% option.set_cases
thf(fact_249_option_Oset__cases,axiom,
    ! [E: produc3843707927480180839at_nat,A: option8699557107911914541at_nat] :
      ( ( member8757157785044589968at_nat @ E @ ( set_op5866586666149159413at_nat @ A ) )
     => ( A
        = ( some_P131194445498448716at_nat @ E ) ) ) ).

% option.set_cases
thf(fact_250_option_Oset__cases,axiom,
    ! [E: a,A: option_a] :
      ( ( member_a @ E @ ( set_option_a2 @ A ) )
     => ( A
        = ( some_a @ E ) ) ) ).

% option.set_cases
thf(fact_251_option_Oset__intros,axiom,
    ! [X23: produc2934264451710624999od_o_o] : ( member444158400953824016od_o_o @ X23 @ ( set_op3337521775309186165od_o_o @ ( some_P7068320699308846284od_o_o @ X23 ) ) ) ).

% option.set_intros
thf(fact_252_option_Oset__intros,axiom,
    ! [X23: produc732395585841259969at_nat] : ( member4095101504841534314at_nat @ X23 @ ( set_op8338180575893423695at_nat @ ( some_P123625206269196070at_nat @ X23 ) ) ) ).

% option.set_intros
thf(fact_253_option_Oset__intros,axiom,
    ! [X23: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X23 @ ( set_op5866586666149159413at_nat @ ( some_P131194445498448716at_nat @ X23 ) ) ) ).

% option.set_intros
thf(fact_254_option_Oset__intros,axiom,
    ! [X23: a] : ( member_a @ X23 @ ( set_option_a2 @ ( some_a @ X23 ) ) ) ).

% option.set_intros
thf(fact_255_ospec,axiom,
    ! [A2: option_a,P3: a > $o,X: a] :
      ( ! [X3: a] :
          ( ( member_a @ X3 @ ( set_option_a2 @ A2 ) )
         => ( P3 @ X3 ) )
     => ( ( A2
          = ( some_a @ X ) )
       => ( P3 @ X ) ) ) ).

% ospec
thf(fact_256_bind__split,axiom,
    ! [P3: option_a > $o,M: option_a,F: a > option_a] :
      ( ( P3 @ ( bind_a_a @ M @ F ) )
      = ( ( ( M = none_a )
         => ( P3 @ none_a ) )
        & ! [V: a] :
            ( ( M
              = ( some_a @ V ) )
           => ( P3 @ ( F @ V ) ) ) ) ) ).

% bind_split
thf(fact_257_bind__split__asm,axiom,
    ! [P3: option_a > $o,M: option_a,F: a > option_a] :
      ( ( P3 @ ( bind_a_a @ M @ F ) )
      = ( ~ ( ( ( M = none_a )
              & ~ ( P3 @ none_a ) )
            | ? [X2: a] :
                ( ( M
                  = ( some_a @ X2 ) )
                & ~ ( P3 @ ( F @ X2 ) ) ) ) ) ) ).

% bind_split_asm
thf(fact_258_option_Osimps_I15_J,axiom,
    ! [X23: a] :
      ( ( set_option_a2 @ ( some_a @ X23 ) )
      = ( insert_a @ X23 @ bot_bot_set_a ) ) ).

% option.simps(15)
thf(fact_259_in__graphD,axiom,
    ! [K: set_Product_prod_o_o,V3: set_Product_prod_o_o,M: set_Product_prod_o_o > option956769437226787789od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ K @ V3 ) @ ( graph_5719763352399009470od_o_o @ M ) )
     => ( ( M @ K )
        = ( some_s1360601300120069868od_o_o @ V3 ) ) ) ).

% in_graphD
thf(fact_260_in__graphD,axiom,
    ! [K: set_Product_prod_o_o,V3: set_Pr1261947904930325089at_nat,M: set_Product_prod_o_o > option8963830502488799655at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ K @ V3 ) @ ( graph_2163970799110208408at_nat @ M ) )
     => ( ( M @ K )
        = ( some_s147305329494351046at_nat @ V3 ) ) ) ).

% in_graphD
thf(fact_261_in__graphD,axiom,
    ! [K: set_Pr1261947904930325089at_nat,V3: set_Pr1261947904930325089at_nat,M: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ K @ V3 ) @ ( graph_2380648924068268862at_nat @ M ) )
     => ( ( M @ K )
        = ( some_s147305329494351046at_nat @ V3 ) ) ) ).

% in_graphD
thf(fact_262_in__graphI,axiom,
    ! [M: set_Product_prod_o_o > option956769437226787789od_o_o,K: set_Product_prod_o_o,V3: set_Product_prod_o_o] :
      ( ( ( M @ K )
        = ( some_s1360601300120069868od_o_o @ V3 ) )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ K @ V3 ) @ ( graph_5719763352399009470od_o_o @ M ) ) ) ).

% in_graphI
thf(fact_263_in__graphI,axiom,
    ! [M: set_Product_prod_o_o > option8963830502488799655at_nat,K: set_Product_prod_o_o,V3: set_Pr1261947904930325089at_nat] :
      ( ( ( M @ K )
        = ( some_s147305329494351046at_nat @ V3 ) )
     => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ K @ V3 ) @ ( graph_2163970799110208408at_nat @ M ) ) ) ).

% in_graphI
thf(fact_264_in__graphI,axiom,
    ! [M: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat,K: set_Pr1261947904930325089at_nat,V3: set_Pr1261947904930325089at_nat] :
      ( ( ( M @ K )
        = ( some_s147305329494351046at_nat @ V3 ) )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ K @ V3 ) @ ( graph_2380648924068268862at_nat @ M ) ) ) ).

% in_graphI
thf(fact_265_restrict__out,axiom,
    ! [X: produc2934264451710624999od_o_o,A2: set_Pr1932065953672099015od_o_o,M: produc2934264451710624999od_o_o > option_a] :
      ( ~ ( member444158400953824016od_o_o @ X @ A2 )
     => ( ( restri4233077244345833607_o_o_a @ M @ A2 @ X )
        = none_a ) ) ).

% restrict_out
thf(fact_266_restrict__out,axiom,
    ! [X: produc732395585841259969at_nat,A2: set_Pr457366540195662369at_nat,M: produc732395585841259969at_nat > option_a] :
      ( ~ ( member4095101504841534314at_nat @ X @ A2 )
     => ( ( restri896928924502181293_nat_a @ M @ A2 @ X )
        = none_a ) ) ).

% restrict_out
thf(fact_267_restrict__out,axiom,
    ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,M: produc3843707927480180839at_nat > option_a] :
      ( ~ ( member8757157785044589968at_nat @ X @ A2 )
     => ( ( restri4040463761431659527_nat_a @ M @ A2 @ X )
        = none_a ) ) ).

% restrict_out
thf(fact_268_restrict__out,axiom,
    ! [X: a,A2: set_a,M: a > option_a] :
      ( ~ ( member_a @ X @ A2 )
     => ( ( restrict_map_a_a @ M @ A2 @ X )
        = none_a ) ) ).

% restrict_out
thf(fact_269_is__none__code_I2_J,axiom,
    ! [X: a] :
      ~ ( is_none_a @ ( some_a @ X ) ) ).

% is_none_code(2)
thf(fact_270_is__none__code_I1_J,axiom,
    is_none_a @ none_a ).

% is_none_code(1)
thf(fact_271_these__insert__None,axiom,
    ! [A2: set_option_a] :
      ( ( these_a @ ( insert_option_a @ none_a @ A2 ) )
      = ( these_a @ A2 ) ) ).

% these_insert_None
thf(fact_272_these__insert__Some,axiom,
    ! [X: a,A2: set_option_a] :
      ( ( these_a @ ( insert_option_a @ ( some_a @ X ) @ A2 ) )
      = ( insert_a @ X @ ( these_a @ A2 ) ) ) ).

% these_insert_Some
thf(fact_273_graph__map__upd,axiom,
    ! [M: set_Product_prod_o_o > option956769437226787789od_o_o,K: set_Product_prod_o_o,V3: set_Product_prod_o_o] :
      ( ( graph_5719763352399009470od_o_o @ ( fun_up3230021793924660483od_o_o @ M @ K @ ( some_s1360601300120069868od_o_o @ V3 ) ) )
      = ( insert3855699742481506999od_o_o @ ( produc763777882069021527od_o_o @ K @ V3 ) @ ( graph_5719763352399009470od_o_o @ ( fun_up3230021793924660483od_o_o @ M @ K @ none_s7246968996079588200od_o_o ) ) ) ) ).

% graph_map_upd
thf(fact_274_graph__map__upd,axiom,
    ! [M: set_Product_prod_o_o > option8963830502488799655at_nat,K: set_Product_prod_o_o,V3: set_Pr1261947904930325089at_nat] :
      ( ( graph_2163970799110208408at_nat @ ( fun_up3688893386320429021at_nat @ M @ K @ ( some_s147305329494351046at_nat @ V3 ) ) )
      = ( insert8109617542356073361at_nat @ ( produc8517790099723286449at_nat @ K @ V3 ) @ ( graph_2163970799110208408at_nat @ ( fun_up3688893386320429021at_nat @ M @ K @ none_s625347054029921090at_nat ) ) ) ) ).

% graph_map_upd
thf(fact_275_graph__map__upd,axiom,
    ! [M: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat,K: set_Pr1261947904930325089at_nat,V3: set_Pr1261947904930325089at_nat] :
      ( ( graph_2380648924068268862at_nat @ ( fun_up1071884767227745027at_nat @ M @ K @ ( some_s147305329494351046at_nat @ V3 ) ) )
      = ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ K @ V3 ) @ ( graph_2380648924068268862at_nat @ ( fun_up1071884767227745027at_nat @ M @ K @ none_s625347054029921090at_nat ) ) ) ) ).

% graph_map_upd
thf(fact_276_graph__restrictD_I1_J,axiom,
    ! [K: set_Product_prod_o_o,V3: set_Product_prod_o_o,M: set_Product_prod_o_o > option956769437226787789od_o_o,A2: set_se491199571785101031od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ K @ V3 ) @ ( graph_5719763352399009470od_o_o @ ( restri2278710580326071152od_o_o @ M @ A2 ) ) )
     => ( member3157015407008874800od_o_o @ K @ A2 ) ) ).

% graph_restrictD(1)
thf(fact_277_graph__restrictD_I1_J,axiom,
    ! [K: set_Product_prod_o_o,V3: set_Pr1261947904930325089at_nat,M: set_Product_prod_o_o > option8963830502488799655at_nat,A2: set_se491199571785101031od_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ K @ V3 ) @ ( graph_2163970799110208408at_nat @ ( restri2174721201111129930at_nat @ M @ A2 ) ) )
     => ( member3157015407008874800od_o_o @ K @ A2 ) ) ).

% graph_restrictD(1)
thf(fact_278_graph__restrictD_I1_J,axiom,
    ! [K: set_Pr1261947904930325089at_nat,V3: set_Pr1261947904930325089at_nat,M: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat,A2: set_se7855581050983116737at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ K @ V3 ) @ ( graph_2380648924068268862at_nat @ ( restri512981303736921584at_nat @ M @ A2 ) ) )
     => ( member2643936169264416010at_nat @ K @ A2 ) ) ).

% graph_restrictD(1)
thf(fact_279_graph__restrictD_I2_J,axiom,
    ! [K: set_Product_prod_o_o,V3: set_Product_prod_o_o,M: set_Product_prod_o_o > option956769437226787789od_o_o,A2: set_se491199571785101031od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ K @ V3 ) @ ( graph_5719763352399009470od_o_o @ ( restri2278710580326071152od_o_o @ M @ A2 ) ) )
     => ( ( M @ K )
        = ( some_s1360601300120069868od_o_o @ V3 ) ) ) ).

% graph_restrictD(2)
thf(fact_280_graph__restrictD_I2_J,axiom,
    ! [K: set_Product_prod_o_o,V3: set_Pr1261947904930325089at_nat,M: set_Product_prod_o_o > option8963830502488799655at_nat,A2: set_se491199571785101031od_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ K @ V3 ) @ ( graph_2163970799110208408at_nat @ ( restri2174721201111129930at_nat @ M @ A2 ) ) )
     => ( ( M @ K )
        = ( some_s147305329494351046at_nat @ V3 ) ) ) ).

% graph_restrictD(2)
thf(fact_281_graph__restrictD_I2_J,axiom,
    ! [K: set_Pr1261947904930325089at_nat,V3: set_Pr1261947904930325089at_nat,M: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat,A2: set_se7855581050983116737at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ K @ V3 ) @ ( graph_2380648924068268862at_nat @ ( restri512981303736921584at_nat @ M @ A2 ) ) )
     => ( ( M @ K )
        = ( some_s147305329494351046at_nat @ V3 ) ) ) ).

% graph_restrictD(2)
thf(fact_282_these__empty__eq,axiom,
    ! [B2: set_option_a] :
      ( ( ( these_a @ B2 )
        = bot_bot_set_a )
      = ( ( B2 = bot_bot_set_option_a )
        | ( B2
          = ( insert_option_a @ none_a @ bot_bot_set_option_a ) ) ) ) ).

% these_empty_eq
thf(fact_283_these__not__empty__eq,axiom,
    ! [B2: set_option_a] :
      ( ( ( these_a @ B2 )
       != bot_bot_set_a )
      = ( ( B2 != bot_bot_set_option_a )
        & ( B2
         != ( insert_option_a @ none_a @ bot_bot_set_option_a ) ) ) ) ).

% these_not_empty_eq
thf(fact_284_restrict__map__def,axiom,
    ( restri4233077244345833607_o_o_a
    = ( ^ [M2: produc2934264451710624999od_o_o > option_a,A7: set_Pr1932065953672099015od_o_o,X2: produc2934264451710624999od_o_o] : ( if_option_a @ ( member444158400953824016od_o_o @ X2 @ A7 ) @ ( M2 @ X2 ) @ none_a ) ) ) ).

% restrict_map_def
thf(fact_285_restrict__map__def,axiom,
    ( restri896928924502181293_nat_a
    = ( ^ [M2: produc732395585841259969at_nat > option_a,A7: set_Pr457366540195662369at_nat,X2: produc732395585841259969at_nat] : ( if_option_a @ ( member4095101504841534314at_nat @ X2 @ A7 ) @ ( M2 @ X2 ) @ none_a ) ) ) ).

% restrict_map_def
thf(fact_286_restrict__map__def,axiom,
    ( restri4040463761431659527_nat_a
    = ( ^ [M2: produc3843707927480180839at_nat > option_a,A7: set_Pr4329608150637261639at_nat,X2: produc3843707927480180839at_nat] : ( if_option_a @ ( member8757157785044589968at_nat @ X2 @ A7 ) @ ( M2 @ X2 ) @ none_a ) ) ) ).

% restrict_map_def
thf(fact_287_restrict__map__def,axiom,
    ( restrict_map_a_a
    = ( ^ [M2: a > option_a,A7: set_a,X2: a] : ( if_option_a @ ( member_a @ X2 @ A7 ) @ ( M2 @ X2 ) @ none_a ) ) ) ).

% restrict_map_def
thf(fact_288_is__none__simps_I2_J,axiom,
    ! [X: a] :
      ~ ( is_none_a @ ( some_a @ X ) ) ).

% is_none_simps(2)
thf(fact_289_Option_Ois__none__def,axiom,
    ( is_none_a
    = ( ^ [X2: option_a] : ( X2 = none_a ) ) ) ).

% Option.is_none_def
thf(fact_290_is__none__simps_I1_J,axiom,
    is_none_a @ none_a ).

% is_none_simps(1)
thf(fact_291_in__these__eq,axiom,
    ! [X: produc2934264451710624999od_o_o,A2: set_op3605315081486705933od_o_o] :
      ( ( member444158400953824016od_o_o @ X @ ( these_2277756779245414180od_o_o @ A2 ) )
      = ( member3623239300863961174od_o_o @ ( some_P7068320699308846284od_o_o @ X ) @ A2 ) ) ).

% in_these_eq
thf(fact_292_in__these__eq,axiom,
    ! [X: produc732395585841259969at_nat,A2: set_op7555165197759865831at_nat] :
      ( ( member4095101504841534314at_nat @ X @ ( these_663420305483081086at_nat @ A2 ) )
      = ( member8056002749114821168at_nat @ ( some_P123625206269196070at_nat @ X ) @ A2 ) ) ).

% in_these_eq
thf(fact_293_in__these__eq,axiom,
    ! [X: produc3843707927480180839at_nat,A2: set_op989438649584373901at_nat] :
      ( ( member8757157785044589968at_nat @ X @ ( these_1872268174106123684at_nat @ A2 ) )
      = ( member4288423094740844502at_nat @ ( some_P131194445498448716at_nat @ X ) @ A2 ) ) ).

% in_these_eq
thf(fact_294_in__these__eq,axiom,
    ! [X: a,A2: set_option_a] :
      ( ( member_a @ X @ ( these_a @ A2 ) )
      = ( member_option_a @ ( some_a @ X ) @ A2 ) ) ).

% in_these_eq
thf(fact_295_fun__upd__None__restrict,axiom,
    ! [X: produc2934264451710624999od_o_o,D: set_Pr1932065953672099015od_o_o,M: produc2934264451710624999od_o_o > option_a] :
      ( ( ( member444158400953824016od_o_o @ X @ D )
       => ( ( fun_up7252388491999432090tion_a @ ( restri4233077244345833607_o_o_a @ M @ D ) @ X @ none_a )
          = ( restri4233077244345833607_o_o_a @ M @ ( minus_5704166846132356910od_o_o @ D @ ( insert3855699742481506999od_o_o @ X @ bot_bo498831808395348787od_o_o ) ) ) ) )
      & ( ~ ( member444158400953824016od_o_o @ X @ D )
       => ( ( fun_up7252388491999432090tion_a @ ( restri4233077244345833607_o_o_a @ M @ D ) @ X @ none_a )
          = ( restri4233077244345833607_o_o_a @ M @ D ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_296_fun__upd__None__restrict,axiom,
    ! [X: produc732395585841259969at_nat,D: set_Pr457366540195662369at_nat,M: produc732395585841259969at_nat > option_a] :
      ( ( ( member4095101504841534314at_nat @ X @ D )
       => ( ( fun_up564627978254483264tion_a @ ( restri896928924502181293_nat_a @ M @ D ) @ X @ none_a )
          = ( restri896928924502181293_nat_a @ M @ ( minus_1608234471674494216at_nat @ D @ ( insert8109617542356073361at_nat @ X @ bot_bo1676454896636820109at_nat ) ) ) ) )
      & ( ~ ( member4095101504841534314at_nat @ X @ D )
       => ( ( fun_up564627978254483264tion_a @ ( restri896928924502181293_nat_a @ M @ D ) @ X @ none_a )
          = ( restri896928924502181293_nat_a @ M @ D ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_297_fun__upd__None__restrict,axiom,
    ! [X: produc3843707927480180839at_nat,D: set_Pr4329608150637261639at_nat,M: produc3843707927480180839at_nat > option_a] :
      ( ( ( member8757157785044589968at_nat @ X @ D )
       => ( ( fun_up7579534627831735322tion_a @ ( restri4040463761431659527_nat_a @ M @ D ) @ X @ none_a )
          = ( restri4040463761431659527_nat_a @ M @ ( minus_3314409938677909166at_nat @ D @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) )
      & ( ~ ( member8757157785044589968at_nat @ X @ D )
       => ( ( fun_up7579534627831735322tion_a @ ( restri4040463761431659527_nat_a @ M @ D ) @ X @ none_a )
          = ( restri4040463761431659527_nat_a @ M @ D ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_298_fun__upd__None__restrict,axiom,
    ! [X: a,D: set_a,M: a > option_a] :
      ( ( ( member_a @ X @ D )
       => ( ( fun_upd_a_option_a @ ( restrict_map_a_a @ M @ D ) @ X @ none_a )
          = ( restrict_map_a_a @ M @ ( minus_minus_set_a @ D @ ( insert_a @ X @ bot_bot_set_a ) ) ) ) )
      & ( ~ ( member_a @ X @ D )
       => ( ( fun_upd_a_option_a @ ( restrict_map_a_a @ M @ D ) @ X @ none_a )
          = ( restrict_map_a_a @ M @ D ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_299_linear__order__on__singleton,axiom,
    ! [X: set_Product_prod_o_o] : ( order_2625247082195685180od_o_o @ ( insert3817420688681518039od_o_o @ X @ bot_bo8006819982598807891od_o_o ) @ ( insert3855699742481506999od_o_o @ ( produc763777882069021527od_o_o @ X @ X ) @ bot_bo498831808395348787od_o_o ) ) ).

% linear_order_on_singleton
thf(fact_300_linear__order__on__singleton,axiom,
    ! [X: set_Pr1261947904930325089at_nat] : ( order_5942792088423767318at_nat @ ( insert9200635055090092081at_nat @ X @ bot_bo3083307316010499117at_nat ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X @ X ) @ bot_bo228742789529271731at_nat ) ) ).

% linear_order_on_singleton
thf(fact_301_image__map__upd,axiom,
    ! [X: produc2934264451710624999od_o_o,A2: set_Pr1932065953672099015od_o_o,M: produc2934264451710624999od_o_o > option_a,Y: a] :
      ( ~ ( member444158400953824016od_o_o @ X @ A2 )
     => ( ( image_1441591353514620194tion_a @ ( fun_up7252388491999432090tion_a @ M @ X @ ( some_a @ Y ) ) @ A2 )
        = ( image_1441591353514620194tion_a @ M @ A2 ) ) ) ).

% image_map_upd
thf(fact_302_image__map__upd,axiom,
    ! [X: produc732395585841259969at_nat,A2: set_Pr457366540195662369at_nat,M: produc732395585841259969at_nat > option_a,Y: a] :
      ( ~ ( member4095101504841534314at_nat @ X @ A2 )
     => ( ( image_6589722576923083464tion_a @ ( fun_up564627978254483264tion_a @ M @ X @ ( some_a @ Y ) ) @ A2 )
        = ( image_6589722576923083464tion_a @ M @ A2 ) ) ) ).

% image_map_upd
thf(fact_303_image__map__upd,axiom,
    ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,M: produc3843707927480180839at_nat > option_a,Y: a] :
      ( ~ ( member8757157785044589968at_nat @ X @ A2 )
     => ( ( image_7626837539197272994tion_a @ ( fun_up7579534627831735322tion_a @ M @ X @ ( some_a @ Y ) ) @ A2 )
        = ( image_7626837539197272994tion_a @ M @ A2 ) ) ) ).

% image_map_upd
thf(fact_304_image__map__upd,axiom,
    ! [X: a,A2: set_a,M: a > option_a,Y: a] :
      ( ~ ( member_a @ X @ A2 )
     => ( ( image_a_option_a @ ( fun_upd_a_option_a @ M @ X @ ( some_a @ Y ) ) @ A2 )
        = ( image_a_option_a @ M @ A2 ) ) ) ).

% image_map_upd
thf(fact_305_these__image__Some__eq,axiom,
    ! [A2: set_a] :
      ( ( these_a @ ( image_a_option_a @ some_a @ A2 ) )
      = A2 ) ).

% these_image_Some_eq
thf(fact_306_inj__Some,axiom,
    ! [A2: set_a] : ( inj_on_a_option_a @ some_a @ A2 ) ).

% inj_Some
thf(fact_307_None__notin__image__Some,axiom,
    ! [A2: set_a] :
      ~ ( member_option_a @ none_a @ ( image_a_option_a @ some_a @ A2 ) ) ).

% None_notin_image_Some
thf(fact_308_Field__insert,axiom,
    ! [A: $o,B: $o,R: set_Product_prod_o_o] :
      ( ( field_o @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A @ B ) @ R ) )
      = ( sup_sup_set_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( field_o @ R ) ) ) ).

% Field_insert
thf(fact_309_Field__insert,axiom,
    ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat] :
      ( ( field_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R ) )
      = ( sup_sup_set_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( field_nat @ R ) ) ) ).

% Field_insert
thf(fact_310_Field__insert,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( field_6101175518749917524od_o_o @ ( insert3855699742481506999od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R ) )
      = ( sup_su1477959037604056251od_o_o @ ( insert3817420688681518039od_o_o @ A @ ( insert3817420688681518039od_o_o @ B @ bot_bo8006819982598807891od_o_o ) ) @ ( field_6101175518749917524od_o_o @ R ) ) ) ).

% Field_insert
thf(fact_311_Field__insert,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( field_3145993188331922222at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) )
      = ( sup_su3642409539654194069at_nat @ ( insert9200635055090092081at_nat @ A @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) @ ( field_3145993188331922222at_nat @ R ) ) ) ).

% Field_insert
thf(fact_312_refl__on__singleton,axiom,
    ! [X: set_Product_prod_o_o] : ( refl_o935183656833700870od_o_o @ ( insert3817420688681518039od_o_o @ X @ bot_bo8006819982598807891od_o_o ) @ ( insert3855699742481506999od_o_o @ ( produc763777882069021527od_o_o @ X @ X ) @ bot_bo498831808395348787od_o_o ) ) ).

% refl_on_singleton
thf(fact_313_refl__on__singleton,axiom,
    ! [X: set_Pr1261947904930325089at_nat] : ( refl_o6955724340487615712at_nat @ ( insert9200635055090092081at_nat @ X @ bot_bo3083307316010499117at_nat ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X @ X ) @ bot_bo228742789529271731at_nat ) ) ).

% refl_on_singleton
thf(fact_314_prod__set__simps_I1_J,axiom,
    ! [X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( basic_3307925540671692871od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) )
      = ( insert3817420688681518039od_o_o @ X @ bot_bo8006819982598807891od_o_o ) ) ).

% prod_set_simps(1)
thf(fact_315_prod__set__simps_I1_J,axiom,
    ! [X: set_Product_prod_o_o,Y: set_Pr1261947904930325089at_nat] :
      ( ( basic_3533134110227475617at_nat @ ( produc8517790099723286449at_nat @ X @ Y ) )
      = ( insert3817420688681518039od_o_o @ X @ bot_bo8006819982598807891od_o_o ) ) ).

% prod_set_simps(1)
thf(fact_316_prod__set__simps_I1_J,axiom,
    ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( basic_3661821009137050567at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) )
      = ( insert9200635055090092081at_nat @ X @ bot_bo3083307316010499117at_nat ) ) ).

% prod_set_simps(1)
thf(fact_317_prod__set__simps_I2_J,axiom,
    ! [X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( basic_2174982398181630341od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) )
      = ( insert3817420688681518039od_o_o @ Y @ bot_bo8006819982598807891od_o_o ) ) ).

% prod_set_simps(2)
thf(fact_318_prod__set__simps_I2_J,axiom,
    ! [X: set_Product_prod_o_o,Y: set_Pr1261947904930325089at_nat] :
      ( ( basic_7607750056555722463at_nat @ ( produc8517790099723286449at_nat @ X @ Y ) )
      = ( insert9200635055090092081at_nat @ Y @ bot_bo3083307316010499117at_nat ) ) ).

% prod_set_simps(2)
thf(fact_319_prod__set__simps_I2_J,axiom,
    ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( basic_484852565060450053at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) )
      = ( insert9200635055090092081at_nat @ Y @ bot_bo3083307316010499117at_nat ) ) ).

% prod_set_simps(2)
thf(fact_320_Range__insert,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( range_1318165146934585909od_o_o @ ( insert3855699742481506999od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R ) )
      = ( insert3817420688681518039od_o_o @ B @ ( range_1318165146934585909od_o_o @ R ) ) ) ).

% Range_insert
thf(fact_321_Range__insert,axiom,
    ! [A: set_Product_prod_o_o,B: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat] :
      ( ( range_8412904782085253007at_nat @ ( insert8109617542356073361at_nat @ ( produc8517790099723286449at_nat @ A @ B ) @ R ) )
      = ( insert9200635055090092081at_nat @ B @ ( range_8412904782085253007at_nat @ R ) ) ) ).

% Range_insert
thf(fact_322_Range__insert,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( range_880292732526890933at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) )
      = ( insert9200635055090092081at_nat @ B @ ( range_880292732526890933at_nat @ R ) ) ) ).

% Range_insert
thf(fact_323_refl__onD2,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( refl_o8365827894042769382od_o_o @ A2 @ R )
     => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ R )
       => ( member444158400953824016od_o_o @ Y @ A2 ) ) ) ).

% refl_onD2
thf(fact_324_refl__onD2,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat] :
      ( ( refl_o3078925143892389184at_nat @ A2 @ R )
     => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ R )
       => ( member4095101504841534314at_nat @ Y @ A2 ) ) ) ).

% refl_onD2
thf(fact_325_refl__onD2,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
      ( ( refl_o7446464703481863270at_nat @ A2 @ R )
     => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R )
       => ( member8757157785044589968at_nat @ Y @ A2 ) ) ) ).

% refl_onD2
thf(fact_326_refl__onD2,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X: a,Y: a] :
      ( ( refl_on_a @ A2 @ R )
     => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R )
       => ( member_a @ Y @ A2 ) ) ) ).

% refl_onD2
thf(fact_327_refl__onD2,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( refl_o935183656833700870od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
       => ( member3157015407008874800od_o_o @ Y @ A2 ) ) ) ).

% refl_onD2
thf(fact_328_refl__onD2,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( refl_o6955724340487615712at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
       => ( member2643936169264416010at_nat @ Y @ A2 ) ) ) ).

% refl_onD2
thf(fact_329_refl__onD1,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( refl_o8365827894042769382od_o_o @ A2 @ R )
     => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ R )
       => ( member444158400953824016od_o_o @ X @ A2 ) ) ) ).

% refl_onD1
thf(fact_330_refl__onD1,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat] :
      ( ( refl_o3078925143892389184at_nat @ A2 @ R )
     => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ R )
       => ( member4095101504841534314at_nat @ X @ A2 ) ) ) ).

% refl_onD1
thf(fact_331_refl__onD1,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
      ( ( refl_o7446464703481863270at_nat @ A2 @ R )
     => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R )
       => ( member8757157785044589968at_nat @ X @ A2 ) ) ) ).

% refl_onD1
thf(fact_332_refl__onD1,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X: a,Y: a] :
      ( ( refl_on_a @ A2 @ R )
     => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R )
       => ( member_a @ X @ A2 ) ) ) ).

% refl_onD1
thf(fact_333_refl__onD1,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( refl_o935183656833700870od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
       => ( member3157015407008874800od_o_o @ X @ A2 ) ) ) ).

% refl_onD1
thf(fact_334_refl__onD1,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( refl_o6955724340487615712at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
       => ( member2643936169264416010at_nat @ X @ A2 ) ) ) ).

% refl_onD1
thf(fact_335_Range__iff,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member3157015407008874800od_o_o @ A @ ( range_1318165146934585909od_o_o @ R ) )
      = ( ? [Y2: set_Product_prod_o_o] : ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y2 @ A ) @ R ) ) ) ).

% Range_iff
thf(fact_336_Range__iff,axiom,
    ! [A: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat] :
      ( ( member2643936169264416010at_nat @ A @ ( range_8412904782085253007at_nat @ R ) )
      = ( ? [Y2: set_Product_prod_o_o] : ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ Y2 @ A ) @ R ) ) ) ).

% Range_iff
thf(fact_337_Range__iff,axiom,
    ! [A: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member2643936169264416010at_nat @ A @ ( range_880292732526890933at_nat @ R ) )
      = ( ? [Y2: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ A ) @ R ) ) ) ).

% Range_iff
thf(fact_338_refl__onD,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o] :
      ( ( refl_o8365827894042769382od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ A @ A2 )
       => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ A ) @ R ) ) ) ).

% refl_onD
thf(fact_339_refl__onD,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat] :
      ( ( refl_o3078925143892389184at_nat @ A2 @ R )
     => ( ( member4095101504841534314at_nat @ A @ A2 )
       => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ A ) @ R ) ) ) ).

% refl_onD
thf(fact_340_refl__onD,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat] :
      ( ( refl_o7446464703481863270at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ A @ A2 )
       => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ A ) @ R ) ) ) ).

% refl_onD
thf(fact_341_refl__onD,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,A: a] :
      ( ( refl_on_a @ A2 @ R )
     => ( ( member_a @ A @ A2 )
       => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ A ) @ R ) ) ) ).

% refl_onD
thf(fact_342_refl__onD,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o] :
      ( ( refl_o935183656833700870od_o_o @ A2 @ R )
     => ( ( member3157015407008874800od_o_o @ A @ A2 )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ A ) @ R ) ) ) ).

% refl_onD
thf(fact_343_refl__onD,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat] :
      ( ( refl_o6955724340487615712at_nat @ A2 @ R )
     => ( ( member2643936169264416010at_nat @ A @ A2 )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ R ) ) ) ).

% refl_onD
thf(fact_344_FieldI2,axiom,
    ! [I: produc2934264451710624999od_o_o,J: produc2934264451710624999od_o_o,R3: set_Pr1013884327308616903od_o_o] :
      ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ I @ J ) @ R3 )
     => ( member444158400953824016od_o_o @ J @ ( field_5121862139100741428od_o_o @ R3 ) ) ) ).

% FieldI2
thf(fact_345_FieldI2,axiom,
    ! [I: produc732395585841259969at_nat,J: produc732395585841259969at_nat,R3: set_Pr4427867301352232263at_nat] :
      ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ I @ J ) @ R3 )
     => ( member4095101504841534314at_nat @ J @ ( field_7361900449976055182at_nat @ R3 ) ) ) ).

% FieldI2
thf(fact_346_FieldI2,axiom,
    ! [I: produc3843707927480180839at_nat,J: produc3843707927480180839at_nat,R3: set_Pr5564308138774400199at_nat] :
      ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J ) @ R3 )
     => ( member8757157785044589968at_nat @ J @ ( field_2862844103579723188at_nat @ R3 ) ) ) ).

% FieldI2
thf(fact_347_FieldI2,axiom,
    ! [I: a,J: a,R3: set_Product_prod_a_a] :
      ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ I @ J ) @ R3 )
     => ( member_a @ J @ ( field_a @ R3 ) ) ) ).

% FieldI2
thf(fact_348_FieldI2,axiom,
    ! [I: $o,J: $o,R3: set_Product_prod_o_o] :
      ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J ) @ R3 )
     => ( member_o @ J @ ( field_o @ R3 ) ) ) ).

% FieldI2
thf(fact_349_FieldI2,axiom,
    ! [I: nat,J: nat,R3: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R3 )
     => ( member_nat @ J @ ( field_nat @ R3 ) ) ) ).

% FieldI2
thf(fact_350_FieldI2,axiom,
    ! [I: set_Product_prod_o_o,J: set_Product_prod_o_o,R3: set_Pr1932065953672099015od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ I @ J ) @ R3 )
     => ( member3157015407008874800od_o_o @ J @ ( field_6101175518749917524od_o_o @ R3 ) ) ) ).

% FieldI2
thf(fact_351_FieldI2,axiom,
    ! [I: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J ) @ R3 )
     => ( member2643936169264416010at_nat @ J @ ( field_3145993188331922222at_nat @ R3 ) ) ) ).

% FieldI2
thf(fact_352_FieldI1,axiom,
    ! [I: produc2934264451710624999od_o_o,J: produc2934264451710624999od_o_o,R3: set_Pr1013884327308616903od_o_o] :
      ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ I @ J ) @ R3 )
     => ( member444158400953824016od_o_o @ I @ ( field_5121862139100741428od_o_o @ R3 ) ) ) ).

% FieldI1
thf(fact_353_FieldI1,axiom,
    ! [I: produc732395585841259969at_nat,J: produc732395585841259969at_nat,R3: set_Pr4427867301352232263at_nat] :
      ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ I @ J ) @ R3 )
     => ( member4095101504841534314at_nat @ I @ ( field_7361900449976055182at_nat @ R3 ) ) ) ).

% FieldI1
thf(fact_354_FieldI1,axiom,
    ! [I: produc3843707927480180839at_nat,J: produc3843707927480180839at_nat,R3: set_Pr5564308138774400199at_nat] :
      ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J ) @ R3 )
     => ( member8757157785044589968at_nat @ I @ ( field_2862844103579723188at_nat @ R3 ) ) ) ).

% FieldI1
thf(fact_355_FieldI1,axiom,
    ! [I: a,J: a,R3: set_Product_prod_a_a] :
      ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ I @ J ) @ R3 )
     => ( member_a @ I @ ( field_a @ R3 ) ) ) ).

% FieldI1
thf(fact_356_FieldI1,axiom,
    ! [I: $o,J: $o,R3: set_Product_prod_o_o] :
      ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J ) @ R3 )
     => ( member_o @ I @ ( field_o @ R3 ) ) ) ).

% FieldI1
thf(fact_357_FieldI1,axiom,
    ! [I: nat,J: nat,R3: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R3 )
     => ( member_nat @ I @ ( field_nat @ R3 ) ) ) ).

% FieldI1
thf(fact_358_FieldI1,axiom,
    ! [I: set_Product_prod_o_o,J: set_Product_prod_o_o,R3: set_Pr1932065953672099015od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ I @ J ) @ R3 )
     => ( member3157015407008874800od_o_o @ I @ ( field_6101175518749917524od_o_o @ R3 ) ) ) ).

% FieldI1
thf(fact_359_FieldI1,axiom,
    ! [I: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J ) @ R3 )
     => ( member2643936169264416010at_nat @ I @ ( field_3145993188331922222at_nat @ R3 ) ) ) ).

% FieldI1
thf(fact_360_RangeE,axiom,
    ! [B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member3157015407008874800od_o_o @ B @ ( range_1318165146934585909od_o_o @ R ) )
     => ~ ! [A4: set_Product_prod_o_o] :
            ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A4 @ B ) @ R ) ) ).

% RangeE
thf(fact_361_RangeE,axiom,
    ! [B: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat] :
      ( ( member2643936169264416010at_nat @ B @ ( range_8412904782085253007at_nat @ R ) )
     => ~ ! [A4: set_Product_prod_o_o] :
            ~ ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A4 @ B ) @ R ) ) ).

% RangeE
thf(fact_362_RangeE,axiom,
    ! [B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member2643936169264416010at_nat @ B @ ( range_880292732526890933at_nat @ R ) )
     => ~ ! [A4: set_Pr1261947904930325089at_nat] :
            ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A4 @ B ) @ R ) ) ).

% RangeE
thf(fact_363_Range_Ointros,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
     => ( member3157015407008874800od_o_o @ B @ ( range_1318165146934585909od_o_o @ R ) ) ) ).

% Range.intros
thf(fact_364_Range_Ointros,axiom,
    ! [A: set_Product_prod_o_o,B: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A @ B ) @ R )
     => ( member2643936169264416010at_nat @ B @ ( range_8412904782085253007at_nat @ R ) ) ) ).

% Range.intros
thf(fact_365_Range_Ointros,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
     => ( member2643936169264416010at_nat @ B @ ( range_880292732526890933at_nat @ R ) ) ) ).

% Range.intros
thf(fact_366_Range_Osimps,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member3157015407008874800od_o_o @ A @ ( range_1318165146934585909od_o_o @ R ) )
      = ( ? [A3: set_Product_prod_o_o,B4: set_Product_prod_o_o] :
            ( ( A = B4 )
            & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A3 @ B4 ) @ R ) ) ) ) ).

% Range.simps
thf(fact_367_Range_Osimps,axiom,
    ! [A: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat] :
      ( ( member2643936169264416010at_nat @ A @ ( range_8412904782085253007at_nat @ R ) )
      = ( ? [A3: set_Product_prod_o_o,B4: set_Pr1261947904930325089at_nat] :
            ( ( A = B4 )
            & ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A3 @ B4 ) @ R ) ) ) ) ).

% Range.simps
thf(fact_368_Range_Osimps,axiom,
    ! [A: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member2643936169264416010at_nat @ A @ ( range_880292732526890933at_nat @ R ) )
      = ( ? [A3: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
            ( ( A = B4 )
            & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A3 @ B4 ) @ R ) ) ) ) ).

% Range.simps
thf(fact_369_Range_Ocases,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member3157015407008874800od_o_o @ A @ ( range_1318165146934585909od_o_o @ R ) )
     => ~ ! [A4: set_Product_prod_o_o] :
            ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A4 @ A ) @ R ) ) ).

% Range.cases
thf(fact_370_Range_Ocases,axiom,
    ! [A: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat] :
      ( ( member2643936169264416010at_nat @ A @ ( range_8412904782085253007at_nat @ R ) )
     => ~ ! [A4: set_Product_prod_o_o] :
            ~ ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A4 @ A ) @ R ) ) ).

% Range.cases
thf(fact_371_Range_Ocases,axiom,
    ! [A: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member2643936169264416010at_nat @ A @ ( range_880292732526890933at_nat @ R ) )
     => ~ ! [A4: set_Pr1261947904930325089at_nat] :
            ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A4 @ A ) @ R ) ) ).

% Range.cases
thf(fact_372_refl__on__domain,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( refl_o8365827894042769382od_o_o @ A2 @ R )
     => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ B ) @ R )
       => ( ( member444158400953824016od_o_o @ A @ A2 )
          & ( member444158400953824016od_o_o @ B @ A2 ) ) ) ) ).

% refl_on_domain
thf(fact_373_refl__on__domain,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat,B: produc732395585841259969at_nat] :
      ( ( refl_o3078925143892389184at_nat @ A2 @ R )
     => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ B ) @ R )
       => ( ( member4095101504841534314at_nat @ A @ A2 )
          & ( member4095101504841534314at_nat @ B @ A2 ) ) ) ) ).

% refl_on_domain
thf(fact_374_refl__on__domain,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
      ( ( refl_o7446464703481863270at_nat @ A2 @ R )
     => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R )
       => ( ( member8757157785044589968at_nat @ A @ A2 )
          & ( member8757157785044589968at_nat @ B @ A2 ) ) ) ) ).

% refl_on_domain
thf(fact_375_refl__on__domain,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,A: a,B: a] :
      ( ( refl_on_a @ A2 @ R )
     => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B ) @ R )
       => ( ( member_a @ A @ A2 )
          & ( member_a @ B @ A2 ) ) ) ) ).

% refl_on_domain
thf(fact_376_refl__on__domain,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( refl_o935183656833700870od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
       => ( ( member3157015407008874800od_o_o @ A @ A2 )
          & ( member3157015407008874800od_o_o @ B @ A2 ) ) ) ) ).

% refl_on_domain
thf(fact_377_refl__on__domain,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( refl_o6955724340487615712at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
       => ( ( member2643936169264416010at_nat @ A @ A2 )
          & ( member2643936169264416010at_nat @ B @ A2 ) ) ) ) ).

% refl_on_domain
thf(fact_378_Domain__insert,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( domain8908270702770587084od_o_o @ ( insert3855699742481506999od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R ) )
      = ( insert3817420688681518039od_o_o @ A @ ( domain8908270702770587084od_o_o @ R ) ) ) ).

% Domain_insert
thf(fact_379_Domain__insert,axiom,
    ! [A: set_Product_prod_o_o,B: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat] :
      ( ( domain8494901049294654374at_nat @ ( insert8109617542356073361at_nat @ ( produc8517790099723286449at_nat @ A @ B ) @ R ) )
      = ( insert3817420688681518039od_o_o @ A @ ( domain8494901049294654374at_nat @ R ) ) ) ).

% Domain_insert
thf(fact_380_Domain__insert,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( domain8802589944165416012at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) )
      = ( insert9200635055090092081at_nat @ A @ ( domain8802589944165416012at_nat @ R ) ) ) ).

% Domain_insert
thf(fact_381_notin__range__Some,axiom,
    ! [X: option_a] :
      ( ( ~ ( member_option_a @ X @ ( image_a_option_a @ some_a @ top_top_set_a ) ) )
      = ( X = none_a ) ) ).

% notin_range_Some
thf(fact_382_notin__range__Some,axiom,
    ! [X: option_nat] :
      ( ( ~ ( member_option_nat @ X @ ( image_nat_option_nat @ some_nat @ top_top_set_nat ) ) )
      = ( X = none_nat ) ) ).

% notin_range_Some
thf(fact_383_Linear__order__in__diff__Id,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( order_91209724698019100od_o_o @ ( field_5121862139100741428od_o_o @ R ) @ R )
     => ( ( member444158400953824016od_o_o @ A @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ B @ ( field_5121862139100741428od_o_o @ R ) )
         => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ B ) @ R )
            = ( ~ ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ B @ A ) @ ( minus_5063024033727795502od_o_o @ R @ id_Pro5927853813057311299od_o_o ) ) ) ) ) ) ) ).

% Linear_order_in_diff_Id
thf(fact_384_Linear__order__in__diff__Id,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat,B: produc732395585841259969at_nat] :
      ( ( order_9086815480479278966at_nat @ ( field_7361900449976055182at_nat @ R ) @ R )
     => ( ( member4095101504841534314at_nat @ A @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( member4095101504841534314at_nat @ B @ ( field_7361900449976055182at_nat @ R ) )
         => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ B ) @ R )
            = ( ~ ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ B @ A ) @ ( minus_2318593706003940014at_nat @ R @ id_Pro6320881530060322077at_nat ) ) ) ) ) ) ) ).

% Linear_order_in_diff_Id
thf(fact_385_Linear__order__in__diff__Id,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
      ( ( order_2711500226769404828at_nat @ ( field_2862844103579723188at_nat @ R ) @ R )
     => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ B @ ( field_2862844103579723188at_nat @ R ) )
         => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R )
            = ( ~ ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ B @ A ) @ ( minus_8235382265540049710at_nat @ R @ id_Pro5428700290092274115at_nat ) ) ) ) ) ) ) ).

% Linear_order_in_diff_Id
thf(fact_386_Linear__order__in__diff__Id,axiom,
    ! [R: set_Product_prod_a_a,A: a,B: a] :
      ( ( order_8768733634509060147r_on_a @ ( field_a @ R ) @ R )
     => ( ( member_a @ A @ ( field_a @ R ) )
       => ( ( member_a @ B @ ( field_a @ R ) )
         => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B ) @ R )
            = ( ~ ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B @ A ) @ ( minus_6817036919807184750od_a_a @ R @ id_a2 ) ) ) ) ) ) ) ).

% Linear_order_in_diff_Id
thf(fact_387_Linear__order__in__diff__Id,axiom,
    ! [R: set_Product_prod_o_o,A: $o,B: $o] :
      ( ( order_6238756238976269133r_on_o @ ( field_o @ R ) @ R )
     => ( ( member_o @ A @ ( field_o @ R ) )
       => ( ( member_o @ B @ ( field_o @ R ) )
         => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ R )
            = ( ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A ) @ ( minus_7052513330764642158od_o_o @ R @ id_o ) ) ) ) ) ) ) ).

% Linear_order_in_diff_Id
thf(fact_388_Linear__order__in__diff__Id,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
      ( ( order_4473980167227706203on_nat @ ( field_nat @ R ) @ R )
     => ( ( member_nat @ A @ ( field_nat @ R ) )
       => ( ( member_nat @ B @ ( field_nat @ R ) )
         => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
            = ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A ) @ ( minus_1356011639430497352at_nat @ R @ id_nat ) ) ) ) ) ) ) ).

% Linear_order_in_diff_Id
thf(fact_389_Linear__order__in__diff__Id,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( order_2625247082195685180od_o_o @ ( field_6101175518749917524od_o_o @ R ) @ R )
     => ( ( member3157015407008874800od_o_o @ A @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( member3157015407008874800od_o_o @ B @ ( field_6101175518749917524od_o_o @ R ) )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
            = ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ A ) @ ( minus_5704166846132356910od_o_o @ R @ id_set2647307015711338339od_o_o ) ) ) ) ) ) ) ).

% Linear_order_in_diff_Id
thf(fact_390_Linear__order__in__diff__Id,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( order_5942792088423767318at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
     => ( ( member2643936169264416010at_nat @ A @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( member2643936169264416010at_nat @ B @ ( field_3145993188331922222at_nat @ R ) )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
            = ( ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ A ) @ ( minus_3314409938677909166at_nat @ R @ id_set1796276052702428605at_nat ) ) ) ) ) ) ) ).

% Linear_order_in_diff_Id
thf(fact_391_cofinal__def,axiom,
    ( bNF_Ca4363140458462388713inal_o
    = ( ^ [A7: set_o,R2: set_Product_prod_o_o] :
        ! [X2: $o] :
          ( ( member_o @ X2 @ ( field_o @ R2 ) )
         => ? [Y2: $o] :
              ( ( member_o @ Y2 @ A7 )
              & ( X2 = (~ Y2) )
              & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y2 ) @ R2 ) ) ) ) ) ).

% cofinal_def
thf(fact_392_cofinal__def,axiom,
    ( bNF_Ca5159621140400407487al_nat
    = ( ^ [A7: set_nat,R2: set_Pr1261947904930325089at_nat] :
        ! [X2: nat] :
          ( ( member_nat @ X2 @ ( field_nat @ R2 ) )
         => ? [Y2: nat] :
              ( ( member_nat @ Y2 @ A7 )
              & ( X2 != Y2 )
              & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ R2 ) ) ) ) ) ).

% cofinal_def
thf(fact_393_cofinal__def,axiom,
    ( bNF_Ca3407573850950408152od_o_o
    = ( ^ [A7: set_se491199571785101031od_o_o,R2: set_Pr1932065953672099015od_o_o] :
        ! [X2: set_Product_prod_o_o] :
          ( ( member3157015407008874800od_o_o @ X2 @ ( field_6101175518749917524od_o_o @ R2 ) )
         => ? [Y2: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ Y2 @ A7 )
              & ( X2 != Y2 )
              & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Y2 ) @ R2 ) ) ) ) ) ).

% cofinal_def
thf(fact_394_cofinal__def,axiom,
    ( bNF_Ca8448034394003515314at_nat
    = ( ^ [A7: set_se7855581050983116737at_nat,R2: set_Pr4329608150637261639at_nat] :
        ! [X2: set_Pr1261947904930325089at_nat] :
          ( ( member2643936169264416010at_nat @ X2 @ ( field_3145993188331922222at_nat @ R2 ) )
         => ? [Y2: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ Y2 @ A7 )
              & ( X2 != Y2 )
              & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y2 ) @ R2 ) ) ) ) ) ).

% cofinal_def
thf(fact_395_Image__singleton__iff,axiom,
    ! [B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o] :
      ( ( member3157015407008874800od_o_o @ B @ ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ A @ bot_bo8006819982598807891od_o_o ) ) )
      = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R ) ) ).

% Image_singleton_iff
thf(fact_396_Image__singleton__iff,axiom,
    ! [B: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat,A: set_Product_prod_o_o] :
      ( ( member2643936169264416010at_nat @ B @ ( image_2461788823225053677at_nat @ R @ ( insert3817420688681518039od_o_o @ A @ bot_bo8006819982598807891od_o_o ) ) )
      = ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A @ B ) @ R ) ) ).

% Image_singleton_iff
thf(fact_397_Image__singleton__iff,axiom,
    ! [B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat] :
      ( ( member2643936169264416010at_nat @ B @ ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ A @ bot_bo3083307316010499117at_nat ) ) )
      = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) ) ).

% Image_singleton_iff
thf(fact_398_ImageI,axiom,
    ! [A: a,B: a,R: set_Product_prod_a_a,A2: set_a] :
      ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B ) @ R )
     => ( ( member_a @ A @ A2 )
       => ( member_a @ B @ ( image_a_a @ R @ A2 ) ) ) ) ).

% ImageI
thf(fact_399_ImageI,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o,A2: set_se491199571785101031od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
     => ( ( member3157015407008874800od_o_o @ A @ A2 )
       => ( member3157015407008874800od_o_o @ B @ ( image_3256184292080368531od_o_o @ R @ A2 ) ) ) ) ).

% ImageI
thf(fact_400_ImageI,axiom,
    ! [A: set_Product_prod_o_o,B: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat,A2: set_se491199571785101031od_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A @ B ) @ R )
     => ( ( member3157015407008874800od_o_o @ A @ A2 )
       => ( member2643936169264416010at_nat @ B @ ( image_2461788823225053677at_nat @ R @ A2 ) ) ) ) ).

% ImageI
thf(fact_401_ImageI,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,A2: set_se7855581050983116737at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
     => ( ( member2643936169264416010at_nat @ A @ A2 )
       => ( member2643936169264416010at_nat @ B @ ( image_3892192845344445203at_nat @ R @ A2 ) ) ) ) ).

% ImageI
thf(fact_402_ImageI,axiom,
    ! [A: produc2934264451710624999od_o_o,B: a,R: set_Pr6196119011418371550_o_o_a,A2: set_Pr1932065953672099015od_o_o] :
      ( ( member1826218620961749927_o_o_a @ ( produc6642224045558206830_o_o_a @ A @ B ) @ R )
     => ( ( member444158400953824016od_o_o @ A @ A2 )
       => ( member_a @ B @ ( image_7612288785953357226_o_o_a @ R @ A2 ) ) ) ) ).

% ImageI
thf(fact_403_ImageI,axiom,
    ! [A: produc732395585841259969at_nat,B: a,R: set_Pr5256879730163711364_nat_a,A2: set_Pr457366540195662369at_nat] :
      ( ( member9163085975106382925_nat_a @ ( produc538889887490039572_nat_a @ A @ B ) @ R )
     => ( ( member4095101504841534314at_nat @ A @ A2 )
       => ( member_a @ B @ ( image_3924149183600524624_nat_a @ R @ A2 ) ) ) ) ).

% ImageI
thf(fact_404_ImageI,axiom,
    ! [A: produc3843707927480180839at_nat,B: a,R: set_Pr7219508552201550942_nat_a,A2: set_Pr4329608150637261639at_nat] :
      ( ( member1060612044916223527_nat_a @ ( produc517308312889114094_nat_a @ A @ B ) @ R )
     => ( ( member8757157785044589968at_nat @ A @ A2 )
       => ( member_a @ B @ ( image_8821586633200209450_nat_a @ R @ A2 ) ) ) ) ).

% ImageI
thf(fact_405_ImageI,axiom,
    ! [A: a,B: produc2934264451710624999od_o_o,R: set_Pr5975447109543910128od_o_o,A2: set_a] :
      ( ( member5845106769783146937od_o_o @ ( produc7371010082742806528od_o_o @ A @ B ) @ R )
     => ( ( member_a @ A @ A2 )
       => ( member444158400953824016od_o_o @ B @ ( image_8341074823137956924od_o_o @ R @ A2 ) ) ) ) ).

% ImageI
thf(fact_406_ImageI,axiom,
    ! [A: a,B: produc732395585841259969at_nat,R: set_Pr1968968238647823434at_nat,A2: set_a] :
      ( ( member6868933294997782035at_nat @ ( produc7802126073954666586at_nat @ A @ B ) @ R )
     => ( ( member_a @ A @ A2 )
       => ( member4095101504841534314at_nat @ B @ ( image_1964013333210375830at_nat @ R @ A2 ) ) ) ) ).

% ImageI
thf(fact_407_ImageI,axiom,
    ! [A: a,B: produc3843707927480180839at_nat,R: set_Pr8044876533244767088at_nat,A2: set_a] :
      ( ( member4313070330384631353at_nat @ ( produc3162473886009270912at_nat @ A @ B ) @ R )
     => ( ( member_a @ A @ A2 )
       => ( member8757157785044589968at_nat @ B @ ( image_2243380169465590460at_nat @ R @ A2 ) ) ) ) ).

% ImageI
thf(fact_408_IdI,axiom,
    ! [A: set_Product_prod_o_o] : ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ A ) @ id_set2647307015711338339od_o_o ) ).

% IdI
thf(fact_409_IdI,axiom,
    ! [A: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ id_set1796276052702428605at_nat ) ).

% IdI
thf(fact_410_pair__in__Id__conv,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ id_set2647307015711338339od_o_o )
      = ( A = B ) ) ).

% pair_in_Id_conv
thf(fact_411_pair__in__Id__conv,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ id_set1796276052702428605at_nat )
      = ( A = B ) ) ).

% pair_in_Id_conv
thf(fact_412_rev__ImageI,axiom,
    ! [A: a,A2: set_a,B: a,R: set_Product_prod_a_a] :
      ( ( member_a @ A @ A2 )
     => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B ) @ R )
       => ( member_a @ B @ ( image_a_a @ R @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_413_rev__ImageI,axiom,
    ! [A: set_Product_prod_o_o,A2: set_se491199571785101031od_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member3157015407008874800od_o_o @ A @ A2 )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
       => ( member3157015407008874800od_o_o @ B @ ( image_3256184292080368531od_o_o @ R @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_414_rev__ImageI,axiom,
    ! [A: set_Product_prod_o_o,A2: set_se491199571785101031od_o_o,B: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat] :
      ( ( member3157015407008874800od_o_o @ A @ A2 )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A @ B ) @ R )
       => ( member2643936169264416010at_nat @ B @ ( image_2461788823225053677at_nat @ R @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_415_rev__ImageI,axiom,
    ! [A: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member2643936169264416010at_nat @ A @ A2 )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
       => ( member2643936169264416010at_nat @ B @ ( image_3892192845344445203at_nat @ R @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_416_rev__ImageI,axiom,
    ! [A: produc2934264451710624999od_o_o,A2: set_Pr1932065953672099015od_o_o,B: a,R: set_Pr6196119011418371550_o_o_a] :
      ( ( member444158400953824016od_o_o @ A @ A2 )
     => ( ( member1826218620961749927_o_o_a @ ( produc6642224045558206830_o_o_a @ A @ B ) @ R )
       => ( member_a @ B @ ( image_7612288785953357226_o_o_a @ R @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_417_rev__ImageI,axiom,
    ! [A: produc732395585841259969at_nat,A2: set_Pr457366540195662369at_nat,B: a,R: set_Pr5256879730163711364_nat_a] :
      ( ( member4095101504841534314at_nat @ A @ A2 )
     => ( ( member9163085975106382925_nat_a @ ( produc538889887490039572_nat_a @ A @ B ) @ R )
       => ( member_a @ B @ ( image_3924149183600524624_nat_a @ R @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_418_rev__ImageI,axiom,
    ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B: a,R: set_Pr7219508552201550942_nat_a] :
      ( ( member8757157785044589968at_nat @ A @ A2 )
     => ( ( member1060612044916223527_nat_a @ ( produc517308312889114094_nat_a @ A @ B ) @ R )
       => ( member_a @ B @ ( image_8821586633200209450_nat_a @ R @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_419_rev__ImageI,axiom,
    ! [A: a,A2: set_a,B: produc2934264451710624999od_o_o,R: set_Pr5975447109543910128od_o_o] :
      ( ( member_a @ A @ A2 )
     => ( ( member5845106769783146937od_o_o @ ( produc7371010082742806528od_o_o @ A @ B ) @ R )
       => ( member444158400953824016od_o_o @ B @ ( image_8341074823137956924od_o_o @ R @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_420_rev__ImageI,axiom,
    ! [A: a,A2: set_a,B: produc732395585841259969at_nat,R: set_Pr1968968238647823434at_nat] :
      ( ( member_a @ A @ A2 )
     => ( ( member6868933294997782035at_nat @ ( produc7802126073954666586at_nat @ A @ B ) @ R )
       => ( member4095101504841534314at_nat @ B @ ( image_1964013333210375830at_nat @ R @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_421_rev__ImageI,axiom,
    ! [A: a,A2: set_a,B: produc3843707927480180839at_nat,R: set_Pr8044876533244767088at_nat] :
      ( ( member_a @ A @ A2 )
     => ( ( member4313070330384631353at_nat @ ( produc3162473886009270912at_nat @ A @ B ) @ R )
       => ( member8757157785044589968at_nat @ B @ ( image_2243380169465590460at_nat @ R @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_422_Image__iff,axiom,
    ! [B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o,A2: set_se491199571785101031od_o_o] :
      ( ( member3157015407008874800od_o_o @ B @ ( image_3256184292080368531od_o_o @ R @ A2 ) )
      = ( ? [X2: set_Product_prod_o_o] :
            ( ( member3157015407008874800od_o_o @ X2 @ A2 )
            & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ B ) @ R ) ) ) ) ).

% Image_iff
thf(fact_423_Image__iff,axiom,
    ! [B: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat,A2: set_se491199571785101031od_o_o] :
      ( ( member2643936169264416010at_nat @ B @ ( image_2461788823225053677at_nat @ R @ A2 ) )
      = ( ? [X2: set_Product_prod_o_o] :
            ( ( member3157015407008874800od_o_o @ X2 @ A2 )
            & ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ X2 @ B ) @ R ) ) ) ) ).

% Image_iff
thf(fact_424_Image__iff,axiom,
    ! [B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,A2: set_se7855581050983116737at_nat] :
      ( ( member2643936169264416010at_nat @ B @ ( image_3892192845344445203at_nat @ R @ A2 ) )
      = ( ? [X2: set_Pr1261947904930325089at_nat] :
            ( ( member2643936169264416010at_nat @ X2 @ A2 )
            & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ B ) @ R ) ) ) ) ).

% Image_iff
thf(fact_425_ImageE,axiom,
    ! [B: a,R: set_Product_prod_a_a,A2: set_a] :
      ( ( member_a @ B @ ( image_a_a @ R @ A2 ) )
     => ~ ! [X3: a] :
            ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X3 @ B ) @ R )
           => ~ ( member_a @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_426_ImageE,axiom,
    ! [B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o,A2: set_se491199571785101031od_o_o] :
      ( ( member3157015407008874800od_o_o @ B @ ( image_3256184292080368531od_o_o @ R @ A2 ) )
     => ~ ! [X3: set_Product_prod_o_o] :
            ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ B ) @ R )
           => ~ ( member3157015407008874800od_o_o @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_427_ImageE,axiom,
    ! [B: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat,A2: set_se491199571785101031od_o_o] :
      ( ( member2643936169264416010at_nat @ B @ ( image_2461788823225053677at_nat @ R @ A2 ) )
     => ~ ! [X3: set_Product_prod_o_o] :
            ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ X3 @ B ) @ R )
           => ~ ( member3157015407008874800od_o_o @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_428_ImageE,axiom,
    ! [B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,A2: set_se7855581050983116737at_nat] :
      ( ( member2643936169264416010at_nat @ B @ ( image_3892192845344445203at_nat @ R @ A2 ) )
     => ~ ! [X3: set_Pr1261947904930325089at_nat] :
            ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ B ) @ R )
           => ~ ( member2643936169264416010at_nat @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_429_ImageE,axiom,
    ! [B: produc2934264451710624999od_o_o,R: set_Pr5975447109543910128od_o_o,A2: set_a] :
      ( ( member444158400953824016od_o_o @ B @ ( image_8341074823137956924od_o_o @ R @ A2 ) )
     => ~ ! [X3: a] :
            ( ( member5845106769783146937od_o_o @ ( produc7371010082742806528od_o_o @ X3 @ B ) @ R )
           => ~ ( member_a @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_430_ImageE,axiom,
    ! [B: produc732395585841259969at_nat,R: set_Pr1968968238647823434at_nat,A2: set_a] :
      ( ( member4095101504841534314at_nat @ B @ ( image_1964013333210375830at_nat @ R @ A2 ) )
     => ~ ! [X3: a] :
            ( ( member6868933294997782035at_nat @ ( produc7802126073954666586at_nat @ X3 @ B ) @ R )
           => ~ ( member_a @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_431_ImageE,axiom,
    ! [B: produc3843707927480180839at_nat,R: set_Pr8044876533244767088at_nat,A2: set_a] :
      ( ( member8757157785044589968at_nat @ B @ ( image_2243380169465590460at_nat @ R @ A2 ) )
     => ~ ! [X3: a] :
            ( ( member4313070330384631353at_nat @ ( produc3162473886009270912at_nat @ X3 @ B ) @ R )
           => ~ ( member_a @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_432_ImageE,axiom,
    ! [B: a,R: set_Pr6196119011418371550_o_o_a,A2: set_Pr1932065953672099015od_o_o] :
      ( ( member_a @ B @ ( image_7612288785953357226_o_o_a @ R @ A2 ) )
     => ~ ! [X3: produc2934264451710624999od_o_o] :
            ( ( member1826218620961749927_o_o_a @ ( produc6642224045558206830_o_o_a @ X3 @ B ) @ R )
           => ~ ( member444158400953824016od_o_o @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_433_ImageE,axiom,
    ! [B: a,R: set_Pr5256879730163711364_nat_a,A2: set_Pr457366540195662369at_nat] :
      ( ( member_a @ B @ ( image_3924149183600524624_nat_a @ R @ A2 ) )
     => ~ ! [X3: produc732395585841259969at_nat] :
            ( ( member9163085975106382925_nat_a @ ( produc538889887490039572_nat_a @ X3 @ B ) @ R )
           => ~ ( member4095101504841534314at_nat @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_434_ImageE,axiom,
    ! [B: a,R: set_Pr7219508552201550942_nat_a,A2: set_Pr4329608150637261639at_nat] :
      ( ( member_a @ B @ ( image_8821586633200209450_nat_a @ R @ A2 ) )
     => ~ ! [X3: produc3843707927480180839at_nat] :
            ( ( member1060612044916223527_nat_a @ ( produc517308312889114094_nat_a @ X3 @ B ) @ R )
           => ~ ( member8757157785044589968at_nat @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_435_IdE,axiom,
    ! [P: produc2934264451710624999od_o_o] :
      ( ( member444158400953824016od_o_o @ P @ id_set2647307015711338339od_o_o )
     => ~ ! [X3: set_Product_prod_o_o] :
            ( P
           != ( produc763777882069021527od_o_o @ X3 @ X3 ) ) ) ).

% IdE
thf(fact_436_IdE,axiom,
    ! [P: produc3843707927480180839at_nat] :
      ( ( member8757157785044589968at_nat @ P @ id_set1796276052702428605at_nat )
     => ~ ! [X3: set_Pr1261947904930325089at_nat] :
            ( P
           != ( produc2922128104949294807at_nat @ X3 @ X3 ) ) ) ).

% IdE
thf(fact_437_Domain_Ocases,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member3157015407008874800od_o_o @ A @ ( domain8908270702770587084od_o_o @ R ) )
     => ~ ! [B3: set_Product_prod_o_o] :
            ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B3 ) @ R ) ) ).

% Domain.cases
thf(fact_438_Domain_Ocases,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr457366540195662369at_nat] :
      ( ( member3157015407008874800od_o_o @ A @ ( domain8494901049294654374at_nat @ R ) )
     => ~ ! [B3: set_Pr1261947904930325089at_nat] :
            ~ ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A @ B3 ) @ R ) ) ).

% Domain.cases
thf(fact_439_Domain_Ocases,axiom,
    ! [A: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member2643936169264416010at_nat @ A @ ( domain8802589944165416012at_nat @ R ) )
     => ~ ! [B3: set_Pr1261947904930325089at_nat] :
            ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B3 ) @ R ) ) ).

% Domain.cases
thf(fact_440_Domain_Osimps,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member3157015407008874800od_o_o @ A @ ( domain8908270702770587084od_o_o @ R ) )
      = ( ? [A3: set_Product_prod_o_o,B4: set_Product_prod_o_o] :
            ( ( A = A3 )
            & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A3 @ B4 ) @ R ) ) ) ) ).

% Domain.simps
thf(fact_441_Domain_Osimps,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr457366540195662369at_nat] :
      ( ( member3157015407008874800od_o_o @ A @ ( domain8494901049294654374at_nat @ R ) )
      = ( ? [A3: set_Product_prod_o_o,B4: set_Pr1261947904930325089at_nat] :
            ( ( A = A3 )
            & ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A3 @ B4 ) @ R ) ) ) ) ).

% Domain.simps
thf(fact_442_Domain_Osimps,axiom,
    ! [A: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member2643936169264416010at_nat @ A @ ( domain8802589944165416012at_nat @ R ) )
      = ( ? [A3: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
            ( ( A = A3 )
            & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A3 @ B4 ) @ R ) ) ) ) ).

% Domain.simps
thf(fact_443_Domain_ODomainI,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
     => ( member3157015407008874800od_o_o @ A @ ( domain8908270702770587084od_o_o @ R ) ) ) ).

% Domain.DomainI
thf(fact_444_Domain_ODomainI,axiom,
    ! [A: set_Product_prod_o_o,B: set_Pr1261947904930325089at_nat,R: set_Pr457366540195662369at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A @ B ) @ R )
     => ( member3157015407008874800od_o_o @ A @ ( domain8494901049294654374at_nat @ R ) ) ) ).

% Domain.DomainI
thf(fact_445_Domain_ODomainI,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
     => ( member2643936169264416010at_nat @ A @ ( domain8802589944165416012at_nat @ R ) ) ) ).

% Domain.DomainI
thf(fact_446_DomainE,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member3157015407008874800od_o_o @ A @ ( domain8908270702770587084od_o_o @ R ) )
     => ~ ! [B3: set_Product_prod_o_o] :
            ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B3 ) @ R ) ) ).

% DomainE
thf(fact_447_DomainE,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr457366540195662369at_nat] :
      ( ( member3157015407008874800od_o_o @ A @ ( domain8494901049294654374at_nat @ R ) )
     => ~ ! [B3: set_Pr1261947904930325089at_nat] :
            ~ ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A @ B3 ) @ R ) ) ).

% DomainE
thf(fact_448_DomainE,axiom,
    ! [A: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member2643936169264416010at_nat @ A @ ( domain8802589944165416012at_nat @ R ) )
     => ~ ! [B3: set_Pr1261947904930325089at_nat] :
            ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B3 ) @ R ) ) ).

% DomainE
thf(fact_449_Domain__iff,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member3157015407008874800od_o_o @ A @ ( domain8908270702770587084od_o_o @ R ) )
      = ( ? [Y2: set_Product_prod_o_o] : ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ Y2 ) @ R ) ) ) ).

% Domain_iff
thf(fact_450_Domain__iff,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr457366540195662369at_nat] :
      ( ( member3157015407008874800od_o_o @ A @ ( domain8494901049294654374at_nat @ R ) )
      = ( ? [Y2: set_Pr1261947904930325089at_nat] : ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ A @ Y2 ) @ R ) ) ) ).

% Domain_iff
thf(fact_451_Domain__iff,axiom,
    ! [A: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member2643936169264416010at_nat @ A @ ( domain8802589944165416012at_nat @ R ) )
      = ( ? [Y2: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ Y2 ) @ R ) ) ) ).

% Domain_iff
thf(fact_452_reflD,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o] :
      ( ( refl_o935183656833700870od_o_o @ top_to1478448522960722999od_o_o @ R )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ A ) @ R ) ) ).

% reflD
thf(fact_453_reflD,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat] :
      ( ( refl_o6955724340487615712at_nat @ top_to7629004291339433233at_nat @ R )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ R ) ) ).

% reflD
thf(fact_454_reflD,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat] :
      ( ( refl_on_nat @ top_top_set_nat @ R )
     => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ).

% reflD
thf(fact_455_reflI,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o] : ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ X3 ) @ R )
     => ( refl_o935183656833700870od_o_o @ top_to1478448522960722999od_o_o @ R ) ) ).

% reflI
thf(fact_456_reflI,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ X3 ) @ R )
     => ( refl_o6955724340487615712at_nat @ top_to7629004291339433233at_nat @ R ) ) ).

% reflI
thf(fact_457_reflI,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ! [X3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ R )
     => ( refl_on_nat @ top_top_set_nat @ R ) ) ).

% reflI
thf(fact_458_UNIV__option__conv,axiom,
    ( top_top_set_option_a
    = ( insert_option_a @ none_a @ ( image_a_option_a @ some_a @ top_top_set_a ) ) ) ).

% UNIV_option_conv
thf(fact_459_UNIV__option__conv,axiom,
    ( top_to8920198386146353926on_nat
    = ( insert_option_nat @ none_nat @ ( image_nat_option_nat @ some_nat @ top_top_set_nat ) ) ) ).

% UNIV_option_conv
thf(fact_460_IdD,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ id_set2647307015711338339od_o_o )
     => ( A = B ) ) ).

% IdD
thf(fact_461_IdD,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ id_set1796276052702428605at_nat )
     => ( A = B ) ) ).

% IdD
thf(fact_462_finite__range__updI,axiom,
    ! [F: nat > option_a,A: nat,B: a] :
      ( ( finite1674126218327898605tion_a @ ( image_nat_option_a @ F @ top_top_set_nat ) )
     => ( finite1674126218327898605tion_a @ ( image_nat_option_a @ ( fun_upd_nat_option_a @ F @ A @ ( some_a @ B ) ) @ top_top_set_nat ) ) ) ).

% finite_range_updI
thf(fact_463_trans__singleton,axiom,
    ! [A: set_Product_prod_o_o] : ( trans_7029024365671003047od_o_o @ top_to1478448522960722999od_o_o @ ( insert3855699742481506999od_o_o @ ( produc763777882069021527od_o_o @ A @ A ) @ bot_bo498831808395348787od_o_o ) ) ).

% trans_singleton
thf(fact_464_trans__singleton,axiom,
    ! [A: set_Pr1261947904930325089at_nat] : ( trans_3732288485672914945at_nat @ top_to7629004291339433233at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ bot_bo228742789529271731at_nat ) ) ).

% trans_singleton
thf(fact_465_trans__singleton,axiom,
    ! [A: nat] : ( trans_on_nat @ top_top_set_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ A ) @ bot_bo2099793752762293965at_nat ) ) ).

% trans_singleton
thf(fact_466_asymI,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
          ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
         => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ X3 ) @ R ) )
     => ( asym_o8381145231034218809od_o_o @ top_to1478448522960722999od_o_o @ R ) ) ).

% asymI
thf(fact_467_asymI,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
          ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
         => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ X3 ) @ R ) )
     => ( asym_o5033339280856310931at_nat @ top_to7629004291339433233at_nat @ R ) ) ).

% asymI
thf(fact_468_asymI,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ! [X3: nat,Y3: nat] :
          ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
         => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X3 ) @ R ) )
     => ( asym_on_nat @ top_top_set_nat @ R ) ) ).

% asymI
thf(fact_469_finite__map__freshness,axiom,
    ! [F: nat > option_a] :
      ( ( finite_finite_nat @ ( dom_nat_a @ F ) )
     => ( ~ ( finite_finite_nat @ top_top_set_nat )
       => ? [X3: nat] :
            ( ( F @ X3 )
            = none_a ) ) ) ).

% finite_map_freshness
thf(fact_470_asym__onI,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o] :
      ( ! [X3: produc2934264451710624999od_o_o,Y3: produc2934264451710624999od_o_o] :
          ( ( member444158400953824016od_o_o @ X3 @ A2 )
         => ( ( member444158400953824016od_o_o @ Y3 @ A2 )
           => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X3 @ Y3 ) @ R )
             => ~ ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y3 @ X3 ) @ R ) ) ) )
     => ( asym_o7797749731265203737od_o_o @ A2 @ R ) ) ).

% asym_onI
thf(fact_471_asym__onI,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat] :
      ( ! [X3: produc732395585841259969at_nat,Y3: produc732395585841259969at_nat] :
          ( ( member4095101504841534314at_nat @ X3 @ A2 )
         => ( ( member4095101504841534314at_nat @ Y3 @ A2 )
           => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X3 @ Y3 ) @ R )
             => ~ ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y3 @ X3 ) @ R ) ) ) )
     => ( asym_o194845430079802867at_nat @ A2 @ R ) ) ).

% asym_onI
thf(fact_472_asym__onI,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat] :
      ( ! [X3: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
          ( ( member8757157785044589968at_nat @ X3 @ A2 )
         => ( ( member8757157785044589968at_nat @ Y3 @ A2 )
           => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X3 @ Y3 ) @ R )
             => ~ ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y3 @ X3 ) @ R ) ) ) )
     => ( asym_o9101232109321078681at_nat @ A2 @ R ) ) ).

% asym_onI
thf(fact_473_asym__onI,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a] :
      ( ! [X3: a,Y3: a] :
          ( ( member_a @ X3 @ A2 )
         => ( ( member_a @ Y3 @ A2 )
           => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
             => ~ ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ R ) ) ) )
     => ( asym_on_a @ A2 @ R ) ) ).

% asym_onI
thf(fact_474_asym__onI,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
          ( ( member3157015407008874800od_o_o @ X3 @ A2 )
         => ( ( member3157015407008874800od_o_o @ Y3 @ A2 )
           => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
             => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ X3 ) @ R ) ) ) )
     => ( asym_o8381145231034218809od_o_o @ A2 @ R ) ) ).

% asym_onI
thf(fact_475_asym__onI,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
          ( ( member2643936169264416010at_nat @ X3 @ A2 )
         => ( ( member2643936169264416010at_nat @ Y3 @ A2 )
           => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
             => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ X3 ) @ R ) ) ) )
     => ( asym_o5033339280856310931at_nat @ A2 @ R ) ) ).

% asym_onI
thf(fact_476_finite__option__UNIV,axiom,
    ( ( finite5523153139673422903on_nat @ top_to8920198386146353926on_nat )
    = ( finite_finite_nat @ top_top_set_nat ) ) ).

% finite_option_UNIV
thf(fact_477_trans__onD,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o,Z: produc2934264451710624999od_o_o] :
      ( ( trans_2549647969203962503od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ X @ A2 )
       => ( ( member444158400953824016od_o_o @ Y @ A2 )
         => ( ( member444158400953824016od_o_o @ Z @ A2 )
           => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ R )
             => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y @ Z ) @ R )
               => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Z ) @ R ) ) ) ) ) ) ) ).

% trans_onD
thf(fact_478_trans__onD,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat,Z: produc732395585841259969at_nat] :
      ( ( trans_3798871764278489953at_nat @ A2 @ R )
     => ( ( member4095101504841534314at_nat @ X @ A2 )
       => ( ( member4095101504841534314at_nat @ Y @ A2 )
         => ( ( member4095101504841534314at_nat @ Z @ A2 )
           => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ R )
             => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y @ Z ) @ R )
               => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Z ) @ R ) ) ) ) ) ) ) ).

% trans_onD
thf(fact_479_trans__onD,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,Z: produc3843707927480180839at_nat] :
      ( ( trans_4802246114490097159at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ X @ A2 )
       => ( ( member8757157785044589968at_nat @ Y @ A2 )
         => ( ( member8757157785044589968at_nat @ Z @ A2 )
           => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R )
             => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y @ Z ) @ R )
               => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Z ) @ R ) ) ) ) ) ) ) ).

% trans_onD
thf(fact_480_trans__onD,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X: a,Y: a,Z: a] :
      ( ( trans_on_a @ A2 @ R )
     => ( ( member_a @ X @ A2 )
       => ( ( member_a @ Y @ A2 )
         => ( ( member_a @ Z @ A2 )
           => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R )
             => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ R )
               => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Z ) @ R ) ) ) ) ) ) ) ).

% trans_onD
thf(fact_481_trans__onD,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o,Z: set_Product_prod_o_o] :
      ( ( trans_7029024365671003047od_o_o @ A2 @ R )
     => ( ( member3157015407008874800od_o_o @ X @ A2 )
       => ( ( member3157015407008874800od_o_o @ Y @ A2 )
         => ( ( member3157015407008874800od_o_o @ Z @ A2 )
           => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
             => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y @ Z ) @ R )
               => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Z ) @ R ) ) ) ) ) ) ) ).

% trans_onD
thf(fact_482_trans__onD,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
      ( ( trans_3732288485672914945at_nat @ A2 @ R )
     => ( ( member2643936169264416010at_nat @ X @ A2 )
       => ( ( member2643936169264416010at_nat @ Y @ A2 )
         => ( ( member2643936169264416010at_nat @ Z @ A2 )
           => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
             => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ Z ) @ R )
               => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Z ) @ R ) ) ) ) ) ) ) ).

% trans_onD
thf(fact_483_trans__onI,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o] :
      ( ! [X3: produc2934264451710624999od_o_o,Y3: produc2934264451710624999od_o_o,Z2: produc2934264451710624999od_o_o] :
          ( ( member444158400953824016od_o_o @ X3 @ A2 )
         => ( ( member444158400953824016od_o_o @ Y3 @ A2 )
           => ( ( member444158400953824016od_o_o @ Z2 @ A2 )
             => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X3 @ Y3 ) @ R )
               => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y3 @ Z2 ) @ R )
                 => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X3 @ Z2 ) @ R ) ) ) ) ) )
     => ( trans_2549647969203962503od_o_o @ A2 @ R ) ) ).

% trans_onI
thf(fact_484_trans__onI,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat] :
      ( ! [X3: produc732395585841259969at_nat,Y3: produc732395585841259969at_nat,Z2: produc732395585841259969at_nat] :
          ( ( member4095101504841534314at_nat @ X3 @ A2 )
         => ( ( member4095101504841534314at_nat @ Y3 @ A2 )
           => ( ( member4095101504841534314at_nat @ Z2 @ A2 )
             => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X3 @ Y3 ) @ R )
               => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y3 @ Z2 ) @ R )
                 => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X3 @ Z2 ) @ R ) ) ) ) ) )
     => ( trans_3798871764278489953at_nat @ A2 @ R ) ) ).

% trans_onI
thf(fact_485_trans__onI,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat] :
      ( ! [X3: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat,Z2: produc3843707927480180839at_nat] :
          ( ( member8757157785044589968at_nat @ X3 @ A2 )
         => ( ( member8757157785044589968at_nat @ Y3 @ A2 )
           => ( ( member8757157785044589968at_nat @ Z2 @ A2 )
             => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X3 @ Y3 ) @ R )
               => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y3 @ Z2 ) @ R )
                 => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X3 @ Z2 ) @ R ) ) ) ) ) )
     => ( trans_4802246114490097159at_nat @ A2 @ R ) ) ).

% trans_onI
thf(fact_486_trans__onI,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a] :
      ( ! [X3: a,Y3: a,Z2: a] :
          ( ( member_a @ X3 @ A2 )
         => ( ( member_a @ Y3 @ A2 )
           => ( ( member_a @ Z2 @ A2 )
             => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
               => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y3 @ Z2 ) @ R )
                 => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X3 @ Z2 ) @ R ) ) ) ) ) )
     => ( trans_on_a @ A2 @ R ) ) ).

% trans_onI
thf(fact_487_trans__onI,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o,Z2: set_Product_prod_o_o] :
          ( ( member3157015407008874800od_o_o @ X3 @ A2 )
         => ( ( member3157015407008874800od_o_o @ Y3 @ A2 )
           => ( ( member3157015407008874800od_o_o @ Z2 @ A2 )
             => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
               => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ Z2 ) @ R )
                 => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Z2 ) @ R ) ) ) ) ) )
     => ( trans_7029024365671003047od_o_o @ A2 @ R ) ) ).

% trans_onI
thf(fact_488_trans__onI,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
          ( ( member2643936169264416010at_nat @ X3 @ A2 )
         => ( ( member2643936169264416010at_nat @ Y3 @ A2 )
           => ( ( member2643936169264416010at_nat @ Z2 @ A2 )
             => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
               => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ Z2 ) @ R )
                 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Z2 ) @ R ) ) ) ) ) )
     => ( trans_3732288485672914945at_nat @ A2 @ R ) ) ).

% trans_onI
thf(fact_489_trans__on__def,axiom,
    ( trans_7029024365671003047od_o_o
    = ( ^ [A7: set_se491199571785101031od_o_o,R2: set_Pr1932065953672099015od_o_o] :
        ! [X2: set_Product_prod_o_o] :
          ( ( member3157015407008874800od_o_o @ X2 @ A7 )
         => ! [Y2: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ Y2 @ A7 )
             => ! [Z3: set_Product_prod_o_o] :
                  ( ( member3157015407008874800od_o_o @ Z3 @ A7 )
                 => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Y2 ) @ R2 )
                   => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y2 @ Z3 ) @ R2 )
                     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Z3 ) @ R2 ) ) ) ) ) ) ) ) ).

% trans_on_def
thf(fact_490_trans__on__def,axiom,
    ( trans_3732288485672914945at_nat
    = ( ^ [A7: set_se7855581050983116737at_nat,R2: set_Pr4329608150637261639at_nat] :
        ! [X2: set_Pr1261947904930325089at_nat] :
          ( ( member2643936169264416010at_nat @ X2 @ A7 )
         => ! [Y2: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ Y2 @ A7 )
             => ! [Z3: set_Pr1261947904930325089at_nat] :
                  ( ( member2643936169264416010at_nat @ Z3 @ A7 )
                 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y2 ) @ R2 )
                   => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ Z3 ) @ R2 )
                     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Z3 ) @ R2 ) ) ) ) ) ) ) ) ).

% trans_on_def
thf(fact_491_asym__on__def,axiom,
    ( asym_o8381145231034218809od_o_o
    = ( ^ [A7: set_se491199571785101031od_o_o,R2: set_Pr1932065953672099015od_o_o] :
        ! [X2: set_Product_prod_o_o] :
          ( ( member3157015407008874800od_o_o @ X2 @ A7 )
         => ! [Y2: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ Y2 @ A7 )
             => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Y2 ) @ R2 )
               => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y2 @ X2 ) @ R2 ) ) ) ) ) ) ).

% asym_on_def
thf(fact_492_asym__on__def,axiom,
    ( asym_o5033339280856310931at_nat
    = ( ^ [A7: set_se7855581050983116737at_nat,R2: set_Pr4329608150637261639at_nat] :
        ! [X2: set_Pr1261947904930325089at_nat] :
          ( ( member2643936169264416010at_nat @ X2 @ A7 )
         => ! [Y2: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ Y2 @ A7 )
             => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y2 ) @ R2 )
               => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ X2 ) @ R2 ) ) ) ) ) ) ).

% asym_on_def
thf(fact_493_asym__onD,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( asym_o7797749731265203737od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ X @ A2 )
       => ( ( member444158400953824016od_o_o @ Y @ A2 )
         => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ R )
           => ~ ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y @ X ) @ R ) ) ) ) ) ).

% asym_onD
thf(fact_494_asym__onD,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat] :
      ( ( asym_o194845430079802867at_nat @ A2 @ R )
     => ( ( member4095101504841534314at_nat @ X @ A2 )
       => ( ( member4095101504841534314at_nat @ Y @ A2 )
         => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ R )
           => ~ ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y @ X ) @ R ) ) ) ) ) ).

% asym_onD
thf(fact_495_asym__onD,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
      ( ( asym_o9101232109321078681at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ X @ A2 )
       => ( ( member8757157785044589968at_nat @ Y @ A2 )
         => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R )
           => ~ ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y @ X ) @ R ) ) ) ) ) ).

% asym_onD
thf(fact_496_asym__onD,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X: a,Y: a] :
      ( ( asym_on_a @ A2 @ R )
     => ( ( member_a @ X @ A2 )
       => ( ( member_a @ Y @ A2 )
         => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R )
           => ~ ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y @ X ) @ R ) ) ) ) ) ).

% asym_onD
thf(fact_497_asym__onD,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( asym_o8381145231034218809od_o_o @ A2 @ R )
     => ( ( member3157015407008874800od_o_o @ X @ A2 )
       => ( ( member3157015407008874800od_o_o @ Y @ A2 )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
           => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y @ X ) @ R ) ) ) ) ) ).

% asym_onD
thf(fact_498_asym__onD,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( asym_o5033339280856310931at_nat @ A2 @ R )
     => ( ( member2643936169264416010at_nat @ X @ A2 )
       => ( ( member2643936169264416010at_nat @ Y @ A2 )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
           => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ X ) @ R ) ) ) ) ) ).

% asym_onD
thf(fact_499_finite__range__Some,axiom,
    ( ( finite1674126218327898605tion_a @ ( image_a_option_a @ some_a @ top_top_set_a ) )
    = ( finite_finite_a @ top_top_set_a ) ) ).

% finite_range_Some
thf(fact_500_finite__range__Some,axiom,
    ( ( finite5523153139673422903on_nat @ ( image_nat_option_nat @ some_nat @ top_top_set_nat ) )
    = ( finite_finite_nat @ top_top_set_nat ) ) ).

% finite_range_Some
thf(fact_501_transD,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o,Z: set_Product_prod_o_o] :
      ( ( trans_7029024365671003047od_o_o @ top_to1478448522960722999od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y @ Z ) @ R )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Z ) @ R ) ) ) ) ).

% transD
thf(fact_502_transD,axiom,
    ! [R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
      ( ( trans_3732288485672914945at_nat @ top_to7629004291339433233at_nat @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ Z ) @ R )
         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Z ) @ R ) ) ) ) ).

% transD
thf(fact_503_transD,axiom,
    ! [R: set_Pr1261947904930325089at_nat,X: nat,Y: nat,Z: nat] :
      ( ( trans_on_nat @ top_top_set_nat @ R )
     => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
       => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ R )
         => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R ) ) ) ) ).

% transD
thf(fact_504_transE,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o,Z: set_Product_prod_o_o] :
      ( ( trans_7029024365671003047od_o_o @ top_to1478448522960722999od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y @ Z ) @ R )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Z ) @ R ) ) ) ) ).

% transE
thf(fact_505_transE,axiom,
    ! [R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
      ( ( trans_3732288485672914945at_nat @ top_to7629004291339433233at_nat @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ Z ) @ R )
         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Z ) @ R ) ) ) ) ).

% transE
thf(fact_506_transE,axiom,
    ! [R: set_Pr1261947904930325089at_nat,X: nat,Y: nat,Z: nat] :
      ( ( trans_on_nat @ top_top_set_nat @ R )
     => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
       => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ R )
         => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R ) ) ) ) ).

% transE
thf(fact_507_transI,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o,Z2: set_Product_prod_o_o] :
          ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ Z2 ) @ R )
           => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Z2 ) @ R ) ) )
     => ( trans_7029024365671003047od_o_o @ top_to1478448522960722999od_o_o @ R ) ) ).

% transI
thf(fact_508_transI,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
          ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ Z2 ) @ R )
           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Z2 ) @ R ) ) )
     => ( trans_3732288485672914945at_nat @ top_to7629004291339433233at_nat @ R ) ) ).

% transI
thf(fact_509_transI,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ! [X3: nat,Y3: nat,Z2: nat] :
          ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
         => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z2 ) @ R )
           => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Z2 ) @ R ) ) )
     => ( trans_on_nat @ top_top_set_nat @ R ) ) ).

% transI
thf(fact_510_asymD,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( asym_o8381145231034218809od_o_o @ top_to1478448522960722999od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
       => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y @ X ) @ R ) ) ) ).

% asymD
thf(fact_511_asymD,axiom,
    ! [R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( asym_o5033339280856310931at_nat @ top_to7629004291339433233at_nat @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
       => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ X ) @ R ) ) ) ).

% asymD
thf(fact_512_asymD,axiom,
    ! [R: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
      ( ( asym_on_nat @ top_top_set_nat @ R )
     => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
       => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ X ) @ R ) ) ) ).

% asymD
thf(fact_513_asym__iff,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ( asym_o8381145231034218809od_o_o @ top_to1478448522960722999od_o_o @ R )
      = ( ! [X2: set_Product_prod_o_o,Y2: set_Product_prod_o_o] :
            ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Y2 ) @ R )
           => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y2 @ X2 ) @ R ) ) ) ) ).

% asym_iff
thf(fact_514_asym__iff,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ( asym_o5033339280856310931at_nat @ top_to7629004291339433233at_nat @ R )
      = ( ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] :
            ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y2 ) @ R )
           => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ X2 ) @ R ) ) ) ) ).

% asym_iff
thf(fact_515_asym__iff,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( asym_on_nat @ top_top_set_nat @ R )
      = ( ! [X2: nat,Y2: nat] :
            ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ R )
           => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ X2 ) @ R ) ) ) ) ).

% asym_iff
thf(fact_516_image2__eqI,axiom,
    ! [B: set_Product_prod_o_o,F: a > set_Product_prod_o_o,X: a,C: set_Product_prod_o_o,G: a > set_Product_prod_o_o,A2: set_a] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member_a @ X @ A2 )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ C ) @ ( bNF_Gr7634195438189357284od_o_o @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_517_image2__eqI,axiom,
    ! [B: set_Product_prod_o_o,F: a > set_Product_prod_o_o,X: a,C: set_Pr1261947904930325089at_nat,G: a > set_Pr1261947904930325089at_nat,A2: set_a] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member_a @ X @ A2 )
         => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ B @ C ) @ ( bNF_Gr4130978120127398590at_nat @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_518_image2__eqI,axiom,
    ! [B: set_Pr1261947904930325089at_nat,F: a > set_Pr1261947904930325089at_nat,X: a,C: set_Pr1261947904930325089at_nat,G: a > set_Pr1261947904930325089at_nat,A2: set_a] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member_a @ X @ A2 )
         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ C ) @ ( bNF_Gr3725372617274885988at_nat @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_519_image2__eqI,axiom,
    ! [B: set_Product_prod_o_o,F: produc2934264451710624999od_o_o > set_Product_prod_o_o,X: produc2934264451710624999od_o_o,C: set_Product_prod_o_o,G: produc2934264451710624999od_o_o > set_Product_prod_o_o,A2: set_Pr1932065953672099015od_o_o] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member444158400953824016od_o_o @ X @ A2 )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ C ) @ ( bNF_Gr1939940824387609677od_o_o @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_520_image2__eqI,axiom,
    ! [B: set_Product_prod_o_o,F: produc732395585841259969at_nat > set_Product_prod_o_o,X: produc732395585841259969at_nat,C: set_Product_prod_o_o,G: produc732395585841259969at_nat > set_Product_prod_o_o,A2: set_Pr457366540195662369at_nat] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member4095101504841534314at_nat @ X @ A2 )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ C ) @ ( bNF_Gr4234126200300082471od_o_o @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_521_image2__eqI,axiom,
    ! [B: set_Product_prod_o_o,F: produc3843707927480180839at_nat > set_Product_prod_o_o,X: produc3843707927480180839at_nat,C: set_Product_prod_o_o,G: produc3843707927480180839at_nat > set_Product_prod_o_o,A2: set_Pr4329608150637261639at_nat] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member8757157785044589968at_nat @ X @ A2 )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ C ) @ ( bNF_Gr325834636694211021od_o_o @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_522_image2__eqI,axiom,
    ! [B: set_Product_prod_o_o,F: produc2934264451710624999od_o_o > set_Product_prod_o_o,X: produc2934264451710624999od_o_o,C: set_Pr1261947904930325089at_nat,G: produc2934264451710624999od_o_o > set_Pr1261947904930325089at_nat,A2: set_Pr1932065953672099015od_o_o] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member444158400953824016od_o_o @ X @ A2 )
         => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ B @ C ) @ ( bNF_Gr9251090155517351at_nat @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_523_image2__eqI,axiom,
    ! [B: set_Product_prod_o_o,F: produc732395585841259969at_nat > set_Product_prod_o_o,X: produc732395585841259969at_nat,C: set_Pr1261947904930325089at_nat,G: produc732395585841259969at_nat > set_Pr1261947904930325089at_nat,A2: set_Pr457366540195662369at_nat] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member4095101504841534314at_nat @ X @ A2 )
         => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ B @ C ) @ ( bNF_Gr3107587960415891841at_nat @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_524_image2__eqI,axiom,
    ! [B: set_Product_prod_o_o,F: produc3843707927480180839at_nat > set_Product_prod_o_o,X: produc3843707927480180839at_nat,C: set_Pr1261947904930325089at_nat,G: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member8757157785044589968at_nat @ X @ A2 )
         => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ B @ C ) @ ( bNF_Gr6396972118715063079at_nat @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_525_image2__eqI,axiom,
    ! [B: set_Pr1261947904930325089at_nat,F: produc2934264451710624999od_o_o > set_Pr1261947904930325089at_nat,X: produc2934264451710624999od_o_o,C: set_Pr1261947904930325089at_nat,G: produc2934264451710624999od_o_o > set_Pr1261947904930325089at_nat,A2: set_Pr1932065953672099015od_o_o] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member444158400953824016od_o_o @ X @ A2 )
         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ C ) @ ( bNF_Gr3579140021203399117at_nat @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_526_subset__Image1__Image1__iff,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( order_3482285145583873534od_o_o @ ( field_5121862139100741428od_o_o @ R ) @ R )
     => ( ( member444158400953824016od_o_o @ A @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ B @ ( field_5121862139100741428od_o_o @ R ) )
         => ( ( ord_le7586318239878589543od_o_o @ ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ A @ bot_bo498831808395348787od_o_o ) ) @ ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ B @ bot_bo498831808395348787od_o_o ) ) )
            = ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ B @ A ) @ R ) ) ) ) ) ).

% subset_Image1_Image1_iff
thf(fact_527_subset__Image1__Image1__iff,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat,B: produc732395585841259969at_nat] :
      ( ( order_8058285401901086552at_nat @ ( field_7361900449976055182at_nat @ R ) @ R )
     => ( ( member4095101504841534314at_nat @ A @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( member4095101504841534314at_nat @ B @ ( field_7361900449976055182at_nat @ R ) )
         => ( ( ord_le4841768313324958145at_nat @ ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ A @ bot_bo1676454896636820109at_nat ) ) @ ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ B @ bot_bo1676454896636820109at_nat ) ) )
            = ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ B @ A ) @ R ) ) ) ) ) ).

% subset_Image1_Image1_iff
thf(fact_528_subset__Image1__Image1__iff,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
      ( ( order_4077073789452270206at_nat @ ( field_2862844103579723188at_nat @ R ) @ R )
     => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ B @ ( field_2862844103579723188at_nat @ R ) )
         => ( ( ord_le1268244103169919719at_nat @ ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) @ ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) )
            = ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ B @ A ) @ R ) ) ) ) ) ).

% subset_Image1_Image1_iff
thf(fact_529_subset__Image1__Image1__iff,axiom,
    ! [R: set_Product_prod_a_a,A: a,B: a] :
      ( ( order_preorder_on_a @ ( field_a @ R ) @ R )
     => ( ( member_a @ A @ ( field_a @ R ) )
       => ( ( member_a @ B @ ( field_a @ R ) )
         => ( ( ord_less_eq_set_a @ ( image_a_a @ R @ ( insert_a @ A @ bot_bot_set_a ) ) @ ( image_a_a @ R @ ( insert_a @ B @ bot_bot_set_a ) ) )
            = ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B @ A ) @ R ) ) ) ) ) ).

% subset_Image1_Image1_iff
thf(fact_530_subset__Image1__Image1__iff,axiom,
    ! [R: set_Product_prod_o_o,A: $o,B: $o] :
      ( ( order_preorder_on_o @ ( field_o @ R ) @ R )
     => ( ( member_o @ A @ ( field_o @ R ) )
       => ( ( member_o @ B @ ( field_o @ R ) )
         => ( ( ord_less_eq_set_o @ ( image_o_o @ R @ ( insert_o @ A @ bot_bot_set_o ) ) @ ( image_o_o @ R @ ( insert_o @ B @ bot_bot_set_o ) ) )
            = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A ) @ R ) ) ) ) ) ).

% subset_Image1_Image1_iff
thf(fact_531_subset__Image1__Image1__iff,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
      ( ( order_4861654808422542329on_nat @ ( field_nat @ R ) @ R )
     => ( ( member_nat @ A @ ( field_nat @ R ) )
       => ( ( member_nat @ B @ ( field_nat @ R ) )
         => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ R @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ ( image_nat_nat @ R @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
            = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A ) @ R ) ) ) ) ) ).

% subset_Image1_Image1_iff
thf(fact_532_subset__Image1__Image1__iff,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( order_6208692358724846110od_o_o @ ( field_6101175518749917524od_o_o @ R ) @ R )
     => ( ( member3157015407008874800od_o_o @ A @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( member3157015407008874800od_o_o @ B @ ( field_6101175518749917524od_o_o @ R ) )
         => ( ( ord_le2654036014095304327od_o_o @ ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ A @ bot_bo8006819982598807891od_o_o ) ) @ ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ B @ bot_bo8006819982598807891od_o_o ) ) )
            = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ A ) @ R ) ) ) ) ) ).

% subset_Image1_Image1_iff
thf(fact_533_subset__Image1__Image1__iff,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( order_7173764778206869240at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
     => ( ( member2643936169264416010at_nat @ A @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( member2643936169264416010at_nat @ B @ ( field_3145993188331922222at_nat @ R ) )
         => ( ( ord_le2077887516847798113at_nat @ ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ A @ bot_bo3083307316010499117at_nat ) ) @ ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) )
            = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ A ) @ R ) ) ) ) ) ).

% subset_Image1_Image1_iff
thf(fact_534_Linear__order__wf__diff__Id,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( order_6238756238976269133r_on_o @ ( field_o @ R ) @ R )
     => ( ( wf_o @ ( minus_7052513330764642158od_o_o @ R @ id_o ) )
        = ( ! [A7: set_o] :
              ( ( ord_less_eq_set_o @ A7 @ ( field_o @ R ) )
             => ( ( A7 != bot_bot_set_o )
               => ? [X2: $o] :
                    ( ( member_o @ X2 @ A7 )
                    & ! [Y2: $o] :
                        ( ( member_o @ Y2 @ A7 )
                       => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y2 ) @ R ) ) ) ) ) ) ) ) ).

% Linear_order_wf_diff_Id
thf(fact_535_Linear__order__wf__diff__Id,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( order_4473980167227706203on_nat @ ( field_nat @ R ) @ R )
     => ( ( wf_nat @ ( minus_1356011639430497352at_nat @ R @ id_nat ) )
        = ( ! [A7: set_nat] :
              ( ( ord_less_eq_set_nat @ A7 @ ( field_nat @ R ) )
             => ( ( A7 != bot_bot_set_nat )
               => ? [X2: nat] :
                    ( ( member_nat @ X2 @ A7 )
                    & ! [Y2: nat] :
                        ( ( member_nat @ Y2 @ A7 )
                       => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ R ) ) ) ) ) ) ) ) ).

% Linear_order_wf_diff_Id
thf(fact_536_Linear__order__wf__diff__Id,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ( order_2625247082195685180od_o_o @ ( field_6101175518749917524od_o_o @ R ) @ R )
     => ( ( wf_set2384217916178216176od_o_o @ ( minus_5704166846132356910od_o_o @ R @ id_set2647307015711338339od_o_o ) )
        = ( ! [A7: set_se491199571785101031od_o_o] :
              ( ( ord_le2654036014095304327od_o_o @ A7 @ ( field_6101175518749917524od_o_o @ R ) )
             => ( ( A7 != bot_bo8006819982598807891od_o_o )
               => ? [X2: set_Product_prod_o_o] :
                    ( ( member3157015407008874800od_o_o @ X2 @ A7 )
                    & ! [Y2: set_Product_prod_o_o] :
                        ( ( member3157015407008874800od_o_o @ Y2 @ A7 )
                       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Y2 ) @ R ) ) ) ) ) ) ) ) ).

% Linear_order_wf_diff_Id
thf(fact_537_Linear__order__wf__diff__Id,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ( order_5942792088423767318at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
     => ( ( wf_set7675013139414177994at_nat @ ( minus_3314409938677909166at_nat @ R @ id_set1796276052702428605at_nat ) )
        = ( ! [A7: set_se7855581050983116737at_nat] :
              ( ( ord_le2077887516847798113at_nat @ A7 @ ( field_3145993188331922222at_nat @ R ) )
             => ( ( A7 != bot_bo3083307316010499117at_nat )
               => ? [X2: set_Pr1261947904930325089at_nat] :
                    ( ( member2643936169264416010at_nat @ X2 @ A7 )
                    & ! [Y2: set_Pr1261947904930325089at_nat] :
                        ( ( member2643936169264416010at_nat @ Y2 @ A7 )
                       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y2 ) @ R ) ) ) ) ) ) ) ) ).

% Linear_order_wf_diff_Id
thf(fact_538_eq__equiv__class,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o,B: produc2934264451710624999od_o_o,A2: set_Pr1932065953672099015od_o_o] :
      ( ( ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ A @ bot_bo498831808395348787od_o_o ) )
        = ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ B @ bot_bo498831808395348787od_o_o ) ) )
     => ( ( equiv_3398664326906728093od_o_o @ A2 @ R )
       => ( ( member444158400953824016od_o_o @ B @ A2 )
         => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ B ) @ R ) ) ) ) ).

% eq_equiv_class
thf(fact_539_eq__equiv__class,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat,B: produc732395585841259969at_nat,A2: set_Pr457366540195662369at_nat] :
      ( ( ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ A @ bot_bo1676454896636820109at_nat ) )
        = ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ B @ bot_bo1676454896636820109at_nat ) ) )
     => ( ( equiv_2520666332425567351at_nat @ A2 @ R )
       => ( ( member4095101504841534314at_nat @ B @ A2 )
         => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ B ) @ R ) ) ) ) ).

% eq_equiv_class
thf(fact_540_eq__equiv__class,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
      ( ( ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) )
        = ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) )
     => ( ( equiv_4443766944827089949at_nat @ A2 @ R )
       => ( ( member8757157785044589968at_nat @ B @ A2 )
         => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R ) ) ) ) ).

% eq_equiv_class
thf(fact_541_eq__equiv__class,axiom,
    ! [R: set_Product_prod_a_a,A: a,B: a,A2: set_a] :
      ( ( ( image_a_a @ R @ ( insert_a @ A @ bot_bot_set_a ) )
        = ( image_a_a @ R @ ( insert_a @ B @ bot_bot_set_a ) ) )
     => ( ( equiv_equiv_a @ A2 @ R )
       => ( ( member_a @ B @ A2 )
         => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B ) @ R ) ) ) ) ).

% eq_equiv_class
thf(fact_542_eq__equiv__class,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o,A2: set_se491199571785101031od_o_o] :
      ( ( ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ A @ bot_bo8006819982598807891od_o_o ) )
        = ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ B @ bot_bo8006819982598807891od_o_o ) ) )
     => ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
       => ( ( member3157015407008874800od_o_o @ B @ A2 )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R ) ) ) ) ).

% eq_equiv_class
thf(fact_543_eq__equiv__class,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat] :
      ( ( ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ A @ bot_bo3083307316010499117at_nat ) )
        = ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) )
     => ( ( equiv_6458487239543531287at_nat @ A2 @ R )
       => ( ( member2643936169264416010at_nat @ B @ A2 )
         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) ) ) ) ).

% eq_equiv_class
thf(fact_544_map__option__eq__Some,axiom,
    ! [F: a > a,Xo: option_a,Y: a] :
      ( ( ( map_option_a_a @ F @ Xo )
        = ( some_a @ Y ) )
      = ( ? [Z3: a] :
            ( ( Xo
              = ( some_a @ Z3 ) )
            & ( ( F @ Z3 )
              = Y ) ) ) ) ).

% map_option_eq_Some
thf(fact_545_None__eq__map__option__iff,axiom,
    ! [F: a > a,X: option_a] :
      ( ( none_a
        = ( map_option_a_a @ F @ X ) )
      = ( X = none_a ) ) ).

% None_eq_map_option_iff
thf(fact_546_map__option__is__None,axiom,
    ! [F: a > a,Opt: option_a] :
      ( ( ( map_option_a_a @ F @ Opt )
        = none_a )
      = ( Opt = none_a ) ) ).

% map_option_is_None
thf(fact_547_option_Omap__disc__iff,axiom,
    ! [F: a > a,A: option_a] :
      ( ( ( map_option_a_a @ F @ A )
        = none_a )
      = ( A = none_a ) ) ).

% option.map_disc_iff
thf(fact_548_subrelI,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,S3: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
          ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ S3 ) )
     => ( ord_le7586318239878589543od_o_o @ R @ S3 ) ) ).

% subrelI
thf(fact_549_subrelI,axiom,
    ! [R: set_Pr457366540195662369at_nat,S3: set_Pr457366540195662369at_nat] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Pr1261947904930325089at_nat] :
          ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ X3 @ Y3 ) @ R )
         => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ X3 @ Y3 ) @ S3 ) )
     => ( ord_le4841768313324958145at_nat @ R @ S3 ) ) ).

% subrelI
thf(fact_550_subrelI,axiom,
    ! [R: set_Pr4329608150637261639at_nat,S3: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
          ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ S3 ) )
     => ( ord_le1268244103169919719at_nat @ R @ S3 ) ) ).

% subrelI
thf(fact_551_option_Osimps_I8_J,axiom,
    ! [F: a > a] :
      ( ( map_option_a_a @ F @ none_a )
      = none_a ) ).

% option.simps(8)
thf(fact_552_option_Osimps_I9_J,axiom,
    ! [F: a > a,X23: a] :
      ( ( map_option_a_a @ F @ ( some_a @ X23 ) )
      = ( some_a @ ( F @ X23 ) ) ) ).

% option.simps(9)
thf(fact_553_option_Omap__ident__strong,axiom,
    ! [T: option8293164206536526765od_o_o,F: produc2934264451710624999od_o_o > produc2934264451710624999od_o_o] :
      ( ! [Z2: produc2934264451710624999od_o_o] :
          ( ( member444158400953824016od_o_o @ Z2 @ ( set_op3337521775309186165od_o_o @ T ) )
         => ( ( F @ Z2 )
            = Z2 ) )
     => ( ( map_op2750206784353119307od_o_o @ F @ T )
        = T ) ) ).

% option.map_ident_strong
thf(fact_554_option_Omap__ident__strong,axiom,
    ! [T: option7754883786268931591at_nat,F: produc732395585841259969at_nat > produc732395585841259969at_nat] :
      ( ! [Z2: produc732395585841259969at_nat] :
          ( ( member4095101504841534314at_nat @ Z2 @ ( set_op8338180575893423695at_nat @ T ) )
         => ( ( F @ Z2 )
            = Z2 ) )
     => ( ( map_op8542782130795478475at_nat @ F @ T )
        = T ) ) ).

% option.map_ident_strong
thf(fact_555_option_Omap__ident__strong,axiom,
    ! [T: option8699557107911914541at_nat,F: produc3843707927480180839at_nat > produc3843707927480180839at_nat] :
      ( ! [Z2: produc3843707927480180839at_nat] :
          ( ( member8757157785044589968at_nat @ Z2 @ ( set_op5866586666149159413at_nat @ T ) )
         => ( ( F @ Z2 )
            = Z2 ) )
     => ( ( map_op4646528093940530251at_nat @ F @ T )
        = T ) ) ).

% option.map_ident_strong
thf(fact_556_option_Omap__ident__strong,axiom,
    ! [T: option_a,F: a > a] :
      ( ! [Z2: a] :
          ( ( member_a @ Z2 @ ( set_option_a2 @ T ) )
         => ( ( F @ Z2 )
            = Z2 ) )
     => ( ( map_option_a_a @ F @ T )
        = T ) ) ).

% option.map_ident_strong
thf(fact_557_map__option__idI,axiom,
    ! [X: option8293164206536526765od_o_o,F: produc2934264451710624999od_o_o > produc2934264451710624999od_o_o] :
      ( ! [Y3: produc2934264451710624999od_o_o] :
          ( ( member444158400953824016od_o_o @ Y3 @ ( set_op3337521775309186165od_o_o @ X ) )
         => ( ( F @ Y3 )
            = Y3 ) )
     => ( ( map_op2750206784353119307od_o_o @ F @ X )
        = X ) ) ).

% map_option_idI
thf(fact_558_map__option__idI,axiom,
    ! [X: option7754883786268931591at_nat,F: produc732395585841259969at_nat > produc732395585841259969at_nat] :
      ( ! [Y3: produc732395585841259969at_nat] :
          ( ( member4095101504841534314at_nat @ Y3 @ ( set_op8338180575893423695at_nat @ X ) )
         => ( ( F @ Y3 )
            = Y3 ) )
     => ( ( map_op8542782130795478475at_nat @ F @ X )
        = X ) ) ).

% map_option_idI
thf(fact_559_map__option__idI,axiom,
    ! [X: option8699557107911914541at_nat,F: produc3843707927480180839at_nat > produc3843707927480180839at_nat] :
      ( ! [Y3: produc3843707927480180839at_nat] :
          ( ( member8757157785044589968at_nat @ Y3 @ ( set_op5866586666149159413at_nat @ X ) )
         => ( ( F @ Y3 )
            = Y3 ) )
     => ( ( map_op4646528093940530251at_nat @ F @ X )
        = X ) ) ).

% map_option_idI
thf(fact_560_map__option__idI,axiom,
    ! [X: option_a,F: a > a] :
      ( ! [Y3: a] :
          ( ( member_a @ Y3 @ ( set_option_a2 @ X ) )
         => ( ( F @ Y3 )
            = Y3 ) )
     => ( ( map_option_a_a @ F @ X )
        = X ) ) ).

% map_option_idI
thf(fact_561_wf__eq__minimal2,axiom,
    ( wf_o
    = ( ^ [R2: set_Product_prod_o_o] :
        ! [A7: set_o] :
          ( ( ( ord_less_eq_set_o @ A7 @ ( field_o @ R2 ) )
            & ( A7 != bot_bot_set_o ) )
         => ? [X2: $o] :
              ( ( member_o @ X2 @ A7 )
              & ! [Y2: $o] :
                  ( ( member_o @ Y2 @ A7 )
                 => ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y2 @ X2 ) @ R2 ) ) ) ) ) ) ).

% wf_eq_minimal2
thf(fact_562_wf__eq__minimal2,axiom,
    ( wf_nat
    = ( ^ [R2: set_Pr1261947904930325089at_nat] :
        ! [A7: set_nat] :
          ( ( ( ord_less_eq_set_nat @ A7 @ ( field_nat @ R2 ) )
            & ( A7 != bot_bot_set_nat ) )
         => ? [X2: nat] :
              ( ( member_nat @ X2 @ A7 )
              & ! [Y2: nat] :
                  ( ( member_nat @ Y2 @ A7 )
                 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ X2 ) @ R2 ) ) ) ) ) ) ).

% wf_eq_minimal2
thf(fact_563_wf__eq__minimal2,axiom,
    ( wf_set2384217916178216176od_o_o
    = ( ^ [R2: set_Pr1932065953672099015od_o_o] :
        ! [A7: set_se491199571785101031od_o_o] :
          ( ( ( ord_le2654036014095304327od_o_o @ A7 @ ( field_6101175518749917524od_o_o @ R2 ) )
            & ( A7 != bot_bo8006819982598807891od_o_o ) )
         => ? [X2: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ X2 @ A7 )
              & ! [Y2: set_Product_prod_o_o] :
                  ( ( member3157015407008874800od_o_o @ Y2 @ A7 )
                 => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y2 @ X2 ) @ R2 ) ) ) ) ) ) ).

% wf_eq_minimal2
thf(fact_564_wf__eq__minimal2,axiom,
    ( wf_set7675013139414177994at_nat
    = ( ^ [R2: set_Pr4329608150637261639at_nat] :
        ! [A7: set_se7855581050983116737at_nat] :
          ( ( ( ord_le2077887516847798113at_nat @ A7 @ ( field_3145993188331922222at_nat @ R2 ) )
            & ( A7 != bot_bo3083307316010499117at_nat ) )
         => ? [X2: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ X2 @ A7 )
              & ! [Y2: set_Pr1261947904930325089at_nat] :
                  ( ( member2643936169264416010at_nat @ Y2 @ A7 )
                 => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ X2 ) @ R2 ) ) ) ) ) ) ).

% wf_eq_minimal2
thf(fact_565_equiv__class__subset,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
       => ( ord_le2654036014095304327od_o_o @ ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ A @ bot_bo8006819982598807891od_o_o ) ) @ ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ B @ bot_bo8006819982598807891od_o_o ) ) ) ) ) ).

% equiv_class_subset
thf(fact_566_equiv__class__subset,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
       => ( ord_le2077887516847798113at_nat @ ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ A @ bot_bo3083307316010499117at_nat ) ) @ ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) ) ) ) ).

% equiv_class_subset
thf(fact_567_subset__equiv__class,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,B: produc2934264451710624999od_o_o,A: produc2934264451710624999od_o_o] :
      ( ( equiv_3398664326906728093od_o_o @ A2 @ R )
     => ( ( ord_le7586318239878589543od_o_o @ ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ B @ bot_bo498831808395348787od_o_o ) ) @ ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ A @ bot_bo498831808395348787od_o_o ) ) )
       => ( ( member444158400953824016od_o_o @ B @ A2 )
         => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ B ) @ R ) ) ) ) ).

% subset_equiv_class
thf(fact_568_subset__equiv__class,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,B: produc732395585841259969at_nat,A: produc732395585841259969at_nat] :
      ( ( equiv_2520666332425567351at_nat @ A2 @ R )
     => ( ( ord_le4841768313324958145at_nat @ ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ B @ bot_bo1676454896636820109at_nat ) ) @ ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ A @ bot_bo1676454896636820109at_nat ) ) )
       => ( ( member4095101504841534314at_nat @ B @ A2 )
         => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ B ) @ R ) ) ) ) ).

% subset_equiv_class
thf(fact_569_subset__equiv__class,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,B: produc3843707927480180839at_nat,A: produc3843707927480180839at_nat] :
      ( ( equiv_4443766944827089949at_nat @ A2 @ R )
     => ( ( ord_le1268244103169919719at_nat @ ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) @ ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
       => ( ( member8757157785044589968at_nat @ B @ A2 )
         => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R ) ) ) ) ).

% subset_equiv_class
thf(fact_570_subset__equiv__class,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,B: a,A: a] :
      ( ( equiv_equiv_a @ A2 @ R )
     => ( ( ord_less_eq_set_a @ ( image_a_a @ R @ ( insert_a @ B @ bot_bot_set_a ) ) @ ( image_a_a @ R @ ( insert_a @ A @ bot_bot_set_a ) ) )
       => ( ( member_a @ B @ A2 )
         => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B ) @ R ) ) ) ) ).

% subset_equiv_class
thf(fact_571_subset__equiv__class,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,B: set_Product_prod_o_o,A: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( ord_le2654036014095304327od_o_o @ ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ B @ bot_bo8006819982598807891od_o_o ) ) @ ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ A @ bot_bo8006819982598807891od_o_o ) ) )
       => ( ( member3157015407008874800od_o_o @ B @ A2 )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R ) ) ) ) ).

% subset_equiv_class
thf(fact_572_subset__equiv__class,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( ord_le2077887516847798113at_nat @ ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) @ ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ A @ bot_bo3083307316010499117at_nat ) ) )
       => ( ( member2643936169264416010at_nat @ B @ A2 )
         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) ) ) ) ).

% subset_equiv_class
thf(fact_573_subset__Image__Image__iff,axiom,
    ! [R: set_Product_prod_o_o,A2: set_o,B2: set_o] :
      ( ( order_preorder_on_o @ ( field_o @ R ) @ R )
     => ( ( ord_less_eq_set_o @ A2 @ ( field_o @ R ) )
       => ( ( ord_less_eq_set_o @ B2 @ ( field_o @ R ) )
         => ( ( ord_less_eq_set_o @ ( image_o_o @ R @ A2 ) @ ( image_o_o @ R @ B2 ) )
            = ( ! [X2: $o] :
                  ( ( member_o @ X2 @ A2 )
                 => ? [Y2: $o] :
                      ( ( member_o @ Y2 @ B2 )
                      & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y2 @ X2 ) @ R ) ) ) ) ) ) ) ) ).

% subset_Image_Image_iff
thf(fact_574_subset__Image__Image__iff,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_nat,B2: set_nat] :
      ( ( order_4861654808422542329on_nat @ ( field_nat @ R ) @ R )
     => ( ( ord_less_eq_set_nat @ A2 @ ( field_nat @ R ) )
       => ( ( ord_less_eq_set_nat @ B2 @ ( field_nat @ R ) )
         => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ R @ A2 ) @ ( image_nat_nat @ R @ B2 ) )
            = ( ! [X2: nat] :
                  ( ( member_nat @ X2 @ A2 )
                 => ? [Y2: nat] :
                      ( ( member_nat @ Y2 @ B2 )
                      & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ X2 ) @ R ) ) ) ) ) ) ) ) ).

% subset_Image_Image_iff
thf(fact_575_subset__Image__Image__iff,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A2: set_se491199571785101031od_o_o,B2: set_se491199571785101031od_o_o] :
      ( ( order_6208692358724846110od_o_o @ ( field_6101175518749917524od_o_o @ R ) @ R )
     => ( ( ord_le2654036014095304327od_o_o @ A2 @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( ord_le2654036014095304327od_o_o @ B2 @ ( field_6101175518749917524od_o_o @ R ) )
         => ( ( ord_le2654036014095304327od_o_o @ ( image_3256184292080368531od_o_o @ R @ A2 ) @ ( image_3256184292080368531od_o_o @ R @ B2 ) )
            = ( ! [X2: set_Product_prod_o_o] :
                  ( ( member3157015407008874800od_o_o @ X2 @ A2 )
                 => ? [Y2: set_Product_prod_o_o] :
                      ( ( member3157015407008874800od_o_o @ Y2 @ B2 )
                      & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y2 @ X2 ) @ R ) ) ) ) ) ) ) ) ).

% subset_Image_Image_iff
thf(fact_576_subset__Image__Image__iff,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A2: set_se7855581050983116737at_nat,B2: set_se7855581050983116737at_nat] :
      ( ( order_7173764778206869240at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
     => ( ( ord_le2077887516847798113at_nat @ A2 @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( ord_le2077887516847798113at_nat @ B2 @ ( field_3145993188331922222at_nat @ R ) )
         => ( ( ord_le2077887516847798113at_nat @ ( image_3892192845344445203at_nat @ R @ A2 ) @ ( image_3892192845344445203at_nat @ R @ B2 ) )
            = ( ! [X2: set_Pr1261947904930325089at_nat] :
                  ( ( member2643936169264416010at_nat @ X2 @ A2 )
                 => ? [Y2: set_Pr1261947904930325089at_nat] :
                      ( ( member2643936169264416010at_nat @ Y2 @ B2 )
                      & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ X2 ) @ R ) ) ) ) ) ) ) ) ).

% subset_Image_Image_iff
thf(fact_577_equiv__class__eq__iff,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( equiv_3398664326906728093od_o_o @ A2 @ R )
     => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ R )
        = ( ( ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ X @ bot_bo498831808395348787od_o_o ) )
            = ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ Y @ bot_bo498831808395348787od_o_o ) ) )
          & ( member444158400953824016od_o_o @ X @ A2 )
          & ( member444158400953824016od_o_o @ Y @ A2 ) ) ) ) ).

% equiv_class_eq_iff
thf(fact_578_equiv__class__eq__iff,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat] :
      ( ( equiv_2520666332425567351at_nat @ A2 @ R )
     => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ R )
        = ( ( ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ X @ bot_bo1676454896636820109at_nat ) )
            = ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ Y @ bot_bo1676454896636820109at_nat ) ) )
          & ( member4095101504841534314at_nat @ X @ A2 )
          & ( member4095101504841534314at_nat @ Y @ A2 ) ) ) ) ).

% equiv_class_eq_iff
thf(fact_579_equiv__class__eq__iff,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
      ( ( equiv_4443766944827089949at_nat @ A2 @ R )
     => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R )
        = ( ( ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
            = ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) ) )
          & ( member8757157785044589968at_nat @ X @ A2 )
          & ( member8757157785044589968at_nat @ Y @ A2 ) ) ) ) ).

% equiv_class_eq_iff
thf(fact_580_equiv__class__eq__iff,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X: a,Y: a] :
      ( ( equiv_equiv_a @ A2 @ R )
     => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R )
        = ( ( ( image_a_a @ R @ ( insert_a @ X @ bot_bot_set_a ) )
            = ( image_a_a @ R @ ( insert_a @ Y @ bot_bot_set_a ) ) )
          & ( member_a @ X @ A2 )
          & ( member_a @ Y @ A2 ) ) ) ) ).

% equiv_class_eq_iff
thf(fact_581_equiv__class__eq__iff,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
        = ( ( ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ X @ bot_bo8006819982598807891od_o_o ) )
            = ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ Y @ bot_bo8006819982598807891od_o_o ) ) )
          & ( member3157015407008874800od_o_o @ X @ A2 )
          & ( member3157015407008874800od_o_o @ Y @ A2 ) ) ) ) ).

% equiv_class_eq_iff
thf(fact_582_equiv__class__eq__iff,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
        = ( ( ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ X @ bot_bo3083307316010499117at_nat ) )
            = ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ Y @ bot_bo3083307316010499117at_nat ) ) )
          & ( member2643936169264416010at_nat @ X @ A2 )
          & ( member2643936169264416010at_nat @ Y @ A2 ) ) ) ) ).

% equiv_class_eq_iff
thf(fact_583_eq__equiv__class__iff,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( equiv_3398664326906728093od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ X @ A2 )
       => ( ( member444158400953824016od_o_o @ Y @ A2 )
         => ( ( ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ X @ bot_bo498831808395348787od_o_o ) )
              = ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ Y @ bot_bo498831808395348787od_o_o ) ) )
            = ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff
thf(fact_584_eq__equiv__class__iff,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat] :
      ( ( equiv_2520666332425567351at_nat @ A2 @ R )
     => ( ( member4095101504841534314at_nat @ X @ A2 )
       => ( ( member4095101504841534314at_nat @ Y @ A2 )
         => ( ( ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ X @ bot_bo1676454896636820109at_nat ) )
              = ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ Y @ bot_bo1676454896636820109at_nat ) ) )
            = ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff
thf(fact_585_eq__equiv__class__iff,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
      ( ( equiv_4443766944827089949at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ X @ A2 )
       => ( ( member8757157785044589968at_nat @ Y @ A2 )
         => ( ( ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
              = ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) ) )
            = ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff
thf(fact_586_eq__equiv__class__iff,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X: a,Y: a] :
      ( ( equiv_equiv_a @ A2 @ R )
     => ( ( member_a @ X @ A2 )
       => ( ( member_a @ Y @ A2 )
         => ( ( ( image_a_a @ R @ ( insert_a @ X @ bot_bot_set_a ) )
              = ( image_a_a @ R @ ( insert_a @ Y @ bot_bot_set_a ) ) )
            = ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff
thf(fact_587_eq__equiv__class__iff,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( member3157015407008874800od_o_o @ X @ A2 )
       => ( ( member3157015407008874800od_o_o @ Y @ A2 )
         => ( ( ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ X @ bot_bo8006819982598807891od_o_o ) )
              = ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ Y @ bot_bo8006819982598807891od_o_o ) ) )
            = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff
thf(fact_588_eq__equiv__class__iff,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( member2643936169264416010at_nat @ X @ A2 )
       => ( ( member2643936169264416010at_nat @ Y @ A2 )
         => ( ( ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ X @ bot_bo3083307316010499117at_nat ) )
              = ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ Y @ bot_bo3083307316010499117at_nat ) ) )
            = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff
thf(fact_589_equiv__class__eq,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
       => ( ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ A @ bot_bo8006819982598807891od_o_o ) )
          = ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ B @ bot_bo8006819982598807891od_o_o ) ) ) ) ) ).

% equiv_class_eq
thf(fact_590_equiv__class__eq,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
       => ( ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ A @ bot_bo3083307316010499117at_nat ) )
          = ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) ) ) ) ).

% equiv_class_eq
thf(fact_591_wfE__min_H,axiom,
    ! [R3: set_Pr1013884327308616903od_o_o,Q4: set_Pr1932065953672099015od_o_o] :
      ( ( wf_Pro3213319136295691984od_o_o @ R3 )
     => ( ( Q4 != bot_bo498831808395348787od_o_o )
       => ~ ! [Z2: produc2934264451710624999od_o_o] :
              ( ( member444158400953824016od_o_o @ Z2 @ Q4 )
             => ~ ! [Y4: produc2934264451710624999od_o_o] :
                    ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member444158400953824016od_o_o @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min'
thf(fact_592_wfE__min_H,axiom,
    ! [R3: set_Pr4427867301352232263at_nat,Q4: set_Pr457366540195662369at_nat] :
      ( ( wf_Pro661967360799104810at_nat @ R3 )
     => ( ( Q4 != bot_bo1676454896636820109at_nat )
       => ~ ! [Z2: produc732395585841259969at_nat] :
              ( ( member4095101504841534314at_nat @ Z2 @ Q4 )
             => ~ ! [Y4: produc732395585841259969at_nat] :
                    ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member4095101504841534314at_nat @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min'
thf(fact_593_wfE__min_H,axiom,
    ! [R3: set_Pr5564308138774400199at_nat,Q4: set_Pr4329608150637261639at_nat] :
      ( ( wf_Pro2357547232388600144at_nat @ R3 )
     => ( ( Q4 != bot_bo228742789529271731at_nat )
       => ~ ! [Z2: produc3843707927480180839at_nat] :
              ( ( member8757157785044589968at_nat @ Z2 @ Q4 )
             => ~ ! [Y4: produc3843707927480180839at_nat] :
                    ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member8757157785044589968at_nat @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min'
thf(fact_594_wfE__min_H,axiom,
    ! [R3: set_Product_prod_a_a,Q4: set_a] :
      ( ( wf_a @ R3 )
     => ( ( Q4 != bot_bot_set_a )
       => ~ ! [Z2: a] :
              ( ( member_a @ Z2 @ Q4 )
             => ~ ! [Y4: a] :
                    ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member_a @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min'
thf(fact_595_wfE__min_H,axiom,
    ! [R3: set_Pr1932065953672099015od_o_o,Q4: set_se491199571785101031od_o_o] :
      ( ( wf_set2384217916178216176od_o_o @ R3 )
     => ( ( Q4 != bot_bo8006819982598807891od_o_o )
       => ~ ! [Z2: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ Z2 @ Q4 )
             => ~ ! [Y4: set_Product_prod_o_o] :
                    ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member3157015407008874800od_o_o @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min'
thf(fact_596_wfE__min_H,axiom,
    ! [R3: set_Pr4329608150637261639at_nat,Q4: set_se7855581050983116737at_nat] :
      ( ( wf_set7675013139414177994at_nat @ R3 )
     => ( ( Q4 != bot_bo3083307316010499117at_nat )
       => ~ ! [Z2: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ Z2 @ Q4 )
             => ~ ! [Y4: set_Pr1261947904930325089at_nat] :
                    ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member2643936169264416010at_nat @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min'
thf(fact_597_proj__iff,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( ord_le2654036014095304327od_o_o @ ( insert3817420688681518039od_o_o @ X @ ( insert3817420688681518039od_o_o @ Y @ bot_bo8006819982598807891od_o_o ) ) @ A2 )
       => ( ( ( equiv_6719278489894859850od_o_o @ R @ X )
            = ( equiv_6719278489894859850od_o_o @ R @ Y ) )
          = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R ) ) ) ) ).

% proj_iff
thf(fact_598_proj__iff,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( ord_le2077887516847798113at_nat @ ( insert9200635055090092081at_nat @ X @ ( insert9200635055090092081at_nat @ Y @ bot_bo3083307316010499117at_nat ) ) @ A2 )
       => ( ( ( equiv_4785085088318667978at_nat @ R @ X )
            = ( equiv_4785085088318667978at_nat @ R @ Y ) )
          = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R ) ) ) ) ).

% proj_iff
thf(fact_599_wf__def,axiom,
    ( wf_set2384217916178216176od_o_o
    = ( ^ [R2: set_Pr1932065953672099015od_o_o] :
        ! [P6: set_Product_prod_o_o > $o] :
          ( ! [X2: set_Product_prod_o_o] :
              ( ! [Y2: set_Product_prod_o_o] :
                  ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y2 @ X2 ) @ R2 )
                 => ( P6 @ Y2 ) )
             => ( P6 @ X2 ) )
         => ! [X6: set_Product_prod_o_o] : ( P6 @ X6 ) ) ) ) ).

% wf_def
thf(fact_600_wf__def,axiom,
    ( wf_set7675013139414177994at_nat
    = ( ^ [R2: set_Pr4329608150637261639at_nat] :
        ! [P6: set_Pr1261947904930325089at_nat > $o] :
          ( ! [X2: set_Pr1261947904930325089at_nat] :
              ( ! [Y2: set_Pr1261947904930325089at_nat] :
                  ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ X2 ) @ R2 )
                 => ( P6 @ Y2 ) )
             => ( P6 @ X2 ) )
         => ! [X6: set_Pr1261947904930325089at_nat] : ( P6 @ X6 ) ) ) ) ).

% wf_def
thf(fact_601_wfE__min,axiom,
    ! [R3: set_Pr1013884327308616903od_o_o,X: produc2934264451710624999od_o_o,Q4: set_Pr1932065953672099015od_o_o] :
      ( ( wf_Pro3213319136295691984od_o_o @ R3 )
     => ( ( member444158400953824016od_o_o @ X @ Q4 )
       => ~ ! [Z2: produc2934264451710624999od_o_o] :
              ( ( member444158400953824016od_o_o @ Z2 @ Q4 )
             => ~ ! [Y4: produc2934264451710624999od_o_o] :
                    ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member444158400953824016od_o_o @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min
thf(fact_602_wfE__min,axiom,
    ! [R3: set_Pr4427867301352232263at_nat,X: produc732395585841259969at_nat,Q4: set_Pr457366540195662369at_nat] :
      ( ( wf_Pro661967360799104810at_nat @ R3 )
     => ( ( member4095101504841534314at_nat @ X @ Q4 )
       => ~ ! [Z2: produc732395585841259969at_nat] :
              ( ( member4095101504841534314at_nat @ Z2 @ Q4 )
             => ~ ! [Y4: produc732395585841259969at_nat] :
                    ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member4095101504841534314at_nat @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min
thf(fact_603_wfE__min,axiom,
    ! [R3: set_Pr5564308138774400199at_nat,X: produc3843707927480180839at_nat,Q4: set_Pr4329608150637261639at_nat] :
      ( ( wf_Pro2357547232388600144at_nat @ R3 )
     => ( ( member8757157785044589968at_nat @ X @ Q4 )
       => ~ ! [Z2: produc3843707927480180839at_nat] :
              ( ( member8757157785044589968at_nat @ Z2 @ Q4 )
             => ~ ! [Y4: produc3843707927480180839at_nat] :
                    ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member8757157785044589968at_nat @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min
thf(fact_604_wfE__min,axiom,
    ! [R3: set_Product_prod_a_a,X: a,Q4: set_a] :
      ( ( wf_a @ R3 )
     => ( ( member_a @ X @ Q4 )
       => ~ ! [Z2: a] :
              ( ( member_a @ Z2 @ Q4 )
             => ~ ! [Y4: a] :
                    ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member_a @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min
thf(fact_605_wfE__min,axiom,
    ! [R3: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Q4: set_se491199571785101031od_o_o] :
      ( ( wf_set2384217916178216176od_o_o @ R3 )
     => ( ( member3157015407008874800od_o_o @ X @ Q4 )
       => ~ ! [Z2: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ Z2 @ Q4 )
             => ~ ! [Y4: set_Product_prod_o_o] :
                    ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member3157015407008874800od_o_o @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min
thf(fact_606_wfE__min,axiom,
    ! [R3: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Q4: set_se7855581050983116737at_nat] :
      ( ( wf_set7675013139414177994at_nat @ R3 )
     => ( ( member2643936169264416010at_nat @ X @ Q4 )
       => ~ ! [Z2: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ Z2 @ Q4 )
             => ~ ! [Y4: set_Pr1261947904930325089at_nat] :
                    ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y4 @ Z2 ) @ R3 )
                   => ~ ( member2643936169264416010at_nat @ Y4 @ Q4 ) ) ) ) ) ).

% wfE_min
thf(fact_607_wf__if__convertible__to__wf,axiom,
    ! [S3: set_Pr1932065953672099015od_o_o,R: set_Pr1932065953672099015od_o_o,F: set_Product_prod_o_o > set_Product_prod_o_o] :
      ( ( wf_set2384217916178216176od_o_o @ S3 )
     => ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
            ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
           => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( F @ X3 ) @ ( F @ Y3 ) ) @ S3 ) )
       => ( wf_set2384217916178216176od_o_o @ R ) ) ) ).

% wf_if_convertible_to_wf
thf(fact_608_wf__if__convertible__to__wf,axiom,
    ! [S3: set_Pr4329608150637261639at_nat,R: set_Pr1932065953672099015od_o_o,F: set_Product_prod_o_o > set_Pr1261947904930325089at_nat] :
      ( ( wf_set7675013139414177994at_nat @ S3 )
     => ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
            ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) @ S3 ) )
       => ( wf_set2384217916178216176od_o_o @ R ) ) ) ).

% wf_if_convertible_to_wf
thf(fact_609_wf__if__convertible__to__wf,axiom,
    ! [S3: set_Pr1932065953672099015od_o_o,R: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Product_prod_o_o] :
      ( ( wf_set2384217916178216176od_o_o @ S3 )
     => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
            ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
           => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( F @ X3 ) @ ( F @ Y3 ) ) @ S3 ) )
       => ( wf_set7675013139414177994at_nat @ R ) ) ) ).

% wf_if_convertible_to_wf
thf(fact_610_wf__if__convertible__to__wf,axiom,
    ! [S3: set_Pr4329608150637261639at_nat,R: set_Pr4329608150637261639at_nat,F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat] :
      ( ( wf_set7675013139414177994at_nat @ S3 )
     => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
            ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) @ S3 ) )
       => ( wf_set7675013139414177994at_nat @ R ) ) ) ).

% wf_if_convertible_to_wf
thf(fact_611_wf__induct__rule,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,P3: set_Product_prod_o_o > $o,A: set_Product_prod_o_o] :
      ( ( wf_set2384217916178216176od_o_o @ R )
     => ( ! [X3: set_Product_prod_o_o] :
            ( ! [Y4: set_Product_prod_o_o] :
                ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y4 @ X3 ) @ R )
               => ( P3 @ Y4 ) )
           => ( P3 @ X3 ) )
       => ( P3 @ A ) ) ) ).

% wf_induct_rule
thf(fact_612_wf__induct__rule,axiom,
    ! [R: set_Pr4329608150637261639at_nat,P3: set_Pr1261947904930325089at_nat > $o,A: set_Pr1261947904930325089at_nat] :
      ( ( wf_set7675013139414177994at_nat @ R )
     => ( ! [X3: set_Pr1261947904930325089at_nat] :
            ( ! [Y4: set_Pr1261947904930325089at_nat] :
                ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y4 @ X3 ) @ R )
               => ( P3 @ Y4 ) )
           => ( P3 @ X3 ) )
       => ( P3 @ A ) ) ) ).

% wf_induct_rule
thf(fact_613_wf__eq__minimal,axiom,
    ( wf_Pro3213319136295691984od_o_o
    = ( ^ [R2: set_Pr1013884327308616903od_o_o] :
        ! [Q5: set_Pr1932065953672099015od_o_o] :
          ( ? [X2: produc2934264451710624999od_o_o] : ( member444158400953824016od_o_o @ X2 @ Q5 )
         => ? [X2: produc2934264451710624999od_o_o] :
              ( ( member444158400953824016od_o_o @ X2 @ Q5 )
              & ! [Y2: produc2934264451710624999od_o_o] :
                  ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y2 @ X2 ) @ R2 )
                 => ~ ( member444158400953824016od_o_o @ Y2 @ Q5 ) ) ) ) ) ) ).

% wf_eq_minimal
thf(fact_614_wf__eq__minimal,axiom,
    ( wf_Pro661967360799104810at_nat
    = ( ^ [R2: set_Pr4427867301352232263at_nat] :
        ! [Q5: set_Pr457366540195662369at_nat] :
          ( ? [X2: produc732395585841259969at_nat] : ( member4095101504841534314at_nat @ X2 @ Q5 )
         => ? [X2: produc732395585841259969at_nat] :
              ( ( member4095101504841534314at_nat @ X2 @ Q5 )
              & ! [Y2: produc732395585841259969at_nat] :
                  ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y2 @ X2 ) @ R2 )
                 => ~ ( member4095101504841534314at_nat @ Y2 @ Q5 ) ) ) ) ) ) ).

% wf_eq_minimal
thf(fact_615_wf__eq__minimal,axiom,
    ( wf_Pro2357547232388600144at_nat
    = ( ^ [R2: set_Pr5564308138774400199at_nat] :
        ! [Q5: set_Pr4329608150637261639at_nat] :
          ( ? [X2: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X2 @ Q5 )
         => ? [X2: produc3843707927480180839at_nat] :
              ( ( member8757157785044589968at_nat @ X2 @ Q5 )
              & ! [Y2: produc3843707927480180839at_nat] :
                  ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y2 @ X2 ) @ R2 )
                 => ~ ( member8757157785044589968at_nat @ Y2 @ Q5 ) ) ) ) ) ) ).

% wf_eq_minimal
thf(fact_616_wf__eq__minimal,axiom,
    ( wf_a
    = ( ^ [R2: set_Product_prod_a_a] :
        ! [Q5: set_a] :
          ( ? [X2: a] : ( member_a @ X2 @ Q5 )
         => ? [X2: a] :
              ( ( member_a @ X2 @ Q5 )
              & ! [Y2: a] :
                  ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y2 @ X2 ) @ R2 )
                 => ~ ( member_a @ Y2 @ Q5 ) ) ) ) ) ) ).

% wf_eq_minimal
thf(fact_617_wf__eq__minimal,axiom,
    ( wf_set2384217916178216176od_o_o
    = ( ^ [R2: set_Pr1932065953672099015od_o_o] :
        ! [Q5: set_se491199571785101031od_o_o] :
          ( ? [X2: set_Product_prod_o_o] : ( member3157015407008874800od_o_o @ X2 @ Q5 )
         => ? [X2: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ X2 @ Q5 )
              & ! [Y2: set_Product_prod_o_o] :
                  ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y2 @ X2 ) @ R2 )
                 => ~ ( member3157015407008874800od_o_o @ Y2 @ Q5 ) ) ) ) ) ) ).

% wf_eq_minimal
thf(fact_618_wf__eq__minimal,axiom,
    ( wf_set7675013139414177994at_nat
    = ( ^ [R2: set_Pr4329608150637261639at_nat] :
        ! [Q5: set_se7855581050983116737at_nat] :
          ( ? [X2: set_Pr1261947904930325089at_nat] : ( member2643936169264416010at_nat @ X2 @ Q5 )
         => ? [X2: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ X2 @ Q5 )
              & ! [Y2: set_Pr1261947904930325089at_nat] :
                  ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ X2 ) @ R2 )
                 => ~ ( member2643936169264416010at_nat @ Y2 @ Q5 ) ) ) ) ) ) ).

% wf_eq_minimal
thf(fact_619_wf__not__refl,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o] :
      ( ( wf_set2384217916178216176od_o_o @ R )
     => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ A ) @ R ) ) ).

% wf_not_refl
thf(fact_620_wf__not__refl,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat] :
      ( ( wf_set7675013139414177994at_nat @ R )
     => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ R ) ) ).

% wf_not_refl
thf(fact_621_wf__not__sym,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,X: set_Product_prod_o_o] :
      ( ( wf_set2384217916178216176od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ X ) @ R )
       => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ A ) @ R ) ) ) ).

% wf_not_sym
thf(fact_622_wf__not__sym,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
      ( ( wf_set7675013139414177994at_nat @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ X ) @ R )
       => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ A ) @ R ) ) ) ).

% wf_not_sym
thf(fact_623_wf__irrefl,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o] :
      ( ( wf_set2384217916178216176od_o_o @ R )
     => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ A ) @ R ) ) ).

% wf_irrefl
thf(fact_624_wf__irrefl,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat] :
      ( ( wf_set7675013139414177994at_nat @ R )
     => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ R ) ) ).

% wf_irrefl
thf(fact_625_wf__induct,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,P3: set_Product_prod_o_o > $o,A: set_Product_prod_o_o] :
      ( ( wf_set2384217916178216176od_o_o @ R )
     => ( ! [X3: set_Product_prod_o_o] :
            ( ! [Y4: set_Product_prod_o_o] :
                ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y4 @ X3 ) @ R )
               => ( P3 @ Y4 ) )
           => ( P3 @ X3 ) )
       => ( P3 @ A ) ) ) ).

% wf_induct
thf(fact_626_wf__induct,axiom,
    ! [R: set_Pr4329608150637261639at_nat,P3: set_Pr1261947904930325089at_nat > $o,A: set_Pr1261947904930325089at_nat] :
      ( ( wf_set7675013139414177994at_nat @ R )
     => ( ! [X3: set_Pr1261947904930325089at_nat] :
            ( ! [Y4: set_Pr1261947904930325089at_nat] :
                ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y4 @ X3 ) @ R )
               => ( P3 @ Y4 ) )
           => ( P3 @ X3 ) )
       => ( P3 @ A ) ) ) ).

% wf_induct
thf(fact_627_wf__asym,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,X: set_Product_prod_o_o] :
      ( ( wf_set2384217916178216176od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ X ) @ R )
       => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ A ) @ R ) ) ) ).

% wf_asym
thf(fact_628_wf__asym,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
      ( ( wf_set7675013139414177994at_nat @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ X ) @ R )
       => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ A ) @ R ) ) ) ).

% wf_asym
thf(fact_629_wfUNIVI,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ! [P7: set_Product_prod_o_o > $o,X3: set_Product_prod_o_o] :
          ( ! [Xa: set_Product_prod_o_o] :
              ( ! [Y3: set_Product_prod_o_o] :
                  ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ Xa ) @ R )
                 => ( P7 @ Y3 ) )
             => ( P7 @ Xa ) )
         => ( P7 @ X3 ) )
     => ( wf_set2384217916178216176od_o_o @ R ) ) ).

% wfUNIVI
thf(fact_630_wfUNIVI,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ! [P7: set_Pr1261947904930325089at_nat > $o,X3: set_Pr1261947904930325089at_nat] :
          ( ! [Xa: set_Pr1261947904930325089at_nat] :
              ( ! [Y3: set_Pr1261947904930325089at_nat] :
                  ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ Xa ) @ R )
                 => ( P7 @ Y3 ) )
             => ( P7 @ Xa ) )
         => ( P7 @ X3 ) )
     => ( wf_set7675013139414177994at_nat @ R ) ) ).

% wfUNIVI
thf(fact_631_wfI__min,axiom,
    ! [R3: set_Pr1013884327308616903od_o_o] :
      ( ! [X3: produc2934264451710624999od_o_o,Q6: set_Pr1932065953672099015od_o_o] :
          ( ( member444158400953824016od_o_o @ X3 @ Q6 )
         => ? [Xa: produc2934264451710624999od_o_o] :
              ( ( member444158400953824016od_o_o @ Xa @ Q6 )
              & ! [Y3: produc2934264451710624999od_o_o] :
                  ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y3 @ Xa ) @ R3 )
                 => ~ ( member444158400953824016od_o_o @ Y3 @ Q6 ) ) ) )
     => ( wf_Pro3213319136295691984od_o_o @ R3 ) ) ).

% wfI_min
thf(fact_632_wfI__min,axiom,
    ! [R3: set_Pr4427867301352232263at_nat] :
      ( ! [X3: produc732395585841259969at_nat,Q6: set_Pr457366540195662369at_nat] :
          ( ( member4095101504841534314at_nat @ X3 @ Q6 )
         => ? [Xa: produc732395585841259969at_nat] :
              ( ( member4095101504841534314at_nat @ Xa @ Q6 )
              & ! [Y3: produc732395585841259969at_nat] :
                  ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y3 @ Xa ) @ R3 )
                 => ~ ( member4095101504841534314at_nat @ Y3 @ Q6 ) ) ) )
     => ( wf_Pro661967360799104810at_nat @ R3 ) ) ).

% wfI_min
thf(fact_633_wfI__min,axiom,
    ! [R3: set_Pr5564308138774400199at_nat] :
      ( ! [X3: produc3843707927480180839at_nat,Q6: set_Pr4329608150637261639at_nat] :
          ( ( member8757157785044589968at_nat @ X3 @ Q6 )
         => ? [Xa: produc3843707927480180839at_nat] :
              ( ( member8757157785044589968at_nat @ Xa @ Q6 )
              & ! [Y3: produc3843707927480180839at_nat] :
                  ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y3 @ Xa ) @ R3 )
                 => ~ ( member8757157785044589968at_nat @ Y3 @ Q6 ) ) ) )
     => ( wf_Pro2357547232388600144at_nat @ R3 ) ) ).

% wfI_min
thf(fact_634_wfI__min,axiom,
    ! [R3: set_Product_prod_a_a] :
      ( ! [X3: a,Q6: set_a] :
          ( ( member_a @ X3 @ Q6 )
         => ? [Xa: a] :
              ( ( member_a @ Xa @ Q6 )
              & ! [Y3: a] :
                  ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y3 @ Xa ) @ R3 )
                 => ~ ( member_a @ Y3 @ Q6 ) ) ) )
     => ( wf_a @ R3 ) ) ).

% wfI_min
thf(fact_635_wfI__min,axiom,
    ! [R3: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o,Q6: set_se491199571785101031od_o_o] :
          ( ( member3157015407008874800od_o_o @ X3 @ Q6 )
         => ? [Xa: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ Xa @ Q6 )
              & ! [Y3: set_Product_prod_o_o] :
                  ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ Xa ) @ R3 )
                 => ~ ( member3157015407008874800od_o_o @ Y3 @ Q6 ) ) ) )
     => ( wf_set2384217916178216176od_o_o @ R3 ) ) ).

% wfI_min
thf(fact_636_wfI__min,axiom,
    ! [R3: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Q6: set_se7855581050983116737at_nat] :
          ( ( member2643936169264416010at_nat @ X3 @ Q6 )
         => ? [Xa: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ Xa @ Q6 )
              & ! [Y3: set_Pr1261947904930325089at_nat] :
                  ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ Xa ) @ R3 )
                 => ~ ( member2643936169264416010at_nat @ Y3 @ Q6 ) ) ) )
     => ( wf_set7675013139414177994at_nat @ R3 ) ) ).

% wfI_min
thf(fact_637_Total__subset__Id,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( total_on_o @ ( field_o @ R ) @ R )
     => ( ( ord_le192195778054999463od_o_o @ R @ id_o )
       => ( ( R = bot_bo7073875226086086771od_o_o )
          | ? [A4: $o] :
              ( R
              = ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A4 @ A4 ) @ bot_bo7073875226086086771od_o_o ) ) ) ) ) ).

% Total_subset_Id
thf(fact_638_Total__subset__Id,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( total_on_nat @ ( field_nat @ R ) @ R )
     => ( ( ord_le3146513528884898305at_nat @ R @ id_nat )
       => ( ( R = bot_bo2099793752762293965at_nat )
          | ? [A4: nat] :
              ( R
              = ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A4 @ A4 ) @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).

% Total_subset_Id
thf(fact_639_Total__subset__Id,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ( total_5784220159268842891od_o_o @ ( field_6101175518749917524od_o_o @ R ) @ R )
     => ( ( ord_le7586318239878589543od_o_o @ R @ id_set2647307015711338339od_o_o )
       => ( ( R = bot_bo498831808395348787od_o_o )
          | ? [A4: set_Product_prod_o_o] :
              ( R
              = ( insert3855699742481506999od_o_o @ ( produc763777882069021527od_o_o @ A4 @ A4 ) @ bot_bo498831808395348787od_o_o ) ) ) ) ) ).

% Total_subset_Id
thf(fact_640_Total__subset__Id,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ( total_7212417256332265445at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
     => ( ( ord_le1268244103169919719at_nat @ R @ id_set1796276052702428605at_nat )
       => ( ( R = bot_bo228742789529271731at_nat )
          | ? [A4: set_Pr1261947904930325089at_nat] :
              ( R
              = ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A4 @ A4 ) @ bot_bo228742789529271731at_nat ) ) ) ) ) ).

% Total_subset_Id
thf(fact_641_disjnt__equiv__class,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( disjnt556417628418099406od_o_o @ ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ A @ bot_bo8006819982598807891od_o_o ) ) @ ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ B @ bot_bo8006819982598807891od_o_o ) ) )
        = ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R ) ) ) ) ).

% disjnt_equiv_class
thf(fact_642_disjnt__equiv__class,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( disjnt2544082741087298984at_nat @ ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ A @ bot_bo3083307316010499117at_nat ) ) @ ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) )
        = ( ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) ) ) ) ).

% disjnt_equiv_class
thf(fact_643_wo__rel_Ocases__Total3,axiom,
    ! [R: set_Product_prod_o_o,A: $o,B: $o,Phi: $o > $o > $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ( ord_less_eq_set_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( field_o @ R ) )
       => ( ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( minus_7052513330764642158od_o_o @ R @ id_o ) )
              | ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A ) @ ( minus_7052513330764642158od_o_o @ R @ id_o ) ) )
           => ( Phi @ A @ B ) )
         => ( ( ( A = B )
             => ( Phi @ A @ B ) )
           => ( Phi @ A @ B ) ) ) ) ) ).

% wo_rel.cases_Total3
thf(fact_644_wo__rel_Ocases__Total3,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat,Phi: nat > nat > $o] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ( ord_less_eq_set_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( field_nat @ R ) )
       => ( ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( minus_1356011639430497352at_nat @ R @ id_nat ) )
              | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A ) @ ( minus_1356011639430497352at_nat @ R @ id_nat ) ) )
           => ( Phi @ A @ B ) )
         => ( ( ( A = B )
             => ( Phi @ A @ B ) )
           => ( Phi @ A @ B ) ) ) ) ) ).

% wo_rel.cases_Total3
thf(fact_645_wo__rel_Ocases__Total3,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o,Phi: set_Product_prod_o_o > set_Product_prod_o_o > $o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( ord_le2654036014095304327od_o_o @ ( insert3817420688681518039od_o_o @ A @ ( insert3817420688681518039od_o_o @ B @ bot_bo8006819982598807891od_o_o ) ) @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ ( minus_5704166846132356910od_o_o @ R @ id_set2647307015711338339od_o_o ) )
              | ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ A ) @ ( minus_5704166846132356910od_o_o @ R @ id_set2647307015711338339od_o_o ) ) )
           => ( Phi @ A @ B ) )
         => ( ( ( A = B )
             => ( Phi @ A @ B ) )
           => ( Phi @ A @ B ) ) ) ) ) ).

% wo_rel.cases_Total3
thf(fact_646_wo__rel_Ocases__Total3,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,Phi: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( ord_le2077887516847798113at_nat @ ( insert9200635055090092081at_nat @ A @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( minus_3314409938677909166at_nat @ R @ id_set1796276052702428605at_nat ) )
              | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ A ) @ ( minus_3314409938677909166at_nat @ R @ id_set1796276052702428605at_nat ) ) )
           => ( Phi @ A @ B ) )
         => ( ( ( A = B )
             => ( Phi @ A @ B ) )
           => ( Phi @ A @ B ) ) ) ) ) ).

% wo_rel.cases_Total3
thf(fact_647_total__on__def,axiom,
    ( total_5784220159268842891od_o_o
    = ( ^ [A7: set_se491199571785101031od_o_o,R2: set_Pr1932065953672099015od_o_o] :
        ! [X2: set_Product_prod_o_o] :
          ( ( member3157015407008874800od_o_o @ X2 @ A7 )
         => ! [Y2: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ Y2 @ A7 )
             => ( ( X2 != Y2 )
               => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Y2 ) @ R2 )
                  | ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y2 @ X2 ) @ R2 ) ) ) ) ) ) ) ).

% total_on_def
thf(fact_648_total__on__def,axiom,
    ( total_7212417256332265445at_nat
    = ( ^ [A7: set_se7855581050983116737at_nat,R2: set_Pr4329608150637261639at_nat] :
        ! [X2: set_Pr1261947904930325089at_nat] :
          ( ( member2643936169264416010at_nat @ X2 @ A7 )
         => ! [Y2: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ Y2 @ A7 )
             => ( ( X2 != Y2 )
               => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y2 ) @ R2 )
                  | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ X2 ) @ R2 ) ) ) ) ) ) ) ).

% total_on_def
thf(fact_649_total__onI,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o] :
      ( ! [X3: produc2934264451710624999od_o_o,Y3: produc2934264451710624999od_o_o] :
          ( ( member444158400953824016od_o_o @ X3 @ A2 )
         => ( ( member444158400953824016od_o_o @ Y3 @ A2 )
           => ( ( X3 != Y3 )
             => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X3 @ Y3 ) @ R )
                | ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y3 @ X3 ) @ R ) ) ) ) )
     => ( total_3055748755304958059od_o_o @ A2 @ R ) ) ).

% total_onI
thf(fact_650_total__onI,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat] :
      ( ! [X3: produc732395585841259969at_nat,Y3: produc732395585841259969at_nat] :
          ( ( member4095101504841534314at_nat @ X3 @ A2 )
         => ( ( member4095101504841534314at_nat @ Y3 @ A2 )
           => ( ( X3 != Y3 )
             => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X3 @ Y3 ) @ R )
                | ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y3 @ X3 ) @ R ) ) ) ) )
     => ( total_8996415722781341509at_nat @ A2 @ R ) ) ).

% total_onI
thf(fact_651_total__onI,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat] :
      ( ! [X3: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
          ( ( member8757157785044589968at_nat @ X3 @ A2 )
         => ( ( member8757157785044589968at_nat @ Y3 @ A2 )
           => ( ( X3 != Y3 )
             => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X3 @ Y3 ) @ R )
                | ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y3 @ X3 ) @ R ) ) ) ) )
     => ( total_1513685709984341995at_nat @ A2 @ R ) ) ).

% total_onI
thf(fact_652_total__onI,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a] :
      ( ! [X3: a,Y3: a] :
          ( ( member_a @ X3 @ A2 )
         => ( ( member_a @ Y3 @ A2 )
           => ( ( X3 != Y3 )
             => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
                | ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ R ) ) ) ) )
     => ( total_on_a @ A2 @ R ) ) ).

% total_onI
thf(fact_653_total__onI,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
          ( ( member3157015407008874800od_o_o @ X3 @ A2 )
         => ( ( member3157015407008874800od_o_o @ Y3 @ A2 )
           => ( ( X3 != Y3 )
             => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
                | ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ X3 ) @ R ) ) ) ) )
     => ( total_5784220159268842891od_o_o @ A2 @ R ) ) ).

% total_onI
thf(fact_654_total__onI,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
          ( ( member2643936169264416010at_nat @ X3 @ A2 )
         => ( ( member2643936169264416010at_nat @ Y3 @ A2 )
           => ( ( X3 != Y3 )
             => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
                | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ X3 ) @ R ) ) ) ) )
     => ( total_7212417256332265445at_nat @ A2 @ R ) ) ).

% total_onI
thf(fact_655_wo__rel_Owell__order__induct,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,P3: set_Product_prod_o_o > $o,A: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ! [X3: set_Product_prod_o_o] :
            ( ! [Y4: set_Product_prod_o_o] :
                ( ( ( Y4 != X3 )
                  & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y4 @ X3 ) @ R ) )
               => ( P3 @ Y4 ) )
           => ( P3 @ X3 ) )
       => ( P3 @ A ) ) ) ).

% wo_rel.well_order_induct
thf(fact_656_wo__rel_Owell__order__induct,axiom,
    ! [R: set_Pr4329608150637261639at_nat,P3: set_Pr1261947904930325089at_nat > $o,A: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ! [X3: set_Pr1261947904930325089at_nat] :
            ( ! [Y4: set_Pr1261947904930325089at_nat] :
                ( ( ( Y4 != X3 )
                  & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y4 @ X3 ) @ R ) )
               => ( P3 @ Y4 ) )
           => ( P3 @ X3 ) )
       => ( P3 @ A ) ) ) ).

% wo_rel.well_order_induct
thf(fact_657_wo__rel_OTOTALS,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ! [X7: $o] :
          ( ( member_o @ X7 @ ( field_o @ R ) )
         => ! [Xa: $o] :
              ( ( member_o @ Xa @ ( field_o @ R ) )
             => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X7 @ Xa ) @ R )
                | ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Xa @ X7 ) @ R ) ) ) ) ) ).

% wo_rel.TOTALS
thf(fact_658_wo__rel_OTOTALS,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ! [X7: nat] :
          ( ( member_nat @ X7 @ ( field_nat @ R ) )
         => ! [Xa: nat] :
              ( ( member_nat @ Xa @ ( field_nat @ R ) )
             => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X7 @ Xa ) @ R )
                | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Xa @ X7 ) @ R ) ) ) ) ) ).

% wo_rel.TOTALS
thf(fact_659_wo__rel_OTOTALS,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ! [X7: set_Product_prod_o_o] :
          ( ( member3157015407008874800od_o_o @ X7 @ ( field_6101175518749917524od_o_o @ R ) )
         => ! [Xa: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ Xa @ ( field_6101175518749917524od_o_o @ R ) )
             => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X7 @ Xa ) @ R )
                | ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Xa @ X7 ) @ R ) ) ) ) ) ).

% wo_rel.TOTALS
thf(fact_660_wo__rel_OTOTALS,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ! [X7: set_Pr1261947904930325089at_nat] :
          ( ( member2643936169264416010at_nat @ X7 @ ( field_3145993188331922222at_nat @ R ) )
         => ! [Xa: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ Xa @ ( field_3145993188331922222at_nat @ R ) )
             => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X7 @ Xa ) @ R )
                | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Xa @ X7 ) @ R ) ) ) ) ) ).

% wo_rel.TOTALS
thf(fact_661_wo__rel_Oin__notinI,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,J: produc2934264451710624999od_o_o,I: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( ~ ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ J @ I ) @ R )
          | ( J = I ) )
       => ( ( member444158400953824016od_o_o @ I @ ( field_5121862139100741428od_o_o @ R ) )
         => ( ( member444158400953824016od_o_o @ J @ ( field_5121862139100741428od_o_o @ R ) )
           => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ I @ J ) @ R ) ) ) ) ) ).

% wo_rel.in_notinI
thf(fact_662_wo__rel_Oin__notinI,axiom,
    ! [R: set_Pr4427867301352232263at_nat,J: produc732395585841259969at_nat,I: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( ~ ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ J @ I ) @ R )
          | ( J = I ) )
       => ( ( member4095101504841534314at_nat @ I @ ( field_7361900449976055182at_nat @ R ) )
         => ( ( member4095101504841534314at_nat @ J @ ( field_7361900449976055182at_nat @ R ) )
           => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ I @ J ) @ R ) ) ) ) ) ).

% wo_rel.in_notinI
thf(fact_663_wo__rel_Oin__notinI,axiom,
    ! [R: set_Pr5564308138774400199at_nat,J: produc3843707927480180839at_nat,I: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( ~ ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ J @ I ) @ R )
          | ( J = I ) )
       => ( ( member8757157785044589968at_nat @ I @ ( field_2862844103579723188at_nat @ R ) )
         => ( ( member8757157785044589968at_nat @ J @ ( field_2862844103579723188at_nat @ R ) )
           => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J ) @ R ) ) ) ) ) ).

% wo_rel.in_notinI
thf(fact_664_wo__rel_Oin__notinI,axiom,
    ! [R: set_Product_prod_a_a,J: a,I: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ~ ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ J @ I ) @ R )
          | ( J = I ) )
       => ( ( member_a @ I @ ( field_a @ R ) )
         => ( ( member_a @ J @ ( field_a @ R ) )
           => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ I @ J ) @ R ) ) ) ) ) ).

% wo_rel.in_notinI
thf(fact_665_wo__rel_Oin__notinI,axiom,
    ! [R: set_Product_prod_o_o,J: $o,I: $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ( ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ J @ I ) @ R )
          | ( J = I ) )
       => ( ( member_o @ I @ ( field_o @ R ) )
         => ( ( member_o @ J @ ( field_o @ R ) )
           => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J ) @ R ) ) ) ) ) ).

% wo_rel.in_notinI
thf(fact_666_wo__rel_Oin__notinI,axiom,
    ! [R: set_Pr1261947904930325089at_nat,J: nat,I: nat] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ J @ I ) @ R )
          | ( J = I ) )
       => ( ( member_nat @ I @ ( field_nat @ R ) )
         => ( ( member_nat @ J @ ( field_nat @ R ) )
           => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R ) ) ) ) ) ).

% wo_rel.in_notinI
thf(fact_667_wo__rel_Oin__notinI,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,J: set_Product_prod_o_o,I: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ J @ I ) @ R )
          | ( J = I ) )
       => ( ( member3157015407008874800od_o_o @ I @ ( field_6101175518749917524od_o_o @ R ) )
         => ( ( member3157015407008874800od_o_o @ J @ ( field_6101175518749917524od_o_o @ R ) )
           => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ I @ J ) @ R ) ) ) ) ) ).

% wo_rel.in_notinI
thf(fact_668_wo__rel_Oin__notinI,axiom,
    ! [R: set_Pr4329608150637261639at_nat,J: set_Pr1261947904930325089at_nat,I: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ J @ I ) @ R )
          | ( J = I ) )
       => ( ( member2643936169264416010at_nat @ I @ ( field_3145993188331922222at_nat @ R ) )
         => ( ( member2643936169264416010at_nat @ J @ ( field_3145993188331922222at_nat @ R ) )
           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J ) @ R ) ) ) ) ) ).

% wo_rel.in_notinI
thf(fact_669_well__order__induct__imp,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,P3: produc2934264451710624999od_o_o > $o,A: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ! [X3: produc2934264451710624999od_o_o] :
            ( ! [Y4: produc2934264451710624999od_o_o] :
                ( ( ( Y4 != X3 )
                  & ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y4 @ X3 ) @ R ) )
               => ( ( member444158400953824016od_o_o @ Y4 @ ( field_5121862139100741428od_o_o @ R ) )
                 => ( P3 @ Y4 ) ) )
           => ( ( member444158400953824016od_o_o @ X3 @ ( field_5121862139100741428od_o_o @ R ) )
             => ( P3 @ X3 ) ) )
       => ( ( member444158400953824016od_o_o @ A @ ( field_5121862139100741428od_o_o @ R ) )
         => ( P3 @ A ) ) ) ) ).

% well_order_induct_imp
thf(fact_670_well__order__induct__imp,axiom,
    ! [R: set_Pr4427867301352232263at_nat,P3: produc732395585841259969at_nat > $o,A: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ! [X3: produc732395585841259969at_nat] :
            ( ! [Y4: produc732395585841259969at_nat] :
                ( ( ( Y4 != X3 )
                  & ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y4 @ X3 ) @ R ) )
               => ( ( member4095101504841534314at_nat @ Y4 @ ( field_7361900449976055182at_nat @ R ) )
                 => ( P3 @ Y4 ) ) )
           => ( ( member4095101504841534314at_nat @ X3 @ ( field_7361900449976055182at_nat @ R ) )
             => ( P3 @ X3 ) ) )
       => ( ( member4095101504841534314at_nat @ A @ ( field_7361900449976055182at_nat @ R ) )
         => ( P3 @ A ) ) ) ) ).

% well_order_induct_imp
thf(fact_671_well__order__induct__imp,axiom,
    ! [R: set_Pr5564308138774400199at_nat,P3: produc3843707927480180839at_nat > $o,A: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ! [X3: produc3843707927480180839at_nat] :
            ( ! [Y4: produc3843707927480180839at_nat] :
                ( ( ( Y4 != X3 )
                  & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y4 @ X3 ) @ R ) )
               => ( ( member8757157785044589968at_nat @ Y4 @ ( field_2862844103579723188at_nat @ R ) )
                 => ( P3 @ Y4 ) ) )
           => ( ( member8757157785044589968at_nat @ X3 @ ( field_2862844103579723188at_nat @ R ) )
             => ( P3 @ X3 ) ) )
       => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
         => ( P3 @ A ) ) ) ) ).

% well_order_induct_imp
thf(fact_672_well__order__induct__imp,axiom,
    ! [R: set_Product_prod_a_a,P3: a > $o,A: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ! [X3: a] :
            ( ! [Y4: a] :
                ( ( ( Y4 != X3 )
                  & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y4 @ X3 ) @ R ) )
               => ( ( member_a @ Y4 @ ( field_a @ R ) )
                 => ( P3 @ Y4 ) ) )
           => ( ( member_a @ X3 @ ( field_a @ R ) )
             => ( P3 @ X3 ) ) )
       => ( ( member_a @ A @ ( field_a @ R ) )
         => ( P3 @ A ) ) ) ) ).

% well_order_induct_imp
thf(fact_673_well__order__induct__imp,axiom,
    ! [R: set_Product_prod_o_o,P3: $o > $o,A: $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ! [X3: $o] :
            ( ! [Y4: $o] :
                ( ( ( Y4 != X3 )
                  & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y4 @ X3 ) @ R ) )
               => ( ( member_o @ Y4 @ ( field_o @ R ) )
                 => ( P3 @ Y4 ) ) )
           => ( ( member_o @ X3 @ ( field_o @ R ) )
             => ( P3 @ X3 ) ) )
       => ( ( member_o @ A @ ( field_o @ R ) )
         => ( P3 @ A ) ) ) ) ).

% well_order_induct_imp
thf(fact_674_well__order__induct__imp,axiom,
    ! [R: set_Pr1261947904930325089at_nat,P3: nat > $o,A: nat] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ! [X3: nat] :
            ( ! [Y4: nat] :
                ( ( ( Y4 != X3 )
                  & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y4 @ X3 ) @ R ) )
               => ( ( member_nat @ Y4 @ ( field_nat @ R ) )
                 => ( P3 @ Y4 ) ) )
           => ( ( member_nat @ X3 @ ( field_nat @ R ) )
             => ( P3 @ X3 ) ) )
       => ( ( member_nat @ A @ ( field_nat @ R ) )
         => ( P3 @ A ) ) ) ) ).

% well_order_induct_imp
thf(fact_675_well__order__induct__imp,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,P3: set_Product_prod_o_o > $o,A: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ! [X3: set_Product_prod_o_o] :
            ( ! [Y4: set_Product_prod_o_o] :
                ( ( ( Y4 != X3 )
                  & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y4 @ X3 ) @ R ) )
               => ( ( member3157015407008874800od_o_o @ Y4 @ ( field_6101175518749917524od_o_o @ R ) )
                 => ( P3 @ Y4 ) ) )
           => ( ( member3157015407008874800od_o_o @ X3 @ ( field_6101175518749917524od_o_o @ R ) )
             => ( P3 @ X3 ) ) )
       => ( ( member3157015407008874800od_o_o @ A @ ( field_6101175518749917524od_o_o @ R ) )
         => ( P3 @ A ) ) ) ) ).

% well_order_induct_imp
thf(fact_676_well__order__induct__imp,axiom,
    ! [R: set_Pr4329608150637261639at_nat,P3: set_Pr1261947904930325089at_nat > $o,A: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ! [X3: set_Pr1261947904930325089at_nat] :
            ( ! [Y4: set_Pr1261947904930325089at_nat] :
                ( ( ( Y4 != X3 )
                  & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y4 @ X3 ) @ R ) )
               => ( ( member2643936169264416010at_nat @ Y4 @ ( field_3145993188331922222at_nat @ R ) )
                 => ( P3 @ Y4 ) ) )
           => ( ( member2643936169264416010at_nat @ X3 @ ( field_3145993188331922222at_nat @ R ) )
             => ( P3 @ X3 ) ) )
       => ( ( member2643936169264416010at_nat @ A @ ( field_3145993188331922222at_nat @ R ) )
         => ( P3 @ A ) ) ) ) ).

% well_order_induct_imp
thf(fact_677_totalI,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
          ( ( X3 != Y3 )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
            | ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ X3 ) @ R ) ) )
     => ( total_5784220159268842891od_o_o @ top_to1478448522960722999od_o_o @ R ) ) ).

% totalI
thf(fact_678_totalI,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
          ( ( X3 != Y3 )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
            | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ X3 ) @ R ) ) )
     => ( total_7212417256332265445at_nat @ top_to7629004291339433233at_nat @ R ) ) ).

% totalI
thf(fact_679_totalI,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ! [X3: nat,Y3: nat] :
          ( ( X3 != Y3 )
         => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
            | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X3 ) @ R ) ) )
     => ( total_on_nat @ top_top_set_nat @ R ) ) ).

% totalI
thf(fact_680_wo__rel_Ocases__Total,axiom,
    ! [R: set_Product_prod_o_o,A: $o,B: $o,Phi: $o > $o > $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ( ord_less_eq_set_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( field_o @ R ) )
       => ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ R )
           => ( Phi @ A @ B ) )
         => ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A ) @ R )
             => ( Phi @ A @ B ) )
           => ( Phi @ A @ B ) ) ) ) ) ).

% wo_rel.cases_Total
thf(fact_681_wo__rel_Ocases__Total,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat,Phi: nat > nat > $o] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ( ord_less_eq_set_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( field_nat @ R ) )
       => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
           => ( Phi @ A @ B ) )
         => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A ) @ R )
             => ( Phi @ A @ B ) )
           => ( Phi @ A @ B ) ) ) ) ) ).

% wo_rel.cases_Total
thf(fact_682_wo__rel_Ocases__Total,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o,Phi: set_Product_prod_o_o > set_Product_prod_o_o > $o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( ord_le2654036014095304327od_o_o @ ( insert3817420688681518039od_o_o @ A @ ( insert3817420688681518039od_o_o @ B @ bot_bo8006819982598807891od_o_o ) ) @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
           => ( Phi @ A @ B ) )
         => ( ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ A ) @ R )
             => ( Phi @ A @ B ) )
           => ( Phi @ A @ B ) ) ) ) ) ).

% wo_rel.cases_Total
thf(fact_683_wo__rel_Ocases__Total,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,Phi: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( ord_le2077887516847798113at_nat @ ( insert9200635055090092081at_nat @ A @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
           => ( Phi @ A @ B ) )
         => ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ A ) @ R )
             => ( Phi @ A @ B ) )
           => ( Phi @ A @ B ) ) ) ) ) ).

% wo_rel.cases_Total
thf(fact_684_wo__rel_Oequals__minim,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,B2: set_Pr1932065953672099015od_o_o,A: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( ord_le7586318239878589543od_o_o @ B2 @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ A @ B2 )
         => ( ! [B3: produc2934264451710624999od_o_o] :
                ( ( member444158400953824016od_o_o @ B3 @ B2 )
               => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ B3 ) @ R ) )
           => ( A
              = ( bNF_We4719373430050929331od_o_o @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_685_wo__rel_Oequals__minim,axiom,
    ! [R: set_Pr4427867301352232263at_nat,B2: set_Pr457366540195662369at_nat,A: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( ord_le4841768313324958145at_nat @ B2 @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( member4095101504841534314at_nat @ A @ B2 )
         => ( ! [B3: produc732395585841259969at_nat] :
                ( ( member4095101504841534314at_nat @ B3 @ B2 )
               => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ B3 ) @ R ) )
           => ( A
              = ( bNF_We6249471513304245645at_nat @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_686_wo__rel_Oequals__minim,axiom,
    ! [R: set_Pr5564308138774400199at_nat,B2: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( ord_le1268244103169919719at_nat @ B2 @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ A @ B2 )
         => ( ! [B3: produc3843707927480180839at_nat] :
                ( ( member8757157785044589968at_nat @ B3 @ B2 )
               => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B3 ) @ R ) )
           => ( A
              = ( bNF_We7473068394052389427at_nat @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_687_wo__rel_Oequals__minim,axiom,
    ! [R: set_Product_prod_a_a,B2: set_a,A: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B2 @ ( field_a @ R ) )
       => ( ( member_a @ A @ B2 )
         => ( ! [B3: a] :
                ( ( member_a @ B3 @ B2 )
               => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B3 ) @ R ) )
           => ( A
              = ( bNF_We5615626441682584778inim_a @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_688_wo__rel_Oequals__minim,axiom,
    ! [R: set_Product_prod_o_o,B2: set_o,A: $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ( ord_less_eq_set_o @ B2 @ ( field_o @ R ) )
       => ( ( member_o @ A @ B2 )
         => ( ! [B3: $o] :
                ( ( member_o @ B3 @ B2 )
               => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B3 ) @ R ) )
           => ( A
              = ( bNF_We537455116209922916inim_o @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_689_wo__rel_Oequals__minim,axiom,
    ! [R: set_Pr1261947904930325089at_nat,B2: set_nat,A: nat] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ( ord_less_eq_set_nat @ B2 @ ( field_nat @ R ) )
       => ( ( member_nat @ A @ B2 )
         => ( ! [B3: nat] :
                ( ( member_nat @ B3 @ B2 )
               => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B3 ) @ R ) )
           => ( A
              = ( bNF_We3275124272252294916im_nat @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_690_wo__rel_Oequals__minim,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,B2: set_se491199571785101031od_o_o,A: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( ord_le2654036014095304327od_o_o @ B2 @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( member3157015407008874800od_o_o @ A @ B2 )
         => ( ! [B3: set_Product_prod_o_o] :
                ( ( member3157015407008874800od_o_o @ B3 @ B2 )
               => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B3 ) @ R ) )
           => ( A
              = ( bNF_We6151898823597705171od_o_o @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_691_wo__rel_Oequals__minim,axiom,
    ! [R: set_Pr4329608150637261639at_nat,B2: set_se7855581050983116737at_nat,A: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( ord_le2077887516847798113at_nat @ B2 @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( member2643936169264416010at_nat @ A @ B2 )
         => ( ! [B3: set_Pr1261947904930325089at_nat] :
                ( ( member2643936169264416010at_nat @ B3 @ B2 )
               => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B3 ) @ R ) )
           => ( A
              = ( bNF_We6832956061294468653at_nat @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_692_wo__rel_Ominim__least,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,B2: set_Pr1932065953672099015od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( ord_le7586318239878589543od_o_o @ B2 @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ B @ B2 )
         => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( bNF_We4719373430050929331od_o_o @ R @ B2 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_693_wo__rel_Ominim__least,axiom,
    ! [R: set_Pr4427867301352232263at_nat,B2: set_Pr457366540195662369at_nat,B: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( ord_le4841768313324958145at_nat @ B2 @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( member4095101504841534314at_nat @ B @ B2 )
         => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( bNF_We6249471513304245645at_nat @ R @ B2 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_694_wo__rel_Ominim__least,axiom,
    ! [R: set_Pr5564308138774400199at_nat,B2: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( ord_le1268244103169919719at_nat @ B2 @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ B @ B2 )
         => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( bNF_We7473068394052389427at_nat @ R @ B2 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_695_wo__rel_Ominim__least,axiom,
    ! [R: set_Product_prod_a_a,B2: set_a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B2 @ ( field_a @ R ) )
       => ( ( member_a @ B @ B2 )
         => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ ( bNF_We5615626441682584778inim_a @ R @ B2 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_696_wo__rel_Ominim__least,axiom,
    ! [R: set_Product_prod_o_o,B2: set_o,B: $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ( ord_less_eq_set_o @ B2 @ ( field_o @ R ) )
       => ( ( member_o @ B @ B2 )
         => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( bNF_We537455116209922916inim_o @ R @ B2 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_697_wo__rel_Ominim__least,axiom,
    ! [R: set_Pr1261947904930325089at_nat,B2: set_nat,B: nat] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ( ord_less_eq_set_nat @ B2 @ ( field_nat @ R ) )
       => ( ( member_nat @ B @ B2 )
         => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( bNF_We3275124272252294916im_nat @ R @ B2 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_698_wo__rel_Ominim__least,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,B2: set_se491199571785101031od_o_o,B: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( ord_le2654036014095304327od_o_o @ B2 @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( member3157015407008874800od_o_o @ B @ B2 )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_We6151898823597705171od_o_o @ R @ B2 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_699_wo__rel_Ominim__least,axiom,
    ! [R: set_Pr4329608150637261639at_nat,B2: set_se7855581050983116737at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( ord_le2077887516847798113at_nat @ B2 @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( member2643936169264416010at_nat @ B @ B2 )
         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_We6832956061294468653at_nat @ R @ B2 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_700_wo__rel_Omax2__greater__among,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ A @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ B @ ( field_5121862139100741428od_o_o @ R ) )
         => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ ( bNF_We5307229915971165237od_o_o @ R @ A @ B ) ) @ R )
            & ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ B @ ( bNF_We5307229915971165237od_o_o @ R @ A @ B ) ) @ R )
            & ( member444158400953824016od_o_o @ ( bNF_We5307229915971165237od_o_o @ R @ A @ B ) @ ( insert3855699742481506999od_o_o @ A @ ( insert3855699742481506999od_o_o @ B @ bot_bo498831808395348787od_o_o ) ) ) ) ) ) ) ).

% wo_rel.max2_greater_among
thf(fact_701_wo__rel_Omax2__greater__among,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat,B: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( member4095101504841534314at_nat @ A @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( member4095101504841534314at_nat @ B @ ( field_7361900449976055182at_nat @ R ) )
         => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ ( bNF_We7253295970193759759at_nat @ R @ A @ B ) ) @ R )
            & ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ B @ ( bNF_We7253295970193759759at_nat @ R @ A @ B ) ) @ R )
            & ( member4095101504841534314at_nat @ ( bNF_We7253295970193759759at_nat @ R @ A @ B ) @ ( insert8109617542356073361at_nat @ A @ ( insert8109617542356073361at_nat @ B @ bot_bo1676454896636820109at_nat ) ) ) ) ) ) ) ).

% wo_rel.max2_greater_among
thf(fact_702_wo__rel_Omax2__greater__among,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ B @ ( field_2862844103579723188at_nat @ R ) )
         => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ ( bNF_We1807050579049552309at_nat @ R @ A @ B ) ) @ R )
            & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ B @ ( bNF_We1807050579049552309at_nat @ R @ A @ B ) ) @ R )
            & ( member8757157785044589968at_nat @ ( bNF_We1807050579049552309at_nat @ R @ A @ B ) @ ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) ) ) ) ) ) ).

% wo_rel.max2_greater_among
thf(fact_703_wo__rel_Omax2__greater__among,axiom,
    ! [R: set_Product_prod_a_a,A: a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( member_a @ A @ ( field_a @ R ) )
       => ( ( member_a @ B @ ( field_a @ R ) )
         => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ ( bNF_We3763454674811381836max2_a @ R @ A @ B ) ) @ R )
            & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B @ ( bNF_We3763454674811381836max2_a @ R @ A @ B ) ) @ R )
            & ( member_a @ ( bNF_We3763454674811381836max2_a @ R @ A @ B ) @ ( insert_a @ A @ ( insert_a @ B @ bot_bot_set_a ) ) ) ) ) ) ) ).

% wo_rel.max2_greater_among
thf(fact_704_wo__rel_Omax2__greater__among,axiom,
    ! [R: set_Product_prod_o_o,A: $o,B: $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ( member_o @ A @ ( field_o @ R ) )
       => ( ( member_o @ B @ ( field_o @ R ) )
         => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ ( bNF_We3104086342435940326max2_o @ R @ A @ B ) ) @ R )
            & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ ( bNF_We3104086342435940326max2_o @ R @ A @ B ) ) @ R )
            & ( member_o @ ( bNF_We3104086342435940326max2_o @ R @ A @ B ) @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ) ) ) ).

% wo_rel.max2_greater_among
thf(fact_705_wo__rel_Omax2__greater__among,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ( member_nat @ A @ ( field_nat @ R ) )
       => ( ( member_nat @ B @ ( field_nat @ R ) )
         => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ ( bNF_We2380939065524664066x2_nat @ R @ A @ B ) ) @ R )
            & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ ( bNF_We2380939065524664066x2_nat @ R @ A @ B ) ) @ R )
            & ( member_nat @ ( bNF_We2380939065524664066x2_nat @ R @ A @ B ) @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ) ) ) ).

% wo_rel.max2_greater_among
thf(fact_706_wo__rel_Omax2__greater__among,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( member3157015407008874800od_o_o @ A @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( member3157015407008874800od_o_o @ B @ ( field_6101175518749917524od_o_o @ R ) )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ ( bNF_We9141258785624724309od_o_o @ R @ A @ B ) ) @ R )
            & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ ( bNF_We9141258785624724309od_o_o @ R @ A @ B ) ) @ R )
            & ( member3157015407008874800od_o_o @ ( bNF_We9141258785624724309od_o_o @ R @ A @ B ) @ ( insert3817420688681518039od_o_o @ A @ ( insert3817420688681518039od_o_o @ B @ bot_bo8006819982598807891od_o_o ) ) ) ) ) ) ) ).

% wo_rel.max2_greater_among
thf(fact_707_wo__rel_Omax2__greater__among,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( member2643936169264416010at_nat @ A @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( member2643936169264416010at_nat @ B @ ( field_3145993188331922222at_nat @ R ) )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ ( bNF_We6094461251688579247at_nat @ R @ A @ B ) ) @ R )
            & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ ( bNF_We6094461251688579247at_nat @ R @ A @ B ) ) @ R )
            & ( member2643936169264416010at_nat @ ( bNF_We6094461251688579247at_nat @ R @ A @ B ) @ ( insert9200635055090092081at_nat @ A @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) ) ) ) ) ) ).

% wo_rel.max2_greater_among
thf(fact_708_in__quotient__imp__in__rel,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X8: set_se491199571785101031od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( member2239101972932892176od_o_o @ X8 @ ( equiv_3134926782319234254od_o_o @ A2 @ R ) )
       => ( ( ord_le2654036014095304327od_o_o @ ( insert3817420688681518039od_o_o @ X @ ( insert3817420688681518039od_o_o @ Y @ bot_bo8006819982598807891od_o_o ) ) @ X8 )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R ) ) ) ) ).

% in_quotient_imp_in_rel
thf(fact_709_in__quotient__imp__in__rel,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X8: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( member8313122109188517482at_nat @ X8 @ ( equiv_7923377459618294184at_nat @ A2 @ R ) )
       => ( ( ord_le2077887516847798113at_nat @ ( insert9200635055090092081at_nat @ X @ ( insert9200635055090092081at_nat @ Y @ bot_bo3083307316010499117at_nat ) ) @ X8 )
         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R ) ) ) ) ).

% in_quotient_imp_in_rel
thf(fact_710_in__quotient__imp__closed,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X8: set_Pr1932065953672099015od_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( equiv_3398664326906728093od_o_o @ A2 @ R )
     => ( ( member4387393612980313840od_o_o @ X8 @ ( equiv_1831625524721748142od_o_o @ A2 @ R ) )
       => ( ( member444158400953824016od_o_o @ X @ X8 )
         => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ R )
           => ( member444158400953824016od_o_o @ Y @ X8 ) ) ) ) ) ).

% in_quotient_imp_closed
thf(fact_711_in__quotient__imp__closed,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X8: set_Pr457366540195662369at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat] :
      ( ( equiv_2520666332425567351at_nat @ A2 @ R )
     => ( ( member3243375828287704010at_nat @ X8 @ ( equiv_2323626691971332616at_nat @ A2 @ R ) )
       => ( ( member4095101504841534314at_nat @ X @ X8 )
         => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ R )
           => ( member4095101504841534314at_nat @ Y @ X8 ) ) ) ) ) ).

% in_quotient_imp_closed
thf(fact_712_in__quotient__imp__closed,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X8: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
      ( ( equiv_4443766944827089949at_nat @ A2 @ R )
     => ( ( member6273874620674182256at_nat @ X8 @ ( equiv_8408515162552411438at_nat @ A2 @ R ) )
       => ( ( member8757157785044589968at_nat @ X @ X8 )
         => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R )
           => ( member8757157785044589968at_nat @ Y @ X8 ) ) ) ) ) ).

% in_quotient_imp_closed
thf(fact_713_in__quotient__imp__closed,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X8: set_a,X: a,Y: a] :
      ( ( equiv_equiv_a @ A2 @ R )
     => ( ( member_set_a @ X8 @ ( equiv_quotient_a @ A2 @ R ) )
       => ( ( member_a @ X @ X8 )
         => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R )
           => ( member_a @ Y @ X8 ) ) ) ) ) ).

% in_quotient_imp_closed
thf(fact_714_in__quotient__imp__closed,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X8: set_se491199571785101031od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( member2239101972932892176od_o_o @ X8 @ ( equiv_3134926782319234254od_o_o @ A2 @ R ) )
       => ( ( member3157015407008874800od_o_o @ X @ X8 )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
           => ( member3157015407008874800od_o_o @ Y @ X8 ) ) ) ) ) ).

% in_quotient_imp_closed
thf(fact_715_in__quotient__imp__closed,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X8: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( member8313122109188517482at_nat @ X8 @ ( equiv_7923377459618294184at_nat @ A2 @ R ) )
       => ( ( member2643936169264416010at_nat @ X @ X8 )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
           => ( member2643936169264416010at_nat @ Y @ X8 ) ) ) ) ) ).

% in_quotient_imp_closed
thf(fact_716_quotient__eq__iff,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X8: set_Pr1932065953672099015od_o_o,Y5: set_Pr1932065953672099015od_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( equiv_3398664326906728093od_o_o @ A2 @ R )
     => ( ( member4387393612980313840od_o_o @ X8 @ ( equiv_1831625524721748142od_o_o @ A2 @ R ) )
       => ( ( member4387393612980313840od_o_o @ Y5 @ ( equiv_1831625524721748142od_o_o @ A2 @ R ) )
         => ( ( member444158400953824016od_o_o @ X @ X8 )
           => ( ( member444158400953824016od_o_o @ Y @ Y5 )
             => ( ( X8 = Y5 )
                = ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ R ) ) ) ) ) ) ) ).

% quotient_eq_iff
thf(fact_717_quotient__eq__iff,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X8: set_Pr457366540195662369at_nat,Y5: set_Pr457366540195662369at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat] :
      ( ( equiv_2520666332425567351at_nat @ A2 @ R )
     => ( ( member3243375828287704010at_nat @ X8 @ ( equiv_2323626691971332616at_nat @ A2 @ R ) )
       => ( ( member3243375828287704010at_nat @ Y5 @ ( equiv_2323626691971332616at_nat @ A2 @ R ) )
         => ( ( member4095101504841534314at_nat @ X @ X8 )
           => ( ( member4095101504841534314at_nat @ Y @ Y5 )
             => ( ( X8 = Y5 )
                = ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ R ) ) ) ) ) ) ) ).

% quotient_eq_iff
thf(fact_718_quotient__eq__iff,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X8: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
      ( ( equiv_4443766944827089949at_nat @ A2 @ R )
     => ( ( member6273874620674182256at_nat @ X8 @ ( equiv_8408515162552411438at_nat @ A2 @ R ) )
       => ( ( member6273874620674182256at_nat @ Y5 @ ( equiv_8408515162552411438at_nat @ A2 @ R ) )
         => ( ( member8757157785044589968at_nat @ X @ X8 )
           => ( ( member8757157785044589968at_nat @ Y @ Y5 )
             => ( ( X8 = Y5 )
                = ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R ) ) ) ) ) ) ) ).

% quotient_eq_iff
thf(fact_719_quotient__eq__iff,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X8: set_a,Y5: set_a,X: a,Y: a] :
      ( ( equiv_equiv_a @ A2 @ R )
     => ( ( member_set_a @ X8 @ ( equiv_quotient_a @ A2 @ R ) )
       => ( ( member_set_a @ Y5 @ ( equiv_quotient_a @ A2 @ R ) )
         => ( ( member_a @ X @ X8 )
           => ( ( member_a @ Y @ Y5 )
             => ( ( X8 = Y5 )
                = ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R ) ) ) ) ) ) ) ).

% quotient_eq_iff
thf(fact_720_quotient__eq__iff,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X8: set_se491199571785101031od_o_o,Y5: set_se491199571785101031od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( member2239101972932892176od_o_o @ X8 @ ( equiv_3134926782319234254od_o_o @ A2 @ R ) )
       => ( ( member2239101972932892176od_o_o @ Y5 @ ( equiv_3134926782319234254od_o_o @ A2 @ R ) )
         => ( ( member3157015407008874800od_o_o @ X @ X8 )
           => ( ( member3157015407008874800od_o_o @ Y @ Y5 )
             => ( ( X8 = Y5 )
                = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R ) ) ) ) ) ) ) ).

% quotient_eq_iff
thf(fact_721_quotient__eq__iff,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X8: set_se7855581050983116737at_nat,Y5: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( member8313122109188517482at_nat @ X8 @ ( equiv_7923377459618294184at_nat @ A2 @ R ) )
       => ( ( member8313122109188517482at_nat @ Y5 @ ( equiv_7923377459618294184at_nat @ A2 @ R ) )
         => ( ( member2643936169264416010at_nat @ X @ X8 )
           => ( ( member2643936169264416010at_nat @ Y @ Y5 )
             => ( ( X8 = Y5 )
                = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R ) ) ) ) ) ) ) ).

% quotient_eq_iff
thf(fact_722_quotient__eqI,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X8: set_Pr1932065953672099015od_o_o,Y5: set_Pr1932065953672099015od_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( equiv_3398664326906728093od_o_o @ A2 @ R )
     => ( ( member4387393612980313840od_o_o @ X8 @ ( equiv_1831625524721748142od_o_o @ A2 @ R ) )
       => ( ( member4387393612980313840od_o_o @ Y5 @ ( equiv_1831625524721748142od_o_o @ A2 @ R ) )
         => ( ( member444158400953824016od_o_o @ X @ X8 )
           => ( ( member444158400953824016od_o_o @ Y @ Y5 )
             => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ R )
               => ( X8 = Y5 ) ) ) ) ) ) ) ).

% quotient_eqI
thf(fact_723_quotient__eqI,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X8: set_Pr457366540195662369at_nat,Y5: set_Pr457366540195662369at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat] :
      ( ( equiv_2520666332425567351at_nat @ A2 @ R )
     => ( ( member3243375828287704010at_nat @ X8 @ ( equiv_2323626691971332616at_nat @ A2 @ R ) )
       => ( ( member3243375828287704010at_nat @ Y5 @ ( equiv_2323626691971332616at_nat @ A2 @ R ) )
         => ( ( member4095101504841534314at_nat @ X @ X8 )
           => ( ( member4095101504841534314at_nat @ Y @ Y5 )
             => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ R )
               => ( X8 = Y5 ) ) ) ) ) ) ) ).

% quotient_eqI
thf(fact_724_quotient__eqI,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X8: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
      ( ( equiv_4443766944827089949at_nat @ A2 @ R )
     => ( ( member6273874620674182256at_nat @ X8 @ ( equiv_8408515162552411438at_nat @ A2 @ R ) )
       => ( ( member6273874620674182256at_nat @ Y5 @ ( equiv_8408515162552411438at_nat @ A2 @ R ) )
         => ( ( member8757157785044589968at_nat @ X @ X8 )
           => ( ( member8757157785044589968at_nat @ Y @ Y5 )
             => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R )
               => ( X8 = Y5 ) ) ) ) ) ) ) ).

% quotient_eqI
thf(fact_725_quotient__eqI,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X8: set_a,Y5: set_a,X: a,Y: a] :
      ( ( equiv_equiv_a @ A2 @ R )
     => ( ( member_set_a @ X8 @ ( equiv_quotient_a @ A2 @ R ) )
       => ( ( member_set_a @ Y5 @ ( equiv_quotient_a @ A2 @ R ) )
         => ( ( member_a @ X @ X8 )
           => ( ( member_a @ Y @ Y5 )
             => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R )
               => ( X8 = Y5 ) ) ) ) ) ) ) ).

% quotient_eqI
thf(fact_726_quotient__eqI,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X8: set_se491199571785101031od_o_o,Y5: set_se491199571785101031od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( member2239101972932892176od_o_o @ X8 @ ( equiv_3134926782319234254od_o_o @ A2 @ R ) )
       => ( ( member2239101972932892176od_o_o @ Y5 @ ( equiv_3134926782319234254od_o_o @ A2 @ R ) )
         => ( ( member3157015407008874800od_o_o @ X @ X8 )
           => ( ( member3157015407008874800od_o_o @ Y @ Y5 )
             => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
               => ( X8 = Y5 ) ) ) ) ) ) ) ).

% quotient_eqI
thf(fact_727_quotient__eqI,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X8: set_se7855581050983116737at_nat,Y5: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( member8313122109188517482at_nat @ X8 @ ( equiv_7923377459618294184at_nat @ A2 @ R ) )
       => ( ( member8313122109188517482at_nat @ Y5 @ ( equiv_7923377459618294184at_nat @ A2 @ R ) )
         => ( ( member2643936169264416010at_nat @ X @ X8 )
           => ( ( member2643936169264416010at_nat @ Y @ Y5 )
             => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
               => ( X8 = Y5 ) ) ) ) ) ) ) ).

% quotient_eqI
thf(fact_728_wo__rel_Omax2__def,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
         => ( ( bNF_We9141258785624724309od_o_o @ R @ A @ B )
            = B ) )
        & ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
         => ( ( bNF_We9141258785624724309od_o_o @ R @ A @ B )
            = A ) ) ) ) ).

% wo_rel.max2_def
thf(fact_729_wo__rel_Omax2__def,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
         => ( ( bNF_We6094461251688579247at_nat @ R @ A @ B )
            = B ) )
        & ( ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
         => ( ( bNF_We6094461251688579247at_nat @ R @ A @ B )
            = A ) ) ) ) ).

% wo_rel.max2_def
thf(fact_730_eq__equiv__class__iff2,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( equiv_3398664326906728093od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ X @ A2 )
       => ( ( member444158400953824016od_o_o @ Y @ A2 )
         => ( ( ( equiv_1831625524721748142od_o_o @ ( insert3855699742481506999od_o_o @ X @ bot_bo498831808395348787od_o_o ) @ R )
              = ( equiv_1831625524721748142od_o_o @ ( insert3855699742481506999od_o_o @ Y @ bot_bo498831808395348787od_o_o ) @ R ) )
            = ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff2
thf(fact_731_eq__equiv__class__iff2,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat] :
      ( ( equiv_2520666332425567351at_nat @ A2 @ R )
     => ( ( member4095101504841534314at_nat @ X @ A2 )
       => ( ( member4095101504841534314at_nat @ Y @ A2 )
         => ( ( ( equiv_2323626691971332616at_nat @ ( insert8109617542356073361at_nat @ X @ bot_bo1676454896636820109at_nat ) @ R )
              = ( equiv_2323626691971332616at_nat @ ( insert8109617542356073361at_nat @ Y @ bot_bo1676454896636820109at_nat ) @ R ) )
            = ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff2
thf(fact_732_eq__equiv__class__iff2,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
      ( ( equiv_4443766944827089949at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ X @ A2 )
       => ( ( member8757157785044589968at_nat @ Y @ A2 )
         => ( ( ( equiv_8408515162552411438at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) @ R )
              = ( equiv_8408515162552411438at_nat @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) @ R ) )
            = ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff2
thf(fact_733_eq__equiv__class__iff2,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X: a,Y: a] :
      ( ( equiv_equiv_a @ A2 @ R )
     => ( ( member_a @ X @ A2 )
       => ( ( member_a @ Y @ A2 )
         => ( ( ( equiv_quotient_a @ ( insert_a @ X @ bot_bot_set_a ) @ R )
              = ( equiv_quotient_a @ ( insert_a @ Y @ bot_bot_set_a ) @ R ) )
            = ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff2
thf(fact_734_eq__equiv__class__iff2,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( member3157015407008874800od_o_o @ X @ A2 )
       => ( ( member3157015407008874800od_o_o @ Y @ A2 )
         => ( ( ( equiv_3134926782319234254od_o_o @ ( insert3817420688681518039od_o_o @ X @ bot_bo8006819982598807891od_o_o ) @ R )
              = ( equiv_3134926782319234254od_o_o @ ( insert3817420688681518039od_o_o @ Y @ bot_bo8006819982598807891od_o_o ) @ R ) )
            = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff2
thf(fact_735_eq__equiv__class__iff2,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( member2643936169264416010at_nat @ X @ A2 )
       => ( ( member2643936169264416010at_nat @ Y @ A2 )
         => ( ( ( equiv_7923377459618294184at_nat @ ( insert9200635055090092081at_nat @ X @ bot_bo3083307316010499117at_nat ) @ R )
              = ( equiv_7923377459618294184at_nat @ ( insert9200635055090092081at_nat @ Y @ bot_bo3083307316010499117at_nat ) @ R ) )
            = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R ) ) ) ) ) ).

% eq_equiv_class_iff2
thf(fact_736_wo__rel_Omax2__equals1,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ A @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ B @ ( field_5121862139100741428od_o_o @ R ) )
         => ( ( ( bNF_We5307229915971165237od_o_o @ R @ A @ B )
              = A )
            = ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ B @ A ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals1
thf(fact_737_wo__rel_Omax2__equals1,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat,B: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( member4095101504841534314at_nat @ A @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( member4095101504841534314at_nat @ B @ ( field_7361900449976055182at_nat @ R ) )
         => ( ( ( bNF_We7253295970193759759at_nat @ R @ A @ B )
              = A )
            = ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ B @ A ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals1
thf(fact_738_wo__rel_Omax2__equals1,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ B @ ( field_2862844103579723188at_nat @ R ) )
         => ( ( ( bNF_We1807050579049552309at_nat @ R @ A @ B )
              = A )
            = ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ B @ A ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals1
thf(fact_739_wo__rel_Omax2__equals1,axiom,
    ! [R: set_Product_prod_a_a,A: a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( member_a @ A @ ( field_a @ R ) )
       => ( ( member_a @ B @ ( field_a @ R ) )
         => ( ( ( bNF_We3763454674811381836max2_a @ R @ A @ B )
              = A )
            = ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B @ A ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals1
thf(fact_740_wo__rel_Omax2__equals1,axiom,
    ! [R: set_Product_prod_o_o,A: $o,B: $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ( member_o @ A @ ( field_o @ R ) )
       => ( ( member_o @ B @ ( field_o @ R ) )
         => ( ( ( bNF_We3104086342435940326max2_o @ R @ A @ B )
              = A )
            = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals1
thf(fact_741_wo__rel_Omax2__equals1,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ( member_nat @ A @ ( field_nat @ R ) )
       => ( ( member_nat @ B @ ( field_nat @ R ) )
         => ( ( ( bNF_We2380939065524664066x2_nat @ R @ A @ B )
              = A )
            = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals1
thf(fact_742_wo__rel_Omax2__equals1,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( member3157015407008874800od_o_o @ A @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( member3157015407008874800od_o_o @ B @ ( field_6101175518749917524od_o_o @ R ) )
         => ( ( ( bNF_We9141258785624724309od_o_o @ R @ A @ B )
              = A )
            = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ A ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals1
thf(fact_743_wo__rel_Omax2__equals1,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( member2643936169264416010at_nat @ A @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( member2643936169264416010at_nat @ B @ ( field_3145993188331922222at_nat @ R ) )
         => ( ( ( bNF_We6094461251688579247at_nat @ R @ A @ B )
              = A )
            = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ A ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals1
thf(fact_744_wo__rel_Omax2__equals2,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ A @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ B @ ( field_5121862139100741428od_o_o @ R ) )
         => ( ( ( bNF_We5307229915971165237od_o_o @ R @ A @ B )
              = B )
            = ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ B ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals2
thf(fact_745_wo__rel_Omax2__equals2,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat,B: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( member4095101504841534314at_nat @ A @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( member4095101504841534314at_nat @ B @ ( field_7361900449976055182at_nat @ R ) )
         => ( ( ( bNF_We7253295970193759759at_nat @ R @ A @ B )
              = B )
            = ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ B ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals2
thf(fact_746_wo__rel_Omax2__equals2,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ B @ ( field_2862844103579723188at_nat @ R ) )
         => ( ( ( bNF_We1807050579049552309at_nat @ R @ A @ B )
              = B )
            = ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals2
thf(fact_747_wo__rel_Omax2__equals2,axiom,
    ! [R: set_Product_prod_a_a,A: a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( member_a @ A @ ( field_a @ R ) )
       => ( ( member_a @ B @ ( field_a @ R ) )
         => ( ( ( bNF_We3763454674811381836max2_a @ R @ A @ B )
              = B )
            = ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals2
thf(fact_748_wo__rel_Omax2__equals2,axiom,
    ! [R: set_Product_prod_o_o,A: $o,B: $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ( member_o @ A @ ( field_o @ R ) )
       => ( ( member_o @ B @ ( field_o @ R ) )
         => ( ( ( bNF_We3104086342435940326max2_o @ R @ A @ B )
              = B )
            = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals2
thf(fact_749_wo__rel_Omax2__equals2,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ( member_nat @ A @ ( field_nat @ R ) )
       => ( ( member_nat @ B @ ( field_nat @ R ) )
         => ( ( ( bNF_We2380939065524664066x2_nat @ R @ A @ B )
              = B )
            = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals2
thf(fact_750_wo__rel_Omax2__equals2,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( member3157015407008874800od_o_o @ A @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( member3157015407008874800od_o_o @ B @ ( field_6101175518749917524od_o_o @ R ) )
         => ( ( ( bNF_We9141258785624724309od_o_o @ R @ A @ B )
              = B )
            = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals2
thf(fact_751_wo__rel_Omax2__equals2,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( member2643936169264416010at_nat @ A @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( member2643936169264416010at_nat @ B @ ( field_3145993188331922222at_nat @ R ) )
         => ( ( ( bNF_We6094461251688579247at_nat @ R @ A @ B )
              = B )
            = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) ) ) ) ) ).

% wo_rel.max2_equals2
thf(fact_752_wo__rel_Omax2__greater,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ A @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ B @ ( field_5121862139100741428od_o_o @ R ) )
         => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ ( bNF_We5307229915971165237od_o_o @ R @ A @ B ) ) @ R )
            & ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ B @ ( bNF_We5307229915971165237od_o_o @ R @ A @ B ) ) @ R ) ) ) ) ) ).

% wo_rel.max2_greater
thf(fact_753_wo__rel_Omax2__greater,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat,B: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( member4095101504841534314at_nat @ A @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( member4095101504841534314at_nat @ B @ ( field_7361900449976055182at_nat @ R ) )
         => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ ( bNF_We7253295970193759759at_nat @ R @ A @ B ) ) @ R )
            & ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ B @ ( bNF_We7253295970193759759at_nat @ R @ A @ B ) ) @ R ) ) ) ) ) ).

% wo_rel.max2_greater
thf(fact_754_wo__rel_Omax2__greater,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ B @ ( field_2862844103579723188at_nat @ R ) )
         => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ ( bNF_We1807050579049552309at_nat @ R @ A @ B ) ) @ R )
            & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ B @ ( bNF_We1807050579049552309at_nat @ R @ A @ B ) ) @ R ) ) ) ) ) ).

% wo_rel.max2_greater
thf(fact_755_wo__rel_Omax2__greater,axiom,
    ! [R: set_Product_prod_a_a,A: a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( member_a @ A @ ( field_a @ R ) )
       => ( ( member_a @ B @ ( field_a @ R ) )
         => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ ( bNF_We3763454674811381836max2_a @ R @ A @ B ) ) @ R )
            & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B @ ( bNF_We3763454674811381836max2_a @ R @ A @ B ) ) @ R ) ) ) ) ) ).

% wo_rel.max2_greater
thf(fact_756_wo__rel_Omax2__greater,axiom,
    ! [R: set_Product_prod_o_o,A: $o,B: $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ( member_o @ A @ ( field_o @ R ) )
       => ( ( member_o @ B @ ( field_o @ R ) )
         => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ ( bNF_We3104086342435940326max2_o @ R @ A @ B ) ) @ R )
            & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ ( bNF_We3104086342435940326max2_o @ R @ A @ B ) ) @ R ) ) ) ) ) ).

% wo_rel.max2_greater
thf(fact_757_wo__rel_Omax2__greater,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ( member_nat @ A @ ( field_nat @ R ) )
       => ( ( member_nat @ B @ ( field_nat @ R ) )
         => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ ( bNF_We2380939065524664066x2_nat @ R @ A @ B ) ) @ R )
            & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ ( bNF_We2380939065524664066x2_nat @ R @ A @ B ) ) @ R ) ) ) ) ) ).

% wo_rel.max2_greater
thf(fact_758_wo__rel_Omax2__greater,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( member3157015407008874800od_o_o @ A @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( member3157015407008874800od_o_o @ B @ ( field_6101175518749917524od_o_o @ R ) )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ ( bNF_We9141258785624724309od_o_o @ R @ A @ B ) ) @ R )
            & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ ( bNF_We9141258785624724309od_o_o @ R @ A @ B ) ) @ R ) ) ) ) ) ).

% wo_rel.max2_greater
thf(fact_759_wo__rel_Omax2__greater,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( member2643936169264416010at_nat @ A @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( member2643936169264416010at_nat @ B @ ( field_3145993188331922222at_nat @ R ) )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ ( bNF_We6094461251688579247at_nat @ R @ A @ B ) ) @ R )
            & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ ( bNF_We6094461251688579247at_nat @ R @ A @ B ) ) @ R ) ) ) ) ) ).

% wo_rel.max2_greater
thf(fact_760_equiv__class__nondisjoint,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X: produc2934264451710624999od_o_o,A: produc2934264451710624999od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( equiv_3398664326906728093od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ X @ ( inf_in6630186493572433077od_o_o @ ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ A @ bot_bo498831808395348787od_o_o ) ) @ ( image_1313870842500862867od_o_o @ R @ ( insert3855699742481506999od_o_o @ B @ bot_bo498831808395348787od_o_o ) ) ) )
       => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ B ) @ R ) ) ) ).

% equiv_class_nondisjoint
thf(fact_761_equiv__class__nondisjoint,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X: produc732395585841259969at_nat,A: produc732395585841259969at_nat,B: produc732395585841259969at_nat] :
      ( ( equiv_2520666332425567351at_nat @ A2 @ R )
     => ( ( member4095101504841534314at_nat @ X @ ( inf_in3075509010647812879at_nat @ ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ A @ bot_bo1676454896636820109at_nat ) ) @ ( image_1966035174115581203at_nat @ R @ ( insert8109617542356073361at_nat @ B @ bot_bo1676454896636820109at_nat ) ) ) )
       => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ B ) @ R ) ) ) ).

% equiv_class_nondisjoint
thf(fact_762_equiv__class__nondisjoint,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X: produc3843707927480180839at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
      ( ( equiv_4443766944827089949at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ X @ ( inf_in7913087082777306421at_nat @ ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) @ ( image_3736809421353964435at_nat @ R @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) ) )
       => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R ) ) ) ).

% equiv_class_nondisjoint
thf(fact_763_equiv__class__nondisjoint,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X: a,A: a,B: a] :
      ( ( equiv_equiv_a @ A2 @ R )
     => ( ( member_a @ X @ ( inf_inf_set_a @ ( image_a_a @ R @ ( insert_a @ A @ bot_bot_set_a ) ) @ ( image_a_a @ R @ ( insert_a @ B @ bot_bot_set_a ) ) ) )
       => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B ) @ R ) ) ) ).

% equiv_class_nondisjoint
thf(fact_764_equiv__class__nondisjoint,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( equiv_4332955795722587581od_o_o @ A2 @ R )
     => ( ( member3157015407008874800od_o_o @ X @ ( inf_in8747346010413679829od_o_o @ ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ A @ bot_bo8006819982598807891od_o_o ) ) @ ( image_3256184292080368531od_o_o @ R @ ( insert3817420688681518039od_o_o @ B @ bot_bo8006819982598807891od_o_o ) ) ) )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R ) ) ) ).

% equiv_class_nondisjoint
thf(fact_765_equiv__class__nondisjoint,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( equiv_6458487239543531287at_nat @ A2 @ R )
     => ( ( member2643936169264416010at_nat @ X @ ( inf_in767997467307849391at_nat @ ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ A @ bot_bo3083307316010499117at_nat ) ) @ ( image_3892192845344445203at_nat @ R @ ( insert9200635055090092081at_nat @ B @ bot_bo3083307316010499117at_nat ) ) ) )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) ) ) ).

% equiv_class_nondisjoint
thf(fact_766_under__incr,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( trans_7029024365671003047od_o_o @ top_to1478448522960722999od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
       => ( ord_le2654036014095304327od_o_o @ ( order_8825441150112336748od_o_o @ R @ A ) @ ( order_8825441150112336748od_o_o @ R @ B ) ) ) ) ).

% under_incr
thf(fact_767_under__incr,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( trans_3732288485672914945at_nat @ top_to7629004291339433233at_nat @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
       => ( ord_le2077887516847798113at_nat @ ( order_8557040927991152966at_nat @ R @ A ) @ ( order_8557040927991152966at_nat @ R @ B ) ) ) ) ).

% under_incr
thf(fact_768_under__incr,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
      ( ( trans_on_nat @ top_top_set_nat @ R )
     => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
       => ( ord_less_eq_set_nat @ ( order_under_nat @ R @ A ) @ ( order_under_nat @ R @ B ) ) ) ) ).

% under_incr
thf(fact_769_Linear__order__Well__order__iff,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( order_6238756238976269133r_on_o @ ( field_o @ R ) @ R )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
        = ( ! [A7: set_o] :
              ( ( ord_less_eq_set_o @ A7 @ ( field_o @ R ) )
             => ( ( A7 != bot_bot_set_o )
               => ? [X2: $o] :
                    ( ( member_o @ X2 @ A7 )
                    & ! [Y2: $o] :
                        ( ( member_o @ Y2 @ A7 )
                       => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y2 ) @ R ) ) ) ) ) ) ) ) ).

% Linear_order_Well_order_iff
thf(fact_770_Linear__order__Well__order__iff,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( order_4473980167227706203on_nat @ ( field_nat @ R ) @ R )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
        = ( ! [A7: set_nat] :
              ( ( ord_less_eq_set_nat @ A7 @ ( field_nat @ R ) )
             => ( ( A7 != bot_bot_set_nat )
               => ? [X2: nat] :
                    ( ( member_nat @ X2 @ A7 )
                    & ! [Y2: nat] :
                        ( ( member_nat @ Y2 @ A7 )
                       => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ R ) ) ) ) ) ) ) ) ).

% Linear_order_Well_order_iff
thf(fact_771_Linear__order__Well__order__iff,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ( order_2625247082195685180od_o_o @ ( field_6101175518749917524od_o_o @ R ) @ R )
     => ( ( order_3767514495197212837od_o_o @ ( field_6101175518749917524od_o_o @ R ) @ R )
        = ( ! [A7: set_se491199571785101031od_o_o] :
              ( ( ord_le2654036014095304327od_o_o @ A7 @ ( field_6101175518749917524od_o_o @ R ) )
             => ( ( A7 != bot_bo8006819982598807891od_o_o )
               => ? [X2: set_Product_prod_o_o] :
                    ( ( member3157015407008874800od_o_o @ X2 @ A7 )
                    & ! [Y2: set_Product_prod_o_o] :
                        ( ( member3157015407008874800od_o_o @ Y2 @ A7 )
                       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Y2 ) @ R ) ) ) ) ) ) ) ) ).

% Linear_order_Well_order_iff
thf(fact_772_Linear__order__Well__order__iff,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ( order_5942792088423767318at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
     => ( ( order_1968183844437341695at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
        = ( ! [A7: set_se7855581050983116737at_nat] :
              ( ( ord_le2077887516847798113at_nat @ A7 @ ( field_3145993188331922222at_nat @ R ) )
             => ( ( A7 != bot_bo3083307316010499117at_nat )
               => ? [X2: set_Pr1261947904930325089at_nat] :
                    ( ( member2643936169264416010at_nat @ X2 @ A7 )
                    & ! [Y2: set_Pr1261947904930325089at_nat] :
                        ( ( member2643936169264416010at_nat @ Y2 @ A7 )
                       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y2 ) @ R ) ) ) ) ) ) ) ) ).

% Linear_order_Well_order_iff
thf(fact_773_well__order__on__domain,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( order_2783320356396525957od_o_o @ A2 @ R )
     => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ B ) @ R )
       => ( ( member444158400953824016od_o_o @ A @ A2 )
          & ( member444158400953824016od_o_o @ B @ A2 ) ) ) ) ).

% well_order_on_domain
thf(fact_774_well__order__on__domain,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat,B: produc732395585841259969at_nat] :
      ( ( order_1951249980326167391at_nat @ A2 @ R )
     => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ B ) @ R )
       => ( ( member4095101504841534314at_nat @ A @ A2 )
          & ( member4095101504841534314at_nat @ B @ A2 ) ) ) ) ).

% well_order_on_domain
thf(fact_775_well__order__on__domain,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
      ( ( order_2339240034117818117at_nat @ A2 @ R )
     => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R )
       => ( ( member8757157785044589968at_nat @ A @ A2 )
          & ( member8757157785044589968at_nat @ B @ A2 ) ) ) ) ).

% well_order_on_domain
thf(fact_776_well__order__on__domain,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,A: a,B: a] :
      ( ( order_6972113574731384220r_on_a @ A2 @ R )
     => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B ) @ R )
       => ( ( member_a @ A @ A2 )
          & ( member_a @ B @ A2 ) ) ) ) ).

% well_order_on_domain
thf(fact_777_well__order__on__domain,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( order_3767514495197212837od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
       => ( ( member3157015407008874800od_o_o @ A @ A2 )
          & ( member3157015407008874800od_o_o @ B @ A2 ) ) ) ) ).

% well_order_on_domain
thf(fact_778_well__order__on__domain,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( order_1968183844437341695at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
       => ( ( member2643936169264416010at_nat @ A @ A2 )
          & ( member2643936169264416010at_nat @ B @ A2 ) ) ) ) ).

% well_order_on_domain
thf(fact_779_underS__incl__iff,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( order_91209724698019100od_o_o @ ( field_5121862139100741428od_o_o @ R ) @ R )
     => ( ( member444158400953824016od_o_o @ A @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ B @ ( field_5121862139100741428od_o_o @ R ) )
         => ( ( ord_le7586318239878589543od_o_o @ ( order_1929855754104155309od_o_o @ R @ A ) @ ( order_1929855754104155309od_o_o @ R @ B ) )
            = ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_780_underS__incl__iff,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat,B: produc732395585841259969at_nat] :
      ( ( order_9086815480479278966at_nat @ ( field_7361900449976055182at_nat @ R ) @ R )
     => ( ( member4095101504841534314at_nat @ A @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( member4095101504841534314at_nat @ B @ ( field_7361900449976055182at_nat @ R ) )
         => ( ( ord_le4841768313324958145at_nat @ ( order_6745690092771398279at_nat @ R @ A ) @ ( order_6745690092771398279at_nat @ R @ B ) )
            = ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_781_underS__incl__iff,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
      ( ( order_2711500226769404828at_nat @ ( field_2862844103579723188at_nat @ R ) @ R )
     => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ B @ ( field_2862844103579723188at_nat @ R ) )
         => ( ( ord_le1268244103169919719at_nat @ ( order_3736018788886245933at_nat @ R @ A ) @ ( order_3736018788886245933at_nat @ R @ B ) )
            = ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_782_underS__incl__iff,axiom,
    ! [R: set_Product_prod_a_a,A: a,B: a] :
      ( ( order_8768733634509060147r_on_a @ ( field_a @ R ) @ R )
     => ( ( member_a @ A @ ( field_a @ R ) )
       => ( ( member_a @ B @ ( field_a @ R ) )
         => ( ( ord_less_eq_set_a @ ( order_underS_a @ R @ A ) @ ( order_underS_a @ R @ B ) )
            = ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_783_underS__incl__iff,axiom,
    ! [R: set_Product_prod_o_o,A: $o,B: $o] :
      ( ( order_6238756238976269133r_on_o @ ( field_o @ R ) @ R )
     => ( ( member_o @ A @ ( field_o @ R ) )
       => ( ( member_o @ B @ ( field_o @ R ) )
         => ( ( ord_less_eq_set_o @ ( order_underS_o @ R @ A ) @ ( order_underS_o @ R @ B ) )
            = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_784_underS__incl__iff,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
      ( ( order_4473980167227706203on_nat @ ( field_nat @ R ) @ R )
     => ( ( member_nat @ A @ ( field_nat @ R ) )
       => ( ( member_nat @ B @ ( field_nat @ R ) )
         => ( ( ord_less_eq_set_nat @ ( order_underS_nat @ R @ A ) @ ( order_underS_nat @ R @ B ) )
            = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_785_underS__incl__iff,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( order_2625247082195685180od_o_o @ ( field_6101175518749917524od_o_o @ R ) @ R )
     => ( ( member3157015407008874800od_o_o @ A @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( member3157015407008874800od_o_o @ B @ ( field_6101175518749917524od_o_o @ R ) )
         => ( ( ord_le2654036014095304327od_o_o @ ( order_3915675016455977933od_o_o @ R @ A ) @ ( order_3915675016455977933od_o_o @ R @ B ) )
            = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_786_underS__incl__iff,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( order_5942792088423767318at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
     => ( ( member2643936169264416010at_nat @ A @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( member2643936169264416010at_nat @ B @ ( field_3145993188331922222at_nat @ R ) )
         => ( ( ord_le2077887516847798113at_nat @ ( order_2644262826035875111at_nat @ R @ A ) @ ( order_2644262826035875111at_nat @ R @ B ) )
            = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_787_max__ext_Omax__extI,axiom,
    ! [X8: set_Pr1932065953672099015od_o_o,Y5: set_Pr1932065953672099015od_o_o,R3: set_Pr1013884327308616903od_o_o] :
      ( ( finite820925532130942480od_o_o @ X8 )
     => ( ( finite820925532130942480od_o_o @ Y5 )
       => ( ( Y5 != bot_bo498831808395348787od_o_o )
         => ( ! [X3: produc2934264451710624999od_o_o] :
                ( ( member444158400953824016od_o_o @ X3 @ X8 )
               => ? [Xa: produc2934264451710624999od_o_o] :
                    ( ( member444158400953824016od_o_o @ Xa @ Y5 )
                    & ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X3 @ Xa ) @ R3 ) ) )
           => ( member3740103928775426832od_o_o @ ( produc2282539314773629783od_o_o @ X8 @ Y5 ) @ ( max_ex9141845325704764834od_o_o @ R3 ) ) ) ) ) ) ).

% max_ext.max_extI
thf(fact_788_max__ext_Omax__extI,axiom,
    ! [X8: set_Pr457366540195662369at_nat,Y5: set_Pr457366540195662369at_nat,R3: set_Pr4427867301352232263at_nat] :
      ( ( finite8072506237346428522at_nat @ X8 )
     => ( ( finite8072506237346428522at_nat @ Y5 )
       => ( ( Y5 != bot_bo1676454896636820109at_nat )
         => ( ! [X3: produc732395585841259969at_nat] :
                ( ( member4095101504841534314at_nat @ X3 @ X8 )
               => ? [Xa: produc732395585841259969at_nat] :
                    ( ( member4095101504841534314at_nat @ Xa @ Y5 )
                    & ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X3 @ Xa ) @ R3 ) ) )
           => ( member7768518508883498896at_nat @ ( produc4325049062531119319at_nat @ X8 @ Y5 ) @ ( max_ex1111939896555521276at_nat @ R3 ) ) ) ) ) ) ).

% max_ext.max_extI
thf(fact_789_max__ext_Omax__extI,axiom,
    ! [X8: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat,R3: set_Pr5564308138774400199at_nat] :
      ( ( finite4343798906461161616at_nat @ X8 )
     => ( ( finite4343798906461161616at_nat @ Y5 )
       => ( ( Y5 != bot_bo228742789529271731at_nat )
         => ( ! [X3: produc3843707927480180839at_nat] :
                ( ( member8757157785044589968at_nat @ X3 @ X8 )
               => ? [Xa: produc3843707927480180839at_nat] :
                    ( ( member8757157785044589968at_nat @ Xa @ Y5 )
                    & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X3 @ Xa ) @ R3 ) ) )
           => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X8 @ Y5 ) @ ( max_ex8833738776070432290at_nat @ R3 ) ) ) ) ) ) ).

% max_ext.max_extI
thf(fact_790_max__ext_Omax__extI,axiom,
    ! [X8: set_a,Y5: set_a,R3: set_Product_prod_a_a] :
      ( ( finite_finite_a @ X8 )
     => ( ( finite_finite_a @ Y5 )
       => ( ( Y5 != bot_bot_set_a )
         => ( ! [X3: a] :
                ( ( member_a @ X3 @ X8 )
               => ? [Xa: a] :
                    ( ( member_a @ Xa @ Y5 )
                    & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X3 @ Xa ) @ R3 ) ) )
           => ( member7983343339038529360_set_a @ ( produc9088192753505129239_set_a @ X8 @ Y5 ) @ ( max_ext_a @ R3 ) ) ) ) ) ) ).

% max_ext.max_extI
thf(fact_791_max__ext_Omax__extI,axiom,
    ! [X8: set_Product_prod_o_o,Y5: set_Product_prod_o_o,R3: set_Pr7011910401827753159od_o_o] :
      ( ( finite6120865539452801872od_o_o @ X8 )
     => ( ( finite6120865539452801872od_o_o @ Y5 )
       => ( ( Y5 != bot_bo7073875226086086771od_o_o )
         => ( ! [X3: product_prod_o_o] :
                ( ( member7466972457876170832od_o_o @ X3 @ X8 )
               => ? [Xa: product_prod_o_o] :
                    ( ( member7466972457876170832od_o_o @ Xa @ Y5 )
                    & ( member3169104723136097040od_o_o @ ( produc3331439552374987607od_o_o @ X3 @ Xa ) @ R3 ) ) )
           => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X8 @ Y5 ) @ ( max_ex7572203241849361634od_o_o @ R3 ) ) ) ) ) ) ).

% max_ext.max_extI
thf(fact_792_max__ext_Omax__extI,axiom,
    ! [X8: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat,R3: set_Pr8693737435421807431at_nat] :
      ( ( finite6177210948735845034at_nat @ X8 )
     => ( ( finite6177210948735845034at_nat @ Y5 )
       => ( ( Y5 != bot_bo2099793752762293965at_nat )
         => ( ! [X3: product_prod_nat_nat] :
                ( ( member8440522571783428010at_nat @ X3 @ X8 )
               => ? [Xa: product_prod_nat_nat] :
                    ( ( member8440522571783428010at_nat @ Xa @ Y5 )
                    & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Xa ) @ R3 ) ) )
           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X8 @ Y5 ) @ ( max_ex8135407076693332796at_nat @ R3 ) ) ) ) ) ) ).

% max_ext.max_extI
thf(fact_793_max__ext_Omax__extI,axiom,
    ! [X8: set_se491199571785101031od_o_o,Y5: set_se491199571785101031od_o_o,R3: set_Pr1932065953672099015od_o_o] :
      ( ( finite9011636195296603184od_o_o @ X8 )
     => ( ( finite9011636195296603184od_o_o @ Y5 )
       => ( ( Y5 != bot_bo8006819982598807891od_o_o )
         => ( ! [X3: set_Product_prod_o_o] :
                ( ( member3157015407008874800od_o_o @ X3 @ X8 )
               => ? [Xa: set_Product_prod_o_o] :
                    ( ( member3157015407008874800od_o_o @ Xa @ Y5 )
                    & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Xa ) @ R3 ) ) )
           => ( member9169340693537962768od_o_o @ ( produc4478624491032480599od_o_o @ X8 @ Y5 ) @ ( max_ex5401630698724402626od_o_o @ R3 ) ) ) ) ) ) ).

% max_ext.max_extI
thf(fact_794_max__ext_Omax__extI,axiom,
    ! [X8: set_se7855581050983116737at_nat,Y5: set_se7855581050983116737at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( ( finite9047747110432174090at_nat @ X8 )
     => ( ( finite9047747110432174090at_nat @ Y5 )
       => ( ( Y5 != bot_bo3083307316010499117at_nat )
         => ( ! [X3: set_Pr1261947904930325089at_nat] :
                ( ( member2643936169264416010at_nat @ X3 @ X8 )
               => ? [Xa: set_Pr1261947904930325089at_nat] :
                    ( ( member2643936169264416010at_nat @ Xa @ Y5 )
                    & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Xa ) @ R3 ) ) )
           => ( member4300370950623927696at_nat @ ( produc7462898802507495127at_nat @ X8 @ Y5 ) @ ( max_ex4535816423174879388at_nat @ R3 ) ) ) ) ) ) ).

% max_ext.max_extI
thf(fact_795_max__ext_Osimps,axiom,
    ! [A1: set_Pr1932065953672099015od_o_o,A22: set_Pr1932065953672099015od_o_o,R3: set_Pr1013884327308616903od_o_o] :
      ( ( member3740103928775426832od_o_o @ ( produc2282539314773629783od_o_o @ A1 @ A22 ) @ ( max_ex9141845325704764834od_o_o @ R3 ) )
      = ( ( finite820925532130942480od_o_o @ A1 )
        & ( finite820925532130942480od_o_o @ A22 )
        & ( A22 != bot_bo498831808395348787od_o_o )
        & ! [X2: produc2934264451710624999od_o_o] :
            ( ( member444158400953824016od_o_o @ X2 @ A1 )
           => ? [Y2: produc2934264451710624999od_o_o] :
                ( ( member444158400953824016od_o_o @ Y2 @ A22 )
                & ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X2 @ Y2 ) @ R3 ) ) ) ) ) ).

% max_ext.simps
thf(fact_796_max__ext_Osimps,axiom,
    ! [A1: set_Pr457366540195662369at_nat,A22: set_Pr457366540195662369at_nat,R3: set_Pr4427867301352232263at_nat] :
      ( ( member7768518508883498896at_nat @ ( produc4325049062531119319at_nat @ A1 @ A22 ) @ ( max_ex1111939896555521276at_nat @ R3 ) )
      = ( ( finite8072506237346428522at_nat @ A1 )
        & ( finite8072506237346428522at_nat @ A22 )
        & ( A22 != bot_bo1676454896636820109at_nat )
        & ! [X2: produc732395585841259969at_nat] :
            ( ( member4095101504841534314at_nat @ X2 @ A1 )
           => ? [Y2: produc732395585841259969at_nat] :
                ( ( member4095101504841534314at_nat @ Y2 @ A22 )
                & ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X2 @ Y2 ) @ R3 ) ) ) ) ) ).

% max_ext.simps
thf(fact_797_max__ext_Osimps,axiom,
    ! [A1: set_Pr4329608150637261639at_nat,A22: set_Pr4329608150637261639at_nat,R3: set_Pr5564308138774400199at_nat] :
      ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A1 @ A22 ) @ ( max_ex8833738776070432290at_nat @ R3 ) )
      = ( ( finite4343798906461161616at_nat @ A1 )
        & ( finite4343798906461161616at_nat @ A22 )
        & ( A22 != bot_bo228742789529271731at_nat )
        & ! [X2: produc3843707927480180839at_nat] :
            ( ( member8757157785044589968at_nat @ X2 @ A1 )
           => ? [Y2: produc3843707927480180839at_nat] :
                ( ( member8757157785044589968at_nat @ Y2 @ A22 )
                & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X2 @ Y2 ) @ R3 ) ) ) ) ) ).

% max_ext.simps
thf(fact_798_max__ext_Osimps,axiom,
    ! [A1: set_a,A22: set_a,R3: set_Product_prod_a_a] :
      ( ( member7983343339038529360_set_a @ ( produc9088192753505129239_set_a @ A1 @ A22 ) @ ( max_ext_a @ R3 ) )
      = ( ( finite_finite_a @ A1 )
        & ( finite_finite_a @ A22 )
        & ( A22 != bot_bot_set_a )
        & ! [X2: a] :
            ( ( member_a @ X2 @ A1 )
           => ? [Y2: a] :
                ( ( member_a @ Y2 @ A22 )
                & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X2 @ Y2 ) @ R3 ) ) ) ) ) ).

% max_ext.simps
thf(fact_799_max__ext_Osimps,axiom,
    ! [A1: set_se491199571785101031od_o_o,A22: set_se491199571785101031od_o_o,R3: set_Pr1932065953672099015od_o_o] :
      ( ( member9169340693537962768od_o_o @ ( produc4478624491032480599od_o_o @ A1 @ A22 ) @ ( max_ex5401630698724402626od_o_o @ R3 ) )
      = ( ( finite9011636195296603184od_o_o @ A1 )
        & ( finite9011636195296603184od_o_o @ A22 )
        & ( A22 != bot_bo8006819982598807891od_o_o )
        & ! [X2: set_Product_prod_o_o] :
            ( ( member3157015407008874800od_o_o @ X2 @ A1 )
           => ? [Y2: set_Product_prod_o_o] :
                ( ( member3157015407008874800od_o_o @ Y2 @ A22 )
                & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Y2 ) @ R3 ) ) ) ) ) ).

% max_ext.simps
thf(fact_800_max__ext_Osimps,axiom,
    ! [A1: set_se7855581050983116737at_nat,A22: set_se7855581050983116737at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( ( member4300370950623927696at_nat @ ( produc7462898802507495127at_nat @ A1 @ A22 ) @ ( max_ex4535816423174879388at_nat @ R3 ) )
      = ( ( finite9047747110432174090at_nat @ A1 )
        & ( finite9047747110432174090at_nat @ A22 )
        & ( A22 != bot_bo3083307316010499117at_nat )
        & ! [X2: set_Pr1261947904930325089at_nat] :
            ( ( member2643936169264416010at_nat @ X2 @ A1 )
           => ? [Y2: set_Pr1261947904930325089at_nat] :
                ( ( member2643936169264416010at_nat @ Y2 @ A22 )
                & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y2 ) @ R3 ) ) ) ) ) ).

% max_ext.simps
thf(fact_801_max__ext_Osimps,axiom,
    ! [A1: set_Product_prod_o_o,A22: set_Product_prod_o_o,R3: set_Pr7011910401827753159od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A1 @ A22 ) @ ( max_ex7572203241849361634od_o_o @ R3 ) )
      = ( ( finite6120865539452801872od_o_o @ A1 )
        & ( finite6120865539452801872od_o_o @ A22 )
        & ( A22 != bot_bo7073875226086086771od_o_o )
        & ! [X2: product_prod_o_o] :
            ( ( member7466972457876170832od_o_o @ X2 @ A1 )
           => ? [Y2: product_prod_o_o] :
                ( ( member7466972457876170832od_o_o @ Y2 @ A22 )
                & ( member3169104723136097040od_o_o @ ( produc3331439552374987607od_o_o @ X2 @ Y2 ) @ R3 ) ) ) ) ) ).

% max_ext.simps
thf(fact_802_max__ext_Osimps,axiom,
    ! [A1: set_Pr1261947904930325089at_nat,A22: set_Pr1261947904930325089at_nat,R3: set_Pr8693737435421807431at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ A22 ) @ ( max_ex8135407076693332796at_nat @ R3 ) )
      = ( ( finite6177210948735845034at_nat @ A1 )
        & ( finite6177210948735845034at_nat @ A22 )
        & ( A22 != bot_bo2099793752762293965at_nat )
        & ! [X2: product_prod_nat_nat] :
            ( ( member8440522571783428010at_nat @ X2 @ A1 )
           => ? [Y2: product_prod_nat_nat] :
                ( ( member8440522571783428010at_nat @ Y2 @ A22 )
                & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y2 ) @ R3 ) ) ) ) ) ).

% max_ext.simps
thf(fact_803_underS__I,axiom,
    ! [I: produc2934264451710624999od_o_o,J: produc2934264451710624999od_o_o,R3: set_Pr1013884327308616903od_o_o] :
      ( ( I != J )
     => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ I @ J ) @ R3 )
       => ( member444158400953824016od_o_o @ I @ ( order_1929855754104155309od_o_o @ R3 @ J ) ) ) ) ).

% underS_I
thf(fact_804_underS__I,axiom,
    ! [I: produc732395585841259969at_nat,J: produc732395585841259969at_nat,R3: set_Pr4427867301352232263at_nat] :
      ( ( I != J )
     => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ I @ J ) @ R3 )
       => ( member4095101504841534314at_nat @ I @ ( order_6745690092771398279at_nat @ R3 @ J ) ) ) ) ).

% underS_I
thf(fact_805_underS__I,axiom,
    ! [I: produc3843707927480180839at_nat,J: produc3843707927480180839at_nat,R3: set_Pr5564308138774400199at_nat] :
      ( ( I != J )
     => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J ) @ R3 )
       => ( member8757157785044589968at_nat @ I @ ( order_3736018788886245933at_nat @ R3 @ J ) ) ) ) ).

% underS_I
thf(fact_806_underS__I,axiom,
    ! [I: a,J: a,R3: set_Product_prod_a_a] :
      ( ( I != J )
     => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ I @ J ) @ R3 )
       => ( member_a @ I @ ( order_underS_a @ R3 @ J ) ) ) ) ).

% underS_I
thf(fact_807_underS__I,axiom,
    ! [I: set_Product_prod_o_o,J: set_Product_prod_o_o,R3: set_Pr1932065953672099015od_o_o] :
      ( ( I != J )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ I @ J ) @ R3 )
       => ( member3157015407008874800od_o_o @ I @ ( order_3915675016455977933od_o_o @ R3 @ J ) ) ) ) ).

% underS_I
thf(fact_808_underS__I,axiom,
    ! [I: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( ( I != J )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J ) @ R3 )
       => ( member2643936169264416010at_nat @ I @ ( order_2644262826035875111at_nat @ R3 @ J ) ) ) ) ).

% underS_I
thf(fact_809_underS__E,axiom,
    ! [I: produc2934264451710624999od_o_o,R3: set_Pr1013884327308616903od_o_o,J: produc2934264451710624999od_o_o] :
      ( ( member444158400953824016od_o_o @ I @ ( order_1929855754104155309od_o_o @ R3 @ J ) )
     => ( ( I != J )
        & ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ I @ J ) @ R3 ) ) ) ).

% underS_E
thf(fact_810_underS__E,axiom,
    ! [I: produc732395585841259969at_nat,R3: set_Pr4427867301352232263at_nat,J: produc732395585841259969at_nat] :
      ( ( member4095101504841534314at_nat @ I @ ( order_6745690092771398279at_nat @ R3 @ J ) )
     => ( ( I != J )
        & ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ I @ J ) @ R3 ) ) ) ).

% underS_E
thf(fact_811_underS__E,axiom,
    ! [I: produc3843707927480180839at_nat,R3: set_Pr5564308138774400199at_nat,J: produc3843707927480180839at_nat] :
      ( ( member8757157785044589968at_nat @ I @ ( order_3736018788886245933at_nat @ R3 @ J ) )
     => ( ( I != J )
        & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J ) @ R3 ) ) ) ).

% underS_E
thf(fact_812_underS__E,axiom,
    ! [I: a,R3: set_Product_prod_a_a,J: a] :
      ( ( member_a @ I @ ( order_underS_a @ R3 @ J ) )
     => ( ( I != J )
        & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ I @ J ) @ R3 ) ) ) ).

% underS_E
thf(fact_813_underS__E,axiom,
    ! [I: set_Product_prod_o_o,R3: set_Pr1932065953672099015od_o_o,J: set_Product_prod_o_o] :
      ( ( member3157015407008874800od_o_o @ I @ ( order_3915675016455977933od_o_o @ R3 @ J ) )
     => ( ( I != J )
        & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ I @ J ) @ R3 ) ) ) ).

% underS_E
thf(fact_814_underS__E,axiom,
    ! [I: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat,J: set_Pr1261947904930325089at_nat] :
      ( ( member2643936169264416010at_nat @ I @ ( order_2644262826035875111at_nat @ R3 @ J ) )
     => ( ( I != J )
        & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J ) @ R3 ) ) ) ).

% underS_E
thf(fact_815_max__ext__additive,axiom,
    ! [A2: set_Product_prod_o_o,B2: set_Product_prod_o_o,R3: set_Pr7011910401827753159od_o_o,C3: set_Product_prod_o_o,D: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A2 @ B2 ) @ ( max_ex7572203241849361634od_o_o @ R3 ) )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ C3 @ D ) @ ( max_ex7572203241849361634od_o_o @ R3 ) )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( sup_su5769328420594410459od_o_o @ A2 @ C3 ) @ ( sup_su5769328420594410459od_o_o @ B2 @ D ) ) @ ( max_ex7572203241849361634od_o_o @ R3 ) ) ) ) ).

% max_ext_additive
thf(fact_816_max__ext__additive,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,R3: set_Pr8693737435421807431at_nat,C3: set_Pr1261947904930325089at_nat,D: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ ( max_ex8135407076693332796at_nat @ R3 ) )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ C3 @ D ) @ ( max_ex8135407076693332796at_nat @ R3 ) )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ C3 ) @ ( sup_su6327502436637775413at_nat @ B2 @ D ) ) @ ( max_ex8135407076693332796at_nat @ R3 ) ) ) ) ).

% max_ext_additive
thf(fact_817_max__ext_Ocases,axiom,
    ! [A1: set_Pr1932065953672099015od_o_o,A22: set_Pr1932065953672099015od_o_o,R3: set_Pr1013884327308616903od_o_o] :
      ( ( member3740103928775426832od_o_o @ ( produc2282539314773629783od_o_o @ A1 @ A22 ) @ ( max_ex9141845325704764834od_o_o @ R3 ) )
     => ~ ( ( finite820925532130942480od_o_o @ A1 )
         => ( ( finite820925532130942480od_o_o @ A22 )
           => ( ( A22 != bot_bo498831808395348787od_o_o )
             => ~ ! [X7: produc2934264451710624999od_o_o] :
                    ( ( member444158400953824016od_o_o @ X7 @ A1 )
                   => ? [Xa2: produc2934264451710624999od_o_o] :
                        ( ( member444158400953824016od_o_o @ Xa2 @ A22 )
                        & ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X7 @ Xa2 ) @ R3 ) ) ) ) ) ) ) ).

% max_ext.cases
thf(fact_818_max__ext_Ocases,axiom,
    ! [A1: set_Pr457366540195662369at_nat,A22: set_Pr457366540195662369at_nat,R3: set_Pr4427867301352232263at_nat] :
      ( ( member7768518508883498896at_nat @ ( produc4325049062531119319at_nat @ A1 @ A22 ) @ ( max_ex1111939896555521276at_nat @ R3 ) )
     => ~ ( ( finite8072506237346428522at_nat @ A1 )
         => ( ( finite8072506237346428522at_nat @ A22 )
           => ( ( A22 != bot_bo1676454896636820109at_nat )
             => ~ ! [X7: produc732395585841259969at_nat] :
                    ( ( member4095101504841534314at_nat @ X7 @ A1 )
                   => ? [Xa2: produc732395585841259969at_nat] :
                        ( ( member4095101504841534314at_nat @ Xa2 @ A22 )
                        & ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X7 @ Xa2 ) @ R3 ) ) ) ) ) ) ) ).

% max_ext.cases
thf(fact_819_max__ext_Ocases,axiom,
    ! [A1: set_Pr4329608150637261639at_nat,A22: set_Pr4329608150637261639at_nat,R3: set_Pr5564308138774400199at_nat] :
      ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A1 @ A22 ) @ ( max_ex8833738776070432290at_nat @ R3 ) )
     => ~ ( ( finite4343798906461161616at_nat @ A1 )
         => ( ( finite4343798906461161616at_nat @ A22 )
           => ( ( A22 != bot_bo228742789529271731at_nat )
             => ~ ! [X7: produc3843707927480180839at_nat] :
                    ( ( member8757157785044589968at_nat @ X7 @ A1 )
                   => ? [Xa2: produc3843707927480180839at_nat] :
                        ( ( member8757157785044589968at_nat @ Xa2 @ A22 )
                        & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X7 @ Xa2 ) @ R3 ) ) ) ) ) ) ) ).

% max_ext.cases
thf(fact_820_max__ext_Ocases,axiom,
    ! [A1: set_a,A22: set_a,R3: set_Product_prod_a_a] :
      ( ( member7983343339038529360_set_a @ ( produc9088192753505129239_set_a @ A1 @ A22 ) @ ( max_ext_a @ R3 ) )
     => ~ ( ( finite_finite_a @ A1 )
         => ( ( finite_finite_a @ A22 )
           => ( ( A22 != bot_bot_set_a )
             => ~ ! [X7: a] :
                    ( ( member_a @ X7 @ A1 )
                   => ? [Xa2: a] :
                        ( ( member_a @ Xa2 @ A22 )
                        & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X7 @ Xa2 ) @ R3 ) ) ) ) ) ) ) ).

% max_ext.cases
thf(fact_821_max__ext_Ocases,axiom,
    ! [A1: set_se491199571785101031od_o_o,A22: set_se491199571785101031od_o_o,R3: set_Pr1932065953672099015od_o_o] :
      ( ( member9169340693537962768od_o_o @ ( produc4478624491032480599od_o_o @ A1 @ A22 ) @ ( max_ex5401630698724402626od_o_o @ R3 ) )
     => ~ ( ( finite9011636195296603184od_o_o @ A1 )
         => ( ( finite9011636195296603184od_o_o @ A22 )
           => ( ( A22 != bot_bo8006819982598807891od_o_o )
             => ~ ! [X7: set_Product_prod_o_o] :
                    ( ( member3157015407008874800od_o_o @ X7 @ A1 )
                   => ? [Xa2: set_Product_prod_o_o] :
                        ( ( member3157015407008874800od_o_o @ Xa2 @ A22 )
                        & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X7 @ Xa2 ) @ R3 ) ) ) ) ) ) ) ).

% max_ext.cases
thf(fact_822_max__ext_Ocases,axiom,
    ! [A1: set_se7855581050983116737at_nat,A22: set_se7855581050983116737at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( ( member4300370950623927696at_nat @ ( produc7462898802507495127at_nat @ A1 @ A22 ) @ ( max_ex4535816423174879388at_nat @ R3 ) )
     => ~ ( ( finite9047747110432174090at_nat @ A1 )
         => ( ( finite9047747110432174090at_nat @ A22 )
           => ( ( A22 != bot_bo3083307316010499117at_nat )
             => ~ ! [X7: set_Pr1261947904930325089at_nat] :
                    ( ( member2643936169264416010at_nat @ X7 @ A1 )
                   => ? [Xa2: set_Pr1261947904930325089at_nat] :
                        ( ( member2643936169264416010at_nat @ Xa2 @ A22 )
                        & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X7 @ Xa2 ) @ R3 ) ) ) ) ) ) ) ).

% max_ext.cases
thf(fact_823_max__ext_Ocases,axiom,
    ! [A1: set_Product_prod_o_o,A22: set_Product_prod_o_o,R3: set_Pr7011910401827753159od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A1 @ A22 ) @ ( max_ex7572203241849361634od_o_o @ R3 ) )
     => ~ ( ( finite6120865539452801872od_o_o @ A1 )
         => ( ( finite6120865539452801872od_o_o @ A22 )
           => ( ( A22 != bot_bo7073875226086086771od_o_o )
             => ~ ! [X7: product_prod_o_o] :
                    ( ( member7466972457876170832od_o_o @ X7 @ A1 )
                   => ? [Xa2: product_prod_o_o] :
                        ( ( member7466972457876170832od_o_o @ Xa2 @ A22 )
                        & ( member3169104723136097040od_o_o @ ( produc3331439552374987607od_o_o @ X7 @ Xa2 ) @ R3 ) ) ) ) ) ) ) ).

% max_ext.cases
thf(fact_824_max__ext_Ocases,axiom,
    ! [A1: set_Pr1261947904930325089at_nat,A22: set_Pr1261947904930325089at_nat,R3: set_Pr8693737435421807431at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ A22 ) @ ( max_ex8135407076693332796at_nat @ R3 ) )
     => ~ ( ( finite6177210948735845034at_nat @ A1 )
         => ( ( finite6177210948735845034at_nat @ A22 )
           => ( ( A22 != bot_bo2099793752762293965at_nat )
             => ~ ! [X7: product_prod_nat_nat] :
                    ( ( member8440522571783428010at_nat @ X7 @ A1 )
                   => ? [Xa2: product_prod_nat_nat] :
                        ( ( member8440522571783428010at_nat @ Xa2 @ A22 )
                        & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X7 @ Xa2 ) @ R3 ) ) ) ) ) ) ) ).

% max_ext.cases
thf(fact_825_underS__incr,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B: set_Product_prod_o_o] :
      ( ( trans_7029024365671003047od_o_o @ top_to1478448522960722999od_o_o @ R )
     => ( ( antisy777991898044409578od_o_o @ top_to1478448522960722999od_o_o @ R )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
         => ( ord_le2654036014095304327od_o_o @ ( order_3915675016455977933od_o_o @ R @ A ) @ ( order_3915675016455977933od_o_o @ R @ B ) ) ) ) ) ).

% underS_incr
thf(fact_826_underS__incr,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( trans_3732288485672914945at_nat @ top_to7629004291339433233at_nat @ R )
     => ( ( antisy1130263102092445124at_nat @ top_to7629004291339433233at_nat @ R )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
         => ( ord_le2077887516847798113at_nat @ ( order_2644262826035875111at_nat @ R @ A ) @ ( order_2644262826035875111at_nat @ R @ B ) ) ) ) ) ).

% underS_incr
thf(fact_827_underS__incr,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat,B: nat] :
      ( ( trans_on_nat @ top_top_set_nat @ R )
     => ( ( antisym_on_nat @ top_top_set_nat @ R )
       => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
         => ( ord_less_eq_set_nat @ ( order_underS_nat @ R @ A ) @ ( order_underS_nat @ R @ B ) ) ) ) ) ).

% underS_incr
thf(fact_828_wo__rel_OisMinim__def,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A2: set_Pr1932065953672099015od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( bNF_We6886001019485585053od_o_o @ R @ A2 @ B )
        = ( ( member444158400953824016od_o_o @ B @ A2 )
          & ! [X2: produc2934264451710624999od_o_o] :
              ( ( member444158400953824016od_o_o @ X2 @ A2 )
             => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ B @ X2 ) @ R ) ) ) ) ) ).

% wo_rel.isMinim_def
thf(fact_829_wo__rel_OisMinim__def,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A2: set_Pr457366540195662369at_nat,B: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( bNF_We6170040095471856759at_nat @ R @ A2 @ B )
        = ( ( member4095101504841534314at_nat @ B @ A2 )
          & ! [X2: produc732395585841259969at_nat] :
              ( ( member4095101504841534314at_nat @ X2 @ A2 )
             => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ B @ X2 ) @ R ) ) ) ) ) ).

% wo_rel.isMinim_def
thf(fact_830_wo__rel_OisMinim__def,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A2: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( bNF_We2939539520719410205at_nat @ R @ A2 @ B )
        = ( ( member8757157785044589968at_nat @ B @ A2 )
          & ! [X2: produc3843707927480180839at_nat] :
              ( ( member8757157785044589968at_nat @ X2 @ A2 )
             => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ B @ X2 ) @ R ) ) ) ) ) ).

% wo_rel.isMinim_def
thf(fact_831_wo__rel_OisMinim__def,axiom,
    ! [R: set_Product_prod_a_a,A2: set_a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( bNF_We6697304935525757620inim_a @ R @ A2 @ B )
        = ( ( member_a @ B @ A2 )
          & ! [X2: a] :
              ( ( member_a @ X2 @ A2 )
             => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B @ X2 ) @ R ) ) ) ) ) ).

% wo_rel.isMinim_def
thf(fact_832_wo__rel_OisMinim__def,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A2: set_se491199571785101031od_o_o,B: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( bNF_We794377122088811965od_o_o @ R @ A2 @ B )
        = ( ( member3157015407008874800od_o_o @ B @ A2 )
          & ! [X2: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ X2 @ A2 )
             => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ X2 ) @ R ) ) ) ) ) ).

% wo_rel.isMinim_def
thf(fact_833_wo__rel_OisMinim__def,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A2: set_se7855581050983116737at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( bNF_We943883530777384727at_nat @ R @ A2 @ B )
        = ( ( member2643936169264416010at_nat @ B @ A2 )
          & ! [X2: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ X2 @ A2 )
             => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ X2 ) @ R ) ) ) ) ) ).

% wo_rel.isMinim_def
thf(fact_834_bsqr__max2,axiom,
    ! [R: set_Product_prod_o_o,A1: $o,A22: $o,B1: $o,B22: $o] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( ( member3169104723136097040od_o_o @ ( produc3331439552374987607od_o_o @ ( product_Pair_o_o @ A1 @ A22 ) @ ( product_Pair_o_o @ B1 @ B22 ) ) @ ( bNF_Wellorder_bsqr_o @ R ) )
       => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( bNF_We3104086342435940326max2_o @ R @ A1 @ A22 ) @ ( bNF_We3104086342435940326max2_o @ R @ B1 @ B22 ) ) @ R ) ) ) ).

% bsqr_max2
thf(fact_835_bsqr__max2,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A1: nat,A22: nat,B1: nat,B22: nat] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( product_Pair_nat_nat @ B1 @ B22 ) ) @ ( bNF_We1732890022510290291qr_nat @ R ) )
       => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( bNF_We2380939065524664066x2_nat @ R @ A1 @ A22 ) @ ( bNF_We2380939065524664066x2_nat @ R @ B1 @ B22 ) ) @ R ) ) ) ).

% bsqr_max2
thf(fact_836_bsqr__max2,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A1: set_Product_prod_o_o,A22: set_Product_prod_o_o,B1: set_Product_prod_o_o,B22: set_Product_prod_o_o] :
      ( ( order_3767514495197212837od_o_o @ ( field_6101175518749917524od_o_o @ R ) @ R )
     => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ A1 @ A22 ) @ ( produc763777882069021527od_o_o @ B1 @ B22 ) ) @ ( bNF_We3935152771354962724od_o_o @ R ) )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_We9141258785624724309od_o_o @ R @ A1 @ A22 ) @ ( bNF_We9141258785624724309od_o_o @ R @ B1 @ B22 ) ) @ R ) ) ) ).

% bsqr_max2
thf(fact_837_bsqr__max2,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A1: set_Pr1261947904930325089at_nat,A22: set_Pr1261947904930325089at_nat,B1: set_Pr1261947904930325089at_nat,B22: set_Pr1261947904930325089at_nat] :
      ( ( order_1968183844437341695at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
     => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ A1 @ A22 ) @ ( produc2922128104949294807at_nat @ B1 @ B22 ) ) @ ( bNF_We6127972852007642366at_nat @ R ) )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_We6094461251688579247at_nat @ R @ A1 @ A22 ) @ ( bNF_We6094461251688579247at_nat @ R @ B1 @ B22 ) ) @ R ) ) ) ).

% bsqr_max2
thf(fact_838_antisym__onD,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( antisy2259881126919591626od_o_o @ A2 @ R )
     => ( ( member444158400953824016od_o_o @ X @ A2 )
       => ( ( member444158400953824016od_o_o @ Y @ A2 )
         => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ R )
           => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y @ X ) @ R )
             => ( X = Y ) ) ) ) ) ) ).

% antisym_onD
thf(fact_839_antisym__onD,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat] :
      ( ( antisy1857962754316978724at_nat @ A2 @ R )
     => ( ( member4095101504841534314at_nat @ X @ A2 )
       => ( ( member4095101504841534314at_nat @ Y @ A2 )
         => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ R )
           => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y @ X ) @ R )
             => ( X = Y ) ) ) ) ) ) ).

% antisym_onD
thf(fact_840_antisym__onD,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
      ( ( antisy6856624793204979530at_nat @ A2 @ R )
     => ( ( member8757157785044589968at_nat @ X @ A2 )
       => ( ( member8757157785044589968at_nat @ Y @ A2 )
         => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ R )
           => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y @ X ) @ R )
             => ( X = Y ) ) ) ) ) ) ).

% antisym_onD
thf(fact_841_antisym__onD,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a,X: a,Y: a] :
      ( ( antisym_on_a @ A2 @ R )
     => ( ( member_a @ X @ A2 )
       => ( ( member_a @ Y @ A2 )
         => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R )
           => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y @ X ) @ R )
             => ( X = Y ) ) ) ) ) ) ).

% antisym_onD
thf(fact_842_antisym__onD,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( antisy777991898044409578od_o_o @ A2 @ R )
     => ( ( member3157015407008874800od_o_o @ X @ A2 )
       => ( ( member3157015407008874800od_o_o @ Y @ A2 )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
           => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y @ X ) @ R )
             => ( X = Y ) ) ) ) ) ) ).

% antisym_onD
thf(fact_843_antisym__onD,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( antisy1130263102092445124at_nat @ A2 @ R )
     => ( ( member2643936169264416010at_nat @ X @ A2 )
       => ( ( member2643936169264416010at_nat @ Y @ A2 )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
           => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ X ) @ R )
             => ( X = Y ) ) ) ) ) ) ).

% antisym_onD
thf(fact_844_antisym__onI,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1013884327308616903od_o_o] :
      ( ! [X3: produc2934264451710624999od_o_o,Y3: produc2934264451710624999od_o_o] :
          ( ( member444158400953824016od_o_o @ X3 @ A2 )
         => ( ( member444158400953824016od_o_o @ Y3 @ A2 )
           => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X3 @ Y3 ) @ R )
             => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ Y3 @ X3 ) @ R )
               => ( X3 = Y3 ) ) ) ) )
     => ( antisy2259881126919591626od_o_o @ A2 @ R ) ) ).

% antisym_onI
thf(fact_845_antisym__onI,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr4427867301352232263at_nat] :
      ( ! [X3: produc732395585841259969at_nat,Y3: produc732395585841259969at_nat] :
          ( ( member4095101504841534314at_nat @ X3 @ A2 )
         => ( ( member4095101504841534314at_nat @ Y3 @ A2 )
           => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X3 @ Y3 ) @ R )
             => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ Y3 @ X3 ) @ R )
               => ( X3 = Y3 ) ) ) ) )
     => ( antisy1857962754316978724at_nat @ A2 @ R ) ) ).

% antisym_onI
thf(fact_846_antisym__onI,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr5564308138774400199at_nat] :
      ( ! [X3: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
          ( ( member8757157785044589968at_nat @ X3 @ A2 )
         => ( ( member8757157785044589968at_nat @ Y3 @ A2 )
           => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X3 @ Y3 ) @ R )
             => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y3 @ X3 ) @ R )
               => ( X3 = Y3 ) ) ) ) )
     => ( antisy6856624793204979530at_nat @ A2 @ R ) ) ).

% antisym_onI
thf(fact_847_antisym__onI,axiom,
    ! [A2: set_a,R: set_Product_prod_a_a] :
      ( ! [X3: a,Y3: a] :
          ( ( member_a @ X3 @ A2 )
         => ( ( member_a @ Y3 @ A2 )
           => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
             => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ R )
               => ( X3 = Y3 ) ) ) ) )
     => ( antisym_on_a @ A2 @ R ) ) ).

% antisym_onI
thf(fact_848_antisym__onI,axiom,
    ! [A2: set_se491199571785101031od_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
          ( ( member3157015407008874800od_o_o @ X3 @ A2 )
         => ( ( member3157015407008874800od_o_o @ Y3 @ A2 )
           => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
             => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ X3 ) @ R )
               => ( X3 = Y3 ) ) ) ) )
     => ( antisy777991898044409578od_o_o @ A2 @ R ) ) ).

% antisym_onI
thf(fact_849_antisym__onI,axiom,
    ! [A2: set_se7855581050983116737at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
          ( ( member2643936169264416010at_nat @ X3 @ A2 )
         => ( ( member2643936169264416010at_nat @ Y3 @ A2 )
           => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
             => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ X3 ) @ R )
               => ( X3 = Y3 ) ) ) ) )
     => ( antisy1130263102092445124at_nat @ A2 @ R ) ) ).

% antisym_onI
thf(fact_850_antisym__on__def,axiom,
    ( antisy777991898044409578od_o_o
    = ( ^ [A7: set_se491199571785101031od_o_o,R2: set_Pr1932065953672099015od_o_o] :
        ! [X2: set_Product_prod_o_o] :
          ( ( member3157015407008874800od_o_o @ X2 @ A7 )
         => ! [Y2: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ Y2 @ A7 )
             => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Y2 ) @ R2 )
               => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y2 @ X2 ) @ R2 )
                 => ( X2 = Y2 ) ) ) ) ) ) ) ).

% antisym_on_def
thf(fact_851_antisym__on__def,axiom,
    ( antisy1130263102092445124at_nat
    = ( ^ [A7: set_se7855581050983116737at_nat,R2: set_Pr4329608150637261639at_nat] :
        ! [X2: set_Pr1261947904930325089at_nat] :
          ( ( member2643936169264416010at_nat @ X2 @ A7 )
         => ! [Y2: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ Y2 @ A7 )
             => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y2 ) @ R2 )
               => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ X2 ) @ R2 )
                 => ( X2 = Y2 ) ) ) ) ) ) ) ).

% antisym_on_def
thf(fact_852_antisymI,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
          ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ X3 ) @ R )
           => ( X3 = Y3 ) ) )
     => ( antisy777991898044409578od_o_o @ top_to1478448522960722999od_o_o @ R ) ) ).

% antisymI
thf(fact_853_antisymI,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
          ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ X3 ) @ R )
           => ( X3 = Y3 ) ) )
     => ( antisy1130263102092445124at_nat @ top_to7629004291339433233at_nat @ R ) ) ).

% antisymI
thf(fact_854_antisymI,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ! [X3: nat,Y3: nat] :
          ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
         => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X3 ) @ R )
           => ( X3 = Y3 ) ) )
     => ( antisym_on_nat @ top_top_set_nat @ R ) ) ).

% antisymI
thf(fact_855_antisymD,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o] :
      ( ( antisy777991898044409578od_o_o @ top_to1478448522960722999od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y @ X ) @ R )
         => ( X = Y ) ) ) ) ).

% antisymD
thf(fact_856_antisymD,axiom,
    ! [R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( antisy1130263102092445124at_nat @ top_to7629004291339433233at_nat @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ X ) @ R )
         => ( X = Y ) ) ) ) ).

% antisymD
thf(fact_857_antisymD,axiom,
    ! [R: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
      ( ( antisym_on_nat @ top_top_set_nat @ R )
     => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
       => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ X ) @ R )
         => ( X = Y ) ) ) ) ).

% antisymD
thf(fact_858_in__finite__psubset,axiom,
    ! [A2: set_Product_prod_o_o,B2: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A2 @ B2 ) @ finite1053609180499918954od_o_o )
      = ( ( ord_le3253702748690112691od_o_o @ A2 @ B2 )
        & ( finite6120865539452801872od_o_o @ B2 ) ) ) ).

% in_finite_psubset
thf(fact_859_in__finite__psubset,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ finite469560695537375940at_nat )
      = ( ( ord_le7866589430770878221at_nat @ A2 @ B2 )
        & ( finite6177210948735845034at_nat @ B2 ) ) ) ).

% in_finite_psubset
thf(fact_860_in__lex__prod,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Product_prod_o_o,A6: set_Pr1261947904930325089at_nat,B5: set_Product_prod_o_o,R: set_Pr4329608150637261639at_nat,S3: set_Pr1932065953672099015od_o_o] :
      ( ( member625886800346054288od_o_o @ ( produc4770972565181134295od_o_o @ ( produc2070086378307464573od_o_o @ A @ B ) @ ( produc2070086378307464573od_o_o @ A6 @ B5 ) ) @ ( lex_pr3343786553352869269od_o_o @ R @ S3 ) )
      = ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A6 ) @ R )
        | ( ( A = A6 )
          & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ B5 ) @ S3 ) ) ) ) ).

% in_lex_prod
thf(fact_861_in__lex__prod,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,A6: set_Product_prod_o_o,B5: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o,S3: set_Pr1932065953672099015od_o_o] :
      ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ ( produc763777882069021527od_o_o @ A6 @ B5 ) ) @ ( lex_pr2209867684007004015od_o_o @ R @ S3 ) )
      = ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ A6 ) @ R )
        | ( ( A = A6 )
          & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ B5 ) @ S3 ) ) ) ) ).

% in_lex_prod
thf(fact_862_in__lex__prod,axiom,
    ! [A: set_Product_prod_o_o,B: set_Pr1261947904930325089at_nat,A6: set_Product_prod_o_o,B5: set_Pr1261947904930325089at_nat,R: set_Pr1932065953672099015od_o_o,S3: set_Pr4329608150637261639at_nat] :
      ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( produc8517790099723286449at_nat @ A @ B ) @ ( produc8517790099723286449at_nat @ A6 @ B5 ) ) @ ( lex_pr568118237913915337at_nat @ R @ S3 ) )
      = ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ A6 ) @ R )
        | ( ( A = A6 )
          & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ B5 ) @ S3 ) ) ) ) ).

% in_lex_prod
thf(fact_863_in__lex__prod,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A6: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,S3: set_Pr4329608150637261639at_nat] :
      ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( produc2922128104949294807at_nat @ A6 @ B5 ) ) @ ( lex_pr8000699672184251119at_nat @ R @ S3 ) )
      = ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A6 ) @ R )
        | ( ( A = A6 )
          & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ B5 ) @ S3 ) ) ) ) ).

% in_lex_prod
thf(fact_864_same__fstI,axiom,
    ! [P3: set_Product_prod_o_o > $o,X: set_Product_prod_o_o,Y6: set_Product_prod_o_o,Y: set_Product_prod_o_o,R3: set_Product_prod_o_o > set_Pr1932065953672099015od_o_o] :
      ( ( P3 @ X )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y6 @ Y ) @ ( R3 @ X ) )
       => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ X @ Y6 ) @ ( produc763777882069021527od_o_o @ X @ Y ) ) @ ( same_f884114232143252012od_o_o @ P3 @ R3 ) ) ) ) ).

% same_fstI
thf(fact_865_same__fstI,axiom,
    ! [P3: set_Product_prod_o_o > $o,X: set_Product_prod_o_o,Y6: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R3: set_Product_prod_o_o > set_Pr4329608150637261639at_nat] :
      ( ( P3 @ X )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y6 @ Y ) @ ( R3 @ X ) )
       => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( produc8517790099723286449at_nat @ X @ Y6 ) @ ( produc8517790099723286449at_nat @ X @ Y ) ) @ ( same_f6937299433074352134at_nat @ P3 @ R3 ) ) ) ) ).

% same_fstI
thf(fact_866_same__fstI,axiom,
    ! [P3: set_Pr1261947904930325089at_nat > $o,X: set_Pr1261947904930325089at_nat,Y6: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R3: set_Pr1261947904930325089at_nat > set_Pr4329608150637261639at_nat] :
      ( ( P3 @ X )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y6 @ Y ) @ ( R3 @ X ) )
       => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ X @ Y6 ) @ ( produc2922128104949294807at_nat @ X @ Y ) ) @ ( same_f1460074399991292076at_nat @ P3 @ R3 ) ) ) ) ).

% same_fstI
thf(fact_867_wo__rel_Osuc__greater,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,B2: set_Pr1932065953672099015od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( ord_le7586318239878589543od_o_o @ B2 @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( ( order_909087248044410034od_o_o @ R @ B2 )
           != bot_bo498831808395348787od_o_o )
         => ( ( member444158400953824016od_o_o @ B @ B2 )
           => ( ( ( bNF_We7386194254115604808od_o_o @ R @ B2 )
               != B )
              & ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ B @ ( bNF_We7386194254115604808od_o_o @ R @ B2 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_868_wo__rel_Osuc__greater,axiom,
    ! [R: set_Pr4427867301352232263at_nat,B2: set_Pr457366540195662369at_nat,B: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( ord_le4841768313324958145at_nat @ B2 @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( ( order_3539579856470909964at_nat @ R @ B2 )
           != bot_bo1676454896636820109at_nat )
         => ( ( member4095101504841534314at_nat @ B @ B2 )
           => ( ( ( bNF_We5419384366696408482at_nat @ R @ B2 )
               != B )
              & ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ B @ ( bNF_We5419384366696408482at_nat @ R @ B2 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_869_wo__rel_Osuc__greater,axiom,
    ! [R: set_Pr5564308138774400199at_nat,B2: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( ord_le1268244103169919719at_nat @ B2 @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( ( order_5334716200017444146at_nat @ R @ B2 )
           != bot_bo228742789529271731at_nat )
         => ( ( member8757157785044589968at_nat @ B @ B2 )
           => ( ( ( bNF_We2397293392365222856at_nat @ R @ B2 )
               != B )
              & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ B @ ( bNF_We2397293392365222856at_nat @ R @ B2 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_870_wo__rel_Osuc__greater,axiom,
    ! [R: set_Product_prod_a_a,B2: set_a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B2 @ ( field_a @ R ) )
       => ( ( ( order_AboveS_a @ R @ B2 )
           != bot_bot_set_a )
         => ( ( member_a @ B @ B2 )
           => ( ( ( bNF_We6154283375207884895_suc_a @ R @ B2 )
               != B )
              & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B @ ( bNF_We6154283375207884895_suc_a @ R @ B2 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_871_wo__rel_Osuc__greater,axiom,
    ! [R: set_Product_prod_o_o,B2: set_o,B: $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ( ord_less_eq_set_o @ B2 @ ( field_o @ R ) )
       => ( ( ( order_AboveS_o @ R @ B2 )
           != bot_bot_set_o )
         => ( ( member_o @ B @ B2 )
           => ( ( ( bNF_We8594000642646999417_suc_o @ R @ B2 )
               != B )
              & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ ( bNF_We8594000642646999417_suc_o @ R @ B2 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_872_wo__rel_Osuc__greater,axiom,
    ! [R: set_Pr1261947904930325089at_nat,B2: set_nat,B: nat] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ( ord_less_eq_set_nat @ B2 @ ( field_nat @ R ) )
       => ( ( ( order_AboveS_nat @ R @ B2 )
           != bot_bot_set_nat )
         => ( ( member_nat @ B @ B2 )
           => ( ( ( bNF_We6243639482952820783uc_nat @ R @ B2 )
               != B )
              & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ ( bNF_We6243639482952820783uc_nat @ R @ B2 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_873_wo__rel_Osuc__greater,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,B2: set_se491199571785101031od_o_o,B: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( ord_le2654036014095304327od_o_o @ B2 @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( ( order_5655281162628242642od_o_o @ R @ B2 )
           != bot_bo8006819982598807891od_o_o )
         => ( ( member3157015407008874800od_o_o @ B @ B2 )
           => ( ( ( bNF_We1257987224342916968od_o_o @ R @ B2 )
               != B )
              & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ ( bNF_We1257987224342916968od_o_o @ R @ B2 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_874_wo__rel_Osuc__greater,axiom,
    ! [R: set_Pr4329608150637261639at_nat,B2: set_se7855581050983116737at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( ord_le2077887516847798113at_nat @ B2 @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( ( order_9095727932502173612at_nat @ R @ B2 )
           != bot_bo3083307316010499117at_nat )
         => ( ( member2643936169264416010at_nat @ B @ B2 )
           => ( ( ( bNF_We3445218718054152002at_nat @ R @ B2 )
               != B )
              & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ ( bNF_We3445218718054152002at_nat @ R @ B2 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_875_wo__rel_Osuc__least__AboveS,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o,B2: set_Pr1932065953672099015od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ A @ ( order_909087248044410034od_o_o @ R @ B2 ) )
       => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( bNF_We7386194254115604808od_o_o @ R @ B2 ) @ A ) @ R ) ) ) ).

% wo_rel.suc_least_AboveS
thf(fact_876_wo__rel_Osuc__least__AboveS,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat,B2: set_Pr457366540195662369at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( member4095101504841534314at_nat @ A @ ( order_3539579856470909964at_nat @ R @ B2 ) )
       => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( bNF_We5419384366696408482at_nat @ R @ B2 ) @ A ) @ R ) ) ) ).

% wo_rel.suc_least_AboveS
thf(fact_877_wo__rel_Osuc__least__AboveS,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( member8757157785044589968at_nat @ A @ ( order_5334716200017444146at_nat @ R @ B2 ) )
       => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( bNF_We2397293392365222856at_nat @ R @ B2 ) @ A ) @ R ) ) ) ).

% wo_rel.suc_least_AboveS
thf(fact_878_wo__rel_Osuc__least__AboveS,axiom,
    ! [R: set_Product_prod_a_a,A: a,B2: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( member_a @ A @ ( order_AboveS_a @ R @ B2 ) )
       => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ ( bNF_We6154283375207884895_suc_a @ R @ B2 ) @ A ) @ R ) ) ) ).

% wo_rel.suc_least_AboveS
thf(fact_879_wo__rel_Osuc__least__AboveS,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o,B2: set_se491199571785101031od_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( member3157015407008874800od_o_o @ A @ ( order_5655281162628242642od_o_o @ R @ B2 ) )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_We1257987224342916968od_o_o @ R @ B2 ) @ A ) @ R ) ) ) ).

% wo_rel.suc_least_AboveS
thf(fact_880_wo__rel_Osuc__least__AboveS,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat,B2: set_se7855581050983116737at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( member2643936169264416010at_nat @ A @ ( order_9095727932502173612at_nat @ R @ B2 ) )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_We3445218718054152002at_nat @ R @ B2 ) @ A ) @ R ) ) ) ).

% wo_rel.suc_least_AboveS
thf(fact_881_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,B2: set_Pr1932065953672099015od_o_o,A: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( ord_le7586318239878589543od_o_o @ B2 @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ A @ ( order_909087248044410034od_o_o @ R @ B2 ) )
         => ( ! [A5: produc2934264451710624999od_o_o] :
                ( ( member444158400953824016od_o_o @ A5 @ ( order_909087248044410034od_o_o @ R @ B2 ) )
               => ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ A5 ) @ R ) )
           => ( A
              = ( bNF_We7386194254115604808od_o_o @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_882_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Pr4427867301352232263at_nat,B2: set_Pr457366540195662369at_nat,A: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( ord_le4841768313324958145at_nat @ B2 @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( member4095101504841534314at_nat @ A @ ( order_3539579856470909964at_nat @ R @ B2 ) )
         => ( ! [A5: produc732395585841259969at_nat] :
                ( ( member4095101504841534314at_nat @ A5 @ ( order_3539579856470909964at_nat @ R @ B2 ) )
               => ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ A5 ) @ R ) )
           => ( A
              = ( bNF_We5419384366696408482at_nat @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_883_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Pr5564308138774400199at_nat,B2: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( ord_le1268244103169919719at_nat @ B2 @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ A @ ( order_5334716200017444146at_nat @ R @ B2 ) )
         => ( ! [A5: produc3843707927480180839at_nat] :
                ( ( member8757157785044589968at_nat @ A5 @ ( order_5334716200017444146at_nat @ R @ B2 ) )
               => ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ A5 ) @ R ) )
           => ( A
              = ( bNF_We2397293392365222856at_nat @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_884_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Product_prod_a_a,B2: set_a,A: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B2 @ ( field_a @ R ) )
       => ( ( member_a @ A @ ( order_AboveS_a @ R @ B2 ) )
         => ( ! [A5: a] :
                ( ( member_a @ A5 @ ( order_AboveS_a @ R @ B2 ) )
               => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ A5 ) @ R ) )
           => ( A
              = ( bNF_We6154283375207884895_suc_a @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_885_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Product_prod_o_o,B2: set_o,A: $o] :
      ( ( bNF_We6437023980930612612_rel_o @ R )
     => ( ( ord_less_eq_set_o @ B2 @ ( field_o @ R ) )
       => ( ( member_o @ A @ ( order_AboveS_o @ R @ B2 ) )
         => ( ! [A5: $o] :
                ( ( member_o @ A5 @ ( order_AboveS_o @ R @ B2 ) )
               => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ A5 ) @ R ) )
           => ( A
              = ( bNF_We8594000642646999417_suc_o @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_886_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Pr1261947904930325089at_nat,B2: set_nat,A: nat] :
      ( ( bNF_We3818239936649020644el_nat @ R )
     => ( ( ord_less_eq_set_nat @ B2 @ ( field_nat @ R ) )
       => ( ( member_nat @ A @ ( order_AboveS_nat @ R @ B2 ) )
         => ( ! [A5: nat] :
                ( ( member_nat @ A5 @ ( order_AboveS_nat @ R @ B2 ) )
               => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A5 ) @ R ) )
           => ( A
              = ( bNF_We6243639482952820783uc_nat @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_887_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,B2: set_se491199571785101031od_o_o,A: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( ord_le2654036014095304327od_o_o @ B2 @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( member3157015407008874800od_o_o @ A @ ( order_5655281162628242642od_o_o @ R @ B2 ) )
         => ( ! [A5: set_Product_prod_o_o] :
                ( ( member3157015407008874800od_o_o @ A5 @ ( order_5655281162628242642od_o_o @ R @ B2 ) )
               => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ A5 ) @ R ) )
           => ( A
              = ( bNF_We1257987224342916968od_o_o @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_888_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Pr4329608150637261639at_nat,B2: set_se7855581050983116737at_nat,A: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( ord_le2077887516847798113at_nat @ B2 @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( member2643936169264416010at_nat @ A @ ( order_9095727932502173612at_nat @ R @ B2 ) )
         => ( ! [A5: set_Pr1261947904930325089at_nat] :
                ( ( member2643936169264416010at_nat @ A5 @ ( order_9095727932502173612at_nat @ R @ B2 ) )
               => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A5 ) @ R ) )
           => ( A
              = ( bNF_We3445218718054152002at_nat @ R @ B2 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_889_wo__rel_Osuc__ofilter__in,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A2: set_Pr1932065953672099015od_o_o,B: produc2934264451710624999od_o_o] :
      ( ( bNF_We8581212502267700435od_o_o @ R )
     => ( ( order_543634532542674813od_o_o @ R @ A2 )
       => ( ( ( order_909087248044410034od_o_o @ R @ A2 )
           != bot_bo498831808395348787od_o_o )
         => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ B @ ( bNF_We7386194254115604808od_o_o @ R @ A2 ) ) @ R )
           => ( ( B
               != ( bNF_We7386194254115604808od_o_o @ R @ A2 ) )
             => ( member444158400953824016od_o_o @ B @ A2 ) ) ) ) ) ) ).

% wo_rel.suc_ofilter_in
thf(fact_890_wo__rel_Osuc__ofilter__in,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A2: set_Pr457366540195662369at_nat,B: produc732395585841259969at_nat] :
      ( ( bNF_We1688423684019388333at_nat @ R )
     => ( ( order_3205064739578148183at_nat @ R @ A2 )
       => ( ( ( order_3539579856470909964at_nat @ R @ A2 )
           != bot_bo1676454896636820109at_nat )
         => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ B @ ( bNF_We5419384366696408482at_nat @ R @ A2 ) ) @ R )
           => ( ( B
               != ( bNF_We5419384366696408482at_nat @ R @ A2 ) )
             => ( member4095101504841534314at_nat @ B @ A2 ) ) ) ) ) ) ).

% wo_rel.suc_ofilter_in
thf(fact_891_wo__rel_Osuc__ofilter__in,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A2: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
      ( ( bNF_We4027175587370390611at_nat @ R )
     => ( ( order_3142731893281451261at_nat @ R @ A2 )
       => ( ( ( order_5334716200017444146at_nat @ R @ A2 )
           != bot_bo228742789529271731at_nat )
         => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ B @ ( bNF_We2397293392365222856at_nat @ R @ A2 ) ) @ R )
           => ( ( B
               != ( bNF_We2397293392365222856at_nat @ R @ A2 ) )
             => ( member8757157785044589968at_nat @ B @ A2 ) ) ) ) ) ) ).

% wo_rel.suc_ofilter_in
thf(fact_892_wo__rel_Osuc__ofilter__in,axiom,
    ! [R: set_Product_prod_a_a,A2: set_a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( order_ofilter_a @ R @ A2 )
       => ( ( ( order_AboveS_a @ R @ A2 )
           != bot_bot_set_a )
         => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B @ ( bNF_We6154283375207884895_suc_a @ R @ A2 ) ) @ R )
           => ( ( B
               != ( bNF_We6154283375207884895_suc_a @ R @ A2 ) )
             => ( member_a @ B @ A2 ) ) ) ) ) ) ).

% wo_rel.suc_ofilter_in
thf(fact_893_wo__rel_Osuc__ofilter__in,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A2: set_se491199571785101031od_o_o,B: set_Product_prod_o_o] :
      ( ( bNF_We6243063140137587187od_o_o @ R )
     => ( ( order_136921456694023837od_o_o @ R @ A2 )
       => ( ( ( order_5655281162628242642od_o_o @ R @ A2 )
           != bot_bo8006819982598807891od_o_o )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ ( bNF_We1257987224342916968od_o_o @ R @ A2 ) ) @ R )
           => ( ( B
               != ( bNF_We1257987224342916968od_o_o @ R @ A2 ) )
             => ( member3157015407008874800od_o_o @ B @ A2 ) ) ) ) ) ) ).

% wo_rel.suc_ofilter_in
thf(fact_894_wo__rel_Osuc__ofilter__in,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A2: set_se7855581050983116737at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( bNF_We5602466822260561997at_nat @ R )
     => ( ( order_6860593127430111223at_nat @ R @ A2 )
       => ( ( ( order_9095727932502173612at_nat @ R @ A2 )
           != bot_bo3083307316010499117at_nat )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ ( bNF_We3445218718054152002at_nat @ R @ A2 ) ) @ R )
           => ( ( B
               != ( bNF_We3445218718054152002at_nat @ R @ A2 ) )
             => ( member2643936169264416010at_nat @ B @ A2 ) ) ) ) ) ) ).

% wo_rel.suc_ofilter_in
thf(fact_895_wf__insert,axiom,
    ! [Y: set_Product_prod_o_o,X: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( wf_set2384217916178216176od_o_o @ ( insert3855699742481506999od_o_o @ ( produc763777882069021527od_o_o @ Y @ X ) @ R ) )
      = ( ( wf_set2384217916178216176od_o_o @ R )
        & ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ ( transi8975321201238539274od_o_o @ R ) ) ) ) ).

% wf_insert
thf(fact_896_wf__insert,axiom,
    ! [Y: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( wf_set7675013139414177994at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ Y @ X ) @ R ) )
      = ( ( wf_set7675013139414177994at_nat @ R )
        & ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( transi6170703685534862052at_nat @ R ) ) ) ) ).

% wf_insert
thf(fact_897_Not__Domain__rtrancl,axiom,
    ! [X: produc2934264451710624999od_o_o,R3: set_Pr1013884327308616903od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ~ ( member444158400953824016od_o_o @ X @ ( domain2187190646820045772od_o_o @ R3 ) )
     => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ X @ Y ) @ ( transi3610599525415160810od_o_o @ R3 ) )
        = ( X = Y ) ) ) ).

% Not_Domain_rtrancl
thf(fact_898_Not__Domain__rtrancl,axiom,
    ! [X: produc732395585841259969at_nat,R3: set_Pr4427867301352232263at_nat,Y: produc732395585841259969at_nat] :
      ( ~ ( member4095101504841534314at_nat @ X @ ( domain8659765193365367884at_nat @ R3 ) )
     => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ X @ Y ) @ ( transi4536970581772660548at_nat @ R3 ) )
        = ( X = Y ) ) ) ).

% Not_Domain_rtrancl
thf(fact_899_Not__Domain__rtrancl,axiom,
    ! [X: produc3843707927480180839at_nat,R3: set_Pr5564308138774400199at_nat,Y: produc3843707927480180839at_nat] :
      ( ~ ( member8757157785044589968at_nat @ X @ ( domain1102310642530566604at_nat @ R3 ) )
     => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X @ Y ) @ ( transi5049001397978532970at_nat @ R3 ) )
        = ( X = Y ) ) ) ).

% Not_Domain_rtrancl
thf(fact_900_Not__Domain__rtrancl,axiom,
    ! [X: a,R3: set_Product_prod_a_a,Y: a] :
      ( ~ ( member_a @ X @ ( domain_a_a @ R3 ) )
     => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( transitive_rtrancl_a @ R3 ) )
        = ( X = Y ) ) ) ).

% Not_Domain_rtrancl
thf(fact_901_Not__Domain__rtrancl,axiom,
    ! [X: set_Product_prod_o_o,R3: set_Pr1932065953672099015od_o_o,Y: set_Product_prod_o_o] :
      ( ~ ( member3157015407008874800od_o_o @ X @ ( domain8908270702770587084od_o_o @ R3 ) )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ ( transi8975321201238539274od_o_o @ R3 ) )
        = ( X = Y ) ) ) ).

% Not_Domain_rtrancl
thf(fact_902_Not__Domain__rtrancl,axiom,
    ! [X: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ~ ( member2643936169264416010at_nat @ X @ ( domain8802589944165416012at_nat @ R3 ) )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( transi6170703685534862052at_nat @ R3 ) )
        = ( X = Y ) ) ) ).

% Not_Domain_rtrancl
thf(fact_903_rtrancl__induct2,axiom,
    ! [Ax: set_Product_prod_o_o,Ay: set_Product_prod_o_o,Bx: set_Product_prod_o_o,By: set_Product_prod_o_o,R: set_Pr1013884327308616903od_o_o,P3: set_Product_prod_o_o > set_Product_prod_o_o > $o] :
      ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ Ax @ Ay ) @ ( produc763777882069021527od_o_o @ Bx @ By ) ) @ ( transi3610599525415160810od_o_o @ R ) )
     => ( ( P3 @ Ax @ Ay )
       => ( ! [A4: set_Product_prod_o_o,B3: set_Product_prod_o_o,Aa: set_Product_prod_o_o,Ba: set_Product_prod_o_o] :
              ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ Ax @ Ay ) @ ( produc763777882069021527od_o_o @ A4 @ B3 ) ) @ ( transi3610599525415160810od_o_o @ R ) )
             => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ A4 @ B3 ) @ ( produc763777882069021527od_o_o @ Aa @ Ba ) ) @ R )
               => ( ( P3 @ A4 @ B3 )
                 => ( P3 @ Aa @ Ba ) ) ) )
         => ( P3 @ Bx @ By ) ) ) ) ).

% rtrancl_induct2
thf(fact_904_rtrancl__induct2,axiom,
    ! [Ax: set_Product_prod_o_o,Ay: set_Pr1261947904930325089at_nat,Bx: set_Product_prod_o_o,By: set_Pr1261947904930325089at_nat,R: set_Pr4427867301352232263at_nat,P3: set_Product_prod_o_o > set_Pr1261947904930325089at_nat > $o] :
      ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( produc8517790099723286449at_nat @ Ax @ Ay ) @ ( produc8517790099723286449at_nat @ Bx @ By ) ) @ ( transi4536970581772660548at_nat @ R ) )
     => ( ( P3 @ Ax @ Ay )
       => ( ! [A4: set_Product_prod_o_o,B3: set_Pr1261947904930325089at_nat,Aa: set_Product_prod_o_o,Ba: set_Pr1261947904930325089at_nat] :
              ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( produc8517790099723286449at_nat @ Ax @ Ay ) @ ( produc8517790099723286449at_nat @ A4 @ B3 ) ) @ ( transi4536970581772660548at_nat @ R ) )
             => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( produc8517790099723286449at_nat @ A4 @ B3 ) @ ( produc8517790099723286449at_nat @ Aa @ Ba ) ) @ R )
               => ( ( P3 @ A4 @ B3 )
                 => ( P3 @ Aa @ Ba ) ) ) )
         => ( P3 @ Bx @ By ) ) ) ) ).

% rtrancl_induct2
thf(fact_905_rtrancl__induct2,axiom,
    ! [Ax: set_Pr1261947904930325089at_nat,Ay: set_Pr1261947904930325089at_nat,Bx: set_Pr1261947904930325089at_nat,By: set_Pr1261947904930325089at_nat,R: set_Pr5564308138774400199at_nat,P3: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
      ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ Ax @ Ay ) @ ( produc2922128104949294807at_nat @ Bx @ By ) ) @ ( transi5049001397978532970at_nat @ R ) )
     => ( ( P3 @ Ax @ Ay )
       => ( ! [A4: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,Aa: set_Pr1261947904930325089at_nat,Ba: set_Pr1261947904930325089at_nat] :
              ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ Ax @ Ay ) @ ( produc2922128104949294807at_nat @ A4 @ B3 ) ) @ ( transi5049001397978532970at_nat @ R ) )
             => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ A4 @ B3 ) @ ( produc2922128104949294807at_nat @ Aa @ Ba ) ) @ R )
               => ( ( P3 @ A4 @ B3 )
                 => ( P3 @ Aa @ Ba ) ) ) )
         => ( P3 @ Bx @ By ) ) ) ) ).

% rtrancl_induct2
thf(fact_906_converse__rtranclE2,axiom,
    ! [Xa3: set_Product_prod_o_o,Xb: set_Product_prod_o_o,Za: set_Product_prod_o_o,Zb: set_Product_prod_o_o,R: set_Pr1013884327308616903od_o_o] :
      ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ Xa3 @ Xb ) @ ( produc763777882069021527od_o_o @ Za @ Zb ) ) @ ( transi3610599525415160810od_o_o @ R ) )
     => ( ( ( produc763777882069021527od_o_o @ Xa3 @ Xb )
         != ( produc763777882069021527od_o_o @ Za @ Zb ) )
       => ~ ! [A4: set_Product_prod_o_o,B3: set_Product_prod_o_o] :
              ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ Xa3 @ Xb ) @ ( produc763777882069021527od_o_o @ A4 @ B3 ) ) @ R )
             => ~ ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ A4 @ B3 ) @ ( produc763777882069021527od_o_o @ Za @ Zb ) ) @ ( transi3610599525415160810od_o_o @ R ) ) ) ) ) ).

% converse_rtranclE2
thf(fact_907_converse__rtranclE2,axiom,
    ! [Xa3: set_Product_prod_o_o,Xb: set_Pr1261947904930325089at_nat,Za: set_Product_prod_o_o,Zb: set_Pr1261947904930325089at_nat,R: set_Pr4427867301352232263at_nat] :
      ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( produc8517790099723286449at_nat @ Xa3 @ Xb ) @ ( produc8517790099723286449at_nat @ Za @ Zb ) ) @ ( transi4536970581772660548at_nat @ R ) )
     => ( ( ( produc8517790099723286449at_nat @ Xa3 @ Xb )
         != ( produc8517790099723286449at_nat @ Za @ Zb ) )
       => ~ ! [A4: set_Product_prod_o_o,B3: set_Pr1261947904930325089at_nat] :
              ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( produc8517790099723286449at_nat @ Xa3 @ Xb ) @ ( produc8517790099723286449at_nat @ A4 @ B3 ) ) @ R )
             => ~ ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( produc8517790099723286449at_nat @ A4 @ B3 ) @ ( produc8517790099723286449at_nat @ Za @ Zb ) ) @ ( transi4536970581772660548at_nat @ R ) ) ) ) ) ).

% converse_rtranclE2
thf(fact_908_converse__rtranclE2,axiom,
    ! [Xa3: set_Pr1261947904930325089at_nat,Xb: set_Pr1261947904930325089at_nat,Za: set_Pr1261947904930325089at_nat,Zb: set_Pr1261947904930325089at_nat,R: set_Pr5564308138774400199at_nat] :
      ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ Xa3 @ Xb ) @ ( produc2922128104949294807at_nat @ Za @ Zb ) ) @ ( transi5049001397978532970at_nat @ R ) )
     => ( ( ( produc2922128104949294807at_nat @ Xa3 @ Xb )
         != ( produc2922128104949294807at_nat @ Za @ Zb ) )
       => ~ ! [A4: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
              ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ Xa3 @ Xb ) @ ( produc2922128104949294807at_nat @ A4 @ B3 ) ) @ R )
             => ~ ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ A4 @ B3 ) @ ( produc2922128104949294807at_nat @ Za @ Zb ) ) @ ( transi5049001397978532970at_nat @ R ) ) ) ) ) ).

% converse_rtranclE2
thf(fact_909_converse__rtrancl__induct2,axiom,
    ! [Ax: set_Product_prod_o_o,Ay: set_Product_prod_o_o,Bx: set_Product_prod_o_o,By: set_Product_prod_o_o,R: set_Pr1013884327308616903od_o_o,P3: set_Product_prod_o_o > set_Product_prod_o_o > $o] :
      ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ Ax @ Ay ) @ ( produc763777882069021527od_o_o @ Bx @ By ) ) @ ( transi3610599525415160810od_o_o @ R ) )
     => ( ( P3 @ Bx @ By )
       => ( ! [A4: set_Product_prod_o_o,B3: set_Product_prod_o_o,Aa: set_Product_prod_o_o,Ba: set_Product_prod_o_o] :
              ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ A4 @ B3 ) @ ( produc763777882069021527od_o_o @ Aa @ Ba ) ) @ R )
             => ( ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ ( produc763777882069021527od_o_o @ Aa @ Ba ) @ ( produc763777882069021527od_o_o @ Bx @ By ) ) @ ( transi3610599525415160810od_o_o @ R ) )
               => ( ( P3 @ Aa @ Ba )
                 => ( P3 @ A4 @ B3 ) ) ) )
         => ( P3 @ Ax @ Ay ) ) ) ) ).

% converse_rtrancl_induct2
thf(fact_910_converse__rtrancl__induct2,axiom,
    ! [Ax: set_Product_prod_o_o,Ay: set_Pr1261947904930325089at_nat,Bx: set_Product_prod_o_o,By: set_Pr1261947904930325089at_nat,R: set_Pr4427867301352232263at_nat,P3: set_Product_prod_o_o > set_Pr1261947904930325089at_nat > $o] :
      ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( produc8517790099723286449at_nat @ Ax @ Ay ) @ ( produc8517790099723286449at_nat @ Bx @ By ) ) @ ( transi4536970581772660548at_nat @ R ) )
     => ( ( P3 @ Bx @ By )
       => ( ! [A4: set_Product_prod_o_o,B3: set_Pr1261947904930325089at_nat,Aa: set_Product_prod_o_o,Ba: set_Pr1261947904930325089at_nat] :
              ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( produc8517790099723286449at_nat @ A4 @ B3 ) @ ( produc8517790099723286449at_nat @ Aa @ Ba ) ) @ R )
             => ( ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ ( produc8517790099723286449at_nat @ Aa @ Ba ) @ ( produc8517790099723286449at_nat @ Bx @ By ) ) @ ( transi4536970581772660548at_nat @ R ) )
               => ( ( P3 @ Aa @ Ba )
                 => ( P3 @ A4 @ B3 ) ) ) )
         => ( P3 @ Ax @ Ay ) ) ) ) ).

% converse_rtrancl_induct2
thf(fact_911_converse__rtrancl__induct2,axiom,
    ! [Ax: set_Pr1261947904930325089at_nat,Ay: set_Pr1261947904930325089at_nat,Bx: set_Pr1261947904930325089at_nat,By: set_Pr1261947904930325089at_nat,R: set_Pr5564308138774400199at_nat,P3: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
      ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ Ax @ Ay ) @ ( produc2922128104949294807at_nat @ Bx @ By ) ) @ ( transi5049001397978532970at_nat @ R ) )
     => ( ( P3 @ Bx @ By )
       => ( ! [A4: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,Aa: set_Pr1261947904930325089at_nat,Ba: set_Pr1261947904930325089at_nat] :
              ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ A4 @ B3 ) @ ( produc2922128104949294807at_nat @ Aa @ Ba ) ) @ R )
             => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ ( produc2922128104949294807at_nat @ Aa @ Ba ) @ ( produc2922128104949294807at_nat @ Bx @ By ) ) @ ( transi5049001397978532970at_nat @ R ) )
               => ( ( P3 @ Aa @ Ba )
                 => ( P3 @ A4 @ B3 ) ) ) )
         => ( P3 @ Ax @ Ay ) ) ) ) ).

% converse_rtrancl_induct2
thf(fact_912_rtrancl__Un__separatorE,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,P3: set_Pr1932065953672099015od_o_o,Q4: set_Pr1932065953672099015od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ ( transi8975321201238539274od_o_o @ ( sup_su4078869789063261851od_o_o @ P3 @ Q4 ) ) )
     => ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
            ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ X3 ) @ ( transi8975321201238539274od_o_o @ P3 ) )
           => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ Q4 )
             => ( X3 = Y3 ) ) )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ ( transi8975321201238539274od_o_o @ P3 ) ) ) ) ).

% rtrancl_Un_separatorE
thf(fact_913_rtrancl__Un__separatorE,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,P3: set_Pr4329608150637261639at_nat,Q4: set_Pr4329608150637261639at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( transi6170703685534862052at_nat @ ( sup_su5525570899277871387at_nat @ P3 @ Q4 ) ) )
     => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
            ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ X3 ) @ ( transi6170703685534862052at_nat @ P3 ) )
           => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ Q4 )
             => ( X3 = Y3 ) ) )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( transi6170703685534862052at_nat @ P3 ) ) ) ) ).

% rtrancl_Un_separatorE
thf(fact_914_rtrancl__Un__separator__converseE,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,P3: set_Pr1932065953672099015od_o_o,Q4: set_Pr1932065953672099015od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ ( transi8975321201238539274od_o_o @ ( sup_su4078869789063261851od_o_o @ P3 @ Q4 ) ) )
     => ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o] :
            ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ B ) @ ( transi8975321201238539274od_o_o @ P3 ) )
           => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ X3 ) @ Q4 )
             => ( Y3 = X3 ) ) )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ ( transi8975321201238539274od_o_o @ P3 ) ) ) ) ).

% rtrancl_Un_separator_converseE
thf(fact_915_rtrancl__Un__separator__converseE,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,P3: set_Pr4329608150637261639at_nat,Q4: set_Pr4329608150637261639at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( transi6170703685534862052at_nat @ ( sup_su5525570899277871387at_nat @ P3 @ Q4 ) ) )
     => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
            ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ B ) @ ( transi6170703685534862052at_nat @ P3 ) )
           => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ X3 ) @ Q4 )
             => ( Y3 = X3 ) ) )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( transi6170703685534862052at_nat @ P3 ) ) ) ) ).

% rtrancl_Un_separator_converseE
thf(fact_916_converse__rtrancl__into__rtrancl,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o,C: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ C ) @ ( transi8975321201238539274od_o_o @ R ) )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ C ) @ ( transi8975321201238539274od_o_o @ R ) ) ) ) ).

% converse_rtrancl_into_rtrancl
thf(fact_917_converse__rtrancl__into__rtrancl,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,C: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ C ) @ ( transi6170703685534862052at_nat @ R ) )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ C ) @ ( transi6170703685534862052at_nat @ R ) ) ) ) ).

% converse_rtrancl_into_rtrancl
thf(fact_918_converse__rtrancl__induct,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o,P3: set_Product_prod_o_o > $o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ ( transi8975321201238539274od_o_o @ R ) )
     => ( ( P3 @ B )
       => ( ! [Y3: set_Product_prod_o_o,Z2: set_Product_prod_o_o] :
              ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ Z2 ) @ R )
             => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Z2 @ B ) @ ( transi8975321201238539274od_o_o @ R ) )
               => ( ( P3 @ Z2 )
                 => ( P3 @ Y3 ) ) ) )
         => ( P3 @ A ) ) ) ) ).

% converse_rtrancl_induct
thf(fact_919_converse__rtrancl__induct,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,P3: set_Pr1261947904930325089at_nat > $o] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( transi6170703685534862052at_nat @ R ) )
     => ( ( P3 @ B )
       => ( ! [Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
              ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ Z2 ) @ R )
             => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Z2 @ B ) @ ( transi6170703685534862052at_nat @ R ) )
               => ( ( P3 @ Z2 )
                 => ( P3 @ Y3 ) ) ) )
         => ( P3 @ A ) ) ) ) ).

% converse_rtrancl_induct
thf(fact_920_converse__rtranclE,axiom,
    ! [X: set_Product_prod_o_o,Z: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Z ) @ ( transi8975321201238539274od_o_o @ R ) )
     => ( ( X != Z )
       => ~ ! [Y3: set_Product_prod_o_o] :
              ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y3 ) @ R )
             => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ Z ) @ ( transi8975321201238539274od_o_o @ R ) ) ) ) ) ).

% converse_rtranclE
thf(fact_921_converse__rtranclE,axiom,
    ! [X: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Z ) @ ( transi6170703685534862052at_nat @ R ) )
     => ( ( X != Z )
       => ~ ! [Y3: set_Pr1261947904930325089at_nat] :
              ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y3 ) @ R )
             => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ Z ) @ ( transi6170703685534862052at_nat @ R ) ) ) ) ) ).

% converse_rtranclE
thf(fact_922_rtrancl__induct,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o,P3: set_Product_prod_o_o > $o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ ( transi8975321201238539274od_o_o @ R ) )
     => ( ( P3 @ A )
       => ( ! [Y3: set_Product_prod_o_o,Z2: set_Product_prod_o_o] :
              ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ Y3 ) @ ( transi8975321201238539274od_o_o @ R ) )
             => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ Z2 ) @ R )
               => ( ( P3 @ Y3 )
                 => ( P3 @ Z2 ) ) ) )
         => ( P3 @ B ) ) ) ) ).

% rtrancl_induct
thf(fact_923_rtrancl__induct,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,P3: set_Pr1261947904930325089at_nat > $o] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( transi6170703685534862052at_nat @ R ) )
     => ( ( P3 @ A )
       => ( ! [Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
              ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ Y3 ) @ ( transi6170703685534862052at_nat @ R ) )
             => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ Z2 ) @ R )
               => ( ( P3 @ Y3 )
                 => ( P3 @ Z2 ) ) ) )
         => ( P3 @ B ) ) ) ) ).

% rtrancl_induct
thf(fact_924_rtrancl__trans,axiom,
    ! [X: set_Product_prod_o_o,Y: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o,Z: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ ( transi8975321201238539274od_o_o @ R ) )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y @ Z ) @ ( transi8975321201238539274od_o_o @ R ) )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Z ) @ ( transi8975321201238539274od_o_o @ R ) ) ) ) ).

% rtrancl_trans
thf(fact_925_rtrancl__trans,axiom,
    ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,Z: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( transi6170703685534862052at_nat @ R ) )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ Z ) @ ( transi6170703685534862052at_nat @ R ) )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Z ) @ ( transi6170703685534862052at_nat @ R ) ) ) ) ).

% rtrancl_trans
thf(fact_926_rtranclE,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ ( transi8975321201238539274od_o_o @ R ) )
     => ( ( A != B )
       => ~ ! [Y3: set_Product_prod_o_o] :
              ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ Y3 ) @ ( transi8975321201238539274od_o_o @ R ) )
             => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y3 @ B ) @ R ) ) ) ) ).

% rtranclE
thf(fact_927_rtranclE,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( transi6170703685534862052at_nat @ R ) )
     => ( ( A != B )
       => ~ ! [Y3: set_Pr1261947904930325089at_nat] :
              ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ Y3 ) @ ( transi6170703685534862052at_nat @ R ) )
             => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y3 @ B ) @ R ) ) ) ) ).

% rtranclE
thf(fact_928_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [A: set_Product_prod_o_o,B: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o,C: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ B ) @ ( transi8975321201238539274od_o_o @ R ) )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B @ C ) @ R )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ C ) @ ( transi8975321201238539274od_o_o @ R ) ) ) ) ).

% rtrancl.rtrancl_into_rtrancl
thf(fact_929_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,C: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( transi6170703685534862052at_nat @ R ) )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ C ) @ R )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ C ) @ ( transi6170703685534862052at_nat @ R ) ) ) ) ).

% rtrancl.rtrancl_into_rtrancl
thf(fact_930_rtrancl_Ortrancl__refl,axiom,
    ! [A: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] : ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ A ) @ ( transi8975321201238539274od_o_o @ R ) ) ).

% rtrancl.rtrancl_refl
thf(fact_931_rtrancl_Ortrancl__refl,axiom,
    ! [A: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ A ) @ ( transi6170703685534862052at_nat @ R ) ) ).

% rtrancl.rtrancl_refl
thf(fact_932_rtrancl_Osimps,axiom,
    ! [A1: set_Product_prod_o_o,A22: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A1 @ A22 ) @ ( transi8975321201238539274od_o_o @ R ) )
      = ( ? [A3: set_Product_prod_o_o] :
            ( ( A1 = A3 )
            & ( A22 = A3 ) )
        | ? [A3: set_Product_prod_o_o,B4: set_Product_prod_o_o,C2: set_Product_prod_o_o] :
            ( ( A1 = A3 )
            & ( A22 = C2 )
            & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A3 @ B4 ) @ ( transi8975321201238539274od_o_o @ R ) )
            & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B4 @ C2 ) @ R ) ) ) ) ).

% rtrancl.simps
thf(fact_933_rtrancl_Osimps,axiom,
    ! [A1: set_Pr1261947904930325089at_nat,A22: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ A22 ) @ ( transi6170703685534862052at_nat @ R ) )
      = ( ? [A3: set_Pr1261947904930325089at_nat] :
            ( ( A1 = A3 )
            & ( A22 = A3 ) )
        | ? [A3: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
            ( ( A1 = A3 )
            & ( A22 = C2 )
            & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A3 @ B4 ) @ ( transi6170703685534862052at_nat @ R ) )
            & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B4 @ C2 ) @ R ) ) ) ) ).

% rtrancl.simps
thf(fact_934_rtrancl_Ocases,axiom,
    ! [A1: set_Product_prod_o_o,A22: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A1 @ A22 ) @ ( transi8975321201238539274od_o_o @ R ) )
     => ( ( A22 != A1 )
       => ~ ! [B3: set_Product_prod_o_o] :
              ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A1 @ B3 ) @ ( transi8975321201238539274od_o_o @ R ) )
             => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B3 @ A22 ) @ R ) ) ) ) ).

% rtrancl.cases
thf(fact_935_rtrancl_Ocases,axiom,
    ! [A1: set_Pr1261947904930325089at_nat,A22: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ A22 ) @ ( transi6170703685534862052at_nat @ R ) )
     => ( ( A22 != A1 )
       => ~ ! [B3: set_Pr1261947904930325089at_nat] :
              ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ B3 ) @ ( transi6170703685534862052at_nat @ R ) )
             => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B3 @ A22 ) @ R ) ) ) ) ).

% rtrancl.cases
thf(fact_936_acyclic__insert,axiom,
    ! [Y: set_Product_prod_o_o,X: set_Product_prod_o_o,R: set_Pr1932065953672099015od_o_o] :
      ( ( transi6732886088652640214od_o_o @ ( insert3855699742481506999od_o_o @ ( produc763777882069021527od_o_o @ Y @ X ) @ R ) )
      = ( ( transi6732886088652640214od_o_o @ R )
        & ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ ( transi8975321201238539274od_o_o @ R ) ) ) ) ).

% acyclic_insert
thf(fact_937_acyclic__insert,axiom,
    ! [Y: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
      ( ( transi5940216143853766832at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ Y @ X ) @ R ) )
      = ( ( transi5940216143853766832at_nat @ R )
        & ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( transi6170703685534862052at_nat @ R ) ) ) ) ).

% acyclic_insert
thf(fact_938_comp__the__Some,axiom,
    ( ( comp_option_a_a_a @ the_a @ some_a )
    = id_a ) ).

% comp_the_Some
thf(fact_939_single__valued__confluent,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o,Z: set_Product_prod_o_o] :
      ( ( single7370670047157432131od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ ( transi8975321201238539274od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Z ) @ ( transi8975321201238539274od_o_o @ R ) )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y @ Z ) @ ( transi8975321201238539274od_o_o @ R ) )
            | ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Z @ Y ) @ ( transi8975321201238539274od_o_o @ R ) ) ) ) ) ) ).

% single_valued_confluent
thf(fact_940_single__valued__confluent,axiom,
    ! [R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
      ( ( single6503460853754975939at_nat @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( transi6170703685534862052at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Z ) @ ( transi6170703685534862052at_nat @ R ) )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ Z ) @ ( transi6170703685534862052at_nat @ R ) )
            | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Z @ Y ) @ ( transi6170703685534862052at_nat @ R ) ) ) ) ) ) ).

% single_valued_confluent
thf(fact_941_finite__ordLess__infinite,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 )
       => ( ( finite_finite_nat @ ( field_nat @ R ) )
         => ( ~ ( finite_finite_o @ ( field_o @ R4 ) )
           => ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We2061588309931968636_nat_o ) ) ) ) ) ).

% finite_ordLess_infinite
thf(fact_942_finite__ordLess__infinite,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 )
       => ( ( finite_finite_o @ ( field_o @ R ) )
         => ( ~ ( finite_finite_o @ ( field_o @ R4 ) )
           => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ) ) ).

% finite_ordLess_infinite
thf(fact_943_finite__ordLess__infinite,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 )
       => ( ( finite_finite_nat @ ( field_nat @ R ) )
         => ( ~ ( finite_finite_nat @ ( field_nat @ R4 ) )
           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We3448473429330749420at_nat ) ) ) ) ) ).

% finite_ordLess_infinite
thf(fact_944_finite__ordLess__infinite,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 )
       => ( ( finite_finite_o @ ( field_o @ R ) )
         => ( ~ ( finite_finite_nat @ ( field_nat @ R4 ) )
           => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat ) ) ) ) ) ).

% finite_ordLess_infinite
thf(fact_945_infinite__Card__order__limit,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o] :
      ( ( bNF_Ca4198200952365436517od_o_o @ ( field_5121862139100741428od_o_o @ R ) @ R )
     => ( ~ ( finite820925532130942480od_o_o @ ( field_5121862139100741428od_o_o @ R ) )
       => ( ( member444158400953824016od_o_o @ A @ ( field_5121862139100741428od_o_o @ R ) )
         => ? [X3: produc2934264451710624999od_o_o] :
              ( ( member444158400953824016od_o_o @ X3 @ ( field_5121862139100741428od_o_o @ R ) )
              & ( A != X3 )
              & ( member5560047953027865360od_o_o @ ( produc6658621592305443671od_o_o @ A @ X3 ) @ R ) ) ) ) ) ).

% infinite_Card_order_limit
thf(fact_946_infinite__Card__order__limit,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat] :
      ( ( bNF_Ca7438713789483989055at_nat @ ( field_7361900449976055182at_nat @ R ) @ R )
     => ( ~ ( finite8072506237346428522at_nat @ ( field_7361900449976055182at_nat @ R ) )
       => ( ( member4095101504841534314at_nat @ A @ ( field_7361900449976055182at_nat @ R ) )
         => ? [X3: produc732395585841259969at_nat] :
              ( ( member4095101504841534314at_nat @ X3 @ ( field_7361900449976055182at_nat @ R ) )
              & ( A != X3 )
              & ( member208136763105818512at_nat @ ( produc4785852428192286935at_nat @ A @ X3 ) @ R ) ) ) ) ) ).

% infinite_Card_order_limit
thf(fact_947_infinite__Card__order__limit,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat] :
      ( ( bNF_Ca8230877790521596901at_nat @ ( field_2862844103579723188at_nat @ R ) @ R )
     => ( ~ ( finite4343798906461161616at_nat @ ( field_2862844103579723188at_nat @ R ) )
       => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
         => ? [X3: produc3843707927480180839at_nat] :
              ( ( member8757157785044589968at_nat @ X3 @ ( field_2862844103579723188at_nat @ R ) )
              & ( A != X3 )
              & ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A @ X3 ) @ R ) ) ) ) ) ).

% infinite_Card_order_limit
thf(fact_948_infinite__Card__order__limit,axiom,
    ! [R: set_Product_prod_a_a,A: a] :
      ( ( bNF_Ca453948448923306620r_on_a @ ( field_a @ R ) @ R )
     => ( ~ ( finite_finite_a @ ( field_a @ R ) )
       => ( ( member_a @ A @ ( field_a @ R ) )
         => ? [X3: a] :
              ( ( member_a @ X3 @ ( field_a @ R ) )
              & ( A != X3 )
              & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ X3 ) @ R ) ) ) ) ) ).

% infinite_Card_order_limit
thf(fact_949_infinite__Card__order__limit,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat] :
      ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
     => ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
       => ( ( member_nat @ A @ ( field_nat @ R ) )
         => ? [X3: nat] :
              ( ( member_nat @ X3 @ ( field_nat @ R ) )
              & ( A != X3 )
              & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ X3 ) @ R ) ) ) ) ) ).

% infinite_Card_order_limit
thf(fact_950_infinite__Card__order__limit,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,A: set_Product_prod_o_o] :
      ( ( bNF_Ca4526578624105657733od_o_o @ ( field_6101175518749917524od_o_o @ R ) @ R )
     => ( ~ ( finite9011636195296603184od_o_o @ ( field_6101175518749917524od_o_o @ R ) )
       => ( ( member3157015407008874800od_o_o @ A @ ( field_6101175518749917524od_o_o @ R ) )
         => ? [X3: set_Product_prod_o_o] :
              ( ( member3157015407008874800od_o_o @ X3 @ ( field_6101175518749917524od_o_o @ R ) )
              & ( A != X3 )
              & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ A @ X3 ) @ R ) ) ) ) ) ).

% infinite_Card_order_limit
thf(fact_951_infinite__Card__order__limit,axiom,
    ! [R: set_Pr4329608150637261639at_nat,A: set_Pr1261947904930325089at_nat] :
      ( ( bNF_Ca4062989147270679263at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
     => ( ~ ( finite9047747110432174090at_nat @ ( field_3145993188331922222at_nat @ R ) )
       => ( ( member2643936169264416010at_nat @ A @ ( field_3145993188331922222at_nat @ R ) )
         => ? [X3: set_Pr1261947904930325089at_nat] :
              ( ( member2643936169264416010at_nat @ X3 @ ( field_3145993188331922222at_nat @ R ) )
              & ( A != X3 )
              & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ X3 ) @ R ) ) ) ) ) ).

% infinite_Card_order_limit
thf(fact_952_infinite__Card__order__limit,axiom,
    ! [R: set_Product_prod_o_o,A: $o] :
      ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
     => ( ~ ( finite_finite_o @ ( field_o @ R ) )
       => ( ( member_o @ A @ ( field_o @ R ) )
         => ? [X3: $o] :
              ( ( member_o @ X3 @ ( field_o @ R ) )
              & ( A = (~ X3) )
              & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ X3 ) @ R ) ) ) ) ) ).

% infinite_Card_order_limit
thf(fact_953_ordLess__irreflexive,axiom,
    ! [R: set_Product_prod_o_o] :
      ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R ) @ bNF_We2568191115274586186ss_o_o ) ).

% ordLess_irreflexive
thf(fact_954_ordLess__irreflexive,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R ) @ bNF_We3448473429330749420at_nat ) ).

% ordLess_irreflexive
thf(fact_955_ordLess__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R5 ) @ bNF_We2568191115274586186ss_o_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% ordLess_transitive
thf(fact_956_ordLess__transitive,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We3448473429330749420at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We3448473429330749420at_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% ordLess_transitive
thf(fact_957_ordLess__transitive,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We2061588309931968636_nat_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We8182288985678559134_o_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% ordLess_transitive
thf(fact_958_ordLess__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We8182288985678559134_o_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We8182288985678559134_o_nat ) ) ) ).

% ordLess_transitive
thf(fact_959_ordLess__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R5 ) @ bNF_We2061588309931968636_nat_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% ordLess_transitive
thf(fact_960_ordLess__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We3448473429330749420at_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We8182288985678559134_o_nat ) ) ) ).

% ordLess_transitive
thf(fact_961_single__valuedD,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o,Z: set_Product_prod_o_o] :
      ( ( single7370670047157432131od_o_o @ R )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Z ) @ R )
         => ( Y = Z ) ) ) ) ).

% single_valuedD
thf(fact_962_single__valuedD,axiom,
    ! [R: set_Pr457366540195662369at_nat,X: set_Product_prod_o_o,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
      ( ( single7212042597521132957at_nat @ R )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ X @ Y ) @ R )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ X @ Z ) @ R )
         => ( Y = Z ) ) ) ) ).

% single_valuedD
thf(fact_963_single__valuedD,axiom,
    ! [R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
      ( ( single6503460853754975939at_nat @ R )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Z ) @ R )
         => ( Y = Z ) ) ) ) ).

% single_valuedD
thf(fact_964_single__valuedI,axiom,
    ! [R: set_Pr1932065953672099015od_o_o] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Product_prod_o_o,Z2: set_Product_prod_o_o] :
          ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Y3 ) @ R )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Z2 ) @ R )
           => ( Y3 = Z2 ) ) )
     => ( single7370670047157432131od_o_o @ R ) ) ).

% single_valuedI
thf(fact_965_single__valuedI,axiom,
    ! [R: set_Pr457366540195662369at_nat] :
      ( ! [X3: set_Product_prod_o_o,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
          ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ X3 @ Y3 ) @ R )
         => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ X3 @ Z2 ) @ R )
           => ( Y3 = Z2 ) ) )
     => ( single7212042597521132957at_nat @ R ) ) ).

% single_valuedI
thf(fact_966_single__valuedI,axiom,
    ! [R: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
          ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Z2 ) @ R )
           => ( Y3 = Z2 ) ) )
     => ( single6503460853754975939at_nat @ R ) ) ).

% single_valuedI
thf(fact_967_single__valued__def,axiom,
    ( single7370670047157432131od_o_o
    = ( ^ [R2: set_Pr1932065953672099015od_o_o] :
        ! [X2: set_Product_prod_o_o,Y2: set_Product_prod_o_o] :
          ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Y2 ) @ R2 )
         => ! [Z3: set_Product_prod_o_o] :
              ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X2 @ Z3 ) @ R2 )
             => ( Y2 = Z3 ) ) ) ) ) ).

% single_valued_def
thf(fact_968_single__valued__def,axiom,
    ( single7212042597521132957at_nat
    = ( ^ [R2: set_Pr457366540195662369at_nat] :
        ! [X2: set_Product_prod_o_o,Y2: set_Pr1261947904930325089at_nat] :
          ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ X2 @ Y2 ) @ R2 )
         => ! [Z3: set_Pr1261947904930325089at_nat] :
              ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ X2 @ Z3 ) @ R2 )
             => ( Y2 = Z3 ) ) ) ) ) ).

% single_valued_def
thf(fact_969_single__valued__def,axiom,
    ( single6503460853754975939at_nat
    = ( ^ [R2: set_Pr4329608150637261639at_nat] :
        ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] :
          ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y2 ) @ R2 )
         => ! [Z3: set_Pr1261947904930325089at_nat] :
              ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Z3 ) @ R2 )
             => ( Y2 = Z3 ) ) ) ) ) ).

% single_valued_def
thf(fact_970_Card__order__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,X: nat,Y: nat,Z: nat] :
      ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
     => ( ( X != Y )
       => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
         => ( ( Y != Z )
           => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ R )
             => ( ( X != Z )
                & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R ) ) ) ) ) ) ) ).

% Card_order_trans
thf(fact_971_Card__order__trans,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,X: set_Product_prod_o_o,Y: set_Product_prod_o_o,Z: set_Product_prod_o_o] :
      ( ( bNF_Ca4526578624105657733od_o_o @ ( field_6101175518749917524od_o_o @ R ) @ R )
     => ( ( X != Y )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ R )
         => ( ( Y != Z )
           => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ Y @ Z ) @ R )
             => ( ( X != Z )
                & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Z ) @ R ) ) ) ) ) ) ) ).

% Card_order_trans
thf(fact_972_Card__order__trans,axiom,
    ! [R: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
      ( ( bNF_Ca4062989147270679263at_nat @ ( field_3145993188331922222at_nat @ R ) @ R )
     => ( ( X != Y )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
         => ( ( Y != Z )
           => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ Z ) @ R )
             => ( ( X != Z )
                & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Z ) @ R ) ) ) ) ) ) ) ).

% Card_order_trans
thf(fact_973_Card__order__trans,axiom,
    ! [R: set_Product_prod_o_o,X: $o,Y: $o,Z: $o] :
      ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
     => ( ( X != Y )
       => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R )
         => ( ( Y != Z )
           => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y @ Z ) @ R )
             => ( ( X != Z )
                & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Z ) @ R ) ) ) ) ) ) ) ).

% Card_order_trans
thf(fact_974_wf__bounded__measure,axiom,
    ! [R: set_Pr1932065953672099015od_o_o,Ub: set_Product_prod_o_o > nat,F: set_Product_prod_o_o > nat] :
      ( ! [A4: set_Product_prod_o_o,B3: set_Product_prod_o_o] :
          ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ B3 @ A4 ) @ R )
         => ( ( ord_less_eq_nat @ ( Ub @ B3 ) @ ( Ub @ A4 ) )
            & ( ord_less_eq_nat @ ( F @ B3 ) @ ( Ub @ A4 ) )
            & ( ord_less_nat @ ( F @ A4 ) @ ( F @ B3 ) ) ) )
     => ( wf_set2384217916178216176od_o_o @ R ) ) ).

% wf_bounded_measure
thf(fact_975_wf__bounded__measure,axiom,
    ! [R: set_Pr4329608150637261639at_nat,Ub: set_Pr1261947904930325089at_nat > nat,F: set_Pr1261947904930325089at_nat > nat] :
      ( ! [A4: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
          ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B3 @ A4 ) @ R )
         => ( ( ord_less_eq_nat @ ( Ub @ B3 ) @ ( Ub @ A4 ) )
            & ( ord_less_eq_nat @ ( F @ B3 ) @ ( Ub @ A4 ) )
            & ( ord_less_nat @ ( F @ A4 ) @ ( F @ B3 ) ) ) )
     => ( wf_set7675013139414177994at_nat @ R ) ) ).

% wf_bounded_measure
thf(fact_976_in__measure,axiom,
    ! [X: set_Product_prod_o_o,Y: set_Product_prod_o_o,F: set_Product_prod_o_o > nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X @ Y ) @ ( measur5705974739304014543od_o_o @ F ) )
      = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).

% in_measure
thf(fact_977_in__measure,axiom,
    ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,F: set_Pr1261947904930325089at_nat > nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur1827424007717751593at_nat @ F ) )
      = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).

% in_measure
thf(fact_978_card__of__Un__ordLess__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_nat,B2: set_nat] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We3448473429330749420at_nat )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We3448473429330749420at_nat )
           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ R ) @ bNF_We3448473429330749420at_nat ) ) ) ) ) ).

% card_of_Un_ordLess_infinite_Field
thf(fact_979_card__of__Un__ordLess__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We8182288985678559134_o_nat )
         => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We8182288985678559134_o_nat )
           => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ ( sup_sup_set_o @ A2 @ B2 ) ) @ R ) @ bNF_We8182288985678559134_o_nat ) ) ) ) ) ).

% card_of_Un_ordLess_infinite_Field
thf(fact_980_card__of__Un__ordLess__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We2568191115274586186ss_o_o )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We2568191115274586186ss_o_o )
           => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ ( sup_sup_set_o @ A2 @ B2 ) ) @ R ) @ bNF_We2568191115274586186ss_o_o ) ) ) ) ) ).

% card_of_Un_ordLess_infinite_Field
thf(fact_981_card__of__Un__ordLess__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_nat,B2: set_nat] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We2061588309931968636_nat_o )
         => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We2061588309931968636_nat_o )
           => ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ R ) @ bNF_We2061588309931968636_nat_o ) ) ) ) ) ).

% card_of_Un_ordLess_infinite_Field
thf(fact_982_BNF__Cardinal__Order__Relation_OordLess__Field,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ ( field_o @ R ) ) @ R4 ) @ bNF_We2568191115274586186ss_o_o ) ) ).

% BNF_Cardinal_Order_Relation.ordLess_Field
thf(fact_983_BNF__Cardinal__Order__Relation_OordLess__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We3448473429330749420at_nat )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ R ) ) @ R4 ) @ bNF_We3448473429330749420at_nat ) ) ).

% BNF_Cardinal_Order_Relation.ordLess_Field
thf(fact_984_BNF__Cardinal__Order__Relation_OordLess__Field,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat )
     => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ ( field_o @ R ) ) @ R4 ) @ bNF_We8182288985678559134_o_nat ) ) ).

% BNF_Cardinal_Order_Relation.ordLess_Field
thf(fact_985_card__of__ordLess2,axiom,
    ! [B2: set_o,A2: set_o] :
      ( ( B2 != bot_bot_set_o )
     => ( ( ~ ? [F2: $o > $o] :
                ( ( image_o_o2 @ F2 @ A2 )
                = B2 ) )
        = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% card_of_ordLess2
thf(fact_986_card__of__ordLess2,axiom,
    ! [B2: set_nat,A2: set_nat] :
      ( ( B2 != bot_bot_set_nat )
     => ( ( ~ ? [F2: nat > nat] :
                ( ( image_nat_nat2 @ F2 @ A2 )
                = B2 ) )
        = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% card_of_ordLess2
thf(fact_987_card__of__ordLess2,axiom,
    ! [B2: set_nat,A2: set_o] :
      ( ( B2 != bot_bot_set_nat )
     => ( ( ~ ? [F2: $o > nat] :
                ( ( image_o_nat @ F2 @ A2 )
                = B2 ) )
        = ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We8182288985678559134_o_nat ) ) ) ).

% card_of_ordLess2
thf(fact_988_card__of__Un__ordLess__infinite,axiom,
    ! [C3: set_o,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_o @ C3 )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We2568191115274586186ss_o_o )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We2568191115274586186ss_o_o )
         => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ ( sup_sup_set_o @ A2 @ B2 ) ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We2568191115274586186ss_o_o ) ) ) ) ).

% card_of_Un_ordLess_infinite
thf(fact_989_card__of__Un__ordLess__infinite,axiom,
    ! [C3: set_nat,A2: set_nat,B2: set_nat] :
      ( ~ ( finite_finite_nat @ C3 )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We3448473429330749420at_nat )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We3448473429330749420at_nat )
         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We3448473429330749420at_nat ) ) ) ) ).

% card_of_Un_ordLess_infinite
thf(fact_990_card__of__Un__ordLess__infinite,axiom,
    ! [C3: set_nat,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_nat @ C3 )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We8182288985678559134_o_nat )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We8182288985678559134_o_nat )
         => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ ( sup_sup_set_o @ A2 @ B2 ) ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We8182288985678559134_o_nat ) ) ) ) ).

% card_of_Un_ordLess_infinite
thf(fact_991_card__of__ordLess,axiom,
    ! [A2: set_o,B2: set_o] :
      ( ( ~ ? [F2: $o > $o] :
              ( ( inj_on_o_o @ F2 @ A2 )
              & ( ord_less_eq_set_o @ ( image_o_o2 @ F2 @ A2 ) @ B2 ) ) )
      = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) ) @ bNF_We2568191115274586186ss_o_o ) ) ).

% card_of_ordLess
thf(fact_992_card__of__ordLess,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( ~ ? [F2: nat > nat] :
              ( ( inj_on_nat_nat @ F2 @ A2 )
              & ( ord_less_eq_set_nat @ ( image_nat_nat2 @ F2 @ A2 ) @ B2 ) ) )
      = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We3448473429330749420at_nat ) ) ).

% card_of_ordLess
thf(fact_993_card__of__ordLess,axiom,
    ! [A2: set_nat,B2: set_o] :
      ( ( ~ ? [F2: nat > $o] :
              ( ( inj_on_nat_o @ F2 @ A2 )
              & ( ord_less_eq_set_o @ ( image_nat_o @ F2 @ A2 ) @ B2 ) ) )
      = ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We8182288985678559134_o_nat ) ) ).

% card_of_ordLess
thf(fact_994_card__of__underS,axiom,
    ! [R: set_Pr1013884327308616903od_o_o,A: produc2934264451710624999od_o_o] :
      ( ( bNF_Ca4198200952365436517od_o_o @ ( field_5121862139100741428od_o_o @ R ) @ R )
     => ( ( member444158400953824016od_o_o @ A @ ( field_5121862139100741428od_o_o @ R ) )
       => ( member2182030262393914128od_o_o @ ( produc23025780167396183od_o_o @ ( bNF_Ca6121500631330824515od_o_o @ ( order_1929855754104155309od_o_o @ R @ A ) ) @ R ) @ bNF_We9142809693765176714od_o_o ) ) ) ).

% card_of_underS
thf(fact_995_card__of__underS,axiom,
    ! [R: set_Pr4427867301352232263at_nat,A: produc732395585841259969at_nat] :
      ( ( bNF_Ca7438713789483989055at_nat @ ( field_7361900449976055182at_nat @ R ) @ R )
     => ( ( member4095101504841534314at_nat @ A @ ( field_7361900449976055182at_nat @ R ) )
       => ( member4079835277323035408at_nat @ ( produc8612946581105484631at_nat @ ( bNF_Ca8664924986033767453at_nat @ ( order_6745690092771398279at_nat @ R @ A ) ) @ R ) @ bNF_We1318246335796365322at_nat ) ) ) ).

% card_of_underS
thf(fact_996_card__of__underS,axiom,
    ! [R: set_Pr5564308138774400199at_nat,A: produc3843707927480180839at_nat] :
      ( ( bNF_Ca8230877790521596901at_nat @ ( field_2862844103579723188at_nat @ R ) @ R )
     => ( ( member8757157785044589968at_nat @ A @ ( field_2862844103579723188at_nat @ R ) )
       => ( member2845199937591886608at_nat @ ( produc7545183385222921047at_nat @ ( bNF_Ca9194600574093320387at_nat @ ( order_3736018788886245933at_nat @ R @ A ) ) @ R ) @ bNF_We2594139806602030986at_nat ) ) ) ).

% card_of_underS
thf(fact_997_card__of__underS,axiom,
    ! [R: set_Product_prod_a_a,A: a] :
      ( ( bNF_Ca453948448923306620r_on_a @ ( field_a @ R ) @ R )
     => ( ( member_a @ A @ ( field_a @ R ) )
       => ( member4903802553882211088od_a_a @ ( produc3372137660326521687od_a_a @ ( bNF_Ca1104715389982341978d_of_a @ ( order_underS_a @ R @ A ) ) @ R ) @ bNF_We3281422121813167946ss_a_a ) ) ) ).

% card_of_underS
thf(fact_998_card__of__underS,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A: nat] :
      ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
     => ( ( member_nat @ A @ ( field_nat @ R ) )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( order_underS_nat @ R @ A ) ) @ R ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% card_of_underS
thf(fact_999_card__of__underS,axiom,
    ! [R: set_Product_prod_o_o,A: $o] :
      ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
     => ( ( member_o @ A @ ( field_o @ R ) )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ ( order_underS_o @ R @ A ) ) @ R ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% card_of_underS
thf(fact_1000_card__of__Plus__ordLess__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_nat,B2: set_nat] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We3448473429330749420at_nat )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We3448473429330749420at_nat )
           => ( member3047918529990910514at_nat @ ( produc6460772959230282105at_nat @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ A2 @ B2 ) ) @ R ) @ bNF_We7041958966232365723at_nat ) ) ) ) ) ).

% card_of_Plus_ordLess_infinite_Field
thf(fact_1001_card__of__Plus__ordLess__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_nat,B2: set_o] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We3448473429330749420at_nat )
         => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We8182288985678559134_o_nat )
           => ( member4812592190795650218at_nat @ ( produc5868257188881964785at_nat @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ A2 @ B2 ) ) @ R ) @ bNF_We4935586570105487173_o_nat ) ) ) ) ) ).

% card_of_Plus_ordLess_infinite_Field
thf(fact_1002_card__of__Plus__ordLess__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_o,B2: set_nat] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We8182288985678559134_o_nat )
         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We3448473429330749420at_nat )
           => ( member6178483945413987626at_nat @ ( produc7234148943500302193at_nat @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ A2 @ B2 ) ) @ R ) @ bNF_We1194315142955236767at_nat ) ) ) ) ) ).

% card_of_Plus_ordLess_infinite_Field
thf(fact_1003_card__of__Plus__ordLess__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We8182288985678559134_o_nat )
         => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We8182288985678559134_o_nat )
           => ( member989342599902505446at_nat @ ( produc4966347635449911085at_nat @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ A2 @ B2 ) ) @ R ) @ bNF_We7066948511106741057_o_nat ) ) ) ) ) ).

% card_of_Plus_ordLess_infinite_Field
thf(fact_1004_card__of__Plus__ordLess__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We2568191115274586186ss_o_o )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We2568191115274586186ss_o_o )
           => ( member8030178841557499788od_o_o @ ( produc5317466613051064531od_o_o @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ A2 @ B2 ) ) @ R ) @ bNF_We7847786823715778023_o_o_o ) ) ) ) ) ).

% card_of_Plus_ordLess_infinite_Field
thf(fact_1005_card__of__Plus__ordLess__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_o,B2: set_nat] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We2568191115274586186ss_o_o )
         => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We2061588309931968636_nat_o )
           => ( member121125266993124560od_o_o @ ( produc8931464078238085911od_o_o @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ A2 @ B2 ) ) @ R ) @ bNF_We2130777192033087497_nat_o ) ) ) ) ) ).

% card_of_Plus_ordLess_infinite_Field
thf(fact_1006_card__of__Plus__ordLess__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_nat,B2: set_o] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We2061588309931968636_nat_o )
         => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We2568191115274586186ss_o_o )
           => ( member4590549062032530512od_o_o @ ( produc4177515836422716055od_o_o @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ A2 @ B2 ) ) @ R ) @ bNF_We1503459268740929763at_o_o ) ) ) ) ) ).

% card_of_Plus_ordLess_infinite_Field
thf(fact_1007_card__of__Plus__ordLess__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_nat,B2: set_nat] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We2061588309931968636_nat_o )
         => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We2061588309931968636_nat_o )
           => ( member3285728679383846360od_o_o @ ( produc9174727453167716639od_o_o @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ A2 @ B2 ) ) @ R ) @ bNF_We9222787287886609421_nat_o ) ) ) ) ) ).

% card_of_Plus_ordLess_infinite_Field
thf(fact_1008_card__of__empty1,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
        | ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R ) )
     => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ bot_bot_set_o ) @ R ) @ bNF_We3435943820185352641_o_nat ) ) ).

% card_of_empty1
thf(fact_1009_card__of__empty1,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
        | ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R ) )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ bot_bot_set_nat ) @ R ) @ bNF_We2031159114419172489at_nat ) ) ).

% card_of_empty1
thf(fact_1010_card__of__empty1,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
        | ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R ) )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ bot_bot_set_o ) @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% card_of_empty1
thf(fact_1011_card__of__empty1,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
        | ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R ) )
     => ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ bot_bot_set_nat ) @ R ) @ bNF_We6538615181293537951_nat_o ) ) ).

% card_of_empty1
thf(fact_1012_card__of__Un__Plus__ordLeq,axiom,
    ! [A2: set_nat,B2: set_nat] : ( member7606898804734335598at_nat @ ( produc7668796723872103605at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ A2 @ B2 ) ) ) @ bNF_We4444846861891280440at_nat ) ).

% card_of_Un_Plus_ordLeq
thf(fact_1013_ordLeq__Plus__mono,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,P: set_Pr1261947904930325089at_nat,P8: set_Product_prod_o_o] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ P @ P8 ) @ bNF_We6538615181293537951_nat_o )
       => ( member952642050024735836um_o_o @ ( produc3837620720005901475um_o_o @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ ( field_nat @ R ) @ ( field_nat @ P ) ) ) @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ ( field_o @ R4 ) @ ( field_o @ P8 ) ) ) ) @ bNF_We7217180388603359757um_o_o ) ) ) ).

% ordLeq_Plus_mono
thf(fact_1014_ordLeq__Plus__mono,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,P: set_Product_prod_o_o,P8: set_Product_prod_o_o] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P @ P8 ) @ bNF_We8115293805659342695eq_o_o )
       => ( member8262324088718329556um_o_o @ ( produc4585484280506290715um_o_o @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ ( field_nat @ R ) @ ( field_o @ P ) ) ) @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ ( field_o @ R4 ) @ ( field_o @ P8 ) ) ) ) @ bNF_We1079009337437905725um_o_o ) ) ) ).

% ordLeq_Plus_mono
thf(fact_1015_ordLeq__Plus__mono,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,P: set_Product_prod_o_o,P8: set_Pr1261947904930325089at_nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P @ P8 ) @ bNF_We3435943820185352641_o_nat )
       => ( member6655200516074465936_o_nat @ ( produc4410791399313715927_o_nat @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ ( field_nat @ R ) @ ( field_o @ P ) ) ) @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ ( field_o @ R4 ) @ ( field_nat @ P8 ) ) ) ) @ bNF_We2094493454282013185_o_nat ) ) ) ).

% ordLeq_Plus_mono
thf(fact_1016_ordLeq__Plus__mono,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,P: set_Pr1261947904930325089at_nat,P8: set_Pr1261947904930325089at_nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P @ P8 ) @ bNF_We2031159114419172489at_nat )
       => ( member6975117218213954584_o_nat @ ( produc2864506647045777759_o_nat @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ ( field_nat @ R ) @ ( field_nat @ P ) ) ) @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ ( field_o @ R4 ) @ ( field_nat @ P8 ) ) ) ) @ bNF_We7239028013353664305_o_nat ) ) ) ).

% ordLeq_Plus_mono
thf(fact_1017_ordLeq__Plus__mono,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,P: set_Pr1261947904930325089at_nat,P8: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ P @ P8 ) @ bNF_We6538615181293537951_nat_o )
       => ( member8826396524424052564um_o_o @ ( produc5149556716212013723um_o_o @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ ( field_o @ R ) @ ( field_nat @ P ) ) ) @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ ( field_o @ R4 ) @ ( field_o @ P8 ) ) ) ) @ bNF_We8976728017661452183um_o_o ) ) ) ).

% ordLeq_Plus_mono
thf(fact_1018_ordLeq__Plus__mono,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,P: set_Product_prod_o_o,P8: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P @ P8 ) @ bNF_We8115293805659342695eq_o_o )
       => ( member3483138326940501008um_o_o @ ( produc1030987845608174167um_o_o @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ ( field_o @ R ) @ ( field_o @ P ) ) ) @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ ( field_o @ R4 ) @ ( field_o @ P8 ) ) ) ) @ bNF_We8987810345020088115um_o_o ) ) ) ).

% ordLeq_Plus_mono
thf(fact_1019_ordLeq__Plus__mono,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,P: set_Product_prod_o_o,P8: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P @ P8 ) @ bNF_We3435943820185352641_o_nat )
       => ( member3365704633057040844_o_nat @ ( produc3782849074957862163_o_nat @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ ( field_o @ R ) @ ( field_o @ P ) ) ) @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ ( field_o @ R4 ) @ ( field_nat @ P8 ) ) ) ) @ bNF_We3854041083340105611_o_nat ) ) ) ).

% ordLeq_Plus_mono
thf(fact_1020_ordLeq__Plus__mono,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,P: set_Pr1261947904930325089at_nat,P8: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P @ P8 ) @ bNF_We2031159114419172489at_nat )
       => ( member2972727061379769104_o_nat @ ( produc728317944619019095_o_nat @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ ( field_o @ R ) @ ( field_nat @ P ) ) ) @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ ( field_o @ R4 ) @ ( field_nat @ P8 ) ) ) ) @ bNF_We8273322497166968871_o_nat ) ) ) ).

% ordLeq_Plus_mono
thf(fact_1021_ordLeq__Plus__mono,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat,P8: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ P @ P8 ) @ bNF_We6538615181293537951_nat_o )
       => ( member7051533951421365136_nat_o @ ( produc5765749630380524503_nat_o @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ ( field_o @ R ) @ ( field_nat @ P ) ) ) @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ ( field_nat @ R4 ) @ ( field_o @ P8 ) ) ) ) @ bNF_We2558484984367686093_nat_o ) ) ) ).

% ordLeq_Plus_mono
thf(fact_1022_ordLeq__Plus__mono,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,P: set_Product_prod_o_o,P8: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P @ P8 ) @ bNF_We8115293805659342695eq_o_o )
       => ( member7444511523098636876_nat_o @ ( produc8820280760719367571_nat_o @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ ( field_o @ R ) @ ( field_o @ P ) ) ) @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ ( field_nat @ R4 ) @ ( field_o @ P8 ) ) ) ) @ bNF_We7362575607395598641_nat_o ) ) ) ).

% ordLeq_Plus_mono
thf(fact_1023_card__of__Plus__mono,axiom,
    ! [A2: set_o,B2: set_o,C3: set_o,D: set_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) @ ( bNF_Ca3172636760949973492d_of_o @ D ) ) @ bNF_We8115293805659342695eq_o_o )
       => ( member3483138326940501008um_o_o @ ( produc1030987845608174167um_o_o @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ A2 @ C3 ) ) @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ B2 @ D ) ) ) @ bNF_We8987810345020088115um_o_o ) ) ) ).

% card_of_Plus_mono
thf(fact_1024_card__of__Plus__mono,axiom,
    ! [A2: set_o,B2: set_o,C3: set_o,D: set_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) @ ( bNF_Ca3793111618940312692of_nat @ D ) ) @ bNF_We3435943820185352641_o_nat )
       => ( member3365704633057040844_o_nat @ ( produc3782849074957862163_o_nat @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ A2 @ C3 ) ) @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ B2 @ D ) ) ) @ bNF_We3854041083340105611_o_nat ) ) ) ).

% card_of_Plus_mono
thf(fact_1025_card__of__Plus__mono,axiom,
    ! [A2: set_o,B2: set_o,C3: set_nat,D: set_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ C3 ) @ ( bNF_Ca3793111618940312692of_nat @ D ) ) @ bNF_We2031159114419172489at_nat )
       => ( member2972727061379769104_o_nat @ ( produc728317944619019095_o_nat @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ A2 @ C3 ) ) @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ B2 @ D ) ) ) @ bNF_We8273322497166968871_o_nat ) ) ) ).

% card_of_Plus_mono
thf(fact_1026_card__of__Plus__mono,axiom,
    ! [A2: set_o,B2: set_nat,C3: set_o,D: set_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) @ ( bNF_Ca3172636760949973492d_of_o @ D ) ) @ bNF_We8115293805659342695eq_o_o )
       => ( member7444511523098636876_nat_o @ ( produc8820280760719367571_nat_o @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ A2 @ C3 ) ) @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ B2 @ D ) ) ) @ bNF_We7362575607395598641_nat_o ) ) ) ).

% card_of_Plus_mono
thf(fact_1027_card__of__Plus__mono,axiom,
    ! [A2: set_o,B2: set_nat,C3: set_o,D: set_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) @ ( bNF_Ca3793111618940312692of_nat @ D ) ) @ bNF_We3435943820185352641_o_nat )
       => ( member9006821182645044420at_nat @ ( produc6767169964153735947at_nat @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ A2 @ C3 ) ) @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ B2 @ D ) ) ) @ bNF_We1329699954732187917at_nat ) ) ) ).

% card_of_Plus_mono
thf(fact_1028_card__of__Plus__mono,axiom,
    ! [A2: set_o,B2: set_nat,C3: set_nat,D: set_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ C3 ) @ ( bNF_Ca3793111618940312692of_nat @ D ) ) @ bNF_We2031159114419172489at_nat )
       => ( member234890756356643848at_nat @ ( produc5352410120312684367at_nat @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ A2 @ C3 ) ) @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ B2 @ D ) ) ) @ bNF_We7431878391334027121at_nat ) ) ) ).

% card_of_Plus_mono
thf(fact_1029_card__of__Plus__mono,axiom,
    ! [A2: set_nat,B2: set_nat,C3: set_o,D: set_o] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We2031159114419172489at_nat )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) @ ( bNF_Ca3172636760949973492d_of_o @ D ) ) @ bNF_We8115293805659342695eq_o_o )
       => ( member1510635369261286160_nat_o @ ( produc224851048220445527_nat_o @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ A2 @ C3 ) ) @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ B2 @ D ) ) ) @ bNF_We5603027978337506215_nat_o ) ) ) ).

% card_of_Plus_mono
thf(fact_1030_card__of__Plus__mono,axiom,
    ! [A2: set_nat,B2: set_nat,C3: set_o,D: set_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We2031159114419172489at_nat )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) @ ( bNF_Ca3793111618940312692of_nat @ D ) ) @ bNF_We3435943820185352641_o_nat )
       => ( member7654646017578591112at_nat @ ( produc3548793344679855823at_nat @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ A2 @ C3 ) ) @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ B2 @ D ) ) ) @ bNF_We295405470918883351at_nat ) ) ) ).

% card_of_Plus_mono
thf(fact_1031_card__of__Plus__mono,axiom,
    ! [A2: set_nat,B2: set_nat,C3: set_nat,D: set_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We2031159114419172489at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ C3 ) @ ( bNF_Ca3793111618940312692of_nat @ D ) ) @ bNF_We2031159114419172489at_nat )
       => ( member3674313732307032336at_nat @ ( produc2112825387572549975at_nat @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ A2 @ C3 ) ) @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ B2 @ D ) ) ) @ bNF_We5082115074515246823at_nat ) ) ) ).

% card_of_Plus_mono
thf(fact_1032_card__of__Plus__ordLeq__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We3435943820185352641_o_nat )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We3435943820185352641_o_nat )
         => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
           => ( member989342599902505446at_nat @ ( produc4966347635449911085at_nat @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ A2 @ B2 ) ) @ R ) @ bNF_We3900823710022635230_o_nat ) ) ) ) ) ).

% card_of_Plus_ordLeq_infinite_Field
thf(fact_1033_card__of__Plus__ordLeq__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_o,B2: set_nat] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We3435943820185352641_o_nat )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We2031159114419172489at_nat )
         => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
           => ( member6178483945413987626at_nat @ ( produc7234148943500302193at_nat @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ A2 @ B2 ) ) @ R ) @ bNF_We7395407223230661442at_nat ) ) ) ) ) ).

% card_of_Plus_ordLeq_infinite_Field
thf(fact_1034_card__of__Plus__ordLeq__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_nat,B2: set_o] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We2031159114419172489at_nat )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We3435943820185352641_o_nat )
         => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
           => ( member4812592190795650218at_nat @ ( produc5868257188881964785at_nat @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ A2 @ B2 ) ) @ R ) @ bNF_We1913306613526136040_o_nat ) ) ) ) ) ).

% card_of_Plus_ordLeq_infinite_Field
thf(fact_1035_card__of__Plus__ordLeq__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_nat,B2: set_nat] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We2031159114419172489at_nat )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We2031159114419172489at_nat )
         => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
           => ( member3047918529990910514at_nat @ ( produc6460772959230282105at_nat @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ A2 @ B2 ) ) @ R ) @ bNF_We5086521355153908664at_nat ) ) ) ) ) ).

% card_of_Plus_ordLeq_infinite_Field
thf(fact_1036_card__of__Plus__ordLeq__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We8115293805659342695eq_o_o )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We8115293805659342695eq_o_o )
         => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
           => ( member8030178841557499788od_o_o @ ( produc5317466613051064531od_o_o @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ A2 @ B2 ) ) @ R ) @ bNF_We3513324756044439818_o_o_o ) ) ) ) ) ).

% card_of_Plus_ordLeq_infinite_Field
thf(fact_1037_card__of__Plus__ordLeq__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_o,B2: set_nat] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We8115293805659342695eq_o_o )
       => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We6538615181293537951_nat_o )
         => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
           => ( member121125266993124560od_o_o @ ( produc8931464078238085911od_o_o @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ A2 @ B2 ) ) @ R ) @ bNF_We8188024427803757478_nat_o ) ) ) ) ) ).

% card_of_Plus_ordLeq_infinite_Field
thf(fact_1038_card__of__Plus__ordLeq__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_nat,B2: set_o] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We6538615181293537951_nat_o )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We8115293805659342695eq_o_o )
         => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
           => ( member4590549062032530512od_o_o @ ( produc4177515836422716055od_o_o @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ A2 @ B2 ) ) @ R ) @ bNF_We7560706504511599744at_o_o ) ) ) ) ) ).

% card_of_Plus_ordLeq_infinite_Field
thf(fact_1039_card__of__Plus__ordLeq__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_nat,B2: set_nat] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We6538615181293537951_nat_o )
       => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We6538615181293537951_nat_o )
         => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
           => ( member3285728679383846360od_o_o @ ( produc9174727453167716639od_o_o @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ A2 @ B2 ) ) @ R ) @ bNF_We6200507331307258288_nat_o ) ) ) ) ) ).

% card_of_Plus_ordLeq_infinite_Field
thf(fact_1040_ordLeq__transitive,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We3435943820185352641_o_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We2031159114419172489at_nat ) ) ) ).

% ordLeq_transitive
thf(fact_1041_ordLeq__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R5 ) @ bNF_We8115293805659342695eq_o_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We8115293805659342695eq_o_o ) ) ) ).

% ordLeq_transitive
thf(fact_1042_ordLeq__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We3435943820185352641_o_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We3435943820185352641_o_nat ) ) ) ).

% ordLeq_transitive
thf(fact_1043_ordLeq__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R5 ) @ bNF_We6538615181293537951_nat_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We8115293805659342695eq_o_o ) ) ) ).

% ordLeq_transitive
thf(fact_1044_ordLeq__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We2031159114419172489at_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We3435943820185352641_o_nat ) ) ) ).

% ordLeq_transitive
thf(fact_1045_ordLeq__transitive,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We2031159114419172489at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We2031159114419172489at_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We2031159114419172489at_nat ) ) ) ).

% ordLeq_transitive
thf(fact_1046_infinite__iff__card__of__nat,axiom,
    ! [A2: set_nat] :
      ( ( ~ ( finite_finite_nat @ A2 ) )
      = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ top_top_set_nat ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We2031159114419172489at_nat ) ) ).

% infinite_iff_card_of_nat
thf(fact_1047_ordLess__ordLeq__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We2061588309931968636_nat_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We3435943820185352641_o_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% ordLess_ordLeq_trans
thf(fact_1048_ordLess__ordLeq__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R5 ) @ bNF_We8115293805659342695eq_o_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% ordLess_ordLeq_trans
thf(fact_1049_ordLess__ordLeq__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We3448473429330749420at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We2031159114419172489at_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% ordLess_ordLeq_trans
thf(fact_1050_ordLess__ordLeq__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We3435943820185352641_o_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We8182288985678559134_o_nat ) ) ) ).

% ordLess_ordLeq_trans
thf(fact_1051_ordLess__ordLeq__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R5 ) @ bNF_We6538615181293537951_nat_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% ordLess_ordLeq_trans
thf(fact_1052_ordLess__ordLeq__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We2031159114419172489at_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We8182288985678559134_o_nat ) ) ) ).

% ordLess_ordLeq_trans
thf(fact_1053_ordLeq__ordLess__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R5 ) @ bNF_We2568191115274586186ss_o_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% ordLeq_ordLess_trans
thf(fact_1054_ordLeq__ordLess__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R5 ) @ bNF_We2061588309931968636_nat_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% ordLeq_ordLess_trans
thf(fact_1055_ordLeq__ordLess__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We2031159114419172489at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We3448473429330749420at_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% ordLeq_ordLess_trans
thf(fact_1056_ordLeq__ordLess__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We3448473429330749420at_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We8182288985678559134_o_nat ) ) ) ).

% ordLeq_ordLess_trans
thf(fact_1057_ordLeq__ordLess__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We8182288985678559134_o_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% ordLeq_ordLess_trans
thf(fact_1058_ordLeq__ordLess__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We8182288985678559134_o_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We8182288985678559134_o_nat ) ) ) ).

% ordLeq_ordLess_trans
thf(fact_1059_ordLess__imp__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% ordLess_imp_ordLeq
thf(fact_1060_ordLess__imp__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We3448473429330749420at_nat )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We2031159114419172489at_nat ) ) ).

% ordLess_imp_ordLeq
thf(fact_1061_ordLess__imp__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat )
     => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat ) ) ).

% ordLess_imp_ordLeq
thf(fact_1062_not__ordLess__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We2061588309931968636_nat_o )
     => ~ ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R ) @ bNF_We3435943820185352641_o_nat ) ) ).

% not_ordLess_ordLeq
thf(fact_1063_not__ordLess__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o )
     => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% not_ordLess_ordLeq
thf(fact_1064_not__ordLess__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We3448473429330749420at_nat )
     => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R ) @ bNF_We2031159114419172489at_nat ) ) ).

% not_ordLess_ordLeq
thf(fact_1065_not__ordLess__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat )
     => ~ ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R ) @ bNF_We6538615181293537951_nat_o ) ) ).

% not_ordLess_ordLeq
thf(fact_1066_not__ordLeq__ordLess,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R ) @ bNF_We2568191115274586186ss_o_o ) ) ).

% not_ordLeq_ordLess
thf(fact_1067_not__ordLeq__ordLess,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
     => ~ ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R ) @ bNF_We2061588309931968636_nat_o ) ) ).

% not_ordLeq_ordLess
thf(fact_1068_not__ordLeq__ordLess,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We2031159114419172489at_nat )
     => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R ) @ bNF_We3448473429330749420at_nat ) ) ).

% not_ordLeq_ordLess
thf(fact_1069_not__ordLeq__ordLess,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
     => ~ ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R ) @ bNF_We8182288985678559134_o_nat ) ) ).

% not_ordLeq_ordLess
thf(fact_1070_card__of__image,axiom,
    ! [F: $o > $o,A2: set_o] : ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ ( image_o_o2 @ F @ A2 ) ) @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) ) @ bNF_We8115293805659342695eq_o_o ) ).

% card_of_image
thf(fact_1071_card__of__image,axiom,
    ! [F: nat > $o,A2: set_nat] : ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ ( image_nat_o @ F @ A2 ) ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We3435943820185352641_o_nat ) ).

% card_of_image
thf(fact_1072_card__of__image,axiom,
    ! [F: nat > nat,A2: set_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( image_nat_nat2 @ F @ A2 ) ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We2031159114419172489at_nat ) ).

% card_of_image
thf(fact_1073_card__of__empty,axiom,
    ! [A2: set_o] : ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ bot_bot_set_o ) @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) ) @ bNF_We8115293805659342695eq_o_o ) ).

% card_of_empty
thf(fact_1074_card__of__empty,axiom,
    ! [A2: set_nat] : ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ bot_bot_set_o ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We3435943820185352641_o_nat ) ).

% card_of_empty
thf(fact_1075_card__of__empty,axiom,
    ! [A2: set_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ bot_bot_set_nat ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We2031159114419172489at_nat ) ).

% card_of_empty
thf(fact_1076_card__of__empty3,axiom,
    ! [A2: set_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ bot_bot_set_o ) ) @ bNF_We8115293805659342695eq_o_o )
     => ( A2 = bot_bot_set_o ) ) ).

% card_of_empty3
thf(fact_1077_card__of__empty3,axiom,
    ! [A2: set_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ bot_bot_set_nat ) ) @ bNF_We3435943820185352641_o_nat )
     => ( A2 = bot_bot_set_o ) ) ).

% card_of_empty3
thf(fact_1078_card__of__empty3,axiom,
    ! [A2: set_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ bot_bot_set_nat ) ) @ bNF_We2031159114419172489at_nat )
     => ( A2 = bot_bot_set_nat ) ) ).

% card_of_empty3
thf(fact_1079_card__of__ordLeq__finite,axiom,
    ! [A2: set_o,B2: set_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( finite_finite_o @ B2 )
       => ( finite_finite_o @ A2 ) ) ) ).

% card_of_ordLeq_finite
thf(fact_1080_card__of__ordLeq__finite,axiom,
    ! [A2: set_o,B2: set_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We3435943820185352641_o_nat )
     => ( ( finite_finite_nat @ B2 )
       => ( finite_finite_o @ A2 ) ) ) ).

% card_of_ordLeq_finite
thf(fact_1081_card__of__ordLeq__finite,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We2031159114419172489at_nat )
     => ( ( finite_finite_nat @ B2 )
       => ( finite_finite_nat @ A2 ) ) ) ).

% card_of_ordLeq_finite
thf(fact_1082_card__of__ordLeq__infinite,axiom,
    ! [A2: set_o,B2: set_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) ) @ bNF_We8115293805659342695eq_o_o )
     => ( ~ ( finite_finite_o @ A2 )
       => ~ ( finite_finite_o @ B2 ) ) ) ).

% card_of_ordLeq_infinite
thf(fact_1083_card__of__ordLeq__infinite,axiom,
    ! [A2: set_o,B2: set_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We3435943820185352641_o_nat )
     => ( ~ ( finite_finite_o @ A2 )
       => ~ ( finite_finite_nat @ B2 ) ) ) ).

% card_of_ordLeq_infinite
thf(fact_1084_card__of__ordLeq__infinite,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We2031159114419172489at_nat )
     => ( ~ ( finite_finite_nat @ A2 )
       => ~ ( finite_finite_nat @ B2 ) ) ) ).

% card_of_ordLeq_infinite
thf(fact_1085_card__of__mono1,axiom,
    ! [A2: set_o,B2: set_o] :
      ( ( ord_less_eq_set_o @ A2 @ B2 )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% card_of_mono1
thf(fact_1086_card__of__mono1,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ B2 )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We2031159114419172489at_nat ) ) ).

% card_of_mono1
thf(fact_1087_card__of__mono2,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ ( field_o @ R ) ) @ ( bNF_Ca3172636760949973492d_of_o @ ( field_o @ R4 ) ) ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% card_of_mono2
thf(fact_1088_card__of__mono2,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
     => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ ( field_o @ R ) ) @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ R4 ) ) ) @ bNF_We3435943820185352641_o_nat ) ) ).

% card_of_mono2
thf(fact_1089_card__of__mono2,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
     => ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ R ) ) @ ( bNF_Ca3172636760949973492d_of_o @ ( field_o @ R4 ) ) ) @ bNF_We6538615181293537951_nat_o ) ) ).

% card_of_mono2
thf(fact_1090_card__of__mono2,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We2031159114419172489at_nat )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ R ) ) @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ R4 ) ) ) @ bNF_We2031159114419172489at_nat ) ) ).

% card_of_mono2
thf(fact_1091_exists__minim__Card__order,axiom,
    ! [R3: set_se7855581050983116737at_nat] :
      ( ( R3 != bot_bo3083307316010499117at_nat )
     => ( ! [X3: set_Pr1261947904930325089at_nat] :
            ( ( member2643936169264416010at_nat @ X3 @ R3 )
           => ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ X3 ) @ X3 ) )
       => ? [X3: set_Pr1261947904930325089at_nat] :
            ( ( member2643936169264416010at_nat @ X3 @ R3 )
            & ! [Xa: set_Pr1261947904930325089at_nat] :
                ( ( member2643936169264416010at_nat @ Xa @ R3 )
               => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Xa ) @ bNF_We2031159114419172489at_nat ) ) ) ) ) ).

% exists_minim_Card_order
thf(fact_1092_exists__minim__Card__order,axiom,
    ! [R3: set_se491199571785101031od_o_o] :
      ( ( R3 != bot_bo8006819982598807891od_o_o )
     => ( ! [X3: set_Product_prod_o_o] :
            ( ( member3157015407008874800od_o_o @ X3 @ R3 )
           => ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ X3 ) @ X3 ) )
       => ? [X3: set_Product_prod_o_o] :
            ( ( member3157015407008874800od_o_o @ X3 @ R3 )
            & ! [Xa: set_Product_prod_o_o] :
                ( ( member3157015407008874800od_o_o @ Xa @ R3 )
               => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Xa ) @ bNF_We8115293805659342695eq_o_o ) ) ) ) ) ).

% exists_minim_Card_order
thf(fact_1093_card__of__ordLeqI,axiom,
    ! [F: a > a,A2: set_a,B2: set_a] :
      ( ( inj_on_a_a @ F @ A2 )
     => ( ! [A4: a] :
            ( ( member_a @ A4 @ A2 )
           => ( member_a @ ( F @ A4 ) @ B2 ) )
       => ( member4903802553882211088od_a_a @ ( produc3372137660326521687od_a_a @ ( bNF_Ca1104715389982341978d_of_a @ A2 ) @ ( bNF_Ca1104715389982341978d_of_a @ B2 ) ) @ bNF_We6465643273610285415eq_a_a ) ) ) ).

% card_of_ordLeqI
thf(fact_1094_card__of__ordLeqI,axiom,
    ! [F: $o > $o,A2: set_o,B2: set_o] :
      ( ( inj_on_o_o @ F @ A2 )
     => ( ! [A4: $o] :
            ( ( member_o @ A4 @ A2 )
           => ( member_o @ ( F @ A4 ) @ B2 ) )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) ) @ bNF_We8115293805659342695eq_o_o ) ) ) ).

% card_of_ordLeqI
thf(fact_1095_card__of__ordLeqI,axiom,
    ! [F: a > nat,A2: set_a,B2: set_nat] :
      ( ( inj_on_a_nat @ F @ A2 )
     => ( ! [A4: a] :
            ( ( member_a @ A4 @ A2 )
           => ( member_nat @ ( F @ A4 ) @ B2 ) )
       => ( member6858118926070794858at_nat @ ( produc2553196175173902513at_nat @ ( bNF_Ca1104715389982341978d_of_a @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We4671332349262384423_a_nat ) ) ) ).

% card_of_ordLeqI
thf(fact_1096_card__of__ordLeqI,axiom,
    ! [F: $o > nat,A2: set_o,B2: set_nat] :
      ( ( inj_on_o_nat @ F @ A2 )
     => ( ! [A4: $o] :
            ( ( member_o @ A4 @ A2 )
           => ( member_nat @ ( F @ A4 ) @ B2 ) )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We3435943820185352641_o_nat ) ) ) ).

% card_of_ordLeqI
thf(fact_1097_card__of__ordLeqI,axiom,
    ! [F: nat > a,A2: set_nat,B2: set_a] :
      ( ( inj_on_nat_a @ F @ A2 )
     => ( ! [A4: nat] :
            ( ( member_nat @ A4 @ A2 )
           => ( member_a @ ( F @ A4 ) @ B2 ) )
       => ( member5274544965882063670od_a_a @ ( produc6016498021161588349od_a_a @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca1104715389982341978d_of_a @ B2 ) ) @ bNF_We8703263850440670853_nat_a ) ) ) ).

% card_of_ordLeqI
thf(fact_1098_card__of__ordLeqI,axiom,
    ! [F: nat > nat,A2: set_nat,B2: set_nat] :
      ( ( inj_on_nat_nat @ F @ A2 )
     => ( ! [A4: nat] :
            ( ( member_nat @ A4 @ A2 )
           => ( member_nat @ ( F @ A4 ) @ B2 ) )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We2031159114419172489at_nat ) ) ) ).

% card_of_ordLeqI
thf(fact_1099_card__of__ordLeqI,axiom,
    ! [F: produc2934264451710624999od_o_o > a,A2: set_Pr1932065953672099015od_o_o,B2: set_a] :
      ( ( inj_on8505222220193863496_o_o_a @ F @ A2 )
     => ( ! [A4: produc2934264451710624999od_o_o] :
            ( ( member444158400953824016od_o_o @ A4 @ A2 )
           => ( member_a @ ( F @ A4 ) @ B2 ) )
       => ( member2379278310075879248od_a_a @ ( produc6706904248712485783od_a_a @ ( bNF_Ca6121500631330824515od_o_o @ A2 ) @ ( bNF_Ca1104715389982341978d_of_a @ B2 ) ) @ bNF_We8478588574694708158_o_o_a ) ) ) ).

% card_of_ordLeqI
thf(fact_1100_card__of__ordLeqI,axiom,
    ! [F: produc732395585841259969at_nat > a,A2: set_Pr457366540195662369at_nat,B2: set_a] :
      ( ( inj_on258112795223470062_nat_a @ F @ A2 )
     => ( ! [A4: produc732395585841259969at_nat] :
            ( ( member4095101504841534314at_nat @ A4 @ A2 )
           => ( member_a @ ( F @ A4 ) @ B2 ) )
       => ( member7043285137284140240od_a_a @ ( produc6483374742268400407od_a_a @ ( bNF_Ca8664924986033767453at_nat @ A2 ) @ ( bNF_Ca1104715389982341978d_of_a @ B2 ) ) @ bNF_We6709918416631134564_nat_a ) ) ) ).

% card_of_ordLeqI
thf(fact_1101_card__of__ordLeqI,axiom,
    ! [F: produc3843707927480180839at_nat > a,A2: set_Pr4329608150637261639at_nat,B2: set_a] :
      ( ( inj_on258414713793403336_nat_a @ F @ A2 )
     => ( ! [A4: produc3843707927480180839at_nat] :
            ( ( member8757157785044589968at_nat @ A4 @ A2 )
           => ( member_a @ ( F @ A4 ) @ B2 ) )
       => ( member6195182203977450320od_a_a @ ( produc4160138634059301783od_a_a @ ( bNF_Ca9194600574093320387at_nat @ A2 ) @ ( bNF_Ca1104715389982341978d_of_a @ B2 ) ) @ bNF_We3386010043725180990_nat_a ) ) ) ).

% card_of_ordLeqI
thf(fact_1102_card__of__ordLeqI,axiom,
    ! [F: a > produc2934264451710624999od_o_o,A2: set_a,B2: set_Pr1932065953672099015od_o_o] :
      ( ( inj_on10636220523687386od_o_o @ F @ A2 )
     => ( ! [A4: a] :
            ( ( member_a @ A4 @ A2 )
           => ( member444158400953824016od_o_o @ ( F @ A4 ) @ B2 ) )
       => ( member7884865674050070224od_o_o @ ( produc5353641014327778071od_o_o @ ( bNF_Ca1104715389982341978d_of_a @ A2 ) @ ( bNF_Ca6121500631330824515od_o_o @ B2 ) ) @ bNF_We9207374611879307856od_o_o ) ) ) ).

% card_of_ordLeqI
thf(fact_1103_ordLeq__total,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 )
       => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
          | ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R ) @ bNF_We3435943820185352641_o_nat ) ) ) ) ).

% ordLeq_total
thf(fact_1104_ordLeq__total,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
          | ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ) ) ).

% ordLeq_total
thf(fact_1105_ordLeq__total,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
          | ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R ) @ bNF_We6538615181293537951_nat_o ) ) ) ) ).

% ordLeq_total
thf(fact_1106_ordLeq__total,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We2031159114419172489at_nat )
          | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R ) @ bNF_We2031159114419172489at_nat ) ) ) ) ).

% ordLeq_total
thf(fact_1107_ordLeq__reflexive,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% ordLeq_reflexive
thf(fact_1108_ordLeq__reflexive,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R ) @ bNF_We2031159114419172489at_nat ) ) ).

% ordLeq_reflexive
thf(fact_1109_ordLeq__Well__order__simp,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
        & ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 ) ) ) ).

% ordLeq_Well_order_simp
thf(fact_1110_ordLeq__Well__order__simp,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
        & ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 ) ) ) ).

% ordLeq_Well_order_simp
thf(fact_1111_ordLeq__Well__order__simp,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
        & ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 ) ) ) ).

% ordLeq_Well_order_simp
thf(fact_1112_ordLeq__Well__order__simp,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We2031159114419172489at_nat )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
        & ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 ) ) ) ).

% ordLeq_Well_order_simp
thf(fact_1113_exists__minim__Well__order,axiom,
    ! [R3: set_se491199571785101031od_o_o] :
      ( ( R3 != bot_bo8006819982598807891od_o_o )
     => ( ! [X3: set_Product_prod_o_o] :
            ( ( member3157015407008874800od_o_o @ X3 @ R3 )
           => ( order_2615775362358406454r_on_o @ ( field_o @ X3 ) @ X3 ) )
       => ? [X3: set_Product_prod_o_o] :
            ( ( member3157015407008874800od_o_o @ X3 @ R3 )
            & ! [Xa: set_Product_prod_o_o] :
                ( ( member3157015407008874800od_o_o @ Xa @ R3 )
               => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ X3 @ Xa ) @ bNF_We8115293805659342695eq_o_o ) ) ) ) ) ).

% exists_minim_Well_order
thf(fact_1114_exists__minim__Well__order,axiom,
    ! [R3: set_se7855581050983116737at_nat] :
      ( ( R3 != bot_bo3083307316010499117at_nat )
     => ( ! [X3: set_Pr1261947904930325089at_nat] :
            ( ( member2643936169264416010at_nat @ X3 @ R3 )
           => ( order_2888998067076097458on_nat @ ( field_nat @ X3 ) @ X3 ) )
       => ? [X3: set_Pr1261947904930325089at_nat] :
            ( ( member2643936169264416010at_nat @ X3 @ R3 )
            & ! [Xa: set_Pr1261947904930325089at_nat] :
                ( ( member2643936169264416010at_nat @ Xa @ R3 )
               => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Xa ) @ bNF_We2031159114419172489at_nat ) ) ) ) ) ).

% exists_minim_Well_order
thf(fact_1115_card__of__least,axiom,
    ! [A2: set_o,R: set_Product_prod_o_o] :
      ( ( order_2615775362358406454r_on_o @ A2 @ R )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% card_of_least
thf(fact_1116_card__of__least,axiom,
    ! [A2: set_nat,R: set_Pr1261947904930325089at_nat] :
      ( ( order_2888998067076097458on_nat @ A2 @ R )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We2031159114419172489at_nat ) ) ).

% card_of_least
thf(fact_1117_card__order__on__def,axiom,
    ( bNF_Ca1281551314933786834on_nat
    = ( ^ [A7: set_nat,R2: set_Pr1261947904930325089at_nat] :
          ( ( order_2888998067076097458on_nat @ A7 @ R2 )
          & ! [R6: set_Pr1261947904930325089at_nat] :
              ( ( order_2888998067076097458on_nat @ A7 @ R6 )
             => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R2 @ R6 ) @ bNF_We2031159114419172489at_nat ) ) ) ) ) ).

% card_order_on_def
thf(fact_1118_card__order__on__def,axiom,
    ( bNF_Ca8331644756375544342r_on_o
    = ( ^ [A7: set_o,R2: set_Product_prod_o_o] :
          ( ( order_2615775362358406454r_on_o @ A7 @ R2 )
          & ! [R6: set_Product_prod_o_o] :
              ( ( order_2615775362358406454r_on_o @ A7 @ R6 )
             => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R2 @ R6 ) @ bNF_We8115293805659342695eq_o_o ) ) ) ) ) ).

% card_order_on_def
thf(fact_1119_card__of__ordLeq2,axiom,
    ! [A2: set_o,B2: set_o] :
      ( ( A2 != bot_bot_set_o )
     => ( ( ? [G2: $o > $o] :
              ( ( image_o_o2 @ G2 @ B2 )
              = A2 ) )
        = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) ) @ bNF_We8115293805659342695eq_o_o ) ) ) ).

% card_of_ordLeq2
thf(fact_1120_card__of__ordLeq2,axiom,
    ! [A2: set_o,B2: set_nat] :
      ( ( A2 != bot_bot_set_o )
     => ( ( ? [G2: nat > $o] :
              ( ( image_nat_o @ G2 @ B2 )
              = A2 ) )
        = ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We3435943820185352641_o_nat ) ) ) ).

% card_of_ordLeq2
thf(fact_1121_card__of__ordLeq2,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( A2 != bot_bot_set_nat )
     => ( ( ? [G2: nat > nat] :
              ( ( image_nat_nat2 @ G2 @ B2 )
              = A2 ) )
        = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We2031159114419172489at_nat ) ) ) ).

% card_of_ordLeq2
thf(fact_1122_surj__imp__ordLeq,axiom,
    ! [B2: set_o,F: $o > $o,A2: set_o] :
      ( ( ord_less_eq_set_o @ B2 @ ( image_o_o2 @ F @ A2 ) )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% surj_imp_ordLeq
thf(fact_1123_surj__imp__ordLeq,axiom,
    ! [B2: set_o,F: nat > $o,A2: set_nat] :
      ( ( ord_less_eq_set_o @ B2 @ ( image_nat_o @ F @ A2 ) )
     => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We3435943820185352641_o_nat ) ) ).

% surj_imp_ordLeq
thf(fact_1124_surj__imp__ordLeq,axiom,
    ! [B2: set_nat,F: nat > nat,A2: set_nat] :
      ( ( ord_less_eq_set_nat @ B2 @ ( image_nat_nat2 @ F @ A2 ) )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We2031159114419172489at_nat ) ) ).

% surj_imp_ordLeq
thf(fact_1125_card__of__singl__ordLeq,axiom,
    ! [A2: set_o,B: $o] :
      ( ( A2 != bot_bot_set_o )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% card_of_singl_ordLeq
thf(fact_1126_card__of__singl__ordLeq,axiom,
    ! [A2: set_nat,B: $o] :
      ( ( A2 != bot_bot_set_nat )
     => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We3435943820185352641_o_nat ) ) ).

% card_of_singl_ordLeq
thf(fact_1127_card__of__singl__ordLeq,axiom,
    ! [A2: set_nat,B: nat] :
      ( ( A2 != bot_bot_set_nat )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We2031159114419172489at_nat ) ) ).

% card_of_singl_ordLeq
thf(fact_1128_Card__order__iff__ordLeq__card__of,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
      = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ R ) ) ) @ bNF_We2031159114419172489at_nat ) ) ).

% Card_order_iff_ordLeq_card_of
thf(fact_1129_Card__order__iff__ordLeq__card__of,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
      = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ ( bNF_Ca3172636760949973492d_of_o @ ( field_o @ R ) ) ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% Card_order_iff_ordLeq_card_of
thf(fact_1130_card__of__Field__ordLess,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ ( field_o @ R ) ) @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% card_of_Field_ordLess
thf(fact_1131_card__of__Field__ordLess,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ R ) ) @ R ) @ bNF_We2031159114419172489at_nat ) ) ).

% card_of_Field_ordLess
thf(fact_1132_not__ordLess__iff__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 )
       => ( ( ~ ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R ) @ bNF_We2061588309931968636_nat_o ) )
          = ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat ) ) ) ) ).

% not_ordLess_iff_ordLeq
thf(fact_1133_not__ordLess__iff__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 )
       => ( ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R ) @ bNF_We2568191115274586186ss_o_o ) )
          = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o ) ) ) ) ).

% not_ordLess_iff_ordLeq
thf(fact_1134_not__ordLess__iff__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 )
       => ( ( ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R ) @ bNF_We3448473429330749420at_nat ) )
          = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We2031159114419172489at_nat ) ) ) ) ).

% not_ordLess_iff_ordLeq
thf(fact_1135_not__ordLess__iff__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 )
       => ( ( ~ ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R ) @ bNF_We8182288985678559134_o_nat ) )
          = ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o ) ) ) ) ).

% not_ordLess_iff_ordLeq
thf(fact_1136_not__ordLeq__iff__ordLess,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 )
       => ( ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R ) @ bNF_We8115293805659342695eq_o_o ) )
          = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ) ).

% not_ordLeq_iff_ordLess
thf(fact_1137_not__ordLeq__iff__ordLess,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 )
       => ( ( ~ ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R ) @ bNF_We3435943820185352641_o_nat ) )
          = ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We2061588309931968636_nat_o ) ) ) ) ).

% not_ordLeq_iff_ordLess
thf(fact_1138_not__ordLeq__iff__ordLess,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 )
       => ( ( ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R ) @ bNF_We2031159114419172489at_nat ) )
          = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We3448473429330749420at_nat ) ) ) ) ).

% not_ordLeq_iff_ordLess
thf(fact_1139_not__ordLeq__iff__ordLess,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 )
       => ( ( ~ ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R ) @ bNF_We6538615181293537951_nat_o ) )
          = ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat ) ) ) ) ).

% not_ordLeq_iff_ordLess
thf(fact_1140_ordLess__or__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 )
       => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We2061588309931968636_nat_o )
          | ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R ) @ bNF_We3435943820185352641_o_nat ) ) ) ) ).

% ordLess_or_ordLeq
thf(fact_1141_ordLess__or__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( ( order_2615775362358406454r_on_o @ ( field_o @ R4 ) @ R4 )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o )
          | ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ) ) ).

% ordLess_or_ordLeq
thf(fact_1142_ordLess__or__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( order_2888998067076097458on_nat @ ( field_nat @ R ) @ R )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We3448473429330749420at_nat )
          | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R ) @ bNF_We2031159114419172489at_nat ) ) ) ) ).

% ordLess_or_ordLeq
thf(fact_1143_ordLess__or__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( order_2615775362358406454r_on_o @ ( field_o @ R ) @ R )
     => ( ( order_2888998067076097458on_nat @ ( field_nat @ R4 ) @ R4 )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat )
          | ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R ) @ bNF_We6538615181293537951_nat_o ) ) ) ) ).

% ordLess_or_ordLeq
thf(fact_1144_card__of__Plus__ordLess__infinite,axiom,
    ! [C3: set_o,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_o @ C3 )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We2568191115274586186ss_o_o )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We2568191115274586186ss_o_o )
         => ( member8030178841557499788od_o_o @ ( produc5317466613051064531od_o_o @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ A2 @ B2 ) ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We7847786823715778023_o_o_o ) ) ) ) ).

% card_of_Plus_ordLess_infinite
thf(fact_1145_card__of__Plus__ordLess__infinite,axiom,
    ! [C3: set_o,A2: set_o,B2: set_nat] :
      ( ~ ( finite_finite_o @ C3 )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We2568191115274586186ss_o_o )
       => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We2061588309931968636_nat_o )
         => ( member121125266993124560od_o_o @ ( produc8931464078238085911od_o_o @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ A2 @ B2 ) ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We2130777192033087497_nat_o ) ) ) ) ).

% card_of_Plus_ordLess_infinite
thf(fact_1146_card__of__Plus__ordLess__infinite,axiom,
    ! [C3: set_o,A2: set_nat,B2: set_o] :
      ( ~ ( finite_finite_o @ C3 )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We2061588309931968636_nat_o )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We2568191115274586186ss_o_o )
         => ( member4590549062032530512od_o_o @ ( produc4177515836422716055od_o_o @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ A2 @ B2 ) ) @ ( bNF_Ca3172636760949973492d_of_o @ C3 ) ) @ bNF_We1503459268740929763at_o_o ) ) ) ) ).

% card_of_Plus_ordLess_infinite
thf(fact_1147_card__of__Plus__ordLess__infinite,axiom,
    ! [C3: set_nat,A2: set_nat,B2: set_nat] :
      ( ~ ( finite_finite_nat @ C3 )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We3448473429330749420at_nat )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We3448473429330749420at_nat )
         => ( member3047918529990910514at_nat @ ( produc6460772959230282105at_nat @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ A2 @ B2 ) ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We7041958966232365723at_nat ) ) ) ) ).

% card_of_Plus_ordLess_infinite
thf(fact_1148_card__of__Plus__ordLess__infinite,axiom,
    ! [C3: set_nat,A2: set_nat,B2: set_o] :
      ( ~ ( finite_finite_nat @ C3 )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We3448473429330749420at_nat )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We8182288985678559134_o_nat )
         => ( member4812592190795650218at_nat @ ( produc5868257188881964785at_nat @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ A2 @ B2 ) ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We4935586570105487173_o_nat ) ) ) ) ).

% card_of_Plus_ordLess_infinite
thf(fact_1149_card__of__Plus__ordLess__infinite,axiom,
    ! [C3: set_nat,A2: set_o,B2: set_nat] :
      ( ~ ( finite_finite_nat @ C3 )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We8182288985678559134_o_nat )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We3448473429330749420at_nat )
         => ( member6178483945413987626at_nat @ ( produc7234148943500302193at_nat @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ A2 @ B2 ) ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We1194315142955236767at_nat ) ) ) ) ).

% card_of_Plus_ordLess_infinite
thf(fact_1150_card__of__Plus__ordLess__infinite,axiom,
    ! [C3: set_nat,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_nat @ C3 )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We8182288985678559134_o_nat )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We8182288985678559134_o_nat )
         => ( member989342599902505446at_nat @ ( produc4966347635449911085at_nat @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ A2 @ B2 ) ) @ ( bNF_Ca3793111618940312692of_nat @ C3 ) ) @ bNF_We7066948511106741057_o_nat ) ) ) ) ).

% card_of_Plus_ordLess_infinite
thf(fact_1151_card__of__ordLeq,axiom,
    ! [A2: set_o,B2: set_o] :
      ( ( ? [F2: $o > $o] :
            ( ( inj_on_o_o @ F2 @ A2 )
            & ( ord_less_eq_set_o @ ( image_o_o2 @ F2 @ A2 ) @ B2 ) ) )
      = ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% card_of_ordLeq
thf(fact_1152_card__of__ordLeq,axiom,
    ! [A2: set_o,B2: set_nat] :
      ( ( ? [F2: $o > nat] :
            ( ( inj_on_o_nat @ F2 @ A2 )
            & ( ord_less_eq_set_nat @ ( image_o_nat @ F2 @ A2 ) @ B2 ) ) )
      = ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We3435943820185352641_o_nat ) ) ).

% card_of_ordLeq
thf(fact_1153_card__of__ordLeq,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( ? [F2: nat > nat] :
            ( ( inj_on_nat_nat @ F2 @ A2 )
            & ( ord_less_eq_set_nat @ ( image_nat_nat2 @ F2 @ A2 ) @ B2 ) ) )
      = ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We2031159114419172489at_nat ) ) ).

% card_of_ordLeq
thf(fact_1154_Card__order__empty,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
     => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ bot_bot_set_o ) @ R ) @ bNF_We3435943820185352641_o_nat ) ) ).

% Card_order_empty
thf(fact_1155_Card__order__empty,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ bot_bot_set_nat ) @ R ) @ bNF_We2031159114419172489at_nat ) ) ).

% Card_order_empty
thf(fact_1156_Card__order__empty,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ bot_bot_set_o ) @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% Card_order_empty
thf(fact_1157_Card__order__empty,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
     => ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ bot_bot_set_nat ) @ R ) @ bNF_We6538615181293537951_nat_o ) ) ).

% Card_order_empty
thf(fact_1158_Card__order__singl__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,B: $o] :
      ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
     => ( ( ( field_nat @ R )
         != bot_bot_set_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ ( insert_o @ B @ bot_bot_set_o ) ) @ R ) @ bNF_We3435943820185352641_o_nat ) ) ) ).

% Card_order_singl_ordLeq
thf(fact_1159_Card__order__singl__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,B: nat] :
      ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
     => ( ( ( field_nat @ R )
         != bot_bot_set_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ R ) @ bNF_We2031159114419172489at_nat ) ) ) ).

% Card_order_singl_ordLeq
thf(fact_1160_Card__order__singl__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,B: $o] :
      ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
     => ( ( ( field_o @ R )
         != bot_bot_set_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ ( insert_o @ B @ bot_bot_set_o ) ) @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ) ).

% Card_order_singl_ordLeq
thf(fact_1161_Card__order__singl__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,B: nat] :
      ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
     => ( ( ( field_o @ R )
         != bot_bot_set_o )
       => ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ R ) @ bNF_We6538615181293537951_nat_o ) ) ) ).

% Card_order_singl_ordLeq
thf(fact_1162_card__of__Un__ordLeq__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We3435943820185352641_o_nat )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We3435943820185352641_o_nat )
         => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
           => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ ( sup_sup_set_o @ A2 @ B2 ) ) @ R ) @ bNF_We3435943820185352641_o_nat ) ) ) ) ) ).

% card_of_Un_ordLeq_infinite_Field
thf(fact_1163_card__of__Un__ordLeq__infinite__Field,axiom,
    ! [R: set_Pr1261947904930325089at_nat,A2: set_nat,B2: set_nat] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We2031159114419172489at_nat )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We2031159114419172489at_nat )
         => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ R ) @ bNF_We2031159114419172489at_nat ) ) ) ) ) ).

% card_of_Un_ordLeq_infinite_Field
thf(fact_1164_card__of__Un__ordLeq__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_o,B2: set_o] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We8115293805659342695eq_o_o )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) @ R ) @ bNF_We8115293805659342695eq_o_o )
         => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
           => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ ( sup_sup_set_o @ A2 @ B2 ) ) @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ) ) ) ).

% card_of_Un_ordLeq_infinite_Field
thf(fact_1165_card__of__Un__ordLeq__infinite__Field,axiom,
    ! [R: set_Product_prod_o_o,A2: set_nat,B2: set_nat] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We6538615181293537951_nat_o )
       => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ B2 ) @ R ) @ bNF_We6538615181293537951_nat_o )
         => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
           => ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ R ) @ bNF_We6538615181293537951_nat_o ) ) ) ) ) ).

% card_of_Un_ordLeq_infinite_Field
thf(fact_1166_ordLeq__refl,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R ) @ bNF_We2031159114419172489at_nat ) ) ).

% ordLeq_refl
thf(fact_1167_ordLeq__refl,axiom,
    ! [R: set_Product_prod_o_o] :
      ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% ordLeq_refl
thf(fact_1168_ex__toCard__pred,axiom,
    ! [A2: set_o,R: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We3435943820185352641_o_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ? [X_1: $o > nat] : ( bNF_Gr988296774780055034_o_nat @ A2 @ R @ X_1 ) ) ) ).

% ex_toCard_pred
thf(fact_1169_ex__toCard__pred,axiom,
    ! [A2: set_nat,R: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We2031159114419172489at_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ? [X_1: nat > nat] : ( bNF_Gr4367463400984379536at_nat @ A2 @ R @ X_1 ) ) ) ).

% ex_toCard_pred
thf(fact_1170_ex__toCard__pred,axiom,
    ! [A2: set_o,R: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ? [X_1: $o > $o] : ( bNF_Gr3194703283472089838ed_o_o @ A2 @ R @ X_1 ) ) ) ).

% ex_toCard_pred
thf(fact_1171_ex__toCard__pred,axiom,
    ! [A2: set_nat,R: set_Product_prod_o_o] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We6538615181293537951_nat_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ? [X_1: nat > $o] : ( bNF_Gr4090968135888240344_nat_o @ A2 @ R @ X_1 ) ) ) ).

% ex_toCard_pred
thf(fact_1172_toCard__inj,axiom,
    ! [A2: set_a,R: set_Pr1261947904930325089at_nat,X: a,Y: a] :
      ( ( member6858118926070794858at_nat @ ( produc2553196175173902513at_nat @ ( bNF_Ca1104715389982341978d_of_a @ A2 ) @ R ) @ bNF_We4671332349262384423_a_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member_a @ X @ A2 )
         => ( ( member_a @ Y @ A2 )
           => ( ( ( bNF_Gr1543889757740115745_a_nat @ A2 @ R @ X )
                = ( bNF_Gr1543889757740115745_a_nat @ A2 @ R @ Y ) )
              = ( X = Y ) ) ) ) ) ) ).

% toCard_inj
thf(fact_1173_toCard__inj,axiom,
    ! [A2: set_o,R: set_Pr1261947904930325089at_nat,X: $o,Y: $o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We3435943820185352641_o_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member_o @ X @ A2 )
         => ( ( member_o @ Y @ A2 )
           => ( ( ( bNF_Gr1235702096034787515_o_nat @ A2 @ R @ X )
                = ( bNF_Gr1235702096034787515_o_nat @ A2 @ R @ Y ) )
              = ( X = Y ) ) ) ) ) ) ).

% toCard_inj
thf(fact_1174_toCard__inj,axiom,
    ! [A2: set_nat,R: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We2031159114419172489at_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member_nat @ X @ A2 )
         => ( ( member_nat @ Y @ A2 )
           => ( ( ( bNF_Gr5321390424033619983at_nat @ A2 @ R @ X )
                = ( bNF_Gr5321390424033619983at_nat @ A2 @ R @ Y ) )
              = ( X = Y ) ) ) ) ) ) ).

% toCard_inj
thf(fact_1175_toCard__inj,axiom,
    ! [A2: set_a,R: set_Product_prod_o_o,X: a,Y: a] :
      ( ( member3905523654690943504od_o_o @ ( produc1574450146682772567od_o_o @ ( bNF_Ca1104715389982341978d_of_a @ A2 ) @ R ) @ bNF_We2079833050348105345eq_a_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member_a @ X @ A2 )
         => ( ( member_a @ Y @ A2 )
           => ( ( ( bNF_Gr3684918198958735879rd_a_o @ A2 @ R @ X )
                = ( bNF_Gr3684918198958735879rd_a_o @ A2 @ R @ Y ) )
              = ( X = Y ) ) ) ) ) ) ).

% toCard_inj
thf(fact_1176_toCard__inj,axiom,
    ! [A2: set_o,R: set_Product_prod_o_o,X: $o,Y: $o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member_o @ X @ A2 )
         => ( ( member_o @ Y @ A2 )
           => ( ( ( bNF_Gr748490023993654765rd_o_o @ A2 @ R @ X )
                = ( bNF_Gr748490023993654765rd_o_o @ A2 @ R @ Y ) )
              = ( X = Y ) ) ) ) ) ) ).

% toCard_inj
thf(fact_1177_toCard__inj,axiom,
    ! [A2: set_nat,R: set_Product_prod_o_o,X: nat,Y: nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We6538615181293537951_nat_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member_nat @ X @ A2 )
         => ( ( member_nat @ Y @ A2 )
           => ( ( ( bNF_Gr4338373457142972825_nat_o @ A2 @ R @ X )
                = ( bNF_Gr4338373457142972825_nat_o @ A2 @ R @ Y ) )
              = ( X = Y ) ) ) ) ) ) ).

% toCard_inj
thf(fact_1178_toCard__inj,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1261947904930325089at_nat,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( member7927422385807836842at_nat @ ( produc1598809612926693617at_nat @ ( bNF_Ca6121500631330824515od_o_o @ A2 ) @ R ) @ bNF_We7173072801150825232_o_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member444158400953824016od_o_o @ X @ A2 )
         => ( ( member444158400953824016od_o_o @ Y @ A2 )
           => ( ( ( bNF_Gr2687907518133588746_o_nat @ A2 @ R @ X )
                = ( bNF_Gr2687907518133588746_o_nat @ A2 @ R @ Y ) )
              = ( X = Y ) ) ) ) ) ) ).

% toCard_inj
thf(fact_1179_toCard__inj,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr1261947904930325089at_nat,X: produc732395585841259969at_nat,Y: produc732395585841259969at_nat] :
      ( ( member8415039729195402282at_nat @ ( produc4982878492540823665at_nat @ ( bNF_Ca8664924986033767453at_nat @ A2 ) @ R ) @ bNF_We8470213457150283754at_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member4095101504841534314at_nat @ X @ A2 )
         => ( ( member4095101504841534314at_nat @ Y @ A2 )
           => ( ( ( bNF_Gr859799933468256996at_nat @ A2 @ R @ X )
                = ( bNF_Gr859799933468256996at_nat @ A2 @ R @ Y ) )
              = ( X = Y ) ) ) ) ) ) ).

% toCard_inj
thf(fact_1180_toCard__inj,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr1261947904930325089at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
      ( ( member7359442244455152298at_nat @ ( produc5407148829662812401at_nat @ ( bNF_Ca9194600574093320387at_nat @ A2 ) @ R ) @ bNF_We8384597595354199696at_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member8757157785044589968at_nat @ X @ A2 )
         => ( ( member8757157785044589968at_nat @ Y @ A2 )
           => ( ( ( bNF_Gr8319706499545975946at_nat @ A2 @ R @ X )
                = ( bNF_Gr8319706499545975946at_nat @ A2 @ R @ Y ) )
              = ( X = Y ) ) ) ) ) ) ).

% toCard_inj
thf(fact_1181_toCard__inj,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Product_prod_o_o,X: produc2934264451710624999od_o_o,Y: produc2934264451710624999od_o_o] :
      ( ( member5998968164356017744od_o_o @ ( produc8369371535328480407od_o_o @ ( bNF_Ca6121500631330824515od_o_o @ A2 ) @ R ) @ bNF_We5212295730361461848_o_o_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member444158400953824016od_o_o @ X @ A2 )
         => ( ( member444158400953824016od_o_o @ Y @ A2 )
           => ( ( ( bNF_Gr1716226591470254558_o_o_o @ A2 @ R @ X )
                = ( bNF_Gr1716226591470254558_o_o_o @ A2 @ R @ Y ) )
              = ( X = Y ) ) ) ) ) ) ).

% toCard_inj
thf(fact_1182_toCard__pred__toCard,axiom,
    ! [A2: set_o,R: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We3435943820185352641_o_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( bNF_Gr988296774780055034_o_nat @ A2 @ R @ ( bNF_Gr1235702096034787515_o_nat @ A2 @ R ) ) ) ) ).

% toCard_pred_toCard
thf(fact_1183_toCard__pred__toCard,axiom,
    ! [A2: set_nat,R: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We2031159114419172489at_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( bNF_Gr4367463400984379536at_nat @ A2 @ R @ ( bNF_Gr5321390424033619983at_nat @ A2 @ R ) ) ) ) ).

% toCard_pred_toCard
thf(fact_1184_toCard__pred__toCard,axiom,
    ! [A2: set_o,R: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( bNF_Gr3194703283472089838ed_o_o @ A2 @ R @ ( bNF_Gr748490023993654765rd_o_o @ A2 @ R ) ) ) ) ).

% toCard_pred_toCard
thf(fact_1185_toCard__pred__toCard,axiom,
    ! [A2: set_nat,R: set_Product_prod_o_o] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We6538615181293537951_nat_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( bNF_Gr4090968135888240344_nat_o @ A2 @ R @ ( bNF_Gr4338373457142972825_nat_o @ A2 @ R ) ) ) ) ).

% toCard_pred_toCard
thf(fact_1186_fromCard__toCard,axiom,
    ! [A2: set_a,R: set_Pr1261947904930325089at_nat,B: a] :
      ( ( member6858118926070794858at_nat @ ( produc2553196175173902513at_nat @ ( bNF_Ca1104715389982341978d_of_a @ A2 ) @ R ) @ bNF_We4671332349262384423_a_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member_a @ B @ A2 )
         => ( ( bNF_Gr4132913802490790546_a_nat @ A2 @ R @ ( bNF_Gr1543889757740115745_a_nat @ A2 @ R @ B ) )
            = B ) ) ) ) ).

% fromCard_toCard
thf(fact_1187_fromCard__toCard,axiom,
    ! [A2: set_o,R: set_Pr1261947904930325089at_nat,B: $o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We3435943820185352641_o_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member_o @ B @ A2 )
         => ( ( bNF_Gr6736587135095141548_o_nat @ A2 @ R @ ( bNF_Gr1235702096034787515_o_nat @ A2 @ R @ B ) )
            = B ) ) ) ) ).

% fromCard_toCard
thf(fact_1188_fromCard__toCard,axiom,
    ! [A2: set_nat,R: set_Pr1261947904930325089at_nat,B: nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We2031159114419172489at_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member_nat @ B @ A2 )
         => ( ( bNF_Gr6953169559552526942at_nat @ A2 @ R @ ( bNF_Gr5321390424033619983at_nat @ A2 @ R @ B ) )
            = B ) ) ) ) ).

% fromCard_toCard
thf(fact_1189_fromCard__toCard,axiom,
    ! [A2: set_a,R: set_Product_prod_o_o,B: a] :
      ( ( member3905523654690943504od_o_o @ ( produc1574450146682772567od_o_o @ ( bNF_Ca1104715389982341978d_of_a @ A2 ) @ R ) @ bNF_We2079833050348105345eq_a_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member_a @ B @ A2 )
         => ( ( bNF_Gr1283079227033720918rd_a_o @ A2 @ R @ ( bNF_Gr3684918198958735879rd_a_o @ A2 @ R @ B ) )
            = B ) ) ) ) ).

% fromCard_toCard
thf(fact_1190_fromCard__toCard,axiom,
    ! [A2: set_o,R: set_Product_prod_o_o,B: $o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ R ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member_o @ B @ A2 )
         => ( ( bNF_Gr5731841836078664636rd_o_o @ A2 @ R @ ( bNF_Gr748490023993654765rd_o_o @ A2 @ R @ B ) )
            = B ) ) ) ) ).

% fromCard_toCard
thf(fact_1191_fromCard__toCard,axiom,
    ! [A2: set_nat,R: set_Product_prod_o_o,B: nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ R ) @ bNF_We6538615181293537951_nat_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member_nat @ B @ A2 )
         => ( ( bNF_Gr615886459348551050_nat_o @ A2 @ R @ ( bNF_Gr4338373457142972825_nat_o @ A2 @ R @ B ) )
            = B ) ) ) ) ).

% fromCard_toCard
thf(fact_1192_fromCard__toCard,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Pr1261947904930325089at_nat,B: produc2934264451710624999od_o_o] :
      ( ( member7927422385807836842at_nat @ ( produc1598809612926693617at_nat @ ( bNF_Ca6121500631330824515od_o_o @ A2 ) @ R ) @ bNF_We7173072801150825232_o_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member444158400953824016od_o_o @ B @ A2 )
         => ( ( bNF_Gr6179234852794809723_o_nat @ A2 @ R @ ( bNF_Gr2687907518133588746_o_nat @ A2 @ R @ B ) )
            = B ) ) ) ) ).

% fromCard_toCard
thf(fact_1193_fromCard__toCard,axiom,
    ! [A2: set_Pr457366540195662369at_nat,R: set_Pr1261947904930325089at_nat,B: produc732395585841259969at_nat] :
      ( ( member8415039729195402282at_nat @ ( produc4982878492540823665at_nat @ ( bNF_Ca8664924986033767453at_nat @ A2 ) @ R ) @ bNF_We8470213457150283754at_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member4095101504841534314at_nat @ B @ A2 )
         => ( ( bNF_Gr6550272361737169109at_nat @ A2 @ R @ ( bNF_Gr859799933468256996at_nat @ A2 @ R @ B ) )
            = B ) ) ) ) ).

% fromCard_toCard
thf(fact_1194_fromCard__toCard,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R: set_Pr1261947904930325089at_nat,B: produc3843707927480180839at_nat] :
      ( ( member7359442244455152298at_nat @ ( produc5407148829662812401at_nat @ ( bNF_Ca9194600574093320387at_nat @ A2 ) @ R ) @ bNF_We8384597595354199696at_nat )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member8757157785044589968at_nat @ B @ A2 )
         => ( ( bNF_Gr2810406598121987579at_nat @ A2 @ R @ ( bNF_Gr8319706499545975946at_nat @ A2 @ R @ B ) )
            = B ) ) ) ) ).

% fromCard_toCard
thf(fact_1195_fromCard__toCard,axiom,
    ! [A2: set_Pr1932065953672099015od_o_o,R: set_Product_prod_o_o,B: produc2934264451710624999od_o_o] :
      ( ( member5998968164356017744od_o_o @ ( produc8369371535328480407od_o_o @ ( bNF_Ca6121500631330824515od_o_o @ A2 ) @ R ) @ bNF_We5212295730361461848_o_o_o )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member444158400953824016od_o_o @ B @ A2 )
         => ( ( bNF_Gr3541370040355373357_o_o_o @ A2 @ R @ ( bNF_Gr1716226591470254558_o_o_o @ A2 @ R @ B ) )
            = B ) ) ) ) ).

% fromCard_toCard
thf(fact_1196_Card__order__Plus__infinite,axiom,
    ! [R: set_Pr1261947904930325089at_nat,P: set_Product_prod_o_o] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P @ R ) @ bNF_We3435943820185352641_o_nat )
         => ( ( member4812592190795650218at_nat @ ( produc5868257188881964785at_nat @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ ( field_nat @ R ) @ ( field_o @ P ) ) ) @ R ) @ bNF_We5202279374879649339_o_nat )
            & ( member6178483945413987626at_nat @ ( produc7234148943500302193at_nat @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ ( field_o @ P ) @ ( field_nat @ R ) ) ) @ R ) @ bNF_We1461007947729398933at_nat ) ) ) ) ) ).

% Card_order_Plus_infinite
thf(fact_1197_Card__order__Plus__infinite,axiom,
    ! [R: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat] :
      ( ~ ( finite_finite_nat @ ( field_nat @ R ) )
     => ( ( bNF_Ca1281551314933786834on_nat @ ( field_nat @ R ) @ R )
       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P @ R ) @ bNF_We2031159114419172489at_nat )
         => ( ( member3047918529990910514at_nat @ ( produc6460772959230282105at_nat @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ ( field_nat @ R ) @ ( field_nat @ P ) ) ) @ R ) @ bNF_We4717344193235055909at_nat )
            & ( member3047918529990910514at_nat @ ( produc6460772959230282105at_nat @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ ( field_nat @ P ) @ ( field_nat @ R ) ) ) @ R ) @ bNF_We4717344193235055909at_nat ) ) ) ) ) ).

% Card_order_Plus_infinite
thf(fact_1198_Card__order__Plus__infinite,axiom,
    ! [R: set_Product_prod_o_o,P: set_Pr1261947904930325089at_nat] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ P @ R ) @ bNF_We6538615181293537951_nat_o )
         => ( ( member121125266993124560od_o_o @ ( produc8931464078238085911od_o_o @ ( bNF_Ca1325121287712659829_o_nat @ ( sum_Plus_o_nat @ ( field_o @ R ) @ ( field_nat @ P ) ) ) @ R ) @ bNF_We8455499808419870611_nat_o )
            & ( member4590549062032530512od_o_o @ ( produc4177515836422716055od_o_o @ ( bNF_Ca4833655811768152859_nat_o @ ( sum_Plus_nat_o @ ( field_nat @ P ) @ ( field_o @ R ) ) ) @ R ) @ bNF_We7828181885127712877at_o_o ) ) ) ) ) ).

% Card_order_Plus_infinite
thf(fact_1199_Card__order__Plus__infinite,axiom,
    ! [R: set_Product_prod_o_o,P: set_Product_prod_o_o] :
      ( ~ ( finite_finite_o @ ( field_o @ R ) )
     => ( ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ R ) @ R )
       => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P @ R ) @ bNF_We8115293805659342695eq_o_o )
         => ( ( member8030178841557499788od_o_o @ ( produc5317466613051064531od_o_o @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ ( field_o @ R ) @ ( field_o @ P ) ) ) @ R ) @ bNF_We5455623833347018717_o_o_o )
            & ( member8030178841557499788od_o_o @ ( produc5317466613051064531od_o_o @ ( bNF_Ca5391278176305430217um_o_o @ ( sum_Plus_o_o @ ( field_o @ P ) @ ( field_o @ R ) ) ) @ R ) @ bNF_We5455623833347018717_o_o_o ) ) ) ) ) ).

% Card_order_Plus_infinite
thf(fact_1200_cprod__cong,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Pr1261947904930325089at_nat,P22: set_Product_prod_o_o,R22: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P1 @ R1 ) @ bNF_We4116350175183677332_o_nat )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P22 @ R22 ) @ bNF_We4116350175183677332_o_nat )
       => ( member8717407822839053200at_nat @ ( produc6996284652319478231at_nat @ ( bNF_Ca8659498892590988930od_o_o @ P1 @ P22 ) @ ( bNF_Ca5918273672090100260at_nat @ R1 @ R22 ) ) @ bNF_We4425979316902024558at_nat ) ) ) ).

% cprod_cong
thf(fact_1201_cprod__cong,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Pr1261947904930325089at_nat,P22: set_Product_prod_o_o,R22: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P1 @ R1 ) @ bNF_We4116350175183677332_o_nat )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P22 @ R22 ) @ bNF_We2654380646378065620so_o_o )
       => ( member8824421929673164292_nat_o @ ( produc3218210373639305035_nat_o @ ( bNF_Ca8659498892590988930od_o_o @ P1 @ P22 ) @ ( bNF_Ca3771748454224040004_nat_o @ R1 @ R22 ) ) @ bNF_We6436225757993239184_nat_o ) ) ) ).

% cprod_cong
thf(fact_1202_cprod__cong,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Pr1261947904930325089at_nat,P22: set_Pr1261947904930325089at_nat,R22: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P1 @ R1 ) @ bNF_We4116350175183677332_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P22 @ R22 ) @ bNF_We5258908940166488438at_nat )
       => ( member2414491960730527720at_nat @ ( produc6295173111627586351at_nat @ ( bNF_Ca669077093115854694_o_nat @ P1 @ P22 ) @ ( bNF_Ca5918273672090100260at_nat @ R1 @ R22 ) ) @ bNF_We5155846448255121108at_nat ) ) ) ).

% cprod_cong
thf(fact_1203_cprod__cong,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Product_prod_o_o,P22: set_Product_prod_o_o,R22: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P1 @ R1 ) @ bNF_We2654380646378065620so_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P22 @ R22 ) @ bNF_We4116350175183677332_o_nat )
       => ( member1643650677906951352_o_nat @ ( produc8026554252588472319_o_nat @ ( bNF_Ca8659498892590988930od_o_o @ P1 @ P22 ) @ ( bNF_Ca669077093115854694_o_nat @ R1 @ R22 ) ) @ bNF_We2927691233937746154_o_nat ) ) ) ).

% cprod_cong
thf(fact_1204_cprod__cong,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Product_prod_o_o,P22: set_Product_prod_o_o,R22: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P1 @ R1 ) @ bNF_We2654380646378065620so_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P22 @ R22 ) @ bNF_We2654380646378065620so_o_o )
       => ( member7930742895388902160od_o_o @ ( produc189021232855538519od_o_o @ ( bNF_Ca8659498892590988930od_o_o @ P1 @ P22 ) @ ( bNF_Ca8659498892590988930od_o_o @ R1 @ R22 ) ) @ bNF_We3478797130297825300od_o_o ) ) ) ).

% cprod_cong
thf(fact_1205_cprod__cong,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Product_prod_o_o,P22: set_Pr1261947904930325089at_nat,R22: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P1 @ R1 ) @ bNF_We2654380646378065620so_o_o )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P22 @ R22 ) @ bNF_We5258908940166488438at_nat )
       => ( member6130509595031242000_o_nat @ ( produc5910034646884183383_o_nat @ ( bNF_Ca669077093115854694_o_nat @ P1 @ P22 ) @ ( bNF_Ca669077093115854694_o_nat @ R1 @ R22 ) ) @ bNF_We2916028399495512580_o_nat ) ) ) ).

% cprod_cong
thf(fact_1206_cprod__cong,axiom,
    ! [P1: set_Pr1261947904930325089at_nat,R1: set_Pr1261947904930325089at_nat,P22: set_Product_prod_o_o,R22: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P1 @ R1 ) @ bNF_We5258908940166488438at_nat )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P22 @ R22 ) @ bNF_We4116350175183677332_o_nat )
       => ( member1892715368018688924at_nat @ ( produc5773396518915747555at_nat @ ( bNF_Ca3771748454224040004_nat_o @ P1 @ P22 ) @ ( bNF_Ca5918273672090100260at_nat @ R1 @ R22 ) ) @ bNF_We7873800260583935406at_nat ) ) ) ).

% cprod_cong
thf(fact_1207_cprod__cong,axiom,
    ! [P1: set_Pr1261947904930325089at_nat,R1: set_Pr1261947904930325089at_nat,P22: set_Product_prod_o_o,R22: set_Product_prod_o_o] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P1 @ R1 ) @ bNF_We5258908940166488438at_nat )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P22 @ R22 ) @ bNF_We2654380646378065620so_o_o )
       => ( member6208704584088763408_nat_o @ ( produc3222486542081100375_nat_o @ ( bNF_Ca3771748454224040004_nat_o @ P1 @ P22 ) @ ( bNF_Ca3771748454224040004_nat_o @ R1 @ R22 ) ) @ bNF_We2682271528455076432_nat_o ) ) ) ).

% cprod_cong
thf(fact_1208_cprod__cong,axiom,
    ! [P1: set_Pr1261947904930325089at_nat,R1: set_Pr1261947904930325089at_nat,P22: set_Pr1261947904930325089at_nat,R22: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P1 @ R1 ) @ bNF_We5258908940166488438at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P22 @ R22 ) @ bNF_We5258908940166488438at_nat )
       => ( member5855424355840516880at_nat @ ( produc3236233026405413719at_nat @ ( bNF_Ca5918273672090100260at_nat @ P1 @ P22 ) @ ( bNF_Ca5918273672090100260at_nat @ R1 @ R22 ) ) @ bNF_We4319090096570846868at_nat ) ) ) ).

% cprod_cong
thf(fact_1209_ordIso__symmetric,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We7219021536291862642_nat_o )
     => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R ) @ bNF_We4116350175183677332_o_nat ) ) ).

% ordIso_symmetric
thf(fact_1210_ordIso__symmetric,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We4116350175183677332_o_nat )
     => ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R ) @ bNF_We7219021536291862642_nat_o ) ) ).

% ordIso_symmetric
thf(fact_1211_ordIso__symmetric,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2654380646378065620so_o_o )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R ) @ bNF_We2654380646378065620so_o_o ) ) ).

% ordIso_symmetric
thf(fact_1212_ordIso__symmetric,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We5258908940166488438at_nat )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R ) @ bNF_We5258908940166488438at_nat ) ) ).

% ordIso_symmetric
thf(fact_1213_ordIso__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We4116350175183677332_o_nat )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R5 ) @ bNF_We7219021536291862642_nat_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2654380646378065620so_o_o ) ) ) ).

% ordIso_transitive
thf(fact_1214_ordIso__transitive,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We7219021536291862642_nat_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We4116350175183677332_o_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We5258908940166488438at_nat ) ) ) ).

% ordIso_transitive
thf(fact_1215_ordIso__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We4116350175183677332_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We5258908940166488438at_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We4116350175183677332_o_nat ) ) ) ).

% ordIso_transitive
thf(fact_1216_ordIso__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2654380646378065620so_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We4116350175183677332_o_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We4116350175183677332_o_nat ) ) ) ).

% ordIso_transitive
thf(fact_1217_ordIso__transitive,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2654380646378065620so_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R5 ) @ bNF_We2654380646378065620so_o_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2654380646378065620so_o_o ) ) ) ).

% ordIso_transitive
thf(fact_1218_ordIso__transitive,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We5258908940166488438at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We5258908940166488438at_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We5258908940166488438at_nat ) ) ) ).

% ordIso_transitive
thf(fact_1219_card__of__refl,axiom,
    ! [A2: set_o] : ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) ) @ bNF_We2654380646378065620so_o_o ) ).

% card_of_refl
thf(fact_1220_card__of__refl,axiom,
    ! [A2: set_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ A2 ) ) @ bNF_We5258908940166488438at_nat ) ).

% card_of_refl
thf(fact_1221_card__of__ordIso__subst,axiom,
    ! [A2: set_o,B2: set_o] :
      ( ( A2 = B2 )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ ( bNF_Ca3172636760949973492d_of_o @ A2 ) @ ( bNF_Ca3172636760949973492d_of_o @ B2 ) ) @ bNF_We2654380646378065620so_o_o ) ) ).

% card_of_ordIso_subst
thf(fact_1222_card__of__ordIso__subst,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( A2 = B2 )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ A2 ) @ ( bNF_Ca3793111618940312692of_nat @ B2 ) ) @ bNF_We5258908940166488438at_nat ) ) ).

% card_of_ordIso_subst
thf(fact_1223_card__order__on__ordIso,axiom,
    ! [A2: set_nat,R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( bNF_Ca1281551314933786834on_nat @ A2 @ R )
     => ( ( bNF_Ca1281551314933786834on_nat @ A2 @ R4 )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We5258908940166488438at_nat ) ) ) ).

% card_order_on_ordIso
thf(fact_1224_card__order__on__ordIso,axiom,
    ! [A2: set_o,R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( bNF_Ca8331644756375544342r_on_o @ A2 @ R )
     => ( ( bNF_Ca8331644756375544342r_on_o @ A2 @ R4 )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2654380646378065620so_o_o ) ) ) ).

% card_order_on_ordIso
thf(fact_1225_ordIso__iff__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We7219021536291862642_nat_o )
      = ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
        & ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R ) @ bNF_We3435943820185352641_o_nat ) ) ) ).

% ordIso_iff_ordLeq
thf(fact_1226_ordIso__iff__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We4116350175183677332_o_nat )
      = ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
        & ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R ) @ bNF_We6538615181293537951_nat_o ) ) ) ).

% ordIso_iff_ordLeq
thf(fact_1227_ordIso__iff__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2654380646378065620so_o_o )
      = ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
        & ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R ) @ bNF_We8115293805659342695eq_o_o ) ) ) ).

% ordIso_iff_ordLeq
thf(fact_1228_ordIso__iff__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We5258908940166488438at_nat )
      = ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We2031159114419172489at_nat )
        & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R ) @ bNF_We2031159114419172489at_nat ) ) ) ).

% ordIso_iff_ordLeq
thf(fact_1229_ordIso__imp__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We4116350175183677332_o_nat )
     => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat ) ) ).

% ordIso_imp_ordLeq
thf(fact_1230_ordIso__imp__ordLeq,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2654380646378065620so_o_o )
     => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o ) ) ).

% ordIso_imp_ordLeq
thf(fact_1231_ordIso__imp__ordLeq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We5258908940166488438at_nat )
     => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We2031159114419172489at_nat ) ) ).

% ordIso_imp_ordLeq
thf(fact_1232_ordIso__ordLeq__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We7219021536291862642_nat_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We3435943820185352641_o_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We2031159114419172489at_nat ) ) ) ).

% ordIso_ordLeq_trans
thf(fact_1233_ordIso__ordLeq__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We4116350175183677332_o_nat )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R5 ) @ bNF_We6538615181293537951_nat_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We8115293805659342695eq_o_o ) ) ) ).

% ordIso_ordLeq_trans
thf(fact_1234_ordIso__ordLeq__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We4116350175183677332_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We2031159114419172489at_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We3435943820185352641_o_nat ) ) ) ).

% ordIso_ordLeq_trans
thf(fact_1235_ordIso__ordLeq__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2654380646378065620so_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R5 ) @ bNF_We8115293805659342695eq_o_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We8115293805659342695eq_o_o ) ) ) ).

% ordIso_ordLeq_trans
thf(fact_1236_ordIso__ordLeq__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2654380646378065620so_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We3435943820185352641_o_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We3435943820185352641_o_nat ) ) ) ).

% ordIso_ordLeq_trans
thf(fact_1237_ordIso__ordLeq__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We5258908940166488438at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We2031159114419172489at_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We2031159114419172489at_nat ) ) ) ).

% ordIso_ordLeq_trans
thf(fact_1238_ordLeq__ordIso__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We6538615181293537951_nat_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We4116350175183677332_o_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We2031159114419172489at_nat ) ) ) ).

% ordLeq_ordIso_trans
thf(fact_1239_ordLeq__ordIso__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We4116350175183677332_o_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We3435943820185352641_o_nat ) ) ) ).

% ordLeq_ordIso_trans
thf(fact_1240_ordLeq__ordIso__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R5 ) @ bNF_We7219021536291862642_nat_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We8115293805659342695eq_o_o ) ) ) ).

% ordLeq_ordIso_trans
thf(fact_1241_ordLeq__ordIso__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R5 ) @ bNF_We2654380646378065620so_o_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We8115293805659342695eq_o_o ) ) ) ).

% ordLeq_ordIso_trans
thf(fact_1242_ordLeq__ordIso__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We5258908940166488438at_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We3435943820185352641_o_nat ) ) ) ).

% ordLeq_ordIso_trans
thf(fact_1243_ordLeq__ordIso__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We2031159114419172489at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We5258908940166488438at_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We2031159114419172489at_nat ) ) ) ).

% ordLeq_ordIso_trans
thf(fact_1244_ordLess__ordIso__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We2061588309931968636_nat_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We4116350175183677332_o_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% ordLess_ordIso_trans
thf(fact_1245_ordLess__ordIso__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R5 ) @ bNF_We2654380646378065620so_o_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% ordLess_ordIso_trans
thf(fact_1246_ordLess__ordIso__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We3448473429330749420at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We5258908940166488438at_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% ordLess_ordIso_trans
thf(fact_1247_ordLess__ordIso__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We4116350175183677332_o_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We8182288985678559134_o_nat ) ) ) ).

% ordLess_ordIso_trans
thf(fact_1248_ordLess__ordIso__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R5 ) @ bNF_We7219021536291862642_nat_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% ordLess_ordIso_trans
thf(fact_1249_ordLess__ordIso__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We5258908940166488438at_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We8182288985678559134_o_nat ) ) ) ).

% ordLess_ordIso_trans
thf(fact_1250_ordIso__ordLess__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We4116350175183677332_o_nat )
     => ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R4 @ R5 ) @ bNF_We2061588309931968636_nat_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% ordIso_ordLess_trans
thf(fact_1251_ordIso__ordLess__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2654380646378065620so_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R4 @ R5 ) @ bNF_We2568191115274586186ss_o_o )
       => ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R5 ) @ bNF_We2568191115274586186ss_o_o ) ) ) ).

% ordIso_ordLess_trans
thf(fact_1252_ordIso__ordLess__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We5258908940166488438at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We3448473429330749420at_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% ordIso_ordLess_trans
thf(fact_1253_ordIso__ordLess__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We4116350175183677332_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R4 @ R5 ) @ bNF_We3448473429330749420at_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We8182288985678559134_o_nat ) ) ) ).

% ordIso_ordLess_trans
thf(fact_1254_ordIso__ordLess__trans,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member2037436044582932534od_o_o @ ( produc2070086378307464573od_o_o @ R @ R4 ) @ bNF_We7219021536291862642_nat_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We8182288985678559134_o_nat )
       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R5 ) @ bNF_We3448473429330749420at_nat ) ) ) ).

% ordIso_ordLess_trans
thf(fact_1255_ordIso__ordLess__trans,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o,R5: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2654380646378065620so_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R4 @ R5 ) @ bNF_We8182288985678559134_o_nat )
       => ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R5 ) @ bNF_We8182288985678559134_o_nat ) ) ) ).

% ordIso_ordLess_trans
thf(fact_1256_not__ordLess__ordIso,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2568191115274586186ss_o_o )
     => ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ R @ R4 ) @ bNF_We2654380646378065620so_o_o ) ) ).

% not_ordLess_ordIso
thf(fact_1257_not__ordLess__ordIso,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We3448473429330749420at_nat )
     => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We5258908940166488438at_nat ) ) ).

% not_ordLess_ordIso
thf(fact_1258_not__ordLess__ordIso,axiom,
    ! [R: set_Product_prod_o_o,R4: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We8182288985678559134_o_nat )
     => ~ ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ R @ R4 ) @ bNF_We4116350175183677332_o_nat ) ) ).

% not_ordLess_ordIso
thf(fact_1259_cprod__mono,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Product_prod_o_o,P22: set_Product_prod_o_o,R22: set_Product_prod_o_o] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P1 @ R1 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P22 @ R22 ) @ bNF_We8115293805659342695eq_o_o )
       => ( member7930742895388902160od_o_o @ ( produc189021232855538519od_o_o @ ( bNF_Ca8659498892590988930od_o_o @ P1 @ P22 ) @ ( bNF_Ca8659498892590988930od_o_o @ R1 @ R22 ) ) @ bNF_We5263191010062085543od_o_o ) ) ) ).

% cprod_mono
thf(fact_1260_cprod__mono,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Product_prod_o_o,P22: set_Product_prod_o_o,R22: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P1 @ R1 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P22 @ R22 ) @ bNF_We3435943820185352641_o_nat )
       => ( member1643650677906951352_o_nat @ ( produc8026554252588472319_o_nat @ ( bNF_Ca8659498892590988930od_o_o @ P1 @ P22 ) @ ( bNF_Ca669077093115854694_o_nat @ R1 @ R22 ) ) @ bNF_We5526594851599572503_o_nat ) ) ) ).

% cprod_mono
thf(fact_1261_cprod__mono,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Product_prod_o_o,P22: set_Pr1261947904930325089at_nat,R22: set_Pr1261947904930325089at_nat] :
      ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P1 @ R1 ) @ bNF_We8115293805659342695eq_o_o )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P22 @ R22 ) @ bNF_We2031159114419172489at_nat )
       => ( member6130509595031242000_o_nat @ ( produc5910034646884183383_o_nat @ ( bNF_Ca669077093115854694_o_nat @ P1 @ P22 ) @ ( bNF_Ca669077093115854694_o_nat @ R1 @ R22 ) ) @ bNF_We5517640669336891927_o_nat ) ) ) ).

% cprod_mono
thf(fact_1262_cprod__mono,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Pr1261947904930325089at_nat,P22: set_Product_prod_o_o,R22: set_Product_prod_o_o] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P1 @ R1 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P22 @ R22 ) @ bNF_We8115293805659342695eq_o_o )
       => ( member8824421929673164292_nat_o @ ( produc3218210373639305035_nat_o @ ( bNF_Ca8659498892590988930od_o_o @ P1 @ P22 ) @ ( bNF_Ca3771748454224040004_nat_o @ R1 @ R22 ) ) @ bNF_We9035129375655065533_nat_o ) ) ) ).

% cprod_mono
thf(fact_1263_cprod__mono,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Pr1261947904930325089at_nat,P22: set_Product_prod_o_o,R22: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P1 @ R1 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P22 @ R22 ) @ bNF_We3435943820185352641_o_nat )
       => ( member8717407822839053200at_nat @ ( produc6996284652319478231at_nat @ ( bNF_Ca8659498892590988930od_o_o @ P1 @ P22 ) @ ( bNF_Ca5918273672090100260at_nat @ R1 @ R22 ) ) @ bNF_We7027591586743403905at_nat ) ) ) ).

% cprod_mono
thf(fact_1264_cprod__mono,axiom,
    ! [P1: set_Product_prod_o_o,R1: set_Pr1261947904930325089at_nat,P22: set_Pr1261947904930325089at_nat,R22: set_Pr1261947904930325089at_nat] :
      ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P1 @ R1 ) @ bNF_We3435943820185352641_o_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P22 @ R22 ) @ bNF_We2031159114419172489at_nat )
       => ( member2414491960730527720at_nat @ ( produc6295173111627586351at_nat @ ( bNF_Ca669077093115854694_o_nat @ P1 @ P22 ) @ ( bNF_Ca5918273672090100260at_nat @ R1 @ R22 ) ) @ bNF_We1398974386449396097at_nat ) ) ) ).

% cprod_mono
thf(fact_1265_cprod__mono,axiom,
    ! [P1: set_Pr1261947904930325089at_nat,R1: set_Pr1261947904930325089at_nat,P22: set_Product_prod_o_o,R22: set_Product_prod_o_o] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P1 @ R1 ) @ bNF_We2031159114419172489at_nat )
     => ( ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ P22 @ R22 ) @ bNF_We8115293805659342695eq_o_o )
       => ( member6208704584088763408_nat_o @ ( produc3222486542081100375_nat_o @ ( bNF_Ca3771748454224040004_nat_o @ P1 @ P22 ) @ ( bNF_Ca3771748454224040004_nat_o @ R1 @ R22 ) ) @ bNF_We5283883798296455779_nat_o ) ) ) ).

% cprod_mono
thf(fact_1266_cprod__mono,axiom,
    ! [P1: set_Pr1261947904930325089at_nat,R1: set_Pr1261947904930325089at_nat,P22: set_Product_prod_o_o,R22: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P1 @ R1 ) @ bNF_We2031159114419172489at_nat )
     => ( ( member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ P22 @ R22 ) @ bNF_We3435943820185352641_o_nat )
       => ( member1892715368018688924at_nat @ ( produc5773396518915747555at_nat @ ( bNF_Ca3771748454224040004_nat_o @ P1 @ P22 ) @ ( bNF_Ca5918273672090100260at_nat @ R1 @ R22 ) ) @ bNF_We4116928198778210395at_nat ) ) ) ).

% cprod_mono
thf(fact_1267_cprod__mono,axiom,
    ! [P1: set_Pr1261947904930325089at_nat,R1: set_Pr1261947904930325089at_nat,P22: set_Pr1261947904930325089at_nat,R22: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P1 @ R1 ) @ bNF_We2031159114419172489at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P22 @ R22 ) @ bNF_We2031159114419172489at_nat )
       => ( member5855424355840516880at_nat @ ( produc3236233026405413719at_nat @ ( bNF_Ca5918273672090100260at_nat @ P1 @ P22 ) @ ( bNF_Ca5918273672090100260at_nat @ R1 @ R22 ) ) @ bNF_We145940432564263207at_nat ) ) ) ).

% cprod_mono
thf(fact_1268_ordIso__Plus__cong,axiom,
    ! [R: set_Pr1261947904930325089at_nat,R4: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat,P8: set_Pr1261947904930325089at_nat] :
      ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R @ R4 ) @ bNF_We5258908940166488438at_nat )
     => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ P @ P8 ) @ bNF_We5258908940166488438at_nat )
       => ( member3674313732307032336at_nat @ ( produc2112825387572549975at_nat @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ ( field_nat @ R ) @ ( field_nat @ P ) ) ) @ ( bNF_Ca786952496063569315at_nat @ ( sum_Plus_nat_nat @ ( field_nat @ R4 ) @ ( field_nat @ P8 ) ) ) ) @ bNF_We3455965832816432340at_nat ) ) ) ).

% ordIso_Plus_cong
thf(fact_1269_ctwo__Cnotzero,axiom,
    ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ bNF_Cardinal_ctwo @ bNF_Cardinal_czero_o ) @ bNF_We2654380646378065620so_o_o )
    & ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ bNF_Cardinal_ctwo ) @ bNF_Cardinal_ctwo ) ) ).

% ctwo_Cnotzero
thf(fact_1270_ctwo__ordLess__natLeq,axiom,
    member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ bNF_Cardinal_ctwo @ bNF_Ca8665028551170535155natLeq ) @ bNF_We8182288985678559134_o_nat ).

% ctwo_ordLess_natLeq
thf(fact_1271_card__of__Field__natLeq,axiom,
    member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).

% card_of_Field_natLeq
thf(fact_1272_card__of__nat,axiom,
    member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ top_top_set_nat ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).

% card_of_nat

% Helper facts (3)
thf(help_If_3_1_If_001t__Option__Ooption_Itf__a_J_T,axiom,
    ! [P3: $o] :
      ( ( P3 = $true )
      | ( P3 = $false ) ) ).

thf(help_If_2_1_If_001t__Option__Ooption_Itf__a_J_T,axiom,
    ! [X: option_a,Y: option_a] :
      ( ( if_option_a @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Option__Ooption_Itf__a_J_T,axiom,
    ! [X: option_a,Y: option_a] :
      ( ( if_option_a @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( sat_a_b_c_d @ plus @ mult @ valid @ aaa @ s @ delta @ b2 )
    & ( sat_a_b_c_d @ plus @ mult @ valid @ baa @ s @ delta @ b2 ) ) ).

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