%------------------------------------------------------------------------------
% 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    : FSM_Tests/0080_Test_Suite_Calculation_Refined/prob_00622_025746__21335366_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 2534 ( 745 unt;1250 typ;   0 def)
%            Number of atoms       : 15529 (1647 equ;   0 cnn)
%            Maximal formula atoms :    5 (  12 avg)
%            Number of connectives : 26319 ( 410   ~;  43   |; 281   &;24608   @)
%                                         (   0 <=>; 977  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Number of types       :  289 ( 288 usr)
%            Number of type conns  : 4385 (4385   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  965 ( 962 usr;  43 con; 0-8 aty)
%            Number of variables   : 4471 ( 988   ^;3324   !; 159   ?;4471   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 11:31:06.535
%------------------------------------------------------------------------------
% Could-be-implicit typings (288)
thf(ty_n_t__Product____Type__Oprod_I_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J_M_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J_J,type,
    produc2070398702644967871set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    produc2163030415453158631set_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J_J_J,type,
    set_Pr5589133262920150351set_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_Itf__b2_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J_J_J,type,
    set_Pr5018776704028855922set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J_J,type,
    produc5623429682246142959set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_Itf__b2_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J_J,type,
    produc5199603736692633362set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J_J,type,
    produc3792589628255236696set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J_J,type,
    produc2916914556658279514set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    produc4722691776437566936set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    produc1295556776222662362set_b2: $tType ).

thf(ty_n_t__Set____Impl__Ocomp____fun____commute_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J_J,type,
    set_co4027722269366479532set_c2: $tType ).

thf(ty_n_t__Set____Impl__Ocomp____fun____idem_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J_J,type,
    set_co1666008921066281045set_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J_J,type,
    set_Pr6847959500825436640set_c2: $tType ).

thf(ty_n_t__Set____Impl__Ocomp____fun____commute_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    set_co8648611349764106212set_c2: $tType ).

thf(ty_n_t__Set____Impl__Ocomp____fun____idem_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    set_co4968226104895303821set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc8143631050555101118set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc7091961814400906944set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    produc2111118249776355772set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    produc4134103123222870330set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J,type,
    produc8955508179325214080set_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mtf__c2_J_J,type,
    set_Pr8355152109431543362_c2_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mtf__b2_J_J,type,
    set_Pr6396037720843056387_c2_b2: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma7048095785541752173t_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J,type,
    produc909805953363803304set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    produc2204780078346707822set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mtf__c2_J,type,
    produc3240012945314540428_c2_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mtf__b2_J,type,
    produc3239730657808423629_c2_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_Itf__b2_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J,type,
    produc786840591232948043set_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J_J,type,
    set_Pr5056620919297929171set_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J_J,type,
    set_Pr3221440761411154131set_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J_J,type,
    set_Pr1995104245887189set_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    set_Pr1660683266160182027set_c2: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Nat__Onat_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma7046197049342692319t_unit: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Nat__Onat_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma5169777983910274525t_unit: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Nat__Onat_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma3293358918477856731t_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    produc2833176615615745649set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    produc8629413652255616883set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    produc2702059613074419827set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    produc8498296649714291061set_b2: $tType ).

thf(ty_n_t__Option__Ooption_I_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_M_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Comparator__Oorder_J_J_J,type,
    option6733578312215638292_order: $tType ).

thf(ty_n_t__Option__Ooption_I_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_M_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Comparator__Oorder_J_J_J,type,
    option3340807017899620244_order: $tType ).

thf(ty_n_t__Option__Ooption_I_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J_J,type,
    option9171407760438378004_order: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c2_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma6787449812046583933t_unit: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b2_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma3965075261935132796t_unit: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c2_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma989376966787190651t_unit: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b2_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma7390374453530515322t_unit: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c2_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma4414676158382573177t_unit: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b2_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma1592301608271122040t_unit: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J,type,
    set_Pr517000079023102863set_b2: $tType ).

thf(ty_n_t__Set____Impl__Ocomp____fun____commute_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    set_co427093193105208449set_c2: $tType ).

thf(ty_n_t__Set____Impl__Ocomp____fun____commute_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    set_co8598795993805790083set_b2: $tType ).

thf(ty_n_t__FSM__Ofsm_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Nat__Onat_J,type,
    fsm_ma3562454073340529286c2_nat: $tType ).

thf(ty_n_t__Set____Impl__Ocomp____fun____idem_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    set_co3729585742154134680set_c2: $tType ).

thf(ty_n_t__Set____Impl__Ocomp____fun____idem_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    set_co2677916505999940506set_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J_J_J_J,type,
    set_Pr674799771360982167nat_c1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J_J_J_J,type,
    set_Pr4802260232978741656nat_b1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J_J_J_J,type,
    set_Pr8929720694596501145nat_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc6123186059419489449set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc5071516823265295275set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc4061897789176782763set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc3010228553022588589set_b2: $tType ).

thf(ty_n_t__FSM__Ofsm_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mtf__b2_J,type,
    fsm_ma8761726031752409769_c2_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c2_Mtf__c1_J_J_J_J,type,
    set_Pr3294692748256430457_c2_c1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J_J,type,
    set_Pr1900465899975183225_c1_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b2_Mtf__c1_J_J_J_J,type,
    set_Pr5152245380648846650_b2_c1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J_J,type,
    set_Pr6545474114340275451_b1_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J_J,type,
    set_Pr1967110291850591869_a1_a2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c2_Mtf__b1_J_J_J_J,type,
    set_Pr4220407505314016890_c2_b1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J_J,type,
    set_Pr38725075060093625_c1_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b2_Mtf__b1_J_J_J_J,type,
    set_Pr6077960137706433083_b2_b1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J_J,type,
    set_Pr4683733289425185851_b1_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J_J,type,
    set_Pr105369466935502269_a1_a2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c2_Mtf__a1_J_J_J_J,type,
    set_Pr5146122262371603323_c2_a1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J_J,type,
    set_Pr7400356286999779833_c1_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b2_Mtf__a1_J_J_J_J,type,
    set_Pr7003674894764019516_b2_a1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J_J,type,
    set_Pr2821992464510096251_b1_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J_J,type,
    set_Pr7467000678875188477_a1_a2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    set_Pr7201650869308432135_c1_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    set_Pr1330221890988210569_b1_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    set_Pr4682164949522764811_a1_a2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    set_Pr1798928773911001861_c1_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    set_Pr5150871832445556103_b1_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    set_Pr8502814890980110345_a1_a2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    set_Pr5619578715368347395_c1_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    set_Pr8971521773902901637_b1_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    set_Pr3100092795582680071_a1_a2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc7248990843601126233set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J_J_J,type,
    produc3241757979290108727nat_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J_J_J,type,
    produc3104264649751066808nat_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J_J_J,type,
    produc2966771320212024889nat_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c2_Mtf__c1_J_J_J,type,
    produc2542824572670609817_c2_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    produc6925080600094034841_c1_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b2_Mtf__c1_J_J_J,type,
    produc2995545231740769754_b2_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    produc1053651621773813275_b1_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    produc4405594680308367517_a1_a2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c2_Mtf__b1_J_J_J,type,
    produc7422474658093489946_c2_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    produc8905508286052520665_c1_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b2_Mtf__b1_J_J_J,type,
    produc7875195317163649883_b2_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    produc3034079307732299099_b1_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    produc6386022366266853341_a1_a2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c2_Mtf__a1_J_J_J,type,
    produc3078752706661594267_c2_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    produc1662563935156230681_c1_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b2_Mtf__a1_J_J_J,type,
    produc3531473365731754204_b2_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    produc5014506993690784923_b1_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    produc8366450052225339165_a1_a2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc3071142391596303911_c1_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc7684729609363997097_b1_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    produc3074944790276914475_a1_a2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc6041125926372507941_c1_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc1431341107285425319_b1_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    produc6044928325053118505_a1_a2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc9011109461148711971_c1_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc4401324642061629349_b1_b2: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma5397525271274666640t_unit: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma3658025366143732878t_unit: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Ounit_J,type,
    rBT_ma1918525461012799116t_unit: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Nat__Onat_J_J,type,
    set_Pr2824962942362912377c2_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Nat__Onat_J_J,type,
    set_Pr6819770292282554875b2_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Nat__Onat_J_J,type,
    set_Pr1591205605347421565a2_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    set_Pr6986345755798685983_c1_c2: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J_J,type,
    option5905241969658642574set_c2: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J_J,type,
    option2685796312493375632set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc8179314580630251927set_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    set_Pr6890843339346611005_c1_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    set_Pr1019414361026389439_b1_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    set_Pr4371357419560943681_a1_a2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    set_Pr7226085152747980732_c1_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    set_Pr1354656174427759166_b1_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    set_Pr4706599232962313408_a1_a2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c2_J_J,type,
    set_Pr2267770373837101659_c2_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c1_J_J,type,
    set_Pr2196736333790755674_c2_c1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b2_J_J,type,
    set_Pr308655985248614684_c2_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b1_J_J,type,
    set_Pr237621945202268699_c2_b1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__a1_J_J,type,
    set_Pr7501879593468557532_c2_a1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c2_J_J,type,
    set_Pr5605561542190788829_b2_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c1_J_J,type,
    set_Pr5534527502144442844_b2_c1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b2_J_J,type,
    set_Pr3646447153602301854_b2_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b1_J_J,type,
    set_Pr3575413113555955869_b2_b1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__a1_J_J,type,
    set_Pr1616298724967468894_b2_a1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c2_J_J,type,
    set_Pr8943352710544475999_a2_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c1_J_J,type,
    set_Pr8872318670498130014_a2_c1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b2_J_J,type,
    set_Pr6984238321955989024_a2_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b1_J_J,type,
    set_Pr6913204281909643039_a2_b1: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__a1_J_J,type,
    set_Pr4954089893321156064_a2_a1: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    option781494349862297706set_c2: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J,type,
    option6654706173824968300set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc1711127128284081338set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc7819656566062154093et_nat: $tType ).

thf(ty_n_t__Option__Ooption_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Comparator__Oorder_J_J_J,type,
    option_nat_nat_order: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    set_se755747229750772688set_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J,type,
    set_se6628959053713443282set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J_J,type,
    produc1270467780669282085nat_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J_J,type,
    produc4594776842310734693nat_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J_J,type,
    produc7919085903952187301nat_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Nat__Onat_J,type,
    produc6068224106209279939c2_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Nat__Onat_J,type,
    produc6889135236516123717b2_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Nat__Onat_J,type,
    produc7710046366822967495a2_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc2762000901599049065_c1_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__c2_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc8299335103979204559et_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__b2_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc3882302840724150032et_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_Itf__c2_J_J,type,
    produc89917798969000783set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_Itf__b2_J_J,type,
    produc7354175447235289616set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c2_Mtf__c1_J_J,type,
    produc7301529229928850439_c2_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc6446375336055580167_c1_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b2_Mtf__c1_J_J,type,
    produc4650858799430254792_b2_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc1836590516968497545_b1_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    produc6450177734736190731_a1_a2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c2_Mtf__b1_J_J,type,
    produc8445938924056448711_c2_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc326527381916889606_c1_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b2_Mtf__b1_J_J,type,
    produc5795268493557853064_b2_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc4940114599684582792_b1_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    produc330329780597500170_a1_a2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c2_Mtf__a1_J_J,type,
    produc366976581329271175_c2_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc3430051464632974853_c1_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b2_Mtf__a1_J_J,type,
    produc6939678187685451336_b2_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc8043638682400668039_b1_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    produc3433853863313585417_a1_a2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c2_J,type,
    produc598983362773771301_c2_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c1_J,type,
    produc598983358470542500_c2_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b2_J,type,
    produc598701075267654502_c2_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b1_J,type,
    produc598701070964425701_c2_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__a1_J,type,
    produc598418783458308902_c2_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c2_J,type,
    produc5894011917813406631_b2_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c1_J,type,
    produc5894011913510177830_b2_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b2_J,type,
    produc5893729630307289832_b2_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b1_J,type,
    produc5893729626004061031_b2_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__a1_J,type,
    produc5893447338497944232_b2_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c2_J,type,
    produc1965668435998266153_a2_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c1_J,type,
    produc1965668431695037352_a2_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b2_J,type,
    produc1965386148492149354_a2_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b1_J,type,
    produc1965386144188920553_a2_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__a1_J,type,
    produc1965103856682803754_a2_a1: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_It__Nat__Onat_Mt__Product____Type__Ounit_J,type,
    rBT_ma3908794552746989458t_unit: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    set_c1_option_set_c2: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    set_b1_option_set_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    set_se1646440499870488708_c1_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    set_se4998383558405042950_b1_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    set_se8350326616939597192_a1_a2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__c2_J_Mt__Set__Oset_Itf__c2_J_J,type,
    produc5634799823202231473set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__c2_J_Mt__Set__Oset_Itf__b2_J_J,type,
    produc3675685434613744498set_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__b2_J_Mt__Set__Oset_Itf__c2_J_J,type,
    produc1683908187583642994set_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__b2_J_Mt__Set__Oset_Itf__b2_J_J,type,
    produc8948165835849931827set_b2: $tType ).

thf(ty_n_t__Option__Ooption_I_062_Itf__c2_M_062_Itf__c2_Mt__Comparator__Oorder_J_J_J,type,
    option_c2_c2_order: $tType ).

thf(ty_n_t__Option__Ooption_I_062_Itf__b2_M_062_Itf__b2_Mt__Comparator__Oorder_J_J_J,type,
    option_b2_b2_order: $tType ).

thf(ty_n_t__Option__Ooption_I_062_Itf__a2_M_062_Itf__a2_Mt__Comparator__Oorder_J_J_J,type,
    option_a2_a2_order: $tType ).

thf(ty_n_t__Option__Ooption_I_062_Itf__a1_M_062_Itf__a1_Mt__Comparator__Oorder_J_J_J,type,
    option_a1_a1_order: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_Itf__a2_Mt__Product____Type__Ounit_J,type,
    rBT_ma9198043261057625646t_unit: $tType ).

thf(ty_n_t__RBT____Mapping2__Omapping____rbt_Itf__a1_Mt__Product____Type__Ounit_J,type,
    rBT_ma5247151625439037167t_unit: $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__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    set_ma7306327908849618074set_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    set_ma6254658672695423900set_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c2_Mt__Nat__Onat_J_J,type,
    set_Pr4274324598211246019c2_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b2_Mt__Nat__Onat_J_J,type,
    set_Pr6583197765812888324b2_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mtf__c2_J_J,type,
    set_Pr1911939568122073667nat_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mtf__b2_J_J,type,
    set_Pr9176197216388362500nat_b2: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    list_P5985182332071222990_a1_a2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c2_Mtf__c2_J_J,type,
    set_Pr905085046849247909_c2_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c2_Mtf__b2_J_J,type,
    set_Pr8169342695115536742_c2_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    set_Pr9202269149784407460_c1_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b2_Mtf__c2_J_J,type,
    set_Pr7477786653205428070_b2_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b2_Mtf__b2_J_J,type,
    set_Pr5518672264616941095_b2_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    set_Pr4592484330697324838_b1_b2: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    set_Pr9206071548465018024_a1_a2: $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__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    mapping_c1_set_c2: $tType ).

thf(ty_n_t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    mapping_b1_set_b2: $tType ).

thf(ty_n_t__Mapping__Omapping_Itf__a1_Mt__Set__Oset_Itf__a2_J_J,type,
    mapping_a1_set_a2: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    option_set_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mt__Nat__Onat_J,type,
    product_prod_c2_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mt__Nat__Onat_J,type,
    product_prod_b2_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J,type,
    product_prod_nat_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J,type,
    product_prod_nat_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J,type,
    product_prod_nat_a1: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
    set_set_nat: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_Itf__c2_J_J,type,
    option_set_c2: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_Itf__c1_J_J,type,
    option_set_c1: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_Itf__b2_J_J,type,
    option_set_b2: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_Itf__b1_J_J,type,
    option_set_b1: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_Itf__a2_J_J,type,
    option_set_a2: $tType ).

thf(ty_n_t__Option__Ooption_It__Set__Oset_Itf__a1_J_J,type,
    option_set_a1: $tType ).

thf(ty_n_t__FSM__Ofsm_Itf__c1_Mtf__c2_Mt__Nat__Onat_J,type,
    fsm_c1_c2_nat: $tType ).

thf(ty_n_t__FSM__Ofsm_Itf__b1_Mtf__b2_Mt__Nat__Onat_J,type,
    fsm_b1_b2_nat: $tType ).

thf(ty_n_t__FSM__Ofsm_Itf__a1_Mtf__a2_Mt__Nat__Onat_J,type,
    fsm_a1_a2_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mtf__c2_J,type,
    product_prod_c2_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mtf__c1_J,type,
    product_prod_c2_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mtf__b2_J,type,
    product_prod_c2_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mtf__b1_J,type,
    product_prod_c2_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c2_Mtf__a1_J,type,
    product_prod_c2_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    product_prod_c1_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mtf__c2_J,type,
    product_prod_b2_c2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mtf__c1_J,type,
    product_prod_b2_c1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mtf__b2_J,type,
    product_prod_b2_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mtf__b1_J,type,
    product_prod_b2_b1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b2_Mtf__a1_J,type,
    product_prod_b2_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    product_prod_b1_b2: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a2_Mtf__a1_J,type,
    product_prod_a2_a1: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    product_prod_a1_a2: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__c2_J_J,type,
    set_set_c2: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__b2_J_J,type,
    set_set_b2: $tType ).

thf(ty_n_t__FSM__Ofsm_Itf__c1_Mtf__c2_Mtf__c2_J,type,
    fsm_c1_c2_c2: $tType ).

thf(ty_n_t__FSM__Ofsm_Itf__c1_Mtf__c2_Mtf__b2_J,type,
    fsm_c1_c2_b2: $tType ).

thf(ty_n_t__FSM__Ofsm_Itf__b1_Mtf__b2_Mtf__c2_J,type,
    fsm_b1_b2_c2: $tType ).

thf(ty_n_t__FSM__Ofsm_Itf__b1_Mtf__b2_Mtf__b2_J,type,
    fsm_b1_b2_b2: $tType ).

thf(ty_n_t__FSM__Ofsm_Itf__a1_Mtf__a2_Mtf__c2_J,type,
    fsm_a1_a2_c2: $tType ).

thf(ty_n_t__FSM__Ofsm_Itf__a1_Mtf__a2_Mtf__b2_J,type,
    fsm_a1_a2_b2: $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__c2_J,type,
    option_c2: $tType ).

thf(ty_n_t__Option__Ooption_Itf__b2_J,type,
    option_b2: $tType ).

thf(ty_n_t__Product____Type__Ounit,type,
    product_unit: $tType ).

thf(ty_n_t__List__Olist_Itf__c1_J,type,
    list_c1: $tType ).

thf(ty_n_t__List__Olist_Itf__b1_J,type,
    list_b1: $tType ).

thf(ty_n_t__Set__Oset_Itf__c2_J,type,
    set_c2: $tType ).

thf(ty_n_t__Set__Oset_Itf__c1_J,type,
    set_c1: $tType ).

thf(ty_n_t__Set__Oset_Itf__b2_J,type,
    set_b2: $tType ).

thf(ty_n_t__Set__Oset_Itf__b1_J,type,
    set_b1: $tType ).

thf(ty_n_t__Set__Oset_Itf__a2_J,type,
    set_a2: $tType ).

thf(ty_n_t__Set__Oset_Itf__a1_J,type,
    set_a1: $tType ).

thf(ty_n_t__Comparator__Oorder,type,
    order: $tType ).

thf(ty_n_t__String__Oliteral,type,
    literal: $tType ).

thf(ty_n_t__String__Ochar,type,
    char: $tType ).

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

thf(ty_n_tf__c2,type,
    c2: $tType ).

thf(ty_n_tf__c1,type,
    c1: $tType ).

thf(ty_n_tf__b2,type,
    b2: $tType ).

thf(ty_n_tf__b1,type,
    b1: $tType ).

thf(ty_n_tf__a2,type,
    a2: $tType ).

thf(ty_n_tf__a1,type,
    a1: $tType ).

% Explicit typings (962)
thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001tf__c1_001tf__c2,type,
    bNF_Gr4776719309262608675_c1_c2: set_ma7306327908849618074set_c2 > ( mapping_c1_set_c2 > c1 ) > ( mapping_c1_set_c2 > c2 ) > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__a1_001tf__a2,type,
    bNF_Gr3453814218379376343_a1_a2: set_Pr9206071548465018024_a1_a2 > ( product_prod_a1_a2 > a1 ) > ( product_prod_a1_a2 > a2 ) > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__b1_001tf__b2,type,
    bNF_Gr2818165217774455253_b1_b2: set_Pr9206071548465018024_a1_a2 > ( product_prod_a1_a2 > b1 ) > ( product_prod_a1_a2 > b2 ) > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__c1_001tf__c2,type,
    bNF_Gr2182516217169534163_c1_c2: set_Pr9206071548465018024_a1_a2 > ( product_prod_a1_a2 > c1 ) > ( product_prod_a1_a2 > c2 ) > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__a1_001tf__a2,type,
    bNF_Gr6706359503960630357_a1_a2: set_Pr4592484330697324838_b1_b2 > ( product_prod_b1_b2 > a1 ) > ( product_prod_b1_b2 > a2 ) > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__b1_001tf__b2,type,
    bNF_Gr6070710503355709267_b1_b2: set_Pr4592484330697324838_b1_b2 > ( product_prod_b1_b2 > b1 ) > ( product_prod_b1_b2 > b2 ) > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__c1_001tf__c2,type,
    bNF_Gr5435061502750788177_c1_c2: set_Pr4592484330697324838_b1_b2 > ( product_prod_b1_b2 > c1 ) > ( product_prod_b1_b2 > c2 ) > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__a1_001tf__a2,type,
    bNF_Gr735532752687108563_a1_a2: set_Pr9202269149784407460_c1_c2 > ( product_prod_c1_c2 > a1 ) > ( product_prod_c1_c2 > a2 ) > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__b1_001tf__b2,type,
    bNF_Gr99883752082187473_b1_b2: set_Pr9202269149784407460_c1_c2 > ( product_prod_c1_c2 > b1 ) > ( product_prod_c1_c2 > b2 ) > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__c1_001tf__c2,type,
    bNF_Gr8687606788332042191_c1_c2: set_Pr9202269149784407460_c1_c2 > ( product_prod_c1_c2 > c1 ) > ( product_prod_c1_c2 > c2 ) > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Collection__Order_Occompare__class_Occompare_001t__Nat__Onat,type,
    collec3177673580629085973re_nat: option_nat_nat_order ).

thf(sy_c_Collection__Order_Occompare__class_Occompare_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    collec5371428610649875267_a1_a2: option9171407760438378004_order ).

thf(sy_c_Collection__Order_Occompare__class_Occompare_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    collec4736061897551005377_b1_b2: option3340807017899620244_order ).

thf(sy_c_Collection__Order_Occompare__class_Occompare_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    collec4100695184452135487_c1_c2: option6733578312215638292_order ).

thf(sy_c_Collection__Order_Occompare__class_Occompare_001tf__a1,type,
    collec1018370599034179448are_a1: option_a1_a1_order ).

thf(sy_c_Collection__Order_Occompare__class_Occompare_001tf__a2,type,
    collec1018370599034179449are_a2: option_a2_a2_order ).

thf(sy_c_Collection__Order_Occompare__class_Occompare_001tf__b2,type,
    collec1018370599034245048are_b2: option_b2_b2_order ).

thf(sy_c_Collection__Order_Occompare__class_Occompare_001tf__c2,type,
    collec1018370599034310647are_c2: option_c2_c2_order ).

thf(sy_c_Containers__Auxiliary_OID_001t__Option__Ooption_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Comparator__Oorder_J_J_J,type,
    contai6714475312730102056_order: option_nat_nat_order > option_nat_nat_order ).

thf(sy_c_Containers__Auxiliary_OID_001t__Option__Ooption_I_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J_J,type,
    contai3539521610808799152_order: option9171407760438378004_order > option9171407760438378004_order ).

thf(sy_c_Containers__Auxiliary_OID_001t__Option__Ooption_I_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_M_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Comparator__Oorder_J_J_J,type,
    contai6932292905124817200_order: option3340807017899620244_order > option3340807017899620244_order ).

thf(sy_c_Containers__Auxiliary_OID_001t__Option__Ooption_I_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_M_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Comparator__Oorder_J_J_J,type,
    contai1101692162586059440_order: option6733578312215638292_order > option6733578312215638292_order ).

thf(sy_c_Containers__Auxiliary_OID_001t__Option__Ooption_I_062_Itf__a1_M_062_Itf__a1_Mt__Comparator__Oorder_J_J_J,type,
    contai7102178477343188834_order: option_a1_a1_order > option_a1_a1_order ).

thf(sy_c_Containers__Auxiliary_OID_001t__Option__Ooption_I_062_Itf__a2_M_062_Itf__a2_Mt__Comparator__Oorder_J_J_J,type,
    contai8426371921324108128_order: option_a2_a2_order > option_a2_a2_order ).

thf(sy_c_Containers__Auxiliary_OID_001t__Option__Ooption_I_062_Itf__b2_M_062_Itf__b2_Mt__Comparator__Oorder_J_J_J,type,
    contai8474260527370315490_order: option_b2_b2_order > option_b2_b2_order ).

thf(sy_c_Containers__Auxiliary_OID_001t__Option__Ooption_I_062_Itf__c2_M_062_Itf__c2_Mt__Comparator__Oorder_J_J_J,type,
    contai8522149133416522852_order: option_c2_c2_order > option_c2_c2_order ).

thf(sy_c_Containers__Auxiliary_Oless__eq__prod_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    contai2817698454083569946set_b2: ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > produc8498296649714291061set_b2 > produc8498296649714291061set_b2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__eq__prod_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    contai8556515494464243480set_c2: ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > ( ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o ) > produc2702059613074419827set_c2 > produc2702059613074419827set_c2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__eq__prod_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    contai2948815456624895768set_b2: ( ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o ) > ( ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o ) > ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > produc8629413652255616883set_b2 > produc8629413652255616883set_b2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__eq__prod_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    contai3045741756866854480set_c2: ( mapping_b1_set_b2 > mapping_b1_set_b2 > $o ) > ( mapping_b1_set_b2 > mapping_b1_set_b2 > $o ) > ( mapping_c1_set_c2 > mapping_c1_set_c2 > $o ) > produc4061897789176782763set_c2 > produc4061897789176782763set_c2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__eq__prod_001tf__a1_001tf__a2,type,
    contai5003787414824119917_a1_a2: ( a1 > a1 > $o ) > ( a1 > a1 > $o ) > ( a2 > a2 > $o ) > product_prod_a1_a2 > product_prod_a1_a2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__eq__prod_001tf__b1_001tf__b2,type,
    contai4368138414219198827_b1_b2: ( b1 > b1 > $o ) > ( b1 > b1 > $o ) > ( b2 > b2 > $o ) > product_prod_b1_b2 > product_prod_b1_b2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__eq__prod_001tf__c1_001tf__c2,type,
    contai3732489413614277737_c1_c2: ( c1 > c1 > $o ) > ( c1 > c1 > $o ) > ( c2 > c2 > $o ) > product_prod_c1_c2 > product_prod_c1_c2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__prod_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    contai2668647468241185550set_b2: ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > produc8498296649714291061set_b2 > produc8498296649714291061set_b2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__prod_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    contai8407464508621859084set_c2: ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > ( ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o ) > produc2702059613074419827set_c2 > produc2702059613074419827set_c2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__prod_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    contai2799764470782511372set_b2: ( ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o ) > ( ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o ) > ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > produc8629413652255616883set_b2 > produc8629413652255616883set_b2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__prod_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    contai6005974929653906500set_c2: ( mapping_b1_set_b2 > mapping_b1_set_b2 > $o ) > ( mapping_b1_set_b2 > mapping_b1_set_b2 > $o ) > ( mapping_c1_set_c2 > mapping_c1_set_c2 > $o ) > produc4061897789176782763set_c2 > produc4061897789176782763set_c2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__prod_001tf__a1_001tf__a2,type,
    contai2386566770025630817_a1_a2: ( a1 > a1 > $o ) > ( a1 > a1 > $o ) > ( a2 > a2 > $o ) > product_prod_a1_a2 > product_prod_a1_a2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__prod_001tf__b1_001tf__b2,type,
    contai1750917769420709727_b1_b2: ( b1 > b1 > $o ) > ( b1 > b1 > $o ) > ( b2 > b2 > $o ) > product_prod_b1_b2 > product_prod_b1_b2 > $o ).

thf(sy_c_Containers__Auxiliary_Oless__prod_001tf__c1_001tf__c2,type,
    contai1115268768815788637_c1_c2: ( c1 > c1 > $o ) > ( c1 > c1 > $o ) > ( c2 > c2 > $o ) > product_prod_c1_c2 > product_prod_c1_c2 > $o ).

thf(sy_c_FSM_Oh__out_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Nat__Onat,type,
    h_out_6598019409568368631c2_nat: fsm_ma3562454073340529286c2_nat > produc4061897789176782763set_c2 > set_nat ).

thf(sy_c_FSM_Oh__out_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001tf__b2,type,
    h_out_3266241837355465626_c2_b2: fsm_ma8761726031752409769_c2_b2 > produc4061897789176782763set_c2 > set_b2 ).

thf(sy_c_FSM_Oh__out_001tf__a1_001tf__a2_001t__Nat__Onat,type,
    h_out_a1_a2_nat: fsm_a1_a2_nat > product_prod_a1_a2 > set_nat ).

thf(sy_c_FSM_Oh__out_001tf__a1_001tf__a2_001tf__b2,type,
    h_out_a1_a2_b2: fsm_a1_a2_b2 > product_prod_a1_a2 > set_b2 ).

thf(sy_c_FSM_Oh__out_001tf__a1_001tf__a2_001tf__c2,type,
    h_out_a1_a2_c2: fsm_a1_a2_c2 > product_prod_a1_a2 > set_c2 ).

thf(sy_c_FSM_Oh__out_001tf__b1_001tf__b2_001t__Nat__Onat,type,
    h_out_b1_b2_nat: fsm_b1_b2_nat > product_prod_b1_b2 > set_nat ).

thf(sy_c_FSM_Oh__out_001tf__b1_001tf__b2_001tf__b2,type,
    h_out_b1_b2_b2: fsm_b1_b2_b2 > product_prod_b1_b2 > set_b2 ).

thf(sy_c_FSM_Oh__out_001tf__b1_001tf__b2_001tf__c2,type,
    h_out_b1_b2_c2: fsm_b1_b2_c2 > product_prod_b1_b2 > set_c2 ).

thf(sy_c_FSM_Oh__out_001tf__c1_001tf__c2_001t__Nat__Onat,type,
    h_out_c1_c2_nat: fsm_c1_c2_nat > product_prod_c1_c2 > set_nat ).

thf(sy_c_FSM_Oh__out_001tf__c1_001tf__c2_001tf__b2,type,
    h_out_c1_c2_b2: fsm_c1_c2_b2 > product_prod_c1_c2 > set_b2 ).

thf(sy_c_FSM_Oh__out_001tf__c1_001tf__c2_001tf__c2,type,
    h_out_c1_c2_c2: fsm_c1_c2_c2 > product_prod_c1_c2 > set_c2 ).

thf(sy_c_FSM_Otransitions_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Nat__Onat,type,
    transi1170656512200261639c2_nat: fsm_ma3562454073340529286c2_nat > set_Pr5589133262920150351set_b2 ).

thf(sy_c_FSM_Otransitions_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001tf__b2,type,
    transi3351285373981281194_c2_b2: fsm_ma8761726031752409769_c2_b2 > set_Pr5018776704028855922set_b2 ).

thf(sy_c_FSM_Otransitions_001tf__a1_001tf__a2_001t__Nat__Onat,type,
    transi2824120892608826404a2_nat: fsm_a1_a2_nat > set_Pr8929720694596501145nat_a1 ).

thf(sy_c_FSM_Otransitions_001tf__a1_001tf__a2_001tf__b2,type,
    transitions_a1_a2_b2: fsm_a1_a2_b2 > set_Pr7003674894764019516_b2_a1 ).

thf(sy_c_FSM_Otransitions_001tf__a1_001tf__a2_001tf__c2,type,
    transitions_a1_a2_c2: fsm_a1_a2_c2 > set_Pr5146122262371603323_c2_a1 ).

thf(sy_c_FSM_Otransitions_001tf__b1_001tf__b2_001t__Nat__Onat,type,
    transi2454530297511208738b2_nat: fsm_b1_b2_nat > set_Pr4802260232978741656nat_b1 ).

thf(sy_c_FSM_Otransitions_001tf__b1_001tf__b2_001tf__b2,type,
    transitions_b1_b2_b2: fsm_b1_b2_b2 > set_Pr6077960137706433083_b2_b1 ).

thf(sy_c_FSM_Otransitions_001tf__b1_001tf__b2_001tf__c2,type,
    transitions_b1_b2_c2: fsm_b1_b2_c2 > set_Pr4220407505314016890_c2_b1 ).

thf(sy_c_FSM_Otransitions_001tf__c1_001tf__c2_001t__Nat__Onat,type,
    transi2084939702413591072c2_nat: fsm_c1_c2_nat > set_Pr674799771360982167nat_c1 ).

thf(sy_c_FSM_Otransitions_001tf__c1_001tf__c2_001tf__b2,type,
    transitions_c1_c2_b2: fsm_c1_c2_b2 > set_Pr5152245380648846650_b2_c1 ).

thf(sy_c_FSM_Otransitions_001tf__c1_001tf__c2_001tf__c2,type,
    transitions_c1_c2_c2: fsm_c1_c2_c2 > set_Pr3294692748256430457_c2_c1 ).

thf(sy_c_Finite__Set_Ofinite_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    finite2174808930419575421set_b2: set_ma6254658672695423900set_b2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    finite5621885356302860923set_c2: set_ma7306327908849618074set_c2 > $o ).

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

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    finite199606665216627796set_c2: set_Pr1660683266160182027set_c2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mtf__c2_J,type,
    finite8055457123860967971_c2_c2: set_Pr8355152109431543362_c2_c2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Nat__Onat_J,type,
    finite5082507503679472862a2_nat: set_Pr1591205605347421565a2_nat > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b2_J,type,
    finite2288184041456251137_a2_b2: set_Pr6984238321955989024_a2_b2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c2_J,type,
    finite2288466328962367936_a2_c2: set_Pr8943352710544475999_a2_c2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Nat__Onat_J,type,
    finite4261596373372629084b2_nat: set_Pr6819770292282554875b2_nat > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b2_J,type,
    finite6216527523271391615_b2_b2: set_Pr3646447153602301854_b2_b2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c2_J,type,
    finite6216809810777508414_b2_c2: set_Pr5605561542190788829_b2_c2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Nat__Onat_J,type,
    finite3440685243065785306c2_nat: set_Pr2824962942362912377c2_nat > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b2_J,type,
    finite921498968231756285_c2_b2: set_Pr308655985248614684_c2_b2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c2_J,type,
    finite921781255737873084_c2_c2: set_Pr2267770373837101659_c2_c2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    finite9152749144624424049_a1_a2: set_Pr9206071548465018024_a1_a2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    finite8517382431525554159_b1_b2: set_Pr4592484330697324838_b1_b2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    finite7882015718426684269_c1_c2: set_Pr9202269149784407460_c1_c2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001tf__b2,type,
    finite_finite_b2: set_b2 > $o ).

thf(sy_c_Finite__Set_Ofinite_001tf__c2,type,
    finite_finite_c2: set_c2 > $o ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    comp_b5264233654759695275set_c2: ( ( b1 > option_set_b2 ) > produc8498296649714291061set_b2 ) > ( produc2702059613074419827set_c2 > b1 > option_set_b2 ) > produc2702059613074419827set_c2 > produc8498296649714291061set_b2 ).

thf(sy_c_Fun_Ocomp_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    comp_c1653858145111704749set_c2: ( ( c1 > option_set_c2 ) > produc2833176615615745649set_c2 ) > ( produc2702059613074419827set_c2 > c1 > option_set_c2 ) > produc2702059613074419827set_c2 > produc2833176615615745649set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001_062_It__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_Mt__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    comp_m1545697475630127524_b1_b2: ( mapping_b1_set_b2 > set_ma6254658672695423900set_b2 > set_ma6254658672695423900set_b2 ) > ( product_prod_b1_b2 > mapping_b1_set_b2 ) > product_prod_b1_b2 > set_ma6254658672695423900set_b2 > set_ma6254658672695423900set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    comp_m7925709966048865799set_c2: ( mapping_b1_set_b2 > produc3010228553022588589set_b2 ) > ( produc4061897789176782763set_c2 > mapping_b1_set_b2 ) > produc4061897789176782763set_c2 > produc3010228553022588589set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001_062_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mt__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    comp_m9082150296861661608_c1_c2: ( mapping_c1_set_c2 > set_ma7306327908849618074set_c2 > set_ma7306327908849618074set_c2 ) > ( product_prod_c1_c2 > mapping_c1_set_c2 ) > product_prod_c1_c2 > set_ma7306327908849618074set_c2 > set_ma7306327908849618074set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    comp_m1427541729666086921set_c2: ( mapping_c1_set_c2 > produc6123186059419489449set_c2 ) > ( produc4061897789176782763set_c2 > mapping_c1_set_c2 ) > produc4061897789176782763set_c2 > produc6123186059419489449set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_m7208595679230017097_a1_a2: ( mapping_c1_set_c2 > product_prod_b1_b2 ) > ( product_prod_a1_a2 > mapping_c1_set_c2 ) > product_prod_a1_a2 > product_prod_b1_b2 ).

thf(sy_c_Fun_Ocomp_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    comp_m5937862253032277317_c1_c2: ( mapping_c1_set_c2 > product_prod_b1_b2 ) > ( product_prod_c1_c2 > mapping_c1_set_c2 ) > product_prod_c1_c2 > product_prod_b1_b2 ).

thf(sy_c_Fun_Ocomp_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_m4238612144453813067_a1_a2: ( mapping_c1_set_c2 > product_prod_c1_c2 ) > ( product_prod_a1_a2 > mapping_c1_set_c2 ) > product_prod_a1_a2 > product_prod_c1_c2 ).

thf(sy_c_Fun_Ocomp_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    comp_m2967878718256073287_c1_c2: ( mapping_c1_set_c2 > product_prod_c1_c2 ) > ( product_prod_c1_c2 > mapping_c1_set_c2 ) > product_prod_c1_c2 > product_prod_c1_c2 ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_n5668408791610806888_a1_a2: ( nat > set_nat > set_nat ) > ( product_prod_a1_a2 > nat ) > product_prod_a1_a2 > set_nat > set_nat ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    comp_P6294463794021757207set_b2: ( produc8498296649714291061set_b2 > b1 > option_set_b2 ) > ( produc8498296649714291061set_b2 > produc8498296649714291061set_b2 ) > produc8498296649714291061set_b2 > b1 > option_set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    comp_P498226757381885973set_c2: ( produc8498296649714291061set_b2 > b1 > option_set_b2 ) > ( produc2702059613074419827set_c2 > produc8498296649714291061set_b2 ) > produc2702059613074419827set_c2 > b1 > option_set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    comp_P8468077172411818647set_b2: ( produc2702059613074419827set_c2 > b1 > option_set_b2 ) > ( produc8629413652255616883set_b2 > produc2702059613074419827set_c2 ) > produc8629413652255616883set_b2 > b1 > option_set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    comp_P5777573262574892825set_b2: ( produc2702059613074419827set_c2 > c1 > option_set_c2 ) > ( produc8629413652255616883set_b2 > produc2702059613074419827set_c2 ) > produc8629413652255616883set_b2 > c1 > option_set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    comp_P8909975857928217751set_c2: ( produc8629413652255616883set_b2 > b1 > option_set_b2 ) > ( produc2702059613074419827set_c2 > produc8629413652255616883set_b2 ) > produc2702059613074419827set_c2 > b1 > option_set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    comp_P6219471948091291929set_c2: ( produc8629413652255616883set_b2 > c1 > option_set_c2 ) > ( produc2702059613074419827set_c2 > produc8629413652255616883set_b2 ) > produc2702059613074419827set_c2 > c1 > option_set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    comp_P8261968323940027547set_c2: ( produc2833176615615745649set_c2 > c1 > option_set_c2 ) > ( produc2702059613074419827set_c2 > produc2833176615615745649set_c2 ) > produc2702059613074419827set_c2 > c1 > option_set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    comp_P3116930634664401337set_c2: ( produc3010228553022588589set_b2 > mapping_b1_set_b2 ) > ( produc4061897789176782763set_c2 > produc3010228553022588589set_b2 ) > produc4061897789176782763set_c2 > mapping_b1_set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    comp_P8959985049830094907set_b2: ( produc4061897789176782763set_c2 > mapping_b1_set_b2 ) > ( produc5071516823265295275set_b2 > produc4061897789176782763set_c2 ) > produc5071516823265295275set_b2 > mapping_b1_set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    comp_P6937000176383580349set_b2: ( produc4061897789176782763set_c2 > mapping_c1_set_c2 ) > ( produc5071516823265295275set_b2 > produc4061897789176782763set_c2 ) > produc5071516823265295275set_b2 > mapping_c1_set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    comp_P6715848912171352123set_c2: ( produc5071516823265295275set_b2 > mapping_b1_set_b2 ) > ( produc4061897789176782763set_c2 > produc5071516823265295275set_b2 ) > produc4061897789176782763set_c2 > mapping_b1_set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    comp_P4692864038724837565set_c2: ( produc5071516823265295275set_b2 > mapping_c1_set_c2 ) > ( produc4061897789176782763set_c2 > produc5071516823265295275set_b2 ) > produc4061897789176782763set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    comp_P302927382947242815set_c2: ( produc6123186059419489449set_c2 > mapping_c1_set_c2 ) > ( produc4061897789176782763set_c2 > produc6123186059419489449set_c2 ) > produc4061897789176782763set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P8340592762084473895_a1_a2: ( product_prod_a1_a2 > product_prod_b1_b2 ) > ( product_prod_a1_a2 > product_prod_a1_a2 ) > product_prod_a1_a2 > product_prod_b1_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P5370609227308269865_a1_a2: ( product_prod_a1_a2 > product_prod_c1_c2 ) > ( product_prod_a1_a2 > product_prod_a1_a2 ) > product_prod_a1_a2 > product_prod_c1_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mtf__a1_J,type,
    comp_P7491488837927527918_a2_a1: ( product_prod_a1_a2 > a1 ) > ( product_prod_a2_a1 > product_prod_a1_a2 ) > product_prod_a2_a1 > a1 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__a2_001t__Product____Type__Oprod_Itf__a2_Mtf__a1_J,type,
    comp_P6155438217974833581_a2_a1: ( product_prod_a1_a2 > a2 ) > ( product_prod_a2_a1 > product_prod_a1_a2 ) > product_prod_a2_a1 > a2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001_062_It__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P6401785920660582974_a1_a2: ( product_prod_b1_b2 > set_Pr4592484330697324838_b1_b2 > set_Pr4592484330697324838_b1_b2 ) > ( product_prod_a1_a2 > product_prod_b1_b2 ) > product_prod_a1_a2 > set_Pr4592484330697324838_b1_b2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P9207391564348433789_a1_a2: ( product_prod_b1_b2 > mapping_b1_set_b2 ) > ( product_prod_a1_a2 > product_prod_b1_b2 ) > product_prod_a1_a2 > mapping_b1_set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    comp_P8572024851249563899_b1_b2: ( product_prod_b1_b2 > mapping_b1_set_b2 ) > ( product_prod_b1_b2 > product_prod_b1_b2 ) > product_prod_b1_b2 > mapping_b1_set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P1240307840207828479_a1_a2: ( product_prod_b1_b2 > mapping_c1_set_c2 ) > ( product_prod_a1_a2 > product_prod_b1_b2 ) > product_prod_a1_a2 > mapping_c1_set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    comp_P9192946450864864507_c1_c2: ( product_prod_b1_b2 > mapping_c1_set_c2 ) > ( product_prod_c1_c2 > product_prod_b1_b2 ) > product_prod_c1_c2 > mapping_c1_set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P8403851972257459877_a1_a2: ( product_prod_b1_b2 > product_prod_b1_b2 ) > ( product_prod_a1_a2 > product_prod_b1_b2 ) > product_prod_a1_a2 > product_prod_b1_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P5433868437481255847_a1_a2: ( product_prod_b1_b2 > product_prod_c1_c2 ) > ( product_prod_a1_a2 > product_prod_b1_b2 ) > product_prod_a1_a2 > product_prod_c1_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mtf__b1_J,type,
    comp_P1579807045684501871_b2_b1: ( product_prod_b1_b2 > b1 ) > ( product_prod_b2_b1 > product_prod_b1_b2 ) > product_prod_b2_b1 > b1 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__b2_001t__Product____Type__Oprod_Itf__b2_Mtf__b1_J,type,
    comp_P243756425731807534_b2_b1: ( product_prod_b1_b2 > b2 ) > ( product_prod_b2_b1 > product_prod_b1_b2 ) > product_prod_b2_b1 > b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001_062_It__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_Mt__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P2932605450278441920_a1_a2: ( product_prod_c1_c2 > set_Pr9202269149784407460_c1_c2 > set_Pr9202269149784407460_c1_c2 ) > ( product_prod_a1_a2 > product_prod_c1_c2 ) > product_prod_a1_a2 > set_Pr9202269149784407460_c1_c2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P1762222845428264319_a1_a2: ( product_prod_c1_c2 > mapping_b1_set_b2 ) > ( product_prod_a1_a2 > product_prod_c1_c2 ) > product_prod_a1_a2 > mapping_b1_set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    comp_P1126856132329394429_b1_b2: ( product_prod_c1_c2 > mapping_b1_set_b2 ) > ( product_prod_b1_b2 > product_prod_c1_c2 ) > product_prod_b1_b2 > mapping_b1_set_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P3018511158142434817_a1_a2: ( product_prod_c1_c2 > mapping_c1_set_c2 ) > ( product_prod_a1_a2 > product_prod_c1_c2 ) > product_prod_a1_a2 > mapping_c1_set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    comp_P1747777731944695037_c1_c2: ( product_prod_c1_c2 > mapping_c1_set_c2 ) > ( product_prod_c1_c2 > product_prod_c1_c2 ) > product_prod_c1_c2 > mapping_c1_set_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P8467111182430445859_a1_a2: ( product_prod_c1_c2 > product_prod_b1_b2 ) > ( product_prod_a1_a2 > product_prod_c1_c2 ) > product_prod_a1_a2 > product_prod_b1_b2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_P5497127647654241829_a1_a2: ( product_prod_c1_c2 > product_prod_c1_c2 ) > ( product_prod_a1_a2 > product_prod_c1_c2 ) > product_prod_a1_a2 > product_prod_c1_c2 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mtf__c1_J,type,
    comp_P4891497290296251632_c2_c1: ( product_prod_c1_c2 > c1 ) > ( product_prod_c2_c1 > product_prod_c1_c2 ) > product_prod_c2_c1 > c1 ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__c2_001t__Product____Type__Oprod_Itf__c2_Mtf__c1_J,type,
    comp_P3555446670343557295_c2_c1: ( product_prod_c1_c2 > c2 ) > ( product_prod_c2_c1 > product_prod_c1_c2 ) > product_prod_c2_c1 > c2 ).

thf(sy_c_Fun_Ocomp_001tf__b2_001_062_It__Set__Oset_Itf__b2_J_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_b5600926368682017087_a1_a2: ( b2 > set_b2 > set_b2 ) > ( product_prod_a1_a2 > b2 ) > product_prod_a1_a2 > set_b2 > set_b2 ).

thf(sy_c_Fun_Ocomp_001tf__c2_001_062_It__Set__Oset_Itf__c2_J_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    comp_c1592680653864801986_a1_a2: ( c2 > set_c2 > set_c2 ) > ( product_prod_a1_a2 > c2 ) > product_prod_a1_a2 > set_c2 > set_c2 ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
    minus_minus_nat: nat > nat > nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    minus_3844173815668582389set_b2: set_ma6254658672695423900set_b2 > set_ma6254658672695423900set_b2 > set_ma6254658672695423900set_b2 ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    minus_4895843051822776563set_c2: set_ma7306327908849618074set_c2 > set_ma7306327908849618074set_c2 > set_ma7306327908849618074set_c2 ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
    minus_minus_set_nat: set_nat > set_nat > set_nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    minus_7668950675640249231_a1_a2: set_Pr9206071548465018024_a1_a2 > set_Pr9206071548465018024_a1_a2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    minus_3055363457872556045_b1_b2: set_Pr4592484330697324838_b1_b2 > set_Pr4592484330697324838_b1_b2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    minus_7665148276959638667_c1_c2: set_Pr9202269149784407460_c1_c2 > set_Pr9202269149784407460_c1_c2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__b2_J,type,
    minus_minus_set_b2: set_b2 > set_b2 > set_b2 ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__c2_J,type,
    minus_minus_set_c2: set_c2 > set_c2 > set_c2 ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
    zero_zero_nat: nat ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__String__Oliteral,type,
    zero_zero_literal: literal ).

thf(sy_c_If_001t__Set__Oset_It__Nat__Onat_J,type,
    if_set_nat: $o > set_nat > set_nat > set_nat ).

thf(sy_c_If_001t__Set__Oset_Itf__a2_J,type,
    if_set_a2: $o > set_a2 > set_a2 > set_a2 ).

thf(sy_c_If_001t__Set__Oset_Itf__b2_J,type,
    if_set_b2: $o > set_b2 > set_b2 > set_b2 ).

thf(sy_c_If_001t__Set__Oset_Itf__c2_J,type,
    if_set_c2: $o > set_c2 > set_c2 > set_c2 ).

thf(sy_c_List_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    fold_P366236689040723939set_b2: ( product_prod_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2 ) > list_P5985182332071222990_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2 ).

thf(sy_c_List_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    fold_P3813313114924009441set_c2: ( product_prod_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2 ) > list_P5985182332071222990_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2 ).

thf(sy_c_List_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    fold_P6133368858501377392set_b2: ( product_prod_a1_a2 > produc3010228553022588589set_b2 > produc3010228553022588589set_b2 ) > list_P5985182332071222990_a1_a2 > produc3010228553022588589set_b2 > produc3010228553022588589set_b2 ).

thf(sy_c_List_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    fold_P7185038094655571566set_c2: ( product_prod_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ) > list_P5985182332071222990_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ).

thf(sy_c_List_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    fold_P2573110186453295671set_c2: ( product_prod_a1_a2 > produc4134103123222870330set_c2 > produc4134103123222870330set_c2 ) > list_P5985182332071222990_a1_a2 > produc4134103123222870330set_c2 > produc4134103123222870330set_c2 ).

thf(sy_c_List_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    fold_P8194657128744084078set_b2: ( product_prod_a1_a2 > produc5071516823265295275set_b2 > produc5071516823265295275set_b2 ) > list_P5985182332071222990_a1_a2 > produc5071516823265295275set_b2 > produc5071516823265295275set_b2 ).

thf(sy_c_List_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    fold_P22954328043502444set_c2: ( product_prod_a1_a2 > produc6123186059419489449set_c2 > produc6123186059419489449set_c2 ) > list_P5985182332071222990_a1_a2 > produc6123186059419489449set_c2 > produc6123186059419489449set_c2 ).

thf(sy_c_List_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    fold_P550125313006781113set_c2: ( product_prod_a1_a2 > produc2111118249776355772set_c2 > produc2111118249776355772set_c2 ) > list_P5985182332071222990_a1_a2 > produc2111118249776355772set_c2 > produc2111118249776355772set_c2 ).

thf(sy_c_List_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    fold_P5530968877631332285set_b2: ( product_prod_a1_a2 > produc7091961814400906944set_b2 > produc7091961814400906944set_b2 ) > list_P5985182332071222990_a1_a2 > produc7091961814400906944set_b2 > produc7091961814400906944set_b2 ).

thf(sy_c_List_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    fold_P6582638113785526459set_c2: ( product_prod_a1_a2 > produc8143631050555101118set_c2 > produc8143631050555101118set_c2 ) > list_P5985182332071222990_a1_a2 > produc8143631050555101118set_c2 > produc8143631050555101118set_c2 ).

thf(sy_c_List_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    fold_P7873264179840037930set_c2: ( product_prod_a1_a2 > produc2163030415453158631set_c2 > produc2163030415453158631set_c2 ) > list_P5985182332071222990_a1_a2 > produc2163030415453158631set_c2 > produc2163030415453158631set_c2 ).

thf(sy_c_List_Ofold_001tf__b1_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    fold_b7903347184624473061set_b2: ( b1 > mapping_b1_set_b2 > mapping_b1_set_b2 ) > list_b1 > mapping_b1_set_b2 > mapping_b1_set_b2 ).

thf(sy_c_List_Ofold_001tf__c1_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    fold_c2473469727541406370set_c2: ( c1 > mapping_c1_set_c2 > mapping_c1_set_c2 ) > list_c1 > mapping_c1_set_c2 > mapping_c1_set_c2 ).

thf(sy_c_List_Omap__project_001t__Nat__Onat_001t__Nat__Onat,type,
    map_project_nat_nat: ( nat > option_nat ) > set_nat > set_nat ).

thf(sy_c_List_Omap__project_001t__Nat__Onat_001tf__b2,type,
    map_project_nat_b2: ( nat > option_b2 ) > set_nat > set_b2 ).

thf(sy_c_List_Omap__project_001t__Nat__Onat_001tf__c2,type,
    map_project_nat_c2: ( nat > option_c2 ) > set_nat > set_c2 ).

thf(sy_c_List_Omap__project_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Nat__Onat,type,
    map_pr1385896286841821201a2_nat: ( product_prod_a1_a2 > option_nat ) > set_Pr9206071548465018024_a1_a2 > set_nat ).

thf(sy_c_List_Omap__project_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__b2,type,
    map_pr8920200868248588980_a2_b2: ( product_prod_a1_a2 > option_b2 ) > set_Pr9206071548465018024_a1_a2 > set_b2 ).

thf(sy_c_List_Omap__project_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__c2,type,
    map_pr8920200868248654579_a2_c2: ( product_prod_a1_a2 > option_c2 ) > set_Pr9206071548465018024_a1_a2 > set_c2 ).

thf(sy_c_List_Omap__project_001tf__b2_001t__Nat__Onat,type,
    map_project_b2_nat: ( b2 > option_nat ) > set_b2 > set_nat ).

thf(sy_c_List_Omap__project_001tf__b2_001tf__b2,type,
    map_project_b2_b2: ( b2 > option_b2 ) > set_b2 > set_b2 ).

thf(sy_c_List_Omap__project_001tf__b2_001tf__c2,type,
    map_project_b2_c2: ( b2 > option_c2 ) > set_b2 > set_c2 ).

thf(sy_c_List_Omap__project_001tf__c2_001t__Nat__Onat,type,
    map_project_c2_nat: ( c2 > option_nat ) > set_c2 > set_nat ).

thf(sy_c_List_Omap__project_001tf__c2_001tf__b2,type,
    map_project_c2_b2: ( c2 > option_b2 ) > set_c2 > set_b2 ).

thf(sy_c_List_Omap__project_001tf__c2_001tf__c2,type,
    map_project_c2_c2: ( c2 > option_c2 ) > set_c2 > set_c2 ).

thf(sy_c_Mapping_Oempty_001tf__a1_001t__Set__Oset_Itf__a2_J,type,
    empty_a1_set_a2: mapping_a1_set_a2 ).

thf(sy_c_Mapping_Oempty_001tf__b1_001t__Set__Oset_Itf__b2_J,type,
    empty_b1_set_b2: mapping_b1_set_b2 ).

thf(sy_c_Mapping_Oempty_001tf__c1_001t__Set__Oset_Itf__c2_J,type,
    empty_c1_set_c2: mapping_c1_set_c2 ).

thf(sy_c_Mapping_Olookup_001tf__a1_001t__Set__Oset_Itf__a2_J,type,
    lookup_a1_set_a2: mapping_a1_set_a2 > a1 > option_set_a2 ).

thf(sy_c_Mapping_Olookup_001tf__b1_001t__Set__Oset_Itf__b2_J,type,
    lookup_b1_set_b2: mapping_b1_set_b2 > b1 > option_set_b2 ).

thf(sy_c_Mapping_Olookup_001tf__c1_001t__Set__Oset_Itf__c2_J,type,
    lookup_c1_set_c2: mapping_c1_set_c2 > c1 > option_set_c2 ).

thf(sy_c_Mapping_Omap__entry_001tf__b1_001t__Set__Oset_Itf__b2_J,type,
    map_entry_b1_set_b2: b1 > ( set_b2 > set_b2 ) > mapping_b1_set_b2 > mapping_b1_set_b2 ).

thf(sy_c_Mapping_Omap__entry_001tf__c1_001t__Set__Oset_Itf__c2_J,type,
    map_entry_c1_set_c2: c1 > ( set_c2 > set_c2 ) > mapping_c1_set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Mapping_Otabulate_001tf__b1_001t__Set__Oset_Itf__b2_J,type,
    tabulate_b1_set_b2: list_b1 > ( b1 > set_b2 ) > mapping_b1_set_b2 ).

thf(sy_c_Mapping_Otabulate_001tf__c1_001t__Set__Oset_Itf__c2_J,type,
    tabulate_c1_set_c2: list_c1 > ( c1 > set_c2 ) > mapping_c1_set_c2 ).

thf(sy_c_Mapping_Oupdate_001tf__a1_001t__Set__Oset_Itf__a2_J,type,
    update_a1_set_a2: a1 > set_a2 > mapping_a1_set_a2 > mapping_a1_set_a2 ).

thf(sy_c_Mapping_Oupdate_001tf__b1_001t__Set__Oset_Itf__b2_J,type,
    update_b1_set_b2: b1 > set_b2 > mapping_b1_set_b2 > mapping_b1_set_b2 ).

thf(sy_c_Mapping_Oupdate_001tf__c1_001t__Set__Oset_Itf__c2_J,type,
    update_c1_set_c2: c1 > set_c2 > mapping_c1_set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Option_Ooption_OSome_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    some_P6364418062025833395_order: ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > option9171407760438378004_order ).

thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_Itf__b2_J,type,
    some_set_b2: set_b2 > option_set_b2 ).

thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_Itf__c2_J,type,
    some_set_c2: set_c2 > option_set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001_062_Itf__a1_Mt__Option__Ooption_It__Set__Oset_Itf__a2_J_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o5322456805779026421_order: ( a1 > option_set_a2 ) > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > a1 > option_set_a2 ) > option9171407760438378004_order > a1 > option_set_a2 ).

thf(sy_c_Option_Ooption_Ocase__option_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o6925540419184956023_order: ( b1 > option_set_b2 ) > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > b1 > option_set_b2 ) > option9171407760438378004_order > b1 > option_set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_M_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Comparator__Oorder_J_J,type,
    case_o301092356325575671_order: ( b1 > option_set_b2 ) > ( ( product_prod_b1_b2 > product_prod_b1_b2 > order ) > b1 > option_set_b2 ) > option3340807017899620244_order > b1 > option_set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o8528624032590885625_order: ( c1 > option_set_c2 ) > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > c1 > option_set_c2 ) > option9171407760438378004_order > c1 > option_set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_M_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Comparator__Oorder_J_J,type,
    case_o4503099943726900729_order: ( c1 > option_set_c2 ) > ( ( product_prod_c1_c2 > product_prod_c1_c2 > order ) > c1 > option_set_c2 ) > option6733578312215638292_order > c1 > option_set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Comparator__Oorder_J_J,type,
    case_o3585232611041703993_order: $o > ( ( nat > nat > order ) > $o ) > option_nat_nat_order > $o ).

thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o437269291504840897_order: $o > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > $o ) > option9171407760438378004_order > $o ).

thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Set__Oset_Itf__b2_J,type,
    case_option_o_set_b2: $o > ( set_b2 > $o ) > option_set_b2 > $o ).

thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Set__Oset_Itf__c2_J,type,
    case_option_o_set_c2: $o > ( set_c2 > $o ) > option_set_c2 > $o ).

thf(sy_c_Option_Ooption_Ocase__option_001t__List__Olist_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o1327236596907251723_order: list_P5985182332071222990_a1_a2 > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > list_P5985182332071222990_a1_a2 ) > option9171407760438378004_order > list_P5985182332071222990_a1_a2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Mapping__Omapping_Itf__a1_Mt__Set__Oset_Itf__a2_J_J_001t__Set__Oset_Itf__a2_J,type,
    case_o2651193224077142111set_a2: mapping_a1_set_a2 > ( set_a2 > mapping_a1_set_a2 ) > option_set_a2 > mapping_a1_set_a2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o3110906606155996059_order: mapping_b1_set_b2 > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > mapping_b1_set_b2 ) > option9171407760438378004_order > mapping_b1_set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Set__Oset_Itf__b2_J,type,
    case_o3420813927363517980set_b2: mapping_b1_set_b2 > ( set_b2 > mapping_b1_set_b2 ) > option_set_b2 > mapping_b1_set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o573573238536716829_order: mapping_c1_set_c2 > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > mapping_c1_set_c2 ) > option9171407760438378004_order > mapping_c1_set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Set__Oset_Itf__c2_J,type,
    case_o4190434630649893849set_c2: mapping_c1_set_c2 > ( set_c2 > mapping_c1_set_c2 ) > option_set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o989950291820459046_order: produc2702059613074419827set_c2 > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > produc2702059613074419827set_c2 ) > option9171407760438378004_order > produc2702059613074419827set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o7815954270536807150_order: produc4061897789176782763set_c2 > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > produc4061897789176782763set_c2 ) > option9171407760438378004_order > produc4061897789176782763set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J_001t__Set__Oset_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    case_o4607607441410749453set_b2: set_b1_option_set_b2 > ( set_b1_option_set_b2 > set_b1_option_set_b2 ) > option2685796312493375632set_b2 > set_b1_option_set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J_001t__Set__Oset_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    case_o1308401496032893449set_c2: set_c1_option_set_c2 > ( set_c1_option_set_c2 > set_c1_option_set_c2 ) > option5905241969658642574set_c2 > set_c1_option_set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_001_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_M_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Comparator__Oorder_J_J,type,
    case_o740565870645481573_order: set_ma6254658672695423900set_b2 > ( ( product_prod_b1_b2 > product_prod_b1_b2 > order ) > set_ma6254658672695423900set_b2 ) > option3340807017899620244_order > set_ma6254658672695423900set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_001t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    case_o8937649668621536325set_b2: set_ma6254658672695423900set_b2 > ( set_ma6254658672695423900set_b2 > set_ma6254658672695423900set_b2 ) > option6654706173824968300set_b2 > set_ma6254658672695423900set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_M_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Comparator__Oorder_J_J,type,
    case_o5756018690406977383_order: set_ma7306327908849618074set_c2 > ( ( product_prod_c1_c2 > product_prod_c1_c2 > order ) > set_ma7306327908849618074set_c2 ) > option6733578312215638292_order > set_ma7306327908849618074set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    case_o6909767104305677121set_c2: set_ma7306327908849618074set_c2 > ( set_ma7306327908849618074set_c2 > set_ma7306327908849618074set_c2 ) > option781494349862297706set_c2 > set_ma7306327908849618074set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Nat__Onat_J_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Comparator__Oorder_J_J,type,
    case_o7271898223054362355_order: set_nat > ( ( nat > nat > order ) > set_nat ) > option_nat_nat_order > set_nat ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Nat__Onat_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o1813945580120271995_order: set_nat > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > set_nat ) > option9171407760438378004_order > set_nat ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Nat__Onat_J_001_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_M_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Comparator__Oorder_J_J,type,
    case_o4412869554115667451_order: set_nat > ( ( product_prod_b1_b2 > product_prod_b1_b2 > order ) > set_nat ) > option3340807017899620244_order > set_nat ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Nat__Onat_J_001_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_M_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Comparator__Oorder_J_J,type,
    case_o7011793528111062907_order: set_nat > ( ( product_prod_c1_c2 > product_prod_c1_c2 > order ) > set_nat ) > option6733578312215638292_order > set_nat ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
    case_o4857086424252989667at_nat: set_nat > ( nat > set_nat ) > option_nat > set_nat ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    case_o3272889084017746073et_nat: set_nat > ( set_nat > set_nat ) > option_set_nat > set_nat ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o7275867065294810514_order: set_Pr3100092795582680071_a1_a2 > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > set_Pr3100092795582680071_a1_a2 ) > option9171407760438378004_order > set_Pr3100092795582680071_a1_a2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o939065307356969905_order: set_Pr9206071548465018024_a1_a2 > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > set_Pr9206071548465018024_a1_a2 ) > option9171407760438378004_order > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_001_062_Itf__a1_M_062_Itf__a1_Mt__Comparator__Oorder_J_J,type,
    case_o3237228901688236643_order: set_Pr9206071548465018024_a1_a2 > ( ( a1 > a1 > order ) > set_Pr9206071548465018024_a1_a2 ) > option_a1_a1_order > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_001_062_Itf__a2_M_062_Itf__a2_Mt__Comparator__Oorder_J_J,type,
    case_o7642782717507025761_order: set_Pr9206071548465018024_a1_a2 > ( ( a2 > a2 > order ) > set_Pr9206071548465018024_a1_a2 ) > option_a2_a2_order > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o655157351563703731_order: set_Pr4592484330697324838_b1_b2 > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > set_Pr4592484330697324838_b1_b2 ) > option9171407760438378004_order > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o371249395770437557_order: set_Pr9202269149784407460_c1_c2 > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > set_Pr9202269149784407460_c1_c2 ) > option9171407760438378004_order > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__a1_J_001t__Set__Oset_Itf__a1_J,type,
    case_o2026821128607468383set_a1: set_a1 > ( set_a1 > set_a1 ) > option_set_a1 > set_a1 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__a2_J_001_062_Itf__a1_M_062_Itf__a1_Mt__Comparator__Oorder_J_J,type,
    case_o8386814421925944265_order: set_a2 > ( ( a1 > a1 > order ) > set_a2 ) > option_a1_a1_order > set_a2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__a2_J_001_062_Itf__a2_M_062_Itf__a2_Mt__Comparator__Oorder_J_J,type,
    case_o3568996200889957575_order: set_a2 > ( ( a2 > a2 > order ) > set_a2 ) > option_a2_a2_order > set_a2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__a2_J_001t__Set__Oset_Itf__a2_J,type,
    case_o9125611637161669601set_a2: set_a2 > ( set_a2 > set_a2 ) > option_set_a2 > set_a2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__b1_J_001t__Set__Oset_Itf__b1_J,type,
    case_o5977995051732173661set_b1: set_b1 > ( set_b1 > set_b1 ) > option_set_b1 > set_b1 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__b2_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o3769919036381400216_order: set_b2 > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > set_b2 ) > option9171407760438378004_order > set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__b2_J_001_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_M_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Comparator__Oorder_J_J,type,
    case_o6368843010376795672_order: set_b2 > ( ( product_prod_b1_b2 > product_prod_b1_b2 > order ) > set_b2 ) > option3340807017899620244_order > set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__b2_J_001_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_M_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Comparator__Oorder_J_J,type,
    case_o8967766984372191128_order: set_b2 > ( ( product_prod_c1_c2 > product_prod_c1_c2 > order ) > set_b2 ) > option6733578312215638292_order > set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__b2_J_001_062_Itf__b2_M_062_Itf__b2_Mt__Comparator__Oorder_J_J,type,
    case_o5873507443480046666_order: set_b2 > ( ( b2 > b2 > order ) > set_b2 ) > option_b2_b2_order > set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__b2_J_001t__Set__Oset_Itf__b2_J,type,
    case_o3853413523431599071set_b2: set_b2 > ( set_b2 > set_b2 ) > option_set_b2 > set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__b2_J_001tf__b2,type,
    case_o801698286357362985_b2_b2: set_b2 > ( b2 > set_b2 ) > option_b2 > set_b2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__c1_J_001t__Set__Oset_Itf__c1_J,type,
    case_o705796938002103131set_c1: set_c1 > ( set_c1 > set_c1 ) > option_set_c1 > set_c1 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__c2_J_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Comparator__Oorder_J_J,type,
    case_o3610099362292947737_order: set_c2 > ( ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > set_c2 ) > option9171407760438378004_order > set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__c2_J_001_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_M_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Comparator__Oorder_J_J,type,
    case_o6209023336288343193_order: set_c2 > ( ( product_prod_b1_b2 > product_prod_b1_b2 > order ) > set_c2 ) > option3340807017899620244_order > set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__c2_J_001_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_M_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Comparator__Oorder_J_J,type,
    case_o8807947310283738649_order: set_c2 > ( ( product_prod_c1_c2 > product_prod_c1_c2 > order ) > set_c2 ) > option6733578312215638292_order > set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__c2_J_001_062_Itf__c2_M_062_Itf__c2_Mt__Comparator__Oorder_J_J,type,
    case_o8178018686070135757_order: set_c2 > ( ( c2 > c2 > order ) > set_c2 ) > option_c2_c2_order > set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__c2_J_001t__Set__Oset_Itf__c2_J,type,
    case_o7804587446556304349set_c2: set_c2 > ( set_c2 > set_c2 ) > option_set_c2 > set_c2 ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Set__Oset_Itf__c2_J_001tf__c2,type,
    case_o3452368716856024231_c2_c2: set_c2 > ( c2 > set_c2 ) > option_c2 > set_c2 ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_Eo_J_J,type,
    bot_bo869399545248760286t_b2_o: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_Eo_J_J,type,
    bot_bo8693474189685096288t_c2_o: ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_Eo_J_J,type,
    bot_bo256672798936931680t_b2_o: ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_M_062_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_M_Eo_J_J,type,
    bot_bo7261280182829818792t_c2_o: mapping_b1_set_b2 > mapping_c1_set_c2 > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_M_Eo_J,type,
    bot_bo7720725886485147221t_b2_o: mapping_b1_set_b2 > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_M_Eo_J,type,
    bot_bo699434630920884951t_c2_o: mapping_c1_set_c2 > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
    bot_bot_nat_o: nat > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_M_Eo_J,type,
    bot_bo9928753941511292891_a2_o: product_prod_a1_a2 > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_M_Eo_J,type,
    bot_bo56410028296945648111_b2_o: product_prod_b1_b2 > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_M_Eo_J,type,
    bot_bo10657582283832245251_c2_o: product_prod_c1_c2 > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a1_M_062_Itf__a2_M_Eo_J_J,type,
    bot_bot_a1_a2_o: a1 > a2 > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__b1_M_062_Itf__b2_M_Eo_J_J,type,
    bot_bot_b1_b2_o: b1 > b2 > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__b2_M_Eo_J,type,
    bot_bot_b2_o: b2 > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__c1_M_062_Itf__c2_M_Eo_J_J,type,
    bot_bot_c1_c2_o: c1 > c2 > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__c2_M_Eo_J,type,
    bot_bot_c2_o: c2 > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    bot_bo3047382831089536473et_nat: produc7819656566062154093et_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_Itf__b2_J_J,type,
    bot_bo872470976572166268set_b2: produc7354175447235289616set_b2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_Itf__c2_J_J,type,
    bot_bo2831585365160653243set_c2: produc89917798969000783set_c2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_It__Set__Oset_Itf__b2_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    bot_bo6623970406915802492et_nat: produc3882302840724150032et_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_It__Set__Oset_Itf__b2_J_Mt__Set__Oset_Itf__b2_J_J,type,
    bot_bo6678538799391878303set_b2: produc8948165835849931827set_b2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_It__Set__Oset_Itf__b2_J_Mt__Set__Oset_Itf__c2_J_J,type,
    bot_bo8637653187980365278set_c2: produc1683908187583642994set_c2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_It__Set__Oset_Itf__c2_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    bot_bo1817630633316081211et_nat: produc8299335103979204559et_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_It__Set__Oset_Itf__c2_J_Mt__Set__Oset_Itf__b2_J_J,type,
    bot_bo1406058398155690974set_b2: produc3675685434613744498set_b2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_It__Set__Oset_Itf__c2_J_Mt__Set__Oset_Itf__c2_J_J,type,
    bot_bo3365172786744177949set_c2: produc5634799823202231473set_c2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    bot_bo8415064643751506388set_b2: set_b1_option_set_b2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    bot_bo2618827607111635154set_c2: set_c1_option_set_c2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    bot_bo6532501642720468016set_b2: set_ma6254658672695423900set_b2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    bot_bo7584170878874662190set_c2: set_ma7306327908849618074set_c2 ).

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__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J_J,type,
    bot_bo8945491916674239809set_b2: set_Pr1995104245887189set_b2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J_J,type,
    bot_bo2941565536984730943set_c2: set_Pr3221440761411154131set_c2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J_J,type,
    bot_bo4776745694871505983set_b2: set_Pr5056620919297929171set_b2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    bot_bo8749877030654239607set_c2: set_Pr1660683266160182027set_c2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    bot_bo749279576856311060_a1_a2: set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    bot_bo5359064395943393682_b1_b2: set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    bot_bo745477178175700496_c1_c2: set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a1_J,type,
    bot_bot_set_a1: set_a1 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a2_J,type,
    bot_bot_set_a2: set_a2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__b1_J,type,
    bot_bot_set_b1: set_b1 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__b2_J,type,
    bot_bot_set_b2: set_b2 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__c1_J,type,
    bot_bot_set_c1: set_c1 ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__c2_J,type,
    bot_bot_set_c2: set_c2 ).

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

thf(sy_c_Product__Type_OPair_001_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J_001_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J,type,
    produc844738797994375799set_c2: ( mapping_b1_set_b2 > option781494349862297706set_c2 ) > ( mapping_b1_set_b2 > option781494349862297706set_c2 ) > produc2070398702644967871set_c2 ).

thf(sy_c_Product__Type_OPair_001_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    produc3671601195459724562set_b2: ( mapping_b1_set_b2 > option781494349862297706set_c2 ) > ( b1 > option_set_b2 ) > produc1295556776222662362set_b2 ).

thf(sy_c_Product__Type_OPair_001_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    produc187046198985622288set_c2: ( mapping_b1_set_b2 > option781494349862297706set_c2 ) > ( c1 > option_set_c2 ) > produc4722691776437566936set_c2 ).

thf(sy_c_Product__Type_OPair_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J,type,
    produc8529309635288108306set_c2: ( b1 > option_set_b2 ) > ( mapping_b1_set_b2 > option781494349862297706set_c2 ) > produc2916914556658279514set_c2 ).

thf(sy_c_Product__Type_OPair_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    produc4375337561607790509set_b2: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > produc8498296649714291061set_b2 ).

thf(sy_c_Product__Type_OPair_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    produc890782565133688235set_c2: ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > produc2702059613074419827set_c2 ).

thf(sy_c_Product__Type_OPair_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Option__Ooption_It__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J,type,
    produc181612670030289680set_c2: ( c1 > option_set_c2 ) > ( mapping_b1_set_b2 > option781494349862297706set_c2 ) > produc3792589628255236696set_c2 ).

thf(sy_c_Product__Type_OPair_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    produc4506454564149116331set_b2: ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > produc8629413652255616883set_b2 ).

thf(sy_c_Product__Type_OPair_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    produc1021899567675014057set_c2: ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > produc2833176615615745649set_c2 ).

thf(sy_c_Product__Type_OPair_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc6988475029935306213set_b2: mapping_b1_set_b2 > mapping_b1_set_b2 > produc3010228553022588589set_b2 ).

thf(sy_c_Product__Type_OPair_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    produc1212179418963815907set_c2: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2 ).

thf(sy_c_Product__Type_OPair_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc5597292958132816620set_c2: mapping_b1_set_b2 > produc4061897789176782763set_c2 > produc4134103123222870330set_c2 ).

thf(sy_c_Product__Type_OPair_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J,type,
    produc3698891015744838695set_b2: mapping_b1_set_b2 > produc909805953363803304set_b2 > produc5623429682246142959set_b2 ).

thf(sy_c_Product__Type_OPair_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc9049763300178012899set_b2: mapping_c1_set_c2 > mapping_b1_set_b2 > produc5071516823265295275set_b2 ).

thf(sy_c_Product__Type_OPair_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    produc3273467689206522593set_c2: mapping_c1_set_c2 > mapping_c1_set_c2 > produc6123186059419489449set_c2 ).

thf(sy_c_Product__Type_OPair_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc3574308084686302062set_c2: mapping_c1_set_c2 > produc4061897789176782763set_c2 > produc2111118249776355772set_c2 ).

thf(sy_c_Product__Type_OPair_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc9076999002715555034set_b2: mapping_c1_set_c2 > produc8179314580630251927set_b2 > produc909805953363803304set_b2 ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc198978297537896015set_b2: nat > mapping_b1_set_b2 > produc8179314580630251927set_b2 ).

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__Nat__Onat_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    produc1421920924983023131_c1_c2: nat > product_prod_c1_c2 > produc2762000901599049065_c1_c2 ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001tf__a1,type,
    product_Pair_nat_a1: nat > a1 > product_prod_nat_a1 ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001tf__b1,type,
    product_Pair_nat_b1: nat > b1 > product_prod_nat_b1 ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001tf__c1,type,
    product_Pair_nat_c1: nat > c1 > product_prod_nat_c1 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc1095963423755894970set_b2: produc4061897789176782763set_c2 > mapping_b1_set_b2 > produc7091961814400906944set_b2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    produc4543039849639180472set_c2: produc4061897789176782763set_c2 > mapping_c1_set_c2 > produc8143631050555101118set_c2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc3581607025436495447set_c2: produc4061897789176782763set_c2 > produc4061897789176782763set_c2 > produc2163030415453158631set_c2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001tf__b2,type,
    produc8088469960754140999_c2_b2: produc4061897789176782763set_c2 > b2 > produc3239730657808423629_c2_b2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001tf__c2,type,
    produc8088469960754206598_c2_c2: produc4061897789176782763set_c2 > c2 > produc3240012945314540428_c2_c2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Nat__Onat,type,
    produc8120826788302132289a2_nat: product_prod_a1_a2 > nat > produc7710046366822967495a2_nat ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    produc4690992521244333717_b1_b2: product_prod_a1_a2 > product_prod_b1_b2 > produc4401324642061629349_b1_b2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    produc4055625808145463827_c1_c2: product_prod_a1_a2 > product_prod_c1_c2 > produc9011109461148711971_c1_c2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__a1,type,
    produc9152926222710937252_a2_a1: product_prod_a1_a2 > a1 > produc1965103856682803754_a2_a1 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__b1,type,
    produc9152926222711002851_a2_b1: product_prod_a1_a2 > b1 > produc1965386144188920553_a2_b1 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__b2,type,
    produc9152926222711002852_a2_b2: product_prod_a1_a2 > b2 > produc1965386148492149354_a2_b2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__c1,type,
    produc9152926222711068450_a2_c1: product_prod_a1_a2 > c1 > produc1965668431695037352_a2_c1 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__c2,type,
    produc9152926222711068451_a2_c2: product_prod_a1_a2 > c2 > produc1965668435998266153_a2_c2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Nat__Onat,type,
    produc7299915657995288511b2_nat: product_prod_b1_b2 > nat > produc6889135236516123717b2_nat ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    produc2356375699566999577_a1_a2: product_prod_b1_b2 > product_prod_a1_a2 > produc6044928325053118505_a1_a2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    produc1721008986468129687_b1_b2: product_prod_b1_b2 > product_prod_b1_b2 > produc1431341107285425319_b1_b2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    produc1085642273369259797_c1_c2: product_prod_b1_b2 > product_prod_c1_c2 > produc6041125926372507941_c1_c2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__a1,type,
    produc3857897667671301922_b2_a1: product_prod_b1_b2 > a1 > produc5893447338497944232_b2_a1 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__b1,type,
    produc3857897667671367521_b2_b1: product_prod_b1_b2 > b1 > produc5893729626004061031_b2_b1 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__b2,type,
    produc3857897667671367522_b2_b2: product_prod_b1_b2 > b2 > produc5893729630307289832_b2_b2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__c1,type,
    produc3857897667671433120_b2_c1: product_prod_b1_b2 > c1 > produc5894011913510177830_b2_c1 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__c2,type,
    produc3857897667671433121_b2_c2: product_prod_b1_b2 > c2 > produc5894011917813406631_b2_c2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc2207736761247262035set_b2: product_prod_c1_c2 > mapping_b1_set_b2 > produc7248990843601126233set_b2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Nat__Onat,type,
    produc6479004527688444733c2_nat: product_prod_c1_c2 > nat > produc6068224106209279939c2_nat ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    produc8609764201645571355_a1_a2: product_prod_c1_c2 > product_prod_a1_a2 > produc3074944790276914475_a1_a2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    produc7974397488546701465_b1_b2: product_prod_c1_c2 > product_prod_b1_b2 > produc7684729609363997097_b1_b2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    produc7339030775447831575_c1_c2: product_prod_c1_c2 > product_prod_c1_c2 > produc3071142391596303911_c1_c2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__a1,type,
    produc7786241149486442400_c2_a1: product_prod_c1_c2 > a1 > produc598418783458308902_c2_a1 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__b1,type,
    produc7786241149486507999_c2_b1: product_prod_c1_c2 > b1 > produc598701070964425701_c2_b1 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__b2,type,
    produc7786241149486508000_c2_b2: product_prod_c1_c2 > b2 > produc598701075267654502_c2_b2 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__c1,type,
    produc7786241149486573598_c2_c1: product_prod_c1_c2 > c1 > produc598983358470542500_c2_c1 ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__c2,type,
    produc7786241149486573599_c2_c2: product_prod_c1_c2 > c2 > produc598983362773771301_c2_c2 ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_Itf__b2_J,type,
    produc8111200996048593992set_b2: set_nat > set_b2 > produc7354175447235289616set_b2 ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_Itf__c2_J,type,
    produc8111483283554710791set_c2: set_nat > set_c2 > produc89917798969000783set_c2 ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__b2_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc1842986394327179720et_nat: set_b2 > set_nat > produc3882302840724150032et_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__b2_J_001t__Set__Oset_Itf__b2_J,type,
    produc5265780138349399275set_b2: set_b2 > set_b2 > produc8948165835849931827set_b2 ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__b2_J_001t__Set__Oset_Itf__c2_J,type,
    produc5266062425855516074set_c2: set_b2 > set_c2 > produc1683908187583642994set_c2 ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__c2_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc6260018657582234247et_nat: set_c2 > set_nat > produc8299335103979204559et_nat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__c2_J_001t__Set__Oset_Itf__b2_J,type,
    produc9216671773967987754set_b2: set_c2 > set_b2 > produc3675685434613744498set_b2 ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__c2_J_001t__Set__Oset_Itf__c2_J,type,
    produc9216954061474104553set_c2: set_c2 > set_c2 > produc5634799823202231473set_c2 ).

thf(sy_c_Product__Type_OPair_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J_J,type,
    produc1624364259789891825nat_a1: a1 > produc7919085903952187301nat_a1 > produc2966771320212024889nat_a1 ).

thf(sy_c_Product__Type_OPair_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    produc6879422385039654997_a1_a2: a1 > produc3433853863313585417_a1_a2 > produc8366450052225339165_a1_a2 ).

thf(sy_c_Product__Type_OPair_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc2265835167271961811_b1_b2: a1 > produc8043638682400668039_b1_b2 > produc5014506993690784923_b1_b2 ).

thf(sy_c_Product__Type_OPair_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b2_Mtf__a1_J_J,type,
    produc1161874672556745108_b2_a1: a1 > produc6939678187685451336_b2_a1 > produc3531473365731754204_b2_a1 ).

thf(sy_c_Product__Type_OPair_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc6875619986359044433_c1_c2: a1 > produc3430051464632974853_c1_c2 > produc1662563935156230681_c1_c2 ).

thf(sy_c_Product__Type_OPair_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c2_Mtf__a1_J_J,type,
    produc3812545103055340755_c2_a1: a1 > produc366976581329271175_c2_a1 > produc3078752706661594267_c2_a1 ).

thf(sy_c_Product__Type_OPair_001tf__a1_001tf__a2,type,
    product_Pair_a1_a2: a1 > a2 > product_prod_a1_a2 ).

thf(sy_c_Product__Type_OPair_001tf__a2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J,type,
    produc1440497705562379863nat_a1: a2 > product_prod_nat_a1 > produc7919085903952187301nat_a1 ).

thf(sy_c_Product__Type_OPair_001tf__a2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    produc6870861026727840059_a1_a2: a2 > product_prod_a1_a2 > produc3433853863313585417_a1_a2 ).

thf(sy_c_Product__Type_OPair_001tf__a2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    produc6235494313628970169_b1_b2: a2 > product_prod_b1_b2 > produc8043638682400668039_b1_b2 ).

thf(sy_c_Product__Type_OPair_001tf__a2_001t__Product____Type__Oprod_Itf__b2_Mtf__a1_J,type,
    produc5287120842174929402_b2_a1: a2 > product_prod_b2_a1 > produc6939678187685451336_b2_a1 ).

thf(sy_c_Product__Type_OPair_001tf__a2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    produc5600127600530100279_c1_c2: a2 > product_prod_c1_c2 > produc3430051464632974853_c1_c2 ).

thf(sy_c_Product__Type_OPair_001tf__a2_001t__Product____Type__Oprod_Itf__c2_Mtf__a1_J,type,
    produc4651471841569942713_c2_a1: a2 > product_prod_c2_a1 > produc366976581329271175_c2_a1 ).

thf(sy_c_Product__Type_OPair_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J_J,type,
    produc5580199815858148208nat_b1: b1 > produc4594776842310734693nat_b1 > produc3104264649751066808nat_b1 ).

thf(sy_c_Product__Type_OPair_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    produc2130712429766453653_a1_a2: b1 > produc330329780597500170_a1_a2 > produc6386022366266853341_a1_a2 ).

thf(sy_c_Product__Type_OPair_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc6740497248853536275_b1_b2: b1 > produc4940114599684582792_b1_b2 > produc3034079307732299099_b1_b2 ).

thf(sy_c_Product__Type_OPair_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b2_Mtf__b1_J_J,type,
    produc7595651142726806547_b2_b1: b1 > produc5795268493557853064_b2_b1 > produc7875195317163649883_b2_b1 ).

thf(sy_c_Product__Type_OPair_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc2126910031085843089_c1_c2: b1 > produc326527381916889606_c1_c2 > produc8905508286052520665_c1_c2 ).

thf(sy_c_Product__Type_OPair_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c2_Mtf__b1_J_J,type,
    produc1022949536370626386_c2_b1: b1 > produc8445938924056448711_c2_b1 > produc7422474658093489946_c2_b1 ).

thf(sy_c_Product__Type_OPair_001tf__b1_001tf__b2,type,
    product_Pair_b1_b2: b1 > b2 > product_prod_b1_b2 ).

thf(sy_c_Product__Type_OPair_001tf__b2_001t__Nat__Onat,type,
    product_Pair_b2_nat: b2 > nat > product_prod_b2_nat ).

thf(sy_c_Product__Type_OPair_001tf__b2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J,type,
    produc5380728579693332887nat_b1: b2 > product_prod_nat_b1 > produc4594776842310734693nat_b1 ).

thf(sy_c_Product__Type_OPair_001tf__b2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    produc3767336944011754812_a1_a2: b2 > product_prod_a1_a2 > produc330329780597500170_a1_a2 ).

thf(sy_c_Product__Type_OPair_001tf__b2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    produc3131970230912884922_b1_b2: b2 > product_prod_b1_b2 > produc4940114599684582792_b1_b2 ).

thf(sy_c_Product__Type_OPair_001tf__b2_001t__Product____Type__Oprod_Itf__b2_Mtf__b1_J,type,
    produc2183879046964960954_b2_b1: b2 > product_prod_b2_b1 > produc5795268493557853064_b2_b1 ).

thf(sy_c_Product__Type_OPair_001tf__b2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    produc2496603517814015032_c1_c2: b2 > product_prod_c1_c2 > produc326527381916889606_c1_c2 ).

thf(sy_c_Product__Type_OPair_001tf__b2_001t__Product____Type__Oprod_Itf__c2_Mtf__b1_J,type,
    produc1548230046359974265_c2_b1: b2 > product_prod_c2_b1 > produc8445938924056448711_c2_b1 ).

thf(sy_c_Product__Type_OPair_001tf__b2_001tf__a1,type,
    product_Pair_b2_a1: b2 > a1 > product_prod_b2_a1 ).

thf(sy_c_Product__Type_OPair_001tf__b2_001tf__b1,type,
    product_Pair_b2_b1: b2 > b1 > product_prod_b2_b1 ).

thf(sy_c_Product__Type_OPair_001tf__b2_001tf__b2,type,
    product_Pair_b2_b2: b2 > b2 > product_prod_b2_b2 ).

thf(sy_c_Product__Type_OPair_001tf__b2_001tf__c1,type,
    product_Pair_b2_c1: b2 > c1 > product_prod_b2_c1 ).

thf(sy_c_Product__Type_OPair_001tf__b2_001tf__c2,type,
    product_Pair_b2_c2: b2 > c2 > product_prod_b2_c2 ).

thf(sy_c_Product__Type_OPair_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    produc6401017609378703672set_c2: c1 > produc2204780078346707822set_c2 > produc8955508179325214080set_c2 ).

thf(sy_c_Product__Type_OPair_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J_J,type,
    produc312663335071628783nat_c1: c1 > produc1270467780669282085nat_c1 > produc3241757979290108727nat_c1 ).

thf(sy_c_Product__Type_OPair_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    produc6605374511348028117_a1_a2: c1 > produc6450177734736190731_a1_a2 > produc4405594680308367517_a1_a2 ).

thf(sy_c_Product__Type_OPair_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc1991787293580334931_b1_b2: c1 > produc1836590516968497545_b1_b2 > produc1053651621773813275_b1_b2 ).

thf(sy_c_Product__Type_OPair_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b2_Mtf__c1_J_J,type,
    produc4806055576042092178_b2_c1: c1 > produc4650858799430254792_b2_c1 > produc2995545231740769754_b2_c1 ).

thf(sy_c_Product__Type_OPair_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc6601572112667417553_c1_c2: c1 > produc6446375336055580167_c1_c2 > produc6925080600094034841_c1_c2 ).

thf(sy_c_Product__Type_OPair_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c2_Mtf__c1_J_J,type,
    produc7456726006540687825_c2_c1: c1 > produc7301529229928850439_c2_c1 > produc2542824572670609817_c2_c1 ).

thf(sy_c_Product__Type_OPair_001tf__c1_001tf__c2,type,
    product_Pair_c1_c2: c1 > c2 > product_prod_c1_c2 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001t__Nat__Onat,type,
    product_Pair_c2_nat: c2 > nat > product_prod_c2_nat ).

thf(sy_c_Product__Type_OPair_001tf__c2_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc5508423839735234848set_c2: c2 > produc4061897789176782763set_c2 > produc2204780078346707822set_c2 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J,type,
    produc97587416969510103nat_c1: c2 > product_prod_nat_c1 > produc1270467780669282085nat_c1 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    produc663812861295669565_a1_a2: c2 > product_prod_a1_a2 > produc6450177734736190731_a1_a2 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    produc28446148196799675_b1_b2: c2 > product_prod_b1_b2 > produc1836590516968497545_b1_b2 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001t__Product____Type__Oprod_Itf__b2_Mtf__c1_J,type,
    produc8304009288609768314_b2_c1: c2 > product_prod_b2_c1 > produc4650858799430254792_b2_c1 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    produc8616451471952705593_c1_c2: c2 > product_prod_c1_c2 > produc6446375336055580167_c1_c2 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001t__Product____Type__Oprod_Itf__c2_Mtf__c1_J,type,
    produc7668360288004781625_c2_c1: c2 > product_prod_c2_c1 > produc7301529229928850439_c2_c1 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001tf__a1,type,
    product_Pair_c2_a1: c2 > a1 > product_prod_c2_a1 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001tf__b1,type,
    product_Pair_c2_b1: c2 > b1 > product_prod_c2_b1 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001tf__b2,type,
    product_Pair_c2_b2: c2 > b2 > product_prod_c2_b2 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001tf__c1,type,
    product_Pair_c2_c1: c2 > c1 > product_prod_c2_c1 ).

thf(sy_c_Product__Type_OPair_001tf__c2_001tf__c2,type,
    product_Pair_c2_c2: c2 > c2 > product_prod_c2_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_Eo,type,
    produc2039302432013647190t_b2_o: ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o ) > produc8498296649714291061set_b2 > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    produc8790685608643853619set_b2: ( ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > produc8498296649714291061set_b2 ) > produc8498296649714291061set_b2 > produc8498296649714291061set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    produc444217394335435850set_b2: ( ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > b1 > option_set_b2 ) > produc2702059613074419827set_c2 > b1 > option_set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    produc6183034434716109384set_c2: ( ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > c1 > option_set_c2 ) > produc2702059613074419827set_c2 > c1 > option_set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_Eo,type,
    produc115805034449689560t_c2_o: ( ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > $o ) > produc2702059613074419827set_c2 > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    produc303944662167056563set_c2: ( ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > produc2702059613074419827set_c2 ) > produc2702059613074419827set_c2 > produc2702059613074419827set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    produc6231298701348253619set_b2: ( ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > produc8629413652255616883set_b2 ) > produc2702059613074419827set_c2 > produc8629413652255616883set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_Eo,type,
    produc2533395233176501208t_b2_o: ( ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > $o ) > produc8629413652255616883set_b2 > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    produc5801580654647562419set_c2: ( ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > produc2702059613074419827set_c2 ) > produc8629413652255616883set_b2 > produc2702059613074419827set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    produc2505562656973983667set_b2: ( ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > produc8629413652255616883set_b2 ) > produc8629413652255616883set_b2 > produc8629413652255616883set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc5703754947799223347set_b2: ( mapping_b1_set_b2 > mapping_b1_set_b2 > produc3010228553022588589set_b2 ) > produc3010228553022588589set_b2 > produc3010228553022588589set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001_Eo,type,
    produc7359613910387544480t_c2_o: ( mapping_b1_set_b2 > mapping_c1_set_c2 > $o ) > produc4061897789176782763set_c2 > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc5698048114250851934set_b2: ( mapping_b1_set_b2 > mapping_c1_set_c2 > mapping_b1_set_b2 ) > produc4061897789176782763set_c2 > mapping_b1_set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    produc9145124540134137436set_c2: ( mapping_b1_set_b2 > mapping_c1_set_c2 > mapping_c1_set_c2 ) > produc4061897789176782763set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc4732439310506902963set_c2: ( mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2 ) > produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc5742058344595415475set_b2: ( mapping_b1_set_b2 > mapping_c1_set_c2 > produc5071516823265295275set_b2 ) > produc4061897789176782763set_c2 > produc5071516823265295275set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc3609887524509304657set_b2: ( mapping_b1_set_b2 > mapping_c1_set_c2 > produc7248990843601126233set_b2 ) > produc4061897789176782763set_c2 > produc7248990843601126233set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    produc1393855134008624979set_c2: ( mapping_b1_set_b2 > produc4061897789176782763set_c2 > produc4134103123222870330set_c2 ) > produc4134103123222870330set_c2 > produc4134103123222870330set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_Itf__b2_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mtf__b2_J,type,
    produc1884001382256093484_c2_b2: ( mapping_b1_set_b2 > produc786840591232948043set_b2 > produc3239730657808423629_c2_b2 ) > produc5199603736692633362set_b2 > produc3239730657808423629_c2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc2647557493670480051set_c2: ( mapping_c1_set_c2 > mapping_b1_set_b2 > produc4061897789176782763set_c2 ) > produc5071516823265295275set_b2 > produc4061897789176782763set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc3657176527758992563set_b2: ( mapping_c1_set_c2 > mapping_b1_set_b2 > produc5071516823265295275set_b2 ) > produc5071516823265295275set_b2 > produc5071516823265295275set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc2685860890466672179set_c2: ( mapping_c1_set_c2 > mapping_c1_set_c2 > produc6123186059419489449set_c2 ) > produc6123186059419489449set_c2 > produc6123186059419489449set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    produc1066867050092484183set_c2: ( mapping_c1_set_c2 > produc4061897789176782763set_c2 > produc2111118249776355772set_c2 ) > produc2111118249776355772set_c2 > produc2111118249776355772set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_Itf__b2_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mtf__b2_J,type,
    produc8228876167660460407_c2_b2: ( mapping_c1_set_c2 > produc1711127128284081338set_b2 > produc3239730657808423629_c2_b2 ) > produc786840591232948043set_b2 > produc3239730657808423629_c2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001tf__a1_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Nat__Onat_J,type,
    produc6620951166205106936a2_nat: ( nat > a1 > produc7710046366822967495a2_nat ) > product_prod_nat_a1 > produc7710046366822967495a2_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001tf__b1_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Nat__Onat_J,type,
    produc3856812616753196341b2_nat: ( nat > b1 > produc6889135236516123717b2_nat ) > product_prod_nat_b1 > produc6889135236516123717b2_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001tf__c1_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Nat__Onat_J,type,
    produc1092674067301285746c2_nat: ( nat > c1 > produc6068224106209279939c2_nat ) > product_prod_nat_c1 > produc6068224106209279939c2_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc455242887147150503set_b2: ( produc4061897789176782763set_c2 > mapping_b1_set_b2 > produc7091961814400906944set_b2 ) > produc7091961814400906944set_b2 > produc7091961814400906944set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc723796631715995555set_c2: ( produc4061897789176782763set_c2 > mapping_c1_set_c2 > produc8143631050555101118set_c2 ) > produc8143631050555101118set_c2 > produc8143631050555101118set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J,type,
    produc3639072943575950715set_c2: ( produc4061897789176782763set_c2 > produc4061897789176782763set_c2 > produc2163030415453158631set_c2 ) > produc2163030415453158631set_c2 > produc2163030415453158631set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Nat__Onat_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc180099261456868121et_nat: ( product_prod_a1_a2 > nat > set_nat > set_nat ) > produc7710046366822967495a2_nat > set_nat > set_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__b2_001_062_It__Set__Oset_Itf__b2_J_Mt__Set__Oset_Itf__b2_J_J,type,
    produc299224476509326082set_b2: ( product_prod_a1_a2 > b2 > set_b2 > set_b2 ) > produc1965386148492149354_a2_b2 > set_b2 > set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__c2_001_062_It__Set__Oset_Itf__c2_J_Mt__Set__Oset_Itf__c2_J_J,type,
    produc6555648654604825151set_c2: ( product_prod_a1_a2 > c2 > set_c2 > set_c2 ) > produc1965668435998266153_a2_c2 > set_c2 > set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Nat__Onat_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc6434115961959534999et_nat: ( product_prod_b1_b2 > nat > set_nat > set_nat ) > produc6889135236516123717b2_nat > set_nat > set_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__b2_001_062_It__Set__Oset_Itf__b2_J_Mt__Set__Oset_Itf__b2_J_J,type,
    produc5706168644020670592set_b2: ( product_prod_b1_b2 > b2 > set_b2 > set_b2 ) > produc5893729630307289832_b2_b2 > set_b2 > set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__c2_001_062_It__Set__Oset_Itf__c2_J_Mt__Set__Oset_Itf__c2_J_J,type,
    produc2739220785261393853set_c2: ( product_prod_b1_b2 > c2 > set_c2 > set_c2 ) > produc5894011917813406631_b2_c2 > set_c2 > set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Nat__Onat_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc3464760625607426069et_nat: ( product_prod_c1_c2 > nat > set_nat > set_nat ) > produc6068224106209279939c2_nat > set_nat > set_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__b2_001_062_It__Set__Oset_Itf__b2_J_Mt__Set__Oset_Itf__b2_J_J,type,
    produc1889740774677239294set_b2: ( product_prod_c1_c2 > b2 > set_b2 > set_b2 ) > produc598701075267654502_c2_b2 > set_b2 > set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__c2_001_062_It__Set__Oset_Itf__c2_J_Mt__Set__Oset_Itf__c2_J_J,type,
    produc8146164952772738363set_c2: ( product_prod_c1_c2 > c2 > set_c2 > set_c2 ) > produc598983362773771301_c2_c2 > set_c2 > set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Nat__Onat_J,type,
    produc3930721360717498573a2_nat: ( a1 > produc7919085903952187301nat_a1 > produc7710046366822967495a2_nat ) > produc2966771320212024889nat_a1 > produc7710046366822967495a2_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__a1_J,type,
    produc2782266665979526292_a2_a1: ( a1 > produc3433853863313585417_a1_a2 > produc1965103856682803754_a2_a1 ) > produc8366450052225339165_a1_a2 > produc1965103856682803754_a2_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b1_J,type,
    produc9036565653988309969_a2_b1: ( a1 > produc8043638682400668039_b1_b2 > produc1965386144188920553_a2_b1 ) > produc5014506993690784923_b1_b2 > produc1965386144188920553_a2_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b2_Mtf__a1_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b2_J,type,
    produc4536957107545010963_a2_b2: ( a1 > produc6939678187685451336_b2_a1 > produc1965386148492149354_a2_b2 ) > produc3531473365731754204_b2_a1 > produc1965386148492149354_a2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c1_J,type,
    produc6067492605142317838_a2_c1: ( a1 > produc3430051464632974853_c1_c2 > produc1965668431695037352_a2_c1 ) > produc1662563935156230681_c1_c2 > produc1965668431695037352_a2_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c2_Mtf__a1_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c2_J,type,
    produc7395805801629899793_a2_c2: ( a1 > produc366976581329271175_c2_a1 > produc1965668435998266153_a2_c2 ) > produc3078752706661594267_c2_a1 > produc1965668435998266153_a2_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001_062_It__Mapping__Omapping_Itf__a1_Mt__Set__Oset_Itf__a2_J_J_Mt__Mapping__Omapping_Itf__a1_Mt__Set__Oset_Itf__a2_J_J_J,type,
    produc7487291811606828676set_a2: ( a1 > a2 > mapping_a1_set_a2 > mapping_a1_set_a2 ) > product_prod_a1_a2 > mapping_a1_set_a2 > mapping_a1_set_a2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001_062_It__Set__Oset_Itf__a2_J_Mt__Set__Oset_Itf__a2_J_J,type,
    produc2240735584725524872set_a2: ( a1 > a2 > set_a2 > set_a2 ) > product_prod_a1_a2 > set_a2 > set_a2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001_Eo,type,
    produc26642204215465646751_a2_o: ( a1 > a2 > $o ) > product_prod_a1_a2 > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__a1_J,type,
    produc4820297268878220607_a2_a1: ( a1 > a2 > produc1965103856682803754_a2_a1 ) > product_prod_a1_a2 > produc1965103856682803754_a2_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__a1_J,type,
    produc8748640750693361085_b2_a1: ( a1 > a2 > produc5893447338497944232_b2_a1 ) > product_prod_a1_a2 > produc5893447338497944232_b2_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__a1_J,type,
    produc3453612195653725755_c2_a1: ( a1 > a2 > produc598418783458308902_c2_a1 ) > product_prod_a1_a2 > produc598418783458308902_c2_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    produc2156636514269063795_a1_a2: ( a1 > a2 > product_prod_a1_a2 ) > product_prod_a1_a2 > product_prod_a1_a2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    produc1521269801170193905_b1_b2: ( a1 > a2 > product_prod_b1_b2 ) > product_prod_a1_a2 > product_prod_b1_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    produc885903088071324015_c1_c2: ( a1 > a2 > product_prod_c1_c2 ) > product_prod_a1_a2 > product_prod_c1_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    produc4353239011151223635_a1_a2: ( a1 > a2 > set_Pr9206071548465018024_a1_a2 ) > product_prod_a1_a2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc8963023830238306257_b1_b2: ( a1 > a2 > set_Pr4592484330697324838_b1_b2 ) > product_prod_a1_a2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc4349436612470613071_c1_c2: ( a1 > a2 > set_Pr9202269149784407460_c1_c2 ) > product_prod_a1_a2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Set__Oset_Itf__a1_J,type,
    produc8681895136669590270set_a1: ( a1 > a2 > set_a1 ) > product_prod_a1_a2 > set_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Set__Oset_Itf__b1_J,type,
    produc8682177424175707069set_b1: ( a1 > a2 > set_b1 ) > product_prod_a1_a2 > set_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a1_001tf__a2_001t__Set__Oset_Itf__c1_J,type,
    produc8682459711681823868set_c1: ( a1 > a2 > set_c1 ) > product_prod_a1_a2 > set_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Nat__Onat_J,type,
    produc734751165574281035a2_nat: ( a2 > product_prod_nat_a1 > produc7710046366822967495a2_nat ) > produc7919085903952187301nat_a1 > produc7710046366822967495a2_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__a1_J,type,
    produc6162452088514971538_a2_a1: ( a2 > product_prod_a1_a2 > produc1965103856682803754_a2_a1 ) > produc3433853863313585417_a1_a2 > produc1965103856682803754_a2_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b1_J,type,
    produc6231827184780092879_a2_b1: ( a2 > product_prod_b1_b2 > produc1965386144188920553_a2_b1 ) > produc8043638682400668039_b1_b2 > produc1965386144188920553_a2_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a2_001t__Product____Type__Oprod_Itf__b2_Mtf__a1_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b2_J,type,
    produc6757874213855047057_a2_b2: ( a2 > product_prod_b2_a1 > produc1965386148492149354_a2_b2 ) > produc6939678187685451336_b2_a1 > produc1965386148492149354_a2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c1_J,type,
    produc6301202281045214220_a2_c1: ( a2 > product_prod_c1_c2 > produc1965668431695037352_a2_c1 ) > produc3430051464632974853_c1_c2 > produc1965668431695037352_a2_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a2_001t__Product____Type__Oprod_Itf__c2_Mtf__a1_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c2_J,type,
    produc2849080427214603791_a2_c2: ( a2 > product_prod_c2_a1 > produc1965668435998266153_a2_c2 ) > produc366976581329271175_c2_a1 > produc1965668435998266153_a2_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a2_001tf__a1_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    produc169089168568401139_a1_a2: ( a2 > a1 > product_prod_a1_a2 ) > product_prod_a2_a1 > product_prod_a1_a2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Nat__Onat_J,type,
    produc4114563434916029770b2_nat: ( b1 > produc4594776842310734693nat_b1 > produc6889135236516123717b2_nat ) > produc3104264649751066808nat_b1 > produc6889135236516123717b2_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__a1_J,type,
    produc8363668381017632338_b2_a1: ( b1 > produc330329780597500170_a1_a2 > produc5893447338497944232_b2_a1 ) > produc6386022366266853341_a1_a2 > produc5893447338497944232_b2_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b1_J,type,
    produc5394595332171640207_b2_b1: ( b1 > produc4940114599684582792_b1_b2 > produc5893729626004061031_b2_b1 ) > produc3034079307732299099_b1_b2 > produc5893729626004061031_b2_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b2_Mtf__b1_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b2_J,type,
    produc4290437079652236048_b2_b2: ( b1 > produc5795268493557853064_b2_b1 > produc5893729630307289832_b2_b2 ) > produc7875195317163649883_b2_b1 > produc5893729630307289832_b2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c1_J,type,
    produc2425522283325648076_b2_c1: ( b1 > produc326527381916889606_c1_c2 > produc5894011913510177830_b2_c1 ) > produc8905508286052520665_c1_c2 > produc5894011913510177830_b2_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c2_Mtf__b1_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c2_J,type,
    produc7149285773737124878_b2_c2: ( b1 > produc8445938924056448711_c2_b1 > produc5894011917813406631_b2_c2 ) > produc7422474658093489946_c2_b1 > produc5894011917813406631_b2_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001_062_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc4842154304667325566set_b2: ( b1 > b2 > mapping_b1_set_b2 > mapping_b1_set_b2 ) > product_prod_b1_b2 > mapping_b1_set_b2 > mapping_b1_set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001_Eo,type,
    produc81016565174098426291_b2_o: ( b1 > b2 > $o ) > product_prod_b1_b2 > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc6418488838319782393set_b2: ( b1 > b2 > mapping_b1_set_b2 ) > product_prod_b1_b2 > mapping_b1_set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b1_J,type,
    produc8489689646535437052_a2_b1: ( b1 > b2 > produc1965386144188920553_a2_b1 ) > product_prod_b1_b2 > produc1965386144188920553_a2_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b1_J,type,
    produc3194661091495801722_b2_b1: ( b1 > b2 > produc5893729626004061031_b2_b1 ) > product_prod_b1_b2 > produc5893729626004061031_b2_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b1_J,type,
    produc7123004573310942200_c2_b1: ( b1 > b2 > produc598701070964425701_c2_b1 ) > product_prod_b1_b2 > produc598701070964425701_c2_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    produc5006376033934050163_b1_b2: ( b1 > b2 > product_prod_b1_b2 ) > product_prod_b1_b2 > product_prod_b1_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    produc4371009320835180273_c1_c2: ( b1 > b2 > product_prod_c1_c2 ) > product_prod_b1_b2 > product_prod_c1_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    produc2189613341830760661_a1_a2: ( b1 > b2 > set_Pr9206071548465018024_a1_a2 ) > product_prod_b1_b2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc6799398160917843283_b1_b2: ( b1 > b2 > set_Pr4592484330697324838_b1_b2 ) > product_prod_b1_b2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc2185810943150150097_c1_c2: ( b1 > b2 > set_Pr9202269149784407460_c1_c2 ) > product_prod_b1_b2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Set__Oset_Itf__a1_J,type,
    produc2431610277356004092set_a1: ( b1 > b2 > set_a1 ) > product_prod_b1_b2 > set_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Set__Oset_Itf__b1_J,type,
    produc2431892564862120891set_b1: ( b1 > b2 > set_b1 ) > product_prod_b1_b2 > set_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b1_001tf__b2_001t__Set__Oset_Itf__c1_J,type,
    produc2432174852368237690set_c1: ( b1 > b2 > set_c1 ) > product_prod_b1_b2 > set_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b2_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mtf__b2_J,type,
    produc5447170038687108564_c2_b2: ( b2 > mapping_b1_set_b2 > produc3239730657808423629_c2_b2 ) > produc1711127128284081338set_b2 > produc3239730657808423629_c2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Nat__Onat_J,type,
    produc180919134490359305b2_nat: ( b2 > product_prod_nat_b1 > produc6889135236516123717b2_nat ) > produc4594776842310734693nat_b1 > produc6889135236516123717b2_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__a1_J,type,
    produc2813463618851753745_b2_a1: ( b2 > product_prod_a1_a2 > produc5893447338497944232_b2_a1 ) > produc330329780597500170_a1_a2 > produc5893447338497944232_b2_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b1_J,type,
    produc2882838715116875086_b2_b1: ( b2 > product_prod_b1_b2 > produc5893729626004061031_b2_b1 ) > produc4940114599684582792_b1_b2 > produc5893729626004061031_b2_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b2_001t__Product____Type__Oprod_Itf__b2_Mtf__b1_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b2_J,type,
    produc7387054627097393871_b2_b2: ( b2 > product_prod_b2_b1 > produc5893729630307289832_b2_b2 ) > produc5795268493557853064_b2_b1 > produc5893729630307289832_b2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c1_J,type,
    produc2952213811381996427_b2_c1: ( b2 > product_prod_c1_c2 > produc5894011913510177830_b2_c1 ) > produc326527381916889606_c1_c2 > produc5894011913510177830_b2_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b2_001t__Product____Type__Oprod_Itf__c2_Mtf__b1_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c2_J,type,
    produc3478260840456950605_b2_c2: ( b2 > product_prod_c2_b1 > produc5894011917813406631_b2_c2 ) > produc8445938924056448711_c2_b1 > produc5894011917813406631_b2_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b2_001tf__a1_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b2_J,type,
    produc3451871816419365566_a2_b2: ( b2 > a1 > produc1965386148492149354_a2_b2 ) > product_prod_b2_a1 > produc1965386148492149354_a2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b2_001tf__b1_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b2_J,type,
    produc5735029425677389947_b2_b2: ( b2 > b1 > produc5893729630307289832_b2_b2 ) > product_prod_b2_b1 > produc5893729630307289832_b2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b2_001tf__b1_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    produc3018828688233387507_b1_b2: ( b2 > b1 > product_prod_b1_b2 ) > product_prod_b2_b1 > product_prod_b1_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b2_001tf__c1_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b2_J,type,
    produc8018187034935414328_c2_b2: ( b2 > c1 > produc598701075267654502_c2_b2 ) > product_prod_b2_c1 > produc598701075267654502_c2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc4299517532798192550set_b2: ( c1 > produc2204780078346707822set_c2 > produc7248990843601126233set_b2 ) > produc8955508179325214080set_c2 > produc7248990843601126233set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Nat__Onat_J,type,
    produc4298405509114560967c2_nat: ( c1 > produc1270467780669282085nat_c1 > produc6068224106209279939c2_nat ) > produc3241757979290108727nat_c1 > produc6068224106209279939c2_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__a1_J,type,
    produc4721698059200962576_c2_a1: ( c1 > produc6450177734736190731_a1_a2 > produc598418783458308902_c2_a1 ) > produc4405594680308367517_a1_a2 > produc598418783458308902_c2_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b1_J,type,
    produc1752625010354970445_c2_b1: ( c1 > produc1836590516968497545_b1_b2 > produc598701070964425701_c2_b1 ) > produc1053651621773813275_b1_b2 > produc598701070964425701_c2_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b2_Mtf__c1_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b2_J,type,
    produc4043917051759461133_c2_b2: ( c1 > produc4650858799430254792_b2_c1 > produc598701075267654502_c2_b2 ) > produc2995545231740769754_b2_c1 > produc598701075267654502_c2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c1_J,type,
    produc8006923998363754122_c2_c1: ( c1 > produc6446375336055580167_c1_c2 > produc598983358470542500_c2_c1 ) > produc6925080600094034841_c1_c2 > produc598983358470542500_c2_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c2_Mtf__c1_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c2_J,type,
    produc6902765745844349963_c2_c2: ( c1 > produc7301529229928850439_c2_c1 > produc598983362773771301_c2_c2 ) > produc2542824572670609817_c2_c1 > produc598983362773771301_c2_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001_062_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc2197016797727822456set_c2: ( c1 > c2 > mapping_c1_set_c2 > mapping_c1_set_c2 ) > product_prod_c1_c2 > mapping_c1_set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001_Eo,type,
    produc43157205764183447751_c2_o: ( c1 > c2 > $o ) > product_prod_c1_c2 > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    produc4822369076420559349set_c2: ( c1 > c2 > mapping_c1_set_c2 ) > product_prod_c1_c2 > mapping_c1_set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c1_J,type,
    produc2935709987337877689_a2_c1: ( c1 > c2 > produc1965668431695037352_a2_c1 ) > product_prod_c1_c2 > produc1965668431695037352_a2_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c1_J,type,
    produc6864053469153018167_b2_c1: ( c1 > c2 > produc5894011913510177830_b2_c1 ) > product_prod_c1_c2 > produc5894011913510177830_b2_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c1_J,type,
    produc1569024914113382837_c2_c1: ( c1 > c2 > produc598983358470542500_c2_c1 ) > product_prod_c1_c2 > produc598983358470542500_c2_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    produc9126848979796776311_a1_a2: ( c1 > c2 > product_prod_a1_a2 ) > product_prod_c1_c2 > product_prod_a1_a2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    produc8491482266697906421_b1_b2: ( c1 > c2 > product_prod_b1_b2 ) > product_prod_c1_c2 > product_prod_b1_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    produc7856115553599036531_c1_c2: ( c1 > c2 > product_prod_c1_c2 ) > product_prod_c1_c2 > product_prod_c1_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc8868074789981537069set_b2: ( c1 > c2 > set_ma6254658672695423900set_b2 ) > product_prod_c1_c2 > set_ma6254658672695423900set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    produc696371989280955435set_c2: ( c1 > c2 > set_ma7306327908849618074set_c2 ) > product_prod_c1_c2 > set_ma7306327908849618074set_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    produc25987672510297687_a1_a2: ( c1 > c2 > set_Pr9206071548465018024_a1_a2 ) > product_prod_c1_c2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    produc4635772491597380309_b1_b2: ( c1 > c2 > set_Pr4592484330697324838_b1_b2 ) > product_prod_c1_c2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    produc22185273829687123_c1_c2: ( c1 > c2 > set_Pr9202269149784407460_c1_c2 ) > product_prod_c1_c2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Set__Oset_Itf__a1_J,type,
    produc5404697454897193722set_a1: ( c1 > c2 > set_a1 ) > product_prod_c1_c2 > set_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Set__Oset_Itf__b1_J,type,
    produc5404979742403310521set_b1: ( c1 > c2 > set_b1 ) > product_prod_c1_c2 > set_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c1_001tf__c2_001t__Set__Oset_Itf__c1_J,type,
    produc5405262029909427320set_c1: ( c1 > c2 > set_c1 ) > product_prod_c1_c2 > set_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c2_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc7726091980666125222set_b2: ( c2 > produc4061897789176782763set_c2 > produc7248990843601126233set_b2 ) > produc2204780078346707822set_c2 > produc7248990843601126233set_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Nat__Onat_J,type,
    produc8850459140261213383c2_nat: ( c2 > product_prod_nat_c1 > produc6068224106209279939c2_nat ) > produc1270467780669282085nat_c1 > produc6068224106209279939c2_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__a1_J,type,
    produc8687847186043311760_c2_a1: ( c2 > product_prod_a1_a2 > produc598418783458308902_c2_a1 ) > produc6450177734736190731_a1_a2 > produc598418783458308902_c2_a1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b1_J,type,
    produc8757222282308433101_c2_b1: ( c2 > product_prod_b1_b2 > produc598701070964425701_c2_b1 ) > produc1836590516968497545_b1_b2 > produc598701070964425701_c2_b1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c2_001t__Product____Type__Oprod_Itf__b2_Mtf__c1_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b2_J,type,
    produc8016235040339740685_c2_b2: ( c2 > product_prod_b2_c1 > produc598701075267654502_c2_b2 ) > produc4650858799430254792_b2_c1 > produc598701075267654502_c2_b2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c1_J,type,
    produc8826597378573554442_c2_c1: ( c2 > product_prod_c1_c2 > produc598983358470542500_c2_c1 ) > produc6446375336055580167_c1_c2 > produc598983358470542500_c2_c1 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c2_001t__Product____Type__Oprod_Itf__c2_Mtf__c1_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c2_J,type,
    produc4107441253699297419_c2_c2: ( c2 > product_prod_c2_c1 > produc598983362773771301_c2_c2 ) > produc7301529229928850439_c2_c1 > produc598983362773771301_c2_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c2_001tf__a1_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c2_J,type,
    produc8766450066633698108_a2_c2: ( c2 > a1 > produc1965668435998266153_a2_c2 ) > product_prod_c2_a1 > produc1965668435998266153_a2_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c2_001tf__b1_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c2_J,type,
    produc1826235639036946681_b2_c2: ( c2 > b1 > produc5894011917813406631_b2_c2 ) > product_prod_c2_b1 > produc5894011917813406631_b2_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c2_001tf__c1_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c2_J,type,
    produc4109393248294971062_c2_c2: ( c2 > c1 > produc598983362773771301_c2_c2 ) > product_prod_c2_c1 > produc598983362773771301_c2_c2 ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__c2_001tf__c1_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    produc5868568207898373875_c1_c2: ( c2 > c1 > product_prod_c1_c2 ) > product_prod_c2_c1 > product_prod_c1_c2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    produc6671677333523925913set_b2: produc8498296649714291061set_b2 > b1 > option_set_b2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    produc3187122337049823639set_c2: produc2702059613074419827set_c2 > b1 > option_set_b2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    produc6802794336065251735set_b2: produc8629413652255616883set_b2 > c1 > option_set_c2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    produc3318239339591149461set_c2: produc2833176615615745649set_c2 > c1 > option_set_c2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc591198480904955345set_b2: produc3010228553022588589set_b2 > mapping_b1_set_b2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    produc4038274906788240847set_c2: produc4061897789176782763set_c2 > mapping_b1_set_b2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J,type,
    produc2478237369292639251set_b2: produc5623429682246142959set_b2 > mapping_b1_set_b2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc2652486751147662031set_b2: produc5071516823265295275set_b2 > mapping_c1_set_c2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    produc6099563177030947533set_c2: produc6123186059419489449set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc5923294967876517358set_b2: produc909805953363803304set_b2 > mapping_c1_set_c2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc8741527518219369531set_b2: produc8179314580630251927set_b2 > nat ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001tf__a1,type,
    product_fst_nat_a1: product_prod_nat_a1 > nat ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001tf__b1,type,
    product_fst_nat_b1: product_prod_nat_b1 > nat ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001tf__c1,type,
    product_fst_nat_c1: product_prod_nat_c1 > nat ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J_J,type,
    produc5588523670895036637nat_a1: produc2966771320212024889nat_a1 > a1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b2_Mtf__a1_J_J,type,
    produc3890176417246471040_b2_a1: produc3531473365731754204_b2_a1 > a1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c2_Mtf__a1_J_J,type,
    produc6540846847745066687_c2_a1: produc3078752706661594267_c2_a1 > a1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a1_001tf__a2,type,
    product_fst_a1_a2: product_prod_a1_a2 > a1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J,type,
    produc8908562848147926891nat_a1: produc7919085903952187301nat_a1 > a2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a2_001t__Product____Type__Oprod_Itf__b2_Mtf__a1_J,type,
    produc6040206283587997966_b2_a1: produc6939678187685451336_b2_a1 > a2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a2_001t__Product____Type__Oprod_Itf__c2_Mtf__a1_J,type,
    produc5404557282983011277_c2_a1: produc366976581329271175_c2_a1 > a2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a2_001tf__a1,type,
    product_fst_a2_a1: product_prod_a2_a1 > a2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J_J,type,
    produc320987190108517212nat_b1: produc3104264649751066808nat_b1 > b1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b2_Mtf__b1_J_J,type,
    produc1100580850561756671_b2_b1: produc7875195317163649883_b2_b1 > b1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c2_Mtf__b1_J_J,type,
    produc3751251281060352318_c2_b1: produc7422474658093489946_c2_b1 > b1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b1_001tf__b2,type,
    product_fst_b1_b2: product_prod_b1_b2 > b1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J,type,
    produc3625421685424104107nat_b1: produc4594776842310734693nat_b1 > b2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b2_001t__Product____Type__Oprod_Itf__b2_Mtf__b1_J,type,
    produc2936964488378029518_b2_b1: produc5795268493557853064_b2_b1 > b2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b2_001t__Product____Type__Oprod_Itf__c2_Mtf__b1_J,type,
    produc2301315487773042829_c2_b1: produc8445938924056448711_c2_b1 > b2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b2_001tf__a1,type,
    product_fst_b2_a1: product_prod_b2_a1 > b2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b2_001tf__b1,type,
    product_fst_b2_b1: product_prod_b2_b1 > b2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b2_001tf__c1,type,
    product_fst_b2_c1: product_prod_b2_c1 > b2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J_J,type,
    produc4276822746176773595nat_c1: produc3241757979290108727nat_c1 > c1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b2_Mtf__c1_J_J,type,
    produc7534357320731818110_b2_c1: produc2995545231740769754_b2_c1 > c1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c2_Mtf__c1_J_J,type,
    produc961655714375637949_c2_c1: produc2542824572670609817_c2_c1 > c1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__c1_001tf__c2,type,
    product_fst_c1_c2: product_prod_c1_c2 > c1 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__c2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J,type,
    produc7565652559555057131nat_c1: produc1270467780669282085nat_c1 > c2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__c2_001t__Product____Type__Oprod_Itf__b2_Mtf__c1_J,type,
    produc9057094730022836878_b2_c1: produc4650858799430254792_b2_c1 > c2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__c2_001t__Product____Type__Oprod_Itf__c2_Mtf__c1_J,type,
    produc8421445729417850189_c2_c1: produc7301529229928850439_c2_c1 > c2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__c2_001tf__a1,type,
    product_fst_c2_a1: product_prod_c2_a1 > c2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__c2_001tf__b1,type,
    product_fst_c2_b1: product_prod_c2_b1 > c2 ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__c2_001tf__c1,type,
    product_fst_c2_c1: product_prod_c2_c1 > c2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    produc8060256780431234011set_b2: produc8498296649714291061set_b2 > b1 > option_set_b2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    produc4575701783957131737set_c2: produc2702059613074419827set_c2 > c1 > option_set_c2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    produc8191373782972559833set_b2: produc8629413652255616883set_b2 > b1 > option_set_b2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    produc4706818786498457559set_c2: produc2833176615615745649set_c2 > c1 > option_set_c2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc2585867251076510739set_b2: produc3010228553022588589set_b2 > mapping_b1_set_b2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    produc6032943676959796241set_c2: produc4061897789176782763set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J,type,
    produc2294650927625083477set_b2: produc5623429682246142959set_b2 > produc909805953363803304set_b2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    produc4647155521319217425set_b2: produc5071516823265295275set_b2 > mapping_b1_set_b2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    produc8094231947202502927set_c2: produc6123186059419489449set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    produc5142812559059572012set_b2: produc909805953363803304set_b2 > produc8179314580630251927set_b2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J_J,type,
    produc1581901736610471711nat_a1: produc2966771320212024889nat_a1 > produc7919085903952187301nat_a1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b2_Mtf__a1_J_J,type,
    produc7978553906662079682_b2_a1: produc3531473365731754204_b2_a1 > produc6939678187685451336_b2_a1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a1_001t__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c2_Mtf__a1_J_J,type,
    produc1405852300305899521_c2_a1: produc3078752706661594267_c2_a1 > produc366976581329271175_c2_a1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a1_001tf__a2,type,
    product_snd_a1_a2: product_prod_a1_a2 > a2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J,type,
    produc8679345462480180905nat_a1: produc7919085903952187301nat_a1 > product_prod_nat_a1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a2_001t__Product____Type__Oprod_Itf__b2_Mtf__a1_J,type,
    produc3107942046627181900_b2_a1: produc6939678187685451336_b2_a1 > product_prod_b2_a1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a2_001t__Product____Type__Oprod_Itf__c2_Mtf__a1_J,type,
    produc2472293046022195211_c2_a1: produc366976581329271175_c2_a1 > product_prod_c2_a1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a2_001tf__a1,type,
    product_snd_a2_a1: product_prod_a2_a1 > a1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J_J,type,
    produc5537737292678728094nat_b1: produc3104264649751066808nat_b1 > produc4594776842310734693nat_b1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b2_Mtf__b1_J_J,type,
    produc5188958339977365313_b2_b1: produc7875195317163649883_b2_b1 > produc5795268493557853064_b2_b1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__b1_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c2_Mtf__b1_J_J,type,
    produc7839628770475960960_c2_b1: produc7422474658093489946_c2_b1 > produc8445938924056448711_c2_b1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__b1_001tf__b2,type,
    product_snd_b1_b2: product_prod_b1_b2 > b2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__b2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J,type,
    produc3396204299756358121nat_b1: produc4594776842310734693nat_b1 > product_prod_nat_b1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__b2_001t__Product____Type__Oprod_Itf__b2_Mtf__b1_J,type,
    produc4700251417213452_b2_b1: produc5795268493557853064_b2_b1 > product_prod_b2_b1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__b2_001t__Product____Type__Oprod_Itf__c2_Mtf__b1_J,type,
    produc8592423287667002571_c2_b1: produc8445938924056448711_c2_b1 > product_prod_c2_b1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__b2_001tf__b1,type,
    product_snd_b2_b1: product_prod_b2_b1 > b1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J_J,type,
    produc270200811892208669nat_c1: produc3241757979290108727nat_c1 > produc1270467780669282085nat_c1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b2_Mtf__c1_J_J,type,
    produc2399362773292650944_b2_c1: produc2995545231740769754_b2_c1 > produc4650858799430254792_b2_c1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__c1_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c2_Mtf__c1_J_J,type,
    produc5050033203791246591_c2_c1: produc2542824572670609817_c2_c1 > produc7301529229928850439_c2_c1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__c1_001tf__c2,type,
    product_snd_c1_c2: product_prod_c1_c2 > c2 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__c2_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J,type,
    produc7336435173887311145nat_c1: produc1270467780669282085nat_c1 > product_prod_nat_c1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__c2_001t__Product____Type__Oprod_Itf__b2_Mtf__c1_J,type,
    produc6124830493062020812_b2_c1: produc4650858799430254792_b2_c1 > product_prod_b2_c1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__c2_001t__Product____Type__Oprod_Itf__c2_Mtf__c1_J,type,
    produc5489181492457034123_c2_c1: produc7301529229928850439_c2_c1 > product_prod_c2_c1 ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__c2_001tf__c1,type,
    product_snd_c2_c1: product_prod_c2_c1 > c1 ).

thf(sy_c_Product__Type_Oproduct_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    produc5560993320124916434_a1_a2: set_Pr9206071548465018024_a1_a2 > set_Pr9206071548465018024_a1_a2 > set_Pr3100092795582680071_a1_a2 ).

thf(sy_c_Product__Type_Oproduct_001tf__a1_001tf__a2,type,
    produc1920397763621873979_a1_a2: set_a1 > set_a2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_RBT__Mapping2_Odelete_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Ounit,type,
    rBT_de9134497937230377260t_unit: product_prod_a1_a2 > rBT_ma1918525461012799116t_unit > rBT_ma1918525461012799116t_unit ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    rBT_fo4564858750102097080et_nat: ( produc7710046366822967495a2_nat > set_nat > set_nat ) > rBT_ma3293358918477856731t_unit > set_nat > set_nat ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b2_J_001t__Set__Oset_Itf__b2_J,type,
    rBT_fo1362657609927939326set_b2: ( produc1965386148492149354_a2_b2 > set_b2 > set_b2 ) > rBT_ma1592301608271122040t_unit > set_b2 > set_b2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c2_J_001t__Set__Oset_Itf__c2_J,type,
    rBT_fo5313831533052644604set_c2: ( produc1965668435998266153_a2_c2 > set_c2 > set_c2 ) > rBT_ma4414676158382573177t_unit > set_c2 > set_c2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    rBT_fo1902495449323325494et_nat: ( produc6889135236516123717b2_nat > set_nat > set_nat ) > rBT_ma5169777983910274525t_unit > set_nat > set_nat ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b2_J_001t__Set__Oset_Itf__b2_J,type,
    rBT_fo2313627930490112636set_b2: ( produc5893729630307289832_b2_b2 > set_b2 > set_b2 ) > rBT_ma7390374453530515322t_unit > set_b2 > set_b2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c2_J_001t__Set__Oset_Itf__c2_J,type,
    rBT_fo6264801853614817914set_c2: ( produc5894011917813406631_b2_c2 > set_c2 > set_c2 ) > rBT_ma989376966787190651t_unit > set_c2 > set_c2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    rBT_fo8463504185399329716et_nat: ( produc6068224106209279939c2_nat > set_nat > set_nat ) > rBT_ma7046197049342692319t_unit > set_nat > set_nat ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b2_J_001t__Set__Oset_Itf__b2_J,type,
    rBT_fo3264598251052285946set_b2: ( produc598701075267654502_c2_b2 > set_b2 > set_b2 ) > rBT_ma3965075261935132796t_unit > set_b2 > set_b2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c2_J_001t__Set__Oset_Itf__c2_J,type,
    rBT_fo7215772174176991224set_c2: ( produc598983362773771301_c2_c2 > set_c2 > set_c2 ) > rBT_ma6787449812046583933t_unit > set_c2 > set_c2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__a1_Mt__Set__Oset_Itf__a2_J_J,type,
    rBT_fo797372627954349575set_a2: ( product_prod_a1_a2 > mapping_a1_set_a2 > mapping_a1_set_a2 ) > rBT_ma1918525461012799116t_unit > mapping_a1_set_a2 > mapping_a1_set_a2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    rBT_fo4244449053837635077set_b2: ( product_prod_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2 ) > rBT_ma1918525461012799116t_unit > mapping_b1_set_b2 > mapping_b1_set_b2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    rBT_fo7691525479720920579set_c2: ( product_prod_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2 ) > rBT_ma1918525461012799116t_unit > mapping_c1_set_c2 > mapping_c1_set_c2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    rBT_fo273127210504882324set_c2: ( product_prod_a1_a2 > produc2702059613074419827set_c2 > produc2702059613074419827set_c2 ) > rBT_ma1918525461012799116t_unit > produc2702059613074419827set_c2 > produc2702059613074419827set_c2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    rBT_fo5132325507301440204set_c2: ( product_prod_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ) > rBT_ma1918525461012799116t_unit > produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Set__Oset_It__Nat__Onat_J,type,
    rBT_fo6657384066399703205et_nat: ( product_prod_a1_a2 > set_nat > set_nat ) > rBT_ma1918525461012799116t_unit > set_nat > set_nat ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    rBT_fo2661663730417887303_b1_b2: ( product_prod_a1_a2 > set_Pr4592484330697324838_b1_b2 > set_Pr4592484330697324838_b1_b2 ) > rBT_ma1918525461012799116t_unit > set_Pr4592484330697324838_b1_b2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    rBT_fo7271448549504969925_c1_c2: ( product_prod_a1_a2 > set_Pr9202269149784407460_c1_c2 > set_Pr9202269149784407460_c1_c2 ) > rBT_ma1918525461012799116t_unit > set_Pr9202269149784407460_c1_c2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Set__Oset_Itf__a2_J,type,
    rBT_fo7541262516761446025set_a2: ( product_prod_a1_a2 > set_a2 > set_a2 ) > rBT_ma1918525461012799116t_unit > set_a2 > set_a2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Set__Oset_Itf__b2_J,type,
    rBT_fo7541544804267562824set_b2: ( product_prod_a1_a2 > set_b2 > set_b2 ) > rBT_ma1918525461012799116t_unit > set_b2 > set_b2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Set__Oset_Itf__c2_J,type,
    rBT_fo7541827091773679623set_c2: ( product_prod_a1_a2 > set_c2 > set_c2 ) > rBT_ma1918525461012799116t_unit > set_c2 > set_c2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    rBT_fo95959885664571011set_b2: ( product_prod_b1_b2 > mapping_b1_set_b2 > mapping_b1_set_b2 ) > rBT_ma3658025366143732878t_unit > mapping_b1_set_b2 > mapping_b1_set_b2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    rBT_fo7078035005740980153set_b2: ( product_prod_b1_b2 > set_ma6254658672695423900set_b2 > set_ma6254658672695423900set_b2 ) > rBT_ma3658025366143732878t_unit > set_ma6254658672695423900set_b2 > set_ma6254658672695423900set_b2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    rBT_fo8617919180229568255set_c2: ( product_prod_c1_c2 > mapping_c1_set_c2 > mapping_c1_set_c2 ) > rBT_ma5397525271274666640t_unit > mapping_c1_set_c2 > mapping_c1_set_c2 ).

thf(sy_c_RBT__Set2_Ofold_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    rBT_fo3354280009516849461set_c2: ( product_prod_c1_c2 > set_ma7306327908849618074set_c2 > set_ma7306327908849618074set_c2 ) > rBT_ma5397525271274666640t_unit > set_ma7306327908849618074set_c2 > set_ma7306327908849618074set_c2 ).

thf(sy_c_RBT__Set2_Okeys_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    rBT_ke4861133314182804427_a1_a2: rBT_ma1918525461012799116t_unit > list_P5985182332071222990_a1_a2 ).

thf(sy_c_RBT__Set2_Ominus_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    rBT_mi1323845651579288223_a1_a2: rBT_ma1918525461012799116t_unit > rBT_ma1918525461012799116t_unit > rBT_ma1918525461012799116t_unit ).

thf(sy_c_RBT__Set2_Oproduct_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    rBT_pr457803644961399015_a1_a2: rBT_ma1918525461012799116t_unit > rBT_ma1918525461012799116t_unit > rBT_ma7048095785541752173t_unit ).

thf(sy_c_RBT__Set2_Oproduct_001tf__a1_001tf__a2,type,
    rBT_product_a1_a2: rBT_ma5247151625439037167t_unit > rBT_ma9198043261057625646t_unit > rBT_ma1918525461012799116t_unit ).

thf(sy_c_Relation_OImage_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    image_2434655425071732201set_b2: set_Pr1995104245887189set_b2 > set_b1_option_set_b2 > set_b1_option_set_b2 ).

thf(sy_c_Relation_OImage_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    image_8173472465452405735set_c2: set_Pr3221440761411154131set_c2 > set_b1_option_set_b2 > set_c1_option_set_c2 ).

thf(sy_c_Relation_OImage_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    image_2565772427613058023set_b2: set_Pr5056620919297929171set_b2 > set_c1_option_set_c2 > set_b1_option_set_b2 ).

thf(sy_c_Relation_OImage_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    image_2236567028817877023set_c2: set_Pr1660683266160182027set_c2 > set_ma6254658672695423900set_b2 > set_ma7306327908849618074set_c2 ).

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__Nat__Onat_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_5581968639176954079_c1_c2: set_Pr6986345755798685983_c1_c2 > set_nat > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Relation_OImage_001t__Nat__Onat_001tf__b2,type,
    image_nat_b2: set_Pr9176197216388362500nat_b2 > set_nat > set_b2 ).

thf(sy_c_Relation_OImage_001t__Nat__Onat_001tf__c2,type,
    image_nat_c2: set_Pr1911939568122073667nat_c2 > set_nat > set_c2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Nat__Onat,type,
    image_3057502465641287429a2_nat: set_Pr1591205605347421565a2_nat > set_Pr9206071548465018024_a1_a2 > set_nat ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    image_1472748986238962385_b1_b2: set_Pr8971521773902901637_b1_b2 > set_Pr9206071548465018024_a1_a2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_837382273140092495_c1_c2: set_Pr5619578715368347395_c1_c2 > set_Pr9206071548465018024_a1_a2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__b2,type,
    image_6933982055939307432_a2_b2: set_Pr6984238321955989024_a2_b2 > set_Pr9206071548465018024_a1_a2 > set_b2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__c2,type,
    image_6933982055939373031_a2_c2: set_Pr8943352710544475999_a2_c2 > set_Pr9206071548465018024_a1_a2 > set_c2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Nat__Onat,type,
    image_2236591335334443651b2_nat: set_Pr6819770292282554875b2_nat > set_Pr4592484330697324838_b1_b2 > set_nat ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    image_8361504201416404053_a1_a2: set_Pr8502814890980110345_a1_a2 > set_Pr4592484330697324838_b1_b2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    image_7726137488317534163_b1_b2: set_Pr5150871832445556103_b1_b2 > set_Pr4592484330697324838_b1_b2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_7090770775218664273_c1_c2: set_Pr1798928773911001861_c1_c2 > set_Pr4592484330697324838_b1_b2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__b2,type,
    image_1638953500899672102_b2_b2: set_Pr3646447153602301854_b2_b2 > set_Pr4592484330697324838_b1_b2 > set_b2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__c2,type,
    image_1638953500899737701_b2_c2: set_Pr5605561542190788829_b2_c2 > set_Pr4592484330697324838_b1_b2 > set_c2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Nat__Onat,type,
    image_1415680205027599873c2_nat: set_Pr2824962942362912377c2_nat > set_Pr9202269149784407460_c1_c2 > set_nat ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    image_5391520666640200023_a1_a2: set_Pr4682164949522764811_a1_a2 > set_Pr9202269149784407460_c1_c2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    image_4756153953541330133_b1_b2: set_Pr1330221890988210569_b1_b2 > set_Pr9202269149784407460_c1_c2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_4120787240442460243_c1_c2: set_Pr7201650869308432135_c1_c2 > set_Pr9202269149784407460_c1_c2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__b2,type,
    image_5567296982714812580_c2_b2: set_Pr308655985248614684_c2_b2 > set_Pr9202269149784407460_c1_c2 > set_b2 ).

thf(sy_c_Relation_OImage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__c2,type,
    image_5567296982714878179_c2_c2: set_Pr2267770373837101659_c2_c2 > set_Pr9202269149784407460_c1_c2 > set_c2 ).

thf(sy_c_Relation_OImage_001tf__a1_001tf__a2,type,
    image_a1_a2: set_Pr9206071548465018024_a1_a2 > set_a1 > set_a2 ).

thf(sy_c_Relation_OImage_001tf__b1_001tf__b2,type,
    image_b1_b2: set_Pr4592484330697324838_b1_b2 > set_b1 > set_b2 ).

thf(sy_c_Relation_OImage_001tf__b2_001t__Nat__Onat,type,
    image_b2_nat: set_Pr6583197765812888324b2_nat > set_b2 > set_nat ).

thf(sy_c_Relation_OImage_001tf__b2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    image_1548392777240059392_a1_a2: set_Pr4706599232962313408_a1_a2 > set_b2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Relation_OImage_001tf__b2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    image_913026064141189502_b1_b2: set_Pr1354656174427759166_b1_b2 > set_b2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Relation_OImage_001tf__b2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_277659351042319612_c1_c2: set_Pr7226085152747980732_c1_c2 > set_b2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Relation_OImage_001tf__b2_001tf__b2,type,
    image_b2_b2: set_Pr5518672264616941095_b2_b2 > set_b2 > set_b2 ).

thf(sy_c_Relation_OImage_001tf__b2_001tf__c2,type,
    image_b2_c2: set_Pr7477786653205428070_b2_c2 > set_b2 > set_c2 ).

thf(sy_c_Relation_OImage_001tf__c1_001tf__c2,type,
    image_c1_c2: set_Pr9202269149784407460_c1_c2 > set_c1 > set_c2 ).

thf(sy_c_Relation_OImage_001tf__c2_001t__Nat__Onat,type,
    image_c2_nat: set_Pr4274324598211246019c2_nat > set_c2 > set_nat ).

thf(sy_c_Relation_OImage_001tf__c2_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    image_7668240731378749953_a1_a2: set_Pr4371357419560943681_a1_a2 > set_c2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Relation_OImage_001tf__c2_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    image_7032874018279880063_b1_b2: set_Pr1019414361026389439_b1_b2 > set_c2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Relation_OImage_001tf__c2_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_6397507305181010173_c1_c2: set_Pr6890843339346611005_c1_c2 > set_c2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Relation_OImage_001tf__c2_001tf__b2,type,
    image_c2_b2: set_Pr8169342695115536742_c2_b2 > set_c2 > set_b2 ).

thf(sy_c_Relation_OImage_001tf__c2_001tf__c2,type,
    image_c2_c2: set_Pr905085046849247909_c2_c2 > set_c2 > set_c2 ).

thf(sy_c_Set_OCollect_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    collec6564089916258477499set_b2: ( mapping_b1_set_b2 > $o ) > set_ma6254658672695423900set_b2 ).

thf(sy_c_Set_OCollect_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    collec787794305286987193set_c2: ( mapping_c1_set_c2 > $o ) > set_ma7306327908849618074set_c2 ).

thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    collec6202298912161320542set_c2: ( produc2702059613074419827set_c2 > $o ) > set_Pr3221440761411154131set_c2 ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    collec7917083185581317782set_c2: ( produc4061897789176782763set_c2 > $o ) > set_Pr1660683266160182027set_c2 ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    collec6500329951669444275_a1_a2: ( product_prod_a1_a2 > $o ) > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    collec5864963238570574385_b1_b2: ( product_prod_b1_b2 > $o ) > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    collec5229596525471704495_c1_c2: ( product_prod_c1_c2 > $o ) > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Set_OCollect_001tf__a1,type,
    collect_a1: ( a1 > $o ) > set_a1 ).

thf(sy_c_Set_OCollect_001tf__a2,type,
    collect_a2: ( a2 > $o ) > set_a2 ).

thf(sy_c_Set_OCollect_001tf__b1,type,
    collect_b1: ( b1 > $o ) > set_b1 ).

thf(sy_c_Set_OCollect_001tf__b2,type,
    collect_b2: ( b2 > $o ) > set_b2 ).

thf(sy_c_Set_OCollect_001tf__c1,type,
    collect_c1: ( c1 > $o ) > set_c1 ).

thf(sy_c_Set_OCollect_001tf__c2,type,
    collect_c2: ( c2 > $o ) > set_c2 ).

thf(sy_c_Set_Oimage_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Nat__Onat,type,
    image_1108462827494303035c2_nat: ( mapping_c1_set_c2 > nat ) > set_ma7306327908849618074set_c2 > set_nat ).

thf(sy_c_Set_Oimage_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_7561950101481872025_c1_c2: ( mapping_c1_set_c2 > product_prod_c1_c2 ) > set_ma7306327908849618074set_c2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Set_Oimage_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001tf__b2,type,
    image_1755057678288551646_c2_b2: ( mapping_c1_set_c2 > b2 ) > set_ma7306327908849618074set_c2 > set_b2 ).

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__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_5449807374656740141_c1_c2: ( nat > product_prod_c1_c2 ) > set_nat > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001tf__b2,type,
    image_nat_b22: ( nat > b2 ) > set_nat > set_b2 ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001tf__c2,type,
    image_nat_c22: ( nat > c2 ) > set_nat > set_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    image_7945144516369962181set_c2: ( produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ) > set_Pr1660683266160182027set_c2 > set_Pr1660683266160182027set_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    image_6994757892443185248_b1_b2: ( produc4061897789176782763set_c2 > product_prod_b1_b2 ) > set_Pr1660683266160182027set_c2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_6359391179344315358_c1_c2: ( produc4061897789176782763set_c2 > product_prod_c1_c2 ) > set_Pr1660683266160182027set_c2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_Itf__b2_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mtf__b2_J,type,
    image_2117164528193270170_c2_b2: ( produc5199603736692633362set_b2 > produc3239730657808423629_c2_b2 ) > set_Pr5018776704028855922set_b2 > set_Pr6396037720843056387_c2_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Nat__Onat_J,type,
    image_4004639446857651899a2_nat: ( produc2966771320212024889nat_a1 > produc7710046366822967495a2_nat ) > set_Pr8929720694596501145nat_a1 > set_Pr1591205605347421565a2_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__a1_J,type,
    image_1495601291490685442_a2_a1: ( produc8366450052225339165_a1_a2 > produc1965103856682803754_a2_a1 ) > set_Pr7467000678875188477_a1_a2 > set_Pr4954089893321156064_a2_a1 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b1_J,type,
    image_1116260717980865087_a2_b1: ( produc5014506993690784923_b1_b2 > produc1965386144188920553_a2_b1 ) > set_Pr2821992464510096251_b1_b2 > set_Pr6913204281909643039_a2_b1 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b2_Mtf__a1_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b2_J,type,
    image_8071170937106364673_a2_b2: ( produc3531473365731754204_b2_a1 > produc1965386148492149354_a2_b2 ) > set_Pr7003674894764019516_b2_a1 > set_Pr6984238321955989024_a2_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c1_J,type,
    image_736920144471044732_a2_c1: ( produc1662563935156230681_c1_c2 > produc1965668431695037352_a2_c1 ) > set_Pr7400356286999779833_c1_c2 > set_Pr8872318670498130014_a2_c1 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c2_Mtf__a1_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c2_J,type,
    image_411685745886835327_a2_c2: ( produc3078752706661594267_c2_a1 > produc1965668435998266153_a2_c2 ) > set_Pr5146122262371603323_c2_a1 > set_Pr8943352710544475999_a2_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    image_1611411006170680425set_b2: ( product_prod_a1_a2 > mapping_b1_set_b2 ) > set_Pr9206071548465018024_a1_a2 > set_ma6254658672695423900set_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    image_5058487432053965927set_c2: ( product_prod_a1_a2 > mapping_c1_set_c2 ) > set_Pr9206071548465018024_a1_a2 > set_ma7306327908849618074set_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Nat__Onat,type,
    image_2925341201121073491a2_nat: ( product_prod_a1_a2 > nat ) > set_Pr9206071548465018024_a1_a2 > set_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    image_2033382238453684613_a1_a2: ( product_prod_a1_a2 > product_prod_a1_a2 ) > set_Pr9206071548465018024_a1_a2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    image_1398015525354814723_b1_b2: ( product_prod_a1_a2 > product_prod_b1_b2 ) > set_Pr9206071548465018024_a1_a2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_762648812255944833_c1_c2: ( product_prod_a1_a2 > product_prod_c1_c2 ) > set_Pr9206071548465018024_a1_a2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__b2,type,
    image_7328530426886133494_a2_b2: ( product_prod_a1_a2 > b2 ) > set_Pr9206071548465018024_a1_a2 > set_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__c2,type,
    image_7328530426886199093_a2_c2: ( product_prod_a1_a2 > c2 ) > set_Pr9206071548465018024_a1_a2 > set_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Nat__Onat_J,type,
    image_3810186611424072504b2_nat: ( produc3104264649751066808nat_b1 > produc6889135236516123717b2_nat ) > set_Pr4802260232978741656nat_b1 > set_Pr6819770292282554875b2_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__a1_J,type,
    image_4971143247063921472_b2_a1: ( produc6386022366266853341_a1_a2 > produc5893447338497944232_b2_a1 ) > set_Pr105369466935502269_a1_a2 > set_Pr1616298724967468894_b2_a1 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b1_J,type,
    image_4591802673554101117_b2_b1: ( produc3034079307732299099_b1_b2 > produc5893729626004061031_b2_b1 ) > set_Pr4683733289425185851_b1_b2 > set_Pr3575413113555955869_b2_b1 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b2_Mtf__b1_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b2_J,type,
    image_380113436679758078_b2_b2: ( produc7875195317163649883_b2_b1 > produc5893729630307289832_b2_b2 ) > set_Pr6077960137706433083_b2_b1 > set_Pr3646447153602301854_b2_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c1_J,type,
    image_4212462100044280762_b2_c1: ( produc8905508286052520665_c1_c2 > produc5894011913510177830_b2_c1 ) > set_Pr38725075060093625_c1_c2 > set_Pr5534527502144442844_b2_c1 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c2_Mtf__b1_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c2_J,type,
    image_1944000282315004540_b2_c2: ( produc7422474658093489946_c2_b1 > produc5894011917813406631_b2_c2 ) > set_Pr4220407505314016890_c2_b1 > set_Pr5605561542190788829_b2_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    image_6686293874852392167set_b2: ( product_prod_b1_b2 > mapping_b1_set_b2 ) > set_Pr4592484330697324838_b1_b2 > set_ma6254658672695423900set_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Nat__Onat,type,
    image_2104430070814229713b2_nat: ( product_prod_b1_b2 > nat ) > set_Pr4592484330697324838_b1_b2 > set_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    image_8286770740532256391_a1_a2: ( product_prod_b1_b2 > product_prod_a1_a2 ) > set_Pr4592484330697324838_b1_b2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    image_7651404027433386501_b1_b2: ( product_prod_b1_b2 > product_prod_b1_b2 ) > set_Pr4592484330697324838_b1_b2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_7016037314334516611_c1_c2: ( product_prod_b1_b2 > product_prod_c1_c2 ) > set_Pr4592484330697324838_b1_b2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__b2,type,
    image_2033501871846498164_b2_b2: ( product_prod_b1_b2 > b2 ) > set_Pr4592484330697324838_b1_b2 > set_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__c2,type,
    image_2033501871846563763_b2_c2: ( product_prod_b1_b2 > c2 ) > set_Pr4592484330697324838_b1_b2 > set_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    image_1291399904955362964set_b2: ( produc8955508179325214080set_c2 > produc7248990843601126233set_b2 ) > set_Pr6847959500825436640set_c2 > set_Pr517000079023102863set_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Nat__Onat_J,type,
    image_3615733775990493109c2_nat: ( produc3241757979290108727nat_c1 > produc6068224106209279939c2_nat ) > set_Pr674799771360982167nat_c1 > set_Pr2824962942362912377c2_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__a1_J,type,
    image_8446685202637157502_c2_a1: ( produc4405594680308367517_a1_a2 > produc598418783458308902_c2_a1 ) > set_Pr1967110291850591869_a1_a2 > set_Pr7501879593468557532_c2_a1 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b1_J,type,
    image_8067344629127337147_c2_b1: ( produc1053651621773813275_b1_b2 > produc598701070964425701_c2_b1 ) > set_Pr6545474114340275451_b1_b2 > set_Pr237621945202268699_c2_b1 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b2_Mtf__c1_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b2_J,type,
    image_1912427973107927291_c2_b2: ( produc2995545231740769754_b2_c1 > produc598701075267654502_c2_b2 ) > set_Pr5152245380648846650_b2_c1 > set_Pr308655985248614684_c2_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c1_J,type,
    image_7688004055617516792_c2_c1: ( produc6925080600094034841_c1_c2 > produc598983358470542500_c2_c1 ) > set_Pr1900465899975183225_c1_c2 > set_Pr2196736333790755674_c2_c1 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c2_Mtf__c1_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c2_J,type,
    image_3476314818743173753_c2_c2: ( produc2542824572670609817_c2_c1 > produc598983362773771301_c2_c2 ) > set_Pr3294692748256430457_c2_c1 > set_Pr2267770373837101659_c2_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    image_5984881132562613603set_c2: ( product_prod_c1_c2 > mapping_c1_set_c2 ) > set_Pr9202269149784407460_c1_c2 > set_ma7306327908849618074set_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Nat__Onat,type,
    image_1283518940507385935c2_nat: ( product_prod_c1_c2 > nat ) > set_Pr9202269149784407460_c1_c2 > set_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    image_5316787205756052361_a1_a2: ( product_prod_c1_c2 > product_prod_a1_a2 ) > set_Pr9202269149784407460_c1_c2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    image_4681420492657182471_b1_b2: ( product_prod_c1_c2 > product_prod_b1_b2 ) > set_Pr9202269149784407460_c1_c2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    image_4046053779558312581_c1_c2: ( product_prod_c1_c2 > product_prod_c1_c2 ) > set_Pr9202269149784407460_c1_c2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__b2,type,
    image_5961845353661638642_c2_b2: ( product_prod_c1_c2 > b2 ) > set_Pr9202269149784407460_c1_c2 > set_b2 ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__c2,type,
    image_5961845353661704241_c2_c2: ( product_prod_c1_c2 > c2 ) > set_Pr9202269149784407460_c1_c2 > set_c2 ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_001t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    image_1104638922923574975set_b2: ( set_ma6254658672695423900set_b2 > set_ma6254658672695423900set_b2 ) > set_se6628959053713443282set_b2 > set_se6628959053713443282set_b2 ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001t__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    image_8300128395462491579set_c2: ( set_ma7306327908849618074set_c2 > set_ma7306327908849618074set_c2 ) > set_se755747229750772688set_c2 > set_se755747229750772688set_c2 ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    image_7916887816326733075et_nat: ( set_nat > set_nat ) > set_set_nat > set_set_nat ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    image_576176752478754181_a1_a2: ( set_Pr9206071548465018024_a1_a2 > set_Pr9206071548465018024_a1_a2 ) > set_se8350326616939597192_a1_a2 > set_se8350326616939597192_a1_a2 ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    image_2322887115139085829_b1_b2: ( set_Pr4592484330697324838_b1_b2 > set_Pr4592484330697324838_b1_b2 ) > set_se4998383558405042950_b1_b2 > set_se4998383558405042950_b1_b2 ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    image_4069597477799417477_c1_c2: ( set_Pr9202269149784407460_c1_c2 > set_Pr9202269149784407460_c1_c2 ) > set_se1646440499870488708_c1_c2 > set_se1646440499870488708_c1_c2 ).

thf(sy_c_Set_Oimage_001t__Set__Oset_Itf__b2_J_001t__Set__Oset_Itf__b2_J,type,
    image_set_b2_set_b2: ( set_b2 > set_b2 ) > set_set_b2 > set_set_b2 ).

thf(sy_c_Set_Oimage_001t__Set__Oset_Itf__c2_J_001t__Set__Oset_Itf__c2_J,type,
    image_set_c2_set_c2: ( set_c2 > set_c2 ) > set_set_c2 > set_set_c2 ).

thf(sy_c_Set_Oimage_001tf__b2_001t__Nat__Onat,type,
    image_b2_nat2: ( b2 > nat ) > set_b2 > set_nat ).

thf(sy_c_Set_Oimage_001tf__b2_001tf__b2,type,
    image_b2_b22: ( b2 > b2 ) > set_b2 > set_b2 ).

thf(sy_c_Set_Oimage_001tf__b2_001tf__c2,type,
    image_b2_c22: ( b2 > c2 ) > set_b2 > set_c2 ).

thf(sy_c_Set_Oimage_001tf__c2_001t__Nat__Onat,type,
    image_c2_nat2: ( c2 > nat ) > set_c2 > set_nat ).

thf(sy_c_Set_Oimage_001tf__c2_001tf__b2,type,
    image_c2_b22: ( c2 > b2 ) > set_c2 > set_b2 ).

thf(sy_c_Set_Oimage_001tf__c2_001tf__c2,type,
    image_c2_c22: ( c2 > c2 ) > set_c2 > set_c2 ).

thf(sy_c_Set_Oinsert_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    insert5864948013431823510set_b2: mapping_b1_set_b2 > set_ma6254658672695423900set_b2 > set_ma6254658672695423900set_b2 ).

thf(sy_c_Set_Oinsert_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    insert88652402460333204set_c2: mapping_c1_set_c2 > set_ma7306327908849618074set_c2 > set_ma7306327908849618074set_c2 ).

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

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    insert8428843036715937176_a1_a2: product_prod_a1_a2 > set_Pr9206071548465018024_a1_a2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    insert7793476323617067286_b1_b2: product_prod_b1_b2 > set_Pr4592484330697324838_b1_b2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    insert7158109610518197396_c1_c2: product_prod_c1_c2 > set_Pr9202269149784407460_c1_c2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Set_Oinsert_001tf__a1,type,
    insert_a1: a1 > set_a1 > set_a1 ).

thf(sy_c_Set_Oinsert_001tf__a2,type,
    insert_a2: a2 > set_a2 > set_a2 ).

thf(sy_c_Set_Oinsert_001tf__b1,type,
    insert_b1: b1 > set_b1 > set_b1 ).

thf(sy_c_Set_Oinsert_001tf__b2,type,
    insert_b2: b2 > set_b2 > set_b2 ).

thf(sy_c_Set_Oinsert_001tf__c1,type,
    insert_c1: c1 > set_c1 > set_c1 ).

thf(sy_c_Set_Oinsert_001tf__c2,type,
    insert_c2: c2 > set_c2 > set_c2 ).

thf(sy_c_Set_Ois__singleton_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    is_sin7137739156882022514set_b2: set_ma6254658672695423900set_b2 > $o ).

thf(sy_c_Set_Ois__singleton_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    is_sin1361443545910532208set_c2: set_ma7306327908849618074set_c2 > $o ).

thf(sy_c_Set_Ois__singleton_001t__Nat__Onat,type,
    is_singleton_nat: set_nat > $o ).

thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    is_sin4603980725694467260_a1_a2: set_Pr9206071548465018024_a1_a2 > $o ).

thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    is_sin3968614012595597370_b1_b2: set_Pr4592484330697324838_b1_b2 > $o ).

thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    is_sin3333247299496727480_c1_c2: set_Pr9202269149784407460_c1_c2 > $o ).

thf(sy_c_Set_Ois__singleton_001tf__b2,type,
    is_singleton_b2: set_b2 > $o ).

thf(sy_c_Set_Ois__singleton_001tf__c2,type,
    is_singleton_c2: set_c2 > $o ).

thf(sy_c_Set_Oremove_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    remove1959972985843460289set_b2: mapping_b1_set_b2 > set_ma6254658672695423900set_b2 > set_ma6254658672695423900set_b2 ).

thf(sy_c_Set_Oremove_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    remove5407049411726745791set_c2: mapping_c1_set_c2 > set_ma7306327908849618074set_c2 > set_ma7306327908849618074set_c2 ).

thf(sy_c_Set_Oremove_001t__Nat__Onat,type,
    remove_nat: nat > set_nat > set_nat ).

thf(sy_c_Set_Oremove_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    remove1798067411834080045_a1_a2: product_prod_a1_a2 > set_Pr9206071548465018024_a1_a2 > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Set_Oremove_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    remove1162700698735210155_b1_b2: product_prod_b1_b2 > set_Pr4592484330697324838_b1_b2 > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Set_Oremove_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    remove527333985636340265_c1_c2: product_prod_c1_c2 > set_Pr9202269149784407460_c1_c2 > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Set_Oremove_001tf__b2,type,
    remove_b2: b2 > set_b2 > set_b2 ).

thf(sy_c_Set_Oremove_001tf__c2,type,
    remove_c2: c2 > set_c2 > set_c2 ).

thf(sy_c_Set__Impl_ORBT__set_001t__Nat__Onat,type,
    set_RBT_set_nat: rBT_ma3908794552746989458t_unit > set_nat ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Nat__Onat_J,type,
    set_RB6441065557922404028a2_nat: rBT_ma3293358918477856731t_unit > set_Pr1591205605347421565a2_nat ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    set_RB7405050026841235442_a1_a2: rBT_ma7048095785541752173t_unit > set_Pr3100092795582680071_a1_a2 ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b2_J,type,
    set_RB8879022366592544735_a2_b2: rBT_ma1592301608271122040t_unit > set_Pr6984238321955989024_a2_b2 ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c2_J,type,
    set_RB8879304654098661534_a2_c2: rBT_ma4414676158382573177t_unit > set_Pr8943352710544475999_a2_c2 ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Nat__Onat_J,type,
    set_RB5620154427615560250b2_nat: rBT_ma5169777983910274525t_unit > set_Pr6819770292282554875b2_nat ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b2_J,type,
    set_RB3583993811552909405_b2_b2: rBT_ma7390374453530515322t_unit > set_Pr3646447153602301854_b2_b2 ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c2_J,type,
    set_RB3584276099059026204_b2_c2: rBT_ma989376966787190651t_unit > set_Pr5605561542190788829_b2_c2 ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Nat__Onat_J,type,
    set_RB4799243297308716472c2_nat: rBT_ma7046197049342692319t_unit > set_Pr2824962942362912377c2_nat ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b2_J,type,
    set_RB7512337293368049883_c2_b2: rBT_ma3965075261935132796t_unit > set_Pr308655985248614684_c2_b2 ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c2_J,type,
    set_RB7512619580874166682_c2_c2: rBT_ma6787449812046583933t_unit > set_Pr2267770373837101659_c2_c2 ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    set_RB6720226376580087827_a1_a2: rBT_ma1918525461012799116t_unit > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    set_RB6084859663481217937_b1_b2: rBT_ma3658025366143732878t_unit > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_Set__Impl_ORBT__set_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    set_RB5449492950382348047_c1_c2: rBT_ma5397525271274666640t_unit > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_Set__Impl_ORBT__set_001tf__a1,type,
    set_RBT_set_a1: rBT_ma5247151625439037167t_unit > set_a1 ).

thf(sy_c_Set__Impl_ORBT__set_001tf__a2,type,
    set_RBT_set_a2: rBT_ma9198043261057625646t_unit > set_a2 ).

thf(sy_c_Set__Impl_Ocomp__fun__commute_Ocomp__fun__commute__apply_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    set_co1133346682401797306set_b2: set_co8598795993805790083set_b2 > product_prod_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2 ).

thf(sy_c_Set__Impl_Ocomp__fun__commute_Ocomp__fun__commute__apply_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    set_co4580423108285082808set_c2: set_co427093193105208449set_c2 > product_prod_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Set__Impl_Ocomp__fun__commute_Ocomp__fun__commute__apply_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    set_co8608146164814620447set_c2: set_co4027722269366479532set_c2 > product_prod_a1_a2 > produc2702059613074419827set_c2 > produc2702059613074419827set_c2 ).

thf(sy_c_Set__Impl_Ocomp__fun__commute_Ocomp__fun__commute__apply_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    set_co5036068180762417751set_c2: set_co8648611349764106212set_c2 > product_prod_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ).

thf(sy_c_Set__Impl_Ocomp__fun__idem_Ocomp__fun__idem__apply_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    set_co5767054866228076550set_b2: set_co2677916505999940506set_b2 > product_prod_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2 ).

thf(sy_c_Set__Impl_Ocomp__fun__idem_Ocomp__fun__idem__apply_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    set_co9214131292111362052set_c2: set_co3729585742154134680set_c2 > product_prod_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2 ).

thf(sy_c_Set__Impl_Ocomp__fun__idem_Ocomp__fun__idem__apply_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    set_co1568338092084129491set_c2: set_co1666008921066281045set_c2 > product_prod_a1_a2 > produc2702059613074419827set_c2 > produc2702059613074419827set_c2 ).

thf(sy_c_Set__Impl_Ocomp__fun__idem_Ocomp__fun__idem__apply_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    set_co4303079455494716939set_c2: set_co4968226104895303821set_c2 > product_prod_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ).

thf(sy_c_Set__Impl_Ocsorted__list__of__set_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    set_cs3950026889026203652_a1_a2: set_Pr9206071548465018024_a1_a2 > list_P5985182332071222990_a1_a2 ).

thf(sy_c_Set__Impl_Oset__fold__cfc_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    set_se1353478033518471707set_b2: set_co8598795993805790083set_b2 > mapping_b1_set_b2 > set_Pr9206071548465018024_a1_a2 > mapping_b1_set_b2 ).

thf(sy_c_Set__Impl_Oset__fold__cfc_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    set_se4800554459401757209set_c2: set_co427093193105208449set_c2 > mapping_c1_set_c2 > set_Pr9206071548465018024_a1_a2 > mapping_c1_set_c2 ).

thf(sy_c_Set__Impl_Oset__fold__cfc_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    set_se4474698099260563966set_c2: set_co4027722269366479532set_c2 > produc2702059613074419827set_c2 > set_Pr9206071548465018024_a1_a2 > produc2702059613074419827set_c2 ).

thf(sy_c_Set__Impl_Oset__fold__cfc_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    set_se764104708205941302set_c2: set_co8648611349764106212set_c2 > produc4061897789176782763set_c2 > set_Pr9206071548465018024_a1_a2 > produc4061897789176782763set_c2 ).

thf(sy_c_Set__Impl_Oset__fold__cfi_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    set_se3028378928793307029set_b2: set_co2677916505999940506set_b2 > mapping_b1_set_b2 > set_Pr9206071548465018024_a1_a2 > mapping_b1_set_b2 ).

thf(sy_c_Set__Impl_Oset__fold__cfi_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    set_se6475455354676592531set_c2: set_co3729585742154134680set_c2 > mapping_c1_set_c2 > set_Pr9206071548465018024_a1_a2 > mapping_c1_set_c2 ).

thf(sy_c_Set__Impl_Oset__fold__cfi_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    set_se8655448371823792900set_c2: set_co1666008921066281045set_c2 > produc2702059613074419827set_c2 > set_Pr9206071548465018024_a1_a2 > produc2702059613074419827set_c2 ).

thf(sy_c_Set__Impl_Oset__fold__cfi_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    set_se7927235621780297020set_c2: set_co4968226104895303821set_c2 > produc4061897789176782763set_c2 > set_Pr9206071548465018024_a1_a2 > produc4061897789176782763set_c2 ).

thf(sy_c_String_OCode_Oabort_001_062_Itf__a1_Mt__Option__Ooption_It__Set__Oset_Itf__a2_J_J_J,type,
    abort_4533741113768301507set_a2: literal > ( product_unit > a1 > option_set_a2 ) > a1 > option_set_a2 ).

thf(sy_c_String_OCode_Oabort_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    abort_1049186117294199233set_b2: literal > ( product_unit > b1 > option_set_b2 ) > b1 > option_set_b2 ).

thf(sy_c_String_OCode_Oabort_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    abort_6788003157674872767set_c2: literal > ( product_unit > c1 > option_set_c2 ) > c1 > option_set_c2 ).

thf(sy_c_String_OCode_Oabort_001_Eo,type,
    abort_o: literal > ( product_unit > $o ) > $o ).

thf(sy_c_String_OCode_Oabort_001t__List__Olist_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    abort_5785945136775419735_a1_a2: literal > ( product_unit > list_P5985182332071222990_a1_a2 ) > list_P5985182332071222990_a1_a2 ).

thf(sy_c_String_OCode_Oabort_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    abort_1879577566130638365set_b2: literal > ( product_unit > mapping_b1_set_b2 ) > mapping_b1_set_b2 ).

thf(sy_c_String_OCode_Oabort_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    abort_5326653992013923867set_c2: literal > ( product_unit > mapping_c1_set_c2 ) > mapping_c1_set_c2 ).

thf(sy_c_String_OCode_Oabort_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    abort_2778816509743918716set_c2: literal > ( product_unit > produc2702059613074419827set_c2 ) > produc2702059613074419827set_c2 ).

thf(sy_c_String_OCode_Oabort_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    abort_4986896609014028468set_c2: literal > ( product_unit > produc4061897789176782763set_c2 ) > produc4061897789176782763set_c2 ).

thf(sy_c_String_OCode_Oabort_001t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    abort_7538820938207752019set_b2: literal > ( product_unit > set_ma6254658672695423900set_b2 ) > set_ma6254658672695423900set_b2 ).

thf(sy_c_String_OCode_Oabort_001t__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    abort_8590490174361946193set_c2: literal > ( product_unit > set_ma7306327908849618074set_c2 ) > set_ma7306327908849618074set_c2 ).

thf(sy_c_String_OCode_Oabort_001t__Set__Oset_It__Nat__Onat_J,type,
    abort_set_nat: literal > ( product_unit > set_nat ) > set_nat ).

thf(sy_c_String_OCode_Oabort_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    abort_2970878230164759184_a1_a2: literal > ( product_unit > set_Pr3100092795582680071_a1_a2 ) > set_Pr3100092795582680071_a1_a2 ).

thf(sy_c_String_OCode_Oabort_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    abort_1828026589024592305_a1_a2: literal > ( product_unit > set_Pr9206071548465018024_a1_a2 ) > set_Pr9206071548465018024_a1_a2 ).

thf(sy_c_String_OCode_Oabort_001t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    abort_6437811408111674927_b1_b2: literal > ( product_unit > set_Pr4592484330697324838_b1_b2 ) > set_Pr4592484330697324838_b1_b2 ).

thf(sy_c_String_OCode_Oabort_001t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    abort_1824224190343981741_c1_c2: literal > ( product_unit > set_Pr9202269149784407460_c1_c2 ) > set_Pr9202269149784407460_c1_c2 ).

thf(sy_c_String_OCode_Oabort_001t__Set__Oset_Itf__a2_J,type,
    abort_set_a2: literal > ( product_unit > set_a2 ) > set_a2 ).

thf(sy_c_String_OCode_Oabort_001t__Set__Oset_Itf__b2_J,type,
    abort_set_b2: literal > ( product_unit > set_b2 ) > set_b2 ).

thf(sy_c_String_OCode_Oabort_001t__Set__Oset_Itf__c2_J,type,
    abort_set_c2: literal > ( product_unit > set_c2 ) > set_c2 ).

thf(sy_c_String_OLiteral,type,
    literal2: $o > $o > $o > $o > $o > $o > $o > literal > literal ).

thf(sy_c_String_OLiteral_H,type,
    literal3: $o > $o > $o > $o > $o > $o > $o > literal > literal ).

thf(sy_c_String_Ochar_Osize__char,type,
    size_char: char > nat ).

thf(sy_c_Test__Suite__Calculation__Refined_Odual__set__as__map__image_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    test_S6443642256665625299set_c2: set_Pr1660683266160182027set_c2 > ( produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ) > ( produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ) > produc2070398702644967871set_c2 ).

thf(sy_c_Test__Suite__Calculation__Refined_Odual__set__as__map__image_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001tf__b1_001tf__b2,type,
    test_S4625532478866329070_b1_b2: set_Pr1660683266160182027set_c2 > ( produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ) > ( produc4061897789176782763set_c2 > product_prod_b1_b2 ) > produc1295556776222662362set_b2 ).

thf(sy_c_Test__Suite__Calculation__Refined_Odual__set__as__map__image_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001tf__c1_001tf__c2,type,
    test_S3989883478261407980_c1_c2: set_Pr1660683266160182027set_c2 > ( produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ) > ( produc4061897789176782763set_c2 > product_prod_c1_c2 ) > produc4722691776437566936set_c2 ).

thf(sy_c_Test__Suite__Calculation__Refined_Odual__set__as__map__image_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001tf__b1_001tf__b2_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    test_S1219458079195954926set_c2: set_Pr1660683266160182027set_c2 > ( produc4061897789176782763set_c2 > product_prod_b1_b2 ) > ( produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ) > produc2916914556658279514set_c2 ).

thf(sy_c_Test__Suite__Calculation__Refined_Odual__set__as__map__image_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001tf__c1_001tf__c2_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    test_S6074054486132820972set_c2: set_Pr1660683266160182027set_c2 > ( produc4061897789176782763set_c2 > product_prod_c1_c2 ) > ( produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ) > produc3792589628255236696set_c2 ).

thf(sy_c_Test__Suite__Calculation__Refined_Odual__set__as__map__image_001tf__a1_001tf__a2_001tf__b1_001tf__b2_001tf__b1_001tf__b2,type,
    test_S917631008590620710_b1_b2: set_Pr9206071548465018024_a1_a2 > ( product_prod_a1_a2 > product_prod_b1_b2 ) > ( product_prod_a1_a2 > product_prod_b1_b2 ) > produc8498296649714291061set_b2 ).

thf(sy_c_Test__Suite__Calculation__Refined_Odual__set__as__map__image_001tf__a1_001tf__a2_001tf__b1_001tf__b2_001tf__c1_001tf__c2,type,
    test_S281982007985699620_c1_c2: set_Pr9206071548465018024_a1_a2 > ( product_prod_a1_a2 > product_prod_b1_b2 ) > ( product_prod_a1_a2 > product_prod_c1_c2 ) > produc2702059613074419827set_c2 ).

thf(sy_c_Test__Suite__Calculation__Refined_Odual__set__as__map__image_001tf__a1_001tf__a2_001tf__c1_001tf__c2_001tf__b1_001tf__b2,type,
    test_S8332919854771946788_b1_b2: set_Pr9206071548465018024_a1_a2 > ( product_prod_a1_a2 > product_prod_c1_c2 ) > ( product_prod_a1_a2 > product_prod_b1_b2 ) > produc8629413652255616883set_b2 ).

thf(sy_c_Test__Suite__Calculation__Refined_Odual__set__as__map__image_001tf__a1_001tf__a2_001tf__c1_001tf__c2_001tf__c1_001tf__c2,type,
    test_S7697270854167025698_c1_c2: set_Pr9206071548465018024_a1_a2 > ( product_prod_a1_a2 > product_prod_c1_c2 ) > ( product_prod_a1_a2 > product_prod_c1_c2 ) > produc2833176615615745649set_c2 ).

thf(sy_c_Test__Suite__Calculation__Refined_Oset__as__map__image_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    test_S2264929716748280803set_c2: set_Pr1660683266160182027set_c2 > ( produc4061897789176782763set_c2 > produc4061897789176782763set_c2 ) > mapping_b1_set_b2 > option781494349862297706set_c2 ).

thf(sy_c_Test__Suite__Calculation__Refined_Oset__as__map__image_001tf__a1_001tf__a2_001tf__b1_001tf__b2,type,
    test_S3635035963686295067_b1_b2: set_Pr9206071548465018024_a1_a2 > ( product_prod_a1_a2 > product_prod_b1_b2 ) > b1 > option_set_b2 ).

thf(sy_c_Test__Suite__Calculation__Refined_Oset__as__map__image_001tf__a1_001tf__a2_001tf__c1_001tf__c2,type,
    test_S2999386963081373977_c1_c2: set_Pr9206071548465018024_a1_a2 > ( product_prod_a1_a2 > product_prod_c1_c2 ) > c1 > option_set_c2 ).

thf(sy_c_Util_Oset__as__map_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    set_as1009038886163540748set_b2: set_Pr1995104245887189set_b2 > ( b1 > option_set_b2 ) > option2685796312493375632set_b2 ).

thf(sy_c_Util_Oset__as__map_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    set_as6747855926544214282set_c2: set_Pr3221440761411154131set_c2 > ( b1 > option_set_b2 ) > option5905241969658642574set_c2 ).

thf(sy_c_Util_Oset__as__map_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    set_as1140155888704866570set_b2: set_Pr5056620919297929171set_b2 > ( c1 > option_set_c2 ) > option2685796312493375632set_b2 ).

thf(sy_c_Util_Oset__as__map_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    set_as574257606533379650set_c2: set_Pr1660683266160182027set_c2 > mapping_b1_set_b2 > option781494349862297706set_c2 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_001tf__b2,type,
    set_as5455615909052603816_c2_b2: set_Pr6396037720843056387_c2_b2 > produc4061897789176782763set_c2 > option_set_b2 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001t__Nat__Onat,type,
    set_as6868951283146871074a2_nat: set_Pr1591205605347421565a2_nat > product_prod_a1_a2 > option_set_nat ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__a1,type,
    set_as6226127449179616517_a2_a1: set_Pr4954089893321156064_a2_a1 > product_prod_a1_a2 > option_set_a1 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__b1,type,
    set_as6226127449179682116_a2_b1: set_Pr6913204281909643039_a2_b1 > product_prod_a1_a2 > option_set_b1 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__b2,type,
    set_as6226127449179682117_a2_b2: set_Pr6984238321955989024_a2_b2 > product_prod_a1_a2 > option_set_b2 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__c1,type,
    set_as6226127449179747715_a2_c1: set_Pr8872318670498130014_a2_c1 > product_prod_a1_a2 > option_set_c1 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J_001tf__c2,type,
    set_as6226127449179747716_a2_c2: set_Pr8943352710544475999_a2_c2 > product_prod_a1_a2 > option_set_c2 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001t__Nat__Onat,type,
    set_as6048040152840027296b2_nat: set_Pr6819770292282554875b2_nat > product_prod_b1_b2 > option_set_nat ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__a1,type,
    set_as931098894139981187_b2_a1: set_Pr1616298724967468894_b2_a1 > product_prod_b1_b2 > option_set_a1 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__b1,type,
    set_as931098894140046786_b2_b1: set_Pr3575413113555955869_b2_b1 > product_prod_b1_b2 > option_set_b1 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__b2,type,
    set_as931098894140046787_b2_b2: set_Pr3646447153602301854_b2_b2 > product_prod_b1_b2 > option_set_b2 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__c1,type,
    set_as931098894140112385_b2_c1: set_Pr5534527502144442844_b2_c1 > product_prod_b1_b2 > option_set_c1 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J_001tf__c2,type,
    set_as931098894140112386_b2_c2: set_Pr5605561542190788829_b2_c2 > product_prod_b1_b2 > option_set_c2 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    set_as4538642359510808500set_b2: set_Pr517000079023102863set_b2 > product_prod_c1_c2 > option6654706173824968300set_b2 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001t__Nat__Onat,type,
    set_as5227129022533183518c2_nat: set_Pr2824962942362912377c2_nat > product_prod_c1_c2 > option_set_nat ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__a1,type,
    set_as4859442375955121665_c2_a1: set_Pr7501879593468557532_c2_a1 > product_prod_c1_c2 > option_set_a1 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__b1,type,
    set_as4859442375955187264_c2_b1: set_Pr237621945202268699_c2_b1 > product_prod_c1_c2 > option_set_b1 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__b2,type,
    set_as4859442375955187265_c2_b2: set_Pr308655985248614684_c2_b2 > product_prod_c1_c2 > option_set_b2 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__c1,type,
    set_as4859442375955252863_c2_c1: set_Pr2196736333790755674_c2_c1 > product_prod_c1_c2 > option_set_c1 ).

thf(sy_c_Util_Oset__as__map_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J_001tf__c2,type,
    set_as4859442375955252864_c2_c2: set_Pr2267770373837101659_c2_c2 > product_prod_c1_c2 > option_set_c2 ).

thf(sy_c_Util_Oset__as__map_001tf__a1_001tf__a2,type,
    set_as_map_a1_a2: set_Pr9206071548465018024_a1_a2 > a1 > option_set_a2 ).

thf(sy_c_Util_Oset__as__map_001tf__b1_001tf__b2,type,
    set_as_map_b1_b2: set_Pr4592484330697324838_b1_b2 > b1 > option_set_b2 ).

thf(sy_c_Util_Oset__as__map_001tf__c1_001tf__c2,type,
    set_as_map_c1_c2: set_Pr9202269149784407460_c1_c2 > c1 > option_set_c2 ).

thf(sy_c_member_001_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J,type,
    member3006388138933004577set_b2: ( b1 > option_set_b2 ) > set_b1_option_set_b2 > $o ).

thf(sy_c_member_001_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J,type,
    member8745205179313678111set_c2: ( c1 > option_set_c2 ) > set_c1_option_set_c2 > $o ).

thf(sy_c_member_001t__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J,type,
    member6117332676589958525set_b2: mapping_b1_set_b2 > set_ma6254658672695423900set_b2 > $o ).

thf(sy_c_member_001t__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J,type,
    member341037065618468219set_c2: mapping_c1_set_c2 > set_ma7306327908849618074set_c2 > $o ).

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

thf(sy_c_member_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    member5626741290992238622set_b2: produc8498296649714291061set_b2 > set_Pr1995104245887189set_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_M_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_J,type,
    member9053876291207143196set_c2: produc2702059613074419827set_c2 > set_Pr3221440761411154131set_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_Itf__c1_Mt__Option__Ooption_It__Set__Oset_Itf__c2_J_J_J_M_062_Itf__b1_Mt__Option__Ooption_It__Set__Oset_Itf__b2_J_J_J_J,type,
    member5757858293533564444set_b2: produc8629413652255616883set_b2 > set_Pr5056620919297929171set_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    member419137155788712276set_c2: produc4061897789176782763set_c2 > set_Pr1660683266160182027set_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J_J_J,type,
    member3857524843657475480set_b2: produc5623429682246142959set_b2 > set_Pr5589133262920150351set_b2 > $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__Nat__Onat_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    member958080023357176960_c1_c2: produc2762000901599049065_c1_c2 > set_Pr6986345755798685983_c1_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_Mtf__c2_J,type,
    member4770052056032943395_c2_c2: produc3240012945314540428_c2_c2 > set_Pr8355152109431543362_c2_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Nat__Onat_J,type,
    member5906125488581095390a2_nat: produc7710046366822967495a2_nat > set_Pr1591205605347421565a2_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    member1107764608925283022_b1_b2: produc4401324642061629349_b1_b2 > set_Pr8971521773902901637_b1_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    member5717549428012365644_c1_c2: produc9011109461148711971_c1_c2 > set_Pr5619578715368347395_c1_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__b2_J,type,
    member6016270048498768897_a2_b2: produc1965386148492149354_a2_b2 > set_Pr6984238321955989024_a2_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_Mtf__c2_J,type,
    member6016552336004885696_a2_c2: produc1965668435998266153_a2_c2 > set_Pr8943352710544475999_a2_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Nat__Onat_J,type,
    member5085214358274251612b2_nat: produc6889135236516123717b2_nat > set_Pr6819770292282554875b2_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    member2751368291916772178_a1_a2: produc6044928325053118505_a1_a2 > set_Pr8502814890980110345_a1_a2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    member7361153111003854800_b1_b2: produc1431341107285425319_b1_b2 > set_Pr5150871832445556103_b1_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    member2747565893236161614_c1_c2: produc6041125926372507941_c1_c2 > set_Pr1798928773911001861_c1_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__b2_J,type,
    member721241493459133567_b2_b2: produc5893729630307289832_b2_b2 > set_Pr3646447153602301854_b2_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_Mtf__c2_J,type,
    member721523780965250366_b2_c2: produc5894011917813406631_b2_c2 > set_Pr5605561542190788829_b2_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Nat__Onat_J,type,
    member4264303227967407834c2_nat: produc6068224106209279939c2_nat > set_Pr2824962942362912377c2_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    member9004756793995343956_a1_a2: produc3074944790276914475_a1_a2 > set_Pr4682164949522764811_a1_a2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    member4391169576227650770_b1_b2: produc7684729609363997097_b1_b2 > set_Pr1330221890988210569_b1_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    member9000954395314733392_c1_c2: produc3071142391596303911_c1_c2 > set_Pr7201650869308432135_c1_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__b2_J,type,
    member4649584975274274045_c2_b2: produc598701075267654502_c2_b2 > set_Pr308655985248614684_c2_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_Mtf__c2_J,type,
    member4649867262780390844_c2_c2: produc598983362773771301_c2_c2 > set_Pr2267770373837101659_c2_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__a1_J_J_J,type,
    member2853781444696841186nat_a1: produc2966771320212024889nat_a1 > set_Pr8929720694596501145nat_a1 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    member5072890019088992838_a1_a2: produc8366450052225339165_a1_a2 > set_Pr7467000678875188477_a1_a2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    member1720946960554438596_b1_b2: produc5014506993690784923_b1_b2 > set_Pr2821992464510096251_b1_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__b2_Mtf__a1_J_J_J,type,
    member237913332595407877_b2_a1: produc3531473365731754204_b2_a1 > set_Pr7003674894764019516_b2_a1 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    member7592375938874660162_c1_c2: produc1662563935156230681_c1_c2 > set_Pr7400356286999779833_c1_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a1_Mt__Product____Type__Oprod_Itf__a2_Mt__Product____Type__Oprod_Itf__c2_Mtf__a1_J_J_J,type,
    member9008564710380023748_c2_a1: produc3078752706661594267_c2_a1 > set_Pr5146122262371603323_c2_a1 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a1_Mtf__a2_J,type,
    member2711116448414824817_a1_a2: product_prod_a1_a2 > set_Pr9206071548465018024_a1_a2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__b1_J_J_J,type,
    member2991274774235883105nat_b1: produc3104264649751066808nat_b1 > set_Pr4802260232978741656nat_b1 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    member3092462333130507014_a1_a2: produc6386022366266853341_a1_a2 > set_Pr105369466935502269_a1_a2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    member8963891311450728580_b1_b2: produc3034079307732299099_b1_b2 > set_Pr4683733289425185851_b1_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b2_Mtf__b1_J_J_J,type,
    member4581635284027303556_b2_b1: produc7875195317163649883_b2_b1 > set_Pr6077960137706433083_b2_b1 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    member5611948252916174338_c1_c2: produc8905508286052520665_c1_c2 > set_Pr38725075060093625_c1_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b1_Mt__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c2_Mtf__b1_J_J_J,type,
    member4128914624957143619_c2_b1: produc7422474658093489946_c2_b1 > set_Pr4220407505314016890_c2_b1 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b1_Mtf__b2_J,type,
    member2075749735315954927_b1_b2: product_prod_b1_b2 > set_Pr4592484330697324838_b1_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b2_Mt__Nat__Onat_J,type,
    member2965532670062880717b2_nat: product_prod_b2_nat > set_Pr6583197765812888324b2_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    member4381213680604119713_a1_a2: produc330329780597500170_a1_a2 > set_Pr4706599232962313408_a1_a2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    member8990998499691202335_b1_b2: produc4940114599684582792_b1_b2 > set_Pr1354656174427759166_b1_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    member4377411281923509149_c1_c2: produc326527381916889606_c1_c2 > set_Pr7226085152747980732_c1_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b2_Mtf__b2_J,type,
    member1127658555671259760_b2_b2: product_prod_b2_b2 > set_Pr5518672264616941095_b2_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b2_Mtf__c2_J,type,
    member1127940843177376559_b2_c2: product_prod_b2_c2 > set_Pr7477786653205428070_b2_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_Mt__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J_J_J,type,
    member3625764905904111785set_c2: produc8955508179325214080set_c2 > set_Pr6847959500825436640set_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_It__Nat__Onat_Mtf__c1_J_J_J,type,
    member3128768103774925024nat_c1: produc3241757979290108727nat_c1 > set_Pr674799771360982167nat_c1 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J_J,type,
    member1112034647172021190_a1_a2: produc4405594680308367517_a1_a2 > set_Pr1967110291850591869_a1_a2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J_J,type,
    member6983463625492242756_b1_b2: produc1053651621773813275_b1_b2 > set_Pr6545474114340275451_b1_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b2_Mtf__c1_J_J_J,type,
    member8925357235459199235_b2_c1: produc2995545231740769754_b2_c1 > set_Pr5152245380648846650_b2_c1 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J_J,type,
    member3631520566957688514_c1_c2: produc6925080600094034841_c1_c2 > set_Pr1900465899975183225_c1_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c1_Mt__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c2_Mtf__c1_J_J_J,type,
    member8472636576389039298_c2_c1: produc2542824572670609817_c2_c1 > set_Pr3294692748256430457_c2_c1 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c1_Mtf__c2_J,type,
    member1440383022217085037_c1_c2: product_prod_c1_c2 > set_Pr9202269149784407460_c1_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c2_Mt__Nat__Onat_J,type,
    member1107980037670464524c2_nat: product_prod_c2_nat > set_Pr4274324598211246019c2_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    member1277689597888034466_a1_a2: produc6450177734736190731_a1_a2 > set_Pr4371357419560943681_a1_a2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    member5887474416975117088_b1_b2: produc1836590516968497545_b1_b2 > set_Pr1019414361026389439_b1_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c2_Mt__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    member1273887199207423902_c1_c2: produc6446375336055580167_c1_c2 > set_Pr6890843339346611005_c1_c2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c2_Mtf__b2_J,type,
    member492009555066273071_c2_b2: product_prod_c2_b2 > set_Pr8169342695115536742_c2_b2 > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c2_Mtf__c2_J,type,
    member492291842572389870_c2_c2: product_prod_c2_c2 > set_Pr905085046849247909_c2_c2 > $o ).

thf(sy_c_member_001t__Set__Oset_It__Mapping__Omapping_Itf__b1_Mt__Set__Oset_Itf__b2_J_J_J,type,
    member1943109388073899699set_b2: set_ma6254658672695423900set_b2 > set_se6628959053713443282set_b2 > $o ).

thf(sy_c_member_001t__Set__Oset_It__Mapping__Omapping_Itf__c1_Mt__Set__Oset_Itf__c2_J_J_J,type,
    member2994778624228093873set_c2: set_ma7306327908849618074set_c2 > set_se755747229750772688set_c2 > $o ).

thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
    member_set_nat: set_nat > set_set_nat > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_Itf__a1_Mtf__a2_J_J,type,
    member5409760098207052369_a1_a2: set_Pr9206071548465018024_a1_a2 > set_se8350326616939597192_a1_a2 > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_Itf__b1_Mtf__b2_J_J,type,
    member796172880439359183_b1_b2: set_Pr4592484330697324838_b1_b2 > set_se4998383558405042950_b1_b2 > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_Itf__c1_Mtf__c2_J_J,type,
    member5405957699526441805_c1_c2: set_Pr9202269149784407460_c1_c2 > set_se1646440499870488708_c1_c2 > $o ).

thf(sy_c_member_001t__Set__Oset_Itf__b2_J,type,
    member_set_b2: set_b2 > set_set_b2 > $o ).

thf(sy_c_member_001t__Set__Oset_Itf__c2_J,type,
    member_set_c2: set_c2 > set_set_c2 > $o ).

thf(sy_c_member_001tf__a1,type,
    member_a1: a1 > set_a1 > $o ).

thf(sy_c_member_001tf__a2,type,
    member_a2: a2 > set_a2 > $o ).

thf(sy_c_member_001tf__b1,type,
    member_b1: b1 > set_b1 > $o ).

thf(sy_c_member_001tf__b2,type,
    member_b2: b2 > set_b2 > $o ).

thf(sy_c_member_001tf__c1,type,
    member_c1: c1 > set_c1 > $o ).

thf(sy_c_member_001tf__c2,type,
    member_c2: c2 > set_c2 > $o ).

thf(sy_v_a____,type,
    a: product_prod_a1_a2 > product_prod_a1_a2 > order ).

thf(sy_v_f1,type,
    f1: product_prod_a1_a2 > product_prod_b1_b2 ).

thf(sy_v_f2,type,
    f2: product_prod_a1_a2 > product_prod_c1_c2 ).

thf(sy_v_t,type,
    t: rBT_ma1918525461012799116t_unit ).

% Relevant facts (1274)
thf(fact_0__092_060open_062Mapping_Olookup_A_Ifst_A_IRBT__Set2_Ofold_A_I_092_060lambda_062kv_A_Im1_M_Am2_J_O_A_Icase_Af1_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am1_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am1_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am1_M_Acase_Af2_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am2_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am2_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am2_J_J_At_A_IMapping_Oempty_M_AMapping_Oempty_J_J_J_A_061_Aset__as__map_A_If1_A_096_ARBT__set_At_J_092_060close_062,axiom,
    ( ( lookup_b1_set_b2
      @ ( produc4038274906788240847set_c2
        @ ( rBT_fo5132325507301440204set_c2
          @ ^ [Kv: product_prod_a1_a2] :
              ( produc4732439310506902963set_c2
              @ ^ [M1: mapping_b1_set_b2,M2: mapping_c1_set_c2] :
                  ( produc1212179418963815907set_c2
                  @ ( produc6418488838319782393set_b2
                    @ ^ [X: b1,Z: b2] :
                        ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M1 )
                        @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ Zs ) @ M1 )
                        @ ( lookup_b1_set_b2 @ M1 @ X ) )
                    @ ( f1 @ Kv ) )
                  @ ( produc4822369076420559349set_c2
                    @ ^ [X: c1,Z: c2] :
                        ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M2 )
                        @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ Zs ) @ M2 )
                        @ ( lookup_c1_set_c2 @ M2 @ X ) )
                    @ ( f2 @ Kv ) ) ) )
          @ t
          @ ( produc1212179418963815907set_c2 @ empty_b1_set_b2 @ empty_c1_set_c2 ) ) ) )
    = ( set_as_map_b1_b2 @ ( image_1398015525354814723_b1_b2 @ f1 @ ( set_RB6720226376580087827_a1_a2 @ t ) ) ) ) ).

% \<open>Mapping.lookup (fst (RBT_Set2.fold (\<lambda>kv (m1, m2). (case f1 kv of (x, z) \<Rightarrow> case Mapping.lookup m1 x of None \<Rightarrow> Mapping.update x {z} m1 | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m1, case f2 kv of (x, z) \<Rightarrow> case Mapping.lookup m2 x of None \<Rightarrow> Mapping.update x {z} m2 | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m2)) t (Mapping.empty, Mapping.empty))) = set_as_map (f1 ` RBT_set t)\<close>
thf(fact_1__092_060open_062Mapping_Olookup_A_Isnd_A_IRBT__Set2_Ofold_A_I_092_060lambda_062kv_A_Im1_M_Am2_J_O_A_Icase_Af1_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am1_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am1_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am1_M_Acase_Af2_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am2_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am2_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am2_J_J_At_A_IMapping_Oempty_M_AMapping_Oempty_J_J_J_A_061_Aset__as__map_A_If2_A_096_ARBT__set_At_J_092_060close_062,axiom,
    ( ( lookup_c1_set_c2
      @ ( produc6032943676959796241set_c2
        @ ( rBT_fo5132325507301440204set_c2
          @ ^ [Kv: product_prod_a1_a2] :
              ( produc4732439310506902963set_c2
              @ ^ [M1: mapping_b1_set_b2,M2: mapping_c1_set_c2] :
                  ( produc1212179418963815907set_c2
                  @ ( produc6418488838319782393set_b2
                    @ ^ [X: b1,Z: b2] :
                        ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M1 )
                        @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ Zs ) @ M1 )
                        @ ( lookup_b1_set_b2 @ M1 @ X ) )
                    @ ( f1 @ Kv ) )
                  @ ( produc4822369076420559349set_c2
                    @ ^ [X: c1,Z: c2] :
                        ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M2 )
                        @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ Zs ) @ M2 )
                        @ ( lookup_c1_set_c2 @ M2 @ X ) )
                    @ ( f2 @ Kv ) ) ) )
          @ t
          @ ( produc1212179418963815907set_c2 @ empty_b1_set_b2 @ empty_c1_set_c2 ) ) ) )
    = ( set_as_map_c1_c2 @ ( image_762648812255944833_c1_c2 @ f2 @ ( set_RB6720226376580087827_a1_a2 @ t ) ) ) ) ).

% \<open>Mapping.lookup (snd (RBT_Set2.fold (\<lambda>kv (m1, m2). (case f1 kv of (x, z) \<Rightarrow> case Mapping.lookup m1 x of None \<Rightarrow> Mapping.update x {z} m1 | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m1, case f2 kv of (x, z) \<Rightarrow> case Mapping.lookup m2 x of None \<Rightarrow> Mapping.update x {z} m2 | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m2)) t (Mapping.empty, Mapping.empty))) = set_as_map (f2 ` RBT_set t)\<close>
thf(fact_2_Some,axiom,
    ( ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 )
    = ( some_P6364418062025833395_order @ a ) ) ).

% Some
thf(fact_3__092_060open_062RBT__Set2_Ofold_A_I_092_060lambda_062kv_A_Im1_M_Am2_J_O_A_Icase_Af1_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am1_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am1_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am1_M_Acase_Af2_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am2_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am2_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am2_J_J_At_A_IMapping_Oempty_M_AMapping_Oempty_J_A_061_A_IRBT__Set2_Ofold_A_I_092_060lambda_062kv_Am_O_Acase_Af1_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am_J_At_AMapping_Oempty_M_ARBT__Set2_Ofold_A_I_092_060lambda_062kv_Am_O_Acase_Af2_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am_J_At_AMapping_Oempty_J_092_060close_062,axiom,
    ( ( rBT_fo5132325507301440204set_c2
      @ ^ [Kv: product_prod_a1_a2] :
          ( produc4732439310506902963set_c2
          @ ^ [M1: mapping_b1_set_b2,M2: mapping_c1_set_c2] :
              ( produc1212179418963815907set_c2
              @ ( produc6418488838319782393set_b2
                @ ^ [X: b1,Z: b2] :
                    ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M1 )
                    @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ Zs ) @ M1 )
                    @ ( lookup_b1_set_b2 @ M1 @ X ) )
                @ ( f1 @ Kv ) )
              @ ( produc4822369076420559349set_c2
                @ ^ [X: c1,Z: c2] :
                    ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M2 )
                    @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ Zs ) @ M2 )
                    @ ( lookup_c1_set_c2 @ M2 @ X ) )
                @ ( f2 @ Kv ) ) ) )
      @ t
      @ ( produc1212179418963815907set_c2 @ empty_b1_set_b2 @ empty_c1_set_c2 ) )
    = ( produc1212179418963815907set_c2
      @ ( rBT_fo4244449053837635077set_b2
        @ ^ [Kv: product_prod_a1_a2,M: mapping_b1_set_b2] :
            ( produc6418488838319782393set_b2
            @ ^ [X: b1,Z: b2] :
                ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M )
                @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ Zs ) @ M )
                @ ( lookup_b1_set_b2 @ M @ X ) )
            @ ( f1 @ Kv ) )
        @ t
        @ empty_b1_set_b2 )
      @ ( rBT_fo7691525479720920579set_c2
        @ ^ [Kv: product_prod_a1_a2,M: mapping_c1_set_c2] :
            ( produc4822369076420559349set_c2
            @ ^ [X: c1,Z: c2] :
                ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M )
                @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ Zs ) @ M )
                @ ( lookup_c1_set_c2 @ M @ X ) )
            @ ( f2 @ Kv ) )
        @ t
        @ empty_c1_set_c2 ) ) ) ).

% \<open>RBT_Set2.fold (\<lambda>kv (m1, m2). (case f1 kv of (x, z) \<Rightarrow> case Mapping.lookup m1 x of None \<Rightarrow> Mapping.update x {z} m1 | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m1, case f2 kv of (x, z) \<Rightarrow> case Mapping.lookup m2 x of None \<Rightarrow> Mapping.update x {z} m2 | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m2)) t (Mapping.empty, Mapping.empty) = (RBT_Set2.fold (\<lambda>kv m. case f1 kv of (x, z) \<Rightarrow> case Mapping.lookup m x of None \<Rightarrow> Mapping.update x {z} m | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m) t Mapping.empty, RBT_Set2.fold (\<lambda>kv m. case f2 kv of (x, z) \<Rightarrow> case Mapping.lookup m x of None \<Rightarrow> Mapping.update x {z} m | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m) t Mapping.empty)\<close>
thf(fact_4_dual__set__as__map__image__def,axiom,
    ( test_S6443642256665625299set_c2
    = ( ^ [Xs: set_Pr1660683266160182027set_c2,F1: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,F2: produc4061897789176782763set_c2 > produc4061897789176782763set_c2] : ( produc844738797994375799set_c2 @ ( set_as574257606533379650set_c2 @ ( image_7945144516369962181set_c2 @ F1 @ Xs ) ) @ ( set_as574257606533379650set_c2 @ ( image_7945144516369962181set_c2 @ F2 @ Xs ) ) ) ) ) ).

% dual_set_as_map_image_def
thf(fact_5_dual__set__as__map__image__def,axiom,
    ( test_S4625532478866329070_b1_b2
    = ( ^ [Xs: set_Pr1660683266160182027set_c2,F1: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,F2: produc4061897789176782763set_c2 > product_prod_b1_b2] : ( produc3671601195459724562set_b2 @ ( set_as574257606533379650set_c2 @ ( image_7945144516369962181set_c2 @ F1 @ Xs ) ) @ ( set_as_map_b1_b2 @ ( image_6994757892443185248_b1_b2 @ F2 @ Xs ) ) ) ) ) ).

% dual_set_as_map_image_def
thf(fact_6_dual__set__as__map__image__def,axiom,
    ( test_S3989883478261407980_c1_c2
    = ( ^ [Xs: set_Pr1660683266160182027set_c2,F1: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,F2: produc4061897789176782763set_c2 > product_prod_c1_c2] : ( produc187046198985622288set_c2 @ ( set_as574257606533379650set_c2 @ ( image_7945144516369962181set_c2 @ F1 @ Xs ) ) @ ( set_as_map_c1_c2 @ ( image_6359391179344315358_c1_c2 @ F2 @ Xs ) ) ) ) ) ).

% dual_set_as_map_image_def
thf(fact_7_dual__set__as__map__image__def,axiom,
    ( test_S1219458079195954926set_c2
    = ( ^ [Xs: set_Pr1660683266160182027set_c2,F1: produc4061897789176782763set_c2 > product_prod_b1_b2,F2: produc4061897789176782763set_c2 > produc4061897789176782763set_c2] : ( produc8529309635288108306set_c2 @ ( set_as_map_b1_b2 @ ( image_6994757892443185248_b1_b2 @ F1 @ Xs ) ) @ ( set_as574257606533379650set_c2 @ ( image_7945144516369962181set_c2 @ F2 @ Xs ) ) ) ) ) ).

% dual_set_as_map_image_def
thf(fact_8_dual__set__as__map__image__def,axiom,
    ( test_S6074054486132820972set_c2
    = ( ^ [Xs: set_Pr1660683266160182027set_c2,F1: produc4061897789176782763set_c2 > product_prod_c1_c2,F2: produc4061897789176782763set_c2 > produc4061897789176782763set_c2] : ( produc181612670030289680set_c2 @ ( set_as_map_c1_c2 @ ( image_6359391179344315358_c1_c2 @ F1 @ Xs ) ) @ ( set_as574257606533379650set_c2 @ ( image_7945144516369962181set_c2 @ F2 @ Xs ) ) ) ) ) ).

% dual_set_as_map_image_def
thf(fact_9_dual__set__as__map__image__def,axiom,
    ( test_S917631008590620710_b1_b2
    = ( ^ [Xs: set_Pr9206071548465018024_a1_a2,F1: product_prod_a1_a2 > product_prod_b1_b2,F2: product_prod_a1_a2 > product_prod_b1_b2] : ( produc4375337561607790509set_b2 @ ( set_as_map_b1_b2 @ ( image_1398015525354814723_b1_b2 @ F1 @ Xs ) ) @ ( set_as_map_b1_b2 @ ( image_1398015525354814723_b1_b2 @ F2 @ Xs ) ) ) ) ) ).

% dual_set_as_map_image_def
thf(fact_10_dual__set__as__map__image__def,axiom,
    ( test_S8332919854771946788_b1_b2
    = ( ^ [Xs: set_Pr9206071548465018024_a1_a2,F1: product_prod_a1_a2 > product_prod_c1_c2,F2: product_prod_a1_a2 > product_prod_b1_b2] : ( produc4506454564149116331set_b2 @ ( set_as_map_c1_c2 @ ( image_762648812255944833_c1_c2 @ F1 @ Xs ) ) @ ( set_as_map_b1_b2 @ ( image_1398015525354814723_b1_b2 @ F2 @ Xs ) ) ) ) ) ).

% dual_set_as_map_image_def
thf(fact_11_dual__set__as__map__image__def,axiom,
    ( test_S7697270854167025698_c1_c2
    = ( ^ [Xs: set_Pr9206071548465018024_a1_a2,F1: product_prod_a1_a2 > product_prod_c1_c2,F2: product_prod_a1_a2 > product_prod_c1_c2] : ( produc1021899567675014057set_c2 @ ( set_as_map_c1_c2 @ ( image_762648812255944833_c1_c2 @ F1 @ Xs ) ) @ ( set_as_map_c1_c2 @ ( image_762648812255944833_c1_c2 @ F2 @ Xs ) ) ) ) ) ).

% dual_set_as_map_image_def
thf(fact_12_dual__set__as__map__image__def,axiom,
    ( test_S281982007985699620_c1_c2
    = ( ^ [Xs: set_Pr9206071548465018024_a1_a2,F1: product_prod_a1_a2 > product_prod_b1_b2,F2: product_prod_a1_a2 > product_prod_c1_c2] : ( produc890782565133688235set_c2 @ ( set_as_map_b1_b2 @ ( image_1398015525354814723_b1_b2 @ F1 @ Xs ) ) @ ( set_as_map_c1_c2 @ ( image_762648812255944833_c1_c2 @ F2 @ Xs ) ) ) ) ) ).

% dual_set_as_map_image_def
thf(fact_13_pair__imageI,axiom,
    ! [A: a1,B: a2,A2: set_Pr9206071548465018024_a1_a2,F: a1 > a2 > product_prod_b1_b2] :
      ( ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ A @ B ) @ A2 )
     => ( member2075749735315954927_b1_b2 @ ( F @ A @ B ) @ ( image_1398015525354814723_b1_b2 @ ( produc1521269801170193905_b1_b2 @ F ) @ A2 ) ) ) ).

% pair_imageI
thf(fact_14_pair__imageI,axiom,
    ! [A: a1,B: a2,A2: set_Pr9206071548465018024_a1_a2,F: a1 > a2 > product_prod_c1_c2] :
      ( ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ A @ B ) @ A2 )
     => ( member1440383022217085037_c1_c2 @ ( F @ A @ B ) @ ( image_762648812255944833_c1_c2 @ ( produc885903088071324015_c1_c2 @ F ) @ A2 ) ) ) ).

% pair_imageI
thf(fact_15_pair__imageI,axiom,
    ! [A: b1,B: b2,A2: set_Pr4592484330697324838_b1_b2,F: b1 > b2 > mapping_b1_set_b2] :
      ( ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ A @ B ) @ A2 )
     => ( member6117332676589958525set_b2 @ ( F @ A @ B ) @ ( image_6686293874852392167set_b2 @ ( produc6418488838319782393set_b2 @ F ) @ A2 ) ) ) ).

% pair_imageI
thf(fact_16_pair__imageI,axiom,
    ! [A: c1,B: c2,A2: set_Pr9202269149784407460_c1_c2,F: c1 > c2 > mapping_c1_set_c2] :
      ( ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ A @ B ) @ A2 )
     => ( member341037065618468219set_c2 @ ( F @ A @ B ) @ ( image_5984881132562613603set_c2 @ ( produc4822369076420559349set_c2 @ F ) @ A2 ) ) ) ).

% pair_imageI
thf(fact_17_pair__imageI,axiom,
    ! [A: mapping_b1_set_b2,B: mapping_c1_set_c2,A2: set_Pr1660683266160182027set_c2,F: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2] :
      ( ( member419137155788712276set_c2 @ ( produc1212179418963815907set_c2 @ A @ B ) @ A2 )
     => ( member419137155788712276set_c2 @ ( F @ A @ B ) @ ( image_7945144516369962181set_c2 @ ( produc4732439310506902963set_c2 @ F ) @ A2 ) ) ) ).

% pair_imageI
thf(fact_18_pair__imageI,axiom,
    ! [A: c1,B: c2,A2: set_Pr9202269149784407460_c1_c2,F: c1 > c2 > product_prod_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ A @ B ) @ A2 )
     => ( member1440383022217085037_c1_c2 @ ( F @ A @ B ) @ ( image_4046053779558312581_c1_c2 @ ( produc7856115553599036531_c1_c2 @ F ) @ A2 ) ) ) ).

% pair_imageI
thf(fact_19_pair__imageI,axiom,
    ! [A: c1,B: c2,A2: set_Pr9202269149784407460_c1_c2,F: c1 > c2 > product_prod_b1_b2] :
      ( ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ A @ B ) @ A2 )
     => ( member2075749735315954927_b1_b2 @ ( F @ A @ B ) @ ( image_4681420492657182471_b1_b2 @ ( produc8491482266697906421_b1_b2 @ F ) @ A2 ) ) ) ).

% pair_imageI
thf(fact_20_pair__imageI,axiom,
    ! [A: c1,B: c2,A2: set_Pr9202269149784407460_c1_c2,F: c1 > c2 > product_prod_a1_a2] :
      ( ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ A @ B ) @ A2 )
     => ( member2711116448414824817_a1_a2 @ ( F @ A @ B ) @ ( image_5316787205756052361_a1_a2 @ ( produc9126848979796776311_a1_a2 @ F ) @ A2 ) ) ) ).

% pair_imageI
thf(fact_21_pair__imageI,axiom,
    ! [A: b1,B: b2,A2: set_Pr4592484330697324838_b1_b2,F: b1 > b2 > product_prod_c1_c2] :
      ( ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ A @ B ) @ A2 )
     => ( member1440383022217085037_c1_c2 @ ( F @ A @ B ) @ ( image_7016037314334516611_c1_c2 @ ( produc4371009320835180273_c1_c2 @ F ) @ A2 ) ) ) ).

% pair_imageI
thf(fact_22_pair__imageI,axiom,
    ! [A: b1,B: b2,A2: set_Pr4592484330697324838_b1_b2,F: b1 > b2 > product_prod_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ A @ B ) @ A2 )
     => ( member2075749735315954927_b1_b2 @ ( F @ A @ B ) @ ( image_7651404027433386501_b1_b2 @ ( produc5006376033934050163_b1_b2 @ F ) @ A2 ) ) ) ).

% pair_imageI
thf(fact_23_prod_Ocollapse,axiom,
    ! [Prod: produc8629413652255616883set_b2] :
      ( ( produc4506454564149116331set_b2 @ ( produc6802794336065251735set_b2 @ Prod ) @ ( produc8191373782972559833set_b2 @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_24_prod_Ocollapse,axiom,
    ! [Prod: produc8498296649714291061set_b2] :
      ( ( produc4375337561607790509set_b2 @ ( produc6671677333523925913set_b2 @ Prod ) @ ( produc8060256780431234011set_b2 @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_25_prod_Ocollapse,axiom,
    ! [Prod: product_prod_c1_c2] :
      ( ( product_Pair_c1_c2 @ ( product_fst_c1_c2 @ Prod ) @ ( product_snd_c1_c2 @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_26_prod_Ocollapse,axiom,
    ! [Prod: product_prod_b1_b2] :
      ( ( product_Pair_b1_b2 @ ( product_fst_b1_b2 @ Prod ) @ ( product_snd_b1_b2 @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_27_prod_Ocollapse,axiom,
    ! [Prod: product_prod_a1_a2] :
      ( ( product_Pair_a1_a2 @ ( product_fst_a1_a2 @ Prod ) @ ( product_snd_a1_a2 @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_28_prod_Ocollapse,axiom,
    ! [Prod: produc2702059613074419827set_c2] :
      ( ( produc890782565133688235set_c2 @ ( produc3187122337049823639set_c2 @ Prod ) @ ( produc4575701783957131737set_c2 @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_29_prod_Ocollapse,axiom,
    ! [Prod: produc4061897789176782763set_c2] :
      ( ( produc1212179418963815907set_c2 @ ( produc4038274906788240847set_c2 @ Prod ) @ ( produc6032943676959796241set_c2 @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_30_singleton__conv,axiom,
    ! [A: nat] :
      ( ( collect_nat
        @ ^ [X: nat] : ( X = A ) )
      = ( insert_nat @ A @ bot_bot_set_nat ) ) ).

% singleton_conv
thf(fact_31_singleton__conv,axiom,
    ! [A: b2] :
      ( ( collect_b2
        @ ^ [X: b2] : ( X = A ) )
      = ( insert_b2 @ A @ bot_bot_set_b2 ) ) ).

% singleton_conv
thf(fact_32_singleton__conv,axiom,
    ! [A: c2] :
      ( ( collect_c2
        @ ^ [X: c2] : ( X = A ) )
      = ( insert_c2 @ A @ bot_bot_set_c2 ) ) ).

% singleton_conv
thf(fact_33_singleton__conv2,axiom,
    ! [A: nat] :
      ( ( collect_nat
        @ ( ^ [Y: nat,Z2: nat] : ( Y = Z2 )
          @ A ) )
      = ( insert_nat @ A @ bot_bot_set_nat ) ) ).

% singleton_conv2
thf(fact_34_singleton__conv2,axiom,
    ! [A: b2] :
      ( ( collect_b2
        @ ( ^ [Y: b2,Z2: b2] : ( Y = Z2 )
          @ A ) )
      = ( insert_b2 @ A @ bot_bot_set_b2 ) ) ).

% singleton_conv2
thf(fact_35_singleton__conv2,axiom,
    ! [A: c2] :
      ( ( collect_c2
        @ ( ^ [Y: c2,Z2: c2] : ( Y = Z2 )
          @ A ) )
      = ( insert_c2 @ A @ bot_bot_set_c2 ) ) ).

% singleton_conv2
thf(fact_36_case__prod__conv,axiom,
    ! [F: a1 > a2 > product_prod_c1_c2,A: a1,B: a2] :
      ( ( produc885903088071324015_c1_c2 @ F @ ( product_Pair_a1_a2 @ A @ B ) )
      = ( F @ A @ B ) ) ).

% case_prod_conv
thf(fact_37_case__prod__conv,axiom,
    ! [F: a1 > a2 > product_prod_b1_b2,A: a1,B: a2] :
      ( ( produc1521269801170193905_b1_b2 @ F @ ( product_Pair_a1_a2 @ A @ B ) )
      = ( F @ A @ B ) ) ).

% case_prod_conv
thf(fact_38_case__prod__conv,axiom,
    ! [F: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,A: mapping_b1_set_b2,B: mapping_c1_set_c2] :
      ( ( produc4732439310506902963set_c2 @ F @ ( produc1212179418963815907set_c2 @ A @ B ) )
      = ( F @ A @ B ) ) ).

% case_prod_conv
thf(fact_39_case__prod__conv,axiom,
    ! [F: b1 > b2 > mapping_b1_set_b2,A: b1,B: b2] :
      ( ( produc6418488838319782393set_b2 @ F @ ( product_Pair_b1_b2 @ A @ B ) )
      = ( F @ A @ B ) ) ).

% case_prod_conv
thf(fact_40_case__prod__conv,axiom,
    ! [F: c1 > c2 > mapping_c1_set_c2,A: c1,B: c2] :
      ( ( produc4822369076420559349set_c2 @ F @ ( product_Pair_c1_c2 @ A @ B ) )
      = ( F @ A @ B ) ) ).

% case_prod_conv
thf(fact_41_Mapping_Olookup__update__neq,axiom,
    ! [K: b1,K2: b1,V: set_b2,M3: mapping_b1_set_b2] :
      ( ( K != K2 )
     => ( ( lookup_b1_set_b2 @ ( update_b1_set_b2 @ K @ V @ M3 ) @ K2 )
        = ( lookup_b1_set_b2 @ M3 @ K2 ) ) ) ).

% Mapping.lookup_update_neq
thf(fact_42_Mapping_Olookup__update__neq,axiom,
    ! [K: c1,K2: c1,V: set_c2,M3: mapping_c1_set_c2] :
      ( ( K != K2 )
     => ( ( lookup_c1_set_c2 @ ( update_c1_set_c2 @ K @ V @ M3 ) @ K2 )
        = ( lookup_c1_set_c2 @ M3 @ K2 ) ) ) ).

% Mapping.lookup_update_neq
thf(fact_43_singletonI,axiom,
    ! [A: product_prod_c1_c2] : ( member1440383022217085037_c1_c2 @ A @ ( insert7158109610518197396_c1_c2 @ A @ bot_bo745477178175700496_c1_c2 ) ) ).

% singletonI
thf(fact_44_singletonI,axiom,
    ! [A: product_prod_b1_b2] : ( member2075749735315954927_b1_b2 @ A @ ( insert7793476323617067286_b1_b2 @ A @ bot_bo5359064395943393682_b1_b2 ) ) ).

% singletonI
thf(fact_45_singletonI,axiom,
    ! [A: product_prod_a1_a2] : ( member2711116448414824817_a1_a2 @ A @ ( insert8428843036715937176_a1_a2 @ A @ bot_bo749279576856311060_a1_a2 ) ) ).

% singletonI
thf(fact_46_singletonI,axiom,
    ! [A: mapping_c1_set_c2] : ( member341037065618468219set_c2 @ A @ ( insert88652402460333204set_c2 @ A @ bot_bo7584170878874662190set_c2 ) ) ).

% singletonI
thf(fact_47_singletonI,axiom,
    ! [A: mapping_b1_set_b2] : ( member6117332676589958525set_b2 @ A @ ( insert5864948013431823510set_b2 @ A @ bot_bo6532501642720468016set_b2 ) ) ).

% singletonI
thf(fact_48_singletonI,axiom,
    ! [A: b2] : ( member_b2 @ A @ ( insert_b2 @ A @ bot_bot_set_b2 ) ) ).

% singletonI
thf(fact_49_singletonI,axiom,
    ! [A: c2] : ( member_c2 @ A @ ( insert_c2 @ A @ bot_bot_set_c2 ) ) ).

% singletonI
thf(fact_50_singletonI,axiom,
    ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).

% singletonI
thf(fact_51_image__insert,axiom,
    ! [F: b2 > b2,A: b2,B2: set_b2] :
      ( ( image_b2_b22 @ F @ ( insert_b2 @ A @ B2 ) )
      = ( insert_b2 @ ( F @ A ) @ ( image_b2_b22 @ F @ B2 ) ) ) ).

% image_insert
thf(fact_52_image__insert,axiom,
    ! [F: b2 > c2,A: b2,B2: set_b2] :
      ( ( image_b2_c22 @ F @ ( insert_b2 @ A @ B2 ) )
      = ( insert_c2 @ ( F @ A ) @ ( image_b2_c22 @ F @ B2 ) ) ) ).

% image_insert
thf(fact_53_image__insert,axiom,
    ! [F: b2 > nat,A: b2,B2: set_b2] :
      ( ( image_b2_nat2 @ F @ ( insert_b2 @ A @ B2 ) )
      = ( insert_nat @ ( F @ A ) @ ( image_b2_nat2 @ F @ B2 ) ) ) ).

% image_insert
thf(fact_54_image__insert,axiom,
    ! [F: c2 > b2,A: c2,B2: set_c2] :
      ( ( image_c2_b22 @ F @ ( insert_c2 @ A @ B2 ) )
      = ( insert_b2 @ ( F @ A ) @ ( image_c2_b22 @ F @ B2 ) ) ) ).

% image_insert
thf(fact_55_image__insert,axiom,
    ! [F: c2 > c2,A: c2,B2: set_c2] :
      ( ( image_c2_c22 @ F @ ( insert_c2 @ A @ B2 ) )
      = ( insert_c2 @ ( F @ A ) @ ( image_c2_c22 @ F @ B2 ) ) ) ).

% image_insert
thf(fact_56_image__insert,axiom,
    ! [F: c2 > nat,A: c2,B2: set_c2] :
      ( ( image_c2_nat2 @ F @ ( insert_c2 @ A @ B2 ) )
      = ( insert_nat @ ( F @ A ) @ ( image_c2_nat2 @ F @ B2 ) ) ) ).

% image_insert
thf(fact_57_image__insert,axiom,
    ! [F: nat > b2,A: nat,B2: set_nat] :
      ( ( image_nat_b22 @ F @ ( insert_nat @ A @ B2 ) )
      = ( insert_b2 @ ( F @ A ) @ ( image_nat_b22 @ F @ B2 ) ) ) ).

% image_insert
thf(fact_58_image__insert,axiom,
    ! [F: nat > c2,A: nat,B2: set_nat] :
      ( ( image_nat_c22 @ F @ ( insert_nat @ A @ B2 ) )
      = ( insert_c2 @ ( F @ A ) @ ( image_nat_c22 @ F @ B2 ) ) ) ).

% image_insert
thf(fact_59_image__insert,axiom,
    ! [F: nat > nat,A: nat,B2: set_nat] :
      ( ( image_nat_nat2 @ F @ ( insert_nat @ A @ B2 ) )
      = ( insert_nat @ ( F @ A ) @ ( image_nat_nat2 @ F @ B2 ) ) ) ).

% image_insert
thf(fact_60_image__insert,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2,A: product_prod_a1_a2,B2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_1398015525354814723_b1_b2 @ F @ ( insert8428843036715937176_a1_a2 @ A @ B2 ) )
      = ( insert7793476323617067286_b1_b2 @ ( F @ A ) @ ( image_1398015525354814723_b1_b2 @ F @ B2 ) ) ) ).

% image_insert
thf(fact_61_insert__image,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,F: product_prod_c1_c2 > b2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( insert_b2 @ ( F @ X2 ) @ ( image_5961845353661638642_c2_b2 @ F @ A2 ) )
        = ( image_5961845353661638642_c2_b2 @ F @ A2 ) ) ) ).

% insert_image
thf(fact_62_insert__image,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,F: product_prod_c1_c2 > c2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( insert_c2 @ ( F @ X2 ) @ ( image_5961845353661704241_c2_c2 @ F @ A2 ) )
        = ( image_5961845353661704241_c2_c2 @ F @ A2 ) ) ) ).

% insert_image
thf(fact_63_insert__image,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,F: product_prod_c1_c2 > nat] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( insert_nat @ ( F @ X2 ) @ ( image_1283518940507385935c2_nat @ F @ A2 ) )
        = ( image_1283518940507385935c2_nat @ F @ A2 ) ) ) ).

% insert_image
thf(fact_64_insert__image,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,F: product_prod_b1_b2 > b2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ( insert_b2 @ ( F @ X2 ) @ ( image_2033501871846498164_b2_b2 @ F @ A2 ) )
        = ( image_2033501871846498164_b2_b2 @ F @ A2 ) ) ) ).

% insert_image
thf(fact_65_insert__image,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,F: product_prod_b1_b2 > c2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ( insert_c2 @ ( F @ X2 ) @ ( image_2033501871846563763_b2_c2 @ F @ A2 ) )
        = ( image_2033501871846563763_b2_c2 @ F @ A2 ) ) ) ).

% insert_image
thf(fact_66_insert__image,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,F: product_prod_b1_b2 > nat] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ( insert_nat @ ( F @ X2 ) @ ( image_2104430070814229713b2_nat @ F @ A2 ) )
        = ( image_2104430070814229713b2_nat @ F @ A2 ) ) ) ).

% insert_image
thf(fact_67_insert__image,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,F: product_prod_a1_a2 > b2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ( insert_b2 @ ( F @ X2 ) @ ( image_7328530426886133494_a2_b2 @ F @ A2 ) )
        = ( image_7328530426886133494_a2_b2 @ F @ A2 ) ) ) ).

% insert_image
thf(fact_68_insert__image,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,F: product_prod_a1_a2 > c2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ( insert_c2 @ ( F @ X2 ) @ ( image_7328530426886199093_a2_c2 @ F @ A2 ) )
        = ( image_7328530426886199093_a2_c2 @ F @ A2 ) ) ) ).

% insert_image
thf(fact_69_insert__image,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,F: product_prod_a1_a2 > nat] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ( insert_nat @ ( F @ X2 ) @ ( image_2925341201121073491a2_nat @ F @ A2 ) )
        = ( image_2925341201121073491a2_nat @ F @ A2 ) ) ) ).

% insert_image
thf(fact_70_insert__image,axiom,
    ! [X2: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2,F: mapping_c1_set_c2 > b2] :
      ( ( member341037065618468219set_c2 @ X2 @ A2 )
     => ( ( insert_b2 @ ( F @ X2 ) @ ( image_1755057678288551646_c2_b2 @ F @ A2 ) )
        = ( image_1755057678288551646_c2_b2 @ F @ A2 ) ) ) ).

% insert_image
thf(fact_71_old_Oprod_Oinject,axiom,
    ! [A: b1 > option_set_b2,B: c1 > option_set_c2,A3: b1 > option_set_b2,B3: c1 > option_set_c2] :
      ( ( ( produc890782565133688235set_c2 @ A @ B )
        = ( produc890782565133688235set_c2 @ A3 @ B3 ) )
      = ( ( A = A3 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
thf(fact_72_old_Oprod_Oinject,axiom,
    ! [A: mapping_b1_set_b2,B: mapping_c1_set_c2,A3: mapping_b1_set_b2,B3: mapping_c1_set_c2] :
      ( ( ( produc1212179418963815907set_c2 @ A @ B )
        = ( produc1212179418963815907set_c2 @ A3 @ B3 ) )
      = ( ( A = A3 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
thf(fact_73_old_Oprod_Oinject,axiom,
    ! [A: c1 > option_set_c2,B: b1 > option_set_b2,A3: c1 > option_set_c2,B3: b1 > option_set_b2] :
      ( ( ( produc4506454564149116331set_b2 @ A @ B )
        = ( produc4506454564149116331set_b2 @ A3 @ B3 ) )
      = ( ( A = A3 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
thf(fact_74_old_Oprod_Oinject,axiom,
    ! [A: b1 > option_set_b2,B: b1 > option_set_b2,A3: b1 > option_set_b2,B3: b1 > option_set_b2] :
      ( ( ( produc4375337561607790509set_b2 @ A @ B )
        = ( produc4375337561607790509set_b2 @ A3 @ B3 ) )
      = ( ( A = A3 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
thf(fact_75_old_Oprod_Oinject,axiom,
    ! [A: c1,B: c2,A3: c1,B3: c2] :
      ( ( ( product_Pair_c1_c2 @ A @ B )
        = ( product_Pair_c1_c2 @ A3 @ B3 ) )
      = ( ( A = A3 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
thf(fact_76_old_Oprod_Oinject,axiom,
    ! [A: b1,B: b2,A3: b1,B3: b2] :
      ( ( ( product_Pair_b1_b2 @ A @ B )
        = ( product_Pair_b1_b2 @ A3 @ B3 ) )
      = ( ( A = A3 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
thf(fact_77_old_Oprod_Oinject,axiom,
    ! [A: a1,B: a2,A3: a1,B3: a2] :
      ( ( ( product_Pair_a1_a2 @ A @ B )
        = ( product_Pair_a1_a2 @ A3 @ B3 ) )
      = ( ( A = A3 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
thf(fact_78_prod_Oinject,axiom,
    ! [X1: b1 > option_set_b2,X22: c1 > option_set_c2,Y1: b1 > option_set_b2,Y2: c1 > option_set_c2] :
      ( ( ( produc890782565133688235set_c2 @ X1 @ X22 )
        = ( produc890782565133688235set_c2 @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_79_prod_Oinject,axiom,
    ! [X1: mapping_b1_set_b2,X22: mapping_c1_set_c2,Y1: mapping_b1_set_b2,Y2: mapping_c1_set_c2] :
      ( ( ( produc1212179418963815907set_c2 @ X1 @ X22 )
        = ( produc1212179418963815907set_c2 @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_80_prod_Oinject,axiom,
    ! [X1: c1 > option_set_c2,X22: b1 > option_set_b2,Y1: c1 > option_set_c2,Y2: b1 > option_set_b2] :
      ( ( ( produc4506454564149116331set_b2 @ X1 @ X22 )
        = ( produc4506454564149116331set_b2 @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_81_prod_Oinject,axiom,
    ! [X1: b1 > option_set_b2,X22: b1 > option_set_b2,Y1: b1 > option_set_b2,Y2: b1 > option_set_b2] :
      ( ( ( produc4375337561607790509set_b2 @ X1 @ X22 )
        = ( produc4375337561607790509set_b2 @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_82_prod_Oinject,axiom,
    ! [X1: c1,X22: c2,Y1: c1,Y2: c2] :
      ( ( ( product_Pair_c1_c2 @ X1 @ X22 )
        = ( product_Pair_c1_c2 @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_83_prod_Oinject,axiom,
    ! [X1: b1,X22: b2,Y1: b1,Y2: b2] :
      ( ( ( product_Pair_b1_b2 @ X1 @ X22 )
        = ( product_Pair_b1_b2 @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_84_prod_Oinject,axiom,
    ! [X1: a1,X22: a2,Y1: a1,Y2: a2] :
      ( ( ( product_Pair_a1_a2 @ X1 @ X22 )
        = ( product_Pair_a1_a2 @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_85_image__eqI,axiom,
    ! [B: product_prod_c1_c2,F: product_prod_c1_c2 > product_prod_c1_c2,X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_4046053779558312581_c1_c2 @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_86_image__eqI,axiom,
    ! [B: product_prod_b1_b2,F: product_prod_c1_c2 > product_prod_b1_b2,X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
       => ( member2075749735315954927_b1_b2 @ B @ ( image_4681420492657182471_b1_b2 @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_87_image__eqI,axiom,
    ! [B: product_prod_a1_a2,F: product_prod_c1_c2 > product_prod_a1_a2,X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
       => ( member2711116448414824817_a1_a2 @ B @ ( image_5316787205756052361_a1_a2 @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_88_image__eqI,axiom,
    ! [B: product_prod_c1_c2,F: product_prod_b1_b2 > product_prod_c1_c2,X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_7016037314334516611_c1_c2 @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_89_image__eqI,axiom,
    ! [B: product_prod_b1_b2,F: product_prod_b1_b2 > product_prod_b1_b2,X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
       => ( member2075749735315954927_b1_b2 @ B @ ( image_7651404027433386501_b1_b2 @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_90_image__eqI,axiom,
    ! [B: product_prod_a1_a2,F: product_prod_b1_b2 > product_prod_a1_a2,X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
       => ( member2711116448414824817_a1_a2 @ B @ ( image_8286770740532256391_a1_a2 @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_91_image__eqI,axiom,
    ! [B: product_prod_c1_c2,F: product_prod_a1_a2 > product_prod_c1_c2,X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_762648812255944833_c1_c2 @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_92_image__eqI,axiom,
    ! [B: product_prod_b1_b2,F: product_prod_a1_a2 > product_prod_b1_b2,X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
       => ( member2075749735315954927_b1_b2 @ B @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_93_image__eqI,axiom,
    ! [B: product_prod_a1_a2,F: product_prod_a1_a2 > product_prod_a1_a2,X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
       => ( member2711116448414824817_a1_a2 @ B @ ( image_2033382238453684613_a1_a2 @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_94_image__eqI,axiom,
    ! [B: mapping_c1_set_c2,F: product_prod_c1_c2 > mapping_c1_set_c2,X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
       => ( member341037065618468219set_c2 @ B @ ( image_5984881132562613603set_c2 @ F @ A2 ) ) ) ) ).

% image_eqI
thf(fact_95_empty__Collect__eq,axiom,
    ! [P: b2 > $o] :
      ( ( bot_bot_set_b2
        = ( collect_b2 @ P ) )
      = ( ! [X: b2] :
            ~ ( P @ X ) ) ) ).

% empty_Collect_eq
thf(fact_96_empty__Collect__eq,axiom,
    ! [P: c2 > $o] :
      ( ( bot_bot_set_c2
        = ( collect_c2 @ P ) )
      = ( ! [X: c2] :
            ~ ( P @ X ) ) ) ).

% empty_Collect_eq
thf(fact_97_empty__Collect__eq,axiom,
    ! [P: nat > $o] :
      ( ( bot_bot_set_nat
        = ( collect_nat @ P ) )
      = ( ! [X: nat] :
            ~ ( P @ X ) ) ) ).

% empty_Collect_eq
thf(fact_98_Collect__empty__eq,axiom,
    ! [P: b2 > $o] :
      ( ( ( collect_b2 @ P )
        = bot_bot_set_b2 )
      = ( ! [X: b2] :
            ~ ( P @ X ) ) ) ).

% Collect_empty_eq
thf(fact_99_Collect__empty__eq,axiom,
    ! [P: c2 > $o] :
      ( ( ( collect_c2 @ P )
        = bot_bot_set_c2 )
      = ( ! [X: c2] :
            ~ ( P @ X ) ) ) ).

% Collect_empty_eq
thf(fact_100_Collect__empty__eq,axiom,
    ! [P: nat > $o] :
      ( ( ( collect_nat @ P )
        = bot_bot_set_nat )
      = ( ! [X: nat] :
            ~ ( P @ X ) ) ) ).

% Collect_empty_eq
thf(fact_101_all__not__in__conv,axiom,
    ! [A2: set_Pr9202269149784407460_c1_c2] :
      ( ( ! [X: product_prod_c1_c2] :
            ~ ( member1440383022217085037_c1_c2 @ X @ A2 ) )
      = ( A2 = bot_bo745477178175700496_c1_c2 ) ) ).

% all_not_in_conv
thf(fact_102_all__not__in__conv,axiom,
    ! [A2: set_Pr4592484330697324838_b1_b2] :
      ( ( ! [X: product_prod_b1_b2] :
            ~ ( member2075749735315954927_b1_b2 @ X @ A2 ) )
      = ( A2 = bot_bo5359064395943393682_b1_b2 ) ) ).

% all_not_in_conv
thf(fact_103_all__not__in__conv,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2] :
      ( ( ! [X: product_prod_a1_a2] :
            ~ ( member2711116448414824817_a1_a2 @ X @ A2 ) )
      = ( A2 = bot_bo749279576856311060_a1_a2 ) ) ).

% all_not_in_conv
thf(fact_104_all__not__in__conv,axiom,
    ! [A2: set_ma7306327908849618074set_c2] :
      ( ( ! [X: mapping_c1_set_c2] :
            ~ ( member341037065618468219set_c2 @ X @ A2 ) )
      = ( A2 = bot_bo7584170878874662190set_c2 ) ) ).

% all_not_in_conv
thf(fact_105_all__not__in__conv,axiom,
    ! [A2: set_ma6254658672695423900set_b2] :
      ( ( ! [X: mapping_b1_set_b2] :
            ~ ( member6117332676589958525set_b2 @ X @ A2 ) )
      = ( A2 = bot_bo6532501642720468016set_b2 ) ) ).

% all_not_in_conv
thf(fact_106_all__not__in__conv,axiom,
    ! [A2: set_b2] :
      ( ( ! [X: b2] :
            ~ ( member_b2 @ X @ A2 ) )
      = ( A2 = bot_bot_set_b2 ) ) ).

% all_not_in_conv
thf(fact_107_all__not__in__conv,axiom,
    ! [A2: set_c2] :
      ( ( ! [X: c2] :
            ~ ( member_c2 @ X @ A2 ) )
      = ( A2 = bot_bot_set_c2 ) ) ).

% all_not_in_conv
thf(fact_108_all__not__in__conv,axiom,
    ! [A2: set_nat] :
      ( ( ! [X: nat] :
            ~ ( member_nat @ X @ A2 ) )
      = ( A2 = bot_bot_set_nat ) ) ).

% all_not_in_conv
thf(fact_109_empty__iff,axiom,
    ! [C: product_prod_c1_c2] :
      ~ ( member1440383022217085037_c1_c2 @ C @ bot_bo745477178175700496_c1_c2 ) ).

% empty_iff
thf(fact_110_empty__iff,axiom,
    ! [C: product_prod_b1_b2] :
      ~ ( member2075749735315954927_b1_b2 @ C @ bot_bo5359064395943393682_b1_b2 ) ).

% empty_iff
thf(fact_111_empty__iff,axiom,
    ! [C: product_prod_a1_a2] :
      ~ ( member2711116448414824817_a1_a2 @ C @ bot_bo749279576856311060_a1_a2 ) ).

% empty_iff
thf(fact_112_empty__iff,axiom,
    ! [C: mapping_c1_set_c2] :
      ~ ( member341037065618468219set_c2 @ C @ bot_bo7584170878874662190set_c2 ) ).

% empty_iff
thf(fact_113_empty__iff,axiom,
    ! [C: mapping_b1_set_b2] :
      ~ ( member6117332676589958525set_b2 @ C @ bot_bo6532501642720468016set_b2 ) ).

% empty_iff
thf(fact_114_empty__iff,axiom,
    ! [C: b2] :
      ~ ( member_b2 @ C @ bot_bot_set_b2 ) ).

% empty_iff
thf(fact_115_empty__iff,axiom,
    ! [C: c2] :
      ~ ( member_c2 @ C @ bot_bot_set_c2 ) ).

% empty_iff
thf(fact_116_empty__iff,axiom,
    ! [C: nat] :
      ~ ( member_nat @ C @ bot_bot_set_nat ) ).

% empty_iff
thf(fact_117_insert__absorb2,axiom,
    ! [X2: b2,A2: set_b2] :
      ( ( insert_b2 @ X2 @ ( insert_b2 @ X2 @ A2 ) )
      = ( insert_b2 @ X2 @ A2 ) ) ).

% insert_absorb2
thf(fact_118_insert__absorb2,axiom,
    ! [X2: c2,A2: set_c2] :
      ( ( insert_c2 @ X2 @ ( insert_c2 @ X2 @ A2 ) )
      = ( insert_c2 @ X2 @ A2 ) ) ).

% insert_absorb2
thf(fact_119_insert__absorb2,axiom,
    ! [X2: nat,A2: set_nat] :
      ( ( insert_nat @ X2 @ ( insert_nat @ X2 @ A2 ) )
      = ( insert_nat @ X2 @ A2 ) ) ).

% insert_absorb2
thf(fact_120_insert__iff,axiom,
    ! [A: b2,B: b2,A2: set_b2] :
      ( ( member_b2 @ A @ ( insert_b2 @ B @ A2 ) )
      = ( ( A = B )
        | ( member_b2 @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_121_insert__iff,axiom,
    ! [A: c2,B: c2,A2: set_c2] :
      ( ( member_c2 @ A @ ( insert_c2 @ B @ A2 ) )
      = ( ( A = B )
        | ( member_c2 @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_122_insert__iff,axiom,
    ! [A: nat,B: nat,A2: set_nat] :
      ( ( member_nat @ A @ ( insert_nat @ B @ A2 ) )
      = ( ( A = B )
        | ( member_nat @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_123_insert__iff,axiom,
    ! [A: product_prod_c1_c2,B: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ A @ ( insert7158109610518197396_c1_c2 @ B @ A2 ) )
      = ( ( A = B )
        | ( member1440383022217085037_c1_c2 @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_124_insert__iff,axiom,
    ! [A: product_prod_b1_b2,B: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ A @ ( insert7793476323617067286_b1_b2 @ B @ A2 ) )
      = ( ( A = B )
        | ( member2075749735315954927_b1_b2 @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_125_insert__iff,axiom,
    ! [A: product_prod_a1_a2,B: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ A @ ( insert8428843036715937176_a1_a2 @ B @ A2 ) )
      = ( ( A = B )
        | ( member2711116448414824817_a1_a2 @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_126_insert__iff,axiom,
    ! [A: mapping_c1_set_c2,B: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ A @ ( insert88652402460333204set_c2 @ B @ A2 ) )
      = ( ( A = B )
        | ( member341037065618468219set_c2 @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_127_insert__iff,axiom,
    ! [A: mapping_b1_set_b2,B: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ A @ ( insert5864948013431823510set_b2 @ B @ A2 ) )
      = ( ( A = B )
        | ( member6117332676589958525set_b2 @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_128_insertCI,axiom,
    ! [A: b2,B2: set_b2,B: b2] :
      ( ( ~ ( member_b2 @ A @ B2 )
       => ( A = B ) )
     => ( member_b2 @ A @ ( insert_b2 @ B @ B2 ) ) ) ).

% insertCI
thf(fact_129_insertCI,axiom,
    ! [A: c2,B2: set_c2,B: c2] :
      ( ( ~ ( member_c2 @ A @ B2 )
       => ( A = B ) )
     => ( member_c2 @ A @ ( insert_c2 @ B @ B2 ) ) ) ).

% insertCI
thf(fact_130_insertCI,axiom,
    ! [A: nat,B2: set_nat,B: nat] :
      ( ( ~ ( member_nat @ A @ B2 )
       => ( A = B ) )
     => ( member_nat @ A @ ( insert_nat @ B @ B2 ) ) ) ).

% insertCI
thf(fact_131_insertCI,axiom,
    ! [A: product_prod_c1_c2,B2: set_Pr9202269149784407460_c1_c2,B: product_prod_c1_c2] :
      ( ( ~ ( member1440383022217085037_c1_c2 @ A @ B2 )
       => ( A = B ) )
     => ( member1440383022217085037_c1_c2 @ A @ ( insert7158109610518197396_c1_c2 @ B @ B2 ) ) ) ).

% insertCI
thf(fact_132_insertCI,axiom,
    ! [A: product_prod_b1_b2,B2: set_Pr4592484330697324838_b1_b2,B: product_prod_b1_b2] :
      ( ( ~ ( member2075749735315954927_b1_b2 @ A @ B2 )
       => ( A = B ) )
     => ( member2075749735315954927_b1_b2 @ A @ ( insert7793476323617067286_b1_b2 @ B @ B2 ) ) ) ).

% insertCI
thf(fact_133_insertCI,axiom,
    ! [A: product_prod_a1_a2,B2: set_Pr9206071548465018024_a1_a2,B: product_prod_a1_a2] :
      ( ( ~ ( member2711116448414824817_a1_a2 @ A @ B2 )
       => ( A = B ) )
     => ( member2711116448414824817_a1_a2 @ A @ ( insert8428843036715937176_a1_a2 @ B @ B2 ) ) ) ).

% insertCI
thf(fact_134_insertCI,axiom,
    ! [A: mapping_c1_set_c2,B2: set_ma7306327908849618074set_c2,B: mapping_c1_set_c2] :
      ( ( ~ ( member341037065618468219set_c2 @ A @ B2 )
       => ( A = B ) )
     => ( member341037065618468219set_c2 @ A @ ( insert88652402460333204set_c2 @ B @ B2 ) ) ) ).

% insertCI
thf(fact_135_insertCI,axiom,
    ! [A: mapping_b1_set_b2,B2: set_ma6254658672695423900set_b2,B: mapping_b1_set_b2] :
      ( ( ~ ( member6117332676589958525set_b2 @ A @ B2 )
       => ( A = B ) )
     => ( member6117332676589958525set_b2 @ A @ ( insert5864948013431823510set_b2 @ B @ B2 ) ) ) ).

% insertCI
thf(fact_136_case__prodI2,axiom,
    ! [P2: produc2702059613074419827set_c2,C: ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > $o] :
      ( ! [A4: b1 > option_set_b2,B4: c1 > option_set_c2] :
          ( ( P2
            = ( produc890782565133688235set_c2 @ A4 @ B4 ) )
         => ( C @ A4 @ B4 ) )
     => ( produc115805034449689560t_c2_o @ C @ P2 ) ) ).

% case_prodI2
thf(fact_137_case__prodI2,axiom,
    ! [P2: produc4061897789176782763set_c2,C: mapping_b1_set_b2 > mapping_c1_set_c2 > $o] :
      ( ! [A4: mapping_b1_set_b2,B4: mapping_c1_set_c2] :
          ( ( P2
            = ( produc1212179418963815907set_c2 @ A4 @ B4 ) )
         => ( C @ A4 @ B4 ) )
     => ( produc7359613910387544480t_c2_o @ C @ P2 ) ) ).

% case_prodI2
thf(fact_138_case__prodI2,axiom,
    ! [P2: produc8629413652255616883set_b2,C: ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > $o] :
      ( ! [A4: c1 > option_set_c2,B4: b1 > option_set_b2] :
          ( ( P2
            = ( produc4506454564149116331set_b2 @ A4 @ B4 ) )
         => ( C @ A4 @ B4 ) )
     => ( produc2533395233176501208t_b2_o @ C @ P2 ) ) ).

% case_prodI2
thf(fact_139_case__prodI2,axiom,
    ! [P2: produc8498296649714291061set_b2,C: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o] :
      ( ! [A4: b1 > option_set_b2,B4: b1 > option_set_b2] :
          ( ( P2
            = ( produc4375337561607790509set_b2 @ A4 @ B4 ) )
         => ( C @ A4 @ B4 ) )
     => ( produc2039302432013647190t_b2_o @ C @ P2 ) ) ).

% case_prodI2
thf(fact_140_case__prodI2,axiom,
    ! [P2: product_prod_c1_c2,C: c1 > c2 > $o] :
      ( ! [A4: c1,B4: c2] :
          ( ( P2
            = ( product_Pair_c1_c2 @ A4 @ B4 ) )
         => ( C @ A4 @ B4 ) )
     => ( produc43157205764183447751_c2_o @ C @ P2 ) ) ).

% case_prodI2
thf(fact_141_case__prodI2,axiom,
    ! [P2: product_prod_b1_b2,C: b1 > b2 > $o] :
      ( ! [A4: b1,B4: b2] :
          ( ( P2
            = ( product_Pair_b1_b2 @ A4 @ B4 ) )
         => ( C @ A4 @ B4 ) )
     => ( produc81016565174098426291_b2_o @ C @ P2 ) ) ).

% case_prodI2
thf(fact_142_case__prodI2,axiom,
    ! [P2: product_prod_a1_a2,C: a1 > a2 > $o] :
      ( ! [A4: a1,B4: a2] :
          ( ( P2
            = ( product_Pair_a1_a2 @ A4 @ B4 ) )
         => ( C @ A4 @ B4 ) )
     => ( produc26642204215465646751_a2_o @ C @ P2 ) ) ).

% case_prodI2
thf(fact_143_case__prodI,axiom,
    ! [F: ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > $o,A: b1 > option_set_b2,B: c1 > option_set_c2] :
      ( ( F @ A @ B )
     => ( produc115805034449689560t_c2_o @ F @ ( produc890782565133688235set_c2 @ A @ B ) ) ) ).

% case_prodI
thf(fact_144_case__prodI,axiom,
    ! [F: mapping_b1_set_b2 > mapping_c1_set_c2 > $o,A: mapping_b1_set_b2,B: mapping_c1_set_c2] :
      ( ( F @ A @ B )
     => ( produc7359613910387544480t_c2_o @ F @ ( produc1212179418963815907set_c2 @ A @ B ) ) ) ).

% case_prodI
thf(fact_145_case__prodI,axiom,
    ! [F: ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > $o,A: c1 > option_set_c2,B: b1 > option_set_b2] :
      ( ( F @ A @ B )
     => ( produc2533395233176501208t_b2_o @ F @ ( produc4506454564149116331set_b2 @ A @ B ) ) ) ).

% case_prodI
thf(fact_146_case__prodI,axiom,
    ! [F: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,A: b1 > option_set_b2,B: b1 > option_set_b2] :
      ( ( F @ A @ B )
     => ( produc2039302432013647190t_b2_o @ F @ ( produc4375337561607790509set_b2 @ A @ B ) ) ) ).

% case_prodI
thf(fact_147_case__prodI,axiom,
    ! [F: c1 > c2 > $o,A: c1,B: c2] :
      ( ( F @ A @ B )
     => ( produc43157205764183447751_c2_o @ F @ ( product_Pair_c1_c2 @ A @ B ) ) ) ).

% case_prodI
thf(fact_148_case__prodI,axiom,
    ! [F: b1 > b2 > $o,A: b1,B: b2] :
      ( ( F @ A @ B )
     => ( produc81016565174098426291_b2_o @ F @ ( product_Pair_b1_b2 @ A @ B ) ) ) ).

% case_prodI
thf(fact_149_case__prodI,axiom,
    ! [F: a1 > a2 > $o,A: a1,B: a2] :
      ( ( F @ A @ B )
     => ( produc26642204215465646751_a2_o @ F @ ( product_Pair_a1_a2 @ A @ B ) ) ) ).

% case_prodI
thf(fact_150_mem__case__prodI2,axiom,
    ! [P2: product_prod_c1_c2,Z3: product_prod_c1_c2,C: c1 > c2 > set_Pr9202269149784407460_c1_c2] :
      ( ! [A4: c1,B4: c2] :
          ( ( P2
            = ( product_Pair_c1_c2 @ A4 @ B4 ) )
         => ( member1440383022217085037_c1_c2 @ Z3 @ ( C @ A4 @ B4 ) ) )
     => ( member1440383022217085037_c1_c2 @ Z3 @ ( produc22185273829687123_c1_c2 @ C @ P2 ) ) ) ).

% mem_case_prodI2
thf(fact_151_mem__case__prodI2,axiom,
    ! [P2: product_prod_c1_c2,Z3: product_prod_b1_b2,C: c1 > c2 > set_Pr4592484330697324838_b1_b2] :
      ( ! [A4: c1,B4: c2] :
          ( ( P2
            = ( product_Pair_c1_c2 @ A4 @ B4 ) )
         => ( member2075749735315954927_b1_b2 @ Z3 @ ( C @ A4 @ B4 ) ) )
     => ( member2075749735315954927_b1_b2 @ Z3 @ ( produc4635772491597380309_b1_b2 @ C @ P2 ) ) ) ).

% mem_case_prodI2
thf(fact_152_mem__case__prodI2,axiom,
    ! [P2: product_prod_c1_c2,Z3: product_prod_a1_a2,C: c1 > c2 > set_Pr9206071548465018024_a1_a2] :
      ( ! [A4: c1,B4: c2] :
          ( ( P2
            = ( product_Pair_c1_c2 @ A4 @ B4 ) )
         => ( member2711116448414824817_a1_a2 @ Z3 @ ( C @ A4 @ B4 ) ) )
     => ( member2711116448414824817_a1_a2 @ Z3 @ ( produc25987672510297687_a1_a2 @ C @ P2 ) ) ) ).

% mem_case_prodI2
thf(fact_153_mem__case__prodI2,axiom,
    ! [P2: product_prod_b1_b2,Z3: product_prod_c1_c2,C: b1 > b2 > set_Pr9202269149784407460_c1_c2] :
      ( ! [A4: b1,B4: b2] :
          ( ( P2
            = ( product_Pair_b1_b2 @ A4 @ B4 ) )
         => ( member1440383022217085037_c1_c2 @ Z3 @ ( C @ A4 @ B4 ) ) )
     => ( member1440383022217085037_c1_c2 @ Z3 @ ( produc2185810943150150097_c1_c2 @ C @ P2 ) ) ) ).

% mem_case_prodI2
thf(fact_154_mem__case__prodI2,axiom,
    ! [P2: product_prod_b1_b2,Z3: product_prod_b1_b2,C: b1 > b2 > set_Pr4592484330697324838_b1_b2] :
      ( ! [A4: b1,B4: b2] :
          ( ( P2
            = ( product_Pair_b1_b2 @ A4 @ B4 ) )
         => ( member2075749735315954927_b1_b2 @ Z3 @ ( C @ A4 @ B4 ) ) )
     => ( member2075749735315954927_b1_b2 @ Z3 @ ( produc6799398160917843283_b1_b2 @ C @ P2 ) ) ) ).

% mem_case_prodI2
thf(fact_155_mem__case__prodI2,axiom,
    ! [P2: product_prod_b1_b2,Z3: product_prod_a1_a2,C: b1 > b2 > set_Pr9206071548465018024_a1_a2] :
      ( ! [A4: b1,B4: b2] :
          ( ( P2
            = ( product_Pair_b1_b2 @ A4 @ B4 ) )
         => ( member2711116448414824817_a1_a2 @ Z3 @ ( C @ A4 @ B4 ) ) )
     => ( member2711116448414824817_a1_a2 @ Z3 @ ( produc2189613341830760661_a1_a2 @ C @ P2 ) ) ) ).

% mem_case_prodI2
thf(fact_156_mem__case__prodI2,axiom,
    ! [P2: product_prod_a1_a2,Z3: product_prod_c1_c2,C: a1 > a2 > set_Pr9202269149784407460_c1_c2] :
      ( ! [A4: a1,B4: a2] :
          ( ( P2
            = ( product_Pair_a1_a2 @ A4 @ B4 ) )
         => ( member1440383022217085037_c1_c2 @ Z3 @ ( C @ A4 @ B4 ) ) )
     => ( member1440383022217085037_c1_c2 @ Z3 @ ( produc4349436612470613071_c1_c2 @ C @ P2 ) ) ) ).

% mem_case_prodI2
thf(fact_157_mem__case__prodI2,axiom,
    ! [P2: product_prod_a1_a2,Z3: product_prod_b1_b2,C: a1 > a2 > set_Pr4592484330697324838_b1_b2] :
      ( ! [A4: a1,B4: a2] :
          ( ( P2
            = ( product_Pair_a1_a2 @ A4 @ B4 ) )
         => ( member2075749735315954927_b1_b2 @ Z3 @ ( C @ A4 @ B4 ) ) )
     => ( member2075749735315954927_b1_b2 @ Z3 @ ( produc8963023830238306257_b1_b2 @ C @ P2 ) ) ) ).

% mem_case_prodI2
thf(fact_158_mem__case__prodI2,axiom,
    ! [P2: product_prod_a1_a2,Z3: product_prod_a1_a2,C: a1 > a2 > set_Pr9206071548465018024_a1_a2] :
      ( ! [A4: a1,B4: a2] :
          ( ( P2
            = ( product_Pair_a1_a2 @ A4 @ B4 ) )
         => ( member2711116448414824817_a1_a2 @ Z3 @ ( C @ A4 @ B4 ) ) )
     => ( member2711116448414824817_a1_a2 @ Z3 @ ( produc4353239011151223635_a1_a2 @ C @ P2 ) ) ) ).

% mem_case_prodI2
thf(fact_159_mem__case__prodI2,axiom,
    ! [P2: product_prod_c1_c2,Z3: mapping_c1_set_c2,C: c1 > c2 > set_ma7306327908849618074set_c2] :
      ( ! [A4: c1,B4: c2] :
          ( ( P2
            = ( product_Pair_c1_c2 @ A4 @ B4 ) )
         => ( member341037065618468219set_c2 @ Z3 @ ( C @ A4 @ B4 ) ) )
     => ( member341037065618468219set_c2 @ Z3 @ ( produc696371989280955435set_c2 @ C @ P2 ) ) ) ).

% mem_case_prodI2
thf(fact_160_mem__case__prodI,axiom,
    ! [Z3: product_prod_c1_c2,C: c1 > c2 > set_Pr9202269149784407460_c1_c2,A: c1,B: c2] :
      ( ( member1440383022217085037_c1_c2 @ Z3 @ ( C @ A @ B ) )
     => ( member1440383022217085037_c1_c2 @ Z3 @ ( produc22185273829687123_c1_c2 @ C @ ( product_Pair_c1_c2 @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_161_mem__case__prodI,axiom,
    ! [Z3: product_prod_b1_b2,C: c1 > c2 > set_Pr4592484330697324838_b1_b2,A: c1,B: c2] :
      ( ( member2075749735315954927_b1_b2 @ Z3 @ ( C @ A @ B ) )
     => ( member2075749735315954927_b1_b2 @ Z3 @ ( produc4635772491597380309_b1_b2 @ C @ ( product_Pair_c1_c2 @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_162_mem__case__prodI,axiom,
    ! [Z3: product_prod_a1_a2,C: c1 > c2 > set_Pr9206071548465018024_a1_a2,A: c1,B: c2] :
      ( ( member2711116448414824817_a1_a2 @ Z3 @ ( C @ A @ B ) )
     => ( member2711116448414824817_a1_a2 @ Z3 @ ( produc25987672510297687_a1_a2 @ C @ ( product_Pair_c1_c2 @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_163_mem__case__prodI,axiom,
    ! [Z3: product_prod_c1_c2,C: b1 > b2 > set_Pr9202269149784407460_c1_c2,A: b1,B: b2] :
      ( ( member1440383022217085037_c1_c2 @ Z3 @ ( C @ A @ B ) )
     => ( member1440383022217085037_c1_c2 @ Z3 @ ( produc2185810943150150097_c1_c2 @ C @ ( product_Pair_b1_b2 @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_164_mem__case__prodI,axiom,
    ! [Z3: product_prod_b1_b2,C: b1 > b2 > set_Pr4592484330697324838_b1_b2,A: b1,B: b2] :
      ( ( member2075749735315954927_b1_b2 @ Z3 @ ( C @ A @ B ) )
     => ( member2075749735315954927_b1_b2 @ Z3 @ ( produc6799398160917843283_b1_b2 @ C @ ( product_Pair_b1_b2 @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_165_mem__case__prodI,axiom,
    ! [Z3: product_prod_a1_a2,C: b1 > b2 > set_Pr9206071548465018024_a1_a2,A: b1,B: b2] :
      ( ( member2711116448414824817_a1_a2 @ Z3 @ ( C @ A @ B ) )
     => ( member2711116448414824817_a1_a2 @ Z3 @ ( produc2189613341830760661_a1_a2 @ C @ ( product_Pair_b1_b2 @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_166_mem__case__prodI,axiom,
    ! [Z3: product_prod_c1_c2,C: a1 > a2 > set_Pr9202269149784407460_c1_c2,A: a1,B: a2] :
      ( ( member1440383022217085037_c1_c2 @ Z3 @ ( C @ A @ B ) )
     => ( member1440383022217085037_c1_c2 @ Z3 @ ( produc4349436612470613071_c1_c2 @ C @ ( product_Pair_a1_a2 @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_167_mem__case__prodI,axiom,
    ! [Z3: product_prod_b1_b2,C: a1 > a2 > set_Pr4592484330697324838_b1_b2,A: a1,B: a2] :
      ( ( member2075749735315954927_b1_b2 @ Z3 @ ( C @ A @ B ) )
     => ( member2075749735315954927_b1_b2 @ Z3 @ ( produc8963023830238306257_b1_b2 @ C @ ( product_Pair_a1_a2 @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_168_mem__case__prodI,axiom,
    ! [Z3: product_prod_a1_a2,C: a1 > a2 > set_Pr9206071548465018024_a1_a2,A: a1,B: a2] :
      ( ( member2711116448414824817_a1_a2 @ Z3 @ ( C @ A @ B ) )
     => ( member2711116448414824817_a1_a2 @ Z3 @ ( produc4353239011151223635_a1_a2 @ C @ ( product_Pair_a1_a2 @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_169_mem__case__prodI,axiom,
    ! [Z3: mapping_c1_set_c2,C: c1 > c2 > set_ma7306327908849618074set_c2,A: c1,B: c2] :
      ( ( member341037065618468219set_c2 @ Z3 @ ( C @ A @ B ) )
     => ( member341037065618468219set_c2 @ Z3 @ ( produc696371989280955435set_c2 @ C @ ( product_Pair_c1_c2 @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_170_image__ident,axiom,
    ! [Y3: set_Pr1660683266160182027set_c2] :
      ( ( image_7945144516369962181set_c2
        @ ^ [X: produc4061897789176782763set_c2] : X
        @ Y3 )
      = Y3 ) ).

% image_ident
thf(fact_171_image__is__empty,axiom,
    ! [F: b2 > b2,A2: set_b2] :
      ( ( ( image_b2_b22 @ F @ A2 )
        = bot_bot_set_b2 )
      = ( A2 = bot_bot_set_b2 ) ) ).

% image_is_empty
thf(fact_172_image__is__empty,axiom,
    ! [F: c2 > b2,A2: set_c2] :
      ( ( ( image_c2_b22 @ F @ A2 )
        = bot_bot_set_b2 )
      = ( A2 = bot_bot_set_c2 ) ) ).

% image_is_empty
thf(fact_173_image__is__empty,axiom,
    ! [F: nat > b2,A2: set_nat] :
      ( ( ( image_nat_b22 @ F @ A2 )
        = bot_bot_set_b2 )
      = ( A2 = bot_bot_set_nat ) ) ).

% image_is_empty
thf(fact_174_image__is__empty,axiom,
    ! [F: b2 > c2,A2: set_b2] :
      ( ( ( image_b2_c22 @ F @ A2 )
        = bot_bot_set_c2 )
      = ( A2 = bot_bot_set_b2 ) ) ).

% image_is_empty
thf(fact_175_image__is__empty,axiom,
    ! [F: c2 > c2,A2: set_c2] :
      ( ( ( image_c2_c22 @ F @ A2 )
        = bot_bot_set_c2 )
      = ( A2 = bot_bot_set_c2 ) ) ).

% image_is_empty
thf(fact_176_image__is__empty,axiom,
    ! [F: nat > c2,A2: set_nat] :
      ( ( ( image_nat_c22 @ F @ A2 )
        = bot_bot_set_c2 )
      = ( A2 = bot_bot_set_nat ) ) ).

% image_is_empty
thf(fact_177_image__is__empty,axiom,
    ! [F: b2 > nat,A2: set_b2] :
      ( ( ( image_b2_nat2 @ F @ A2 )
        = bot_bot_set_nat )
      = ( A2 = bot_bot_set_b2 ) ) ).

% image_is_empty
thf(fact_178_image__is__empty,axiom,
    ! [F: c2 > nat,A2: set_c2] :
      ( ( ( image_c2_nat2 @ F @ A2 )
        = bot_bot_set_nat )
      = ( A2 = bot_bot_set_c2 ) ) ).

% image_is_empty
thf(fact_179_image__is__empty,axiom,
    ! [F: nat > nat,A2: set_nat] :
      ( ( ( image_nat_nat2 @ F @ A2 )
        = bot_bot_set_nat )
      = ( A2 = bot_bot_set_nat ) ) ).

% image_is_empty
thf(fact_180_image__is__empty,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( ( image_1398015525354814723_b1_b2 @ F @ A2 )
        = bot_bo5359064395943393682_b1_b2 )
      = ( A2 = bot_bo749279576856311060_a1_a2 ) ) ).

% image_is_empty
thf(fact_181_empty__is__image,axiom,
    ! [F: b2 > b2,A2: set_b2] :
      ( ( bot_bot_set_b2
        = ( image_b2_b22 @ F @ A2 ) )
      = ( A2 = bot_bot_set_b2 ) ) ).

% empty_is_image
thf(fact_182_empty__is__image,axiom,
    ! [F: c2 > b2,A2: set_c2] :
      ( ( bot_bot_set_b2
        = ( image_c2_b22 @ F @ A2 ) )
      = ( A2 = bot_bot_set_c2 ) ) ).

% empty_is_image
thf(fact_183_empty__is__image,axiom,
    ! [F: nat > b2,A2: set_nat] :
      ( ( bot_bot_set_b2
        = ( image_nat_b22 @ F @ A2 ) )
      = ( A2 = bot_bot_set_nat ) ) ).

% empty_is_image
thf(fact_184_empty__is__image,axiom,
    ! [F: b2 > c2,A2: set_b2] :
      ( ( bot_bot_set_c2
        = ( image_b2_c22 @ F @ A2 ) )
      = ( A2 = bot_bot_set_b2 ) ) ).

% empty_is_image
thf(fact_185_empty__is__image,axiom,
    ! [F: c2 > c2,A2: set_c2] :
      ( ( bot_bot_set_c2
        = ( image_c2_c22 @ F @ A2 ) )
      = ( A2 = bot_bot_set_c2 ) ) ).

% empty_is_image
thf(fact_186_empty__is__image,axiom,
    ! [F: nat > c2,A2: set_nat] :
      ( ( bot_bot_set_c2
        = ( image_nat_c22 @ F @ A2 ) )
      = ( A2 = bot_bot_set_nat ) ) ).

% empty_is_image
thf(fact_187_empty__is__image,axiom,
    ! [F: b2 > nat,A2: set_b2] :
      ( ( bot_bot_set_nat
        = ( image_b2_nat2 @ F @ A2 ) )
      = ( A2 = bot_bot_set_b2 ) ) ).

% empty_is_image
thf(fact_188_empty__is__image,axiom,
    ! [F: c2 > nat,A2: set_c2] :
      ( ( bot_bot_set_nat
        = ( image_c2_nat2 @ F @ A2 ) )
      = ( A2 = bot_bot_set_c2 ) ) ).

% empty_is_image
thf(fact_189_empty__is__image,axiom,
    ! [F: nat > nat,A2: set_nat] :
      ( ( bot_bot_set_nat
        = ( image_nat_nat2 @ F @ A2 ) )
      = ( A2 = bot_bot_set_nat ) ) ).

% empty_is_image
thf(fact_190_empty__is__image,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( bot_bo5359064395943393682_b1_b2
        = ( image_1398015525354814723_b1_b2 @ F @ A2 ) )
      = ( A2 = bot_bo749279576856311060_a1_a2 ) ) ).

% empty_is_image
thf(fact_191_image__empty,axiom,
    ! [F: b2 > b2] :
      ( ( image_b2_b22 @ F @ bot_bot_set_b2 )
      = bot_bot_set_b2 ) ).

% image_empty
thf(fact_192_image__empty,axiom,
    ! [F: b2 > c2] :
      ( ( image_b2_c22 @ F @ bot_bot_set_b2 )
      = bot_bot_set_c2 ) ).

% image_empty
thf(fact_193_image__empty,axiom,
    ! [F: b2 > nat] :
      ( ( image_b2_nat2 @ F @ bot_bot_set_b2 )
      = bot_bot_set_nat ) ).

% image_empty
thf(fact_194_image__empty,axiom,
    ! [F: c2 > b2] :
      ( ( image_c2_b22 @ F @ bot_bot_set_c2 )
      = bot_bot_set_b2 ) ).

% image_empty
thf(fact_195_image__empty,axiom,
    ! [F: c2 > c2] :
      ( ( image_c2_c22 @ F @ bot_bot_set_c2 )
      = bot_bot_set_c2 ) ).

% image_empty
thf(fact_196_image__empty,axiom,
    ! [F: c2 > nat] :
      ( ( image_c2_nat2 @ F @ bot_bot_set_c2 )
      = bot_bot_set_nat ) ).

% image_empty
thf(fact_197_image__empty,axiom,
    ! [F: nat > b2] :
      ( ( image_nat_b22 @ F @ bot_bot_set_nat )
      = bot_bot_set_b2 ) ).

% image_empty
thf(fact_198_image__empty,axiom,
    ! [F: nat > c2] :
      ( ( image_nat_c22 @ F @ bot_bot_set_nat )
      = bot_bot_set_c2 ) ).

% image_empty
thf(fact_199_image__empty,axiom,
    ! [F: nat > nat] :
      ( ( image_nat_nat2 @ F @ bot_bot_set_nat )
      = bot_bot_set_nat ) ).

% image_empty
thf(fact_200_image__empty,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2] :
      ( ( image_1398015525354814723_b1_b2 @ F @ bot_bo749279576856311060_a1_a2 )
      = bot_bo5359064395943393682_b1_b2 ) ).

% image_empty
thf(fact_201_Mapping_Olookup__update,axiom,
    ! [K: b1,V: set_b2,M3: mapping_b1_set_b2] :
      ( ( lookup_b1_set_b2 @ ( update_b1_set_b2 @ K @ V @ M3 ) @ K )
      = ( some_set_b2 @ V ) ) ).

% Mapping.lookup_update
thf(fact_202_Mapping_Olookup__update,axiom,
    ! [K: c1,V: set_c2,M3: mapping_c1_set_c2] :
      ( ( lookup_c1_set_c2 @ ( update_c1_set_c2 @ K @ V @ M3 ) @ K )
      = ( some_set_c2 @ V ) ) ).

% Mapping.lookup_update
thf(fact_203_mem__case__prodE,axiom,
    ! [Z3: product_prod_c1_c2,C: c1 > c2 > set_Pr9202269149784407460_c1_c2,P2: product_prod_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ Z3 @ ( produc22185273829687123_c1_c2 @ C @ P2 ) )
     => ~ ! [X3: c1,Y4: c2] :
            ( ( P2
              = ( product_Pair_c1_c2 @ X3 @ Y4 ) )
           => ~ ( member1440383022217085037_c1_c2 @ Z3 @ ( C @ X3 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_204_mem__case__prodE,axiom,
    ! [Z3: product_prod_b1_b2,C: c1 > c2 > set_Pr4592484330697324838_b1_b2,P2: product_prod_c1_c2] :
      ( ( member2075749735315954927_b1_b2 @ Z3 @ ( produc4635772491597380309_b1_b2 @ C @ P2 ) )
     => ~ ! [X3: c1,Y4: c2] :
            ( ( P2
              = ( product_Pair_c1_c2 @ X3 @ Y4 ) )
           => ~ ( member2075749735315954927_b1_b2 @ Z3 @ ( C @ X3 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_205_mem__case__prodE,axiom,
    ! [Z3: product_prod_a1_a2,C: c1 > c2 > set_Pr9206071548465018024_a1_a2,P2: product_prod_c1_c2] :
      ( ( member2711116448414824817_a1_a2 @ Z3 @ ( produc25987672510297687_a1_a2 @ C @ P2 ) )
     => ~ ! [X3: c1,Y4: c2] :
            ( ( P2
              = ( product_Pair_c1_c2 @ X3 @ Y4 ) )
           => ~ ( member2711116448414824817_a1_a2 @ Z3 @ ( C @ X3 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_206_mem__case__prodE,axiom,
    ! [Z3: product_prod_c1_c2,C: b1 > b2 > set_Pr9202269149784407460_c1_c2,P2: product_prod_b1_b2] :
      ( ( member1440383022217085037_c1_c2 @ Z3 @ ( produc2185810943150150097_c1_c2 @ C @ P2 ) )
     => ~ ! [X3: b1,Y4: b2] :
            ( ( P2
              = ( product_Pair_b1_b2 @ X3 @ Y4 ) )
           => ~ ( member1440383022217085037_c1_c2 @ Z3 @ ( C @ X3 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_207_mem__case__prodE,axiom,
    ! [Z3: product_prod_b1_b2,C: b1 > b2 > set_Pr4592484330697324838_b1_b2,P2: product_prod_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ Z3 @ ( produc6799398160917843283_b1_b2 @ C @ P2 ) )
     => ~ ! [X3: b1,Y4: b2] :
            ( ( P2
              = ( product_Pair_b1_b2 @ X3 @ Y4 ) )
           => ~ ( member2075749735315954927_b1_b2 @ Z3 @ ( C @ X3 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_208_mem__case__prodE,axiom,
    ! [Z3: product_prod_a1_a2,C: b1 > b2 > set_Pr9206071548465018024_a1_a2,P2: product_prod_b1_b2] :
      ( ( member2711116448414824817_a1_a2 @ Z3 @ ( produc2189613341830760661_a1_a2 @ C @ P2 ) )
     => ~ ! [X3: b1,Y4: b2] :
            ( ( P2
              = ( product_Pair_b1_b2 @ X3 @ Y4 ) )
           => ~ ( member2711116448414824817_a1_a2 @ Z3 @ ( C @ X3 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_209_mem__case__prodE,axiom,
    ! [Z3: product_prod_c1_c2,C: a1 > a2 > set_Pr9202269149784407460_c1_c2,P2: product_prod_a1_a2] :
      ( ( member1440383022217085037_c1_c2 @ Z3 @ ( produc4349436612470613071_c1_c2 @ C @ P2 ) )
     => ~ ! [X3: a1,Y4: a2] :
            ( ( P2
              = ( product_Pair_a1_a2 @ X3 @ Y4 ) )
           => ~ ( member1440383022217085037_c1_c2 @ Z3 @ ( C @ X3 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_210_mem__case__prodE,axiom,
    ! [Z3: product_prod_b1_b2,C: a1 > a2 > set_Pr4592484330697324838_b1_b2,P2: product_prod_a1_a2] :
      ( ( member2075749735315954927_b1_b2 @ Z3 @ ( produc8963023830238306257_b1_b2 @ C @ P2 ) )
     => ~ ! [X3: a1,Y4: a2] :
            ( ( P2
              = ( product_Pair_a1_a2 @ X3 @ Y4 ) )
           => ~ ( member2075749735315954927_b1_b2 @ Z3 @ ( C @ X3 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_211_mem__case__prodE,axiom,
    ! [Z3: product_prod_a1_a2,C: a1 > a2 > set_Pr9206071548465018024_a1_a2,P2: product_prod_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ Z3 @ ( produc4353239011151223635_a1_a2 @ C @ P2 ) )
     => ~ ! [X3: a1,Y4: a2] :
            ( ( P2
              = ( product_Pair_a1_a2 @ X3 @ Y4 ) )
           => ~ ( member2711116448414824817_a1_a2 @ Z3 @ ( C @ X3 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_212_mem__case__prodE,axiom,
    ! [Z3: mapping_c1_set_c2,C: c1 > c2 > set_ma7306327908849618074set_c2,P2: product_prod_c1_c2] :
      ( ( member341037065618468219set_c2 @ Z3 @ ( produc696371989280955435set_c2 @ C @ P2 ) )
     => ~ ! [X3: c1,Y4: c2] :
            ( ( P2
              = ( product_Pair_c1_c2 @ X3 @ Y4 ) )
           => ~ ( member341037065618468219set_c2 @ Z3 @ ( C @ X3 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_213_case__prodE,axiom,
    ! [C: ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > $o,P2: produc2702059613074419827set_c2] :
      ( ( produc115805034449689560t_c2_o @ C @ P2 )
     => ~ ! [X3: b1 > option_set_b2,Y4: c1 > option_set_c2] :
            ( ( P2
              = ( produc890782565133688235set_c2 @ X3 @ Y4 ) )
           => ~ ( C @ X3 @ Y4 ) ) ) ).

% case_prodE
thf(fact_214_case__prodE,axiom,
    ! [C: mapping_b1_set_b2 > mapping_c1_set_c2 > $o,P2: produc4061897789176782763set_c2] :
      ( ( produc7359613910387544480t_c2_o @ C @ P2 )
     => ~ ! [X3: mapping_b1_set_b2,Y4: mapping_c1_set_c2] :
            ( ( P2
              = ( produc1212179418963815907set_c2 @ X3 @ Y4 ) )
           => ~ ( C @ X3 @ Y4 ) ) ) ).

% case_prodE
thf(fact_215_case__prodE,axiom,
    ! [C: ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > $o,P2: produc8629413652255616883set_b2] :
      ( ( produc2533395233176501208t_b2_o @ C @ P2 )
     => ~ ! [X3: c1 > option_set_c2,Y4: b1 > option_set_b2] :
            ( ( P2
              = ( produc4506454564149116331set_b2 @ X3 @ Y4 ) )
           => ~ ( C @ X3 @ Y4 ) ) ) ).

% case_prodE
thf(fact_216_case__prodE,axiom,
    ! [C: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,P2: produc8498296649714291061set_b2] :
      ( ( produc2039302432013647190t_b2_o @ C @ P2 )
     => ~ ! [X3: b1 > option_set_b2,Y4: b1 > option_set_b2] :
            ( ( P2
              = ( produc4375337561607790509set_b2 @ X3 @ Y4 ) )
           => ~ ( C @ X3 @ Y4 ) ) ) ).

% case_prodE
thf(fact_217_case__prodE,axiom,
    ! [C: c1 > c2 > $o,P2: product_prod_c1_c2] :
      ( ( produc43157205764183447751_c2_o @ C @ P2 )
     => ~ ! [X3: c1,Y4: c2] :
            ( ( P2
              = ( product_Pair_c1_c2 @ X3 @ Y4 ) )
           => ~ ( C @ X3 @ Y4 ) ) ) ).

% case_prodE
thf(fact_218_case__prodE,axiom,
    ! [C: b1 > b2 > $o,P2: product_prod_b1_b2] :
      ( ( produc81016565174098426291_b2_o @ C @ P2 )
     => ~ ! [X3: b1,Y4: b2] :
            ( ( P2
              = ( product_Pair_b1_b2 @ X3 @ Y4 ) )
           => ~ ( C @ X3 @ Y4 ) ) ) ).

% case_prodE
thf(fact_219_case__prodE,axiom,
    ! [C: a1 > a2 > $o,P2: product_prod_a1_a2] :
      ( ( produc26642204215465646751_a2_o @ C @ P2 )
     => ~ ! [X3: a1,Y4: a2] :
            ( ( P2
              = ( product_Pair_a1_a2 @ X3 @ Y4 ) )
           => ~ ( C @ X3 @ Y4 ) ) ) ).

% case_prodE
thf(fact_220_case__prodD,axiom,
    ! [F: ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > $o,A: b1 > option_set_b2,B: c1 > option_set_c2] :
      ( ( produc115805034449689560t_c2_o @ F @ ( produc890782565133688235set_c2 @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_221_case__prodD,axiom,
    ! [F: mapping_b1_set_b2 > mapping_c1_set_c2 > $o,A: mapping_b1_set_b2,B: mapping_c1_set_c2] :
      ( ( produc7359613910387544480t_c2_o @ F @ ( produc1212179418963815907set_c2 @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_222_case__prodD,axiom,
    ! [F: ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > $o,A: c1 > option_set_c2,B: b1 > option_set_b2] :
      ( ( produc2533395233176501208t_b2_o @ F @ ( produc4506454564149116331set_b2 @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_223_case__prodD,axiom,
    ! [F: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,A: b1 > option_set_b2,B: b1 > option_set_b2] :
      ( ( produc2039302432013647190t_b2_o @ F @ ( produc4375337561607790509set_b2 @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_224_case__prodD,axiom,
    ! [F: c1 > c2 > $o,A: c1,B: c2] :
      ( ( produc43157205764183447751_c2_o @ F @ ( product_Pair_c1_c2 @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_225_case__prodD,axiom,
    ! [F: b1 > b2 > $o,A: b1,B: b2] :
      ( ( produc81016565174098426291_b2_o @ F @ ( product_Pair_b1_b2 @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_226_case__prodD,axiom,
    ! [F: a1 > a2 > $o,A: a1,B: a2] :
      ( ( produc26642204215465646751_a2_o @ F @ ( product_Pair_a1_a2 @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_227_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: product_prod_c1_c2,A2: c1 > c2 > $o] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ ( collec5229596525471704495_c1_c2 @ ( produc43157205764183447751_c2_o @ A2 ) ) )
     => ( A2 @ ( product_fst_c1_c2 @ X2 ) @ ( product_snd_c1_c2 @ X2 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_228_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: product_prod_b1_b2,A2: b1 > b2 > $o] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ ( collec5864963238570574385_b1_b2 @ ( produc81016565174098426291_b2_o @ A2 ) ) )
     => ( A2 @ ( product_fst_b1_b2 @ X2 ) @ ( product_snd_b1_b2 @ X2 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_229_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: product_prod_a1_a2,A2: a1 > a2 > $o] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ ( collec6500329951669444275_a1_a2 @ ( produc26642204215465646751_a2_o @ A2 ) ) )
     => ( A2 @ ( product_fst_a1_a2 @ X2 ) @ ( product_snd_a1_a2 @ X2 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_230_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: produc4061897789176782763set_c2,A2: mapping_b1_set_b2 > mapping_c1_set_c2 > $o] :
      ( ( member419137155788712276set_c2 @ X2 @ ( collec7917083185581317782set_c2 @ ( produc7359613910387544480t_c2_o @ A2 ) ) )
     => ( A2 @ ( produc4038274906788240847set_c2 @ X2 ) @ ( produc6032943676959796241set_c2 @ X2 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_231_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: produc2702059613074419827set_c2,A2: ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > $o] :
      ( ( member9053876291207143196set_c2 @ X2 @ ( collec6202298912161320542set_c2 @ ( produc115805034449689560t_c2_o @ A2 ) ) )
     => ( A2 @ ( produc3187122337049823639set_c2 @ X2 ) @ ( produc4575701783957131737set_c2 @ X2 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_232_lookup__update_H,axiom,
    ! [K: b1,K2: b1,V: set_b2,M3: mapping_b1_set_b2] :
      ( ( ( K = K2 )
       => ( ( lookup_b1_set_b2 @ ( update_b1_set_b2 @ K @ V @ M3 ) @ K2 )
          = ( some_set_b2 @ V ) ) )
      & ( ( K != K2 )
       => ( ( lookup_b1_set_b2 @ ( update_b1_set_b2 @ K @ V @ M3 ) @ K2 )
          = ( lookup_b1_set_b2 @ M3 @ K2 ) ) ) ) ).

% lookup_update'
thf(fact_233_lookup__update_H,axiom,
    ! [K: c1,K2: c1,V: set_c2,M3: mapping_c1_set_c2] :
      ( ( ( K = K2 )
       => ( ( lookup_c1_set_c2 @ ( update_c1_set_c2 @ K @ V @ M3 ) @ K2 )
          = ( some_set_c2 @ V ) ) )
      & ( ( K != K2 )
       => ( ( lookup_c1_set_c2 @ ( update_c1_set_c2 @ K @ V @ M3 ) @ K2 )
          = ( lookup_c1_set_c2 @ M3 @ K2 ) ) ) ) ).

% lookup_update'
thf(fact_234_mem__Collect__eq,axiom,
    ! [A: product_prod_c1_c2,P: product_prod_c1_c2 > $o] :
      ( ( member1440383022217085037_c1_c2 @ A @ ( collec5229596525471704495_c1_c2 @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_235_mem__Collect__eq,axiom,
    ! [A: product_prod_b1_b2,P: product_prod_b1_b2 > $o] :
      ( ( member2075749735315954927_b1_b2 @ A @ ( collec5864963238570574385_b1_b2 @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_236_mem__Collect__eq,axiom,
    ! [A: product_prod_a1_a2,P: product_prod_a1_a2 > $o] :
      ( ( member2711116448414824817_a1_a2 @ A @ ( collec6500329951669444275_a1_a2 @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_237_mem__Collect__eq,axiom,
    ! [A: mapping_c1_set_c2,P: mapping_c1_set_c2 > $o] :
      ( ( member341037065618468219set_c2 @ A @ ( collec787794305286987193set_c2 @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_238_mem__Collect__eq,axiom,
    ! [A: mapping_b1_set_b2,P: mapping_b1_set_b2 > $o] :
      ( ( member6117332676589958525set_b2 @ A @ ( collec6564089916258477499set_b2 @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_239_mem__Collect__eq,axiom,
    ! [A: nat,P: nat > $o] :
      ( ( member_nat @ A @ ( collect_nat @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_240_mem__Collect__eq,axiom,
    ! [A: c2,P: c2 > $o] :
      ( ( member_c2 @ A @ ( collect_c2 @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_241_mem__Collect__eq,axiom,
    ! [A: b2,P: b2 > $o] :
      ( ( member_b2 @ A @ ( collect_b2 @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_242_Collect__mem__eq,axiom,
    ! [A2: set_Pr9202269149784407460_c1_c2] :
      ( ( collec5229596525471704495_c1_c2
        @ ^ [X: product_prod_c1_c2] : ( member1440383022217085037_c1_c2 @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_243_Collect__mem__eq,axiom,
    ! [A2: set_Pr4592484330697324838_b1_b2] :
      ( ( collec5864963238570574385_b1_b2
        @ ^ [X: product_prod_b1_b2] : ( member2075749735315954927_b1_b2 @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_244_Collect__mem__eq,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2] :
      ( ( collec6500329951669444275_a1_a2
        @ ^ [X: product_prod_a1_a2] : ( member2711116448414824817_a1_a2 @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_245_Collect__mem__eq,axiom,
    ! [A2: set_ma7306327908849618074set_c2] :
      ( ( collec787794305286987193set_c2
        @ ^ [X: mapping_c1_set_c2] : ( member341037065618468219set_c2 @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_246_Collect__mem__eq,axiom,
    ! [A2: set_ma6254658672695423900set_b2] :
      ( ( collec6564089916258477499set_b2
        @ ^ [X: mapping_b1_set_b2] : ( member6117332676589958525set_b2 @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_247_Collect__mem__eq,axiom,
    ! [A2: set_nat] :
      ( ( collect_nat
        @ ^ [X: nat] : ( member_nat @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_248_Collect__mem__eq,axiom,
    ! [A2: set_c2] :
      ( ( collect_c2
        @ ^ [X: c2] : ( member_c2 @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_249_Collect__mem__eq,axiom,
    ! [A2: set_b2] :
      ( ( collect_b2
        @ ^ [X: b2] : ( member_b2 @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_250_Collect__cong,axiom,
    ! [P: nat > $o,Q: nat > $o] :
      ( ! [X3: nat] :
          ( ( P @ X3 )
          = ( Q @ X3 ) )
     => ( ( collect_nat @ P )
        = ( collect_nat @ Q ) ) ) ).

% Collect_cong
thf(fact_251_Collect__cong,axiom,
    ! [P: c2 > $o,Q: c2 > $o] :
      ( ! [X3: c2] :
          ( ( P @ X3 )
          = ( Q @ X3 ) )
     => ( ( collect_c2 @ P )
        = ( collect_c2 @ Q ) ) ) ).

% Collect_cong
thf(fact_252_Collect__cong,axiom,
    ! [P: b2 > $o,Q: b2 > $o] :
      ( ! [X3: b2] :
          ( ( P @ X3 )
          = ( Q @ X3 ) )
     => ( ( collect_b2 @ P )
        = ( collect_b2 @ Q ) ) ) ).

% Collect_cong
thf(fact_253_Pair__inject,axiom,
    ! [A: b1 > option_set_b2,B: c1 > option_set_c2,A3: b1 > option_set_b2,B3: c1 > option_set_c2] :
      ( ( ( produc890782565133688235set_c2 @ A @ B )
        = ( produc890782565133688235set_c2 @ A3 @ B3 ) )
     => ~ ( ( A = A3 )
         => ( B != B3 ) ) ) ).

% Pair_inject
thf(fact_254_Pair__inject,axiom,
    ! [A: mapping_b1_set_b2,B: mapping_c1_set_c2,A3: mapping_b1_set_b2,B3: mapping_c1_set_c2] :
      ( ( ( produc1212179418963815907set_c2 @ A @ B )
        = ( produc1212179418963815907set_c2 @ A3 @ B3 ) )
     => ~ ( ( A = A3 )
         => ( B != B3 ) ) ) ).

% Pair_inject
thf(fact_255_Pair__inject,axiom,
    ! [A: c1 > option_set_c2,B: b1 > option_set_b2,A3: c1 > option_set_c2,B3: b1 > option_set_b2] :
      ( ( ( produc4506454564149116331set_b2 @ A @ B )
        = ( produc4506454564149116331set_b2 @ A3 @ B3 ) )
     => ~ ( ( A = A3 )
         => ( B != B3 ) ) ) ).

% Pair_inject
thf(fact_256_Pair__inject,axiom,
    ! [A: b1 > option_set_b2,B: b1 > option_set_b2,A3: b1 > option_set_b2,B3: b1 > option_set_b2] :
      ( ( ( produc4375337561607790509set_b2 @ A @ B )
        = ( produc4375337561607790509set_b2 @ A3 @ B3 ) )
     => ~ ( ( A = A3 )
         => ( B != B3 ) ) ) ).

% Pair_inject
thf(fact_257_Pair__inject,axiom,
    ! [A: c1,B: c2,A3: c1,B3: c2] :
      ( ( ( product_Pair_c1_c2 @ A @ B )
        = ( product_Pair_c1_c2 @ A3 @ B3 ) )
     => ~ ( ( A = A3 )
         => ( B != B3 ) ) ) ).

% Pair_inject
thf(fact_258_Pair__inject,axiom,
    ! [A: b1,B: b2,A3: b1,B3: b2] :
      ( ( ( product_Pair_b1_b2 @ A @ B )
        = ( product_Pair_b1_b2 @ A3 @ B3 ) )
     => ~ ( ( A = A3 )
         => ( B != B3 ) ) ) ).

% Pair_inject
thf(fact_259_Pair__inject,axiom,
    ! [A: a1,B: a2,A3: a1,B3: a2] :
      ( ( ( product_Pair_a1_a2 @ A @ B )
        = ( product_Pair_a1_a2 @ A3 @ B3 ) )
     => ~ ( ( A = A3 )
         => ( B != B3 ) ) ) ).

% Pair_inject
thf(fact_260_prod__cases,axiom,
    ! [P: produc2702059613074419827set_c2 > $o,P2: produc2702059613074419827set_c2] :
      ( ! [A4: b1 > option_set_b2,B4: c1 > option_set_c2] : ( P @ ( produc890782565133688235set_c2 @ A4 @ B4 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_261_prod__cases,axiom,
    ! [P: produc4061897789176782763set_c2 > $o,P2: produc4061897789176782763set_c2] :
      ( ! [A4: mapping_b1_set_b2,B4: mapping_c1_set_c2] : ( P @ ( produc1212179418963815907set_c2 @ A4 @ B4 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_262_prod__cases,axiom,
    ! [P: produc8629413652255616883set_b2 > $o,P2: produc8629413652255616883set_b2] :
      ( ! [A4: c1 > option_set_c2,B4: b1 > option_set_b2] : ( P @ ( produc4506454564149116331set_b2 @ A4 @ B4 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_263_prod__cases,axiom,
    ! [P: produc8498296649714291061set_b2 > $o,P2: produc8498296649714291061set_b2] :
      ( ! [A4: b1 > option_set_b2,B4: b1 > option_set_b2] : ( P @ ( produc4375337561607790509set_b2 @ A4 @ B4 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_264_prod__cases,axiom,
    ! [P: product_prod_c1_c2 > $o,P2: product_prod_c1_c2] :
      ( ! [A4: c1,B4: c2] : ( P @ ( product_Pair_c1_c2 @ A4 @ B4 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_265_prod__cases,axiom,
    ! [P: product_prod_b1_b2 > $o,P2: product_prod_b1_b2] :
      ( ! [A4: b1,B4: b2] : ( P @ ( product_Pair_b1_b2 @ A4 @ B4 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_266_prod__cases,axiom,
    ! [P: product_prod_a1_a2 > $o,P2: product_prod_a1_a2] :
      ( ! [A4: a1,B4: a2] : ( P @ ( product_Pair_a1_a2 @ A4 @ B4 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_267_surj__pair,axiom,
    ! [P2: produc2702059613074419827set_c2] :
    ? [X3: b1 > option_set_b2,Y4: c1 > option_set_c2] :
      ( P2
      = ( produc890782565133688235set_c2 @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_268_surj__pair,axiom,
    ! [P2: produc4061897789176782763set_c2] :
    ? [X3: mapping_b1_set_b2,Y4: mapping_c1_set_c2] :
      ( P2
      = ( produc1212179418963815907set_c2 @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_269_surj__pair,axiom,
    ! [P2: produc8629413652255616883set_b2] :
    ? [X3: c1 > option_set_c2,Y4: b1 > option_set_b2] :
      ( P2
      = ( produc4506454564149116331set_b2 @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_270_surj__pair,axiom,
    ! [P2: produc8498296649714291061set_b2] :
    ? [X3: b1 > option_set_b2,Y4: b1 > option_set_b2] :
      ( P2
      = ( produc4375337561607790509set_b2 @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_271_surj__pair,axiom,
    ! [P2: product_prod_c1_c2] :
    ? [X3: c1,Y4: c2] :
      ( P2
      = ( product_Pair_c1_c2 @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_272_surj__pair,axiom,
    ! [P2: product_prod_b1_b2] :
    ? [X3: b1,Y4: b2] :
      ( P2
      = ( product_Pair_b1_b2 @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_273_surj__pair,axiom,
    ! [P2: product_prod_a1_a2] :
    ? [X3: a1,Y4: a2] :
      ( P2
      = ( product_Pair_a1_a2 @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_274_old_Oprod_Oexhaust,axiom,
    ! [Y5: produc2702059613074419827set_c2] :
      ~ ! [A4: b1 > option_set_b2,B4: c1 > option_set_c2] :
          ( Y5
         != ( produc890782565133688235set_c2 @ A4 @ B4 ) ) ).

% old.prod.exhaust
thf(fact_275_old_Oprod_Oexhaust,axiom,
    ! [Y5: produc4061897789176782763set_c2] :
      ~ ! [A4: mapping_b1_set_b2,B4: mapping_c1_set_c2] :
          ( Y5
         != ( produc1212179418963815907set_c2 @ A4 @ B4 ) ) ).

% old.prod.exhaust
thf(fact_276_old_Oprod_Oexhaust,axiom,
    ! [Y5: produc8629413652255616883set_b2] :
      ~ ! [A4: c1 > option_set_c2,B4: b1 > option_set_b2] :
          ( Y5
         != ( produc4506454564149116331set_b2 @ A4 @ B4 ) ) ).

% old.prod.exhaust
thf(fact_277_old_Oprod_Oexhaust,axiom,
    ! [Y5: produc8498296649714291061set_b2] :
      ~ ! [A4: b1 > option_set_b2,B4: b1 > option_set_b2] :
          ( Y5
         != ( produc4375337561607790509set_b2 @ A4 @ B4 ) ) ).

% old.prod.exhaust
thf(fact_278_old_Oprod_Oexhaust,axiom,
    ! [Y5: product_prod_c1_c2] :
      ~ ! [A4: c1,B4: c2] :
          ( Y5
         != ( product_Pair_c1_c2 @ A4 @ B4 ) ) ).

% old.prod.exhaust
thf(fact_279_old_Oprod_Oexhaust,axiom,
    ! [Y5: product_prod_b1_b2] :
      ~ ! [A4: b1,B4: b2] :
          ( Y5
         != ( product_Pair_b1_b2 @ A4 @ B4 ) ) ).

% old.prod.exhaust
thf(fact_280_old_Oprod_Oexhaust,axiom,
    ! [Y5: product_prod_a1_a2] :
      ~ ! [A4: a1,B4: a2] :
          ( Y5
         != ( product_Pair_a1_a2 @ A4 @ B4 ) ) ).

% old.prod.exhaust
thf(fact_281_rev__image__eqI,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B: product_prod_c1_c2,F: product_prod_c1_c2 > product_prod_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( B
          = ( F @ X2 ) )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_4046053779558312581_c1_c2 @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_282_rev__image__eqI,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B: product_prod_b1_b2,F: product_prod_c1_c2 > product_prod_b1_b2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( B
          = ( F @ X2 ) )
       => ( member2075749735315954927_b1_b2 @ B @ ( image_4681420492657182471_b1_b2 @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_283_rev__image__eqI,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B: product_prod_a1_a2,F: product_prod_c1_c2 > product_prod_a1_a2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( B
          = ( F @ X2 ) )
       => ( member2711116448414824817_a1_a2 @ B @ ( image_5316787205756052361_a1_a2 @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_284_rev__image__eqI,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B: product_prod_c1_c2,F: product_prod_b1_b2 > product_prod_c1_c2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ( B
          = ( F @ X2 ) )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_7016037314334516611_c1_c2 @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_285_rev__image__eqI,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B: product_prod_b1_b2,F: product_prod_b1_b2 > product_prod_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ( B
          = ( F @ X2 ) )
       => ( member2075749735315954927_b1_b2 @ B @ ( image_7651404027433386501_b1_b2 @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_286_rev__image__eqI,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B: product_prod_a1_a2,F: product_prod_b1_b2 > product_prod_a1_a2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ( B
          = ( F @ X2 ) )
       => ( member2711116448414824817_a1_a2 @ B @ ( image_8286770740532256391_a1_a2 @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_287_rev__image__eqI,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B: product_prod_c1_c2,F: product_prod_a1_a2 > product_prod_c1_c2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ( B
          = ( F @ X2 ) )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_762648812255944833_c1_c2 @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_288_rev__image__eqI,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B: product_prod_b1_b2,F: product_prod_a1_a2 > product_prod_b1_b2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ( B
          = ( F @ X2 ) )
       => ( member2075749735315954927_b1_b2 @ B @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_289_rev__image__eqI,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B: product_prod_a1_a2,F: product_prod_a1_a2 > product_prod_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ( B
          = ( F @ X2 ) )
       => ( member2711116448414824817_a1_a2 @ B @ ( image_2033382238453684613_a1_a2 @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_290_rev__image__eqI,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B: mapping_c1_set_c2,F: product_prod_c1_c2 > mapping_c1_set_c2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( B
          = ( F @ X2 ) )
       => ( member341037065618468219set_c2 @ B @ ( image_5984881132562613603set_c2 @ F @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_291_ball__imageD,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2,P: product_prod_b1_b2 > $o] :
      ( ! [X3: product_prod_b1_b2] :
          ( ( member2075749735315954927_b1_b2 @ X3 @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) )
         => ( P @ X3 ) )
     => ! [X4: product_prod_a1_a2] :
          ( ( member2711116448414824817_a1_a2 @ X4 @ A2 )
         => ( P @ ( F @ X4 ) ) ) ) ).

% ball_imageD
thf(fact_292_ball__imageD,axiom,
    ! [F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2,P: product_prod_c1_c2 > $o] :
      ( ! [X3: product_prod_c1_c2] :
          ( ( member1440383022217085037_c1_c2 @ X3 @ ( image_762648812255944833_c1_c2 @ F @ A2 ) )
         => ( P @ X3 ) )
     => ! [X4: product_prod_a1_a2] :
          ( ( member2711116448414824817_a1_a2 @ X4 @ A2 )
         => ( P @ ( F @ X4 ) ) ) ) ).

% ball_imageD
thf(fact_293_ball__imageD,axiom,
    ! [F: product_prod_c1_c2 > mapping_c1_set_c2,A2: set_Pr9202269149784407460_c1_c2,P: mapping_c1_set_c2 > $o] :
      ( ! [X3: mapping_c1_set_c2] :
          ( ( member341037065618468219set_c2 @ X3 @ ( image_5984881132562613603set_c2 @ F @ A2 ) )
         => ( P @ X3 ) )
     => ! [X4: product_prod_c1_c2] :
          ( ( member1440383022217085037_c1_c2 @ X4 @ A2 )
         => ( P @ ( F @ X4 ) ) ) ) ).

% ball_imageD
thf(fact_294_ball__imageD,axiom,
    ! [F: product_prod_b1_b2 > mapping_b1_set_b2,A2: set_Pr4592484330697324838_b1_b2,P: mapping_b1_set_b2 > $o] :
      ( ! [X3: mapping_b1_set_b2] :
          ( ( member6117332676589958525set_b2 @ X3 @ ( image_6686293874852392167set_b2 @ F @ A2 ) )
         => ( P @ X3 ) )
     => ! [X4: product_prod_b1_b2] :
          ( ( member2075749735315954927_b1_b2 @ X4 @ A2 )
         => ( P @ ( F @ X4 ) ) ) ) ).

% ball_imageD
thf(fact_295_ball__imageD,axiom,
    ! [F: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,A2: set_Pr1660683266160182027set_c2,P: produc4061897789176782763set_c2 > $o] :
      ( ! [X3: produc4061897789176782763set_c2] :
          ( ( member419137155788712276set_c2 @ X3 @ ( image_7945144516369962181set_c2 @ F @ A2 ) )
         => ( P @ X3 ) )
     => ! [X4: produc4061897789176782763set_c2] :
          ( ( member419137155788712276set_c2 @ X4 @ A2 )
         => ( P @ ( F @ X4 ) ) ) ) ).

% ball_imageD
thf(fact_296_image__cong,axiom,
    ! [M4: set_Pr1660683266160182027set_c2,N: set_Pr1660683266160182027set_c2,F: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,G: produc4061897789176782763set_c2 > produc4061897789176782763set_c2] :
      ( ( M4 = N )
     => ( ! [X3: produc4061897789176782763set_c2] :
            ( ( member419137155788712276set_c2 @ X3 @ N )
           => ( ( F @ X3 )
              = ( G @ X3 ) ) )
       => ( ( image_7945144516369962181set_c2 @ F @ M4 )
          = ( image_7945144516369962181set_c2 @ G @ N ) ) ) ) ).

% image_cong
thf(fact_297_image__cong,axiom,
    ! [M4: set_Pr9202269149784407460_c1_c2,N: set_Pr9202269149784407460_c1_c2,F: product_prod_c1_c2 > mapping_c1_set_c2,G: product_prod_c1_c2 > mapping_c1_set_c2] :
      ( ( M4 = N )
     => ( ! [X3: product_prod_c1_c2] :
            ( ( member1440383022217085037_c1_c2 @ X3 @ N )
           => ( ( F @ X3 )
              = ( G @ X3 ) ) )
       => ( ( image_5984881132562613603set_c2 @ F @ M4 )
          = ( image_5984881132562613603set_c2 @ G @ N ) ) ) ) ).

% image_cong
thf(fact_298_image__cong,axiom,
    ! [M4: set_Pr4592484330697324838_b1_b2,N: set_Pr4592484330697324838_b1_b2,F: product_prod_b1_b2 > mapping_b1_set_b2,G: product_prod_b1_b2 > mapping_b1_set_b2] :
      ( ( M4 = N )
     => ( ! [X3: product_prod_b1_b2] :
            ( ( member2075749735315954927_b1_b2 @ X3 @ N )
           => ( ( F @ X3 )
              = ( G @ X3 ) ) )
       => ( ( image_6686293874852392167set_b2 @ F @ M4 )
          = ( image_6686293874852392167set_b2 @ G @ N ) ) ) ) ).

% image_cong
thf(fact_299_image__cong,axiom,
    ! [M4: set_Pr9206071548465018024_a1_a2,N: set_Pr9206071548465018024_a1_a2,F: product_prod_a1_a2 > product_prod_b1_b2,G: product_prod_a1_a2 > product_prod_b1_b2] :
      ( ( M4 = N )
     => ( ! [X3: product_prod_a1_a2] :
            ( ( member2711116448414824817_a1_a2 @ X3 @ N )
           => ( ( F @ X3 )
              = ( G @ X3 ) ) )
       => ( ( image_1398015525354814723_b1_b2 @ F @ M4 )
          = ( image_1398015525354814723_b1_b2 @ G @ N ) ) ) ) ).

% image_cong
thf(fact_300_image__cong,axiom,
    ! [M4: set_Pr9206071548465018024_a1_a2,N: set_Pr9206071548465018024_a1_a2,F: product_prod_a1_a2 > product_prod_c1_c2,G: product_prod_a1_a2 > product_prod_c1_c2] :
      ( ( M4 = N )
     => ( ! [X3: product_prod_a1_a2] :
            ( ( member2711116448414824817_a1_a2 @ X3 @ N )
           => ( ( F @ X3 )
              = ( G @ X3 ) ) )
       => ( ( image_762648812255944833_c1_c2 @ F @ M4 )
          = ( image_762648812255944833_c1_c2 @ G @ N ) ) ) ) ).

% image_cong
thf(fact_301_bex__imageD,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2,P: product_prod_b1_b2 > $o] :
      ( ? [X4: product_prod_b1_b2] :
          ( ( member2075749735315954927_b1_b2 @ X4 @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) )
          & ( P @ X4 ) )
     => ? [X3: product_prod_a1_a2] :
          ( ( member2711116448414824817_a1_a2 @ X3 @ A2 )
          & ( P @ ( F @ X3 ) ) ) ) ).

% bex_imageD
thf(fact_302_bex__imageD,axiom,
    ! [F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2,P: product_prod_c1_c2 > $o] :
      ( ? [X4: product_prod_c1_c2] :
          ( ( member1440383022217085037_c1_c2 @ X4 @ ( image_762648812255944833_c1_c2 @ F @ A2 ) )
          & ( P @ X4 ) )
     => ? [X3: product_prod_a1_a2] :
          ( ( member2711116448414824817_a1_a2 @ X3 @ A2 )
          & ( P @ ( F @ X3 ) ) ) ) ).

% bex_imageD
thf(fact_303_bex__imageD,axiom,
    ! [F: product_prod_c1_c2 > mapping_c1_set_c2,A2: set_Pr9202269149784407460_c1_c2,P: mapping_c1_set_c2 > $o] :
      ( ? [X4: mapping_c1_set_c2] :
          ( ( member341037065618468219set_c2 @ X4 @ ( image_5984881132562613603set_c2 @ F @ A2 ) )
          & ( P @ X4 ) )
     => ? [X3: product_prod_c1_c2] :
          ( ( member1440383022217085037_c1_c2 @ X3 @ A2 )
          & ( P @ ( F @ X3 ) ) ) ) ).

% bex_imageD
thf(fact_304_bex__imageD,axiom,
    ! [F: product_prod_b1_b2 > mapping_b1_set_b2,A2: set_Pr4592484330697324838_b1_b2,P: mapping_b1_set_b2 > $o] :
      ( ? [X4: mapping_b1_set_b2] :
          ( ( member6117332676589958525set_b2 @ X4 @ ( image_6686293874852392167set_b2 @ F @ A2 ) )
          & ( P @ X4 ) )
     => ? [X3: product_prod_b1_b2] :
          ( ( member2075749735315954927_b1_b2 @ X3 @ A2 )
          & ( P @ ( F @ X3 ) ) ) ) ).

% bex_imageD
thf(fact_305_bex__imageD,axiom,
    ! [F: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,A2: set_Pr1660683266160182027set_c2,P: produc4061897789176782763set_c2 > $o] :
      ( ? [X4: produc4061897789176782763set_c2] :
          ( ( member419137155788712276set_c2 @ X4 @ ( image_7945144516369962181set_c2 @ F @ A2 ) )
          & ( P @ X4 ) )
     => ? [X3: produc4061897789176782763set_c2] :
          ( ( member419137155788712276set_c2 @ X3 @ A2 )
          & ( P @ ( F @ X3 ) ) ) ) ).

% bex_imageD
thf(fact_306_image__iff,axiom,
    ! [Z3: produc4061897789176782763set_c2,F: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,A2: set_Pr1660683266160182027set_c2] :
      ( ( member419137155788712276set_c2 @ Z3 @ ( image_7945144516369962181set_c2 @ F @ A2 ) )
      = ( ? [X: produc4061897789176782763set_c2] :
            ( ( member419137155788712276set_c2 @ X @ A2 )
            & ( Z3
              = ( F @ X ) ) ) ) ) ).

% image_iff
thf(fact_307_image__iff,axiom,
    ! [Z3: product_prod_c1_c2,F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member1440383022217085037_c1_c2 @ Z3 @ ( image_762648812255944833_c1_c2 @ F @ A2 ) )
      = ( ? [X: product_prod_a1_a2] :
            ( ( member2711116448414824817_a1_a2 @ X @ A2 )
            & ( Z3
              = ( F @ X ) ) ) ) ) ).

% image_iff
thf(fact_308_image__iff,axiom,
    ! [Z3: product_prod_b1_b2,F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2075749735315954927_b1_b2 @ Z3 @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) )
      = ( ? [X: product_prod_a1_a2] :
            ( ( member2711116448414824817_a1_a2 @ X @ A2 )
            & ( Z3
              = ( F @ X ) ) ) ) ) ).

% image_iff
thf(fact_309_image__iff,axiom,
    ! [Z3: mapping_c1_set_c2,F: product_prod_c1_c2 > mapping_c1_set_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member341037065618468219set_c2 @ Z3 @ ( image_5984881132562613603set_c2 @ F @ A2 ) )
      = ( ? [X: product_prod_c1_c2] :
            ( ( member1440383022217085037_c1_c2 @ X @ A2 )
            & ( Z3
              = ( F @ X ) ) ) ) ) ).

% image_iff
thf(fact_310_image__iff,axiom,
    ! [Z3: mapping_b1_set_b2,F: product_prod_b1_b2 > mapping_b1_set_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member6117332676589958525set_b2 @ Z3 @ ( image_6686293874852392167set_b2 @ F @ A2 ) )
      = ( ? [X: product_prod_b1_b2] :
            ( ( member2075749735315954927_b1_b2 @ X @ A2 )
            & ( Z3
              = ( F @ X ) ) ) ) ) ).

% image_iff
thf(fact_311_imageI,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,F: product_prod_c1_c2 > product_prod_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( member1440383022217085037_c1_c2 @ ( F @ X2 ) @ ( image_4046053779558312581_c1_c2 @ F @ A2 ) ) ) ).

% imageI
thf(fact_312_imageI,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,F: product_prod_c1_c2 > product_prod_b1_b2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( member2075749735315954927_b1_b2 @ ( F @ X2 ) @ ( image_4681420492657182471_b1_b2 @ F @ A2 ) ) ) ).

% imageI
thf(fact_313_imageI,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,F: product_prod_c1_c2 > product_prod_a1_a2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( member2711116448414824817_a1_a2 @ ( F @ X2 ) @ ( image_5316787205756052361_a1_a2 @ F @ A2 ) ) ) ).

% imageI
thf(fact_314_imageI,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,F: product_prod_b1_b2 > product_prod_c1_c2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( member1440383022217085037_c1_c2 @ ( F @ X2 ) @ ( image_7016037314334516611_c1_c2 @ F @ A2 ) ) ) ).

% imageI
thf(fact_315_imageI,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,F: product_prod_b1_b2 > product_prod_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( member2075749735315954927_b1_b2 @ ( F @ X2 ) @ ( image_7651404027433386501_b1_b2 @ F @ A2 ) ) ) ).

% imageI
thf(fact_316_imageI,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,F: product_prod_b1_b2 > product_prod_a1_a2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( member2711116448414824817_a1_a2 @ ( F @ X2 ) @ ( image_8286770740532256391_a1_a2 @ F @ A2 ) ) ) ).

% imageI
thf(fact_317_imageI,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,F: product_prod_a1_a2 > product_prod_c1_c2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( member1440383022217085037_c1_c2 @ ( F @ X2 ) @ ( image_762648812255944833_c1_c2 @ F @ A2 ) ) ) ).

% imageI
thf(fact_318_imageI,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,F: product_prod_a1_a2 > product_prod_b1_b2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( member2075749735315954927_b1_b2 @ ( F @ X2 ) @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) ) ) ).

% imageI
thf(fact_319_imageI,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,F: product_prod_a1_a2 > product_prod_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( member2711116448414824817_a1_a2 @ ( F @ X2 ) @ ( image_2033382238453684613_a1_a2 @ F @ A2 ) ) ) ).

% imageI
thf(fact_320_imageI,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,F: product_prod_c1_c2 > mapping_c1_set_c2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( member341037065618468219set_c2 @ ( F @ X2 ) @ ( image_5984881132562613603set_c2 @ F @ A2 ) ) ) ).

% imageI
thf(fact_321_ex__in__conv,axiom,
    ! [A2: set_Pr9202269149784407460_c1_c2] :
      ( ( ? [X: product_prod_c1_c2] : ( member1440383022217085037_c1_c2 @ X @ A2 ) )
      = ( A2 != bot_bo745477178175700496_c1_c2 ) ) ).

% ex_in_conv
thf(fact_322_ex__in__conv,axiom,
    ! [A2: set_Pr4592484330697324838_b1_b2] :
      ( ( ? [X: product_prod_b1_b2] : ( member2075749735315954927_b1_b2 @ X @ A2 ) )
      = ( A2 != bot_bo5359064395943393682_b1_b2 ) ) ).

% ex_in_conv
thf(fact_323_ex__in__conv,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2] :
      ( ( ? [X: product_prod_a1_a2] : ( member2711116448414824817_a1_a2 @ X @ A2 ) )
      = ( A2 != bot_bo749279576856311060_a1_a2 ) ) ).

% ex_in_conv
thf(fact_324_ex__in__conv,axiom,
    ! [A2: set_ma7306327908849618074set_c2] :
      ( ( ? [X: mapping_c1_set_c2] : ( member341037065618468219set_c2 @ X @ A2 ) )
      = ( A2 != bot_bo7584170878874662190set_c2 ) ) ).

% ex_in_conv
thf(fact_325_ex__in__conv,axiom,
    ! [A2: set_ma6254658672695423900set_b2] :
      ( ( ? [X: mapping_b1_set_b2] : ( member6117332676589958525set_b2 @ X @ A2 ) )
      = ( A2 != bot_bo6532501642720468016set_b2 ) ) ).

% ex_in_conv
thf(fact_326_ex__in__conv,axiom,
    ! [A2: set_b2] :
      ( ( ? [X: b2] : ( member_b2 @ X @ A2 ) )
      = ( A2 != bot_bot_set_b2 ) ) ).

% ex_in_conv
thf(fact_327_ex__in__conv,axiom,
    ! [A2: set_c2] :
      ( ( ? [X: c2] : ( member_c2 @ X @ A2 ) )
      = ( A2 != bot_bot_set_c2 ) ) ).

% ex_in_conv
thf(fact_328_ex__in__conv,axiom,
    ! [A2: set_nat] :
      ( ( ? [X: nat] : ( member_nat @ X @ A2 ) )
      = ( A2 != bot_bot_set_nat ) ) ).

% ex_in_conv
thf(fact_329_equals0I,axiom,
    ! [A2: set_Pr9202269149784407460_c1_c2] :
      ( ! [Y4: product_prod_c1_c2] :
          ~ ( member1440383022217085037_c1_c2 @ Y4 @ A2 )
     => ( A2 = bot_bo745477178175700496_c1_c2 ) ) ).

% equals0I
thf(fact_330_equals0I,axiom,
    ! [A2: set_Pr4592484330697324838_b1_b2] :
      ( ! [Y4: product_prod_b1_b2] :
          ~ ( member2075749735315954927_b1_b2 @ Y4 @ A2 )
     => ( A2 = bot_bo5359064395943393682_b1_b2 ) ) ).

% equals0I
thf(fact_331_equals0I,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2] :
      ( ! [Y4: product_prod_a1_a2] :
          ~ ( member2711116448414824817_a1_a2 @ Y4 @ A2 )
     => ( A2 = bot_bo749279576856311060_a1_a2 ) ) ).

% equals0I
thf(fact_332_equals0I,axiom,
    ! [A2: set_ma7306327908849618074set_c2] :
      ( ! [Y4: mapping_c1_set_c2] :
          ~ ( member341037065618468219set_c2 @ Y4 @ A2 )
     => ( A2 = bot_bo7584170878874662190set_c2 ) ) ).

% equals0I
thf(fact_333_equals0I,axiom,
    ! [A2: set_ma6254658672695423900set_b2] :
      ( ! [Y4: mapping_b1_set_b2] :
          ~ ( member6117332676589958525set_b2 @ Y4 @ A2 )
     => ( A2 = bot_bo6532501642720468016set_b2 ) ) ).

% equals0I
thf(fact_334_equals0I,axiom,
    ! [A2: set_b2] :
      ( ! [Y4: b2] :
          ~ ( member_b2 @ Y4 @ A2 )
     => ( A2 = bot_bot_set_b2 ) ) ).

% equals0I
thf(fact_335_equals0I,axiom,
    ! [A2: set_c2] :
      ( ! [Y4: c2] :
          ~ ( member_c2 @ Y4 @ A2 )
     => ( A2 = bot_bot_set_c2 ) ) ).

% equals0I
thf(fact_336_equals0I,axiom,
    ! [A2: set_nat] :
      ( ! [Y4: nat] :
          ~ ( member_nat @ Y4 @ A2 )
     => ( A2 = bot_bot_set_nat ) ) ).

% equals0I
thf(fact_337_equals0D,axiom,
    ! [A2: set_Pr9202269149784407460_c1_c2,A: product_prod_c1_c2] :
      ( ( A2 = bot_bo745477178175700496_c1_c2 )
     => ~ ( member1440383022217085037_c1_c2 @ A @ A2 ) ) ).

% equals0D
thf(fact_338_equals0D,axiom,
    ! [A2: set_Pr4592484330697324838_b1_b2,A: product_prod_b1_b2] :
      ( ( A2 = bot_bo5359064395943393682_b1_b2 )
     => ~ ( member2075749735315954927_b1_b2 @ A @ A2 ) ) ).

% equals0D
thf(fact_339_equals0D,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2,A: product_prod_a1_a2] :
      ( ( A2 = bot_bo749279576856311060_a1_a2 )
     => ~ ( member2711116448414824817_a1_a2 @ A @ A2 ) ) ).

% equals0D
thf(fact_340_equals0D,axiom,
    ! [A2: set_ma7306327908849618074set_c2,A: mapping_c1_set_c2] :
      ( ( A2 = bot_bo7584170878874662190set_c2 )
     => ~ ( member341037065618468219set_c2 @ A @ A2 ) ) ).

% equals0D
thf(fact_341_equals0D,axiom,
    ! [A2: set_ma6254658672695423900set_b2,A: mapping_b1_set_b2] :
      ( ( A2 = bot_bo6532501642720468016set_b2 )
     => ~ ( member6117332676589958525set_b2 @ A @ A2 ) ) ).

% equals0D
thf(fact_342_equals0D,axiom,
    ! [A2: set_b2,A: b2] :
      ( ( A2 = bot_bot_set_b2 )
     => ~ ( member_b2 @ A @ A2 ) ) ).

% equals0D
thf(fact_343_equals0D,axiom,
    ! [A2: set_c2,A: c2] :
      ( ( A2 = bot_bot_set_c2 )
     => ~ ( member_c2 @ A @ A2 ) ) ).

% equals0D
thf(fact_344_equals0D,axiom,
    ! [A2: set_nat,A: nat] :
      ( ( A2 = bot_bot_set_nat )
     => ~ ( member_nat @ A @ A2 ) ) ).

% equals0D
thf(fact_345_emptyE,axiom,
    ! [A: product_prod_c1_c2] :
      ~ ( member1440383022217085037_c1_c2 @ A @ bot_bo745477178175700496_c1_c2 ) ).

% emptyE
thf(fact_346_emptyE,axiom,
    ! [A: product_prod_b1_b2] :
      ~ ( member2075749735315954927_b1_b2 @ A @ bot_bo5359064395943393682_b1_b2 ) ).

% emptyE
thf(fact_347_emptyE,axiom,
    ! [A: product_prod_a1_a2] :
      ~ ( member2711116448414824817_a1_a2 @ A @ bot_bo749279576856311060_a1_a2 ) ).

% emptyE
thf(fact_348_emptyE,axiom,
    ! [A: mapping_c1_set_c2] :
      ~ ( member341037065618468219set_c2 @ A @ bot_bo7584170878874662190set_c2 ) ).

% emptyE
thf(fact_349_emptyE,axiom,
    ! [A: mapping_b1_set_b2] :
      ~ ( member6117332676589958525set_b2 @ A @ bot_bo6532501642720468016set_b2 ) ).

% emptyE
thf(fact_350_emptyE,axiom,
    ! [A: b2] :
      ~ ( member_b2 @ A @ bot_bot_set_b2 ) ).

% emptyE
thf(fact_351_emptyE,axiom,
    ! [A: c2] :
      ~ ( member_c2 @ A @ bot_bot_set_c2 ) ).

% emptyE
thf(fact_352_emptyE,axiom,
    ! [A: nat] :
      ~ ( member_nat @ A @ bot_bot_set_nat ) ).

% emptyE
thf(fact_353_mk__disjoint__insert,axiom,
    ! [A: b2,A2: set_b2] :
      ( ( member_b2 @ A @ A2 )
     => ? [B5: set_b2] :
          ( ( A2
            = ( insert_b2 @ A @ B5 ) )
          & ~ ( member_b2 @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_354_mk__disjoint__insert,axiom,
    ! [A: c2,A2: set_c2] :
      ( ( member_c2 @ A @ A2 )
     => ? [B5: set_c2] :
          ( ( A2
            = ( insert_c2 @ A @ B5 ) )
          & ~ ( member_c2 @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_355_mk__disjoint__insert,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( member_nat @ A @ A2 )
     => ? [B5: set_nat] :
          ( ( A2
            = ( insert_nat @ A @ B5 ) )
          & ~ ( member_nat @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_356_mk__disjoint__insert,axiom,
    ! [A: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ A @ A2 )
     => ? [B5: set_Pr9202269149784407460_c1_c2] :
          ( ( A2
            = ( insert7158109610518197396_c1_c2 @ A @ B5 ) )
          & ~ ( member1440383022217085037_c1_c2 @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_357_mk__disjoint__insert,axiom,
    ! [A: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ A @ A2 )
     => ? [B5: set_Pr4592484330697324838_b1_b2] :
          ( ( A2
            = ( insert7793476323617067286_b1_b2 @ A @ B5 ) )
          & ~ ( member2075749735315954927_b1_b2 @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_358_mk__disjoint__insert,axiom,
    ! [A: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ A @ A2 )
     => ? [B5: set_Pr9206071548465018024_a1_a2] :
          ( ( A2
            = ( insert8428843036715937176_a1_a2 @ A @ B5 ) )
          & ~ ( member2711116448414824817_a1_a2 @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_359_mk__disjoint__insert,axiom,
    ! [A: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ A @ A2 )
     => ? [B5: set_ma7306327908849618074set_c2] :
          ( ( A2
            = ( insert88652402460333204set_c2 @ A @ B5 ) )
          & ~ ( member341037065618468219set_c2 @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_360_mk__disjoint__insert,axiom,
    ! [A: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ A @ A2 )
     => ? [B5: set_ma6254658672695423900set_b2] :
          ( ( A2
            = ( insert5864948013431823510set_b2 @ A @ B5 ) )
          & ~ ( member6117332676589958525set_b2 @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_361_insert__commute,axiom,
    ! [X2: b2,Y5: b2,A2: set_b2] :
      ( ( insert_b2 @ X2 @ ( insert_b2 @ Y5 @ A2 ) )
      = ( insert_b2 @ Y5 @ ( insert_b2 @ X2 @ A2 ) ) ) ).

% insert_commute
thf(fact_362_insert__commute,axiom,
    ! [X2: c2,Y5: c2,A2: set_c2] :
      ( ( insert_c2 @ X2 @ ( insert_c2 @ Y5 @ A2 ) )
      = ( insert_c2 @ Y5 @ ( insert_c2 @ X2 @ A2 ) ) ) ).

% insert_commute
thf(fact_363_insert__commute,axiom,
    ! [X2: nat,Y5: nat,A2: set_nat] :
      ( ( insert_nat @ X2 @ ( insert_nat @ Y5 @ A2 ) )
      = ( insert_nat @ Y5 @ ( insert_nat @ X2 @ A2 ) ) ) ).

% insert_commute
thf(fact_364_insert__eq__iff,axiom,
    ! [A: b2,A2: set_b2,B: b2,B2: set_b2] :
      ( ~ ( member_b2 @ A @ A2 )
     => ( ~ ( member_b2 @ B @ B2 )
       => ( ( ( insert_b2 @ A @ A2 )
            = ( insert_b2 @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C2: set_b2] :
                  ( ( A2
                    = ( insert_b2 @ B @ C2 ) )
                  & ~ ( member_b2 @ B @ C2 )
                  & ( B2
                    = ( insert_b2 @ A @ C2 ) )
                  & ~ ( member_b2 @ A @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_365_insert__eq__iff,axiom,
    ! [A: c2,A2: set_c2,B: c2,B2: set_c2] :
      ( ~ ( member_c2 @ A @ A2 )
     => ( ~ ( member_c2 @ B @ B2 )
       => ( ( ( insert_c2 @ A @ A2 )
            = ( insert_c2 @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C2: set_c2] :
                  ( ( A2
                    = ( insert_c2 @ B @ C2 ) )
                  & ~ ( member_c2 @ B @ C2 )
                  & ( B2
                    = ( insert_c2 @ A @ C2 ) )
                  & ~ ( member_c2 @ A @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_366_insert__eq__iff,axiom,
    ! [A: nat,A2: set_nat,B: nat,B2: set_nat] :
      ( ~ ( member_nat @ A @ A2 )
     => ( ~ ( member_nat @ B @ B2 )
       => ( ( ( insert_nat @ A @ A2 )
            = ( insert_nat @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C2: set_nat] :
                  ( ( A2
                    = ( insert_nat @ B @ C2 ) )
                  & ~ ( member_nat @ B @ C2 )
                  & ( B2
                    = ( insert_nat @ A @ C2 ) )
                  & ~ ( member_nat @ A @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_367_insert__eq__iff,axiom,
    ! [A: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B: product_prod_c1_c2,B2: set_Pr9202269149784407460_c1_c2] :
      ( ~ ( member1440383022217085037_c1_c2 @ A @ A2 )
     => ( ~ ( member1440383022217085037_c1_c2 @ B @ B2 )
       => ( ( ( insert7158109610518197396_c1_c2 @ A @ A2 )
            = ( insert7158109610518197396_c1_c2 @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C2: set_Pr9202269149784407460_c1_c2] :
                  ( ( A2
                    = ( insert7158109610518197396_c1_c2 @ B @ C2 ) )
                  & ~ ( member1440383022217085037_c1_c2 @ B @ C2 )
                  & ( B2
                    = ( insert7158109610518197396_c1_c2 @ A @ C2 ) )
                  & ~ ( member1440383022217085037_c1_c2 @ A @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_368_insert__eq__iff,axiom,
    ! [A: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B: product_prod_b1_b2,B2: set_Pr4592484330697324838_b1_b2] :
      ( ~ ( member2075749735315954927_b1_b2 @ A @ A2 )
     => ( ~ ( member2075749735315954927_b1_b2 @ B @ B2 )
       => ( ( ( insert7793476323617067286_b1_b2 @ A @ A2 )
            = ( insert7793476323617067286_b1_b2 @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C2: set_Pr4592484330697324838_b1_b2] :
                  ( ( A2
                    = ( insert7793476323617067286_b1_b2 @ B @ C2 ) )
                  & ~ ( member2075749735315954927_b1_b2 @ B @ C2 )
                  & ( B2
                    = ( insert7793476323617067286_b1_b2 @ A @ C2 ) )
                  & ~ ( member2075749735315954927_b1_b2 @ A @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_369_insert__eq__iff,axiom,
    ! [A: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B: product_prod_a1_a2,B2: set_Pr9206071548465018024_a1_a2] :
      ( ~ ( member2711116448414824817_a1_a2 @ A @ A2 )
     => ( ~ ( member2711116448414824817_a1_a2 @ B @ B2 )
       => ( ( ( insert8428843036715937176_a1_a2 @ A @ A2 )
            = ( insert8428843036715937176_a1_a2 @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C2: set_Pr9206071548465018024_a1_a2] :
                  ( ( A2
                    = ( insert8428843036715937176_a1_a2 @ B @ C2 ) )
                  & ~ ( member2711116448414824817_a1_a2 @ B @ C2 )
                  & ( B2
                    = ( insert8428843036715937176_a1_a2 @ A @ C2 ) )
                  & ~ ( member2711116448414824817_a1_a2 @ A @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_370_insert__eq__iff,axiom,
    ! [A: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2,B: mapping_c1_set_c2,B2: set_ma7306327908849618074set_c2] :
      ( ~ ( member341037065618468219set_c2 @ A @ A2 )
     => ( ~ ( member341037065618468219set_c2 @ B @ B2 )
       => ( ( ( insert88652402460333204set_c2 @ A @ A2 )
            = ( insert88652402460333204set_c2 @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C2: set_ma7306327908849618074set_c2] :
                  ( ( A2
                    = ( insert88652402460333204set_c2 @ B @ C2 ) )
                  & ~ ( member341037065618468219set_c2 @ B @ C2 )
                  & ( B2
                    = ( insert88652402460333204set_c2 @ A @ C2 ) )
                  & ~ ( member341037065618468219set_c2 @ A @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_371_insert__eq__iff,axiom,
    ! [A: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2,B: mapping_b1_set_b2,B2: set_ma6254658672695423900set_b2] :
      ( ~ ( member6117332676589958525set_b2 @ A @ A2 )
     => ( ~ ( member6117332676589958525set_b2 @ B @ B2 )
       => ( ( ( insert5864948013431823510set_b2 @ A @ A2 )
            = ( insert5864948013431823510set_b2 @ B @ B2 ) )
          = ( ( ( A = B )
             => ( A2 = B2 ) )
            & ( ( A != B )
             => ? [C2: set_ma6254658672695423900set_b2] :
                  ( ( A2
                    = ( insert5864948013431823510set_b2 @ B @ C2 ) )
                  & ~ ( member6117332676589958525set_b2 @ B @ C2 )
                  & ( B2
                    = ( insert5864948013431823510set_b2 @ A @ C2 ) )
                  & ~ ( member6117332676589958525set_b2 @ A @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_372_insert__absorb,axiom,
    ! [A: b2,A2: set_b2] :
      ( ( member_b2 @ A @ A2 )
     => ( ( insert_b2 @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_373_insert__absorb,axiom,
    ! [A: c2,A2: set_c2] :
      ( ( member_c2 @ A @ A2 )
     => ( ( insert_c2 @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_374_insert__absorb,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( member_nat @ A @ A2 )
     => ( ( insert_nat @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_375_insert__absorb,axiom,
    ! [A: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ A @ A2 )
     => ( ( insert7158109610518197396_c1_c2 @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_376_insert__absorb,axiom,
    ! [A: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ A @ A2 )
     => ( ( insert7793476323617067286_b1_b2 @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_377_insert__absorb,axiom,
    ! [A: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ A @ A2 )
     => ( ( insert8428843036715937176_a1_a2 @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_378_insert__absorb,axiom,
    ! [A: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ A @ A2 )
     => ( ( insert88652402460333204set_c2 @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_379_insert__absorb,axiom,
    ! [A: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ A @ A2 )
     => ( ( insert5864948013431823510set_b2 @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_380_insert__ident,axiom,
    ! [X2: b2,A2: set_b2,B2: set_b2] :
      ( ~ ( member_b2 @ X2 @ A2 )
     => ( ~ ( member_b2 @ X2 @ B2 )
       => ( ( ( insert_b2 @ X2 @ A2 )
            = ( insert_b2 @ X2 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_381_insert__ident,axiom,
    ! [X2: c2,A2: set_c2,B2: set_c2] :
      ( ~ ( member_c2 @ X2 @ A2 )
     => ( ~ ( member_c2 @ X2 @ B2 )
       => ( ( ( insert_c2 @ X2 @ A2 )
            = ( insert_c2 @ X2 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_382_insert__ident,axiom,
    ! [X2: nat,A2: set_nat,B2: set_nat] :
      ( ~ ( member_nat @ X2 @ A2 )
     => ( ~ ( member_nat @ X2 @ B2 )
       => ( ( ( insert_nat @ X2 @ A2 )
            = ( insert_nat @ X2 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_383_insert__ident,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B2: set_Pr9202269149784407460_c1_c2] :
      ( ~ ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ~ ( member1440383022217085037_c1_c2 @ X2 @ B2 )
       => ( ( ( insert7158109610518197396_c1_c2 @ X2 @ A2 )
            = ( insert7158109610518197396_c1_c2 @ X2 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_384_insert__ident,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B2: set_Pr4592484330697324838_b1_b2] :
      ( ~ ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ~ ( member2075749735315954927_b1_b2 @ X2 @ B2 )
       => ( ( ( insert7793476323617067286_b1_b2 @ X2 @ A2 )
            = ( insert7793476323617067286_b1_b2 @ X2 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_385_insert__ident,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B2: set_Pr9206071548465018024_a1_a2] :
      ( ~ ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ~ ( member2711116448414824817_a1_a2 @ X2 @ B2 )
       => ( ( ( insert8428843036715937176_a1_a2 @ X2 @ A2 )
            = ( insert8428843036715937176_a1_a2 @ X2 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_386_insert__ident,axiom,
    ! [X2: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2,B2: set_ma7306327908849618074set_c2] :
      ( ~ ( member341037065618468219set_c2 @ X2 @ A2 )
     => ( ~ ( member341037065618468219set_c2 @ X2 @ B2 )
       => ( ( ( insert88652402460333204set_c2 @ X2 @ A2 )
            = ( insert88652402460333204set_c2 @ X2 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_387_insert__ident,axiom,
    ! [X2: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2,B2: set_ma6254658672695423900set_b2] :
      ( ~ ( member6117332676589958525set_b2 @ X2 @ A2 )
     => ( ~ ( member6117332676589958525set_b2 @ X2 @ B2 )
       => ( ( ( insert5864948013431823510set_b2 @ X2 @ A2 )
            = ( insert5864948013431823510set_b2 @ X2 @ B2 ) )
          = ( A2 = B2 ) ) ) ) ).

% insert_ident
thf(fact_388_Set_Oset__insert,axiom,
    ! [X2: b2,A2: set_b2] :
      ( ( member_b2 @ X2 @ A2 )
     => ~ ! [B5: set_b2] :
            ( ( A2
              = ( insert_b2 @ X2 @ B5 ) )
           => ( member_b2 @ X2 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_389_Set_Oset__insert,axiom,
    ! [X2: c2,A2: set_c2] :
      ( ( member_c2 @ X2 @ A2 )
     => ~ ! [B5: set_c2] :
            ( ( A2
              = ( insert_c2 @ X2 @ B5 ) )
           => ( member_c2 @ X2 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_390_Set_Oset__insert,axiom,
    ! [X2: nat,A2: set_nat] :
      ( ( member_nat @ X2 @ A2 )
     => ~ ! [B5: set_nat] :
            ( ( A2
              = ( insert_nat @ X2 @ B5 ) )
           => ( member_nat @ X2 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_391_Set_Oset__insert,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ~ ! [B5: set_Pr9202269149784407460_c1_c2] :
            ( ( A2
              = ( insert7158109610518197396_c1_c2 @ X2 @ B5 ) )
           => ( member1440383022217085037_c1_c2 @ X2 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_392_Set_Oset__insert,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ~ ! [B5: set_Pr4592484330697324838_b1_b2] :
            ( ( A2
              = ( insert7793476323617067286_b1_b2 @ X2 @ B5 ) )
           => ( member2075749735315954927_b1_b2 @ X2 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_393_Set_Oset__insert,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ~ ! [B5: set_Pr9206071548465018024_a1_a2] :
            ( ( A2
              = ( insert8428843036715937176_a1_a2 @ X2 @ B5 ) )
           => ( member2711116448414824817_a1_a2 @ X2 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_394_Set_Oset__insert,axiom,
    ! [X2: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ X2 @ A2 )
     => ~ ! [B5: set_ma7306327908849618074set_c2] :
            ( ( A2
              = ( insert88652402460333204set_c2 @ X2 @ B5 ) )
           => ( member341037065618468219set_c2 @ X2 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_395_Set_Oset__insert,axiom,
    ! [X2: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ X2 @ A2 )
     => ~ ! [B5: set_ma6254658672695423900set_b2] :
            ( ( A2
              = ( insert5864948013431823510set_b2 @ X2 @ B5 ) )
           => ( member6117332676589958525set_b2 @ X2 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_396_insertI2,axiom,
    ! [A: b2,B2: set_b2,B: b2] :
      ( ( member_b2 @ A @ B2 )
     => ( member_b2 @ A @ ( insert_b2 @ B @ B2 ) ) ) ).

% insertI2
thf(fact_397_insertI2,axiom,
    ! [A: c2,B2: set_c2,B: c2] :
      ( ( member_c2 @ A @ B2 )
     => ( member_c2 @ A @ ( insert_c2 @ B @ B2 ) ) ) ).

% insertI2
thf(fact_398_insertI2,axiom,
    ! [A: nat,B2: set_nat,B: nat] :
      ( ( member_nat @ A @ B2 )
     => ( member_nat @ A @ ( insert_nat @ B @ B2 ) ) ) ).

% insertI2
thf(fact_399_insertI2,axiom,
    ! [A: product_prod_c1_c2,B2: set_Pr9202269149784407460_c1_c2,B: product_prod_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ A @ B2 )
     => ( member1440383022217085037_c1_c2 @ A @ ( insert7158109610518197396_c1_c2 @ B @ B2 ) ) ) ).

% insertI2
thf(fact_400_insertI2,axiom,
    ! [A: product_prod_b1_b2,B2: set_Pr4592484330697324838_b1_b2,B: product_prod_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ A @ B2 )
     => ( member2075749735315954927_b1_b2 @ A @ ( insert7793476323617067286_b1_b2 @ B @ B2 ) ) ) ).

% insertI2
thf(fact_401_insertI2,axiom,
    ! [A: product_prod_a1_a2,B2: set_Pr9206071548465018024_a1_a2,B: product_prod_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ A @ B2 )
     => ( member2711116448414824817_a1_a2 @ A @ ( insert8428843036715937176_a1_a2 @ B @ B2 ) ) ) ).

% insertI2
thf(fact_402_insertI2,axiom,
    ! [A: mapping_c1_set_c2,B2: set_ma7306327908849618074set_c2,B: mapping_c1_set_c2] :
      ( ( member341037065618468219set_c2 @ A @ B2 )
     => ( member341037065618468219set_c2 @ A @ ( insert88652402460333204set_c2 @ B @ B2 ) ) ) ).

% insertI2
thf(fact_403_insertI2,axiom,
    ! [A: mapping_b1_set_b2,B2: set_ma6254658672695423900set_b2,B: mapping_b1_set_b2] :
      ( ( member6117332676589958525set_b2 @ A @ B2 )
     => ( member6117332676589958525set_b2 @ A @ ( insert5864948013431823510set_b2 @ B @ B2 ) ) ) ).

% insertI2
thf(fact_404_insertI1,axiom,
    ! [A: b2,B2: set_b2] : ( member_b2 @ A @ ( insert_b2 @ A @ B2 ) ) ).

% insertI1
thf(fact_405_insertI1,axiom,
    ! [A: c2,B2: set_c2] : ( member_c2 @ A @ ( insert_c2 @ A @ B2 ) ) ).

% insertI1
thf(fact_406_insertI1,axiom,
    ! [A: nat,B2: set_nat] : ( member_nat @ A @ ( insert_nat @ A @ B2 ) ) ).

% insertI1
thf(fact_407_insertI1,axiom,
    ! [A: product_prod_c1_c2,B2: set_Pr9202269149784407460_c1_c2] : ( member1440383022217085037_c1_c2 @ A @ ( insert7158109610518197396_c1_c2 @ A @ B2 ) ) ).

% insertI1
thf(fact_408_insertI1,axiom,
    ! [A: product_prod_b1_b2,B2: set_Pr4592484330697324838_b1_b2] : ( member2075749735315954927_b1_b2 @ A @ ( insert7793476323617067286_b1_b2 @ A @ B2 ) ) ).

% insertI1
thf(fact_409_insertI1,axiom,
    ! [A: product_prod_a1_a2,B2: set_Pr9206071548465018024_a1_a2] : ( member2711116448414824817_a1_a2 @ A @ ( insert8428843036715937176_a1_a2 @ A @ B2 ) ) ).

% insertI1
thf(fact_410_insertI1,axiom,
    ! [A: mapping_c1_set_c2,B2: set_ma7306327908849618074set_c2] : ( member341037065618468219set_c2 @ A @ ( insert88652402460333204set_c2 @ A @ B2 ) ) ).

% insertI1
thf(fact_411_insertI1,axiom,
    ! [A: mapping_b1_set_b2,B2: set_ma6254658672695423900set_b2] : ( member6117332676589958525set_b2 @ A @ ( insert5864948013431823510set_b2 @ A @ B2 ) ) ).

% insertI1
thf(fact_412_insertE,axiom,
    ! [A: b2,B: b2,A2: set_b2] :
      ( ( member_b2 @ A @ ( insert_b2 @ B @ A2 ) )
     => ( ( A != B )
       => ( member_b2 @ A @ A2 ) ) ) ).

% insertE
thf(fact_413_insertE,axiom,
    ! [A: c2,B: c2,A2: set_c2] :
      ( ( member_c2 @ A @ ( insert_c2 @ B @ A2 ) )
     => ( ( A != B )
       => ( member_c2 @ A @ A2 ) ) ) ).

% insertE
thf(fact_414_insertE,axiom,
    ! [A: nat,B: nat,A2: set_nat] :
      ( ( member_nat @ A @ ( insert_nat @ B @ A2 ) )
     => ( ( A != B )
       => ( member_nat @ A @ A2 ) ) ) ).

% insertE
thf(fact_415_insertE,axiom,
    ! [A: product_prod_c1_c2,B: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ A @ ( insert7158109610518197396_c1_c2 @ B @ A2 ) )
     => ( ( A != B )
       => ( member1440383022217085037_c1_c2 @ A @ A2 ) ) ) ).

% insertE
thf(fact_416_insertE,axiom,
    ! [A: product_prod_b1_b2,B: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ A @ ( insert7793476323617067286_b1_b2 @ B @ A2 ) )
     => ( ( A != B )
       => ( member2075749735315954927_b1_b2 @ A @ A2 ) ) ) ).

% insertE
thf(fact_417_insertE,axiom,
    ! [A: product_prod_a1_a2,B: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ A @ ( insert8428843036715937176_a1_a2 @ B @ A2 ) )
     => ( ( A != B )
       => ( member2711116448414824817_a1_a2 @ A @ A2 ) ) ) ).

% insertE
thf(fact_418_insertE,axiom,
    ! [A: mapping_c1_set_c2,B: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ A @ ( insert88652402460333204set_c2 @ B @ A2 ) )
     => ( ( A != B )
       => ( member341037065618468219set_c2 @ A @ A2 ) ) ) ).

% insertE
thf(fact_419_insertE,axiom,
    ! [A: mapping_b1_set_b2,B: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ A @ ( insert5864948013431823510set_b2 @ B @ A2 ) )
     => ( ( A != B )
       => ( member6117332676589958525set_b2 @ A @ A2 ) ) ) ).

% insertE
thf(fact_420_update__update_I1_J,axiom,
    ! [K: b1,V: set_b2,W: set_b2,M3: mapping_b1_set_b2] :
      ( ( update_b1_set_b2 @ K @ V @ ( update_b1_set_b2 @ K @ W @ M3 ) )
      = ( update_b1_set_b2 @ K @ V @ M3 ) ) ).

% update_update(1)
thf(fact_421_update__update_I1_J,axiom,
    ! [K: c1,V: set_c2,W: set_c2,M3: mapping_c1_set_c2] :
      ( ( update_c1_set_c2 @ K @ V @ ( update_c1_set_c2 @ K @ W @ M3 ) )
      = ( update_c1_set_c2 @ K @ V @ M3 ) ) ).

% update_update(1)
thf(fact_422_update__update_I2_J,axiom,
    ! [K: b1,L: b1,V: set_b2,W: set_b2,M3: mapping_b1_set_b2] :
      ( ( K != L )
     => ( ( update_b1_set_b2 @ K @ V @ ( update_b1_set_b2 @ L @ W @ M3 ) )
        = ( update_b1_set_b2 @ L @ W @ ( update_b1_set_b2 @ K @ V @ M3 ) ) ) ) ).

% update_update(2)
thf(fact_423_update__update_I2_J,axiom,
    ! [K: c1,L: c1,V: set_c2,W: set_c2,M3: mapping_c1_set_c2] :
      ( ( K != L )
     => ( ( update_c1_set_c2 @ K @ V @ ( update_c1_set_c2 @ L @ W @ M3 ) )
        = ( update_c1_set_c2 @ L @ W @ ( update_c1_set_c2 @ K @ V @ M3 ) ) ) ) ).

% update_update(2)
thf(fact_424_mapping__eqI,axiom,
    ! [M3: mapping_b1_set_b2,M5: mapping_b1_set_b2] :
      ( ! [X3: b1] :
          ( ( lookup_b1_set_b2 @ M3 @ X3 )
          = ( lookup_b1_set_b2 @ M5 @ X3 ) )
     => ( M3 = M5 ) ) ).

% mapping_eqI
thf(fact_425_mapping__eqI,axiom,
    ! [M3: mapping_c1_set_c2,M5: mapping_c1_set_c2] :
      ( ! [X3: c1] :
          ( ( lookup_c1_set_c2 @ M3 @ X3 )
          = ( lookup_c1_set_c2 @ M5 @ X3 ) )
     => ( M3 = M5 ) ) ).

% mapping_eqI
thf(fact_426_Compr__image__eq,axiom,
    ! [F: nat > nat,A2: set_nat,P: nat > $o] :
      ( ( collect_nat
        @ ^ [X: nat] :
            ( ( member_nat @ X @ ( image_nat_nat2 @ F @ A2 ) )
            & ( P @ X ) ) )
      = ( image_nat_nat2 @ F
        @ ( collect_nat
          @ ^ [X: nat] :
              ( ( member_nat @ X @ A2 )
              & ( P @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_427_Compr__image__eq,axiom,
    ! [F: c2 > nat,A2: set_c2,P: nat > $o] :
      ( ( collect_nat
        @ ^ [X: nat] :
            ( ( member_nat @ X @ ( image_c2_nat2 @ F @ A2 ) )
            & ( P @ X ) ) )
      = ( image_c2_nat2 @ F
        @ ( collect_c2
          @ ^ [X: c2] :
              ( ( member_c2 @ X @ A2 )
              & ( P @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_428_Compr__image__eq,axiom,
    ! [F: b2 > nat,A2: set_b2,P: nat > $o] :
      ( ( collect_nat
        @ ^ [X: nat] :
            ( ( member_nat @ X @ ( image_b2_nat2 @ F @ A2 ) )
            & ( P @ X ) ) )
      = ( image_b2_nat2 @ F
        @ ( collect_b2
          @ ^ [X: b2] :
              ( ( member_b2 @ X @ A2 )
              & ( P @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_429_Compr__image__eq,axiom,
    ! [F: nat > c2,A2: set_nat,P: c2 > $o] :
      ( ( collect_c2
        @ ^ [X: c2] :
            ( ( member_c2 @ X @ ( image_nat_c22 @ F @ A2 ) )
            & ( P @ X ) ) )
      = ( image_nat_c22 @ F
        @ ( collect_nat
          @ ^ [X: nat] :
              ( ( member_nat @ X @ A2 )
              & ( P @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_430_Compr__image__eq,axiom,
    ! [F: c2 > c2,A2: set_c2,P: c2 > $o] :
      ( ( collect_c2
        @ ^ [X: c2] :
            ( ( member_c2 @ X @ ( image_c2_c22 @ F @ A2 ) )
            & ( P @ X ) ) )
      = ( image_c2_c22 @ F
        @ ( collect_c2
          @ ^ [X: c2] :
              ( ( member_c2 @ X @ A2 )
              & ( P @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_431_Compr__image__eq,axiom,
    ! [F: b2 > c2,A2: set_b2,P: c2 > $o] :
      ( ( collect_c2
        @ ^ [X: c2] :
            ( ( member_c2 @ X @ ( image_b2_c22 @ F @ A2 ) )
            & ( P @ X ) ) )
      = ( image_b2_c22 @ F
        @ ( collect_b2
          @ ^ [X: b2] :
              ( ( member_b2 @ X @ A2 )
              & ( P @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_432_Compr__image__eq,axiom,
    ! [F: nat > b2,A2: set_nat,P: b2 > $o] :
      ( ( collect_b2
        @ ^ [X: b2] :
            ( ( member_b2 @ X @ ( image_nat_b22 @ F @ A2 ) )
            & ( P @ X ) ) )
      = ( image_nat_b22 @ F
        @ ( collect_nat
          @ ^ [X: nat] :
              ( ( member_nat @ X @ A2 )
              & ( P @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_433_Compr__image__eq,axiom,
    ! [F: c2 > b2,A2: set_c2,P: b2 > $o] :
      ( ( collect_b2
        @ ^ [X: b2] :
            ( ( member_b2 @ X @ ( image_c2_b22 @ F @ A2 ) )
            & ( P @ X ) ) )
      = ( image_c2_b22 @ F
        @ ( collect_c2
          @ ^ [X: c2] :
              ( ( member_c2 @ X @ A2 )
              & ( P @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_434_Compr__image__eq,axiom,
    ! [F: b2 > b2,A2: set_b2,P: b2 > $o] :
      ( ( collect_b2
        @ ^ [X: b2] :
            ( ( member_b2 @ X @ ( image_b2_b22 @ F @ A2 ) )
            & ( P @ X ) ) )
      = ( image_b2_b22 @ F
        @ ( collect_b2
          @ ^ [X: b2] :
              ( ( member_b2 @ X @ A2 )
              & ( P @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_435_Compr__image__eq,axiom,
    ! [F: nat > product_prod_c1_c2,A2: set_nat,P: product_prod_c1_c2 > $o] :
      ( ( collec5229596525471704495_c1_c2
        @ ^ [X: product_prod_c1_c2] :
            ( ( member1440383022217085037_c1_c2 @ X @ ( image_5449807374656740141_c1_c2 @ F @ A2 ) )
            & ( P @ X ) ) )
      = ( image_5449807374656740141_c1_c2 @ F
        @ ( collect_nat
          @ ^ [X: nat] :
              ( ( member_nat @ X @ A2 )
              & ( P @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_436_image__image,axiom,
    ! [F: product_prod_b1_b2 > product_prod_b1_b2,G: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_7651404027433386501_b1_b2 @ F @ ( image_1398015525354814723_b1_b2 @ G @ A2 ) )
      = ( image_1398015525354814723_b1_b2
        @ ^ [X: product_prod_a1_a2] : ( F @ ( G @ X ) )
        @ A2 ) ) ).

% image_image
thf(fact_437_image__image,axiom,
    ! [F: product_prod_b1_b2 > product_prod_c1_c2,G: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_7016037314334516611_c1_c2 @ F @ ( image_1398015525354814723_b1_b2 @ G @ A2 ) )
      = ( image_762648812255944833_c1_c2
        @ ^ [X: product_prod_a1_a2] : ( F @ ( G @ X ) )
        @ A2 ) ) ).

% image_image
thf(fact_438_image__image,axiom,
    ! [F: product_prod_c1_c2 > product_prod_b1_b2,G: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_4681420492657182471_b1_b2 @ F @ ( image_762648812255944833_c1_c2 @ G @ A2 ) )
      = ( image_1398015525354814723_b1_b2
        @ ^ [X: product_prod_a1_a2] : ( F @ ( G @ X ) )
        @ A2 ) ) ).

% image_image
thf(fact_439_image__image,axiom,
    ! [F: product_prod_c1_c2 > product_prod_c1_c2,G: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_4046053779558312581_c1_c2 @ F @ ( image_762648812255944833_c1_c2 @ G @ A2 ) )
      = ( image_762648812255944833_c1_c2
        @ ^ [X: product_prod_a1_a2] : ( F @ ( G @ X ) )
        @ A2 ) ) ).

% image_image
thf(fact_440_image__image,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2,G: product_prod_a1_a2 > product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_1398015525354814723_b1_b2 @ F @ ( image_2033382238453684613_a1_a2 @ G @ A2 ) )
      = ( image_1398015525354814723_b1_b2
        @ ^ [X: product_prod_a1_a2] : ( F @ ( G @ X ) )
        @ A2 ) ) ).

% image_image
thf(fact_441_image__image,axiom,
    ! [F: product_prod_a1_a2 > product_prod_c1_c2,G: product_prod_a1_a2 > product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_762648812255944833_c1_c2 @ F @ ( image_2033382238453684613_a1_a2 @ G @ A2 ) )
      = ( image_762648812255944833_c1_c2
        @ ^ [X: product_prod_a1_a2] : ( F @ ( G @ X ) )
        @ A2 ) ) ).

% image_image
thf(fact_442_image__image,axiom,
    ! [F: product_prod_c1_c2 > mapping_c1_set_c2,G: product_prod_c1_c2 > product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( image_5984881132562613603set_c2 @ F @ ( image_4046053779558312581_c1_c2 @ G @ A2 ) )
      = ( image_5984881132562613603set_c2
        @ ^ [X: product_prod_c1_c2] : ( F @ ( G @ X ) )
        @ A2 ) ) ).

% image_image
thf(fact_443_image__image,axiom,
    ! [F: product_prod_c1_c2 > mapping_c1_set_c2,G: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_5984881132562613603set_c2 @ F @ ( image_762648812255944833_c1_c2 @ G @ A2 ) )
      = ( image_5058487432053965927set_c2
        @ ^ [X: product_prod_a1_a2] : ( F @ ( G @ X ) )
        @ A2 ) ) ).

% image_image
thf(fact_444_image__image,axiom,
    ! [F: product_prod_b1_b2 > mapping_b1_set_b2,G: product_prod_b1_b2 > product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( image_6686293874852392167set_b2 @ F @ ( image_7651404027433386501_b1_b2 @ G @ A2 ) )
      = ( image_6686293874852392167set_b2
        @ ^ [X: product_prod_b1_b2] : ( F @ ( G @ X ) )
        @ A2 ) ) ).

% image_image
thf(fact_445_image__image,axiom,
    ! [F: product_prod_b1_b2 > mapping_b1_set_b2,G: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_6686293874852392167set_b2 @ F @ ( image_1398015525354814723_b1_b2 @ G @ A2 ) )
      = ( image_1611411006170680425set_b2
        @ ^ [X: product_prod_a1_a2] : ( F @ ( G @ X ) )
        @ A2 ) ) ).

% image_image
thf(fact_446_imageE,axiom,
    ! [B: product_prod_c1_c2,F: product_prod_c1_c2 > product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( image_4046053779558312581_c1_c2 @ F @ A2 ) )
     => ~ ! [X3: product_prod_c1_c2] :
            ( ( B
              = ( F @ X3 ) )
           => ~ ( member1440383022217085037_c1_c2 @ X3 @ A2 ) ) ) ).

% imageE
thf(fact_447_imageE,axiom,
    ! [B: product_prod_c1_c2,F: product_prod_b1_b2 > product_prod_c1_c2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( image_7016037314334516611_c1_c2 @ F @ A2 ) )
     => ~ ! [X3: product_prod_b1_b2] :
            ( ( B
              = ( F @ X3 ) )
           => ~ ( member2075749735315954927_b1_b2 @ X3 @ A2 ) ) ) ).

% imageE
thf(fact_448_imageE,axiom,
    ! [B: product_prod_c1_c2,F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( image_762648812255944833_c1_c2 @ F @ A2 ) )
     => ~ ! [X3: product_prod_a1_a2] :
            ( ( B
              = ( F @ X3 ) )
           => ~ ( member2711116448414824817_a1_a2 @ X3 @ A2 ) ) ) ).

% imageE
thf(fact_449_imageE,axiom,
    ! [B: product_prod_b1_b2,F: product_prod_c1_c2 > product_prod_b1_b2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member2075749735315954927_b1_b2 @ B @ ( image_4681420492657182471_b1_b2 @ F @ A2 ) )
     => ~ ! [X3: product_prod_c1_c2] :
            ( ( B
              = ( F @ X3 ) )
           => ~ ( member1440383022217085037_c1_c2 @ X3 @ A2 ) ) ) ).

% imageE
thf(fact_450_imageE,axiom,
    ! [B: product_prod_b1_b2,F: product_prod_b1_b2 > product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ B @ ( image_7651404027433386501_b1_b2 @ F @ A2 ) )
     => ~ ! [X3: product_prod_b1_b2] :
            ( ( B
              = ( F @ X3 ) )
           => ~ ( member2075749735315954927_b1_b2 @ X3 @ A2 ) ) ) ).

% imageE
thf(fact_451_imageE,axiom,
    ! [B: product_prod_b1_b2,F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2075749735315954927_b1_b2 @ B @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) )
     => ~ ! [X3: product_prod_a1_a2] :
            ( ( B
              = ( F @ X3 ) )
           => ~ ( member2711116448414824817_a1_a2 @ X3 @ A2 ) ) ) ).

% imageE
thf(fact_452_imageE,axiom,
    ! [B: product_prod_a1_a2,F: product_prod_c1_c2 > product_prod_a1_a2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member2711116448414824817_a1_a2 @ B @ ( image_5316787205756052361_a1_a2 @ F @ A2 ) )
     => ~ ! [X3: product_prod_c1_c2] :
            ( ( B
              = ( F @ X3 ) )
           => ~ ( member1440383022217085037_c1_c2 @ X3 @ A2 ) ) ) ).

% imageE
thf(fact_453_imageE,axiom,
    ! [B: product_prod_a1_a2,F: product_prod_b1_b2 > product_prod_a1_a2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2711116448414824817_a1_a2 @ B @ ( image_8286770740532256391_a1_a2 @ F @ A2 ) )
     => ~ ! [X3: product_prod_b1_b2] :
            ( ( B
              = ( F @ X3 ) )
           => ~ ( member2075749735315954927_b1_b2 @ X3 @ A2 ) ) ) ).

% imageE
thf(fact_454_imageE,axiom,
    ! [B: product_prod_a1_a2,F: product_prod_a1_a2 > product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ B @ ( image_2033382238453684613_a1_a2 @ F @ A2 ) )
     => ~ ! [X3: product_prod_a1_a2] :
            ( ( B
              = ( F @ X3 ) )
           => ~ ( member2711116448414824817_a1_a2 @ X3 @ A2 ) ) ) ).

% imageE
thf(fact_455_imageE,axiom,
    ! [B: product_prod_c1_c2,F: mapping_c1_set_c2 > product_prod_c1_c2,A2: set_ma7306327908849618074set_c2] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( image_7561950101481872025_c1_c2 @ F @ A2 ) )
     => ~ ! [X3: mapping_c1_set_c2] :
            ( ( B
              = ( F @ X3 ) )
           => ~ ( member341037065618468219set_c2 @ X3 @ A2 ) ) ) ).

% imageE
thf(fact_456_Set_Oempty__def,axiom,
    ( bot_bot_set_b2
    = ( collect_b2
      @ ^ [X: b2] : $false ) ) ).

% Set.empty_def
thf(fact_457_Set_Oempty__def,axiom,
    ( bot_bot_set_c2
    = ( collect_c2
      @ ^ [X: c2] : $false ) ) ).

% Set.empty_def
thf(fact_458_Set_Oempty__def,axiom,
    ( bot_bot_set_nat
    = ( collect_nat
      @ ^ [X: nat] : $false ) ) ).

% Set.empty_def
thf(fact_459_prod_Ocase__distrib,axiom,
    ! [H: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,F: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,Prod: produc4061897789176782763set_c2] :
      ( ( H @ ( produc4732439310506902963set_c2 @ F @ Prod ) )
      = ( produc4732439310506902963set_c2
        @ ^ [X12: mapping_b1_set_b2,X23: mapping_c1_set_c2] : ( H @ ( F @ X12 @ X23 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_460_prod_Ocase__distrib,axiom,
    ! [H: mapping_b1_set_b2 > mapping_b1_set_b2,F: b1 > b2 > mapping_b1_set_b2,Prod: product_prod_b1_b2] :
      ( ( H @ ( produc6418488838319782393set_b2 @ F @ Prod ) )
      = ( produc6418488838319782393set_b2
        @ ^ [X12: b1,X23: b2] : ( H @ ( F @ X12 @ X23 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_461_prod_Ocase__distrib,axiom,
    ! [H: mapping_c1_set_c2 > mapping_c1_set_c2,F: c1 > c2 > mapping_c1_set_c2,Prod: product_prod_c1_c2] :
      ( ( H @ ( produc4822369076420559349set_c2 @ F @ Prod ) )
      = ( produc4822369076420559349set_c2
        @ ^ [X12: c1,X23: c2] : ( H @ ( F @ X12 @ X23 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_462_prod_Ocase__distrib,axiom,
    ! [H: product_prod_c1_c2 > product_prod_c1_c2,F: a1 > a2 > product_prod_c1_c2,Prod: product_prod_a1_a2] :
      ( ( H @ ( produc885903088071324015_c1_c2 @ F @ Prod ) )
      = ( produc885903088071324015_c1_c2
        @ ^ [X12: a1,X23: a2] : ( H @ ( F @ X12 @ X23 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_463_prod_Ocase__distrib,axiom,
    ! [H: product_prod_c1_c2 > product_prod_b1_b2,F: a1 > a2 > product_prod_c1_c2,Prod: product_prod_a1_a2] :
      ( ( H @ ( produc885903088071324015_c1_c2 @ F @ Prod ) )
      = ( produc1521269801170193905_b1_b2
        @ ^ [X12: a1,X23: a2] : ( H @ ( F @ X12 @ X23 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_464_prod_Ocase__distrib,axiom,
    ! [H: product_prod_b1_b2 > product_prod_c1_c2,F: a1 > a2 > product_prod_b1_b2,Prod: product_prod_a1_a2] :
      ( ( H @ ( produc1521269801170193905_b1_b2 @ F @ Prod ) )
      = ( produc885903088071324015_c1_c2
        @ ^ [X12: a1,X23: a2] : ( H @ ( F @ X12 @ X23 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_465_prod_Ocase__distrib,axiom,
    ! [H: product_prod_b1_b2 > product_prod_b1_b2,F: a1 > a2 > product_prod_b1_b2,Prod: product_prod_a1_a2] :
      ( ( H @ ( produc1521269801170193905_b1_b2 @ F @ Prod ) )
      = ( produc1521269801170193905_b1_b2
        @ ^ [X12: a1,X23: a2] : ( H @ ( F @ X12 @ X23 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_466_insert__Collect,axiom,
    ! [A: nat,P: nat > $o] :
      ( ( insert_nat @ A @ ( collect_nat @ P ) )
      = ( collect_nat
        @ ^ [U: nat] :
            ( ( U != A )
           => ( P @ U ) ) ) ) ).

% insert_Collect
thf(fact_467_insert__Collect,axiom,
    ! [A: c2,P: c2 > $o] :
      ( ( insert_c2 @ A @ ( collect_c2 @ P ) )
      = ( collect_c2
        @ ^ [U: c2] :
            ( ( U != A )
           => ( P @ U ) ) ) ) ).

% insert_Collect
thf(fact_468_insert__Collect,axiom,
    ! [A: b2,P: b2 > $o] :
      ( ( insert_b2 @ A @ ( collect_b2 @ P ) )
      = ( collect_b2
        @ ^ [U: b2] :
            ( ( U != A )
           => ( P @ U ) ) ) ) ).

% insert_Collect
thf(fact_469_insert__compr,axiom,
    ( insert7158109610518197396_c1_c2
    = ( ^ [A5: product_prod_c1_c2,B6: set_Pr9202269149784407460_c1_c2] :
          ( collec5229596525471704495_c1_c2
          @ ^ [X: product_prod_c1_c2] :
              ( ( X = A5 )
              | ( member1440383022217085037_c1_c2 @ X @ B6 ) ) ) ) ) ).

% insert_compr
thf(fact_470_insert__compr,axiom,
    ( insert7793476323617067286_b1_b2
    = ( ^ [A5: product_prod_b1_b2,B6: set_Pr4592484330697324838_b1_b2] :
          ( collec5864963238570574385_b1_b2
          @ ^ [X: product_prod_b1_b2] :
              ( ( X = A5 )
              | ( member2075749735315954927_b1_b2 @ X @ B6 ) ) ) ) ) ).

% insert_compr
thf(fact_471_insert__compr,axiom,
    ( insert8428843036715937176_a1_a2
    = ( ^ [A5: product_prod_a1_a2,B6: set_Pr9206071548465018024_a1_a2] :
          ( collec6500329951669444275_a1_a2
          @ ^ [X: product_prod_a1_a2] :
              ( ( X = A5 )
              | ( member2711116448414824817_a1_a2 @ X @ B6 ) ) ) ) ) ).

% insert_compr
thf(fact_472_insert__compr,axiom,
    ( insert88652402460333204set_c2
    = ( ^ [A5: mapping_c1_set_c2,B6: set_ma7306327908849618074set_c2] :
          ( collec787794305286987193set_c2
          @ ^ [X: mapping_c1_set_c2] :
              ( ( X = A5 )
              | ( member341037065618468219set_c2 @ X @ B6 ) ) ) ) ) ).

% insert_compr
thf(fact_473_insert__compr,axiom,
    ( insert5864948013431823510set_b2
    = ( ^ [A5: mapping_b1_set_b2,B6: set_ma6254658672695423900set_b2] :
          ( collec6564089916258477499set_b2
          @ ^ [X: mapping_b1_set_b2] :
              ( ( X = A5 )
              | ( member6117332676589958525set_b2 @ X @ B6 ) ) ) ) ) ).

% insert_compr
thf(fact_474_insert__compr,axiom,
    ( insert_nat
    = ( ^ [A5: nat,B6: set_nat] :
          ( collect_nat
          @ ^ [X: nat] :
              ( ( X = A5 )
              | ( member_nat @ X @ B6 ) ) ) ) ) ).

% insert_compr
thf(fact_475_insert__compr,axiom,
    ( insert_c2
    = ( ^ [A5: c2,B6: set_c2] :
          ( collect_c2
          @ ^ [X: c2] :
              ( ( X = A5 )
              | ( member_c2 @ X @ B6 ) ) ) ) ) ).

% insert_compr
thf(fact_476_insert__compr,axiom,
    ( insert_b2
    = ( ^ [A5: b2,B6: set_b2] :
          ( collect_b2
          @ ^ [X: b2] :
              ( ( X = A5 )
              | ( member_b2 @ X @ B6 ) ) ) ) ) ).

% insert_compr
thf(fact_477_snd__conv,axiom,
    ! [X1: c1 > option_set_c2,X22: b1 > option_set_b2] :
      ( ( produc8191373782972559833set_b2 @ ( produc4506454564149116331set_b2 @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_478_snd__conv,axiom,
    ! [X1: b1 > option_set_b2,X22: b1 > option_set_b2] :
      ( ( produc8060256780431234011set_b2 @ ( produc4375337561607790509set_b2 @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_479_snd__conv,axiom,
    ! [X1: c1,X22: c2] :
      ( ( product_snd_c1_c2 @ ( product_Pair_c1_c2 @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_480_snd__conv,axiom,
    ! [X1: b1,X22: b2] :
      ( ( product_snd_b1_b2 @ ( product_Pair_b1_b2 @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_481_snd__conv,axiom,
    ! [X1: a1,X22: a2] :
      ( ( product_snd_a1_a2 @ ( product_Pair_a1_a2 @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_482_snd__conv,axiom,
    ! [X1: mapping_b1_set_b2,X22: mapping_c1_set_c2] :
      ( ( produc6032943676959796241set_c2 @ ( produc1212179418963815907set_c2 @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_483_snd__conv,axiom,
    ! [X1: b1 > option_set_b2,X22: c1 > option_set_c2] :
      ( ( produc4575701783957131737set_c2 @ ( produc890782565133688235set_c2 @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_484_snd__eqD,axiom,
    ! [X2: c1 > option_set_c2,Y5: b1 > option_set_b2,A: b1 > option_set_b2] :
      ( ( ( produc8191373782972559833set_b2 @ ( produc4506454564149116331set_b2 @ X2 @ Y5 ) )
        = A )
     => ( Y5 = A ) ) ).

% snd_eqD
thf(fact_485_snd__eqD,axiom,
    ! [X2: b1 > option_set_b2,Y5: b1 > option_set_b2,A: b1 > option_set_b2] :
      ( ( ( produc8060256780431234011set_b2 @ ( produc4375337561607790509set_b2 @ X2 @ Y5 ) )
        = A )
     => ( Y5 = A ) ) ).

% snd_eqD
thf(fact_486_snd__eqD,axiom,
    ! [X2: c1,Y5: c2,A: c2] :
      ( ( ( product_snd_c1_c2 @ ( product_Pair_c1_c2 @ X2 @ Y5 ) )
        = A )
     => ( Y5 = A ) ) ).

% snd_eqD
thf(fact_487_snd__eqD,axiom,
    ! [X2: b1,Y5: b2,A: b2] :
      ( ( ( product_snd_b1_b2 @ ( product_Pair_b1_b2 @ X2 @ Y5 ) )
        = A )
     => ( Y5 = A ) ) ).

% snd_eqD
thf(fact_488_snd__eqD,axiom,
    ! [X2: a1,Y5: a2,A: a2] :
      ( ( ( product_snd_a1_a2 @ ( product_Pair_a1_a2 @ X2 @ Y5 ) )
        = A )
     => ( Y5 = A ) ) ).

% snd_eqD
thf(fact_489_snd__eqD,axiom,
    ! [X2: mapping_b1_set_b2,Y5: mapping_c1_set_c2,A: mapping_c1_set_c2] :
      ( ( ( produc6032943676959796241set_c2 @ ( produc1212179418963815907set_c2 @ X2 @ Y5 ) )
        = A )
     => ( Y5 = A ) ) ).

% snd_eqD
thf(fact_490_snd__eqD,axiom,
    ! [X2: b1 > option_set_b2,Y5: c1 > option_set_c2,A: c1 > option_set_c2] :
      ( ( ( produc4575701783957131737set_c2 @ ( produc890782565133688235set_c2 @ X2 @ Y5 ) )
        = A )
     => ( Y5 = A ) ) ).

% snd_eqD
thf(fact_491_fst__conv,axiom,
    ! [X1: c1 > option_set_c2,X22: b1 > option_set_b2] :
      ( ( produc6802794336065251735set_b2 @ ( produc4506454564149116331set_b2 @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_492_fst__conv,axiom,
    ! [X1: b1 > option_set_b2,X22: b1 > option_set_b2] :
      ( ( produc6671677333523925913set_b2 @ ( produc4375337561607790509set_b2 @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_493_fst__conv,axiom,
    ! [X1: c1,X22: c2] :
      ( ( product_fst_c1_c2 @ ( product_Pair_c1_c2 @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_494_fst__conv,axiom,
    ! [X1: b1,X22: b2] :
      ( ( product_fst_b1_b2 @ ( product_Pair_b1_b2 @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_495_fst__conv,axiom,
    ! [X1: a1,X22: a2] :
      ( ( product_fst_a1_a2 @ ( product_Pair_a1_a2 @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_496_fst__conv,axiom,
    ! [X1: mapping_b1_set_b2,X22: mapping_c1_set_c2] :
      ( ( produc4038274906788240847set_c2 @ ( produc1212179418963815907set_c2 @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_497_fst__conv,axiom,
    ! [X1: b1 > option_set_b2,X22: c1 > option_set_c2] :
      ( ( produc3187122337049823639set_c2 @ ( produc890782565133688235set_c2 @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_498_fst__eqD,axiom,
    ! [X2: c1 > option_set_c2,Y5: b1 > option_set_b2,A: c1 > option_set_c2] :
      ( ( ( produc6802794336065251735set_b2 @ ( produc4506454564149116331set_b2 @ X2 @ Y5 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_499_fst__eqD,axiom,
    ! [X2: b1 > option_set_b2,Y5: b1 > option_set_b2,A: b1 > option_set_b2] :
      ( ( ( produc6671677333523925913set_b2 @ ( produc4375337561607790509set_b2 @ X2 @ Y5 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_500_fst__eqD,axiom,
    ! [X2: c1,Y5: c2,A: c1] :
      ( ( ( product_fst_c1_c2 @ ( product_Pair_c1_c2 @ X2 @ Y5 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_501_fst__eqD,axiom,
    ! [X2: b1,Y5: b2,A: b1] :
      ( ( ( product_fst_b1_b2 @ ( product_Pair_b1_b2 @ X2 @ Y5 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_502_fst__eqD,axiom,
    ! [X2: a1,Y5: a2,A: a1] :
      ( ( ( product_fst_a1_a2 @ ( product_Pair_a1_a2 @ X2 @ Y5 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_503_fst__eqD,axiom,
    ! [X2: mapping_b1_set_b2,Y5: mapping_c1_set_c2,A: mapping_b1_set_b2] :
      ( ( ( produc4038274906788240847set_c2 @ ( produc1212179418963815907set_c2 @ X2 @ Y5 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_504_fst__eqD,axiom,
    ! [X2: b1 > option_set_b2,Y5: c1 > option_set_c2,A: b1 > option_set_b2] :
      ( ( ( produc3187122337049823639set_c2 @ ( produc890782565133688235set_c2 @ X2 @ Y5 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_505_old_Oprod_Ocase,axiom,
    ! [F: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,X1: mapping_b1_set_b2,X22: mapping_c1_set_c2] :
      ( ( produc4732439310506902963set_c2 @ F @ ( produc1212179418963815907set_c2 @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_506_old_Oprod_Ocase,axiom,
    ! [F: b1 > b2 > mapping_b1_set_b2,X1: b1,X22: b2] :
      ( ( produc6418488838319782393set_b2 @ F @ ( product_Pair_b1_b2 @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_507_old_Oprod_Ocase,axiom,
    ! [F: c1 > c2 > mapping_c1_set_c2,X1: c1,X22: c2] :
      ( ( produc4822369076420559349set_c2 @ F @ ( product_Pair_c1_c2 @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_508_old_Oprod_Ocase,axiom,
    ! [F: a1 > a2 > product_prod_c1_c2,X1: a1,X22: a2] :
      ( ( produc885903088071324015_c1_c2 @ F @ ( product_Pair_a1_a2 @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_509_old_Oprod_Ocase,axiom,
    ! [F: a1 > a2 > product_prod_b1_b2,X1: a1,X22: a2] :
      ( ( produc1521269801170193905_b1_b2 @ F @ ( product_Pair_a1_a2 @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_510_prod__eq__iff,axiom,
    ( ( ^ [Y: produc4061897789176782763set_c2,Z2: produc4061897789176782763set_c2] : ( Y = Z2 ) )
    = ( ^ [S: produc4061897789176782763set_c2,T: produc4061897789176782763set_c2] :
          ( ( ( produc4038274906788240847set_c2 @ S )
            = ( produc4038274906788240847set_c2 @ T ) )
          & ( ( produc6032943676959796241set_c2 @ S )
            = ( produc6032943676959796241set_c2 @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_511_prod__eq__iff,axiom,
    ( ( ^ [Y: produc2702059613074419827set_c2,Z2: produc2702059613074419827set_c2] : ( Y = Z2 ) )
    = ( ^ [S: produc2702059613074419827set_c2,T: produc2702059613074419827set_c2] :
          ( ( ( produc3187122337049823639set_c2 @ S )
            = ( produc3187122337049823639set_c2 @ T ) )
          & ( ( produc4575701783957131737set_c2 @ S )
            = ( produc4575701783957131737set_c2 @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_512_prod__eqI,axiom,
    ! [P2: produc4061897789176782763set_c2,Q2: produc4061897789176782763set_c2] :
      ( ( ( produc4038274906788240847set_c2 @ P2 )
        = ( produc4038274906788240847set_c2 @ Q2 ) )
     => ( ( ( produc6032943676959796241set_c2 @ P2 )
          = ( produc6032943676959796241set_c2 @ Q2 ) )
       => ( P2 = Q2 ) ) ) ).

% prod_eqI
thf(fact_513_prod__eqI,axiom,
    ! [P2: produc2702059613074419827set_c2,Q2: produc2702059613074419827set_c2] :
      ( ( ( produc3187122337049823639set_c2 @ P2 )
        = ( produc3187122337049823639set_c2 @ Q2 ) )
     => ( ( ( produc4575701783957131737set_c2 @ P2 )
          = ( produc4575701783957131737set_c2 @ Q2 ) )
       => ( P2 = Q2 ) ) ) ).

% prod_eqI
thf(fact_514_prod_Oexpand,axiom,
    ! [Prod: produc4061897789176782763set_c2,Prod2: produc4061897789176782763set_c2] :
      ( ( ( ( produc4038274906788240847set_c2 @ Prod )
          = ( produc4038274906788240847set_c2 @ Prod2 ) )
        & ( ( produc6032943676959796241set_c2 @ Prod )
          = ( produc6032943676959796241set_c2 @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_515_prod_Oexpand,axiom,
    ! [Prod: produc2702059613074419827set_c2,Prod2: produc2702059613074419827set_c2] :
      ( ( ( ( produc3187122337049823639set_c2 @ Prod )
          = ( produc3187122337049823639set_c2 @ Prod2 ) )
        & ( ( produc4575701783957131737set_c2 @ Prod )
          = ( produc4575701783957131737set_c2 @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_516_singleton__inject,axiom,
    ! [A: b2,B: b2] :
      ( ( ( insert_b2 @ A @ bot_bot_set_b2 )
        = ( insert_b2 @ B @ bot_bot_set_b2 ) )
     => ( A = B ) ) ).

% singleton_inject
thf(fact_517_singleton__inject,axiom,
    ! [A: c2,B: c2] :
      ( ( ( insert_c2 @ A @ bot_bot_set_c2 )
        = ( insert_c2 @ B @ bot_bot_set_c2 ) )
     => ( A = B ) ) ).

% singleton_inject
thf(fact_518_singleton__inject,axiom,
    ! [A: nat,B: nat] :
      ( ( ( insert_nat @ A @ bot_bot_set_nat )
        = ( insert_nat @ B @ bot_bot_set_nat ) )
     => ( A = B ) ) ).

% singleton_inject
thf(fact_519_insert__not__empty,axiom,
    ! [A: b2,A2: set_b2] :
      ( ( insert_b2 @ A @ A2 )
     != bot_bot_set_b2 ) ).

% insert_not_empty
thf(fact_520_insert__not__empty,axiom,
    ! [A: c2,A2: set_c2] :
      ( ( insert_c2 @ A @ A2 )
     != bot_bot_set_c2 ) ).

% insert_not_empty
thf(fact_521_insert__not__empty,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( insert_nat @ A @ A2 )
     != bot_bot_set_nat ) ).

% insert_not_empty
thf(fact_522_doubleton__eq__iff,axiom,
    ! [A: b2,B: b2,C: b2,D: b2] :
      ( ( ( insert_b2 @ A @ ( insert_b2 @ B @ bot_bot_set_b2 ) )
        = ( insert_b2 @ C @ ( insert_b2 @ D @ bot_bot_set_b2 ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_523_doubleton__eq__iff,axiom,
    ! [A: c2,B: c2,C: c2,D: c2] :
      ( ( ( insert_c2 @ A @ ( insert_c2 @ B @ bot_bot_set_c2 ) )
        = ( insert_c2 @ C @ ( insert_c2 @ D @ bot_bot_set_c2 ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_524_doubleton__eq__iff,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) )
        = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_525_singleton__iff,axiom,
    ! [B: product_prod_c1_c2,A: product_prod_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( insert7158109610518197396_c1_c2 @ A @ bot_bo745477178175700496_c1_c2 ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_526_singleton__iff,axiom,
    ! [B: product_prod_b1_b2,A: product_prod_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ B @ ( insert7793476323617067286_b1_b2 @ A @ bot_bo5359064395943393682_b1_b2 ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_527_singleton__iff,axiom,
    ! [B: product_prod_a1_a2,A: product_prod_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ B @ ( insert8428843036715937176_a1_a2 @ A @ bot_bo749279576856311060_a1_a2 ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_528_singleton__iff,axiom,
    ! [B: mapping_c1_set_c2,A: mapping_c1_set_c2] :
      ( ( member341037065618468219set_c2 @ B @ ( insert88652402460333204set_c2 @ A @ bot_bo7584170878874662190set_c2 ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_529_singleton__iff,axiom,
    ! [B: mapping_b1_set_b2,A: mapping_b1_set_b2] :
      ( ( member6117332676589958525set_b2 @ B @ ( insert5864948013431823510set_b2 @ A @ bot_bo6532501642720468016set_b2 ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_530_singleton__iff,axiom,
    ! [B: b2,A: b2] :
      ( ( member_b2 @ B @ ( insert_b2 @ A @ bot_bot_set_b2 ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_531_singleton__iff,axiom,
    ! [B: c2,A: c2] :
      ( ( member_c2 @ B @ ( insert_c2 @ A @ bot_bot_set_c2 ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_532_singleton__iff,axiom,
    ! [B: nat,A: nat] :
      ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_533_singletonD,axiom,
    ! [B: product_prod_c1_c2,A: product_prod_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( insert7158109610518197396_c1_c2 @ A @ bot_bo745477178175700496_c1_c2 ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_534_singletonD,axiom,
    ! [B: product_prod_b1_b2,A: product_prod_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ B @ ( insert7793476323617067286_b1_b2 @ A @ bot_bo5359064395943393682_b1_b2 ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_535_singletonD,axiom,
    ! [B: product_prod_a1_a2,A: product_prod_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ B @ ( insert8428843036715937176_a1_a2 @ A @ bot_bo749279576856311060_a1_a2 ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_536_singletonD,axiom,
    ! [B: mapping_c1_set_c2,A: mapping_c1_set_c2] :
      ( ( member341037065618468219set_c2 @ B @ ( insert88652402460333204set_c2 @ A @ bot_bo7584170878874662190set_c2 ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_537_singletonD,axiom,
    ! [B: mapping_b1_set_b2,A: mapping_b1_set_b2] :
      ( ( member6117332676589958525set_b2 @ B @ ( insert5864948013431823510set_b2 @ A @ bot_bo6532501642720468016set_b2 ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_538_singletonD,axiom,
    ! [B: b2,A: b2] :
      ( ( member_b2 @ B @ ( insert_b2 @ A @ bot_bot_set_b2 ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_539_singletonD,axiom,
    ! [B: c2,A: c2] :
      ( ( member_c2 @ B @ ( insert_c2 @ A @ bot_bot_set_c2 ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_540_singletonD,axiom,
    ! [B: nat,A: nat] :
      ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_541_cond__case__prod__eta,axiom,
    ! [F: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,G: produc4061897789176782763set_c2 > produc4061897789176782763set_c2] :
      ( ! [X3: mapping_b1_set_b2,Y4: mapping_c1_set_c2] :
          ( ( F @ X3 @ Y4 )
          = ( G @ ( produc1212179418963815907set_c2 @ X3 @ Y4 ) ) )
     => ( ( produc4732439310506902963set_c2 @ F )
        = G ) ) ).

% cond_case_prod_eta
thf(fact_542_cond__case__prod__eta,axiom,
    ! [F: b1 > b2 > mapping_b1_set_b2,G: product_prod_b1_b2 > mapping_b1_set_b2] :
      ( ! [X3: b1,Y4: b2] :
          ( ( F @ X3 @ Y4 )
          = ( G @ ( product_Pair_b1_b2 @ X3 @ Y4 ) ) )
     => ( ( produc6418488838319782393set_b2 @ F )
        = G ) ) ).

% cond_case_prod_eta
thf(fact_543_cond__case__prod__eta,axiom,
    ! [F: c1 > c2 > mapping_c1_set_c2,G: product_prod_c1_c2 > mapping_c1_set_c2] :
      ( ! [X3: c1,Y4: c2] :
          ( ( F @ X3 @ Y4 )
          = ( G @ ( product_Pair_c1_c2 @ X3 @ Y4 ) ) )
     => ( ( produc4822369076420559349set_c2 @ F )
        = G ) ) ).

% cond_case_prod_eta
thf(fact_544_cond__case__prod__eta,axiom,
    ! [F: a1 > a2 > product_prod_c1_c2,G: product_prod_a1_a2 > product_prod_c1_c2] :
      ( ! [X3: a1,Y4: a2] :
          ( ( F @ X3 @ Y4 )
          = ( G @ ( product_Pair_a1_a2 @ X3 @ Y4 ) ) )
     => ( ( produc885903088071324015_c1_c2 @ F )
        = G ) ) ).

% cond_case_prod_eta
thf(fact_545_cond__case__prod__eta,axiom,
    ! [F: a1 > a2 > product_prod_b1_b2,G: product_prod_a1_a2 > product_prod_b1_b2] :
      ( ! [X3: a1,Y4: a2] :
          ( ( F @ X3 @ Y4 )
          = ( G @ ( product_Pair_a1_a2 @ X3 @ Y4 ) ) )
     => ( ( produc1521269801170193905_b1_b2 @ F )
        = G ) ) ).

% cond_case_prod_eta
thf(fact_546_case__prod__eta,axiom,
    ! [F: produc4061897789176782763set_c2 > produc4061897789176782763set_c2] :
      ( ( produc4732439310506902963set_c2
        @ ^ [X: mapping_b1_set_b2,Y6: mapping_c1_set_c2] : ( F @ ( produc1212179418963815907set_c2 @ X @ Y6 ) ) )
      = F ) ).

% case_prod_eta
thf(fact_547_case__prod__eta,axiom,
    ! [F: product_prod_b1_b2 > mapping_b1_set_b2] :
      ( ( produc6418488838319782393set_b2
        @ ^ [X: b1,Y6: b2] : ( F @ ( product_Pair_b1_b2 @ X @ Y6 ) ) )
      = F ) ).

% case_prod_eta
thf(fact_548_case__prod__eta,axiom,
    ! [F: product_prod_c1_c2 > mapping_c1_set_c2] :
      ( ( produc4822369076420559349set_c2
        @ ^ [X: c1,Y6: c2] : ( F @ ( product_Pair_c1_c2 @ X @ Y6 ) ) )
      = F ) ).

% case_prod_eta
thf(fact_549_case__prod__eta,axiom,
    ! [F: product_prod_a1_a2 > product_prod_c1_c2] :
      ( ( produc885903088071324015_c1_c2
        @ ^ [X: a1,Y6: a2] : ( F @ ( product_Pair_a1_a2 @ X @ Y6 ) ) )
      = F ) ).

% case_prod_eta
thf(fact_550_case__prod__eta,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2] :
      ( ( produc1521269801170193905_b1_b2
        @ ^ [X: a1,Y6: a2] : ( F @ ( product_Pair_a1_a2 @ X @ Y6 ) ) )
      = F ) ).

% case_prod_eta
thf(fact_551_case__prodE2,axiom,
    ! [Q: produc4061897789176782763set_c2 > $o,P: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,Z3: produc4061897789176782763set_c2] :
      ( ( Q @ ( produc4732439310506902963set_c2 @ P @ Z3 ) )
     => ~ ! [X3: mapping_b1_set_b2,Y4: mapping_c1_set_c2] :
            ( ( Z3
              = ( produc1212179418963815907set_c2 @ X3 @ Y4 ) )
           => ~ ( Q @ ( P @ X3 @ Y4 ) ) ) ) ).

% case_prodE2
thf(fact_552_case__prodE2,axiom,
    ! [Q: mapping_b1_set_b2 > $o,P: b1 > b2 > mapping_b1_set_b2,Z3: product_prod_b1_b2] :
      ( ( Q @ ( produc6418488838319782393set_b2 @ P @ Z3 ) )
     => ~ ! [X3: b1,Y4: b2] :
            ( ( Z3
              = ( product_Pair_b1_b2 @ X3 @ Y4 ) )
           => ~ ( Q @ ( P @ X3 @ Y4 ) ) ) ) ).

% case_prodE2
thf(fact_553_case__prodE2,axiom,
    ! [Q: mapping_c1_set_c2 > $o,P: c1 > c2 > mapping_c1_set_c2,Z3: product_prod_c1_c2] :
      ( ( Q @ ( produc4822369076420559349set_c2 @ P @ Z3 ) )
     => ~ ! [X3: c1,Y4: c2] :
            ( ( Z3
              = ( product_Pair_c1_c2 @ X3 @ Y4 ) )
           => ~ ( Q @ ( P @ X3 @ Y4 ) ) ) ) ).

% case_prodE2
thf(fact_554_case__prodE2,axiom,
    ! [Q: product_prod_c1_c2 > $o,P: a1 > a2 > product_prod_c1_c2,Z3: product_prod_a1_a2] :
      ( ( Q @ ( produc885903088071324015_c1_c2 @ P @ Z3 ) )
     => ~ ! [X3: a1,Y4: a2] :
            ( ( Z3
              = ( product_Pair_a1_a2 @ X3 @ Y4 ) )
           => ~ ( Q @ ( P @ X3 @ Y4 ) ) ) ) ).

% case_prodE2
thf(fact_555_case__prodE2,axiom,
    ! [Q: product_prod_b1_b2 > $o,P: a1 > a2 > product_prod_b1_b2,Z3: product_prod_a1_a2] :
      ( ( Q @ ( produc1521269801170193905_b1_b2 @ P @ Z3 ) )
     => ~ ! [X3: a1,Y4: a2] :
            ( ( Z3
              = ( product_Pair_a1_a2 @ X3 @ Y4 ) )
           => ~ ( Q @ ( P @ X3 @ Y4 ) ) ) ) ).

% case_prodE2
thf(fact_556_snd__def,axiom,
    ( produc6032943676959796241set_c2
    = ( produc9145124540134137436set_c2
      @ ^ [X12: mapping_b1_set_b2,X23: mapping_c1_set_c2] : X23 ) ) ).

% snd_def
thf(fact_557_snd__def,axiom,
    ( produc4575701783957131737set_c2
    = ( produc6183034434716109384set_c2
      @ ^ [X12: b1 > option_set_b2,X23: c1 > option_set_c2] : X23 ) ) ).

% snd_def
thf(fact_558_fst__def,axiom,
    ( produc4038274906788240847set_c2
    = ( produc5698048114250851934set_b2
      @ ^ [X12: mapping_b1_set_b2,X23: mapping_c1_set_c2] : X12 ) ) ).

% fst_def
thf(fact_559_fst__def,axiom,
    ( produc3187122337049823639set_c2
    = ( produc444217394335435850set_b2
      @ ^ [X12: b1 > option_set_b2,X23: c1 > option_set_c2] : X12 ) ) ).

% fst_def
thf(fact_560_Collect__conv__if2,axiom,
    ! [P: b2 > $o,A: b2] :
      ( ( ( P @ A )
       => ( ( collect_b2
            @ ^ [X: b2] :
                ( ( A = X )
                & ( P @ X ) ) )
          = ( insert_b2 @ A @ bot_bot_set_b2 ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_b2
            @ ^ [X: b2] :
                ( ( A = X )
                & ( P @ X ) ) )
          = bot_bot_set_b2 ) ) ) ).

% Collect_conv_if2
thf(fact_561_Collect__conv__if2,axiom,
    ! [P: c2 > $o,A: c2] :
      ( ( ( P @ A )
       => ( ( collect_c2
            @ ^ [X: c2] :
                ( ( A = X )
                & ( P @ X ) ) )
          = ( insert_c2 @ A @ bot_bot_set_c2 ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_c2
            @ ^ [X: c2] :
                ( ( A = X )
                & ( P @ X ) ) )
          = bot_bot_set_c2 ) ) ) ).

% Collect_conv_if2
thf(fact_562_Collect__conv__if2,axiom,
    ! [P: nat > $o,A: nat] :
      ( ( ( P @ A )
       => ( ( collect_nat
            @ ^ [X: nat] :
                ( ( A = X )
                & ( P @ X ) ) )
          = ( insert_nat @ A @ bot_bot_set_nat ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_nat
            @ ^ [X: nat] :
                ( ( A = X )
                & ( P @ X ) ) )
          = bot_bot_set_nat ) ) ) ).

% Collect_conv_if2
thf(fact_563_Collect__conv__if,axiom,
    ! [P: b2 > $o,A: b2] :
      ( ( ( P @ A )
       => ( ( collect_b2
            @ ^ [X: b2] :
                ( ( X = A )
                & ( P @ X ) ) )
          = ( insert_b2 @ A @ bot_bot_set_b2 ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_b2
            @ ^ [X: b2] :
                ( ( X = A )
                & ( P @ X ) ) )
          = bot_bot_set_b2 ) ) ) ).

% Collect_conv_if
thf(fact_564_Collect__conv__if,axiom,
    ! [P: c2 > $o,A: c2] :
      ( ( ( P @ A )
       => ( ( collect_c2
            @ ^ [X: c2] :
                ( ( X = A )
                & ( P @ X ) ) )
          = ( insert_c2 @ A @ bot_bot_set_c2 ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_c2
            @ ^ [X: c2] :
                ( ( X = A )
                & ( P @ X ) ) )
          = bot_bot_set_c2 ) ) ) ).

% Collect_conv_if
thf(fact_565_Collect__conv__if,axiom,
    ! [P: nat > $o,A: nat] :
      ( ( ( P @ A )
       => ( ( collect_nat
            @ ^ [X: nat] :
                ( ( X = A )
                & ( P @ X ) ) )
          = ( insert_nat @ A @ bot_bot_set_nat ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_nat
            @ ^ [X: nat] :
                ( ( X = A )
                & ( P @ X ) ) )
          = bot_bot_set_nat ) ) ) ).

% Collect_conv_if
thf(fact_566_surjective__pairing,axiom,
    ! [T2: produc8629413652255616883set_b2] :
      ( T2
      = ( produc4506454564149116331set_b2 @ ( produc6802794336065251735set_b2 @ T2 ) @ ( produc8191373782972559833set_b2 @ T2 ) ) ) ).

% surjective_pairing
thf(fact_567_surjective__pairing,axiom,
    ! [T2: produc8498296649714291061set_b2] :
      ( T2
      = ( produc4375337561607790509set_b2 @ ( produc6671677333523925913set_b2 @ T2 ) @ ( produc8060256780431234011set_b2 @ T2 ) ) ) ).

% surjective_pairing
thf(fact_568_surjective__pairing,axiom,
    ! [T2: product_prod_c1_c2] :
      ( T2
      = ( product_Pair_c1_c2 @ ( product_fst_c1_c2 @ T2 ) @ ( product_snd_c1_c2 @ T2 ) ) ) ).

% surjective_pairing
thf(fact_569_surjective__pairing,axiom,
    ! [T2: product_prod_b1_b2] :
      ( T2
      = ( product_Pair_b1_b2 @ ( product_fst_b1_b2 @ T2 ) @ ( product_snd_b1_b2 @ T2 ) ) ) ).

% surjective_pairing
thf(fact_570_surjective__pairing,axiom,
    ! [T2: product_prod_a1_a2] :
      ( T2
      = ( product_Pair_a1_a2 @ ( product_fst_a1_a2 @ T2 ) @ ( product_snd_a1_a2 @ T2 ) ) ) ).

% surjective_pairing
thf(fact_571_surjective__pairing,axiom,
    ! [T2: produc4061897789176782763set_c2] :
      ( T2
      = ( produc1212179418963815907set_c2 @ ( produc4038274906788240847set_c2 @ T2 ) @ ( produc6032943676959796241set_c2 @ T2 ) ) ) ).

% surjective_pairing
thf(fact_572_surjective__pairing,axiom,
    ! [T2: produc2702059613074419827set_c2] :
      ( T2
      = ( produc890782565133688235set_c2 @ ( produc3187122337049823639set_c2 @ T2 ) @ ( produc4575701783957131737set_c2 @ T2 ) ) ) ).

% surjective_pairing
thf(fact_573_prod_Oexhaust__sel,axiom,
    ! [Prod: produc8629413652255616883set_b2] :
      ( Prod
      = ( produc4506454564149116331set_b2 @ ( produc6802794336065251735set_b2 @ Prod ) @ ( produc8191373782972559833set_b2 @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_574_prod_Oexhaust__sel,axiom,
    ! [Prod: produc8498296649714291061set_b2] :
      ( Prod
      = ( produc4375337561607790509set_b2 @ ( produc6671677333523925913set_b2 @ Prod ) @ ( produc8060256780431234011set_b2 @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_575_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_c1_c2] :
      ( Prod
      = ( product_Pair_c1_c2 @ ( product_fst_c1_c2 @ Prod ) @ ( product_snd_c1_c2 @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_576_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_b1_b2] :
      ( Prod
      = ( product_Pair_b1_b2 @ ( product_fst_b1_b2 @ Prod ) @ ( product_snd_b1_b2 @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_577_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_a1_a2] :
      ( Prod
      = ( product_Pair_a1_a2 @ ( product_fst_a1_a2 @ Prod ) @ ( product_snd_a1_a2 @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_578_prod_Oexhaust__sel,axiom,
    ! [Prod: produc4061897789176782763set_c2] :
      ( Prod
      = ( produc1212179418963815907set_c2 @ ( produc4038274906788240847set_c2 @ Prod ) @ ( produc6032943676959796241set_c2 @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_579_prod_Oexhaust__sel,axiom,
    ! [Prod: produc2702059613074419827set_c2] :
      ( Prod
      = ( produc890782565133688235set_c2 @ ( produc3187122337049823639set_c2 @ Prod ) @ ( produc4575701783957131737set_c2 @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_580_case__prod__beta,axiom,
    ( produc4732439310506902963set_c2
    = ( ^ [F3: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,P3: produc4061897789176782763set_c2] : ( F3 @ ( produc4038274906788240847set_c2 @ P3 ) @ ( produc6032943676959796241set_c2 @ P3 ) ) ) ) ).

% case_prod_beta
thf(fact_581_case__prod__beta,axiom,
    ( produc6418488838319782393set_b2
    = ( ^ [F3: b1 > b2 > mapping_b1_set_b2,P3: product_prod_b1_b2] : ( F3 @ ( product_fst_b1_b2 @ P3 ) @ ( product_snd_b1_b2 @ P3 ) ) ) ) ).

% case_prod_beta
thf(fact_582_case__prod__beta,axiom,
    ( produc4822369076420559349set_c2
    = ( ^ [F3: c1 > c2 > mapping_c1_set_c2,P3: product_prod_c1_c2] : ( F3 @ ( product_fst_c1_c2 @ P3 ) @ ( product_snd_c1_c2 @ P3 ) ) ) ) ).

% case_prod_beta
thf(fact_583_case__prod__beta,axiom,
    ( produc885903088071324015_c1_c2
    = ( ^ [F3: a1 > a2 > product_prod_c1_c2,P3: product_prod_a1_a2] : ( F3 @ ( product_fst_a1_a2 @ P3 ) @ ( product_snd_a1_a2 @ P3 ) ) ) ) ).

% case_prod_beta
thf(fact_584_case__prod__beta,axiom,
    ( produc1521269801170193905_b1_b2
    = ( ^ [F3: a1 > a2 > product_prod_b1_b2,P3: product_prod_a1_a2] : ( F3 @ ( product_fst_a1_a2 @ P3 ) @ ( product_snd_a1_a2 @ P3 ) ) ) ) ).

% case_prod_beta
thf(fact_585_split__beta,axiom,
    ( produc4732439310506902963set_c2
    = ( ^ [F3: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,Prod3: produc4061897789176782763set_c2] : ( F3 @ ( produc4038274906788240847set_c2 @ Prod3 ) @ ( produc6032943676959796241set_c2 @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_586_split__beta,axiom,
    ( produc6418488838319782393set_b2
    = ( ^ [F3: b1 > b2 > mapping_b1_set_b2,Prod3: product_prod_b1_b2] : ( F3 @ ( product_fst_b1_b2 @ Prod3 ) @ ( product_snd_b1_b2 @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_587_split__beta,axiom,
    ( produc4822369076420559349set_c2
    = ( ^ [F3: c1 > c2 > mapping_c1_set_c2,Prod3: product_prod_c1_c2] : ( F3 @ ( product_fst_c1_c2 @ Prod3 ) @ ( product_snd_c1_c2 @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_588_split__beta,axiom,
    ( produc885903088071324015_c1_c2
    = ( ^ [F3: a1 > a2 > product_prod_c1_c2,Prod3: product_prod_a1_a2] : ( F3 @ ( product_fst_a1_a2 @ Prod3 ) @ ( product_snd_a1_a2 @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_589_split__beta,axiom,
    ( produc1521269801170193905_b1_b2
    = ( ^ [F3: a1 > a2 > product_prod_b1_b2,Prod3: product_prod_a1_a2] : ( F3 @ ( product_fst_a1_a2 @ Prod3 ) @ ( product_snd_a1_a2 @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_590_case__prod__unfold,axiom,
    ( produc4732439310506902963set_c2
    = ( ^ [C3: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,P3: produc4061897789176782763set_c2] : ( C3 @ ( produc4038274906788240847set_c2 @ P3 ) @ ( produc6032943676959796241set_c2 @ P3 ) ) ) ) ).

% case_prod_unfold
thf(fact_591_case__prod__unfold,axiom,
    ( produc6418488838319782393set_b2
    = ( ^ [C3: b1 > b2 > mapping_b1_set_b2,P3: product_prod_b1_b2] : ( C3 @ ( product_fst_b1_b2 @ P3 ) @ ( product_snd_b1_b2 @ P3 ) ) ) ) ).

% case_prod_unfold
thf(fact_592_case__prod__unfold,axiom,
    ( produc4822369076420559349set_c2
    = ( ^ [C3: c1 > c2 > mapping_c1_set_c2,P3: product_prod_c1_c2] : ( C3 @ ( product_fst_c1_c2 @ P3 ) @ ( product_snd_c1_c2 @ P3 ) ) ) ) ).

% case_prod_unfold
thf(fact_593_case__prod__unfold,axiom,
    ( produc885903088071324015_c1_c2
    = ( ^ [C3: a1 > a2 > product_prod_c1_c2,P3: product_prod_a1_a2] : ( C3 @ ( product_fst_a1_a2 @ P3 ) @ ( product_snd_a1_a2 @ P3 ) ) ) ) ).

% case_prod_unfold
thf(fact_594_case__prod__unfold,axiom,
    ( produc1521269801170193905_b1_b2
    = ( ^ [C3: a1 > a2 > product_prod_b1_b2,P3: product_prod_a1_a2] : ( C3 @ ( product_fst_a1_a2 @ P3 ) @ ( product_snd_a1_a2 @ P3 ) ) ) ) ).

% case_prod_unfold
thf(fact_595_case__prod__beta_H,axiom,
    ( produc4732439310506902963set_c2
    = ( ^ [F3: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,X: produc4061897789176782763set_c2] : ( F3 @ ( produc4038274906788240847set_c2 @ X ) @ ( produc6032943676959796241set_c2 @ X ) ) ) ) ).

% case_prod_beta'
thf(fact_596_case__prod__beta_H,axiom,
    ( produc6418488838319782393set_b2
    = ( ^ [F3: b1 > b2 > mapping_b1_set_b2,X: product_prod_b1_b2] : ( F3 @ ( product_fst_b1_b2 @ X ) @ ( product_snd_b1_b2 @ X ) ) ) ) ).

% case_prod_beta'
thf(fact_597_case__prod__beta_H,axiom,
    ( produc4822369076420559349set_c2
    = ( ^ [F3: c1 > c2 > mapping_c1_set_c2,X: product_prod_c1_c2] : ( F3 @ ( product_fst_c1_c2 @ X ) @ ( product_snd_c1_c2 @ X ) ) ) ) ).

% case_prod_beta'
thf(fact_598_case__prod__beta_H,axiom,
    ( produc885903088071324015_c1_c2
    = ( ^ [F3: a1 > a2 > product_prod_c1_c2,X: product_prod_a1_a2] : ( F3 @ ( product_fst_a1_a2 @ X ) @ ( product_snd_a1_a2 @ X ) ) ) ) ).

% case_prod_beta'
thf(fact_599_case__prod__beta_H,axiom,
    ( produc1521269801170193905_b1_b2
    = ( ^ [F3: a1 > a2 > product_prod_b1_b2,X: product_prod_a1_a2] : ( F3 @ ( product_fst_a1_a2 @ X ) @ ( product_snd_a1_a2 @ X ) ) ) ) ).

% case_prod_beta'
thf(fact_600_image__constant__conv,axiom,
    ! [A2: set_b2,C: b2] :
      ( ( ( A2 = bot_bot_set_b2 )
       => ( ( image_b2_b22
            @ ^ [X: b2] : C
            @ A2 )
          = bot_bot_set_b2 ) )
      & ( ( A2 != bot_bot_set_b2 )
       => ( ( image_b2_b22
            @ ^ [X: b2] : C
            @ A2 )
          = ( insert_b2 @ C @ bot_bot_set_b2 ) ) ) ) ).

% image_constant_conv
thf(fact_601_image__constant__conv,axiom,
    ! [A2: set_b2,C: c2] :
      ( ( ( A2 = bot_bot_set_b2 )
       => ( ( image_b2_c22
            @ ^ [X: b2] : C
            @ A2 )
          = bot_bot_set_c2 ) )
      & ( ( A2 != bot_bot_set_b2 )
       => ( ( image_b2_c22
            @ ^ [X: b2] : C
            @ A2 )
          = ( insert_c2 @ C @ bot_bot_set_c2 ) ) ) ) ).

% image_constant_conv
thf(fact_602_image__constant__conv,axiom,
    ! [A2: set_b2,C: nat] :
      ( ( ( A2 = bot_bot_set_b2 )
       => ( ( image_b2_nat2
            @ ^ [X: b2] : C
            @ A2 )
          = bot_bot_set_nat ) )
      & ( ( A2 != bot_bot_set_b2 )
       => ( ( image_b2_nat2
            @ ^ [X: b2] : C
            @ A2 )
          = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ).

% image_constant_conv
thf(fact_603_image__constant__conv,axiom,
    ! [A2: set_c2,C: b2] :
      ( ( ( A2 = bot_bot_set_c2 )
       => ( ( image_c2_b22
            @ ^ [X: c2] : C
            @ A2 )
          = bot_bot_set_b2 ) )
      & ( ( A2 != bot_bot_set_c2 )
       => ( ( image_c2_b22
            @ ^ [X: c2] : C
            @ A2 )
          = ( insert_b2 @ C @ bot_bot_set_b2 ) ) ) ) ).

% image_constant_conv
thf(fact_604_image__constant__conv,axiom,
    ! [A2: set_c2,C: c2] :
      ( ( ( A2 = bot_bot_set_c2 )
       => ( ( image_c2_c22
            @ ^ [X: c2] : C
            @ A2 )
          = bot_bot_set_c2 ) )
      & ( ( A2 != bot_bot_set_c2 )
       => ( ( image_c2_c22
            @ ^ [X: c2] : C
            @ A2 )
          = ( insert_c2 @ C @ bot_bot_set_c2 ) ) ) ) ).

% image_constant_conv
thf(fact_605_image__constant__conv,axiom,
    ! [A2: set_c2,C: nat] :
      ( ( ( A2 = bot_bot_set_c2 )
       => ( ( image_c2_nat2
            @ ^ [X: c2] : C
            @ A2 )
          = bot_bot_set_nat ) )
      & ( ( A2 != bot_bot_set_c2 )
       => ( ( image_c2_nat2
            @ ^ [X: c2] : C
            @ A2 )
          = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ).

% image_constant_conv
thf(fact_606_image__constant__conv,axiom,
    ! [A2: set_nat,C: b2] :
      ( ( ( A2 = bot_bot_set_nat )
       => ( ( image_nat_b22
            @ ^ [X: nat] : C
            @ A2 )
          = bot_bot_set_b2 ) )
      & ( ( A2 != bot_bot_set_nat )
       => ( ( image_nat_b22
            @ ^ [X: nat] : C
            @ A2 )
          = ( insert_b2 @ C @ bot_bot_set_b2 ) ) ) ) ).

% image_constant_conv
thf(fact_607_image__constant__conv,axiom,
    ! [A2: set_nat,C: c2] :
      ( ( ( A2 = bot_bot_set_nat )
       => ( ( image_nat_c22
            @ ^ [X: nat] : C
            @ A2 )
          = bot_bot_set_c2 ) )
      & ( ( A2 != bot_bot_set_nat )
       => ( ( image_nat_c22
            @ ^ [X: nat] : C
            @ A2 )
          = ( insert_c2 @ C @ bot_bot_set_c2 ) ) ) ) ).

% image_constant_conv
thf(fact_608_image__constant__conv,axiom,
    ! [A2: set_nat,C: nat] :
      ( ( ( A2 = bot_bot_set_nat )
       => ( ( image_nat_nat2
            @ ^ [X: nat] : C
            @ A2 )
          = bot_bot_set_nat ) )
      & ( ( A2 != bot_bot_set_nat )
       => ( ( image_nat_nat2
            @ ^ [X: nat] : C
            @ A2 )
          = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ).

% image_constant_conv
thf(fact_609_image__constant__conv,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2,C: product_prod_b1_b2] :
      ( ( ( A2 = bot_bo749279576856311060_a1_a2 )
       => ( ( image_1398015525354814723_b1_b2
            @ ^ [X: product_prod_a1_a2] : C
            @ A2 )
          = bot_bo5359064395943393682_b1_b2 ) )
      & ( ( A2 != bot_bo749279576856311060_a1_a2 )
       => ( ( image_1398015525354814723_b1_b2
            @ ^ [X: product_prod_a1_a2] : C
            @ A2 )
          = ( insert7793476323617067286_b1_b2 @ C @ bot_bo5359064395943393682_b1_b2 ) ) ) ) ).

% image_constant_conv
thf(fact_610_image__constant,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,C: b2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( image_5961845353661638642_c2_b2
          @ ^ [X: product_prod_c1_c2] : C
          @ A2 )
        = ( insert_b2 @ C @ bot_bot_set_b2 ) ) ) ).

% image_constant
thf(fact_611_image__constant,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,C: b2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ( image_2033501871846498164_b2_b2
          @ ^ [X: product_prod_b1_b2] : C
          @ A2 )
        = ( insert_b2 @ C @ bot_bot_set_b2 ) ) ) ).

% image_constant
thf(fact_612_image__constant,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,C: b2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ( image_7328530426886133494_a2_b2
          @ ^ [X: product_prod_a1_a2] : C
          @ A2 )
        = ( insert_b2 @ C @ bot_bot_set_b2 ) ) ) ).

% image_constant
thf(fact_613_image__constant,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,C: c2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( image_5961845353661704241_c2_c2
          @ ^ [X: product_prod_c1_c2] : C
          @ A2 )
        = ( insert_c2 @ C @ bot_bot_set_c2 ) ) ) ).

% image_constant
thf(fact_614_image__constant,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,C: c2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ( image_2033501871846563763_b2_c2
          @ ^ [X: product_prod_b1_b2] : C
          @ A2 )
        = ( insert_c2 @ C @ bot_bot_set_c2 ) ) ) ).

% image_constant
thf(fact_615_image__constant,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,C: c2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ( image_7328530426886199093_a2_c2
          @ ^ [X: product_prod_a1_a2] : C
          @ A2 )
        = ( insert_c2 @ C @ bot_bot_set_c2 ) ) ) ).

% image_constant
thf(fact_616_image__constant,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,C: nat] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( image_1283518940507385935c2_nat
          @ ^ [X: product_prod_c1_c2] : C
          @ A2 )
        = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ).

% image_constant
thf(fact_617_image__constant,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,C: nat] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ( image_2104430070814229713b2_nat
          @ ^ [X: product_prod_b1_b2] : C
          @ A2 )
        = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ).

% image_constant
thf(fact_618_image__constant,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,C: nat] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ( image_2925341201121073491a2_nat
          @ ^ [X: product_prod_a1_a2] : C
          @ A2 )
        = ( insert_nat @ C @ bot_bot_set_nat ) ) ) ).

% image_constant
thf(fact_619_image__constant,axiom,
    ! [X2: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2,C: b2] :
      ( ( member341037065618468219set_c2 @ X2 @ A2 )
     => ( ( image_1755057678288551646_c2_b2
          @ ^ [X: mapping_c1_set_c2] : C
          @ A2 )
        = ( insert_b2 @ C @ bot_bot_set_b2 ) ) ) ).

% image_constant
thf(fact_620_prod_Osplit__sel__asm,axiom,
    ! [P: produc4061897789176782763set_c2 > $o,F: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,Prod: produc4061897789176782763set_c2] :
      ( ( P @ ( produc4732439310506902963set_c2 @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( produc1212179418963815907set_c2 @ ( produc4038274906788240847set_c2 @ Prod ) @ ( produc6032943676959796241set_c2 @ Prod ) ) )
            & ~ ( P @ ( F @ ( produc4038274906788240847set_c2 @ Prod ) @ ( produc6032943676959796241set_c2 @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_621_prod_Osplit__sel__asm,axiom,
    ! [P: mapping_b1_set_b2 > $o,F: b1 > b2 > mapping_b1_set_b2,Prod: product_prod_b1_b2] :
      ( ( P @ ( produc6418488838319782393set_b2 @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( product_Pair_b1_b2 @ ( product_fst_b1_b2 @ Prod ) @ ( product_snd_b1_b2 @ Prod ) ) )
            & ~ ( P @ ( F @ ( product_fst_b1_b2 @ Prod ) @ ( product_snd_b1_b2 @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_622_prod_Osplit__sel__asm,axiom,
    ! [P: mapping_c1_set_c2 > $o,F: c1 > c2 > mapping_c1_set_c2,Prod: product_prod_c1_c2] :
      ( ( P @ ( produc4822369076420559349set_c2 @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( product_Pair_c1_c2 @ ( product_fst_c1_c2 @ Prod ) @ ( product_snd_c1_c2 @ Prod ) ) )
            & ~ ( P @ ( F @ ( product_fst_c1_c2 @ Prod ) @ ( product_snd_c1_c2 @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_623_prod_Osplit__sel__asm,axiom,
    ! [P: product_prod_c1_c2 > $o,F: a1 > a2 > product_prod_c1_c2,Prod: product_prod_a1_a2] :
      ( ( P @ ( produc885903088071324015_c1_c2 @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( product_Pair_a1_a2 @ ( product_fst_a1_a2 @ Prod ) @ ( product_snd_a1_a2 @ Prod ) ) )
            & ~ ( P @ ( F @ ( product_fst_a1_a2 @ Prod ) @ ( product_snd_a1_a2 @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_624_prod_Osplit__sel__asm,axiom,
    ! [P: product_prod_b1_b2 > $o,F: a1 > a2 > product_prod_b1_b2,Prod: product_prod_a1_a2] :
      ( ( P @ ( produc1521269801170193905_b1_b2 @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( product_Pair_a1_a2 @ ( product_fst_a1_a2 @ Prod ) @ ( product_snd_a1_a2 @ Prod ) ) )
            & ~ ( P @ ( F @ ( product_fst_a1_a2 @ Prod ) @ ( product_snd_a1_a2 @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_625_prod_Osplit__sel,axiom,
    ! [P: produc4061897789176782763set_c2 > $o,F: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,Prod: produc4061897789176782763set_c2] :
      ( ( P @ ( produc4732439310506902963set_c2 @ F @ Prod ) )
      = ( ( Prod
          = ( produc1212179418963815907set_c2 @ ( produc4038274906788240847set_c2 @ Prod ) @ ( produc6032943676959796241set_c2 @ Prod ) ) )
       => ( P @ ( F @ ( produc4038274906788240847set_c2 @ Prod ) @ ( produc6032943676959796241set_c2 @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_626_prod_Osplit__sel,axiom,
    ! [P: mapping_b1_set_b2 > $o,F: b1 > b2 > mapping_b1_set_b2,Prod: product_prod_b1_b2] :
      ( ( P @ ( produc6418488838319782393set_b2 @ F @ Prod ) )
      = ( ( Prod
          = ( product_Pair_b1_b2 @ ( product_fst_b1_b2 @ Prod ) @ ( product_snd_b1_b2 @ Prod ) ) )
       => ( P @ ( F @ ( product_fst_b1_b2 @ Prod ) @ ( product_snd_b1_b2 @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_627_prod_Osplit__sel,axiom,
    ! [P: mapping_c1_set_c2 > $o,F: c1 > c2 > mapping_c1_set_c2,Prod: product_prod_c1_c2] :
      ( ( P @ ( produc4822369076420559349set_c2 @ F @ Prod ) )
      = ( ( Prod
          = ( product_Pair_c1_c2 @ ( product_fst_c1_c2 @ Prod ) @ ( product_snd_c1_c2 @ Prod ) ) )
       => ( P @ ( F @ ( product_fst_c1_c2 @ Prod ) @ ( product_snd_c1_c2 @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_628_prod_Osplit__sel,axiom,
    ! [P: product_prod_c1_c2 > $o,F: a1 > a2 > product_prod_c1_c2,Prod: product_prod_a1_a2] :
      ( ( P @ ( produc885903088071324015_c1_c2 @ F @ Prod ) )
      = ( ( Prod
          = ( product_Pair_a1_a2 @ ( product_fst_a1_a2 @ Prod ) @ ( product_snd_a1_a2 @ Prod ) ) )
       => ( P @ ( F @ ( product_fst_a1_a2 @ Prod ) @ ( product_snd_a1_a2 @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_629_prod_Osplit__sel,axiom,
    ! [P: product_prod_b1_b2 > $o,F: a1 > a2 > product_prod_b1_b2,Prod: product_prod_a1_a2] :
      ( ( P @ ( produc1521269801170193905_b1_b2 @ F @ Prod ) )
      = ( ( Prod
          = ( product_Pair_a1_a2 @ ( product_fst_a1_a2 @ Prod ) @ ( product_snd_a1_a2 @ Prod ) ) )
       => ( P @ ( F @ ( product_fst_a1_a2 @ Prod ) @ ( product_snd_a1_a2 @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_630_exE__realizer,axiom,
    ! [P: mapping_c1_set_c2 > mapping_b1_set_b2 > $o,P2: produc4061897789176782763set_c2,Q: produc4061897789176782763set_c2 > $o,F: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2] :
      ( ( P @ ( produc6032943676959796241set_c2 @ P2 ) @ ( produc4038274906788240847set_c2 @ P2 ) )
     => ( ! [X3: mapping_b1_set_b2,Y4: mapping_c1_set_c2] :
            ( ( P @ Y4 @ X3 )
           => ( Q @ ( F @ X3 @ Y4 ) ) )
       => ( Q @ ( produc4732439310506902963set_c2 @ F @ P2 ) ) ) ) ).

% exE_realizer
thf(fact_631_exE__realizer,axiom,
    ! [P: b2 > b1 > $o,P2: product_prod_b1_b2,Q: mapping_b1_set_b2 > $o,F: b1 > b2 > mapping_b1_set_b2] :
      ( ( P @ ( product_snd_b1_b2 @ P2 ) @ ( product_fst_b1_b2 @ P2 ) )
     => ( ! [X3: b1,Y4: b2] :
            ( ( P @ Y4 @ X3 )
           => ( Q @ ( F @ X3 @ Y4 ) ) )
       => ( Q @ ( produc6418488838319782393set_b2 @ F @ P2 ) ) ) ) ).

% exE_realizer
thf(fact_632_exE__realizer,axiom,
    ! [P: c2 > c1 > $o,P2: product_prod_c1_c2,Q: mapping_c1_set_c2 > $o,F: c1 > c2 > mapping_c1_set_c2] :
      ( ( P @ ( product_snd_c1_c2 @ P2 ) @ ( product_fst_c1_c2 @ P2 ) )
     => ( ! [X3: c1,Y4: c2] :
            ( ( P @ Y4 @ X3 )
           => ( Q @ ( F @ X3 @ Y4 ) ) )
       => ( Q @ ( produc4822369076420559349set_c2 @ F @ P2 ) ) ) ) ).

% exE_realizer
thf(fact_633_exE__realizer,axiom,
    ! [P: a2 > a1 > $o,P2: product_prod_a1_a2,Q: product_prod_c1_c2 > $o,F: a1 > a2 > product_prod_c1_c2] :
      ( ( P @ ( product_snd_a1_a2 @ P2 ) @ ( product_fst_a1_a2 @ P2 ) )
     => ( ! [X3: a1,Y4: a2] :
            ( ( P @ Y4 @ X3 )
           => ( Q @ ( F @ X3 @ Y4 ) ) )
       => ( Q @ ( produc885903088071324015_c1_c2 @ F @ P2 ) ) ) ) ).

% exE_realizer
thf(fact_634_exE__realizer,axiom,
    ! [P: a2 > a1 > $o,P2: product_prod_a1_a2,Q: product_prod_b1_b2 > $o,F: a1 > a2 > product_prod_b1_b2] :
      ( ( P @ ( product_snd_a1_a2 @ P2 ) @ ( product_fst_a1_a2 @ P2 ) )
     => ( ! [X3: a1,Y4: a2] :
            ( ( P @ Y4 @ X3 )
           => ( Q @ ( F @ X3 @ Y4 ) ) )
       => ( Q @ ( produc1521269801170193905_b1_b2 @ F @ P2 ) ) ) ) ).

% exE_realizer
thf(fact_635__092_060open_062_092_060And_062xs_O_Afold_A_I_092_060lambda_062kv_A_Im1_M_Am2_J_O_A_Icase_Af1_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am1_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am1_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am1_M_Acase_Af2_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am2_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am2_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am2_J_J_Axs_A_IMapping_Oempty_M_AMapping_Oempty_J_A_061_A_Ifold_A_I_092_060lambda_062kv_Am_O_Acase_Af1_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am_J_Axs_AMapping_Oempty_M_Afold_A_I_092_060lambda_062kv_Am_O_Acase_Af2_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am_J_Axs_AMapping_Oempty_J_092_060close_062,axiom,
    ! [Xs2: list_P5985182332071222990_a1_a2] :
      ( ( fold_P7185038094655571566set_c2
        @ ^ [Kv: product_prod_a1_a2] :
            ( produc4732439310506902963set_c2
            @ ^ [M1: mapping_b1_set_b2,M2: mapping_c1_set_c2] :
                ( produc1212179418963815907set_c2
                @ ( produc6418488838319782393set_b2
                  @ ^ [X: b1,Z: b2] :
                      ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M1 )
                      @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ Zs ) @ M1 )
                      @ ( lookup_b1_set_b2 @ M1 @ X ) )
                  @ ( f1 @ Kv ) )
                @ ( produc4822369076420559349set_c2
                  @ ^ [X: c1,Z: c2] :
                      ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M2 )
                      @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ Zs ) @ M2 )
                      @ ( lookup_c1_set_c2 @ M2 @ X ) )
                  @ ( f2 @ Kv ) ) ) )
        @ Xs2
        @ ( produc1212179418963815907set_c2 @ empty_b1_set_b2 @ empty_c1_set_c2 ) )
      = ( produc1212179418963815907set_c2
        @ ( fold_P366236689040723939set_b2
          @ ^ [Kv: product_prod_a1_a2,M: mapping_b1_set_b2] :
              ( produc6418488838319782393set_b2
              @ ^ [X: b1,Z: b2] :
                  ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M )
                  @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ Zs ) @ M )
                  @ ( lookup_b1_set_b2 @ M @ X ) )
              @ ( f1 @ Kv ) )
          @ Xs2
          @ empty_b1_set_b2 )
        @ ( fold_P3813313114924009441set_c2
          @ ^ [Kv: product_prod_a1_a2,M: mapping_c1_set_c2] :
              ( produc4822369076420559349set_c2
              @ ^ [X: c1,Z: c2] :
                  ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M )
                  @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ Zs ) @ M )
                  @ ( lookup_c1_set_c2 @ M @ X ) )
              @ ( f2 @ Kv ) )
          @ Xs2
          @ empty_c1_set_c2 ) ) ) ).

% \<open>\<And>xs. fold (\<lambda>kv (m1, m2). (case f1 kv of (x, z) \<Rightarrow> case Mapping.lookup m1 x of None \<Rightarrow> Mapping.update x {z} m1 | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m1, case f2 kv of (x, z) \<Rightarrow> case Mapping.lookup m2 x of None \<Rightarrow> Mapping.update x {z} m2 | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m2)) xs (Mapping.empty, Mapping.empty) = (fold (\<lambda>kv m. case f1 kv of (x, z) \<Rightarrow> case Mapping.lookup m x of None \<Rightarrow> Mapping.update x {z} m | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m) xs Mapping.empty, fold (\<lambda>kv m. case f2 kv of (x, z) \<Rightarrow> case Mapping.lookup m x of None \<Rightarrow> Mapping.update x {z} m | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m) xs Mapping.empty)\<close>
thf(fact_636_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > $o,X2: c1 > option_set_c2,Y5: b1 > option_set_b2,A: produc8629413652255616883set_b2] :
      ( ( P @ X2 @ Y5 )
     => ( ( A
          = ( produc4506454564149116331set_b2 @ X2 @ Y5 ) )
       => ( P @ ( produc6802794336065251735set_b2 @ A ) @ ( produc8191373782972559833set_b2 @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_637_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,X2: b1 > option_set_b2,Y5: b1 > option_set_b2,A: produc8498296649714291061set_b2] :
      ( ( P @ X2 @ Y5 )
     => ( ( A
          = ( produc4375337561607790509set_b2 @ X2 @ Y5 ) )
       => ( P @ ( produc6671677333523925913set_b2 @ A ) @ ( produc8060256780431234011set_b2 @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_638_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: c1 > c2 > $o,X2: c1,Y5: c2,A: product_prod_c1_c2] :
      ( ( P @ X2 @ Y5 )
     => ( ( A
          = ( product_Pair_c1_c2 @ X2 @ Y5 ) )
       => ( P @ ( product_fst_c1_c2 @ A ) @ ( product_snd_c1_c2 @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_639_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: b1 > b2 > $o,X2: b1,Y5: b2,A: product_prod_b1_b2] :
      ( ( P @ X2 @ Y5 )
     => ( ( A
          = ( product_Pair_b1_b2 @ X2 @ Y5 ) )
       => ( P @ ( product_fst_b1_b2 @ A ) @ ( product_snd_b1_b2 @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_640_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: a1 > a2 > $o,X2: a1,Y5: a2,A: product_prod_a1_a2] :
      ( ( P @ X2 @ Y5 )
     => ( ( A
          = ( product_Pair_a1_a2 @ X2 @ Y5 ) )
       => ( P @ ( product_fst_a1_a2 @ A ) @ ( product_snd_a1_a2 @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_641_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: mapping_b1_set_b2 > mapping_c1_set_c2 > $o,X2: mapping_b1_set_b2,Y5: mapping_c1_set_c2,A: produc4061897789176782763set_c2] :
      ( ( P @ X2 @ Y5 )
     => ( ( A
          = ( produc1212179418963815907set_c2 @ X2 @ Y5 ) )
       => ( P @ ( produc4038274906788240847set_c2 @ A ) @ ( produc6032943676959796241set_c2 @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_642_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > $o,X2: b1 > option_set_b2,Y5: c1 > option_set_c2,A: produc2702059613074419827set_c2] :
      ( ( P @ X2 @ Y5 )
     => ( ( A
          = ( produc890782565133688235set_c2 @ X2 @ Y5 ) )
       => ( P @ ( produc3187122337049823639set_c2 @ A ) @ ( produc4575701783957131737set_c2 @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_643_conjI__realizer,axiom,
    ! [P: ( c1 > option_set_c2 ) > $o,P2: c1 > option_set_c2,Q: ( b1 > option_set_b2 ) > $o,Q2: b1 > option_set_b2] :
      ( ( P @ P2 )
     => ( ( Q @ Q2 )
       => ( ( P @ ( produc6802794336065251735set_b2 @ ( produc4506454564149116331set_b2 @ P2 @ Q2 ) ) )
          & ( Q @ ( produc8191373782972559833set_b2 @ ( produc4506454564149116331set_b2 @ P2 @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_644_conjI__realizer,axiom,
    ! [P: ( b1 > option_set_b2 ) > $o,P2: b1 > option_set_b2,Q: ( b1 > option_set_b2 ) > $o,Q2: b1 > option_set_b2] :
      ( ( P @ P2 )
     => ( ( Q @ Q2 )
       => ( ( P @ ( produc6671677333523925913set_b2 @ ( produc4375337561607790509set_b2 @ P2 @ Q2 ) ) )
          & ( Q @ ( produc8060256780431234011set_b2 @ ( produc4375337561607790509set_b2 @ P2 @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_645_conjI__realizer,axiom,
    ! [P: c1 > $o,P2: c1,Q: c2 > $o,Q2: c2] :
      ( ( P @ P2 )
     => ( ( Q @ Q2 )
       => ( ( P @ ( product_fst_c1_c2 @ ( product_Pair_c1_c2 @ P2 @ Q2 ) ) )
          & ( Q @ ( product_snd_c1_c2 @ ( product_Pair_c1_c2 @ P2 @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_646_conjI__realizer,axiom,
    ! [P: b1 > $o,P2: b1,Q: b2 > $o,Q2: b2] :
      ( ( P @ P2 )
     => ( ( Q @ Q2 )
       => ( ( P @ ( product_fst_b1_b2 @ ( product_Pair_b1_b2 @ P2 @ Q2 ) ) )
          & ( Q @ ( product_snd_b1_b2 @ ( product_Pair_b1_b2 @ P2 @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_647_conjI__realizer,axiom,
    ! [P: a1 > $o,P2: a1,Q: a2 > $o,Q2: a2] :
      ( ( P @ P2 )
     => ( ( Q @ Q2 )
       => ( ( P @ ( product_fst_a1_a2 @ ( product_Pair_a1_a2 @ P2 @ Q2 ) ) )
          & ( Q @ ( product_snd_a1_a2 @ ( product_Pair_a1_a2 @ P2 @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_648_conjI__realizer,axiom,
    ! [P: mapping_b1_set_b2 > $o,P2: mapping_b1_set_b2,Q: mapping_c1_set_c2 > $o,Q2: mapping_c1_set_c2] :
      ( ( P @ P2 )
     => ( ( Q @ Q2 )
       => ( ( P @ ( produc4038274906788240847set_c2 @ ( produc1212179418963815907set_c2 @ P2 @ Q2 ) ) )
          & ( Q @ ( produc6032943676959796241set_c2 @ ( produc1212179418963815907set_c2 @ P2 @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_649_conjI__realizer,axiom,
    ! [P: ( b1 > option_set_b2 ) > $o,P2: b1 > option_set_b2,Q: ( c1 > option_set_c2 ) > $o,Q2: c1 > option_set_c2] :
      ( ( P @ P2 )
     => ( ( Q @ Q2 )
       => ( ( P @ ( produc3187122337049823639set_c2 @ ( produc890782565133688235set_c2 @ P2 @ Q2 ) ) )
          & ( Q @ ( produc4575701783957131737set_c2 @ ( produc890782565133688235set_c2 @ P2 @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_650_exI__realizer,axiom,
    ! [P: ( b1 > option_set_b2 ) > ( c1 > option_set_c2 ) > $o,Y5: b1 > option_set_b2,X2: c1 > option_set_c2] :
      ( ( P @ Y5 @ X2 )
     => ( P @ ( produc8191373782972559833set_b2 @ ( produc4506454564149116331set_b2 @ X2 @ Y5 ) ) @ ( produc6802794336065251735set_b2 @ ( produc4506454564149116331set_b2 @ X2 @ Y5 ) ) ) ) ).

% exI_realizer
thf(fact_651_exI__realizer,axiom,
    ! [P: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,Y5: b1 > option_set_b2,X2: b1 > option_set_b2] :
      ( ( P @ Y5 @ X2 )
     => ( P @ ( produc8060256780431234011set_b2 @ ( produc4375337561607790509set_b2 @ X2 @ Y5 ) ) @ ( produc6671677333523925913set_b2 @ ( produc4375337561607790509set_b2 @ X2 @ Y5 ) ) ) ) ).

% exI_realizer
thf(fact_652_exI__realizer,axiom,
    ! [P: c2 > c1 > $o,Y5: c2,X2: c1] :
      ( ( P @ Y5 @ X2 )
     => ( P @ ( product_snd_c1_c2 @ ( product_Pair_c1_c2 @ X2 @ Y5 ) ) @ ( product_fst_c1_c2 @ ( product_Pair_c1_c2 @ X2 @ Y5 ) ) ) ) ).

% exI_realizer
thf(fact_653_exI__realizer,axiom,
    ! [P: b2 > b1 > $o,Y5: b2,X2: b1] :
      ( ( P @ Y5 @ X2 )
     => ( P @ ( product_snd_b1_b2 @ ( product_Pair_b1_b2 @ X2 @ Y5 ) ) @ ( product_fst_b1_b2 @ ( product_Pair_b1_b2 @ X2 @ Y5 ) ) ) ) ).

% exI_realizer
thf(fact_654_exI__realizer,axiom,
    ! [P: a2 > a1 > $o,Y5: a2,X2: a1] :
      ( ( P @ Y5 @ X2 )
     => ( P @ ( product_snd_a1_a2 @ ( product_Pair_a1_a2 @ X2 @ Y5 ) ) @ ( product_fst_a1_a2 @ ( product_Pair_a1_a2 @ X2 @ Y5 ) ) ) ) ).

% exI_realizer
thf(fact_655_exI__realizer,axiom,
    ! [P: mapping_c1_set_c2 > mapping_b1_set_b2 > $o,Y5: mapping_c1_set_c2,X2: mapping_b1_set_b2] :
      ( ( P @ Y5 @ X2 )
     => ( P @ ( produc6032943676959796241set_c2 @ ( produc1212179418963815907set_c2 @ X2 @ Y5 ) ) @ ( produc4038274906788240847set_c2 @ ( produc1212179418963815907set_c2 @ X2 @ Y5 ) ) ) ) ).

% exI_realizer
thf(fact_656_exI__realizer,axiom,
    ! [P: ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > $o,Y5: c1 > option_set_c2,X2: b1 > option_set_b2] :
      ( ( P @ Y5 @ X2 )
     => ( P @ ( produc4575701783957131737set_c2 @ ( produc890782565133688235set_c2 @ X2 @ Y5 ) ) @ ( produc3187122337049823639set_c2 @ ( produc890782565133688235set_c2 @ X2 @ Y5 ) ) ) ) ).

% exI_realizer
thf(fact_657__092_060open_062fold_A_I_092_060lambda_062kv_A_Im1_M_Am2_J_O_A_Icase_Af1_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am1_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am1_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am1_M_Acase_Af2_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am2_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am2_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am2_J_J_A_IRBT__Set2_Okeys_At_J_A_IMapping_Oempty_M_AMapping_Oempty_J_A_061_A_Ifold_A_I_092_060lambda_062kv_Am_O_Acase_Af1_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am_J_A_IRBT__Set2_Okeys_At_J_AMapping_Oempty_M_Afold_A_I_092_060lambda_062kv_Am_O_Acase_Af2_Akv_Aof_A_Ix_M_Az_J_A_092_060Rightarrow_062_Acase_AMapping_Olookup_Am_Ax_Aof_ANone_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_123z_125_Am_A_124_ASome_Azs_A_092_060Rightarrow_062_AMapping_Oupdate_Ax_A_ISet_Oinsert_Az_Azs_J_Am_J_A_IRBT__Set2_Okeys_At_J_AMapping_Oempty_J_092_060close_062,axiom,
    ( ( fold_P7185038094655571566set_c2
      @ ^ [Kv: product_prod_a1_a2] :
          ( produc4732439310506902963set_c2
          @ ^ [M1: mapping_b1_set_b2,M2: mapping_c1_set_c2] :
              ( produc1212179418963815907set_c2
              @ ( produc6418488838319782393set_b2
                @ ^ [X: b1,Z: b2] :
                    ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M1 )
                    @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ Zs ) @ M1 )
                    @ ( lookup_b1_set_b2 @ M1 @ X ) )
                @ ( f1 @ Kv ) )
              @ ( produc4822369076420559349set_c2
                @ ^ [X: c1,Z: c2] :
                    ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M2 )
                    @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ Zs ) @ M2 )
                    @ ( lookup_c1_set_c2 @ M2 @ X ) )
                @ ( f2 @ Kv ) ) ) )
      @ ( rBT_ke4861133314182804427_a1_a2 @ t )
      @ ( produc1212179418963815907set_c2 @ empty_b1_set_b2 @ empty_c1_set_c2 ) )
    = ( produc1212179418963815907set_c2
      @ ( fold_P366236689040723939set_b2
        @ ^ [Kv: product_prod_a1_a2,M: mapping_b1_set_b2] :
            ( produc6418488838319782393set_b2
            @ ^ [X: b1,Z: b2] :
                ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M )
                @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ X @ ( insert_b2 @ Z @ Zs ) @ M )
                @ ( lookup_b1_set_b2 @ M @ X ) )
            @ ( f1 @ Kv ) )
        @ ( rBT_ke4861133314182804427_a1_a2 @ t )
        @ empty_b1_set_b2 )
      @ ( fold_P3813313114924009441set_c2
        @ ^ [Kv: product_prod_a1_a2,M: mapping_c1_set_c2] :
            ( produc4822369076420559349set_c2
            @ ^ [X: c1,Z: c2] :
                ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M )
                @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ X @ ( insert_c2 @ Z @ Zs ) @ M )
                @ ( lookup_c1_set_c2 @ M @ X ) )
            @ ( f2 @ Kv ) )
        @ ( rBT_ke4861133314182804427_a1_a2 @ t )
        @ empty_c1_set_c2 ) ) ) ).

% \<open>fold (\<lambda>kv (m1, m2). (case f1 kv of (x, z) \<Rightarrow> case Mapping.lookup m1 x of None \<Rightarrow> Mapping.update x {z} m1 | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m1, case f2 kv of (x, z) \<Rightarrow> case Mapping.lookup m2 x of None \<Rightarrow> Mapping.update x {z} m2 | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m2)) (RBT_Set2.keys t) (Mapping.empty, Mapping.empty) = (fold (\<lambda>kv m. case f1 kv of (x, z) \<Rightarrow> case Mapping.lookup m x of None \<Rightarrow> Mapping.update x {z} m | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m) (RBT_Set2.keys t) Mapping.empty, fold (\<lambda>kv m. case f2 kv of (x, z) \<Rightarrow> case Mapping.lookup m x of None \<Rightarrow> Mapping.update x {z} m | Some zs \<Rightarrow> Mapping.update x (Set.insert z zs) m) (RBT_Set2.keys t) Mapping.empty)\<close>
thf(fact_658_option_Oinject,axiom,
    ! [X22: product_prod_a1_a2 > product_prod_a1_a2 > order,Y2: product_prod_a1_a2 > product_prod_a1_a2 > order] :
      ( ( ( some_P6364418062025833395_order @ X22 )
        = ( some_P6364418062025833395_order @ Y2 ) )
      = ( X22 = Y2 ) ) ).

% option.inject
thf(fact_659_case__prod__Pair__iden,axiom,
    ! [P2: produc2702059613074419827set_c2] :
      ( ( produc303944662167056563set_c2 @ produc890782565133688235set_c2 @ P2 )
      = P2 ) ).

% case_prod_Pair_iden
thf(fact_660_case__prod__Pair__iden,axiom,
    ! [P2: produc8629413652255616883set_b2] :
      ( ( produc2505562656973983667set_b2 @ produc4506454564149116331set_b2 @ P2 )
      = P2 ) ).

% case_prod_Pair_iden
thf(fact_661_case__prod__Pair__iden,axiom,
    ! [P2: produc8498296649714291061set_b2] :
      ( ( produc8790685608643853619set_b2 @ produc4375337561607790509set_b2 @ P2 )
      = P2 ) ).

% case_prod_Pair_iden
thf(fact_662_case__prod__Pair__iden,axiom,
    ! [P2: product_prod_c1_c2] :
      ( ( produc7856115553599036531_c1_c2 @ product_Pair_c1_c2 @ P2 )
      = P2 ) ).

% case_prod_Pair_iden
thf(fact_663_case__prod__Pair__iden,axiom,
    ! [P2: product_prod_b1_b2] :
      ( ( produc5006376033934050163_b1_b2 @ product_Pair_b1_b2 @ P2 )
      = P2 ) ).

% case_prod_Pair_iden
thf(fact_664_case__prod__Pair__iden,axiom,
    ! [P2: product_prod_a1_a2] :
      ( ( produc2156636514269063795_a1_a2 @ product_Pair_a1_a2 @ P2 )
      = P2 ) ).

% case_prod_Pair_iden
thf(fact_665_case__prod__Pair__iden,axiom,
    ! [P2: produc4061897789176782763set_c2] :
      ( ( produc4732439310506902963set_c2 @ produc1212179418963815907set_c2 @ P2 )
      = P2 ) ).

% case_prod_Pair_iden
thf(fact_666_fold__dual,axiom,
    ! [G1: product_prod_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2,G2: product_prod_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2,Xs2: list_P5985182332071222990_a1_a2,A1: produc4061897789176782763set_c2,A22: produc4061897789176782763set_c2] :
      ( ( fold_P7873264179840037930set_c2
        @ ^ [X: product_prod_a1_a2] :
            ( produc3639072943575950715set_c2
            @ ^ [A12: produc4061897789176782763set_c2,A23: produc4061897789176782763set_c2] : ( produc3581607025436495447set_c2 @ ( G1 @ X @ A12 ) @ ( G2 @ X @ A23 ) ) )
        @ Xs2
        @ ( produc3581607025436495447set_c2 @ A1 @ A22 ) )
      = ( produc3581607025436495447set_c2 @ ( fold_P7185038094655571566set_c2 @ G1 @ Xs2 @ A1 ) @ ( fold_P7185038094655571566set_c2 @ G2 @ Xs2 @ A22 ) ) ) ).

% fold_dual
thf(fact_667_fold__dual,axiom,
    ! [G1: product_prod_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2,G2: product_prod_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2,Xs2: list_P5985182332071222990_a1_a2,A1: produc4061897789176782763set_c2,A22: mapping_b1_set_b2] :
      ( ( fold_P5530968877631332285set_b2
        @ ^ [X: product_prod_a1_a2] :
            ( produc455242887147150503set_b2
            @ ^ [A12: produc4061897789176782763set_c2,A23: mapping_b1_set_b2] : ( produc1095963423755894970set_b2 @ ( G1 @ X @ A12 ) @ ( G2 @ X @ A23 ) ) )
        @ Xs2
        @ ( produc1095963423755894970set_b2 @ A1 @ A22 ) )
      = ( produc1095963423755894970set_b2 @ ( fold_P7185038094655571566set_c2 @ G1 @ Xs2 @ A1 ) @ ( fold_P366236689040723939set_b2 @ G2 @ Xs2 @ A22 ) ) ) ).

% fold_dual
thf(fact_668_fold__dual,axiom,
    ! [G1: product_prod_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2,G2: product_prod_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2,Xs2: list_P5985182332071222990_a1_a2,A1: produc4061897789176782763set_c2,A22: mapping_c1_set_c2] :
      ( ( fold_P6582638113785526459set_c2
        @ ^ [X: product_prod_a1_a2] :
            ( produc723796631715995555set_c2
            @ ^ [A12: produc4061897789176782763set_c2,A23: mapping_c1_set_c2] : ( produc4543039849639180472set_c2 @ ( G1 @ X @ A12 ) @ ( G2 @ X @ A23 ) ) )
        @ Xs2
        @ ( produc4543039849639180472set_c2 @ A1 @ A22 ) )
      = ( produc4543039849639180472set_c2 @ ( fold_P7185038094655571566set_c2 @ G1 @ Xs2 @ A1 ) @ ( fold_P3813313114924009441set_c2 @ G2 @ Xs2 @ A22 ) ) ) ).

% fold_dual
thf(fact_669_fold__dual,axiom,
    ! [G1: product_prod_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2,G2: product_prod_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2,Xs2: list_P5985182332071222990_a1_a2,A1: mapping_b1_set_b2,A22: produc4061897789176782763set_c2] :
      ( ( fold_P2573110186453295671set_c2
        @ ^ [X: product_prod_a1_a2] :
            ( produc1393855134008624979set_c2
            @ ^ [A12: mapping_b1_set_b2,A23: produc4061897789176782763set_c2] : ( produc5597292958132816620set_c2 @ ( G1 @ X @ A12 ) @ ( G2 @ X @ A23 ) ) )
        @ Xs2
        @ ( produc5597292958132816620set_c2 @ A1 @ A22 ) )
      = ( produc5597292958132816620set_c2 @ ( fold_P366236689040723939set_b2 @ G1 @ Xs2 @ A1 ) @ ( fold_P7185038094655571566set_c2 @ G2 @ Xs2 @ A22 ) ) ) ).

% fold_dual
thf(fact_670_fold__dual,axiom,
    ! [G1: product_prod_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2,G2: product_prod_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2,Xs2: list_P5985182332071222990_a1_a2,A1: mapping_b1_set_b2,A22: mapping_b1_set_b2] :
      ( ( fold_P6133368858501377392set_b2
        @ ^ [X: product_prod_a1_a2] :
            ( produc5703754947799223347set_b2
            @ ^ [A12: mapping_b1_set_b2,A23: mapping_b1_set_b2] : ( produc6988475029935306213set_b2 @ ( G1 @ X @ A12 ) @ ( G2 @ X @ A23 ) ) )
        @ Xs2
        @ ( produc6988475029935306213set_b2 @ A1 @ A22 ) )
      = ( produc6988475029935306213set_b2 @ ( fold_P366236689040723939set_b2 @ G1 @ Xs2 @ A1 ) @ ( fold_P366236689040723939set_b2 @ G2 @ Xs2 @ A22 ) ) ) ).

% fold_dual
thf(fact_671_fold__dual,axiom,
    ! [G1: product_prod_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2,G2: product_prod_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2,Xs2: list_P5985182332071222990_a1_a2,A1: mapping_c1_set_c2,A22: produc4061897789176782763set_c2] :
      ( ( fold_P550125313006781113set_c2
        @ ^ [X: product_prod_a1_a2] :
            ( produc1066867050092484183set_c2
            @ ^ [A12: mapping_c1_set_c2,A23: produc4061897789176782763set_c2] : ( produc3574308084686302062set_c2 @ ( G1 @ X @ A12 ) @ ( G2 @ X @ A23 ) ) )
        @ Xs2
        @ ( produc3574308084686302062set_c2 @ A1 @ A22 ) )
      = ( produc3574308084686302062set_c2 @ ( fold_P3813313114924009441set_c2 @ G1 @ Xs2 @ A1 ) @ ( fold_P7185038094655571566set_c2 @ G2 @ Xs2 @ A22 ) ) ) ).

% fold_dual
thf(fact_672_fold__dual,axiom,
    ! [G1: product_prod_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2,G2: product_prod_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2,Xs2: list_P5985182332071222990_a1_a2,A1: mapping_c1_set_c2,A22: mapping_b1_set_b2] :
      ( ( fold_P8194657128744084078set_b2
        @ ^ [X: product_prod_a1_a2] :
            ( produc3657176527758992563set_b2
            @ ^ [A12: mapping_c1_set_c2,A23: mapping_b1_set_b2] : ( produc9049763300178012899set_b2 @ ( G1 @ X @ A12 ) @ ( G2 @ X @ A23 ) ) )
        @ Xs2
        @ ( produc9049763300178012899set_b2 @ A1 @ A22 ) )
      = ( produc9049763300178012899set_b2 @ ( fold_P3813313114924009441set_c2 @ G1 @ Xs2 @ A1 ) @ ( fold_P366236689040723939set_b2 @ G2 @ Xs2 @ A22 ) ) ) ).

% fold_dual
thf(fact_673_fold__dual,axiom,
    ! [G1: product_prod_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2,G2: product_prod_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2,Xs2: list_P5985182332071222990_a1_a2,A1: mapping_c1_set_c2,A22: mapping_c1_set_c2] :
      ( ( fold_P22954328043502444set_c2
        @ ^ [X: product_prod_a1_a2] :
            ( produc2685860890466672179set_c2
            @ ^ [A12: mapping_c1_set_c2,A23: mapping_c1_set_c2] : ( produc3273467689206522593set_c2 @ ( G1 @ X @ A12 ) @ ( G2 @ X @ A23 ) ) )
        @ Xs2
        @ ( produc3273467689206522593set_c2 @ A1 @ A22 ) )
      = ( produc3273467689206522593set_c2 @ ( fold_P3813313114924009441set_c2 @ G1 @ Xs2 @ A1 ) @ ( fold_P3813313114924009441set_c2 @ G2 @ Xs2 @ A22 ) ) ) ).

% fold_dual
thf(fact_674_fold__dual,axiom,
    ! [G1: product_prod_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2,G2: product_prod_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2,Xs2: list_P5985182332071222990_a1_a2,A1: mapping_b1_set_b2,A22: mapping_c1_set_c2] :
      ( ( fold_P7185038094655571566set_c2
        @ ^ [X: product_prod_a1_a2] :
            ( produc4732439310506902963set_c2
            @ ^ [A12: mapping_b1_set_b2,A23: mapping_c1_set_c2] : ( produc1212179418963815907set_c2 @ ( G1 @ X @ A12 ) @ ( G2 @ X @ A23 ) ) )
        @ Xs2
        @ ( produc1212179418963815907set_c2 @ A1 @ A22 ) )
      = ( produc1212179418963815907set_c2 @ ( fold_P366236689040723939set_b2 @ G1 @ Xs2 @ A1 ) @ ( fold_P3813313114924009441set_c2 @ G2 @ Xs2 @ A22 ) ) ) ).

% fold_dual
thf(fact_675_bot__set__def,axiom,
    ( bot_bot_set_b2
    = ( collect_b2 @ bot_bot_b2_o ) ) ).

% bot_set_def
thf(fact_676_bot__set__def,axiom,
    ( bot_bot_set_c2
    = ( collect_c2 @ bot_bot_c2_o ) ) ).

% bot_set_def
thf(fact_677_bot__set__def,axiom,
    ( bot_bot_set_nat
    = ( collect_nat @ bot_bot_nat_o ) ) ).

% bot_set_def
thf(fact_678_set__as__map__elem,axiom,
    ! [Y5: c1 > option_set_c2,Xs2: set_Pr3221440761411154131set_c2,X2: b1 > option_set_b2] :
      ( ( member8745205179313678111set_c2 @ Y5
        @ ( case_o1308401496032893449set_c2 @ bot_bo2618827607111635154set_c2
          @ ^ [Xs: set_c1_option_set_c2] : Xs
          @ ( set_as6747855926544214282set_c2 @ Xs2 @ X2 ) ) )
     => ( member9053876291207143196set_c2 @ ( produc890782565133688235set_c2 @ X2 @ Y5 ) @ Xs2 ) ) ).

% set_as_map_elem
thf(fact_679_set__as__map__elem,axiom,
    ! [Y5: mapping_c1_set_c2,Xs2: set_Pr1660683266160182027set_c2,X2: mapping_b1_set_b2] :
      ( ( member341037065618468219set_c2 @ Y5
        @ ( case_o6909767104305677121set_c2 @ bot_bo7584170878874662190set_c2
          @ ^ [Xs: set_ma7306327908849618074set_c2] : Xs
          @ ( set_as574257606533379650set_c2 @ Xs2 @ X2 ) ) )
     => ( member419137155788712276set_c2 @ ( produc1212179418963815907set_c2 @ X2 @ Y5 ) @ Xs2 ) ) ).

% set_as_map_elem
thf(fact_680_set__as__map__elem,axiom,
    ! [Y5: b1 > option_set_b2,Xs2: set_Pr5056620919297929171set_b2,X2: c1 > option_set_c2] :
      ( ( member3006388138933004577set_b2 @ Y5
        @ ( case_o4607607441410749453set_b2 @ bot_bo8415064643751506388set_b2
          @ ^ [Xs: set_b1_option_set_b2] : Xs
          @ ( set_as1140155888704866570set_b2 @ Xs2 @ X2 ) ) )
     => ( member5757858293533564444set_b2 @ ( produc4506454564149116331set_b2 @ X2 @ Y5 ) @ Xs2 ) ) ).

% set_as_map_elem
thf(fact_681_set__as__map__elem,axiom,
    ! [Y5: b1 > option_set_b2,Xs2: set_Pr1995104245887189set_b2,X2: b1 > option_set_b2] :
      ( ( member3006388138933004577set_b2 @ Y5
        @ ( case_o4607607441410749453set_b2 @ bot_bo8415064643751506388set_b2
          @ ^ [Xs: set_b1_option_set_b2] : Xs
          @ ( set_as1009038886163540748set_b2 @ Xs2 @ X2 ) ) )
     => ( member5626741290992238622set_b2 @ ( produc4375337561607790509set_b2 @ X2 @ Y5 ) @ Xs2 ) ) ).

% set_as_map_elem
thf(fact_682_set__as__map__elem,axiom,
    ! [Y5: a2,Xs2: set_Pr9206071548465018024_a1_a2,X2: a1] :
      ( ( member_a2 @ Y5
        @ ( case_o9125611637161669601set_a2 @ bot_bot_set_a2
          @ ^ [Xs: set_a2] : Xs
          @ ( set_as_map_a1_a2 @ Xs2 @ X2 ) ) )
     => ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ X2 @ Y5 ) @ Xs2 ) ) ).

% set_as_map_elem
thf(fact_683_set__as__map__elem,axiom,
    ! [Y5: b2,Xs2: set_Pr4592484330697324838_b1_b2,X2: b1] :
      ( ( member_b2 @ Y5
        @ ( case_o3853413523431599071set_b2 @ bot_bot_set_b2
          @ ^ [Xs: set_b2] : Xs
          @ ( set_as_map_b1_b2 @ Xs2 @ X2 ) ) )
     => ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ X2 @ Y5 ) @ Xs2 ) ) ).

% set_as_map_elem
thf(fact_684_set__as__map__elem,axiom,
    ! [Y5: c2,Xs2: set_Pr9202269149784407460_c1_c2,X2: c1] :
      ( ( member_c2 @ Y5
        @ ( case_o7804587446556304349set_c2 @ bot_bot_set_c2
          @ ^ [Xs: set_c2] : Xs
          @ ( set_as_map_c1_c2 @ Xs2 @ X2 ) ) )
     => ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ X2 @ Y5 ) @ Xs2 ) ) ).

% set_as_map_elem
thf(fact_685_set__as__map__containment,axiom,
    ! [X2: b1 > option_set_b2,Y5: c1 > option_set_c2,Zs2: set_Pr3221440761411154131set_c2] :
      ( ( member9053876291207143196set_c2 @ ( produc890782565133688235set_c2 @ X2 @ Y5 ) @ Zs2 )
     => ( member8745205179313678111set_c2 @ Y5
        @ ( case_o1308401496032893449set_c2 @ bot_bo2618827607111635154set_c2
          @ ^ [Xs: set_c1_option_set_c2] : Xs
          @ ( set_as6747855926544214282set_c2 @ Zs2 @ X2 ) ) ) ) ).

% set_as_map_containment
thf(fact_686_set__as__map__containment,axiom,
    ! [X2: mapping_b1_set_b2,Y5: mapping_c1_set_c2,Zs2: set_Pr1660683266160182027set_c2] :
      ( ( member419137155788712276set_c2 @ ( produc1212179418963815907set_c2 @ X2 @ Y5 ) @ Zs2 )
     => ( member341037065618468219set_c2 @ Y5
        @ ( case_o6909767104305677121set_c2 @ bot_bo7584170878874662190set_c2
          @ ^ [Xs: set_ma7306327908849618074set_c2] : Xs
          @ ( set_as574257606533379650set_c2 @ Zs2 @ X2 ) ) ) ) ).

% set_as_map_containment
thf(fact_687_set__as__map__containment,axiom,
    ! [X2: c1 > option_set_c2,Y5: b1 > option_set_b2,Zs2: set_Pr5056620919297929171set_b2] :
      ( ( member5757858293533564444set_b2 @ ( produc4506454564149116331set_b2 @ X2 @ Y5 ) @ Zs2 )
     => ( member3006388138933004577set_b2 @ Y5
        @ ( case_o4607607441410749453set_b2 @ bot_bo8415064643751506388set_b2
          @ ^ [Xs: set_b1_option_set_b2] : Xs
          @ ( set_as1140155888704866570set_b2 @ Zs2 @ X2 ) ) ) ) ).

% set_as_map_containment
thf(fact_688_set__as__map__containment,axiom,
    ! [X2: b1 > option_set_b2,Y5: b1 > option_set_b2,Zs2: set_Pr1995104245887189set_b2] :
      ( ( member5626741290992238622set_b2 @ ( produc4375337561607790509set_b2 @ X2 @ Y5 ) @ Zs2 )
     => ( member3006388138933004577set_b2 @ Y5
        @ ( case_o4607607441410749453set_b2 @ bot_bo8415064643751506388set_b2
          @ ^ [Xs: set_b1_option_set_b2] : Xs
          @ ( set_as1009038886163540748set_b2 @ Zs2 @ X2 ) ) ) ) ).

% set_as_map_containment
thf(fact_689_set__as__map__containment,axiom,
    ! [X2: a1,Y5: a2,Zs2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ X2 @ Y5 ) @ Zs2 )
     => ( member_a2 @ Y5
        @ ( case_o9125611637161669601set_a2 @ bot_bot_set_a2
          @ ^ [Xs: set_a2] : Xs
          @ ( set_as_map_a1_a2 @ Zs2 @ X2 ) ) ) ) ).

% set_as_map_containment
thf(fact_690_set__as__map__containment,axiom,
    ! [X2: b1,Y5: b2,Zs2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ X2 @ Y5 ) @ Zs2 )
     => ( member_b2 @ Y5
        @ ( case_o3853413523431599071set_b2 @ bot_bot_set_b2
          @ ^ [Xs: set_b2] : Xs
          @ ( set_as_map_b1_b2 @ Zs2 @ X2 ) ) ) ) ).

% set_as_map_containment
thf(fact_691_set__as__map__containment,axiom,
    ! [X2: c1,Y5: c2,Zs2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ X2 @ Y5 ) @ Zs2 )
     => ( member_c2 @ Y5
        @ ( case_o7804587446556304349set_c2 @ bot_bot_set_c2
          @ ^ [Xs: set_c2] : Xs
          @ ( set_as_map_c1_c2 @ Zs2 @ X2 ) ) ) ) ).

% set_as_map_containment
thf(fact_692_zero__reorient,axiom,
    ! [X2: literal] :
      ( ( zero_zero_literal = X2 )
      = ( X2 = zero_zero_literal ) ) ).

% zero_reorient
thf(fact_693_zero__reorient,axiom,
    ! [X2: nat] :
      ( ( zero_zero_nat = X2 )
      = ( X2 = zero_zero_nat ) ) ).

% zero_reorient
thf(fact_694_option_Ocase__distrib,axiom,
    ! [H: produc2702059613074419827set_c2 > produc2702059613074419827set_c2,F12: produc2702059613074419827set_c2,F22: ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > produc2702059613074419827set_c2,Option: option9171407760438378004_order] :
      ( ( H @ ( case_o989950291820459046_order @ F12 @ F22 @ Option ) )
      = ( case_o989950291820459046_order @ ( H @ F12 )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( H @ ( F22 @ X ) )
        @ Option ) ) ).

% option.case_distrib
thf(fact_695_option_Ocase__distrib,axiom,
    ! [H: mapping_b1_set_b2 > mapping_b1_set_b2,F12: mapping_b1_set_b2,F22: set_b2 > mapping_b1_set_b2,Option: option_set_b2] :
      ( ( H @ ( case_o3420813927363517980set_b2 @ F12 @ F22 @ Option ) )
      = ( case_o3420813927363517980set_b2 @ ( H @ F12 )
        @ ^ [X: set_b2] : ( H @ ( F22 @ X ) )
        @ Option ) ) ).

% option.case_distrib
thf(fact_696_option_Ocase__distrib,axiom,
    ! [H: mapping_c1_set_c2 > mapping_c1_set_c2,F12: mapping_c1_set_c2,F22: set_c2 > mapping_c1_set_c2,Option: option_set_c2] :
      ( ( H @ ( case_o4190434630649893849set_c2 @ F12 @ F22 @ Option ) )
      = ( case_o4190434630649893849set_c2 @ ( H @ F12 )
        @ ^ [X: set_c2] : ( H @ ( F22 @ X ) )
        @ Option ) ) ).

% option.case_distrib
thf(fact_697_disjE__realizer2,axiom,
    ! [P: $o,Q: ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > $o,X2: option9171407760438378004_order,R: produc2702059613074419827set_c2 > $o,F: produc2702059613074419827set_c2,G: ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > produc2702059613074419827set_c2] :
      ( ( case_o437269291504840897_order @ P @ Q @ X2 )
     => ( ( P
         => ( R @ F ) )
       => ( ! [Q3: product_prod_a1_a2 > product_prod_a1_a2 > order] :
              ( ( Q @ Q3 )
             => ( R @ ( G @ Q3 ) ) )
         => ( R @ ( case_o989950291820459046_order @ F @ G @ X2 ) ) ) ) ) ).

% disjE_realizer2
thf(fact_698_disjE__realizer2,axiom,
    ! [P: $o,Q: set_b2 > $o,X2: option_set_b2,R: mapping_b1_set_b2 > $o,F: mapping_b1_set_b2,G: set_b2 > mapping_b1_set_b2] :
      ( ( case_option_o_set_b2 @ P @ Q @ X2 )
     => ( ( P
         => ( R @ F ) )
       => ( ! [Q3: set_b2] :
              ( ( Q @ Q3 )
             => ( R @ ( G @ Q3 ) ) )
         => ( R @ ( case_o3420813927363517980set_b2 @ F @ G @ X2 ) ) ) ) ) ).

% disjE_realizer2
thf(fact_699_disjE__realizer2,axiom,
    ! [P: $o,Q: set_c2 > $o,X2: option_set_c2,R: mapping_c1_set_c2 > $o,F: mapping_c1_set_c2,G: set_c2 > mapping_c1_set_c2] :
      ( ( case_option_o_set_c2 @ P @ Q @ X2 )
     => ( ( P
         => ( R @ F ) )
       => ( ! [Q3: set_c2] :
              ( ( Q @ Q3 )
             => ( R @ ( G @ Q3 ) ) )
         => ( R @ ( case_o4190434630649893849set_c2 @ F @ G @ X2 ) ) ) ) ) ).

% disjE_realizer2
thf(fact_700_exE__realizer_H,axiom,
    ! [P: mapping_c1_set_c2 > mapping_b1_set_b2 > $o,P2: produc4061897789176782763set_c2] :
      ( ( P @ ( produc6032943676959796241set_c2 @ P2 ) @ ( produc4038274906788240847set_c2 @ P2 ) )
     => ~ ! [X3: mapping_b1_set_b2,Y4: mapping_c1_set_c2] :
            ~ ( P @ Y4 @ X3 ) ) ).

% exE_realizer'
thf(fact_701_exE__realizer_H,axiom,
    ! [P: ( c1 > option_set_c2 ) > ( b1 > option_set_b2 ) > $o,P2: produc2702059613074419827set_c2] :
      ( ( P @ ( produc4575701783957131737set_c2 @ P2 ) @ ( produc3187122337049823639set_c2 @ P2 ) )
     => ~ ! [X3: b1 > option_set_b2,Y4: c1 > option_set_c2] :
            ~ ( P @ Y4 @ X3 ) ) ).

% exE_realizer'
thf(fact_702_option_Osimps_I5_J,axiom,
    ! [F12: produc2702059613074419827set_c2,F22: ( product_prod_a1_a2 > product_prod_a1_a2 > order ) > produc2702059613074419827set_c2,X22: product_prod_a1_a2 > product_prod_a1_a2 > order] :
      ( ( case_o989950291820459046_order @ F12 @ F22 @ ( some_P6364418062025833395_order @ X22 ) )
      = ( F22 @ X22 ) ) ).

% option.simps(5)
thf(fact_703_option_Osimps_I5_J,axiom,
    ! [F12: mapping_b1_set_b2,F22: set_b2 > mapping_b1_set_b2,X22: set_b2] :
      ( ( case_o3420813927363517980set_b2 @ F12 @ F22 @ ( some_set_b2 @ X22 ) )
      = ( F22 @ X22 ) ) ).

% option.simps(5)
thf(fact_704_option_Osimps_I5_J,axiom,
    ! [F12: mapping_c1_set_c2,F22: set_c2 > mapping_c1_set_c2,X22: set_c2] :
      ( ( case_o4190434630649893849set_c2 @ F12 @ F22 @ ( some_set_c2 @ X22 ) )
      = ( F22 @ X22 ) ) ).

% option.simps(5)
thf(fact_705_fold__conv__fold__keys,axiom,
    ( rBT_fo5132325507301440204set_c2
    = ( ^ [F3: product_prod_a1_a2 > produc4061897789176782763set_c2 > produc4061897789176782763set_c2,Rbt: rBT_ma1918525461012799116t_unit] : ( fold_P7185038094655571566set_c2 @ F3 @ ( rBT_ke4861133314182804427_a1_a2 @ Rbt ) ) ) ) ).

% fold_conv_fold_keys
thf(fact_706_fold__conv__fold__keys,axiom,
    ( rBT_fo4244449053837635077set_b2
    = ( ^ [F3: product_prod_a1_a2 > mapping_b1_set_b2 > mapping_b1_set_b2,Rbt: rBT_ma1918525461012799116t_unit] : ( fold_P366236689040723939set_b2 @ F3 @ ( rBT_ke4861133314182804427_a1_a2 @ Rbt ) ) ) ) ).

% fold_conv_fold_keys
thf(fact_707_fold__conv__fold__keys,axiom,
    ( rBT_fo7691525479720920579set_c2
    = ( ^ [F3: product_prod_a1_a2 > mapping_c1_set_c2 > mapping_c1_set_c2,Rbt: rBT_ma1918525461012799116t_unit] : ( fold_P3813313114924009441set_c2 @ F3 @ ( rBT_ke4861133314182804427_a1_a2 @ Rbt ) ) ) ) ).

% fold_conv_fold_keys
thf(fact_708_String_OLiteral__eq__iff,axiom,
    ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,S2: literal,C0: $o,C1: $o,C22: $o,C32: $o,C4: $o,C5: $o,C6: $o,T2: literal] :
      ( ( ( literal2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ S2 )
        = ( literal2 @ C0 @ C1 @ C22 @ C32 @ C4 @ C5 @ C6 @ T2 ) )
      = ( ( B0 = C0 )
        & ( B1 = C1 )
        & ( B22 = C22 )
        & ( B32 = C32 )
        & ( B42 = C4 )
        & ( B52 = C5 )
        & ( B62 = C6 )
        & ( S2 = T2 ) ) ) ).

% String.Literal_eq_iff
thf(fact_709_set__as__map__image__def,axiom,
    ( test_S2264929716748280803set_c2
    = ( ^ [Xs: set_Pr1660683266160182027set_c2,F3: produc4061897789176782763set_c2 > produc4061897789176782763set_c2] : ( set_as574257606533379650set_c2 @ ( image_7945144516369962181set_c2 @ F3 @ Xs ) ) ) ) ).

% set_as_map_image_def
thf(fact_710_set__as__map__image__def,axiom,
    ( test_S3635035963686295067_b1_b2
    = ( ^ [Xs: set_Pr9206071548465018024_a1_a2,F3: product_prod_a1_a2 > product_prod_b1_b2] : ( set_as_map_b1_b2 @ ( image_1398015525354814723_b1_b2 @ F3 @ Xs ) ) ) ) ).

% set_as_map_image_def
thf(fact_711_set__as__map__image__def,axiom,
    ( test_S2999386963081373977_c1_c2
    = ( ^ [Xs: set_Pr9206071548465018024_a1_a2,F3: product_prod_a1_a2 > product_prod_c1_c2] : ( set_as_map_c1_c2 @ ( image_762648812255944833_c1_c2 @ F3 @ Xs ) ) ) ) ).

% set_as_map_image_def
thf(fact_712_is__singletonI,axiom,
    ! [X2: b2] : ( is_singleton_b2 @ ( insert_b2 @ X2 @ bot_bot_set_b2 ) ) ).

% is_singletonI
thf(fact_713_is__singletonI,axiom,
    ! [X2: c2] : ( is_singleton_c2 @ ( insert_c2 @ X2 @ bot_bot_set_c2 ) ) ).

% is_singletonI
thf(fact_714_is__singletonI,axiom,
    ! [X2: nat] : ( is_singleton_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).

% is_singletonI
thf(fact_715_tabulate__fold,axiom,
    ( tabulate_b1_set_b2
    = ( ^ [Xs: list_b1,F3: b1 > set_b2] :
          ( fold_b7903347184624473061set_b2
          @ ^ [K3: b1] : ( update_b1_set_b2 @ K3 @ ( F3 @ K3 ) )
          @ Xs
          @ empty_b1_set_b2 ) ) ) ).

% tabulate_fold
thf(fact_716_tabulate__fold,axiom,
    ( tabulate_c1_set_c2
    = ( ^ [Xs: list_c1,F3: c1 > set_c2] :
          ( fold_c2473469727541406370set_c2
          @ ^ [K3: c1] : ( update_c1_set_c2 @ K3 @ ( F3 @ K3 ) )
          @ Xs
          @ empty_c1_set_c2 ) ) ) ).

% tabulate_fold
thf(fact_717_set__as__map__refined_I1_J,axiom,
    ! [T2: rBT_ma3658025366143732878t_unit] :
      ( ( set_as_map_b1_b2 @ ( set_RB6084859663481217937_b1_b2 @ T2 ) )
      = ( case_o301092356325575671_order
        @ ( abort_1049186117294199233set_b2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_as_map_b1_b2 @ ( set_RB6084859663481217937_b1_b2 @ T2 ) ) )
        @ ^ [X: product_prod_b1_b2 > product_prod_b1_b2 > order] :
            ( lookup_b1_set_b2
            @ ( rBT_fo95959885664571011set_b2
              @ ( produc4842154304667325566set_b2
                @ ^ [Y6: b1,Z: b2,M: mapping_b1_set_b2] :
                    ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ Y6 @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M )
                    @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ Y6 @ ( insert_b2 @ Z @ Zs ) @ M )
                    @ ( lookup_b1_set_b2 @ M @ Y6 ) ) )
              @ T2
              @ empty_b1_set_b2 ) )
        @ ( contai6932292905124817200_order @ collec4736061897551005377_b1_b2 ) ) ) ).

% set_as_map_refined(1)
thf(fact_718_set__as__map__refined_I1_J,axiom,
    ! [T2: rBT_ma5397525271274666640t_unit] :
      ( ( set_as_map_c1_c2 @ ( set_RB5449492950382348047_c1_c2 @ T2 ) )
      = ( case_o4503099943726900729_order
        @ ( abort_6788003157674872767set_c2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_as_map_c1_c2 @ ( set_RB5449492950382348047_c1_c2 @ T2 ) ) )
        @ ^ [X: product_prod_c1_c2 > product_prod_c1_c2 > order] :
            ( lookup_c1_set_c2
            @ ( rBT_fo8617919180229568255set_c2
              @ ( produc2197016797727822456set_c2
                @ ^ [Y6: c1,Z: c2,M: mapping_c1_set_c2] :
                    ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ Y6 @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M )
                    @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ Y6 @ ( insert_c2 @ Z @ Zs ) @ M )
                    @ ( lookup_c1_set_c2 @ M @ Y6 ) ) )
              @ T2
              @ empty_c1_set_c2 ) )
        @ ( contai1101692162586059440_order @ collec4100695184452135487_c1_c2 ) ) ) ).

% set_as_map_refined(1)
thf(fact_719_set__as__map__refined_I1_J,axiom,
    ! [T2: rBT_ma1918525461012799116t_unit] :
      ( ( set_as_map_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ T2 ) )
      = ( case_o5322456805779026421_order
        @ ( abort_4533741113768301507set_a2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_as_map_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ T2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] :
            ( lookup_a1_set_a2
            @ ( rBT_fo797372627954349575set_a2
              @ ( produc7487291811606828676set_a2
                @ ^ [Y6: a1,Z: a2,M: mapping_a1_set_a2] :
                    ( case_o2651193224077142111set_a2 @ ( update_a1_set_a2 @ Y6 @ ( insert_a2 @ Z @ bot_bot_set_a2 ) @ M )
                    @ ^ [Zs: set_a2] : ( update_a1_set_a2 @ Y6 @ ( insert_a2 @ Z @ Zs ) @ M )
                    @ ( lookup_a1_set_a2 @ M @ Y6 ) ) )
              @ T2
              @ empty_a1_set_a2 ) )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% set_as_map_refined(1)
thf(fact_720_set__as__map__image__code,axiom,
    ! [T2: rBT_ma1918525461012799116t_unit,F12: product_prod_a1_a2 > product_prod_b1_b2] :
      ( ( test_S3635035963686295067_b1_b2 @ ( set_RB6720226376580087827_a1_a2 @ T2 ) @ F12 )
      = ( case_o6925540419184956023_order
        @ ( abort_1049186117294199233set_b2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( test_S3635035963686295067_b1_b2 @ ( set_RB6720226376580087827_a1_a2 @ T2 ) @ F12 ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] :
            ( lookup_b1_set_b2
            @ ( rBT_fo4244449053837635077set_b2
              @ ^ [Kv: product_prod_a1_a2,M1: mapping_b1_set_b2] :
                  ( produc6418488838319782393set_b2
                  @ ^ [Y6: b1,Z: b2] :
                      ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ Y6 @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M1 )
                      @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ Y6 @ ( insert_b2 @ Z @ Zs ) @ M1 )
                      @ ( lookup_b1_set_b2 @ M1 @ Y6 ) )
                  @ ( F12 @ Kv ) )
              @ T2
              @ empty_b1_set_b2 ) )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% set_as_map_image_code
thf(fact_721_set__as__map__image__code,axiom,
    ! [T2: rBT_ma1918525461012799116t_unit,F12: product_prod_a1_a2 > product_prod_c1_c2] :
      ( ( test_S2999386963081373977_c1_c2 @ ( set_RB6720226376580087827_a1_a2 @ T2 ) @ F12 )
      = ( case_o8528624032590885625_order
        @ ( abort_6788003157674872767set_c2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( test_S2999386963081373977_c1_c2 @ ( set_RB6720226376580087827_a1_a2 @ T2 ) @ F12 ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] :
            ( lookup_c1_set_c2
            @ ( rBT_fo7691525479720920579set_c2
              @ ^ [Kv: product_prod_a1_a2,M1: mapping_c1_set_c2] :
                  ( produc4822369076420559349set_c2
                  @ ^ [Y6: c1,Z: c2] :
                      ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ Y6 @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M1 )
                      @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ Y6 @ ( insert_c2 @ Z @ Zs ) @ M1 )
                      @ ( lookup_c1_set_c2 @ M1 @ Y6 ) )
                  @ ( F12 @ Kv ) )
              @ T2
              @ empty_c1_set_c2 ) )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% set_as_map_image_code
thf(fact_722_ID__Some,axiom,
    ! [X2: product_prod_a1_a2 > product_prod_a1_a2 > order] :
      ( ( contai3539521610808799152_order @ ( some_P6364418062025833395_order @ X2 ) )
      = ( some_P6364418062025833395_order @ X2 ) ) ).

% ID_Some
thf(fact_723_String_Oempty__neq__Literal,axiom,
    ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,S2: literal] :
      ( zero_zero_literal
     != ( literal2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ S2 ) ) ).

% String.empty_neq_Literal
thf(fact_724_is__singletonI_H,axiom,
    ! [A2: set_Pr9202269149784407460_c1_c2] :
      ( ( A2 != bot_bo745477178175700496_c1_c2 )
     => ( ! [X3: product_prod_c1_c2,Y4: product_prod_c1_c2] :
            ( ( member1440383022217085037_c1_c2 @ X3 @ A2 )
           => ( ( member1440383022217085037_c1_c2 @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_sin3333247299496727480_c1_c2 @ A2 ) ) ) ).

% is_singletonI'
thf(fact_725_is__singletonI_H,axiom,
    ! [A2: set_Pr4592484330697324838_b1_b2] :
      ( ( A2 != bot_bo5359064395943393682_b1_b2 )
     => ( ! [X3: product_prod_b1_b2,Y4: product_prod_b1_b2] :
            ( ( member2075749735315954927_b1_b2 @ X3 @ A2 )
           => ( ( member2075749735315954927_b1_b2 @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_sin3968614012595597370_b1_b2 @ A2 ) ) ) ).

% is_singletonI'
thf(fact_726_is__singletonI_H,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2] :
      ( ( A2 != bot_bo749279576856311060_a1_a2 )
     => ( ! [X3: product_prod_a1_a2,Y4: product_prod_a1_a2] :
            ( ( member2711116448414824817_a1_a2 @ X3 @ A2 )
           => ( ( member2711116448414824817_a1_a2 @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_sin4603980725694467260_a1_a2 @ A2 ) ) ) ).

% is_singletonI'
thf(fact_727_is__singletonI_H,axiom,
    ! [A2: set_ma7306327908849618074set_c2] :
      ( ( A2 != bot_bo7584170878874662190set_c2 )
     => ( ! [X3: mapping_c1_set_c2,Y4: mapping_c1_set_c2] :
            ( ( member341037065618468219set_c2 @ X3 @ A2 )
           => ( ( member341037065618468219set_c2 @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_sin1361443545910532208set_c2 @ A2 ) ) ) ).

% is_singletonI'
thf(fact_728_is__singletonI_H,axiom,
    ! [A2: set_ma6254658672695423900set_b2] :
      ( ( A2 != bot_bo6532501642720468016set_b2 )
     => ( ! [X3: mapping_b1_set_b2,Y4: mapping_b1_set_b2] :
            ( ( member6117332676589958525set_b2 @ X3 @ A2 )
           => ( ( member6117332676589958525set_b2 @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_sin7137739156882022514set_b2 @ A2 ) ) ) ).

% is_singletonI'
thf(fact_729_is__singletonI_H,axiom,
    ! [A2: set_b2] :
      ( ( A2 != bot_bot_set_b2 )
     => ( ! [X3: b2,Y4: b2] :
            ( ( member_b2 @ X3 @ A2 )
           => ( ( member_b2 @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_singleton_b2 @ A2 ) ) ) ).

% is_singletonI'
thf(fact_730_is__singletonI_H,axiom,
    ! [A2: set_c2] :
      ( ( A2 != bot_bot_set_c2 )
     => ( ! [X3: c2,Y4: c2] :
            ( ( member_c2 @ X3 @ A2 )
           => ( ( member_c2 @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_singleton_c2 @ A2 ) ) ) ).

% is_singletonI'
thf(fact_731_is__singletonI_H,axiom,
    ! [A2: set_nat] :
      ( ( A2 != bot_bot_set_nat )
     => ( ! [X3: nat,Y4: nat] :
            ( ( member_nat @ X3 @ A2 )
           => ( ( member_nat @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_singleton_nat @ A2 ) ) ) ).

% is_singletonI'
thf(fact_732_ID__code,axiom,
    ( contai3539521610808799152_order
    = ( ^ [X: option9171407760438378004_order] : X ) ) ).

% ID_code
thf(fact_733_Code_Oabort__cong,axiom,
    ! [Msg: literal,Msg2: literal,F: product_unit > produc2702059613074419827set_c2] :
      ( ( Msg = Msg2 )
     => ( ( abort_2778816509743918716set_c2 @ Msg @ F )
        = ( abort_2778816509743918716set_c2 @ Msg2 @ F ) ) ) ).

% Code.abort_cong
thf(fact_734_is__singleton__def,axiom,
    ( is_singleton_b2
    = ( ^ [A6: set_b2] :
        ? [X: b2] :
          ( A6
          = ( insert_b2 @ X @ bot_bot_set_b2 ) ) ) ) ).

% is_singleton_def
thf(fact_735_is__singleton__def,axiom,
    ( is_singleton_c2
    = ( ^ [A6: set_c2] :
        ? [X: c2] :
          ( A6
          = ( insert_c2 @ X @ bot_bot_set_c2 ) ) ) ) ).

% is_singleton_def
thf(fact_736_is__singleton__def,axiom,
    ( is_singleton_nat
    = ( ^ [A6: set_nat] :
        ? [X: nat] :
          ( A6
          = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).

% is_singleton_def
thf(fact_737_is__singletonE,axiom,
    ! [A2: set_b2] :
      ( ( is_singleton_b2 @ A2 )
     => ~ ! [X3: b2] :
            ( A2
           != ( insert_b2 @ X3 @ bot_bot_set_b2 ) ) ) ).

% is_singletonE
thf(fact_738_is__singletonE,axiom,
    ! [A2: set_c2] :
      ( ( is_singleton_c2 @ A2 )
     => ~ ! [X3: c2] :
            ( A2
           != ( insert_c2 @ X3 @ bot_bot_set_c2 ) ) ) ).

% is_singletonE
thf(fact_739_is__singletonE,axiom,
    ! [A2: set_nat] :
      ( ( is_singleton_nat @ A2 )
     => ~ ! [X3: nat] :
            ( A2
           != ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).

% is_singletonE
thf(fact_740_less__eq__prod__simps,axiom,
    ! [Leq_a: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,Less_a: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,Leq_b: ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o,X1: b1 > option_set_b2,X22: c1 > option_set_c2,Y1: b1 > option_set_b2,Y2: c1 > option_set_c2] :
      ( ( contai8556515494464243480set_c2 @ Leq_a @ Less_a @ Leq_b @ ( produc890782565133688235set_c2 @ X1 @ X22 ) @ ( produc890782565133688235set_c2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Leq_b @ X22 @ Y2 ) ) ) ) ).

% less_eq_prod_simps
thf(fact_741_less__eq__prod__simps,axiom,
    ! [Leq_a: mapping_b1_set_b2 > mapping_b1_set_b2 > $o,Less_a: mapping_b1_set_b2 > mapping_b1_set_b2 > $o,Leq_b: mapping_c1_set_c2 > mapping_c1_set_c2 > $o,X1: mapping_b1_set_b2,X22: mapping_c1_set_c2,Y1: mapping_b1_set_b2,Y2: mapping_c1_set_c2] :
      ( ( contai3045741756866854480set_c2 @ Leq_a @ Less_a @ Leq_b @ ( produc1212179418963815907set_c2 @ X1 @ X22 ) @ ( produc1212179418963815907set_c2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Leq_b @ X22 @ Y2 ) ) ) ) ).

% less_eq_prod_simps
thf(fact_742_less__eq__prod__simps,axiom,
    ! [Leq_a: ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o,Less_a: ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o,Leq_b: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,X1: c1 > option_set_c2,X22: b1 > option_set_b2,Y1: c1 > option_set_c2,Y2: b1 > option_set_b2] :
      ( ( contai2948815456624895768set_b2 @ Leq_a @ Less_a @ Leq_b @ ( produc4506454564149116331set_b2 @ X1 @ X22 ) @ ( produc4506454564149116331set_b2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Leq_b @ X22 @ Y2 ) ) ) ) ).

% less_eq_prod_simps
thf(fact_743_less__eq__prod__simps,axiom,
    ! [Leq_a: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,Less_a: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,Leq_b: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,X1: b1 > option_set_b2,X22: b1 > option_set_b2,Y1: b1 > option_set_b2,Y2: b1 > option_set_b2] :
      ( ( contai2817698454083569946set_b2 @ Leq_a @ Less_a @ Leq_b @ ( produc4375337561607790509set_b2 @ X1 @ X22 ) @ ( produc4375337561607790509set_b2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Leq_b @ X22 @ Y2 ) ) ) ) ).

% less_eq_prod_simps
thf(fact_744_less__eq__prod__simps,axiom,
    ! [Leq_a: c1 > c1 > $o,Less_a: c1 > c1 > $o,Leq_b: c2 > c2 > $o,X1: c1,X22: c2,Y1: c1,Y2: c2] :
      ( ( contai3732489413614277737_c1_c2 @ Leq_a @ Less_a @ Leq_b @ ( product_Pair_c1_c2 @ X1 @ X22 ) @ ( product_Pair_c1_c2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Leq_b @ X22 @ Y2 ) ) ) ) ).

% less_eq_prod_simps
thf(fact_745_less__eq__prod__simps,axiom,
    ! [Leq_a: b1 > b1 > $o,Less_a: b1 > b1 > $o,Leq_b: b2 > b2 > $o,X1: b1,X22: b2,Y1: b1,Y2: b2] :
      ( ( contai4368138414219198827_b1_b2 @ Leq_a @ Less_a @ Leq_b @ ( product_Pair_b1_b2 @ X1 @ X22 ) @ ( product_Pair_b1_b2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Leq_b @ X22 @ Y2 ) ) ) ) ).

% less_eq_prod_simps
thf(fact_746_less__eq__prod__simps,axiom,
    ! [Leq_a: a1 > a1 > $o,Less_a: a1 > a1 > $o,Leq_b: a2 > a2 > $o,X1: a1,X22: a2,Y1: a1,Y2: a2] :
      ( ( contai5003787414824119917_a1_a2 @ Leq_a @ Less_a @ Leq_b @ ( product_Pair_a1_a2 @ X1 @ X22 ) @ ( product_Pair_a1_a2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Leq_b @ X22 @ Y2 ) ) ) ) ).

% less_eq_prod_simps
thf(fact_747_Collect__empty__eq__bot,axiom,
    ! [P: b2 > $o] :
      ( ( ( collect_b2 @ P )
        = bot_bot_set_b2 )
      = ( P = bot_bot_b2_o ) ) ).

% Collect_empty_eq_bot
thf(fact_748_Collect__empty__eq__bot,axiom,
    ! [P: c2 > $o] :
      ( ( ( collect_c2 @ P )
        = bot_bot_set_c2 )
      = ( P = bot_bot_c2_o ) ) ).

% Collect_empty_eq_bot
thf(fact_749_Collect__empty__eq__bot,axiom,
    ! [P: nat > $o] :
      ( ( ( collect_nat @ P )
        = bot_bot_set_nat )
      = ( P = bot_bot_nat_o ) ) ).

% Collect_empty_eq_bot
thf(fact_750_bot__empty__eq,axiom,
    ( bot_bo10657582283832245251_c2_o
    = ( ^ [X: product_prod_c1_c2] : ( member1440383022217085037_c1_c2 @ X @ bot_bo745477178175700496_c1_c2 ) ) ) ).

% bot_empty_eq
thf(fact_751_bot__empty__eq,axiom,
    ( bot_bo56410028296945648111_b2_o
    = ( ^ [X: product_prod_b1_b2] : ( member2075749735315954927_b1_b2 @ X @ bot_bo5359064395943393682_b1_b2 ) ) ) ).

% bot_empty_eq
thf(fact_752_bot__empty__eq,axiom,
    ( bot_bo9928753941511292891_a2_o
    = ( ^ [X: product_prod_a1_a2] : ( member2711116448414824817_a1_a2 @ X @ bot_bo749279576856311060_a1_a2 ) ) ) ).

% bot_empty_eq
thf(fact_753_bot__empty__eq,axiom,
    ( bot_bo699434630920884951t_c2_o
    = ( ^ [X: mapping_c1_set_c2] : ( member341037065618468219set_c2 @ X @ bot_bo7584170878874662190set_c2 ) ) ) ).

% bot_empty_eq
thf(fact_754_bot__empty__eq,axiom,
    ( bot_bo7720725886485147221t_b2_o
    = ( ^ [X: mapping_b1_set_b2] : ( member6117332676589958525set_b2 @ X @ bot_bo6532501642720468016set_b2 ) ) ) ).

% bot_empty_eq
thf(fact_755_bot__empty__eq,axiom,
    ( bot_bot_b2_o
    = ( ^ [X: b2] : ( member_b2 @ X @ bot_bot_set_b2 ) ) ) ).

% bot_empty_eq
thf(fact_756_bot__empty__eq,axiom,
    ( bot_bot_c2_o
    = ( ^ [X: c2] : ( member_c2 @ X @ bot_bot_set_c2 ) ) ) ).

% bot_empty_eq
thf(fact_757_bot__empty__eq,axiom,
    ( bot_bot_nat_o
    = ( ^ [X: nat] : ( member_nat @ X @ bot_bot_set_nat ) ) ) ).

% bot_empty_eq
thf(fact_758_String_OLiteral_H__def,axiom,
    literal3 = literal2 ).

% String.Literal'_def
thf(fact_759_split__cong,axiom,
    ! [Q2: produc4061897789176782763set_c2,F: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,G: mapping_b1_set_b2 > mapping_c1_set_c2 > produc4061897789176782763set_c2,P2: produc4061897789176782763set_c2] :
      ( ! [X3: mapping_b1_set_b2,Y4: mapping_c1_set_c2] :
          ( ( ( produc1212179418963815907set_c2 @ X3 @ Y4 )
            = Q2 )
         => ( ( F @ X3 @ Y4 )
            = ( G @ X3 @ Y4 ) ) )
     => ( ( P2 = Q2 )
       => ( ( produc4732439310506902963set_c2 @ F @ P2 )
          = ( produc4732439310506902963set_c2 @ G @ Q2 ) ) ) ) ).

% split_cong
thf(fact_760_split__cong,axiom,
    ! [Q2: product_prod_b1_b2,F: b1 > b2 > mapping_b1_set_b2,G: b1 > b2 > mapping_b1_set_b2,P2: product_prod_b1_b2] :
      ( ! [X3: b1,Y4: b2] :
          ( ( ( product_Pair_b1_b2 @ X3 @ Y4 )
            = Q2 )
         => ( ( F @ X3 @ Y4 )
            = ( G @ X3 @ Y4 ) ) )
     => ( ( P2 = Q2 )
       => ( ( produc6418488838319782393set_b2 @ F @ P2 )
          = ( produc6418488838319782393set_b2 @ G @ Q2 ) ) ) ) ).

% split_cong
thf(fact_761_split__cong,axiom,
    ! [Q2: product_prod_c1_c2,F: c1 > c2 > mapping_c1_set_c2,G: c1 > c2 > mapping_c1_set_c2,P2: product_prod_c1_c2] :
      ( ! [X3: c1,Y4: c2] :
          ( ( ( product_Pair_c1_c2 @ X3 @ Y4 )
            = Q2 )
         => ( ( F @ X3 @ Y4 )
            = ( G @ X3 @ Y4 ) ) )
     => ( ( P2 = Q2 )
       => ( ( produc4822369076420559349set_c2 @ F @ P2 )
          = ( produc4822369076420559349set_c2 @ G @ Q2 ) ) ) ) ).

% split_cong
thf(fact_762_split__cong,axiom,
    ! [Q2: product_prod_a1_a2,F: a1 > a2 > product_prod_c1_c2,G: a1 > a2 > product_prod_c1_c2,P2: product_prod_a1_a2] :
      ( ! [X3: a1,Y4: a2] :
          ( ( ( product_Pair_a1_a2 @ X3 @ Y4 )
            = Q2 )
         => ( ( F @ X3 @ Y4 )
            = ( G @ X3 @ Y4 ) ) )
     => ( ( P2 = Q2 )
       => ( ( produc885903088071324015_c1_c2 @ F @ P2 )
          = ( produc885903088071324015_c1_c2 @ G @ Q2 ) ) ) ) ).

% split_cong
thf(fact_763_split__cong,axiom,
    ! [Q2: product_prod_a1_a2,F: a1 > a2 > product_prod_b1_b2,G: a1 > a2 > product_prod_b1_b2,P2: product_prod_a1_a2] :
      ( ! [X3: a1,Y4: a2] :
          ( ( ( product_Pair_a1_a2 @ X3 @ Y4 )
            = Q2 )
         => ( ( F @ X3 @ Y4 )
            = ( G @ X3 @ Y4 ) ) )
     => ( ( P2 = Q2 )
       => ( ( produc1521269801170193905_b1_b2 @ F @ P2 )
          = ( produc1521269801170193905_b1_b2 @ G @ Q2 ) ) ) ) ).

% split_cong
thf(fact_764_bot__prod__def,axiom,
    ( bot_bo6678538799391878303set_b2
    = ( produc5265780138349399275set_b2 @ bot_bot_set_b2 @ bot_bot_set_b2 ) ) ).

% bot_prod_def
thf(fact_765_bot__prod__def,axiom,
    ( bot_bo8637653187980365278set_c2
    = ( produc5266062425855516074set_c2 @ bot_bot_set_b2 @ bot_bot_set_c2 ) ) ).

% bot_prod_def
thf(fact_766_bot__prod__def,axiom,
    ( bot_bo6623970406915802492et_nat
    = ( produc1842986394327179720et_nat @ bot_bot_set_b2 @ bot_bot_set_nat ) ) ).

% bot_prod_def
thf(fact_767_bot__prod__def,axiom,
    ( bot_bo1406058398155690974set_b2
    = ( produc9216671773967987754set_b2 @ bot_bot_set_c2 @ bot_bot_set_b2 ) ) ).

% bot_prod_def
thf(fact_768_bot__prod__def,axiom,
    ( bot_bo3365172786744177949set_c2
    = ( produc9216954061474104553set_c2 @ bot_bot_set_c2 @ bot_bot_set_c2 ) ) ).

% bot_prod_def
thf(fact_769_bot__prod__def,axiom,
    ( bot_bo1817630633316081211et_nat
    = ( produc6260018657582234247et_nat @ bot_bot_set_c2 @ bot_bot_set_nat ) ) ).

% bot_prod_def
thf(fact_770_bot__prod__def,axiom,
    ( bot_bo872470976572166268set_b2
    = ( produc8111200996048593992set_b2 @ bot_bot_set_nat @ bot_bot_set_b2 ) ) ).

% bot_prod_def
thf(fact_771_bot__prod__def,axiom,
    ( bot_bo2831585365160653243set_c2
    = ( produc8111483283554710791set_c2 @ bot_bot_set_nat @ bot_bot_set_c2 ) ) ).

% bot_prod_def
thf(fact_772_bot__prod__def,axiom,
    ( bot_bo3047382831089536473et_nat
    = ( produc4532415448927165861et_nat @ bot_bot_set_nat @ bot_bot_set_nat ) ) ).

% bot_prod_def
thf(fact_773_eq__fst__iff,axiom,
    ! [A: c1 > option_set_c2,P2: produc8629413652255616883set_b2] :
      ( ( A
        = ( produc6802794336065251735set_b2 @ P2 ) )
      = ( ? [B7: b1 > option_set_b2] :
            ( P2
            = ( produc4506454564149116331set_b2 @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_774_eq__fst__iff,axiom,
    ! [A: b1 > option_set_b2,P2: produc8498296649714291061set_b2] :
      ( ( A
        = ( produc6671677333523925913set_b2 @ P2 ) )
      = ( ? [B7: b1 > option_set_b2] :
            ( P2
            = ( produc4375337561607790509set_b2 @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_775_eq__fst__iff,axiom,
    ! [A: c1,P2: product_prod_c1_c2] :
      ( ( A
        = ( product_fst_c1_c2 @ P2 ) )
      = ( ? [B7: c2] :
            ( P2
            = ( product_Pair_c1_c2 @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_776_eq__fst__iff,axiom,
    ! [A: b1,P2: product_prod_b1_b2] :
      ( ( A
        = ( product_fst_b1_b2 @ P2 ) )
      = ( ? [B7: b2] :
            ( P2
            = ( product_Pair_b1_b2 @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_777_eq__fst__iff,axiom,
    ! [A: a1,P2: product_prod_a1_a2] :
      ( ( A
        = ( product_fst_a1_a2 @ P2 ) )
      = ( ? [B7: a2] :
            ( P2
            = ( product_Pair_a1_a2 @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_778_eq__fst__iff,axiom,
    ! [A: mapping_b1_set_b2,P2: produc4061897789176782763set_c2] :
      ( ( A
        = ( produc4038274906788240847set_c2 @ P2 ) )
      = ( ? [B7: mapping_c1_set_c2] :
            ( P2
            = ( produc1212179418963815907set_c2 @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_779_eq__fst__iff,axiom,
    ! [A: b1 > option_set_b2,P2: produc2702059613074419827set_c2] :
      ( ( A
        = ( produc3187122337049823639set_c2 @ P2 ) )
      = ( ? [B7: c1 > option_set_c2] :
            ( P2
            = ( produc890782565133688235set_c2 @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_780_fstI,axiom,
    ! [X2: produc8629413652255616883set_b2,Y5: c1 > option_set_c2,Z3: b1 > option_set_b2] :
      ( ( X2
        = ( produc4506454564149116331set_b2 @ Y5 @ Z3 ) )
     => ( ( produc6802794336065251735set_b2 @ X2 )
        = Y5 ) ) ).

% fstI
thf(fact_781_fstI,axiom,
    ! [X2: produc8498296649714291061set_b2,Y5: b1 > option_set_b2,Z3: b1 > option_set_b2] :
      ( ( X2
        = ( produc4375337561607790509set_b2 @ Y5 @ Z3 ) )
     => ( ( produc6671677333523925913set_b2 @ X2 )
        = Y5 ) ) ).

% fstI
thf(fact_782_fstI,axiom,
    ! [X2: product_prod_c1_c2,Y5: c1,Z3: c2] :
      ( ( X2
        = ( product_Pair_c1_c2 @ Y5 @ Z3 ) )
     => ( ( product_fst_c1_c2 @ X2 )
        = Y5 ) ) ).

% fstI
thf(fact_783_fstI,axiom,
    ! [X2: product_prod_b1_b2,Y5: b1,Z3: b2] :
      ( ( X2
        = ( product_Pair_b1_b2 @ Y5 @ Z3 ) )
     => ( ( product_fst_b1_b2 @ X2 )
        = Y5 ) ) ).

% fstI
thf(fact_784_fstI,axiom,
    ! [X2: product_prod_a1_a2,Y5: a1,Z3: a2] :
      ( ( X2
        = ( product_Pair_a1_a2 @ Y5 @ Z3 ) )
     => ( ( product_fst_a1_a2 @ X2 )
        = Y5 ) ) ).

% fstI
thf(fact_785_fstI,axiom,
    ! [X2: produc4061897789176782763set_c2,Y5: mapping_b1_set_b2,Z3: mapping_c1_set_c2] :
      ( ( X2
        = ( produc1212179418963815907set_c2 @ Y5 @ Z3 ) )
     => ( ( produc4038274906788240847set_c2 @ X2 )
        = Y5 ) ) ).

% fstI
thf(fact_786_fstI,axiom,
    ! [X2: produc2702059613074419827set_c2,Y5: b1 > option_set_b2,Z3: c1 > option_set_c2] :
      ( ( X2
        = ( produc890782565133688235set_c2 @ Y5 @ Z3 ) )
     => ( ( produc3187122337049823639set_c2 @ X2 )
        = Y5 ) ) ).

% fstI
thf(fact_787_bot__empty__eq2,axiom,
    ( bot_bo8693474189685096288t_c2_o
    = ( ^ [X: b1 > option_set_b2,Y6: c1 > option_set_c2] : ( member9053876291207143196set_c2 @ ( produc890782565133688235set_c2 @ X @ Y6 ) @ bot_bo2941565536984730943set_c2 ) ) ) ).

% bot_empty_eq2
thf(fact_788_bot__empty__eq2,axiom,
    ( bot_bo7261280182829818792t_c2_o
    = ( ^ [X: mapping_b1_set_b2,Y6: mapping_c1_set_c2] : ( member419137155788712276set_c2 @ ( produc1212179418963815907set_c2 @ X @ Y6 ) @ bot_bo8749877030654239607set_c2 ) ) ) ).

% bot_empty_eq2
thf(fact_789_bot__empty__eq2,axiom,
    ( bot_bo256672798936931680t_b2_o
    = ( ^ [X: c1 > option_set_c2,Y6: b1 > option_set_b2] : ( member5757858293533564444set_b2 @ ( produc4506454564149116331set_b2 @ X @ Y6 ) @ bot_bo4776745694871505983set_b2 ) ) ) ).

% bot_empty_eq2
thf(fact_790_bot__empty__eq2,axiom,
    ( bot_bo869399545248760286t_b2_o
    = ( ^ [X: b1 > option_set_b2,Y6: b1 > option_set_b2] : ( member5626741290992238622set_b2 @ ( produc4375337561607790509set_b2 @ X @ Y6 ) @ bot_bo8945491916674239809set_b2 ) ) ) ).

% bot_empty_eq2
thf(fact_791_bot__empty__eq2,axiom,
    ( bot_bot_c1_c2_o
    = ( ^ [X: c1,Y6: c2] : ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ X @ Y6 ) @ bot_bo745477178175700496_c1_c2 ) ) ) ).

% bot_empty_eq2
thf(fact_792_bot__empty__eq2,axiom,
    ( bot_bot_b1_b2_o
    = ( ^ [X: b1,Y6: b2] : ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ X @ Y6 ) @ bot_bo5359064395943393682_b1_b2 ) ) ) ).

% bot_empty_eq2
thf(fact_793_bot__empty__eq2,axiom,
    ( bot_bot_a1_a2_o
    = ( ^ [X: a1,Y6: a2] : ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ X @ Y6 ) @ bot_bo749279576856311060_a1_a2 ) ) ) ).

% bot_empty_eq2
thf(fact_794_pred__equals__eq2,axiom,
    ! [R: set_Pr3221440761411154131set_c2,S3: set_Pr3221440761411154131set_c2] :
      ( ( ( ^ [X: b1 > option_set_b2,Y6: c1 > option_set_c2] : ( member9053876291207143196set_c2 @ ( produc890782565133688235set_c2 @ X @ Y6 ) @ R ) )
        = ( ^ [X: b1 > option_set_b2,Y6: c1 > option_set_c2] : ( member9053876291207143196set_c2 @ ( produc890782565133688235set_c2 @ X @ Y6 ) @ S3 ) ) )
      = ( R = S3 ) ) ).

% pred_equals_eq2
thf(fact_795_pred__equals__eq2,axiom,
    ! [R: set_Pr1660683266160182027set_c2,S3: set_Pr1660683266160182027set_c2] :
      ( ( ( ^ [X: mapping_b1_set_b2,Y6: mapping_c1_set_c2] : ( member419137155788712276set_c2 @ ( produc1212179418963815907set_c2 @ X @ Y6 ) @ R ) )
        = ( ^ [X: mapping_b1_set_b2,Y6: mapping_c1_set_c2] : ( member419137155788712276set_c2 @ ( produc1212179418963815907set_c2 @ X @ Y6 ) @ S3 ) ) )
      = ( R = S3 ) ) ).

% pred_equals_eq2
thf(fact_796_pred__equals__eq2,axiom,
    ! [R: set_Pr5056620919297929171set_b2,S3: set_Pr5056620919297929171set_b2] :
      ( ( ( ^ [X: c1 > option_set_c2,Y6: b1 > option_set_b2] : ( member5757858293533564444set_b2 @ ( produc4506454564149116331set_b2 @ X @ Y6 ) @ R ) )
        = ( ^ [X: c1 > option_set_c2,Y6: b1 > option_set_b2] : ( member5757858293533564444set_b2 @ ( produc4506454564149116331set_b2 @ X @ Y6 ) @ S3 ) ) )
      = ( R = S3 ) ) ).

% pred_equals_eq2
thf(fact_797_pred__equals__eq2,axiom,
    ! [R: set_Pr1995104245887189set_b2,S3: set_Pr1995104245887189set_b2] :
      ( ( ( ^ [X: b1 > option_set_b2,Y6: b1 > option_set_b2] : ( member5626741290992238622set_b2 @ ( produc4375337561607790509set_b2 @ X @ Y6 ) @ R ) )
        = ( ^ [X: b1 > option_set_b2,Y6: b1 > option_set_b2] : ( member5626741290992238622set_b2 @ ( produc4375337561607790509set_b2 @ X @ Y6 ) @ S3 ) ) )
      = ( R = S3 ) ) ).

% pred_equals_eq2
thf(fact_798_pred__equals__eq2,axiom,
    ! [R: set_Pr9202269149784407460_c1_c2,S3: set_Pr9202269149784407460_c1_c2] :
      ( ( ( ^ [X: c1,Y6: c2] : ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ X @ Y6 ) @ R ) )
        = ( ^ [X: c1,Y6: c2] : ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ X @ Y6 ) @ S3 ) ) )
      = ( R = S3 ) ) ).

% pred_equals_eq2
thf(fact_799_pred__equals__eq2,axiom,
    ! [R: set_Pr4592484330697324838_b1_b2,S3: set_Pr4592484330697324838_b1_b2] :
      ( ( ( ^ [X: b1,Y6: b2] : ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ X @ Y6 ) @ R ) )
        = ( ^ [X: b1,Y6: b2] : ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ X @ Y6 ) @ S3 ) ) )
      = ( R = S3 ) ) ).

% pred_equals_eq2
thf(fact_800_pred__equals__eq2,axiom,
    ! [R: set_Pr9206071548465018024_a1_a2,S3: set_Pr9206071548465018024_a1_a2] :
      ( ( ( ^ [X: a1,Y6: a2] : ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ X @ Y6 ) @ R ) )
        = ( ^ [X: a1,Y6: a2] : ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ X @ Y6 ) @ S3 ) ) )
      = ( R = S3 ) ) ).

% pred_equals_eq2
thf(fact_801_sndI,axiom,
    ! [X2: produc8629413652255616883set_b2,Y5: c1 > option_set_c2,Z3: b1 > option_set_b2] :
      ( ( X2
        = ( produc4506454564149116331set_b2 @ Y5 @ Z3 ) )
     => ( ( produc8191373782972559833set_b2 @ X2 )
        = Z3 ) ) ).

% sndI
thf(fact_802_sndI,axiom,
    ! [X2: produc8498296649714291061set_b2,Y5: b1 > option_set_b2,Z3: b1 > option_set_b2] :
      ( ( X2
        = ( produc4375337561607790509set_b2 @ Y5 @ Z3 ) )
     => ( ( produc8060256780431234011set_b2 @ X2 )
        = Z3 ) ) ).

% sndI
thf(fact_803_sndI,axiom,
    ! [X2: product_prod_c1_c2,Y5: c1,Z3: c2] :
      ( ( X2
        = ( product_Pair_c1_c2 @ Y5 @ Z3 ) )
     => ( ( product_snd_c1_c2 @ X2 )
        = Z3 ) ) ).

% sndI
thf(fact_804_sndI,axiom,
    ! [X2: product_prod_b1_b2,Y5: b1,Z3: b2] :
      ( ( X2
        = ( product_Pair_b1_b2 @ Y5 @ Z3 ) )
     => ( ( product_snd_b1_b2 @ X2 )
        = Z3 ) ) ).

% sndI
thf(fact_805_sndI,axiom,
    ! [X2: product_prod_a1_a2,Y5: a1,Z3: a2] :
      ( ( X2
        = ( product_Pair_a1_a2 @ Y5 @ Z3 ) )
     => ( ( product_snd_a1_a2 @ X2 )
        = Z3 ) ) ).

% sndI
thf(fact_806_sndI,axiom,
    ! [X2: produc4061897789176782763set_c2,Y5: mapping_b1_set_b2,Z3: mapping_c1_set_c2] :
      ( ( X2
        = ( produc1212179418963815907set_c2 @ Y5 @ Z3 ) )
     => ( ( produc6032943676959796241set_c2 @ X2 )
        = Z3 ) ) ).

% sndI
thf(fact_807_sndI,axiom,
    ! [X2: produc2702059613074419827set_c2,Y5: b1 > option_set_b2,Z3: c1 > option_set_c2] :
      ( ( X2
        = ( produc890782565133688235set_c2 @ Y5 @ Z3 ) )
     => ( ( produc4575701783957131737set_c2 @ X2 )
        = Z3 ) ) ).

% sndI
thf(fact_808_eq__snd__iff,axiom,
    ! [B: b1 > option_set_b2,P2: produc8629413652255616883set_b2] :
      ( ( B
        = ( produc8191373782972559833set_b2 @ P2 ) )
      = ( ? [A5: c1 > option_set_c2] :
            ( P2
            = ( produc4506454564149116331set_b2 @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_809_eq__snd__iff,axiom,
    ! [B: b1 > option_set_b2,P2: produc8498296649714291061set_b2] :
      ( ( B
        = ( produc8060256780431234011set_b2 @ P2 ) )
      = ( ? [A5: b1 > option_set_b2] :
            ( P2
            = ( produc4375337561607790509set_b2 @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_810_eq__snd__iff,axiom,
    ! [B: c2,P2: product_prod_c1_c2] :
      ( ( B
        = ( product_snd_c1_c2 @ P2 ) )
      = ( ? [A5: c1] :
            ( P2
            = ( product_Pair_c1_c2 @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_811_eq__snd__iff,axiom,
    ! [B: b2,P2: product_prod_b1_b2] :
      ( ( B
        = ( product_snd_b1_b2 @ P2 ) )
      = ( ? [A5: b1] :
            ( P2
            = ( product_Pair_b1_b2 @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_812_eq__snd__iff,axiom,
    ! [B: a2,P2: product_prod_a1_a2] :
      ( ( B
        = ( product_snd_a1_a2 @ P2 ) )
      = ( ? [A5: a1] :
            ( P2
            = ( product_Pair_a1_a2 @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_813_eq__snd__iff,axiom,
    ! [B: mapping_c1_set_c2,P2: produc4061897789176782763set_c2] :
      ( ( B
        = ( produc6032943676959796241set_c2 @ P2 ) )
      = ( ? [A5: mapping_b1_set_b2] :
            ( P2
            = ( produc1212179418963815907set_c2 @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_814_eq__snd__iff,axiom,
    ! [B: c1 > option_set_c2,P2: produc2702059613074419827set_c2] :
      ( ( B
        = ( produc4575701783957131737set_c2 @ P2 ) )
      = ( ? [A5: b1 > option_set_b2] :
            ( P2
            = ( produc890782565133688235set_c2 @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_815_map__project__code_I3_J,axiom,
    ! [H: product_prod_a1_a2 > option_b2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( map_pr8920200868248588980_a2_b2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o3769919036381400216_order
        @ ( abort_set_b2 @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( map_pr8920200868248588980_a2_b2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] :
            ( rBT_fo7541544804267562824set_b2
            @ ^ [Y6: product_prod_a1_a2,A6: set_b2] :
                ( case_o801698286357362985_b2_b2 @ A6
                @ ^ [Z: b2] : ( insert_b2 @ Z @ A6 )
                @ ( H @ Y6 ) )
            @ Rbt2
            @ bot_bot_set_b2 )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% map_project_code(3)
thf(fact_816_map__project__code_I3_J,axiom,
    ! [H: product_prod_a1_a2 > option_c2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( map_pr8920200868248654579_a2_c2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o3610099362292947737_order
        @ ( abort_set_c2 @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( map_pr8920200868248654579_a2_c2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] :
            ( rBT_fo7541827091773679623set_c2
            @ ^ [Y6: product_prod_a1_a2,A6: set_c2] :
                ( case_o3452368716856024231_c2_c2 @ A6
                @ ^ [Z: c2] : ( insert_c2 @ Z @ A6 )
                @ ( H @ Y6 ) )
            @ Rbt2
            @ bot_bot_set_c2 )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% map_project_code(3)
thf(fact_817_map__project__code_I3_J,axiom,
    ! [H: product_prod_a1_a2 > option_nat,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( map_pr1385896286841821201a2_nat @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o1813945580120271995_order
        @ ( abort_set_nat @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( map_pr1385896286841821201a2_nat @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] :
            ( rBT_fo6657384066399703205et_nat
            @ ^ [Y6: product_prod_a1_a2,A6: set_nat] :
                ( case_o4857086424252989667at_nat @ A6
                @ ^ [Z: nat] : ( insert_nat @ Z @ A6 )
                @ ( H @ Y6 ) )
            @ Rbt2
            @ bot_bot_set_nat )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% map_project_code(3)
thf(fact_818_h__out__impl__helper,axiom,
    ! [A2: set_Pr1900465899975183225_c1_c2] :
      ( ( produc5405262029909427320set_c1
        @ ^ [Q4: c1,X: c2] :
            ( collect_c1
            @ ^ [Y6: c1] :
              ? [Q5: c2] : ( member3631520566957688514_c1_c2 @ ( produc6601572112667417553_c1_c2 @ Q4 @ ( produc8616451471952705593_c1_c2 @ X @ ( product_Pair_c1_c2 @ Y6 @ Q5 ) ) ) @ A2 ) ) )
      = ( ^ [Qx: product_prod_c1_c2] :
            ( case_o705796938002103131set_c1 @ bot_bot_set_c1
            @ ^ [Yqs: set_c1] : Yqs
            @ ( set_as4859442375955252863_c2_c1
              @ ( image_7688004055617516792_c2_c1
                @ ( produc8006923998363754122_c2_c1
                  @ ^ [Q4: c1] :
                      ( produc8826597378573554442_c2_c1
                      @ ^ [X: c2] :
                          ( produc1569024914113382837_c2_c1
                          @ ^ [Y6: c1,Q5: c2] : ( produc7786241149486573598_c2_c1 @ ( product_Pair_c1_c2 @ Q4 @ X ) @ Y6 ) ) ) )
                @ A2 )
              @ Qx ) ) ) ) ).

% h_out_impl_helper
thf(fact_819_h__out__impl__helper,axiom,
    ! [A2: set_Pr38725075060093625_c1_c2] :
      ( ( produc2432174852368237690set_c1
        @ ^ [Q4: b1,X: b2] :
            ( collect_c1
            @ ^ [Y6: c1] :
              ? [Q5: c2] : ( member5611948252916174338_c1_c2 @ ( produc2126910031085843089_c1_c2 @ Q4 @ ( produc2496603517814015032_c1_c2 @ X @ ( product_Pair_c1_c2 @ Y6 @ Q5 ) ) ) @ A2 ) ) )
      = ( ^ [Qx: product_prod_b1_b2] :
            ( case_o705796938002103131set_c1 @ bot_bot_set_c1
            @ ^ [Yqs: set_c1] : Yqs
            @ ( set_as931098894140112385_b2_c1
              @ ( image_4212462100044280762_b2_c1
                @ ( produc2425522283325648076_b2_c1
                  @ ^ [Q4: b1] :
                      ( produc2952213811381996427_b2_c1
                      @ ^ [X: b2] :
                          ( produc6864053469153018167_b2_c1
                          @ ^ [Y6: c1,Q5: c2] : ( produc3857897667671433120_b2_c1 @ ( product_Pair_b1_b2 @ Q4 @ X ) @ Y6 ) ) ) )
                @ A2 )
              @ Qx ) ) ) ) ).

% h_out_impl_helper
thf(fact_820_h__out__impl__helper,axiom,
    ! [A2: set_Pr7400356286999779833_c1_c2] :
      ( ( produc8682459711681823868set_c1
        @ ^ [Q4: a1,X: a2] :
            ( collect_c1
            @ ^ [Y6: c1] :
              ? [Q5: c2] : ( member7592375938874660162_c1_c2 @ ( produc6875619986359044433_c1_c2 @ Q4 @ ( produc5600127600530100279_c1_c2 @ X @ ( product_Pair_c1_c2 @ Y6 @ Q5 ) ) ) @ A2 ) ) )
      = ( ^ [Qx: product_prod_a1_a2] :
            ( case_o705796938002103131set_c1 @ bot_bot_set_c1
            @ ^ [Yqs: set_c1] : Yqs
            @ ( set_as6226127449179747715_a2_c1
              @ ( image_736920144471044732_a2_c1
                @ ( produc6067492605142317838_a2_c1
                  @ ^ [Q4: a1] :
                      ( produc6301202281045214220_a2_c1
                      @ ^ [X: a2] :
                          ( produc2935709987337877689_a2_c1
                          @ ^ [Y6: c1,Q5: c2] : ( produc9152926222711068450_a2_c1 @ ( product_Pair_a1_a2 @ Q4 @ X ) @ Y6 ) ) ) )
                @ A2 )
              @ Qx ) ) ) ) ).

% h_out_impl_helper
thf(fact_821_h__out__impl__helper,axiom,
    ! [A2: set_Pr6545474114340275451_b1_b2] :
      ( ( produc5404979742403310521set_b1
        @ ^ [Q4: c1,X: c2] :
            ( collect_b1
            @ ^ [Y6: b1] :
              ? [Q5: b2] : ( member6983463625492242756_b1_b2 @ ( produc1991787293580334931_b1_b2 @ Q4 @ ( produc28446148196799675_b1_b2 @ X @ ( product_Pair_b1_b2 @ Y6 @ Q5 ) ) ) @ A2 ) ) )
      = ( ^ [Qx: product_prod_c1_c2] :
            ( case_o5977995051732173661set_b1 @ bot_bot_set_b1
            @ ^ [Yqs: set_b1] : Yqs
            @ ( set_as4859442375955187264_c2_b1
              @ ( image_8067344629127337147_c2_b1
                @ ( produc1752625010354970445_c2_b1
                  @ ^ [Q4: c1] :
                      ( produc8757222282308433101_c2_b1
                      @ ^ [X: c2] :
                          ( produc7123004573310942200_c2_b1
                          @ ^ [Y6: b1,Q5: b2] : ( produc7786241149486507999_c2_b1 @ ( product_Pair_c1_c2 @ Q4 @ X ) @ Y6 ) ) ) )
                @ A2 )
              @ Qx ) ) ) ) ).

% h_out_impl_helper
thf(fact_822_h__out__impl__helper,axiom,
    ! [A2: set_Pr4683733289425185851_b1_b2] :
      ( ( produc2431892564862120891set_b1
        @ ^ [Q4: b1,X: b2] :
            ( collect_b1
            @ ^ [Y6: b1] :
              ? [Q5: b2] : ( member8963891311450728580_b1_b2 @ ( produc6740497248853536275_b1_b2 @ Q4 @ ( produc3131970230912884922_b1_b2 @ X @ ( product_Pair_b1_b2 @ Y6 @ Q5 ) ) ) @ A2 ) ) )
      = ( ^ [Qx: product_prod_b1_b2] :
            ( case_o5977995051732173661set_b1 @ bot_bot_set_b1
            @ ^ [Yqs: set_b1] : Yqs
            @ ( set_as931098894140046786_b2_b1
              @ ( image_4591802673554101117_b2_b1
                @ ( produc5394595332171640207_b2_b1
                  @ ^ [Q4: b1] :
                      ( produc2882838715116875086_b2_b1
                      @ ^ [X: b2] :
                          ( produc3194661091495801722_b2_b1
                          @ ^ [Y6: b1,Q5: b2] : ( produc3857897667671367521_b2_b1 @ ( product_Pair_b1_b2 @ Q4 @ X ) @ Y6 ) ) ) )
                @ A2 )
              @ Qx ) ) ) ) ).

% h_out_impl_helper
thf(fact_823_h__out__impl__helper,axiom,
    ! [A2: set_Pr2821992464510096251_b1_b2] :
      ( ( produc8682177424175707069set_b1
        @ ^ [Q4: a1,X: a2] :
            ( collect_b1
            @ ^ [Y6: b1] :
              ? [Q5: b2] : ( member1720946960554438596_b1_b2 @ ( produc2265835167271961811_b1_b2 @ Q4 @ ( produc6235494313628970169_b1_b2 @ X @ ( product_Pair_b1_b2 @ Y6 @ Q5 ) ) ) @ A2 ) ) )
      = ( ^ [Qx: product_prod_a1_a2] :
            ( case_o5977995051732173661set_b1 @ bot_bot_set_b1
            @ ^ [Yqs: set_b1] : Yqs
            @ ( set_as6226127449179682116_a2_b1
              @ ( image_1116260717980865087_a2_b1
                @ ( produc9036565653988309969_a2_b1
                  @ ^ [Q4: a1] :
                      ( produc6231827184780092879_a2_b1
                      @ ^ [X: a2] :
                          ( produc8489689646535437052_a2_b1
                          @ ^ [Y6: b1,Q5: b2] : ( produc9152926222711002851_a2_b1 @ ( product_Pair_a1_a2 @ Q4 @ X ) @ Y6 ) ) ) )
                @ A2 )
              @ Qx ) ) ) ) ).

% h_out_impl_helper
thf(fact_824_h__out__impl__helper,axiom,
    ! [A2: set_Pr1967110291850591869_a1_a2] :
      ( ( produc5404697454897193722set_a1
        @ ^ [Q4: c1,X: c2] :
            ( collect_a1
            @ ^ [Y6: a1] :
              ? [Q5: a2] : ( member1112034647172021190_a1_a2 @ ( produc6605374511348028117_a1_a2 @ Q4 @ ( produc663812861295669565_a1_a2 @ X @ ( product_Pair_a1_a2 @ Y6 @ Q5 ) ) ) @ A2 ) ) )
      = ( ^ [Qx: product_prod_c1_c2] :
            ( case_o2026821128607468383set_a1 @ bot_bot_set_a1
            @ ^ [Yqs: set_a1] : Yqs
            @ ( set_as4859442375955121665_c2_a1
              @ ( image_8446685202637157502_c2_a1
                @ ( produc4721698059200962576_c2_a1
                  @ ^ [Q4: c1] :
                      ( produc8687847186043311760_c2_a1
                      @ ^ [X: c2] :
                          ( produc3453612195653725755_c2_a1
                          @ ^ [Y6: a1,Q5: a2] : ( produc7786241149486442400_c2_a1 @ ( product_Pair_c1_c2 @ Q4 @ X ) @ Y6 ) ) ) )
                @ A2 )
              @ Qx ) ) ) ) ).

% h_out_impl_helper
thf(fact_825_h__out__impl__helper,axiom,
    ! [A2: set_Pr105369466935502269_a1_a2] :
      ( ( produc2431610277356004092set_a1
        @ ^ [Q4: b1,X: b2] :
            ( collect_a1
            @ ^ [Y6: a1] :
              ? [Q5: a2] : ( member3092462333130507014_a1_a2 @ ( produc2130712429766453653_a1_a2 @ Q4 @ ( produc3767336944011754812_a1_a2 @ X @ ( product_Pair_a1_a2 @ Y6 @ Q5 ) ) ) @ A2 ) ) )
      = ( ^ [Qx: product_prod_b1_b2] :
            ( case_o2026821128607468383set_a1 @ bot_bot_set_a1
            @ ^ [Yqs: set_a1] : Yqs
            @ ( set_as931098894139981187_b2_a1
              @ ( image_4971143247063921472_b2_a1
                @ ( produc8363668381017632338_b2_a1
                  @ ^ [Q4: b1] :
                      ( produc2813463618851753745_b2_a1
                      @ ^ [X: b2] :
                          ( produc8748640750693361085_b2_a1
                          @ ^ [Y6: a1,Q5: a2] : ( produc3857897667671301922_b2_a1 @ ( product_Pair_b1_b2 @ Q4 @ X ) @ Y6 ) ) ) )
                @ A2 )
              @ Qx ) ) ) ) ).

% h_out_impl_helper
thf(fact_826_h__out__impl__helper,axiom,
    ! [A2: set_Pr7467000678875188477_a1_a2] :
      ( ( produc8681895136669590270set_a1
        @ ^ [Q4: a1,X: a2] :
            ( collect_a1
            @ ^ [Y6: a1] :
              ? [Q5: a2] : ( member5072890019088992838_a1_a2 @ ( produc6879422385039654997_a1_a2 @ Q4 @ ( produc6870861026727840059_a1_a2 @ X @ ( product_Pair_a1_a2 @ Y6 @ Q5 ) ) ) @ A2 ) ) )
      = ( ^ [Qx: product_prod_a1_a2] :
            ( case_o2026821128607468383set_a1 @ bot_bot_set_a1
            @ ^ [Yqs: set_a1] : Yqs
            @ ( set_as6226127449179616517_a2_a1
              @ ( image_1495601291490685442_a2_a1
                @ ( produc2782266665979526292_a2_a1
                  @ ^ [Q4: a1] :
                      ( produc6162452088514971538_a2_a1
                      @ ^ [X: a2] :
                          ( produc4820297268878220607_a2_a1
                          @ ^ [Y6: a1,Q5: a2] : ( produc9152926222710937252_a2_a1 @ ( product_Pair_a1_a2 @ Q4 @ X ) @ Y6 ) ) ) )
                @ A2 )
              @ Qx ) ) ) ) ).

% h_out_impl_helper
thf(fact_827_h__out__impl__helper,axiom,
    ! [A2: set_Pr6847959500825436640set_c2] :
      ( ( produc8868074789981537069set_b2
        @ ^ [Q4: c1,X: c2] :
            ( collec6564089916258477499set_b2
            @ ^ [Y6: mapping_b1_set_b2] :
              ? [Q5: mapping_c1_set_c2] : ( member3625764905904111785set_c2 @ ( produc6401017609378703672set_c2 @ Q4 @ ( produc5508423839735234848set_c2 @ X @ ( produc1212179418963815907set_c2 @ Y6 @ Q5 ) ) ) @ A2 ) ) )
      = ( ^ [Qx: product_prod_c1_c2] :
            ( case_o8937649668621536325set_b2 @ bot_bo6532501642720468016set_b2
            @ ^ [Yqs: set_ma6254658672695423900set_b2] : Yqs
            @ ( set_as4538642359510808500set_b2
              @ ( image_1291399904955362964set_b2
                @ ( produc4299517532798192550set_b2
                  @ ^ [Q4: c1] :
                      ( produc7726091980666125222set_b2
                      @ ^ [X: c2] :
                          ( produc3609887524509304657set_b2
                          @ ^ [Y6: mapping_b1_set_b2,Q5: mapping_c1_set_c2] : ( produc2207736761247262035set_b2 @ ( product_Pair_c1_c2 @ Q4 @ X ) @ Y6 ) ) ) )
                @ A2 )
              @ Qx ) ) ) ) ).

% h_out_impl_helper
thf(fact_828_csorted__list__of__set__code_I1_J,axiom,
    ! [Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( set_cs3950026889026203652_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o1327236596907251723_order
        @ ( abort_5785945136775419735_a1_a2 @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_cs3950026889026203652_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_ke4861133314182804427_a1_a2 @ Rbt2 )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% csorted_list_of_set_code(1)
thf(fact_829_map__entry__code,axiom,
    ( map_entry_b1_set_b2
    = ( ^ [K3: b1,F3: set_b2 > set_b2,M: mapping_b1_set_b2] :
          ( case_o3420813927363517980set_b2 @ M
          @ ^ [V2: set_b2] : ( update_b1_set_b2 @ K3 @ ( F3 @ V2 ) @ M )
          @ ( lookup_b1_set_b2 @ M @ K3 ) ) ) ) ).

% map_entry_code
thf(fact_830_map__entry__code,axiom,
    ( map_entry_c1_set_c2
    = ( ^ [K3: c1,F3: set_c2 > set_c2,M: mapping_c1_set_c2] :
          ( case_o4190434630649893849set_c2 @ M
          @ ^ [V2: set_c2] : ( update_c1_set_c2 @ K3 @ ( F3 @ V2 ) @ M )
          @ ( lookup_c1_set_c2 @ M @ K3 ) ) ) ) ).

% map_entry_code
thf(fact_831_Set__image__code_I5_J,axiom,
    ! [H: product_prod_c1_c2 > mapping_c1_set_c2,Rbt2: rBT_ma5397525271274666640t_unit] :
      ( ( image_5984881132562613603set_c2 @ H @ ( set_RB5449492950382348047_c1_c2 @ Rbt2 ) )
      = ( case_o5756018690406977383_order
        @ ( abort_8590490174361946193set_c2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_5984881132562613603set_c2 @ H @ ( set_RB5449492950382348047_c1_c2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_c1_c2 > product_prod_c1_c2 > order] : ( rBT_fo3354280009516849461set_c2 @ ( comp_m9082150296861661608_c1_c2 @ insert88652402460333204set_c2 @ H ) @ Rbt2 @ bot_bo7584170878874662190set_c2 )
        @ ( contai1101692162586059440_order @ collec4100695184452135487_c1_c2 ) ) ) ).

% Set_image_code(5)
thf(fact_832_Set__image__code_I5_J,axiom,
    ! [H: product_prod_b1_b2 > mapping_b1_set_b2,Rbt2: rBT_ma3658025366143732878t_unit] :
      ( ( image_6686293874852392167set_b2 @ H @ ( set_RB6084859663481217937_b1_b2 @ Rbt2 ) )
      = ( case_o740565870645481573_order
        @ ( abort_7538820938207752019set_b2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_6686293874852392167set_b2 @ H @ ( set_RB6084859663481217937_b1_b2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_b1_b2 > product_prod_b1_b2 > order] : ( rBT_fo7078035005740980153set_b2 @ ( comp_m1545697475630127524_b1_b2 @ insert5864948013431823510set_b2 @ H ) @ Rbt2 @ bot_bo6532501642720468016set_b2 )
        @ ( contai6932292905124817200_order @ collec4736061897551005377_b1_b2 ) ) ) ).

% Set_image_code(5)
thf(fact_833_Set__image__code_I5_J,axiom,
    ! [H: product_prod_a1_a2 > product_prod_b1_b2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( image_1398015525354814723_b1_b2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o655157351563703731_order
        @ ( abort_6437811408111674927_b1_b2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_1398015525354814723_b1_b2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo2661663730417887303_b1_b2 @ ( comp_P6401785920660582974_a1_a2 @ insert7793476323617067286_b1_b2 @ H ) @ Rbt2 @ bot_bo5359064395943393682_b1_b2 )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Set_image_code(5)
thf(fact_834_Set__image__code_I5_J,axiom,
    ! [H: product_prod_a1_a2 > product_prod_c1_c2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( image_762648812255944833_c1_c2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o371249395770437557_order
        @ ( abort_1824224190343981741_c1_c2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_762648812255944833_c1_c2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo7271448549504969925_c1_c2 @ ( comp_P2932605450278441920_a1_a2 @ insert7158109610518197396_c1_c2 @ H ) @ Rbt2 @ bot_bo745477178175700496_c1_c2 )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Set_image_code(5)
thf(fact_835_Set__image__code_I5_J,axiom,
    ! [H: product_prod_a1_a2 > b2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( image_7328530426886133494_a2_b2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o3769919036381400216_order
        @ ( abort_set_b2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_7328530426886133494_a2_b2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo7541544804267562824set_b2 @ ( comp_b5600926368682017087_a1_a2 @ insert_b2 @ H ) @ Rbt2 @ bot_bot_set_b2 )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Set_image_code(5)
thf(fact_836_Set__image__code_I5_J,axiom,
    ! [H: product_prod_a1_a2 > c2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( image_7328530426886199093_a2_c2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o3610099362292947737_order
        @ ( abort_set_c2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_7328530426886199093_a2_c2 @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo7541827091773679623set_c2 @ ( comp_c1592680653864801986_a1_a2 @ insert_c2 @ H ) @ Rbt2 @ bot_bot_set_c2 )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Set_image_code(5)
thf(fact_837_Set__image__code_I5_J,axiom,
    ! [H: product_prod_a1_a2 > nat,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( image_2925341201121073491a2_nat @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o1813945580120271995_order
        @ ( abort_set_nat @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_2925341201121073491a2_nat @ H @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo6657384066399703205et_nat @ ( comp_n5668408791610806888_a1_a2 @ insert_nat @ H ) @ Rbt2 @ bot_bot_set_nat )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Set_image_code(5)
thf(fact_838_Image__code_I4_J,axiom,
    ! [Rbt2: rBT_ma1918525461012799116t_unit,C7: set_a1] :
      ( ( image_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) @ C7 )
      = ( case_o8386814421925944265_order
        @ ( abort_set_a2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) @ C7 ) )
        @ ^ [X: a1 > a1 > order] :
            ( case_o3568996200889957575_order
            @ ( abort_set_a2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( image_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) @ C7 ) )
            @ ^ [Y6: a2 > a2 > order] :
                ( rBT_fo7541262516761446025set_a2
                @ ( produc2240735584725524872set_a2
                  @ ^ [Z: a1,Aa: a2,Acc: set_a2] : ( if_set_a2 @ ( member_a1 @ Z @ C7 ) @ ( insert_a2 @ Aa @ Acc ) @ Acc ) )
                @ Rbt2
                @ bot_bot_set_a2 )
            @ ( contai8426371921324108128_order @ collec1018370599034179449are_a2 ) )
        @ ( contai7102178477343188834_order @ collec1018370599034179448are_a1 ) ) ) ).

% Image_code(4)
thf(fact_839_Image__code_I4_J,axiom,
    ! [Rbt2: rBT_ma3965075261935132796t_unit,C7: set_Pr9202269149784407460_c1_c2] :
      ( ( image_5567296982714812580_c2_b2 @ ( set_RB7512337293368049883_c2_b2 @ Rbt2 ) @ C7 )
      = ( case_o8967766984372191128_order
        @ ( abort_set_b2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_5567296982714812580_c2_b2 @ ( set_RB7512337293368049883_c2_b2 @ Rbt2 ) @ C7 ) )
        @ ^ [X: product_prod_c1_c2 > product_prod_c1_c2 > order] :
            ( case_o5873507443480046666_order
            @ ( abort_set_b2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( image_5567296982714812580_c2_b2 @ ( set_RB7512337293368049883_c2_b2 @ Rbt2 ) @ C7 ) )
            @ ^ [Y6: b2 > b2 > order] :
                ( rBT_fo3264598251052285946set_b2
                @ ( produc1889740774677239294set_b2
                  @ ^ [Z: product_prod_c1_c2,Aa: b2,Acc: set_b2] : ( if_set_b2 @ ( member1440383022217085037_c1_c2 @ Z @ C7 ) @ ( insert_b2 @ Aa @ Acc ) @ Acc ) )
                @ Rbt2
                @ bot_bot_set_b2 )
            @ ( contai8474260527370315490_order @ collec1018370599034245048are_b2 ) )
        @ ( contai1101692162586059440_order @ collec4100695184452135487_c1_c2 ) ) ) ).

% Image_code(4)
thf(fact_840_Image__code_I4_J,axiom,
    ! [Rbt2: rBT_ma7390374453530515322t_unit,C7: set_Pr4592484330697324838_b1_b2] :
      ( ( image_1638953500899672102_b2_b2 @ ( set_RB3583993811552909405_b2_b2 @ Rbt2 ) @ C7 )
      = ( case_o6368843010376795672_order
        @ ( abort_set_b2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_1638953500899672102_b2_b2 @ ( set_RB3583993811552909405_b2_b2 @ Rbt2 ) @ C7 ) )
        @ ^ [X: product_prod_b1_b2 > product_prod_b1_b2 > order] :
            ( case_o5873507443480046666_order
            @ ( abort_set_b2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( image_1638953500899672102_b2_b2 @ ( set_RB3583993811552909405_b2_b2 @ Rbt2 ) @ C7 ) )
            @ ^ [Y6: b2 > b2 > order] :
                ( rBT_fo2313627930490112636set_b2
                @ ( produc5706168644020670592set_b2
                  @ ^ [Z: product_prod_b1_b2,Aa: b2,Acc: set_b2] : ( if_set_b2 @ ( member2075749735315954927_b1_b2 @ Z @ C7 ) @ ( insert_b2 @ Aa @ Acc ) @ Acc ) )
                @ Rbt2
                @ bot_bot_set_b2 )
            @ ( contai8474260527370315490_order @ collec1018370599034245048are_b2 ) )
        @ ( contai6932292905124817200_order @ collec4736061897551005377_b1_b2 ) ) ) ).

% Image_code(4)
thf(fact_841_Image__code_I4_J,axiom,
    ! [Rbt2: rBT_ma6787449812046583933t_unit,C7: set_Pr9202269149784407460_c1_c2] :
      ( ( image_5567296982714878179_c2_c2 @ ( set_RB7512619580874166682_c2_c2 @ Rbt2 ) @ C7 )
      = ( case_o8807947310283738649_order
        @ ( abort_set_c2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_5567296982714878179_c2_c2 @ ( set_RB7512619580874166682_c2_c2 @ Rbt2 ) @ C7 ) )
        @ ^ [X: product_prod_c1_c2 > product_prod_c1_c2 > order] :
            ( case_o8178018686070135757_order
            @ ( abort_set_c2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( image_5567296982714878179_c2_c2 @ ( set_RB7512619580874166682_c2_c2 @ Rbt2 ) @ C7 ) )
            @ ^ [Y6: c2 > c2 > order] :
                ( rBT_fo7215772174176991224set_c2
                @ ( produc8146164952772738363set_c2
                  @ ^ [Z: product_prod_c1_c2,Aa: c2,Acc: set_c2] : ( if_set_c2 @ ( member1440383022217085037_c1_c2 @ Z @ C7 ) @ ( insert_c2 @ Aa @ Acc ) @ Acc ) )
                @ Rbt2
                @ bot_bot_set_c2 )
            @ ( contai8522149133416522852_order @ collec1018370599034310647are_c2 ) )
        @ ( contai1101692162586059440_order @ collec4100695184452135487_c1_c2 ) ) ) ).

% Image_code(4)
thf(fact_842_Image__code_I4_J,axiom,
    ! [Rbt2: rBT_ma989376966787190651t_unit,C7: set_Pr4592484330697324838_b1_b2] :
      ( ( image_1638953500899737701_b2_c2 @ ( set_RB3584276099059026204_b2_c2 @ Rbt2 ) @ C7 )
      = ( case_o6209023336288343193_order
        @ ( abort_set_c2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_1638953500899737701_b2_c2 @ ( set_RB3584276099059026204_b2_c2 @ Rbt2 ) @ C7 ) )
        @ ^ [X: product_prod_b1_b2 > product_prod_b1_b2 > order] :
            ( case_o8178018686070135757_order
            @ ( abort_set_c2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( image_1638953500899737701_b2_c2 @ ( set_RB3584276099059026204_b2_c2 @ Rbt2 ) @ C7 ) )
            @ ^ [Y6: c2 > c2 > order] :
                ( rBT_fo6264801853614817914set_c2
                @ ( produc2739220785261393853set_c2
                  @ ^ [Z: product_prod_b1_b2,Aa: c2,Acc: set_c2] : ( if_set_c2 @ ( member2075749735315954927_b1_b2 @ Z @ C7 ) @ ( insert_c2 @ Aa @ Acc ) @ Acc ) )
                @ Rbt2
                @ bot_bot_set_c2 )
            @ ( contai8522149133416522852_order @ collec1018370599034310647are_c2 ) )
        @ ( contai6932292905124817200_order @ collec4736061897551005377_b1_b2 ) ) ) ).

% Image_code(4)
thf(fact_843_Image__code_I4_J,axiom,
    ! [Rbt2: rBT_ma7046197049342692319t_unit,C7: set_Pr9202269149784407460_c1_c2] :
      ( ( image_1415680205027599873c2_nat @ ( set_RB4799243297308716472c2_nat @ Rbt2 ) @ C7 )
      = ( case_o7011793528111062907_order
        @ ( abort_set_nat @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_1415680205027599873c2_nat @ ( set_RB4799243297308716472c2_nat @ Rbt2 ) @ C7 ) )
        @ ^ [X: product_prod_c1_c2 > product_prod_c1_c2 > order] :
            ( case_o7271898223054362355_order
            @ ( abort_set_nat @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( image_1415680205027599873c2_nat @ ( set_RB4799243297308716472c2_nat @ Rbt2 ) @ C7 ) )
            @ ^ [Y6: nat > nat > order] :
                ( rBT_fo8463504185399329716et_nat
                @ ( produc3464760625607426069et_nat
                  @ ^ [Z: product_prod_c1_c2,Aa: nat,Acc: set_nat] : ( if_set_nat @ ( member1440383022217085037_c1_c2 @ Z @ C7 ) @ ( insert_nat @ Aa @ Acc ) @ Acc ) )
                @ Rbt2
                @ bot_bot_set_nat )
            @ ( contai6714475312730102056_order @ collec3177673580629085973re_nat ) )
        @ ( contai1101692162586059440_order @ collec4100695184452135487_c1_c2 ) ) ) ).

% Image_code(4)
thf(fact_844_Image__code_I4_J,axiom,
    ! [Rbt2: rBT_ma5169777983910274525t_unit,C7: set_Pr4592484330697324838_b1_b2] :
      ( ( image_2236591335334443651b2_nat @ ( set_RB5620154427615560250b2_nat @ Rbt2 ) @ C7 )
      = ( case_o4412869554115667451_order
        @ ( abort_set_nat @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_2236591335334443651b2_nat @ ( set_RB5620154427615560250b2_nat @ Rbt2 ) @ C7 ) )
        @ ^ [X: product_prod_b1_b2 > product_prod_b1_b2 > order] :
            ( case_o7271898223054362355_order
            @ ( abort_set_nat @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( image_2236591335334443651b2_nat @ ( set_RB5620154427615560250b2_nat @ Rbt2 ) @ C7 ) )
            @ ^ [Y6: nat > nat > order] :
                ( rBT_fo1902495449323325494et_nat
                @ ( produc6434115961959534999et_nat
                  @ ^ [Z: product_prod_b1_b2,Aa: nat,Acc: set_nat] : ( if_set_nat @ ( member2075749735315954927_b1_b2 @ Z @ C7 ) @ ( insert_nat @ Aa @ Acc ) @ Acc ) )
                @ Rbt2
                @ bot_bot_set_nat )
            @ ( contai6714475312730102056_order @ collec3177673580629085973re_nat ) )
        @ ( contai6932292905124817200_order @ collec4736061897551005377_b1_b2 ) ) ) ).

% Image_code(4)
thf(fact_845_Image__code_I4_J,axiom,
    ! [Rbt2: rBT_ma1592301608271122040t_unit,C7: set_Pr9206071548465018024_a1_a2] :
      ( ( image_6933982055939307432_a2_b2 @ ( set_RB8879022366592544735_a2_b2 @ Rbt2 ) @ C7 )
      = ( case_o3769919036381400216_order
        @ ( abort_set_b2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_6933982055939307432_a2_b2 @ ( set_RB8879022366592544735_a2_b2 @ Rbt2 ) @ C7 ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] :
            ( case_o5873507443480046666_order
            @ ( abort_set_b2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( image_6933982055939307432_a2_b2 @ ( set_RB8879022366592544735_a2_b2 @ Rbt2 ) @ C7 ) )
            @ ^ [Y6: b2 > b2 > order] :
                ( rBT_fo1362657609927939326set_b2
                @ ( produc299224476509326082set_b2
                  @ ^ [Z: product_prod_a1_a2,Aa: b2,Acc: set_b2] : ( if_set_b2 @ ( member2711116448414824817_a1_a2 @ Z @ C7 ) @ ( insert_b2 @ Aa @ Acc ) @ Acc ) )
                @ Rbt2
                @ bot_bot_set_b2 )
            @ ( contai8474260527370315490_order @ collec1018370599034245048are_b2 ) )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Image_code(4)
thf(fact_846_Image__code_I4_J,axiom,
    ! [Rbt2: rBT_ma4414676158382573177t_unit,C7: set_Pr9206071548465018024_a1_a2] :
      ( ( image_6933982055939373031_a2_c2 @ ( set_RB8879304654098661534_a2_c2 @ Rbt2 ) @ C7 )
      = ( case_o3610099362292947737_order
        @ ( abort_set_c2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_6933982055939373031_a2_c2 @ ( set_RB8879304654098661534_a2_c2 @ Rbt2 ) @ C7 ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] :
            ( case_o8178018686070135757_order
            @ ( abort_set_c2 @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( image_6933982055939373031_a2_c2 @ ( set_RB8879304654098661534_a2_c2 @ Rbt2 ) @ C7 ) )
            @ ^ [Y6: c2 > c2 > order] :
                ( rBT_fo5313831533052644604set_c2
                @ ( produc6555648654604825151set_c2
                  @ ^ [Z: product_prod_a1_a2,Aa: c2,Acc: set_c2] : ( if_set_c2 @ ( member2711116448414824817_a1_a2 @ Z @ C7 ) @ ( insert_c2 @ Aa @ Acc ) @ Acc ) )
                @ Rbt2
                @ bot_bot_set_c2 )
            @ ( contai8522149133416522852_order @ collec1018370599034310647are_c2 ) )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Image_code(4)
thf(fact_847_Image__code_I4_J,axiom,
    ! [Rbt2: rBT_ma3293358918477856731t_unit,C7: set_Pr9206071548465018024_a1_a2] :
      ( ( image_3057502465641287429a2_nat @ ( set_RB6441065557922404028a2_nat @ Rbt2 ) @ C7 )
      = ( case_o1813945580120271995_order
        @ ( abort_set_nat @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( image_3057502465641287429a2_nat @ ( set_RB6441065557922404028a2_nat @ Rbt2 ) @ C7 ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] :
            ( case_o7271898223054362355_order
            @ ( abort_set_nat @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( image_3057502465641287429a2_nat @ ( set_RB6441065557922404028a2_nat @ Rbt2 ) @ C7 ) )
            @ ^ [Y6: nat > nat > order] :
                ( rBT_fo4564858750102097080et_nat
                @ ( produc180099261456868121et_nat
                  @ ^ [Z: product_prod_a1_a2,Aa: nat,Acc: set_nat] : ( if_set_nat @ ( member2711116448414824817_a1_a2 @ Z @ C7 ) @ ( insert_nat @ Aa @ Acc ) @ Acc ) )
                @ Rbt2
                @ bot_bot_set_nat )
            @ ( contai6714475312730102056_order @ collec3177673580629085973re_nat ) )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Image_code(4)
thf(fact_848_set__fold__cfc__code_I5_J,axiom,
    ! [F4: set_co8648611349764106212set_c2,B: produc4061897789176782763set_c2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( set_se764104708205941302set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o7815954270536807150_order
        @ ( abort_4986896609014028468set_c2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_se764104708205941302set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo5132325507301440204set_c2 @ ( set_co5036068180762417751set_c2 @ F4 ) @ Rbt2 @ B )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% set_fold_cfc_code(5)
thf(fact_849_set__fold__cfc__code_I5_J,axiom,
    ! [F4: set_co8598795993805790083set_b2,B: mapping_b1_set_b2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( set_se1353478033518471707set_b2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o3110906606155996059_order
        @ ( abort_1879577566130638365set_b2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_se1353478033518471707set_b2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo4244449053837635077set_b2 @ ( set_co1133346682401797306set_b2 @ F4 ) @ Rbt2 @ B )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% set_fold_cfc_code(5)
thf(fact_850_set__fold__cfc__code_I5_J,axiom,
    ! [F4: set_co427093193105208449set_c2,B: mapping_c1_set_c2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( set_se4800554459401757209set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o573573238536716829_order
        @ ( abort_5326653992013923867set_c2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_se4800554459401757209set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo7691525479720920579set_c2 @ ( set_co4580423108285082808set_c2 @ F4 ) @ Rbt2 @ B )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% set_fold_cfc_code(5)
thf(fact_851_set__fold__cfc__code_I5_J,axiom,
    ! [F4: set_co4027722269366479532set_c2,B: produc2702059613074419827set_c2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( set_se4474698099260563966set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o989950291820459046_order
        @ ( abort_2778816509743918716set_c2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_se4474698099260563966set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo273127210504882324set_c2 @ ( set_co8608146164814620447set_c2 @ F4 ) @ Rbt2 @ B )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% set_fold_cfc_code(5)
thf(fact_852_ImageI,axiom,
    ! [A: c1,B: c2,R2: set_Pr9202269149784407460_c1_c2,A2: set_c1] :
      ( ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ A @ B ) @ R2 )
     => ( ( member_c1 @ A @ A2 )
       => ( member_c2 @ B @ ( image_c1_c2 @ R2 @ A2 ) ) ) ) ).

% ImageI
thf(fact_853_ImageI,axiom,
    ! [A: b1,B: b2,R2: set_Pr4592484330697324838_b1_b2,A2: set_b1] :
      ( ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ A @ B ) @ R2 )
     => ( ( member_b1 @ A @ A2 )
       => ( member_b2 @ B @ ( image_b1_b2 @ R2 @ A2 ) ) ) ) ).

% ImageI
thf(fact_854_ImageI,axiom,
    ! [A: a1,B: a2,R2: set_Pr9206071548465018024_a1_a2,A2: set_a1] :
      ( ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ A @ B ) @ R2 )
     => ( ( member_a1 @ A @ A2 )
       => ( member_a2 @ B @ ( image_a1_a2 @ R2 @ A2 ) ) ) ) ).

% ImageI
thf(fact_855_ImageI,axiom,
    ! [A: product_prod_c1_c2,B: product_prod_c1_c2,R2: set_Pr7201650869308432135_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member9000954395314733392_c1_c2 @ ( produc7339030775447831575_c1_c2 @ A @ B ) @ R2 )
     => ( ( member1440383022217085037_c1_c2 @ A @ A2 )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_4120787240442460243_c1_c2 @ R2 @ A2 ) ) ) ) ).

% ImageI
thf(fact_856_ImageI,axiom,
    ! [A: product_prod_c1_c2,B: product_prod_b1_b2,R2: set_Pr1330221890988210569_b1_b2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member4391169576227650770_b1_b2 @ ( produc7974397488546701465_b1_b2 @ A @ B ) @ R2 )
     => ( ( member1440383022217085037_c1_c2 @ A @ A2 )
       => ( member2075749735315954927_b1_b2 @ B @ ( image_4756153953541330133_b1_b2 @ R2 @ A2 ) ) ) ) ).

% ImageI
thf(fact_857_ImageI,axiom,
    ! [A: product_prod_c1_c2,B: product_prod_a1_a2,R2: set_Pr4682164949522764811_a1_a2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member9004756793995343956_a1_a2 @ ( produc8609764201645571355_a1_a2 @ A @ B ) @ R2 )
     => ( ( member1440383022217085037_c1_c2 @ A @ A2 )
       => ( member2711116448414824817_a1_a2 @ B @ ( image_5391520666640200023_a1_a2 @ R2 @ A2 ) ) ) ) ).

% ImageI
thf(fact_858_ImageI,axiom,
    ! [A: product_prod_b1_b2,B: product_prod_c1_c2,R2: set_Pr1798928773911001861_c1_c2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2747565893236161614_c1_c2 @ ( produc1085642273369259797_c1_c2 @ A @ B ) @ R2 )
     => ( ( member2075749735315954927_b1_b2 @ A @ A2 )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_7090770775218664273_c1_c2 @ R2 @ A2 ) ) ) ) ).

% ImageI
thf(fact_859_ImageI,axiom,
    ! [A: product_prod_b1_b2,B: product_prod_b1_b2,R2: set_Pr5150871832445556103_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member7361153111003854800_b1_b2 @ ( produc1721008986468129687_b1_b2 @ A @ B ) @ R2 )
     => ( ( member2075749735315954927_b1_b2 @ A @ A2 )
       => ( member2075749735315954927_b1_b2 @ B @ ( image_7726137488317534163_b1_b2 @ R2 @ A2 ) ) ) ) ).

% ImageI
thf(fact_860_ImageI,axiom,
    ! [A: product_prod_b1_b2,B: product_prod_a1_a2,R2: set_Pr8502814890980110345_a1_a2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2751368291916772178_a1_a2 @ ( produc2356375699566999577_a1_a2 @ A @ B ) @ R2 )
     => ( ( member2075749735315954927_b1_b2 @ A @ A2 )
       => ( member2711116448414824817_a1_a2 @ B @ ( image_8361504201416404053_a1_a2 @ R2 @ A2 ) ) ) ) ).

% ImageI
thf(fact_861_ImageI,axiom,
    ! [A: product_prod_a1_a2,B: product_prod_c1_c2,R2: set_Pr5619578715368347395_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member5717549428012365644_c1_c2 @ ( produc4055625808145463827_c1_c2 @ A @ B ) @ R2 )
     => ( ( member2711116448414824817_a1_a2 @ A @ A2 )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_837382273140092495_c1_c2 @ R2 @ A2 ) ) ) ) ).

% ImageI
thf(fact_862_Image__empty2,axiom,
    ! [R: set_Pr5518672264616941095_b2_b2] :
      ( ( image_b2_b2 @ R @ bot_bot_set_b2 )
      = bot_bot_set_b2 ) ).

% Image_empty2
thf(fact_863_Image__empty2,axiom,
    ! [R: set_Pr7477786653205428070_b2_c2] :
      ( ( image_b2_c2 @ R @ bot_bot_set_b2 )
      = bot_bot_set_c2 ) ).

% Image_empty2
thf(fact_864_Image__empty2,axiom,
    ! [R: set_Pr6583197765812888324b2_nat] :
      ( ( image_b2_nat @ R @ bot_bot_set_b2 )
      = bot_bot_set_nat ) ).

% Image_empty2
thf(fact_865_Image__empty2,axiom,
    ! [R: set_Pr8169342695115536742_c2_b2] :
      ( ( image_c2_b2 @ R @ bot_bot_set_c2 )
      = bot_bot_set_b2 ) ).

% Image_empty2
thf(fact_866_Image__empty2,axiom,
    ! [R: set_Pr905085046849247909_c2_c2] :
      ( ( image_c2_c2 @ R @ bot_bot_set_c2 )
      = bot_bot_set_c2 ) ).

% Image_empty2
thf(fact_867_Image__empty2,axiom,
    ! [R: set_Pr4274324598211246019c2_nat] :
      ( ( image_c2_nat @ R @ bot_bot_set_c2 )
      = bot_bot_set_nat ) ).

% Image_empty2
thf(fact_868_Image__empty2,axiom,
    ! [R: set_Pr9176197216388362500nat_b2] :
      ( ( image_nat_b2 @ R @ bot_bot_set_nat )
      = bot_bot_set_b2 ) ).

% Image_empty2
thf(fact_869_Image__empty2,axiom,
    ! [R: set_Pr1911939568122073667nat_c2] :
      ( ( image_nat_c2 @ R @ bot_bot_set_nat )
      = bot_bot_set_c2 ) ).

% Image_empty2
thf(fact_870_Image__empty2,axiom,
    ! [R: set_Pr1261947904930325089at_nat] :
      ( ( image_nat_nat @ R @ bot_bot_set_nat )
      = bot_bot_set_nat ) ).

% Image_empty2
thf(fact_871_Image__singleton__iff,axiom,
    ! [B: c2,R2: set_Pr9202269149784407460_c1_c2,A: c1] :
      ( ( member_c2 @ B @ ( image_c1_c2 @ R2 @ ( insert_c1 @ A @ bot_bot_set_c1 ) ) )
      = ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ A @ B ) @ R2 ) ) ).

% Image_singleton_iff
thf(fact_872_Image__singleton__iff,axiom,
    ! [B: b2,R2: set_Pr4592484330697324838_b1_b2,A: b1] :
      ( ( member_b2 @ B @ ( image_b1_b2 @ R2 @ ( insert_b1 @ A @ bot_bot_set_b1 ) ) )
      = ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ A @ B ) @ R2 ) ) ).

% Image_singleton_iff
thf(fact_873_Image__singleton__iff,axiom,
    ! [B: a2,R2: set_Pr9206071548465018024_a1_a2,A: a1] :
      ( ( member_a2 @ B @ ( image_a1_a2 @ R2 @ ( insert_a1 @ A @ bot_bot_set_a1 ) ) )
      = ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ A @ B ) @ R2 ) ) ).

% Image_singleton_iff
thf(fact_874_Image__singleton__iff,axiom,
    ! [B: product_prod_c1_c2,R2: set_Pr7226085152747980732_c1_c2,A: b2] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( image_277659351042319612_c1_c2 @ R2 @ ( insert_b2 @ A @ bot_bot_set_b2 ) ) )
      = ( member4377411281923509149_c1_c2 @ ( produc2496603517814015032_c1_c2 @ A @ B ) @ R2 ) ) ).

% Image_singleton_iff
thf(fact_875_Image__singleton__iff,axiom,
    ! [B: product_prod_b1_b2,R2: set_Pr1354656174427759166_b1_b2,A: b2] :
      ( ( member2075749735315954927_b1_b2 @ B @ ( image_913026064141189502_b1_b2 @ R2 @ ( insert_b2 @ A @ bot_bot_set_b2 ) ) )
      = ( member8990998499691202335_b1_b2 @ ( produc3131970230912884922_b1_b2 @ A @ B ) @ R2 ) ) ).

% Image_singleton_iff
thf(fact_876_Image__singleton__iff,axiom,
    ! [B: product_prod_a1_a2,R2: set_Pr4706599232962313408_a1_a2,A: b2] :
      ( ( member2711116448414824817_a1_a2 @ B @ ( image_1548392777240059392_a1_a2 @ R2 @ ( insert_b2 @ A @ bot_bot_set_b2 ) ) )
      = ( member4381213680604119713_a1_a2 @ ( produc3767336944011754812_a1_a2 @ A @ B ) @ R2 ) ) ).

% Image_singleton_iff
thf(fact_877_Image__singleton__iff,axiom,
    ! [B: product_prod_c1_c2,R2: set_Pr6890843339346611005_c1_c2,A: c2] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( image_6397507305181010173_c1_c2 @ R2 @ ( insert_c2 @ A @ bot_bot_set_c2 ) ) )
      = ( member1273887199207423902_c1_c2 @ ( produc8616451471952705593_c1_c2 @ A @ B ) @ R2 ) ) ).

% Image_singleton_iff
thf(fact_878_Image__singleton__iff,axiom,
    ! [B: product_prod_b1_b2,R2: set_Pr1019414361026389439_b1_b2,A: c2] :
      ( ( member2075749735315954927_b1_b2 @ B @ ( image_7032874018279880063_b1_b2 @ R2 @ ( insert_c2 @ A @ bot_bot_set_c2 ) ) )
      = ( member5887474416975117088_b1_b2 @ ( produc28446148196799675_b1_b2 @ A @ B ) @ R2 ) ) ).

% Image_singleton_iff
thf(fact_879_Image__singleton__iff,axiom,
    ! [B: product_prod_a1_a2,R2: set_Pr4371357419560943681_a1_a2,A: c2] :
      ( ( member2711116448414824817_a1_a2 @ B @ ( image_7668240731378749953_a1_a2 @ R2 @ ( insert_c2 @ A @ bot_bot_set_c2 ) ) )
      = ( member1277689597888034466_a1_a2 @ ( produc663812861295669565_a1_a2 @ A @ B ) @ R2 ) ) ).

% Image_singleton_iff
thf(fact_880_Image__singleton__iff,axiom,
    ! [B: product_prod_c1_c2,R2: set_Pr6986345755798685983_c1_c2,A: nat] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( image_5581968639176954079_c1_c2 @ R2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
      = ( member958080023357176960_c1_c2 @ ( produc1421920924983023131_c1_c2 @ A @ B ) @ R2 ) ) ).

% Image_singleton_iff
thf(fact_881_map__project__empty,axiom,
    ! [F: b2 > option_b2] :
      ( ( map_project_b2_b2 @ F @ bot_bot_set_b2 )
      = bot_bot_set_b2 ) ).

% map_project_empty
thf(fact_882_map__project__empty,axiom,
    ! [F: b2 > option_c2] :
      ( ( map_project_b2_c2 @ F @ bot_bot_set_b2 )
      = bot_bot_set_c2 ) ).

% map_project_empty
thf(fact_883_map__project__empty,axiom,
    ! [F: b2 > option_nat] :
      ( ( map_project_b2_nat @ F @ bot_bot_set_b2 )
      = bot_bot_set_nat ) ).

% map_project_empty
thf(fact_884_map__project__empty,axiom,
    ! [F: c2 > option_b2] :
      ( ( map_project_c2_b2 @ F @ bot_bot_set_c2 )
      = bot_bot_set_b2 ) ).

% map_project_empty
thf(fact_885_map__project__empty,axiom,
    ! [F: c2 > option_c2] :
      ( ( map_project_c2_c2 @ F @ bot_bot_set_c2 )
      = bot_bot_set_c2 ) ).

% map_project_empty
thf(fact_886_map__project__empty,axiom,
    ! [F: c2 > option_nat] :
      ( ( map_project_c2_nat @ F @ bot_bot_set_c2 )
      = bot_bot_set_nat ) ).

% map_project_empty
thf(fact_887_map__project__empty,axiom,
    ! [F: nat > option_b2] :
      ( ( map_project_nat_b2 @ F @ bot_bot_set_nat )
      = bot_bot_set_b2 ) ).

% map_project_empty
thf(fact_888_map__project__empty,axiom,
    ! [F: nat > option_c2] :
      ( ( map_project_nat_c2 @ F @ bot_bot_set_nat )
      = bot_bot_set_c2 ) ).

% map_project_empty
thf(fact_889_map__project__empty,axiom,
    ! [F: nat > option_nat] :
      ( ( map_project_nat_nat @ F @ bot_bot_set_nat )
      = bot_bot_set_nat ) ).

% map_project_empty
thf(fact_890_ImageE,axiom,
    ! [B: c2,R2: set_Pr9202269149784407460_c1_c2,A2: set_c1] :
      ( ( member_c2 @ B @ ( image_c1_c2 @ R2 @ A2 ) )
     => ~ ! [X3: c1] :
            ( ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ X3 @ B ) @ R2 )
           => ~ ( member_c1 @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_891_ImageE,axiom,
    ! [B: b2,R2: set_Pr4592484330697324838_b1_b2,A2: set_b1] :
      ( ( member_b2 @ B @ ( image_b1_b2 @ R2 @ A2 ) )
     => ~ ! [X3: b1] :
            ( ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ X3 @ B ) @ R2 )
           => ~ ( member_b1 @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_892_ImageE,axiom,
    ! [B: a2,R2: set_Pr9206071548465018024_a1_a2,A2: set_a1] :
      ( ( member_a2 @ B @ ( image_a1_a2 @ R2 @ A2 ) )
     => ~ ! [X3: a1] :
            ( ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ X3 @ B ) @ R2 )
           => ~ ( member_a1 @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_893_ImageE,axiom,
    ! [B: product_prod_c1_c2,R2: set_Pr7201650869308432135_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( image_4120787240442460243_c1_c2 @ R2 @ A2 ) )
     => ~ ! [X3: product_prod_c1_c2] :
            ( ( member9000954395314733392_c1_c2 @ ( produc7339030775447831575_c1_c2 @ X3 @ B ) @ R2 )
           => ~ ( member1440383022217085037_c1_c2 @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_894_ImageE,axiom,
    ! [B: product_prod_c1_c2,R2: set_Pr1798928773911001861_c1_c2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( image_7090770775218664273_c1_c2 @ R2 @ A2 ) )
     => ~ ! [X3: product_prod_b1_b2] :
            ( ( member2747565893236161614_c1_c2 @ ( produc1085642273369259797_c1_c2 @ X3 @ B ) @ R2 )
           => ~ ( member2075749735315954927_b1_b2 @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_895_ImageE,axiom,
    ! [B: product_prod_c1_c2,R2: set_Pr5619578715368347395_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member1440383022217085037_c1_c2 @ B @ ( image_837382273140092495_c1_c2 @ R2 @ A2 ) )
     => ~ ! [X3: product_prod_a1_a2] :
            ( ( member5717549428012365644_c1_c2 @ ( produc4055625808145463827_c1_c2 @ X3 @ B ) @ R2 )
           => ~ ( member2711116448414824817_a1_a2 @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_896_ImageE,axiom,
    ! [B: product_prod_b1_b2,R2: set_Pr1330221890988210569_b1_b2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member2075749735315954927_b1_b2 @ B @ ( image_4756153953541330133_b1_b2 @ R2 @ A2 ) )
     => ~ ! [X3: product_prod_c1_c2] :
            ( ( member4391169576227650770_b1_b2 @ ( produc7974397488546701465_b1_b2 @ X3 @ B ) @ R2 )
           => ~ ( member1440383022217085037_c1_c2 @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_897_ImageE,axiom,
    ! [B: product_prod_b1_b2,R2: set_Pr5150871832445556103_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ B @ ( image_7726137488317534163_b1_b2 @ R2 @ A2 ) )
     => ~ ! [X3: product_prod_b1_b2] :
            ( ( member7361153111003854800_b1_b2 @ ( produc1721008986468129687_b1_b2 @ X3 @ B ) @ R2 )
           => ~ ( member2075749735315954927_b1_b2 @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_898_ImageE,axiom,
    ! [B: product_prod_b1_b2,R2: set_Pr8971521773902901637_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2075749735315954927_b1_b2 @ B @ ( image_1472748986238962385_b1_b2 @ R2 @ A2 ) )
     => ~ ! [X3: product_prod_a1_a2] :
            ( ( member1107764608925283022_b1_b2 @ ( produc4690992521244333717_b1_b2 @ X3 @ B ) @ R2 )
           => ~ ( member2711116448414824817_a1_a2 @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_899_ImageE,axiom,
    ! [B: product_prod_a1_a2,R2: set_Pr4682164949522764811_a1_a2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member2711116448414824817_a1_a2 @ B @ ( image_5391520666640200023_a1_a2 @ R2 @ A2 ) )
     => ~ ! [X3: product_prod_c1_c2] :
            ( ( member9004756793995343956_a1_a2 @ ( produc8609764201645571355_a1_a2 @ X3 @ B ) @ R2 )
           => ~ ( member1440383022217085037_c1_c2 @ X3 @ A2 ) ) ) ).

% ImageE
thf(fact_900_Image__iff,axiom,
    ! [B: c1 > option_set_c2,R2: set_Pr3221440761411154131set_c2,A2: set_b1_option_set_b2] :
      ( ( member8745205179313678111set_c2 @ B @ ( image_8173472465452405735set_c2 @ R2 @ A2 ) )
      = ( ? [X: b1 > option_set_b2] :
            ( ( member3006388138933004577set_b2 @ X @ A2 )
            & ( member9053876291207143196set_c2 @ ( produc890782565133688235set_c2 @ X @ B ) @ R2 ) ) ) ) ).

% Image_iff
thf(fact_901_Image__iff,axiom,
    ! [B: mapping_c1_set_c2,R2: set_Pr1660683266160182027set_c2,A2: set_ma6254658672695423900set_b2] :
      ( ( member341037065618468219set_c2 @ B @ ( image_2236567028817877023set_c2 @ R2 @ A2 ) )
      = ( ? [X: mapping_b1_set_b2] :
            ( ( member6117332676589958525set_b2 @ X @ A2 )
            & ( member419137155788712276set_c2 @ ( produc1212179418963815907set_c2 @ X @ B ) @ R2 ) ) ) ) ).

% Image_iff
thf(fact_902_Image__iff,axiom,
    ! [B: b1 > option_set_b2,R2: set_Pr5056620919297929171set_b2,A2: set_c1_option_set_c2] :
      ( ( member3006388138933004577set_b2 @ B @ ( image_2565772427613058023set_b2 @ R2 @ A2 ) )
      = ( ? [X: c1 > option_set_c2] :
            ( ( member8745205179313678111set_c2 @ X @ A2 )
            & ( member5757858293533564444set_b2 @ ( produc4506454564149116331set_b2 @ X @ B ) @ R2 ) ) ) ) ).

% Image_iff
thf(fact_903_Image__iff,axiom,
    ! [B: b1 > option_set_b2,R2: set_Pr1995104245887189set_b2,A2: set_b1_option_set_b2] :
      ( ( member3006388138933004577set_b2 @ B @ ( image_2434655425071732201set_b2 @ R2 @ A2 ) )
      = ( ? [X: b1 > option_set_b2] :
            ( ( member3006388138933004577set_b2 @ X @ A2 )
            & ( member5626741290992238622set_b2 @ ( produc4375337561607790509set_b2 @ X @ B ) @ R2 ) ) ) ) ).

% Image_iff
thf(fact_904_Image__iff,axiom,
    ! [B: c2,R2: set_Pr9202269149784407460_c1_c2,A2: set_c1] :
      ( ( member_c2 @ B @ ( image_c1_c2 @ R2 @ A2 ) )
      = ( ? [X: c1] :
            ( ( member_c1 @ X @ A2 )
            & ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ X @ B ) @ R2 ) ) ) ) ).

% Image_iff
thf(fact_905_Image__iff,axiom,
    ! [B: b2,R2: set_Pr4592484330697324838_b1_b2,A2: set_b1] :
      ( ( member_b2 @ B @ ( image_b1_b2 @ R2 @ A2 ) )
      = ( ? [X: b1] :
            ( ( member_b1 @ X @ A2 )
            & ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ X @ B ) @ R2 ) ) ) ) ).

% Image_iff
thf(fact_906_Image__iff,axiom,
    ! [B: a2,R2: set_Pr9206071548465018024_a1_a2,A2: set_a1] :
      ( ( member_a2 @ B @ ( image_a1_a2 @ R2 @ A2 ) )
      = ( ? [X: a1] :
            ( ( member_a1 @ X @ A2 )
            & ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ X @ B ) @ R2 ) ) ) ) ).

% Image_iff
thf(fact_907_rev__ImageI,axiom,
    ! [A: c1,A2: set_c1,B: c2,R2: set_Pr9202269149784407460_c1_c2] :
      ( ( member_c1 @ A @ A2 )
     => ( ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ A @ B ) @ R2 )
       => ( member_c2 @ B @ ( image_c1_c2 @ R2 @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_908_rev__ImageI,axiom,
    ! [A: b1,A2: set_b1,B: b2,R2: set_Pr4592484330697324838_b1_b2] :
      ( ( member_b1 @ A @ A2 )
     => ( ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ A @ B ) @ R2 )
       => ( member_b2 @ B @ ( image_b1_b2 @ R2 @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_909_rev__ImageI,axiom,
    ! [A: a1,A2: set_a1,B: a2,R2: set_Pr9206071548465018024_a1_a2] :
      ( ( member_a1 @ A @ A2 )
     => ( ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ A @ B ) @ R2 )
       => ( member_a2 @ B @ ( image_a1_a2 @ R2 @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_910_rev__ImageI,axiom,
    ! [A: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B: product_prod_c1_c2,R2: set_Pr7201650869308432135_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ A @ A2 )
     => ( ( member9000954395314733392_c1_c2 @ ( produc7339030775447831575_c1_c2 @ A @ B ) @ R2 )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_4120787240442460243_c1_c2 @ R2 @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_911_rev__ImageI,axiom,
    ! [A: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B: product_prod_b1_b2,R2: set_Pr1330221890988210569_b1_b2] :
      ( ( member1440383022217085037_c1_c2 @ A @ A2 )
     => ( ( member4391169576227650770_b1_b2 @ ( produc7974397488546701465_b1_b2 @ A @ B ) @ R2 )
       => ( member2075749735315954927_b1_b2 @ B @ ( image_4756153953541330133_b1_b2 @ R2 @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_912_rev__ImageI,axiom,
    ! [A: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B: product_prod_a1_a2,R2: set_Pr4682164949522764811_a1_a2] :
      ( ( member1440383022217085037_c1_c2 @ A @ A2 )
     => ( ( member9004756793995343956_a1_a2 @ ( produc8609764201645571355_a1_a2 @ A @ B ) @ R2 )
       => ( member2711116448414824817_a1_a2 @ B @ ( image_5391520666640200023_a1_a2 @ R2 @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_913_rev__ImageI,axiom,
    ! [A: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B: product_prod_c1_c2,R2: set_Pr1798928773911001861_c1_c2] :
      ( ( member2075749735315954927_b1_b2 @ A @ A2 )
     => ( ( member2747565893236161614_c1_c2 @ ( produc1085642273369259797_c1_c2 @ A @ B ) @ R2 )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_7090770775218664273_c1_c2 @ R2 @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_914_rev__ImageI,axiom,
    ! [A: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B: product_prod_b1_b2,R2: set_Pr5150871832445556103_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ A @ A2 )
     => ( ( member7361153111003854800_b1_b2 @ ( produc1721008986468129687_b1_b2 @ A @ B ) @ R2 )
       => ( member2075749735315954927_b1_b2 @ B @ ( image_7726137488317534163_b1_b2 @ R2 @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_915_rev__ImageI,axiom,
    ! [A: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B: product_prod_a1_a2,R2: set_Pr8502814890980110345_a1_a2] :
      ( ( member2075749735315954927_b1_b2 @ A @ A2 )
     => ( ( member2751368291916772178_a1_a2 @ ( produc2356375699566999577_a1_a2 @ A @ B ) @ R2 )
       => ( member2711116448414824817_a1_a2 @ B @ ( image_8361504201416404053_a1_a2 @ R2 @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_916_rev__ImageI,axiom,
    ! [A: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B: product_prod_c1_c2,R2: set_Pr5619578715368347395_c1_c2] :
      ( ( member2711116448414824817_a1_a2 @ A @ A2 )
     => ( ( member5717549428012365644_c1_c2 @ ( produc4055625808145463827_c1_c2 @ A @ B ) @ R2 )
       => ( member1440383022217085037_c1_c2 @ B @ ( image_837382273140092495_c1_c2 @ R2 @ A2 ) ) ) ) ).

% rev_ImageI
thf(fact_917_setcompr__eq__image,axiom,
    ! [F: nat > nat,P: nat > $o] :
      ( ( collect_nat
        @ ^ [Uu: nat] :
          ? [X: nat] :
            ( ( Uu
              = ( F @ X ) )
            & ( P @ X ) ) )
      = ( image_nat_nat2 @ F @ ( collect_nat @ P ) ) ) ).

% setcompr_eq_image
thf(fact_918_setcompr__eq__image,axiom,
    ! [F: c2 > nat,P: c2 > $o] :
      ( ( collect_nat
        @ ^ [Uu: nat] :
          ? [X: c2] :
            ( ( Uu
              = ( F @ X ) )
            & ( P @ X ) ) )
      = ( image_c2_nat2 @ F @ ( collect_c2 @ P ) ) ) ).

% setcompr_eq_image
thf(fact_919_setcompr__eq__image,axiom,
    ! [F: b2 > nat,P: b2 > $o] :
      ( ( collect_nat
        @ ^ [Uu: nat] :
          ? [X: b2] :
            ( ( Uu
              = ( F @ X ) )
            & ( P @ X ) ) )
      = ( image_b2_nat2 @ F @ ( collect_b2 @ P ) ) ) ).

% setcompr_eq_image
thf(fact_920_setcompr__eq__image,axiom,
    ! [F: nat > c2,P: nat > $o] :
      ( ( collect_c2
        @ ^ [Uu: c2] :
          ? [X: nat] :
            ( ( Uu
              = ( F @ X ) )
            & ( P @ X ) ) )
      = ( image_nat_c22 @ F @ ( collect_nat @ P ) ) ) ).

% setcompr_eq_image
thf(fact_921_setcompr__eq__image,axiom,
    ! [F: c2 > c2,P: c2 > $o] :
      ( ( collect_c2
        @ ^ [Uu: c2] :
          ? [X: c2] :
            ( ( Uu
              = ( F @ X ) )
            & ( P @ X ) ) )
      = ( image_c2_c22 @ F @ ( collect_c2 @ P ) ) ) ).

% setcompr_eq_image
thf(fact_922_setcompr__eq__image,axiom,
    ! [F: b2 > c2,P: b2 > $o] :
      ( ( collect_c2
        @ ^ [Uu: c2] :
          ? [X: b2] :
            ( ( Uu
              = ( F @ X ) )
            & ( P @ X ) ) )
      = ( image_b2_c22 @ F @ ( collect_b2 @ P ) ) ) ).

% setcompr_eq_image
thf(fact_923_setcompr__eq__image,axiom,
    ! [F: nat > b2,P: nat > $o] :
      ( ( collect_b2
        @ ^ [Uu: b2] :
          ? [X: nat] :
            ( ( Uu
              = ( F @ X ) )
            & ( P @ X ) ) )
      = ( image_nat_b22 @ F @ ( collect_nat @ P ) ) ) ).

% setcompr_eq_image
thf(fact_924_setcompr__eq__image,axiom,
    ! [F: c2 > b2,P: c2 > $o] :
      ( ( collect_b2
        @ ^ [Uu: b2] :
          ? [X: c2] :
            ( ( Uu
              = ( F @ X ) )
            & ( P @ X ) ) )
      = ( image_c2_b22 @ F @ ( collect_c2 @ P ) ) ) ).

% setcompr_eq_image
thf(fact_925_setcompr__eq__image,axiom,
    ! [F: b2 > b2,P: b2 > $o] :
      ( ( collect_b2
        @ ^ [Uu: b2] :
          ? [X: b2] :
            ( ( Uu
              = ( F @ X ) )
            & ( P @ X ) ) )
      = ( image_b2_b22 @ F @ ( collect_b2 @ P ) ) ) ).

% setcompr_eq_image
thf(fact_926_setcompr__eq__image,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2,P: product_prod_a1_a2 > $o] :
      ( ( collec5864963238570574385_b1_b2
        @ ^ [Uu: product_prod_b1_b2] :
          ? [X: product_prod_a1_a2] :
            ( ( Uu
              = ( F @ X ) )
            & ( P @ X ) ) )
      = ( image_1398015525354814723_b1_b2 @ F @ ( collec6500329951669444275_a1_a2 @ P ) ) ) ).

% setcompr_eq_image
thf(fact_927_Setcompr__eq__image,axiom,
    ! [F: product_prod_c1_c2 > nat,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( collect_nat
        @ ^ [Uu: nat] :
          ? [X: product_prod_c1_c2] :
            ( ( Uu
              = ( F @ X ) )
            & ( member1440383022217085037_c1_c2 @ X @ A2 ) ) )
      = ( image_1283518940507385935c2_nat @ F @ A2 ) ) ).

% Setcompr_eq_image
thf(fact_928_Setcompr__eq__image,axiom,
    ! [F: product_prod_b1_b2 > nat,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( collect_nat
        @ ^ [Uu: nat] :
          ? [X: product_prod_b1_b2] :
            ( ( Uu
              = ( F @ X ) )
            & ( member2075749735315954927_b1_b2 @ X @ A2 ) ) )
      = ( image_2104430070814229713b2_nat @ F @ A2 ) ) ).

% Setcompr_eq_image
thf(fact_929_Setcompr__eq__image,axiom,
    ! [F: product_prod_a1_a2 > nat,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( collect_nat
        @ ^ [Uu: nat] :
          ? [X: product_prod_a1_a2] :
            ( ( Uu
              = ( F @ X ) )
            & ( member2711116448414824817_a1_a2 @ X @ A2 ) ) )
      = ( image_2925341201121073491a2_nat @ F @ A2 ) ) ).

% Setcompr_eq_image
thf(fact_930_Setcompr__eq__image,axiom,
    ! [F: product_prod_c1_c2 > c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( collect_c2
        @ ^ [Uu: c2] :
          ? [X: product_prod_c1_c2] :
            ( ( Uu
              = ( F @ X ) )
            & ( member1440383022217085037_c1_c2 @ X @ A2 ) ) )
      = ( image_5961845353661704241_c2_c2 @ F @ A2 ) ) ).

% Setcompr_eq_image
thf(fact_931_Setcompr__eq__image,axiom,
    ! [F: product_prod_b1_b2 > c2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( collect_c2
        @ ^ [Uu: c2] :
          ? [X: product_prod_b1_b2] :
            ( ( Uu
              = ( F @ X ) )
            & ( member2075749735315954927_b1_b2 @ X @ A2 ) ) )
      = ( image_2033501871846563763_b2_c2 @ F @ A2 ) ) ).

% Setcompr_eq_image
thf(fact_932_Setcompr__eq__image,axiom,
    ! [F: product_prod_a1_a2 > c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( collect_c2
        @ ^ [Uu: c2] :
          ? [X: product_prod_a1_a2] :
            ( ( Uu
              = ( F @ X ) )
            & ( member2711116448414824817_a1_a2 @ X @ A2 ) ) )
      = ( image_7328530426886199093_a2_c2 @ F @ A2 ) ) ).

% Setcompr_eq_image
thf(fact_933_Setcompr__eq__image,axiom,
    ! [F: product_prod_c1_c2 > b2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( collect_b2
        @ ^ [Uu: b2] :
          ? [X: product_prod_c1_c2] :
            ( ( Uu
              = ( F @ X ) )
            & ( member1440383022217085037_c1_c2 @ X @ A2 ) ) )
      = ( image_5961845353661638642_c2_b2 @ F @ A2 ) ) ).

% Setcompr_eq_image
thf(fact_934_Setcompr__eq__image,axiom,
    ! [F: product_prod_b1_b2 > b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( collect_b2
        @ ^ [Uu: b2] :
          ? [X: product_prod_b1_b2] :
            ( ( Uu
              = ( F @ X ) )
            & ( member2075749735315954927_b1_b2 @ X @ A2 ) ) )
      = ( image_2033501871846498164_b2_b2 @ F @ A2 ) ) ).

% Setcompr_eq_image
thf(fact_935_Setcompr__eq__image,axiom,
    ! [F: product_prod_a1_a2 > b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( collect_b2
        @ ^ [Uu: b2] :
          ? [X: product_prod_a1_a2] :
            ( ( Uu
              = ( F @ X ) )
            & ( member2711116448414824817_a1_a2 @ X @ A2 ) ) )
      = ( image_7328530426886133494_a2_b2 @ F @ A2 ) ) ).

% Setcompr_eq_image
thf(fact_936_Setcompr__eq__image,axiom,
    ! [F: mapping_c1_set_c2 > nat,A2: set_ma7306327908849618074set_c2] :
      ( ( collect_nat
        @ ^ [Uu: nat] :
          ? [X: mapping_c1_set_c2] :
            ( ( Uu
              = ( F @ X ) )
            & ( member341037065618468219set_c2 @ X @ A2 ) ) )
      = ( image_1108462827494303035c2_nat @ F @ A2 ) ) ).

% Setcompr_eq_image
thf(fact_937_lookup__map__entry__neq,axiom,
    ! [X2: b1,Y5: b1,F: set_b2 > set_b2,M3: mapping_b1_set_b2] :
      ( ( X2 != Y5 )
     => ( ( lookup_b1_set_b2 @ ( map_entry_b1_set_b2 @ X2 @ F @ M3 ) @ Y5 )
        = ( lookup_b1_set_b2 @ M3 @ Y5 ) ) ) ).

% lookup_map_entry_neq
thf(fact_938_lookup__map__entry__neq,axiom,
    ! [X2: c1,Y5: c1,F: set_c2 > set_c2,M3: mapping_c1_set_c2] :
      ( ( X2 != Y5 )
     => ( ( lookup_c1_set_c2 @ ( map_entry_c1_set_c2 @ X2 @ F @ M3 ) @ Y5 )
        = ( lookup_c1_set_c2 @ M3 @ Y5 ) ) ) ).

% lookup_map_entry_neq
thf(fact_939_map__project__insert,axiom,
    ! [F: b2 > option_b2,X2: b2,A2: set_b2] :
      ( ( map_project_b2_b2 @ F @ ( insert_b2 @ X2 @ A2 ) )
      = ( case_o801698286357362985_b2_b2 @ ( map_project_b2_b2 @ F @ A2 )
        @ ^ [Y6: b2] : ( insert_b2 @ Y6 @ ( map_project_b2_b2 @ F @ A2 ) )
        @ ( F @ X2 ) ) ) ).

% map_project_insert
thf(fact_940_map__project__insert,axiom,
    ! [F: b2 > option_c2,X2: b2,A2: set_b2] :
      ( ( map_project_b2_c2 @ F @ ( insert_b2 @ X2 @ A2 ) )
      = ( case_o3452368716856024231_c2_c2 @ ( map_project_b2_c2 @ F @ A2 )
        @ ^ [Y6: c2] : ( insert_c2 @ Y6 @ ( map_project_b2_c2 @ F @ A2 ) )
        @ ( F @ X2 ) ) ) ).

% map_project_insert
thf(fact_941_map__project__insert,axiom,
    ! [F: b2 > option_nat,X2: b2,A2: set_b2] :
      ( ( map_project_b2_nat @ F @ ( insert_b2 @ X2 @ A2 ) )
      = ( case_o4857086424252989667at_nat @ ( map_project_b2_nat @ F @ A2 )
        @ ^ [Y6: nat] : ( insert_nat @ Y6 @ ( map_project_b2_nat @ F @ A2 ) )
        @ ( F @ X2 ) ) ) ).

% map_project_insert
thf(fact_942_map__project__insert,axiom,
    ! [F: c2 > option_b2,X2: c2,A2: set_c2] :
      ( ( map_project_c2_b2 @ F @ ( insert_c2 @ X2 @ A2 ) )
      = ( case_o801698286357362985_b2_b2 @ ( map_project_c2_b2 @ F @ A2 )
        @ ^ [Y6: b2] : ( insert_b2 @ Y6 @ ( map_project_c2_b2 @ F @ A2 ) )
        @ ( F @ X2 ) ) ) ).

% map_project_insert
thf(fact_943_map__project__insert,axiom,
    ! [F: c2 > option_c2,X2: c2,A2: set_c2] :
      ( ( map_project_c2_c2 @ F @ ( insert_c2 @ X2 @ A2 ) )
      = ( case_o3452368716856024231_c2_c2 @ ( map_project_c2_c2 @ F @ A2 )
        @ ^ [Y6: c2] : ( insert_c2 @ Y6 @ ( map_project_c2_c2 @ F @ A2 ) )
        @ ( F @ X2 ) ) ) ).

% map_project_insert
thf(fact_944_map__project__insert,axiom,
    ! [F: c2 > option_nat,X2: c2,A2: set_c2] :
      ( ( map_project_c2_nat @ F @ ( insert_c2 @ X2 @ A2 ) )
      = ( case_o4857086424252989667at_nat @ ( map_project_c2_nat @ F @ A2 )
        @ ^ [Y6: nat] : ( insert_nat @ Y6 @ ( map_project_c2_nat @ F @ A2 ) )
        @ ( F @ X2 ) ) ) ).

% map_project_insert
thf(fact_945_map__project__insert,axiom,
    ! [F: nat > option_b2,X2: nat,A2: set_nat] :
      ( ( map_project_nat_b2 @ F @ ( insert_nat @ X2 @ A2 ) )
      = ( case_o801698286357362985_b2_b2 @ ( map_project_nat_b2 @ F @ A2 )
        @ ^ [Y6: b2] : ( insert_b2 @ Y6 @ ( map_project_nat_b2 @ F @ A2 ) )
        @ ( F @ X2 ) ) ) ).

% map_project_insert
thf(fact_946_map__project__insert,axiom,
    ! [F: nat > option_c2,X2: nat,A2: set_nat] :
      ( ( map_project_nat_c2 @ F @ ( insert_nat @ X2 @ A2 ) )
      = ( case_o3452368716856024231_c2_c2 @ ( map_project_nat_c2 @ F @ A2 )
        @ ^ [Y6: c2] : ( insert_c2 @ Y6 @ ( map_project_nat_c2 @ F @ A2 ) )
        @ ( F @ X2 ) ) ) ).

% map_project_insert
thf(fact_947_map__project__insert,axiom,
    ! [F: nat > option_nat,X2: nat,A2: set_nat] :
      ( ( map_project_nat_nat @ F @ ( insert_nat @ X2 @ A2 ) )
      = ( case_o4857086424252989667at_nat @ ( map_project_nat_nat @ F @ A2 )
        @ ^ [Y6: nat] : ( insert_nat @ Y6 @ ( map_project_nat_nat @ F @ A2 ) )
        @ ( F @ X2 ) ) ) ).

% map_project_insert
thf(fact_948_Image__singleton,axiom,
    ! [R2: set_Pr9202269149784407460_c1_c2,A: c1] :
      ( ( image_c1_c2 @ R2 @ ( insert_c1 @ A @ bot_bot_set_c1 ) )
      = ( collect_c2
        @ ^ [B7: c2] : ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ A @ B7 ) @ R2 ) ) ) ).

% Image_singleton
thf(fact_949_Image__singleton,axiom,
    ! [R2: set_Pr4592484330697324838_b1_b2,A: b1] :
      ( ( image_b1_b2 @ R2 @ ( insert_b1 @ A @ bot_bot_set_b1 ) )
      = ( collect_b2
        @ ^ [B7: b2] : ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ A @ B7 ) @ R2 ) ) ) ).

% Image_singleton
thf(fact_950_Image__singleton,axiom,
    ! [R2: set_Pr9206071548465018024_a1_a2,A: a1] :
      ( ( image_a1_a2 @ R2 @ ( insert_a1 @ A @ bot_bot_set_a1 ) )
      = ( collect_a2
        @ ^ [B7: a2] : ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ A @ B7 ) @ R2 ) ) ) ).

% Image_singleton
thf(fact_951_Image__singleton,axiom,
    ! [R2: set_Pr6583197765812888324b2_nat,A: b2] :
      ( ( image_b2_nat @ R2 @ ( insert_b2 @ A @ bot_bot_set_b2 ) )
      = ( collect_nat
        @ ^ [B7: nat] : ( member2965532670062880717b2_nat @ ( product_Pair_b2_nat @ A @ B7 ) @ R2 ) ) ) ).

% Image_singleton
thf(fact_952_Image__singleton,axiom,
    ! [R2: set_Pr7477786653205428070_b2_c2,A: b2] :
      ( ( image_b2_c2 @ R2 @ ( insert_b2 @ A @ bot_bot_set_b2 ) )
      = ( collect_c2
        @ ^ [B7: c2] : ( member1127940843177376559_b2_c2 @ ( product_Pair_b2_c2 @ A @ B7 ) @ R2 ) ) ) ).

% Image_singleton
thf(fact_953_Image__singleton,axiom,
    ! [R2: set_Pr5518672264616941095_b2_b2,A: b2] :
      ( ( image_b2_b2 @ R2 @ ( insert_b2 @ A @ bot_bot_set_b2 ) )
      = ( collect_b2
        @ ^ [B7: b2] : ( member1127658555671259760_b2_b2 @ ( product_Pair_b2_b2 @ A @ B7 ) @ R2 ) ) ) ).

% Image_singleton
thf(fact_954_Image__singleton,axiom,
    ! [R2: set_Pr4274324598211246019c2_nat,A: c2] :
      ( ( image_c2_nat @ R2 @ ( insert_c2 @ A @ bot_bot_set_c2 ) )
      = ( collect_nat
        @ ^ [B7: nat] : ( member1107980037670464524c2_nat @ ( product_Pair_c2_nat @ A @ B7 ) @ R2 ) ) ) ).

% Image_singleton
thf(fact_955_Image__singleton,axiom,
    ! [R2: set_Pr905085046849247909_c2_c2,A: c2] :
      ( ( image_c2_c2 @ R2 @ ( insert_c2 @ A @ bot_bot_set_c2 ) )
      = ( collect_c2
        @ ^ [B7: c2] : ( member492291842572389870_c2_c2 @ ( product_Pair_c2_c2 @ A @ B7 ) @ R2 ) ) ) ).

% Image_singleton
thf(fact_956_Image__singleton,axiom,
    ! [R2: set_Pr8169342695115536742_c2_b2,A: c2] :
      ( ( image_c2_b2 @ R2 @ ( insert_c2 @ A @ bot_bot_set_c2 ) )
      = ( collect_b2
        @ ^ [B7: b2] : ( member492009555066273071_c2_b2 @ ( product_Pair_c2_b2 @ A @ B7 ) @ R2 ) ) ) ).

% Image_singleton
thf(fact_957_Image__singleton,axiom,
    ! [R2: set_Pr1261947904930325089at_nat,A: nat] :
      ( ( image_nat_nat @ R2 @ ( insert_nat @ A @ bot_bot_set_nat ) )
      = ( collect_nat
        @ ^ [B7: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B7 ) @ R2 ) ) ) ).

% Image_singleton
thf(fact_958_image2__def,axiom,
    ( bNF_Gr8687606788332042191_c1_c2
    = ( ^ [A6: set_Pr9202269149784407460_c1_c2,F3: product_prod_c1_c2 > c1,G3: product_prod_c1_c2 > c2] :
          ( collec5229596525471704495_c1_c2
          @ ^ [Uu: product_prod_c1_c2] :
            ? [A5: product_prod_c1_c2] :
              ( ( Uu
                = ( product_Pair_c1_c2 @ ( F3 @ A5 ) @ ( G3 @ A5 ) ) )
              & ( member1440383022217085037_c1_c2 @ A5 @ A6 ) ) ) ) ) ).

% image2_def
thf(fact_959_image2__def,axiom,
    ( bNF_Gr5435061502750788177_c1_c2
    = ( ^ [A6: set_Pr4592484330697324838_b1_b2,F3: product_prod_b1_b2 > c1,G3: product_prod_b1_b2 > c2] :
          ( collec5229596525471704495_c1_c2
          @ ^ [Uu: product_prod_c1_c2] :
            ? [A5: product_prod_b1_b2] :
              ( ( Uu
                = ( product_Pair_c1_c2 @ ( F3 @ A5 ) @ ( G3 @ A5 ) ) )
              & ( member2075749735315954927_b1_b2 @ A5 @ A6 ) ) ) ) ) ).

% image2_def
thf(fact_960_image2__def,axiom,
    ( bNF_Gr2182516217169534163_c1_c2
    = ( ^ [A6: set_Pr9206071548465018024_a1_a2,F3: product_prod_a1_a2 > c1,G3: product_prod_a1_a2 > c2] :
          ( collec5229596525471704495_c1_c2
          @ ^ [Uu: product_prod_c1_c2] :
            ? [A5: product_prod_a1_a2] :
              ( ( Uu
                = ( product_Pair_c1_c2 @ ( F3 @ A5 ) @ ( G3 @ A5 ) ) )
              & ( member2711116448414824817_a1_a2 @ A5 @ A6 ) ) ) ) ) ).

% image2_def
thf(fact_961_image2__def,axiom,
    ( bNF_Gr99883752082187473_b1_b2
    = ( ^ [A6: set_Pr9202269149784407460_c1_c2,F3: product_prod_c1_c2 > b1,G3: product_prod_c1_c2 > b2] :
          ( collec5864963238570574385_b1_b2
          @ ^ [Uu: product_prod_b1_b2] :
            ? [A5: product_prod_c1_c2] :
              ( ( Uu
                = ( product_Pair_b1_b2 @ ( F3 @ A5 ) @ ( G3 @ A5 ) ) )
              & ( member1440383022217085037_c1_c2 @ A5 @ A6 ) ) ) ) ) ).

% image2_def
thf(fact_962_image2__def,axiom,
    ( bNF_Gr6070710503355709267_b1_b2
    = ( ^ [A6: set_Pr4592484330697324838_b1_b2,F3: product_prod_b1_b2 > b1,G3: product_prod_b1_b2 > b2] :
          ( collec5864963238570574385_b1_b2
          @ ^ [Uu: product_prod_b1_b2] :
            ? [A5: product_prod_b1_b2] :
              ( ( Uu
                = ( product_Pair_b1_b2 @ ( F3 @ A5 ) @ ( G3 @ A5 ) ) )
              & ( member2075749735315954927_b1_b2 @ A5 @ A6 ) ) ) ) ) ).

% image2_def
thf(fact_963_image2__def,axiom,
    ( bNF_Gr2818165217774455253_b1_b2
    = ( ^ [A6: set_Pr9206071548465018024_a1_a2,F3: product_prod_a1_a2 > b1,G3: product_prod_a1_a2 > b2] :
          ( collec5864963238570574385_b1_b2
          @ ^ [Uu: product_prod_b1_b2] :
            ? [A5: product_prod_a1_a2] :
              ( ( Uu
                = ( product_Pair_b1_b2 @ ( F3 @ A5 ) @ ( G3 @ A5 ) ) )
              & ( member2711116448414824817_a1_a2 @ A5 @ A6 ) ) ) ) ) ).

% image2_def
thf(fact_964_image2__def,axiom,
    ( bNF_Gr735532752687108563_a1_a2
    = ( ^ [A6: set_Pr9202269149784407460_c1_c2,F3: product_prod_c1_c2 > a1,G3: product_prod_c1_c2 > a2] :
          ( collec6500329951669444275_a1_a2
          @ ^ [Uu: product_prod_a1_a2] :
            ? [A5: product_prod_c1_c2] :
              ( ( Uu
                = ( product_Pair_a1_a2 @ ( F3 @ A5 ) @ ( G3 @ A5 ) ) )
              & ( member1440383022217085037_c1_c2 @ A5 @ A6 ) ) ) ) ) ).

% image2_def
thf(fact_965_image2__def,axiom,
    ( bNF_Gr6706359503960630357_a1_a2
    = ( ^ [A6: set_Pr4592484330697324838_b1_b2,F3: product_prod_b1_b2 > a1,G3: product_prod_b1_b2 > a2] :
          ( collec6500329951669444275_a1_a2
          @ ^ [Uu: product_prod_a1_a2] :
            ? [A5: product_prod_b1_b2] :
              ( ( Uu
                = ( product_Pair_a1_a2 @ ( F3 @ A5 ) @ ( G3 @ A5 ) ) )
              & ( member2075749735315954927_b1_b2 @ A5 @ A6 ) ) ) ) ) ).

% image2_def
thf(fact_966_image2__def,axiom,
    ( bNF_Gr3453814218379376343_a1_a2
    = ( ^ [A6: set_Pr9206071548465018024_a1_a2,F3: product_prod_a1_a2 > a1,G3: product_prod_a1_a2 > a2] :
          ( collec6500329951669444275_a1_a2
          @ ^ [Uu: product_prod_a1_a2] :
            ? [A5: product_prod_a1_a2] :
              ( ( Uu
                = ( product_Pair_a1_a2 @ ( F3 @ A5 ) @ ( G3 @ A5 ) ) )
              & ( member2711116448414824817_a1_a2 @ A5 @ A6 ) ) ) ) ) ).

% image2_def
thf(fact_967_image2__def,axiom,
    ( bNF_Gr4776719309262608675_c1_c2
    = ( ^ [A6: set_ma7306327908849618074set_c2,F3: mapping_c1_set_c2 > c1,G3: mapping_c1_set_c2 > c2] :
          ( collec5229596525471704495_c1_c2
          @ ^ [Uu: product_prod_c1_c2] :
            ? [A5: mapping_c1_set_c2] :
              ( ( Uu
                = ( product_Pair_c1_c2 @ ( F3 @ A5 ) @ ( G3 @ A5 ) ) )
              & ( member341037065618468219set_c2 @ A5 @ A6 ) ) ) ) ) ).

% image2_def
thf(fact_968_Inf_OINF__image,axiom,
    ! [Inf: set_Pr4592484330697324838_b1_b2 > product_prod_b1_b2,G: product_prod_b1_b2 > product_prod_b1_b2,F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Inf @ ( image_7651404027433386501_b1_b2 @ G @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) ) )
      = ( Inf @ ( image_1398015525354814723_b1_b2 @ ( comp_P8403851972257459877_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Inf.INF_image
thf(fact_969_Inf_OINF__image,axiom,
    ! [Inf: set_Pr9202269149784407460_c1_c2 > product_prod_c1_c2,G: product_prod_b1_b2 > product_prod_c1_c2,F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Inf @ ( image_7016037314334516611_c1_c2 @ G @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) ) )
      = ( Inf @ ( image_762648812255944833_c1_c2 @ ( comp_P5433868437481255847_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Inf.INF_image
thf(fact_970_Inf_OINF__image,axiom,
    ! [Inf: set_Pr4592484330697324838_b1_b2 > product_prod_b1_b2,G: product_prod_c1_c2 > product_prod_b1_b2,F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Inf @ ( image_4681420492657182471_b1_b2 @ G @ ( image_762648812255944833_c1_c2 @ F @ A2 ) ) )
      = ( Inf @ ( image_1398015525354814723_b1_b2 @ ( comp_P8467111182430445859_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Inf.INF_image
thf(fact_971_Inf_OINF__image,axiom,
    ! [Inf: set_Pr9202269149784407460_c1_c2 > product_prod_c1_c2,G: product_prod_c1_c2 > product_prod_c1_c2,F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Inf @ ( image_4046053779558312581_c1_c2 @ G @ ( image_762648812255944833_c1_c2 @ F @ A2 ) ) )
      = ( Inf @ ( image_762648812255944833_c1_c2 @ ( comp_P5497127647654241829_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Inf.INF_image
thf(fact_972_Inf_OINF__image,axiom,
    ! [Inf: set_Pr4592484330697324838_b1_b2 > product_prod_b1_b2,G: product_prod_a1_a2 > product_prod_b1_b2,F: product_prod_a1_a2 > product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Inf @ ( image_1398015525354814723_b1_b2 @ G @ ( image_2033382238453684613_a1_a2 @ F @ A2 ) ) )
      = ( Inf @ ( image_1398015525354814723_b1_b2 @ ( comp_P8340592762084473895_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Inf.INF_image
thf(fact_973_Inf_OINF__image,axiom,
    ! [Inf: set_Pr9202269149784407460_c1_c2 > product_prod_c1_c2,G: product_prod_a1_a2 > product_prod_c1_c2,F: product_prod_a1_a2 > product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Inf @ ( image_762648812255944833_c1_c2 @ G @ ( image_2033382238453684613_a1_a2 @ F @ A2 ) ) )
      = ( Inf @ ( image_762648812255944833_c1_c2 @ ( comp_P5370609227308269865_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Inf.INF_image
thf(fact_974_Inf_OINF__image,axiom,
    ! [Inf: set_ma7306327908849618074set_c2 > mapping_c1_set_c2,G: product_prod_c1_c2 > mapping_c1_set_c2,F: product_prod_c1_c2 > product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( Inf @ ( image_5984881132562613603set_c2 @ G @ ( image_4046053779558312581_c1_c2 @ F @ A2 ) ) )
      = ( Inf @ ( image_5984881132562613603set_c2 @ ( comp_P1747777731944695037_c1_c2 @ G @ F ) @ A2 ) ) ) ).

% Inf.INF_image
thf(fact_975_Inf_OINF__image,axiom,
    ! [Inf: set_ma7306327908849618074set_c2 > mapping_c1_set_c2,G: product_prod_c1_c2 > mapping_c1_set_c2,F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Inf @ ( image_5984881132562613603set_c2 @ G @ ( image_762648812255944833_c1_c2 @ F @ A2 ) ) )
      = ( Inf @ ( image_5058487432053965927set_c2 @ ( comp_P3018511158142434817_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Inf.INF_image
thf(fact_976_Inf_OINF__image,axiom,
    ! [Inf: set_ma6254658672695423900set_b2 > mapping_b1_set_b2,G: product_prod_b1_b2 > mapping_b1_set_b2,F: product_prod_b1_b2 > product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( Inf @ ( image_6686293874852392167set_b2 @ G @ ( image_7651404027433386501_b1_b2 @ F @ A2 ) ) )
      = ( Inf @ ( image_6686293874852392167set_b2 @ ( comp_P8572024851249563899_b1_b2 @ G @ F ) @ A2 ) ) ) ).

% Inf.INF_image
thf(fact_977_Inf_OINF__image,axiom,
    ! [Inf: set_ma6254658672695423900set_b2 > mapping_b1_set_b2,G: product_prod_b1_b2 > mapping_b1_set_b2,F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Inf @ ( image_6686293874852392167set_b2 @ G @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) ) )
      = ( Inf @ ( image_1611411006170680425set_b2 @ ( comp_P9207391564348433789_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Inf.INF_image
thf(fact_978_Sup_OSUP__image,axiom,
    ! [Sup: set_Pr4592484330697324838_b1_b2 > product_prod_b1_b2,G: product_prod_b1_b2 > product_prod_b1_b2,F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Sup @ ( image_7651404027433386501_b1_b2 @ G @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) ) )
      = ( Sup @ ( image_1398015525354814723_b1_b2 @ ( comp_P8403851972257459877_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Sup.SUP_image
thf(fact_979_Sup_OSUP__image,axiom,
    ! [Sup: set_Pr9202269149784407460_c1_c2 > product_prod_c1_c2,G: product_prod_b1_b2 > product_prod_c1_c2,F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Sup @ ( image_7016037314334516611_c1_c2 @ G @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) ) )
      = ( Sup @ ( image_762648812255944833_c1_c2 @ ( comp_P5433868437481255847_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Sup.SUP_image
thf(fact_980_Sup_OSUP__image,axiom,
    ! [Sup: set_Pr4592484330697324838_b1_b2 > product_prod_b1_b2,G: product_prod_c1_c2 > product_prod_b1_b2,F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Sup @ ( image_4681420492657182471_b1_b2 @ G @ ( image_762648812255944833_c1_c2 @ F @ A2 ) ) )
      = ( Sup @ ( image_1398015525354814723_b1_b2 @ ( comp_P8467111182430445859_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Sup.SUP_image
thf(fact_981_Sup_OSUP__image,axiom,
    ! [Sup: set_Pr9202269149784407460_c1_c2 > product_prod_c1_c2,G: product_prod_c1_c2 > product_prod_c1_c2,F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Sup @ ( image_4046053779558312581_c1_c2 @ G @ ( image_762648812255944833_c1_c2 @ F @ A2 ) ) )
      = ( Sup @ ( image_762648812255944833_c1_c2 @ ( comp_P5497127647654241829_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Sup.SUP_image
thf(fact_982_Sup_OSUP__image,axiom,
    ! [Sup: set_Pr4592484330697324838_b1_b2 > product_prod_b1_b2,G: product_prod_a1_a2 > product_prod_b1_b2,F: product_prod_a1_a2 > product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Sup @ ( image_1398015525354814723_b1_b2 @ G @ ( image_2033382238453684613_a1_a2 @ F @ A2 ) ) )
      = ( Sup @ ( image_1398015525354814723_b1_b2 @ ( comp_P8340592762084473895_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Sup.SUP_image
thf(fact_983_Sup_OSUP__image,axiom,
    ! [Sup: set_Pr9202269149784407460_c1_c2 > product_prod_c1_c2,G: product_prod_a1_a2 > product_prod_c1_c2,F: product_prod_a1_a2 > product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Sup @ ( image_762648812255944833_c1_c2 @ G @ ( image_2033382238453684613_a1_a2 @ F @ A2 ) ) )
      = ( Sup @ ( image_762648812255944833_c1_c2 @ ( comp_P5370609227308269865_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Sup.SUP_image
thf(fact_984_Sup_OSUP__image,axiom,
    ! [Sup: set_ma7306327908849618074set_c2 > mapping_c1_set_c2,G: product_prod_c1_c2 > mapping_c1_set_c2,F: product_prod_c1_c2 > product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( Sup @ ( image_5984881132562613603set_c2 @ G @ ( image_4046053779558312581_c1_c2 @ F @ A2 ) ) )
      = ( Sup @ ( image_5984881132562613603set_c2 @ ( comp_P1747777731944695037_c1_c2 @ G @ F ) @ A2 ) ) ) ).

% Sup.SUP_image
thf(fact_985_Sup_OSUP__image,axiom,
    ! [Sup: set_ma7306327908849618074set_c2 > mapping_c1_set_c2,G: product_prod_c1_c2 > mapping_c1_set_c2,F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Sup @ ( image_5984881132562613603set_c2 @ G @ ( image_762648812255944833_c1_c2 @ F @ A2 ) ) )
      = ( Sup @ ( image_5058487432053965927set_c2 @ ( comp_P3018511158142434817_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Sup.SUP_image
thf(fact_986_Sup_OSUP__image,axiom,
    ! [Sup: set_ma6254658672695423900set_b2 > mapping_b1_set_b2,G: product_prod_b1_b2 > mapping_b1_set_b2,F: product_prod_b1_b2 > product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( Sup @ ( image_6686293874852392167set_b2 @ G @ ( image_7651404027433386501_b1_b2 @ F @ A2 ) ) )
      = ( Sup @ ( image_6686293874852392167set_b2 @ ( comp_P8572024851249563899_b1_b2 @ G @ F ) @ A2 ) ) ) ).

% Sup.SUP_image
thf(fact_987_Sup_OSUP__image,axiom,
    ! [Sup: set_ma6254658672695423900set_b2 > mapping_b1_set_b2,G: product_prod_b1_b2 > mapping_b1_set_b2,F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( Sup @ ( image_6686293874852392167set_b2 @ G @ ( image_1398015525354814723_b1_b2 @ F @ A2 ) ) )
      = ( Sup @ ( image_1611411006170680425set_b2 @ ( comp_P9207391564348433789_a1_a2 @ G @ F ) @ A2 ) ) ) ).

% Sup.SUP_image
thf(fact_988_image__comp,axiom,
    ! [F: product_prod_b1_b2 > product_prod_b1_b2,G: product_prod_a1_a2 > product_prod_b1_b2,R2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_7651404027433386501_b1_b2 @ F @ ( image_1398015525354814723_b1_b2 @ G @ R2 ) )
      = ( image_1398015525354814723_b1_b2 @ ( comp_P8403851972257459877_a1_a2 @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_989_image__comp,axiom,
    ! [F: product_prod_b1_b2 > product_prod_c1_c2,G: product_prod_a1_a2 > product_prod_b1_b2,R2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_7016037314334516611_c1_c2 @ F @ ( image_1398015525354814723_b1_b2 @ G @ R2 ) )
      = ( image_762648812255944833_c1_c2 @ ( comp_P5433868437481255847_a1_a2 @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_990_image__comp,axiom,
    ! [F: product_prod_c1_c2 > product_prod_b1_b2,G: product_prod_a1_a2 > product_prod_c1_c2,R2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_4681420492657182471_b1_b2 @ F @ ( image_762648812255944833_c1_c2 @ G @ R2 ) )
      = ( image_1398015525354814723_b1_b2 @ ( comp_P8467111182430445859_a1_a2 @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_991_image__comp,axiom,
    ! [F: product_prod_c1_c2 > product_prod_c1_c2,G: product_prod_a1_a2 > product_prod_c1_c2,R2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_4046053779558312581_c1_c2 @ F @ ( image_762648812255944833_c1_c2 @ G @ R2 ) )
      = ( image_762648812255944833_c1_c2 @ ( comp_P5497127647654241829_a1_a2 @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_992_image__comp,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2,G: product_prod_a1_a2 > product_prod_a1_a2,R2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_1398015525354814723_b1_b2 @ F @ ( image_2033382238453684613_a1_a2 @ G @ R2 ) )
      = ( image_1398015525354814723_b1_b2 @ ( comp_P8340592762084473895_a1_a2 @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_993_image__comp,axiom,
    ! [F: product_prod_a1_a2 > product_prod_c1_c2,G: product_prod_a1_a2 > product_prod_a1_a2,R2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_762648812255944833_c1_c2 @ F @ ( image_2033382238453684613_a1_a2 @ G @ R2 ) )
      = ( image_762648812255944833_c1_c2 @ ( comp_P5370609227308269865_a1_a2 @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_994_image__comp,axiom,
    ! [F: product_prod_c1_c2 > mapping_c1_set_c2,G: product_prod_c1_c2 > product_prod_c1_c2,R2: set_Pr9202269149784407460_c1_c2] :
      ( ( image_5984881132562613603set_c2 @ F @ ( image_4046053779558312581_c1_c2 @ G @ R2 ) )
      = ( image_5984881132562613603set_c2 @ ( comp_P1747777731944695037_c1_c2 @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_995_image__comp,axiom,
    ! [F: product_prod_c1_c2 > mapping_c1_set_c2,G: product_prod_a1_a2 > product_prod_c1_c2,R2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_5984881132562613603set_c2 @ F @ ( image_762648812255944833_c1_c2 @ G @ R2 ) )
      = ( image_5058487432053965927set_c2 @ ( comp_P3018511158142434817_a1_a2 @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_996_image__comp,axiom,
    ! [F: product_prod_b1_b2 > mapping_b1_set_b2,G: product_prod_b1_b2 > product_prod_b1_b2,R2: set_Pr4592484330697324838_b1_b2] :
      ( ( image_6686293874852392167set_b2 @ F @ ( image_7651404027433386501_b1_b2 @ G @ R2 ) )
      = ( image_6686293874852392167set_b2 @ ( comp_P8572024851249563899_b1_b2 @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_997_image__comp,axiom,
    ! [F: product_prod_b1_b2 > mapping_b1_set_b2,G: product_prod_a1_a2 > product_prod_b1_b2,R2: set_Pr9206071548465018024_a1_a2] :
      ( ( image_6686293874852392167set_b2 @ F @ ( image_1398015525354814723_b1_b2 @ G @ R2 ) )
      = ( image_1611411006170680425set_b2 @ ( comp_P9207391564348433789_a1_a2 @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_998_image__eq__imp__comp,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2,G: product_prod_a1_a2 > product_prod_b1_b2,B2: set_Pr9206071548465018024_a1_a2,H: product_prod_b1_b2 > product_prod_b1_b2] :
      ( ( ( image_1398015525354814723_b1_b2 @ F @ A2 )
        = ( image_1398015525354814723_b1_b2 @ G @ B2 ) )
     => ( ( image_1398015525354814723_b1_b2 @ ( comp_P8403851972257459877_a1_a2 @ H @ F ) @ A2 )
        = ( image_1398015525354814723_b1_b2 @ ( comp_P8403851972257459877_a1_a2 @ H @ G ) @ B2 ) ) ) ).

% image_eq_imp_comp
thf(fact_999_image__eq__imp__comp,axiom,
    ! [F: product_prod_a1_a2 > product_prod_b1_b2,A2: set_Pr9206071548465018024_a1_a2,G: product_prod_a1_a2 > product_prod_b1_b2,B2: set_Pr9206071548465018024_a1_a2,H: product_prod_b1_b2 > product_prod_c1_c2] :
      ( ( ( image_1398015525354814723_b1_b2 @ F @ A2 )
        = ( image_1398015525354814723_b1_b2 @ G @ B2 ) )
     => ( ( image_762648812255944833_c1_c2 @ ( comp_P5433868437481255847_a1_a2 @ H @ F ) @ A2 )
        = ( image_762648812255944833_c1_c2 @ ( comp_P5433868437481255847_a1_a2 @ H @ G ) @ B2 ) ) ) ).

% image_eq_imp_comp
thf(fact_1000_image__eq__imp__comp,axiom,
    ! [F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2,G: product_prod_a1_a2 > product_prod_c1_c2,B2: set_Pr9206071548465018024_a1_a2,H: product_prod_c1_c2 > product_prod_b1_b2] :
      ( ( ( image_762648812255944833_c1_c2 @ F @ A2 )
        = ( image_762648812255944833_c1_c2 @ G @ B2 ) )
     => ( ( image_1398015525354814723_b1_b2 @ ( comp_P8467111182430445859_a1_a2 @ H @ F ) @ A2 )
        = ( image_1398015525354814723_b1_b2 @ ( comp_P8467111182430445859_a1_a2 @ H @ G ) @ B2 ) ) ) ).

% image_eq_imp_comp
thf(fact_1001_image__eq__imp__comp,axiom,
    ! [F: product_prod_a1_a2 > product_prod_c1_c2,A2: set_Pr9206071548465018024_a1_a2,G: product_prod_a1_a2 > product_prod_c1_c2,B2: set_Pr9206071548465018024_a1_a2,H: product_prod_c1_c2 > product_prod_c1_c2] :
      ( ( ( image_762648812255944833_c1_c2 @ F @ A2 )
        = ( image_762648812255944833_c1_c2 @ G @ B2 ) )
     => ( ( image_762648812255944833_c1_c2 @ ( comp_P5497127647654241829_a1_a2 @ H @ F ) @ A2 )
        = ( image_762648812255944833_c1_c2 @ ( comp_P5497127647654241829_a1_a2 @ H @ G ) @ B2 ) ) ) ).

% image_eq_imp_comp
thf(fact_1002_image__eq__imp__comp,axiom,
    ! [F: product_prod_c1_c2 > product_prod_b1_b2,A2: set_Pr9202269149784407460_c1_c2,G: product_prod_a1_a2 > product_prod_b1_b2,B2: set_Pr9206071548465018024_a1_a2,H: product_prod_b1_b2 > mapping_c1_set_c2] :
      ( ( ( image_4681420492657182471_b1_b2 @ F @ A2 )
        = ( image_1398015525354814723_b1_b2 @ G @ B2 ) )
     => ( ( image_5984881132562613603set_c2 @ ( comp_P9192946450864864507_c1_c2 @ H @ F ) @ A2 )
        = ( image_5058487432053965927set_c2 @ ( comp_P1240307840207828479_a1_a2 @ H @ G ) @ B2 ) ) ) ).

% image_eq_imp_comp
thf(fact_1003_image__eq__imp__comp,axiom,
    ! [F: product_prod_b1_b2 > product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,G: product_prod_a1_a2 > product_prod_b1_b2,B2: set_Pr9206071548465018024_a1_a2,H: product_prod_b1_b2 > mapping_b1_set_b2] :
      ( ( ( image_7651404027433386501_b1_b2 @ F @ A2 )
        = ( image_1398015525354814723_b1_b2 @ G @ B2 ) )
     => ( ( image_6686293874852392167set_b2 @ ( comp_P8572024851249563899_b1_b2 @ H @ F ) @ A2 )
        = ( image_1611411006170680425set_b2 @ ( comp_P9207391564348433789_a1_a2 @ H @ G ) @ B2 ) ) ) ).

% image_eq_imp_comp
thf(fact_1004_image__eq__imp__comp,axiom,
    ! [F: product_prod_c1_c2 > product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,G: product_prod_a1_a2 > product_prod_c1_c2,B2: set_Pr9206071548465018024_a1_a2,H: product_prod_c1_c2 > mapping_c1_set_c2] :
      ( ( ( image_4046053779558312581_c1_c2 @ F @ A2 )
        = ( image_762648812255944833_c1_c2 @ G @ B2 ) )
     => ( ( image_5984881132562613603set_c2 @ ( comp_P1747777731944695037_c1_c2 @ H @ F ) @ A2 )
        = ( image_5058487432053965927set_c2 @ ( comp_P3018511158142434817_a1_a2 @ H @ G ) @ B2 ) ) ) ).

% image_eq_imp_comp
thf(fact_1005_image__eq__imp__comp,axiom,
    ! [F: product_prod_b1_b2 > product_prod_c1_c2,A2: set_Pr4592484330697324838_b1_b2,G: product_prod_a1_a2 > product_prod_c1_c2,B2: set_Pr9206071548465018024_a1_a2,H: product_prod_c1_c2 > mapping_b1_set_b2] :
      ( ( ( image_7016037314334516611_c1_c2 @ F @ A2 )
        = ( image_762648812255944833_c1_c2 @ G @ B2 ) )
     => ( ( image_6686293874852392167set_b2 @ ( comp_P1126856132329394429_b1_b2 @ H @ F ) @ A2 )
        = ( image_1611411006170680425set_b2 @ ( comp_P1762222845428264319_a1_a2 @ H @ G ) @ B2 ) ) ) ).

% image_eq_imp_comp
thf(fact_1006_image__eq__imp__comp,axiom,
    ! [F: product_prod_a1_a2 > mapping_c1_set_c2,A2: set_Pr9206071548465018024_a1_a2,G: product_prod_c1_c2 > mapping_c1_set_c2,B2: set_Pr9202269149784407460_c1_c2,H: mapping_c1_set_c2 > product_prod_b1_b2] :
      ( ( ( image_5058487432053965927set_c2 @ F @ A2 )
        = ( image_5984881132562613603set_c2 @ G @ B2 ) )
     => ( ( image_1398015525354814723_b1_b2 @ ( comp_m7208595679230017097_a1_a2 @ H @ F ) @ A2 )
        = ( image_4681420492657182471_b1_b2 @ ( comp_m5937862253032277317_c1_c2 @ H @ G ) @ B2 ) ) ) ).

% image_eq_imp_comp
thf(fact_1007_image__eq__imp__comp,axiom,
    ! [F: product_prod_a1_a2 > mapping_c1_set_c2,A2: set_Pr9206071548465018024_a1_a2,G: product_prod_c1_c2 > mapping_c1_set_c2,B2: set_Pr9202269149784407460_c1_c2,H: mapping_c1_set_c2 > product_prod_c1_c2] :
      ( ( ( image_5058487432053965927set_c2 @ F @ A2 )
        = ( image_5984881132562613603set_c2 @ G @ B2 ) )
     => ( ( image_762648812255944833_c1_c2 @ ( comp_m4238612144453813067_a1_a2 @ H @ F ) @ A2 )
        = ( image_4046053779558312581_c1_c2 @ ( comp_m2967878718256073287_c1_c2 @ H @ G ) @ B2 ) ) ) ).

% image_eq_imp_comp
thf(fact_1008_Set__remove__code_I3_J,axiom,
    ! [X2: product_prod_a1_a2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( remove1798067411834080045_a1_a2 @ X2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o939065307356969905_order
        @ ( abort_1828026589024592305_a1_a2 @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( remove1798067411834080045_a1_a2 @ X2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [Xa: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( set_RB6720226376580087827_a1_a2 @ ( rBT_de9134497937230377260t_unit @ X2 @ Rbt2 ) )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Set_remove_code(3)
thf(fact_1009_Set_Omember__remove,axiom,
    ! [X2: product_prod_c1_c2,Y5: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ ( remove527333985636340265_c1_c2 @ Y5 @ A2 ) )
      = ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
        & ( X2 != Y5 ) ) ) ).

% Set.member_remove
thf(fact_1010_Set_Omember__remove,axiom,
    ! [X2: product_prod_b1_b2,Y5: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ ( remove1162700698735210155_b1_b2 @ Y5 @ A2 ) )
      = ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
        & ( X2 != Y5 ) ) ) ).

% Set.member_remove
thf(fact_1011_Set_Omember__remove,axiom,
    ! [X2: product_prod_a1_a2,Y5: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ ( remove1798067411834080045_a1_a2 @ Y5 @ A2 ) )
      = ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
        & ( X2 != Y5 ) ) ) ).

% Set.member_remove
thf(fact_1012_Set_Omember__remove,axiom,
    ! [X2: mapping_c1_set_c2,Y5: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ X2 @ ( remove5407049411726745791set_c2 @ Y5 @ A2 ) )
      = ( ( member341037065618468219set_c2 @ X2 @ A2 )
        & ( X2 != Y5 ) ) ) ).

% Set.member_remove
thf(fact_1013_Set_Omember__remove,axiom,
    ! [X2: mapping_b1_set_b2,Y5: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ X2 @ ( remove1959972985843460289set_b2 @ Y5 @ A2 ) )
      = ( ( member6117332676589958525set_b2 @ X2 @ A2 )
        & ( X2 != Y5 ) ) ) ).

% Set.member_remove
thf(fact_1014_snd__diag__snd,axiom,
    ( ( comp_P302927382947242815set_c2 @ produc8094231947202502927set_c2
      @ ( comp_m1427541729666086921set_c2
        @ ^ [X: mapping_c1_set_c2] : ( produc3273467689206522593set_c2 @ X @ X )
        @ produc6032943676959796241set_c2 ) )
    = produc6032943676959796241set_c2 ) ).

% snd_diag_snd
thf(fact_1015_snd__diag__snd,axiom,
    ( ( comp_P8261968323940027547set_c2 @ produc4706818786498457559set_c2
      @ ( comp_c1653858145111704749set_c2
        @ ^ [X: c1 > option_set_c2] : ( produc1021899567675014057set_c2 @ X @ X )
        @ produc4575701783957131737set_c2 ) )
    = produc4575701783957131737set_c2 ) ).

% snd_diag_snd
thf(fact_1016_fst__diag__fst,axiom,
    ( ( comp_P3116930634664401337set_c2 @ produc591198480904955345set_b2
      @ ( comp_m7925709966048865799set_c2
        @ ^ [X: mapping_b1_set_b2] : ( produc6988475029935306213set_b2 @ X @ X )
        @ produc4038274906788240847set_c2 ) )
    = produc4038274906788240847set_c2 ) ).

% fst_diag_fst
thf(fact_1017_fst__diag__fst,axiom,
    ( ( comp_P498226757381885973set_c2 @ produc6671677333523925913set_b2
      @ ( comp_b5264233654759695275set_c2
        @ ^ [X: b1 > option_set_b2] : ( produc4375337561607790509set_b2 @ X @ X )
        @ produc3187122337049823639set_c2 ) )
    = produc3187122337049823639set_c2 ) ).

% fst_diag_fst
thf(fact_1018_fst__diag__snd,axiom,
    ( ( comp_P302927382947242815set_c2 @ produc6099563177030947533set_c2
      @ ( comp_m1427541729666086921set_c2
        @ ^ [X: mapping_c1_set_c2] : ( produc3273467689206522593set_c2 @ X @ X )
        @ produc6032943676959796241set_c2 ) )
    = produc6032943676959796241set_c2 ) ).

% fst_diag_snd
thf(fact_1019_fst__diag__snd,axiom,
    ( ( comp_P8261968323940027547set_c2 @ produc3318239339591149461set_c2
      @ ( comp_c1653858145111704749set_c2
        @ ^ [X: c1 > option_set_c2] : ( produc1021899567675014057set_c2 @ X @ X )
        @ produc4575701783957131737set_c2 ) )
    = produc4575701783957131737set_c2 ) ).

% fst_diag_snd
thf(fact_1020_snd__diag__fst,axiom,
    ( ( comp_P3116930634664401337set_c2 @ produc2585867251076510739set_b2
      @ ( comp_m7925709966048865799set_c2
        @ ^ [X: mapping_b1_set_b2] : ( produc6988475029935306213set_b2 @ X @ X )
        @ produc4038274906788240847set_c2 ) )
    = produc4038274906788240847set_c2 ) ).

% snd_diag_fst
thf(fact_1021_snd__diag__fst,axiom,
    ( ( comp_P498226757381885973set_c2 @ produc8060256780431234011set_b2
      @ ( comp_b5264233654759695275set_c2
        @ ^ [X: b1 > option_set_b2] : ( produc4375337561607790509set_b2 @ X @ X )
        @ produc3187122337049823639set_c2 ) )
    = produc3187122337049823639set_c2 ) ).

% snd_diag_fst
thf(fact_1022_Inf_OINF__cong,axiom,
    ! [A2: set_Pr1660683266160182027set_c2,B2: set_Pr1660683266160182027set_c2,C7: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,D2: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,Inf: set_Pr1660683266160182027set_c2 > produc4061897789176782763set_c2] :
      ( ( A2 = B2 )
     => ( ! [X3: produc4061897789176782763set_c2] :
            ( ( member419137155788712276set_c2 @ X3 @ B2 )
           => ( ( C7 @ X3 )
              = ( D2 @ X3 ) ) )
       => ( ( Inf @ ( image_7945144516369962181set_c2 @ C7 @ A2 ) )
          = ( Inf @ ( image_7945144516369962181set_c2 @ D2 @ B2 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_1023_Inf_OINF__cong,axiom,
    ! [A2: set_Pr9202269149784407460_c1_c2,B2: set_Pr9202269149784407460_c1_c2,C7: product_prod_c1_c2 > mapping_c1_set_c2,D2: product_prod_c1_c2 > mapping_c1_set_c2,Inf: set_ma7306327908849618074set_c2 > mapping_c1_set_c2] :
      ( ( A2 = B2 )
     => ( ! [X3: product_prod_c1_c2] :
            ( ( member1440383022217085037_c1_c2 @ X3 @ B2 )
           => ( ( C7 @ X3 )
              = ( D2 @ X3 ) ) )
       => ( ( Inf @ ( image_5984881132562613603set_c2 @ C7 @ A2 ) )
          = ( Inf @ ( image_5984881132562613603set_c2 @ D2 @ B2 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_1024_Inf_OINF__cong,axiom,
    ! [A2: set_Pr4592484330697324838_b1_b2,B2: set_Pr4592484330697324838_b1_b2,C7: product_prod_b1_b2 > mapping_b1_set_b2,D2: product_prod_b1_b2 > mapping_b1_set_b2,Inf: set_ma6254658672695423900set_b2 > mapping_b1_set_b2] :
      ( ( A2 = B2 )
     => ( ! [X3: product_prod_b1_b2] :
            ( ( member2075749735315954927_b1_b2 @ X3 @ B2 )
           => ( ( C7 @ X3 )
              = ( D2 @ X3 ) ) )
       => ( ( Inf @ ( image_6686293874852392167set_b2 @ C7 @ A2 ) )
          = ( Inf @ ( image_6686293874852392167set_b2 @ D2 @ B2 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_1025_Inf_OINF__cong,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2,B2: set_Pr9206071548465018024_a1_a2,C7: product_prod_a1_a2 > product_prod_b1_b2,D2: product_prod_a1_a2 > product_prod_b1_b2,Inf: set_Pr4592484330697324838_b1_b2 > product_prod_b1_b2] :
      ( ( A2 = B2 )
     => ( ! [X3: product_prod_a1_a2] :
            ( ( member2711116448414824817_a1_a2 @ X3 @ B2 )
           => ( ( C7 @ X3 )
              = ( D2 @ X3 ) ) )
       => ( ( Inf @ ( image_1398015525354814723_b1_b2 @ C7 @ A2 ) )
          = ( Inf @ ( image_1398015525354814723_b1_b2 @ D2 @ B2 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_1026_Inf_OINF__cong,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2,B2: set_Pr9206071548465018024_a1_a2,C7: product_prod_a1_a2 > product_prod_c1_c2,D2: product_prod_a1_a2 > product_prod_c1_c2,Inf: set_Pr9202269149784407460_c1_c2 > product_prod_c1_c2] :
      ( ( A2 = B2 )
     => ( ! [X3: product_prod_a1_a2] :
            ( ( member2711116448414824817_a1_a2 @ X3 @ B2 )
           => ( ( C7 @ X3 )
              = ( D2 @ X3 ) ) )
       => ( ( Inf @ ( image_762648812255944833_c1_c2 @ C7 @ A2 ) )
          = ( Inf @ ( image_762648812255944833_c1_c2 @ D2 @ B2 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_1027_Sup_OSUP__cong,axiom,
    ! [A2: set_Pr1660683266160182027set_c2,B2: set_Pr1660683266160182027set_c2,C7: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,D2: produc4061897789176782763set_c2 > produc4061897789176782763set_c2,Sup: set_Pr1660683266160182027set_c2 > produc4061897789176782763set_c2] :
      ( ( A2 = B2 )
     => ( ! [X3: produc4061897789176782763set_c2] :
            ( ( member419137155788712276set_c2 @ X3 @ B2 )
           => ( ( C7 @ X3 )
              = ( D2 @ X3 ) ) )
       => ( ( Sup @ ( image_7945144516369962181set_c2 @ C7 @ A2 ) )
          = ( Sup @ ( image_7945144516369962181set_c2 @ D2 @ B2 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_1028_Sup_OSUP__cong,axiom,
    ! [A2: set_Pr9202269149784407460_c1_c2,B2: set_Pr9202269149784407460_c1_c2,C7: product_prod_c1_c2 > mapping_c1_set_c2,D2: product_prod_c1_c2 > mapping_c1_set_c2,Sup: set_ma7306327908849618074set_c2 > mapping_c1_set_c2] :
      ( ( A2 = B2 )
     => ( ! [X3: product_prod_c1_c2] :
            ( ( member1440383022217085037_c1_c2 @ X3 @ B2 )
           => ( ( C7 @ X3 )
              = ( D2 @ X3 ) ) )
       => ( ( Sup @ ( image_5984881132562613603set_c2 @ C7 @ A2 ) )
          = ( Sup @ ( image_5984881132562613603set_c2 @ D2 @ B2 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_1029_Sup_OSUP__cong,axiom,
    ! [A2: set_Pr4592484330697324838_b1_b2,B2: set_Pr4592484330697324838_b1_b2,C7: product_prod_b1_b2 > mapping_b1_set_b2,D2: product_prod_b1_b2 > mapping_b1_set_b2,Sup: set_ma6254658672695423900set_b2 > mapping_b1_set_b2] :
      ( ( A2 = B2 )
     => ( ! [X3: product_prod_b1_b2] :
            ( ( member2075749735315954927_b1_b2 @ X3 @ B2 )
           => ( ( C7 @ X3 )
              = ( D2 @ X3 ) ) )
       => ( ( Sup @ ( image_6686293874852392167set_b2 @ C7 @ A2 ) )
          = ( Sup @ ( image_6686293874852392167set_b2 @ D2 @ B2 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_1030_Sup_OSUP__cong,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2,B2: set_Pr9206071548465018024_a1_a2,C7: product_prod_a1_a2 > product_prod_b1_b2,D2: product_prod_a1_a2 > product_prod_b1_b2,Sup: set_Pr4592484330697324838_b1_b2 > product_prod_b1_b2] :
      ( ( A2 = B2 )
     => ( ! [X3: product_prod_a1_a2] :
            ( ( member2711116448414824817_a1_a2 @ X3 @ B2 )
           => ( ( C7 @ X3 )
              = ( D2 @ X3 ) ) )
       => ( ( Sup @ ( image_1398015525354814723_b1_b2 @ C7 @ A2 ) )
          = ( Sup @ ( image_1398015525354814723_b1_b2 @ D2 @ B2 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_1031_Sup_OSUP__cong,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2,B2: set_Pr9206071548465018024_a1_a2,C7: product_prod_a1_a2 > product_prod_c1_c2,D2: product_prod_a1_a2 > product_prod_c1_c2,Sup: set_Pr9202269149784407460_c1_c2 > product_prod_c1_c2] :
      ( ( A2 = B2 )
     => ( ! [X3: product_prod_a1_a2] :
            ( ( member2711116448414824817_a1_a2 @ X3 @ B2 )
           => ( ( C7 @ X3 )
              = ( D2 @ X3 ) ) )
       => ( ( Sup @ ( image_762648812255944833_c1_c2 @ C7 @ A2 ) )
          = ( Sup @ ( image_762648812255944833_c1_c2 @ D2 @ B2 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_1032_image2__eqI,axiom,
    ! [B: c1,F: product_prod_c1_c2 > c1,X2: product_prod_c1_c2,C: c2,G: product_prod_c1_c2 > c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C
          = ( G @ X2 ) )
       => ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
         => ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ B @ C ) @ ( bNF_Gr8687606788332042191_c1_c2 @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_1033_image2__eqI,axiom,
    ! [B: c1,F: product_prod_b1_b2 > c1,X2: product_prod_b1_b2,C: c2,G: product_prod_b1_b2 > c2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C
          = ( G @ X2 ) )
       => ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
         => ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ B @ C ) @ ( bNF_Gr5435061502750788177_c1_c2 @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_1034_image2__eqI,axiom,
    ! [B: c1,F: product_prod_a1_a2 > c1,X2: product_prod_a1_a2,C: c2,G: product_prod_a1_a2 > c2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C
          = ( G @ X2 ) )
       => ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
         => ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ B @ C ) @ ( bNF_Gr2182516217169534163_c1_c2 @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_1035_image2__eqI,axiom,
    ! [B: b1,F: product_prod_c1_c2 > b1,X2: product_prod_c1_c2,C: b2,G: product_prod_c1_c2 > b2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C
          = ( G @ X2 ) )
       => ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
         => ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ B @ C ) @ ( bNF_Gr99883752082187473_b1_b2 @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_1036_image2__eqI,axiom,
    ! [B: b1,F: product_prod_b1_b2 > b1,X2: product_prod_b1_b2,C: b2,G: product_prod_b1_b2 > b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C
          = ( G @ X2 ) )
       => ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
         => ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ B @ C ) @ ( bNF_Gr6070710503355709267_b1_b2 @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_1037_image2__eqI,axiom,
    ! [B: b1,F: product_prod_a1_a2 > b1,X2: product_prod_a1_a2,C: b2,G: product_prod_a1_a2 > b2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C
          = ( G @ X2 ) )
       => ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
         => ( member2075749735315954927_b1_b2 @ ( product_Pair_b1_b2 @ B @ C ) @ ( bNF_Gr2818165217774455253_b1_b2 @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_1038_image2__eqI,axiom,
    ! [B: a1,F: product_prod_c1_c2 > a1,X2: product_prod_c1_c2,C: a2,G: product_prod_c1_c2 > a2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C
          = ( G @ X2 ) )
       => ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
         => ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ B @ C ) @ ( bNF_Gr735532752687108563_a1_a2 @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_1039_image2__eqI,axiom,
    ! [B: a1,F: product_prod_b1_b2 > a1,X2: product_prod_b1_b2,C: a2,G: product_prod_b1_b2 > a2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C
          = ( G @ X2 ) )
       => ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
         => ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ B @ C ) @ ( bNF_Gr6706359503960630357_a1_a2 @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_1040_image2__eqI,axiom,
    ! [B: a1,F: product_prod_a1_a2 > a1,X2: product_prod_a1_a2,C: a2,G: product_prod_a1_a2 > a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C
          = ( G @ X2 ) )
       => ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
         => ( member2711116448414824817_a1_a2 @ ( product_Pair_a1_a2 @ B @ C ) @ ( bNF_Gr3453814218379376343_a1_a2 @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_1041_image2__eqI,axiom,
    ! [B: c1,F: mapping_c1_set_c2 > c1,X2: mapping_c1_set_c2,C: c2,G: mapping_c1_set_c2 > c2,A2: set_ma7306327908849618074set_c2] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C
          = ( G @ X2 ) )
       => ( ( member341037065618468219set_c2 @ X2 @ A2 )
         => ( member1440383022217085037_c1_c2 @ ( product_Pair_c1_c2 @ B @ C ) @ ( bNF_Gr4776719309262608675_c1_c2 @ A2 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_1042_fst__snd__flip,axiom,
    ( produc6671677333523925913set_b2
    = ( comp_P6294463794021757207set_b2 @ produc8060256780431234011set_b2
      @ ( produc8790685608643853619set_b2
        @ ^ [X: b1 > option_set_b2,Y6: b1 > option_set_b2] : ( produc4375337561607790509set_b2 @ Y6 @ X ) ) ) ) ).

% fst_snd_flip
thf(fact_1043_fst__snd__flip,axiom,
    ( product_fst_c2_c1
    = ( comp_P3555446670343557295_c2_c1 @ product_snd_c1_c2
      @ ( produc5868568207898373875_c1_c2
        @ ^ [X: c2,Y6: c1] : ( product_Pair_c1_c2 @ Y6 @ X ) ) ) ) ).

% fst_snd_flip
thf(fact_1044_fst__snd__flip,axiom,
    ( product_fst_b2_b1
    = ( comp_P243756425731807534_b2_b1 @ product_snd_b1_b2
      @ ( produc3018828688233387507_b1_b2
        @ ^ [X: b2,Y6: b1] : ( product_Pair_b1_b2 @ Y6 @ X ) ) ) ) ).

% fst_snd_flip
thf(fact_1045_fst__snd__flip,axiom,
    ( product_fst_a2_a1
    = ( comp_P6155438217974833581_a2_a1 @ product_snd_a1_a2
      @ ( produc169089168568401139_a1_a2
        @ ^ [X: a2,Y6: a1] : ( product_Pair_a1_a2 @ Y6 @ X ) ) ) ) ).

% fst_snd_flip
thf(fact_1046_fst__snd__flip,axiom,
    ( produc4038274906788240847set_c2
    = ( comp_P6715848912171352123set_c2 @ produc4647155521319217425set_b2
      @ ( produc5742058344595415475set_b2
        @ ^ [X: mapping_b1_set_b2,Y6: mapping_c1_set_c2] : ( produc9049763300178012899set_b2 @ Y6 @ X ) ) ) ) ).

% fst_snd_flip
thf(fact_1047_fst__snd__flip,axiom,
    ( produc3187122337049823639set_c2
    = ( comp_P8909975857928217751set_c2 @ produc8191373782972559833set_b2
      @ ( produc6231298701348253619set_b2
        @ ^ [X: b1 > option_set_b2,Y6: c1 > option_set_c2] : ( produc4506454564149116331set_b2 @ Y6 @ X ) ) ) ) ).

% fst_snd_flip
thf(fact_1048_fst__snd__flip,axiom,
    ( produc2652486751147662031set_b2
    = ( comp_P6937000176383580349set_b2 @ produc6032943676959796241set_c2
      @ ( produc2647557493670480051set_c2
        @ ^ [X: mapping_c1_set_c2,Y6: mapping_b1_set_b2] : ( produc1212179418963815907set_c2 @ Y6 @ X ) ) ) ) ).

% fst_snd_flip
thf(fact_1049_fst__snd__flip,axiom,
    ( produc6802794336065251735set_b2
    = ( comp_P5777573262574892825set_b2 @ produc4575701783957131737set_c2
      @ ( produc5801580654647562419set_c2
        @ ^ [X: c1 > option_set_c2,Y6: b1 > option_set_b2] : ( produc890782565133688235set_c2 @ Y6 @ X ) ) ) ) ).

% fst_snd_flip
thf(fact_1050_snd__fst__flip,axiom,
    ( produc8060256780431234011set_b2
    = ( comp_P6294463794021757207set_b2 @ produc6671677333523925913set_b2
      @ ( produc8790685608643853619set_b2
        @ ^ [X: b1 > option_set_b2,Y6: b1 > option_set_b2] : ( produc4375337561607790509set_b2 @ Y6 @ X ) ) ) ) ).

% snd_fst_flip
thf(fact_1051_snd__fst__flip,axiom,
    ( product_snd_c2_c1
    = ( comp_P4891497290296251632_c2_c1 @ product_fst_c1_c2
      @ ( produc5868568207898373875_c1_c2
        @ ^ [X: c2,Y6: c1] : ( product_Pair_c1_c2 @ Y6 @ X ) ) ) ) ).

% snd_fst_flip
thf(fact_1052_snd__fst__flip,axiom,
    ( product_snd_b2_b1
    = ( comp_P1579807045684501871_b2_b1 @ product_fst_b1_b2
      @ ( produc3018828688233387507_b1_b2
        @ ^ [X: b2,Y6: b1] : ( product_Pair_b1_b2 @ Y6 @ X ) ) ) ) ).

% snd_fst_flip
thf(fact_1053_snd__fst__flip,axiom,
    ( product_snd_a2_a1
    = ( comp_P7491488837927527918_a2_a1 @ product_fst_a1_a2
      @ ( produc169089168568401139_a1_a2
        @ ^ [X: a2,Y6: a1] : ( product_Pair_a1_a2 @ Y6 @ X ) ) ) ) ).

% snd_fst_flip
thf(fact_1054_snd__fst__flip,axiom,
    ( produc4647155521319217425set_b2
    = ( comp_P8959985049830094907set_b2 @ produc4038274906788240847set_c2
      @ ( produc2647557493670480051set_c2
        @ ^ [X: mapping_c1_set_c2,Y6: mapping_b1_set_b2] : ( produc1212179418963815907set_c2 @ Y6 @ X ) ) ) ) ).

% snd_fst_flip
thf(fact_1055_snd__fst__flip,axiom,
    ( produc8191373782972559833set_b2
    = ( comp_P8468077172411818647set_b2 @ produc3187122337049823639set_c2
      @ ( produc5801580654647562419set_c2
        @ ^ [X: c1 > option_set_c2,Y6: b1 > option_set_b2] : ( produc890782565133688235set_c2 @ Y6 @ X ) ) ) ) ).

% snd_fst_flip
thf(fact_1056_snd__fst__flip,axiom,
    ( produc6032943676959796241set_c2
    = ( comp_P4692864038724837565set_c2 @ produc2652486751147662031set_b2
      @ ( produc5742058344595415475set_b2
        @ ^ [X: mapping_b1_set_b2,Y6: mapping_c1_set_c2] : ( produc9049763300178012899set_b2 @ Y6 @ X ) ) ) ) ).

% snd_fst_flip
thf(fact_1057_snd__fst__flip,axiom,
    ( produc4575701783957131737set_c2
    = ( comp_P6219471948091291929set_c2 @ produc6802794336065251735set_b2
      @ ( produc6231298701348253619set_b2
        @ ^ [X: b1 > option_set_b2,Y6: c1 > option_set_c2] : ( produc4506454564149116331set_b2 @ Y6 @ X ) ) ) ) ).

% snd_fst_flip
thf(fact_1058_Inf_OINF__identity__eq,axiom,
    ! [Inf: set_Pr1660683266160182027set_c2 > produc4061897789176782763set_c2,A2: set_Pr1660683266160182027set_c2] :
      ( ( Inf
        @ ( image_7945144516369962181set_c2
          @ ^ [X: produc4061897789176782763set_c2] : X
          @ A2 ) )
      = ( Inf @ A2 ) ) ).

% Inf.INF_identity_eq
thf(fact_1059_Sup_OSUP__identity__eq,axiom,
    ! [Sup: set_Pr1660683266160182027set_c2 > produc4061897789176782763set_c2,A2: set_Pr1660683266160182027set_c2] :
      ( ( Sup
        @ ( image_7945144516369962181set_c2
          @ ^ [X: produc4061897789176782763set_c2] : X
          @ A2 ) )
      = ( Sup @ A2 ) ) ).

% Sup.SUP_identity_eq
thf(fact_1060_Set__Impl_Oproduct__code_I8_J,axiom,
    ! [Rbt1: rBT_ma5247151625439037167t_unit,Rbt22: rBT_ma9198043261057625646t_unit] :
      ( ( produc1920397763621873979_a1_a2 @ ( set_RBT_set_a1 @ Rbt1 ) @ ( set_RBT_set_a2 @ Rbt22 ) )
      = ( case_o3237228901688236643_order
        @ ( abort_1828026589024592305_a1_a2 @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( produc1920397763621873979_a1_a2 @ ( set_RBT_set_a1 @ Rbt1 ) @ ( set_RBT_set_a2 @ Rbt22 ) ) )
        @ ^ [X: a1 > a1 > order] :
            ( case_o7642782717507025761_order
            @ ( abort_1828026589024592305_a1_a2 @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( produc1920397763621873979_a1_a2 @ ( set_RBT_set_a1 @ Rbt1 ) @ ( set_RBT_set_a2 @ Rbt22 ) ) )
            @ ^ [Y6: a2 > a2 > order] : ( set_RB6720226376580087827_a1_a2 @ ( rBT_product_a1_a2 @ Rbt1 @ Rbt22 ) )
            @ ( contai8426371921324108128_order @ collec1018370599034179449are_a2 ) )
        @ ( contai7102178477343188834_order @ collec1018370599034179448are_a1 ) ) ) ).

% Set_Impl.product_code(8)
thf(fact_1061_Set__Impl_Oproduct__code_I8_J,axiom,
    ! [Rbt1: rBT_ma1918525461012799116t_unit,Rbt22: rBT_ma1918525461012799116t_unit] :
      ( ( produc5560993320124916434_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt1 ) @ ( set_RB6720226376580087827_a1_a2 @ Rbt22 ) )
      = ( case_o7275867065294810514_order
        @ ( abort_2970878230164759184_a1_a2 @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( produc5560993320124916434_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt1 ) @ ( set_RB6720226376580087827_a1_a2 @ Rbt22 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] :
            ( case_o7275867065294810514_order
            @ ( abort_2970878230164759184_a1_a2 @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
              @ ^ [Uu: product_unit] : ( produc5560993320124916434_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt1 ) @ ( set_RB6720226376580087827_a1_a2 @ Rbt22 ) ) )
            @ ^ [Y6: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( set_RB7405050026841235442_a1_a2 @ ( rBT_pr457803644961399015_a1_a2 @ Rbt1 @ Rbt22 ) )
            @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Set_Impl.product_code(8)
thf(fact_1062_set__fold__cfi__code_I5_J,axiom,
    ! [F4: set_co4968226104895303821set_c2,B: produc4061897789176782763set_c2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( set_se7927235621780297020set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o7815954270536807150_order
        @ ( abort_4986896609014028468set_c2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_se7927235621780297020set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo5132325507301440204set_c2 @ ( set_co4303079455494716939set_c2 @ F4 ) @ Rbt2 @ B )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% set_fold_cfi_code(5)
thf(fact_1063_set__fold__cfi__code_I5_J,axiom,
    ! [F4: set_co2677916505999940506set_b2,B: mapping_b1_set_b2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( set_se3028378928793307029set_b2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o3110906606155996059_order
        @ ( abort_1879577566130638365set_b2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_se3028378928793307029set_b2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo4244449053837635077set_b2 @ ( set_co5767054866228076550set_b2 @ F4 ) @ Rbt2 @ B )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% set_fold_cfi_code(5)
thf(fact_1064_set__fold__cfi__code_I5_J,axiom,
    ! [F4: set_co3729585742154134680set_c2,B: mapping_c1_set_c2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( set_se6475455354676592531set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o573573238536716829_order
        @ ( abort_5326653992013923867set_c2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_se6475455354676592531set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo7691525479720920579set_c2 @ ( set_co9214131292111362052set_c2 @ F4 ) @ Rbt2 @ B )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% set_fold_cfi_code(5)
thf(fact_1065_set__fold__cfi__code_I5_J,axiom,
    ! [F4: set_co1666008921066281045set_c2,B: produc2702059613074419827set_c2,Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( set_se8655448371823792900set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o989950291820459046_order
        @ ( abort_2778816509743918716set_c2 @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( set_se8655448371823792900set_c2 @ F4 @ B @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( rBT_fo273127210504882324set_c2 @ ( set_co1568338092084129491set_c2 @ F4 ) @ Rbt2 @ B )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% set_fold_cfi_code(5)
thf(fact_1066_Set__Impl_Ofinite__code_I2_J,axiom,
    ! [Rbt2: rBT_ma3908794552746989458t_unit] :
      ( ( finite_finite_nat @ ( set_RBT_set_nat @ Rbt2 ) )
      = ( case_o3585232611041703993_order
        @ ( abort_o @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( finite_finite_nat @ ( set_RBT_set_nat @ Rbt2 ) ) )
        @ ^ [X: nat > nat > order] : $true
        @ ( contai6714475312730102056_order @ collec3177673580629085973re_nat ) ) ) ).

% Set_Impl.finite_code(2)
thf(fact_1067_Set__Impl_Ofinite__code_I2_J,axiom,
    ! [Rbt2: rBT_ma1918525461012799116t_unit] :
      ( ( finite9152749144624424049_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) )
      = ( case_o437269291504840897_order
        @ ( abort_o @ ( literal2 @ $false @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( finite9152749144624424049_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt2 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : $true
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Set_Impl.finite_code(2)
thf(fact_1068_Set__minus__code_I2_J,axiom,
    ! [Rbt1: rBT_ma1918525461012799116t_unit,Rbt22: rBT_ma1918525461012799116t_unit] :
      ( ( minus_7668950675640249231_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt1 ) @ ( set_RB6720226376580087827_a1_a2 @ Rbt22 ) )
      = ( case_o939065307356969905_order
        @ ( abort_1828026589024592305_a1_a2 @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ^ [Uu: product_unit] : ( minus_7668950675640249231_a1_a2 @ ( set_RB6720226376580087827_a1_a2 @ Rbt1 ) @ ( set_RB6720226376580087827_a1_a2 @ Rbt22 ) ) )
        @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] : ( set_RB6720226376580087827_a1_a2 @ ( rBT_mi1323845651579288223_a1_a2 @ Rbt1 @ Rbt22 ) )
        @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

% Set_minus_code(2)
thf(fact_1069_h__out__code,axiom,
    ( h_out_c1_c2_b2
    = ( ^ [M6: fsm_c1_c2_b2,Qx: product_prod_c1_c2] :
          ( case_o3853413523431599071set_b2 @ bot_bot_set_b2
          @ ^ [Yqs: set_b2] : Yqs
          @ ( set_as4859442375955187265_c2_b2
            @ ( image_1912427973107927291_c2_b2
              @ ( produc4043917051759461133_c2_b2
                @ ^ [Q4: c1] :
                    ( produc8016235040339740685_c2_b2
                    @ ^ [X: c2] :
                        ( produc8018187034935414328_c2_b2
                        @ ^ [Y6: b2,Q5: c1] : ( produc7786241149486508000_c2_b2 @ ( product_Pair_c1_c2 @ Q4 @ X ) @ Y6 ) ) ) )
              @ ( transitions_c1_c2_b2 @ M6 ) )
            @ Qx ) ) ) ) ).

% h_out_code
thf(fact_1070_h__out__code,axiom,
    ( h_out_b1_b2_b2
    = ( ^ [M6: fsm_b1_b2_b2,Qx: product_prod_b1_b2] :
          ( case_o3853413523431599071set_b2 @ bot_bot_set_b2
          @ ^ [Yqs: set_b2] : Yqs
          @ ( set_as931098894140046787_b2_b2
            @ ( image_380113436679758078_b2_b2
              @ ( produc4290437079652236048_b2_b2
                @ ^ [Q4: b1] :
                    ( produc7387054627097393871_b2_b2
                    @ ^ [X: b2] :
                        ( produc5735029425677389947_b2_b2
                        @ ^ [Y6: b2,Q5: b1] : ( produc3857897667671367522_b2_b2 @ ( product_Pair_b1_b2 @ Q4 @ X ) @ Y6 ) ) ) )
              @ ( transitions_b1_b2_b2 @ M6 ) )
            @ Qx ) ) ) ) ).

% h_out_code
thf(fact_1071_h__out__code,axiom,
    ( h_out_a1_a2_b2
    = ( ^ [M6: fsm_a1_a2_b2,Qx: product_prod_a1_a2] :
          ( case_o3853413523431599071set_b2 @ bot_bot_set_b2
          @ ^ [Yqs: set_b2] : Yqs
          @ ( set_as6226127449179682117_a2_b2
            @ ( image_8071170937106364673_a2_b2
              @ ( produc4536957107545010963_a2_b2
                @ ^ [Q4: a1] :
                    ( produc6757874213855047057_a2_b2
                    @ ^ [X: a2] :
                        ( produc3451871816419365566_a2_b2
                        @ ^ [Y6: b2,Q5: a1] : ( produc9152926222711002852_a2_b2 @ ( product_Pair_a1_a2 @ Q4 @ X ) @ Y6 ) ) ) )
              @ ( transitions_a1_a2_b2 @ M6 ) )
            @ Qx ) ) ) ) ).

% h_out_code
thf(fact_1072_h__out__code,axiom,
    ( h_out_c1_c2_c2
    = ( ^ [M6: fsm_c1_c2_c2,Qx: product_prod_c1_c2] :
          ( case_o7804587446556304349set_c2 @ bot_bot_set_c2
          @ ^ [Yqs: set_c2] : Yqs
          @ ( set_as4859442375955252864_c2_c2
            @ ( image_3476314818743173753_c2_c2
              @ ( produc6902765745844349963_c2_c2
                @ ^ [Q4: c1] :
                    ( produc4107441253699297419_c2_c2
                    @ ^ [X: c2] :
                        ( produc4109393248294971062_c2_c2
                        @ ^ [Y6: c2,Q5: c1] : ( produc7786241149486573599_c2_c2 @ ( product_Pair_c1_c2 @ Q4 @ X ) @ Y6 ) ) ) )
              @ ( transitions_c1_c2_c2 @ M6 ) )
            @ Qx ) ) ) ) ).

% h_out_code
thf(fact_1073_h__out__code,axiom,
    ( h_out_b1_b2_c2
    = ( ^ [M6: fsm_b1_b2_c2,Qx: product_prod_b1_b2] :
          ( case_o7804587446556304349set_c2 @ bot_bot_set_c2
          @ ^ [Yqs: set_c2] : Yqs
          @ ( set_as931098894140112386_b2_c2
            @ ( image_1944000282315004540_b2_c2
              @ ( produc7149285773737124878_b2_c2
                @ ^ [Q4: b1] :
                    ( produc3478260840456950605_b2_c2
                    @ ^ [X: b2] :
                        ( produc1826235639036946681_b2_c2
                        @ ^ [Y6: c2,Q5: b1] : ( produc3857897667671433121_b2_c2 @ ( product_Pair_b1_b2 @ Q4 @ X ) @ Y6 ) ) ) )
              @ ( transitions_b1_b2_c2 @ M6 ) )
            @ Qx ) ) ) ) ).

% h_out_code
thf(fact_1074_h__out__code,axiom,
    ( h_out_a1_a2_c2
    = ( ^ [M6: fsm_a1_a2_c2,Qx: product_prod_a1_a2] :
          ( case_o7804587446556304349set_c2 @ bot_bot_set_c2
          @ ^ [Yqs: set_c2] : Yqs
          @ ( set_as6226127449179747716_a2_c2
            @ ( image_411685745886835327_a2_c2
              @ ( produc7395805801629899793_a2_c2
                @ ^ [Q4: a1] :
                    ( produc2849080427214603791_a2_c2
                    @ ^ [X: a2] :
                        ( produc8766450066633698108_a2_c2
                        @ ^ [Y6: c2,Q5: a1] : ( produc9152926222711068451_a2_c2 @ ( product_Pair_a1_a2 @ Q4 @ X ) @ Y6 ) ) ) )
              @ ( transitions_a1_a2_c2 @ M6 ) )
            @ Qx ) ) ) ) ).

% h_out_code
thf(fact_1075_h__out__code,axiom,
    ( h_out_c1_c2_nat
    = ( ^ [M6: fsm_c1_c2_nat,Qx: product_prod_c1_c2] :
          ( case_o3272889084017746073et_nat @ bot_bot_set_nat
          @ ^ [Yqs: set_nat] : Yqs
          @ ( set_as5227129022533183518c2_nat
            @ ( image_3615733775990493109c2_nat
              @ ( produc4298405509114560967c2_nat
                @ ^ [Q4: c1] :
                    ( produc8850459140261213383c2_nat
                    @ ^ [X: c2] :
                        ( produc1092674067301285746c2_nat
                        @ ^ [Y6: nat,Q5: c1] : ( produc6479004527688444733c2_nat @ ( product_Pair_c1_c2 @ Q4 @ X ) @ Y6 ) ) ) )
              @ ( transi2084939702413591072c2_nat @ M6 ) )
            @ Qx ) ) ) ) ).

% h_out_code
thf(fact_1076_h__out__code,axiom,
    ( h_out_b1_b2_nat
    = ( ^ [M6: fsm_b1_b2_nat,Qx: product_prod_b1_b2] :
          ( case_o3272889084017746073et_nat @ bot_bot_set_nat
          @ ^ [Yqs: set_nat] : Yqs
          @ ( set_as6048040152840027296b2_nat
            @ ( image_3810186611424072504b2_nat
              @ ( produc4114563434916029770b2_nat
                @ ^ [Q4: b1] :
                    ( produc180919134490359305b2_nat
                    @ ^ [X: b2] :
                        ( produc3856812616753196341b2_nat
                        @ ^ [Y6: nat,Q5: b1] : ( produc7299915657995288511b2_nat @ ( product_Pair_b1_b2 @ Q4 @ X ) @ Y6 ) ) ) )
              @ ( transi2454530297511208738b2_nat @ M6 ) )
            @ Qx ) ) ) ) ).

% h_out_code
thf(fact_1077_h__out__code,axiom,
    ( h_out_a1_a2_nat
    = ( ^ [M6: fsm_a1_a2_nat,Qx: product_prod_a1_a2] :
          ( case_o3272889084017746073et_nat @ bot_bot_set_nat
          @ ^ [Yqs: set_nat] : Yqs
          @ ( set_as6868951283146871074a2_nat
            @ ( image_4004639446857651899a2_nat
              @ ( produc3930721360717498573a2_nat
                @ ^ [Q4: a1] :
                    ( produc734751165574281035a2_nat
                    @ ^ [X: a2] :
                        ( produc6620951166205106936a2_nat
                        @ ^ [Y6: nat,Q5: a1] : ( produc8120826788302132289a2_nat @ ( product_Pair_a1_a2 @ Q4 @ X ) @ Y6 ) ) ) )
              @ ( transi2824120892608826404a2_nat @ M6 ) )
            @ Qx ) ) ) ) ).

% h_out_code
thf(fact_1078_h__out__code,axiom,
    ( h_out_3266241837355465626_c2_b2
    = ( ^ [M6: fsm_ma8761726031752409769_c2_b2,Qx: produc4061897789176782763set_c2] :
          ( case_o3853413523431599071set_b2 @ bot_bot_set_b2
          @ ^ [Yqs: set_b2] : Yqs
          @ ( set_as5455615909052603816_c2_b2
            @ ( image_2117164528193270170_c2_b2
              @ ( produc1884001382256093484_c2_b2
                @ ^ [Q4: mapping_b1_set_b2] :
                    ( produc8228876167660460407_c2_b2
                    @ ^ [X: mapping_c1_set_c2] :
                        ( produc5447170038687108564_c2_b2
                        @ ^ [Y6: b2,Q5: mapping_b1_set_b2] : ( produc8088469960754140999_c2_b2 @ ( produc1212179418963815907set_c2 @ Q4 @ X ) @ Y6 ) ) ) )
              @ ( transi3351285373981281194_c2_b2 @ M6 ) )
            @ Qx ) ) ) ) ).

% h_out_code
thf(fact_1079_Diff__iff,axiom,
    ! [C: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ C @ ( minus_7665148276959638667_c1_c2 @ A2 @ B2 ) )
      = ( ( member1440383022217085037_c1_c2 @ C @ A2 )
        & ~ ( member1440383022217085037_c1_c2 @ C @ B2 ) ) ) ).

% Diff_iff
thf(fact_1080_Diff__iff,axiom,
    ! [C: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ C @ ( minus_3055363457872556045_b1_b2 @ A2 @ B2 ) )
      = ( ( member2075749735315954927_b1_b2 @ C @ A2 )
        & ~ ( member2075749735315954927_b1_b2 @ C @ B2 ) ) ) ).

% Diff_iff
thf(fact_1081_Diff__iff,axiom,
    ! [C: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ C @ ( minus_7668950675640249231_a1_a2 @ A2 @ B2 ) )
      = ( ( member2711116448414824817_a1_a2 @ C @ A2 )
        & ~ ( member2711116448414824817_a1_a2 @ C @ B2 ) ) ) ).

% Diff_iff
thf(fact_1082_Diff__iff,axiom,
    ! [C: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2,B2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ C @ ( minus_4895843051822776563set_c2 @ A2 @ B2 ) )
      = ( ( member341037065618468219set_c2 @ C @ A2 )
        & ~ ( member341037065618468219set_c2 @ C @ B2 ) ) ) ).

% Diff_iff
thf(fact_1083_Diff__iff,axiom,
    ! [C: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2,B2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ C @ ( minus_3844173815668582389set_b2 @ A2 @ B2 ) )
      = ( ( member6117332676589958525set_b2 @ C @ A2 )
        & ~ ( member6117332676589958525set_b2 @ C @ B2 ) ) ) ).

% Diff_iff
thf(fact_1084_DiffI,axiom,
    ! [C: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ C @ A2 )
     => ( ~ ( member1440383022217085037_c1_c2 @ C @ B2 )
       => ( member1440383022217085037_c1_c2 @ C @ ( minus_7665148276959638667_c1_c2 @ A2 @ B2 ) ) ) ) ).

% DiffI
thf(fact_1085_DiffI,axiom,
    ! [C: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ C @ A2 )
     => ( ~ ( member2075749735315954927_b1_b2 @ C @ B2 )
       => ( member2075749735315954927_b1_b2 @ C @ ( minus_3055363457872556045_b1_b2 @ A2 @ B2 ) ) ) ) ).

% DiffI
thf(fact_1086_DiffI,axiom,
    ! [C: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ C @ A2 )
     => ( ~ ( member2711116448414824817_a1_a2 @ C @ B2 )
       => ( member2711116448414824817_a1_a2 @ C @ ( minus_7668950675640249231_a1_a2 @ A2 @ B2 ) ) ) ) ).

% DiffI
thf(fact_1087_DiffI,axiom,
    ! [C: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2,B2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ C @ A2 )
     => ( ~ ( member341037065618468219set_c2 @ C @ B2 )
       => ( member341037065618468219set_c2 @ C @ ( minus_4895843051822776563set_c2 @ A2 @ B2 ) ) ) ) ).

% DiffI
thf(fact_1088_DiffI,axiom,
    ! [C: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2,B2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ C @ A2 )
     => ( ~ ( member6117332676589958525set_b2 @ C @ B2 )
       => ( member6117332676589958525set_b2 @ C @ ( minus_3844173815668582389set_b2 @ A2 @ B2 ) ) ) ) ).

% DiffI
thf(fact_1089_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
    ! [A: nat] :
      ( ( minus_minus_nat @ A @ A )
      = zero_zero_nat ) ).

% cancel_comm_monoid_add_class.diff_cancel
thf(fact_1090_diff__zero,axiom,
    ! [A: nat] :
      ( ( minus_minus_nat @ A @ zero_zero_nat )
      = A ) ).

% diff_zero
thf(fact_1091_zero__diff,axiom,
    ! [A: nat] :
      ( ( minus_minus_nat @ zero_zero_nat @ A )
      = zero_zero_nat ) ).

% zero_diff
thf(fact_1092_Diff__cancel,axiom,
    ! [A2: set_b2] :
      ( ( minus_minus_set_b2 @ A2 @ A2 )
      = bot_bot_set_b2 ) ).

% Diff_cancel
thf(fact_1093_Diff__cancel,axiom,
    ! [A2: set_c2] :
      ( ( minus_minus_set_c2 @ A2 @ A2 )
      = bot_bot_set_c2 ) ).

% Diff_cancel
thf(fact_1094_Diff__cancel,axiom,
    ! [A2: set_nat] :
      ( ( minus_minus_set_nat @ A2 @ A2 )
      = bot_bot_set_nat ) ).

% Diff_cancel
thf(fact_1095_empty__Diff,axiom,
    ! [A2: set_b2] :
      ( ( minus_minus_set_b2 @ bot_bot_set_b2 @ A2 )
      = bot_bot_set_b2 ) ).

% empty_Diff
thf(fact_1096_empty__Diff,axiom,
    ! [A2: set_c2] :
      ( ( minus_minus_set_c2 @ bot_bot_set_c2 @ A2 )
      = bot_bot_set_c2 ) ).

% empty_Diff
thf(fact_1097_empty__Diff,axiom,
    ! [A2: set_nat] :
      ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
      = bot_bot_set_nat ) ).

% empty_Diff
thf(fact_1098_Diff__empty,axiom,
    ! [A2: set_b2] :
      ( ( minus_minus_set_b2 @ A2 @ bot_bot_set_b2 )
      = A2 ) ).

% Diff_empty
thf(fact_1099_Diff__empty,axiom,
    ! [A2: set_c2] :
      ( ( minus_minus_set_c2 @ A2 @ bot_bot_set_c2 )
      = A2 ) ).

% Diff_empty
thf(fact_1100_Diff__empty,axiom,
    ! [A2: set_nat] :
      ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
      = A2 ) ).

% Diff_empty
thf(fact_1101_insert__Diff1,axiom,
    ! [X2: b2,B2: set_b2,A2: set_b2] :
      ( ( member_b2 @ X2 @ B2 )
     => ( ( minus_minus_set_b2 @ ( insert_b2 @ X2 @ A2 ) @ B2 )
        = ( minus_minus_set_b2 @ A2 @ B2 ) ) ) ).

% insert_Diff1
thf(fact_1102_insert__Diff1,axiom,
    ! [X2: c2,B2: set_c2,A2: set_c2] :
      ( ( member_c2 @ X2 @ B2 )
     => ( ( minus_minus_set_c2 @ ( insert_c2 @ X2 @ A2 ) @ B2 )
        = ( minus_minus_set_c2 @ A2 @ B2 ) ) ) ).

% insert_Diff1
thf(fact_1103_insert__Diff1,axiom,
    ! [X2: nat,B2: set_nat,A2: set_nat] :
      ( ( member_nat @ X2 @ B2 )
     => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A2 ) @ B2 )
        = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).

% insert_Diff1
thf(fact_1104_insert__Diff1,axiom,
    ! [X2: product_prod_c1_c2,B2: set_Pr9202269149784407460_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ X2 @ B2 )
     => ( ( minus_7665148276959638667_c1_c2 @ ( insert7158109610518197396_c1_c2 @ X2 @ A2 ) @ B2 )
        = ( minus_7665148276959638667_c1_c2 @ A2 @ B2 ) ) ) ).

% insert_Diff1
thf(fact_1105_insert__Diff1,axiom,
    ! [X2: product_prod_b1_b2,B2: set_Pr4592484330697324838_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ X2 @ B2 )
     => ( ( minus_3055363457872556045_b1_b2 @ ( insert7793476323617067286_b1_b2 @ X2 @ A2 ) @ B2 )
        = ( minus_3055363457872556045_b1_b2 @ A2 @ B2 ) ) ) ).

% insert_Diff1
thf(fact_1106_insert__Diff1,axiom,
    ! [X2: product_prod_a1_a2,B2: set_Pr9206071548465018024_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ X2 @ B2 )
     => ( ( minus_7668950675640249231_a1_a2 @ ( insert8428843036715937176_a1_a2 @ X2 @ A2 ) @ B2 )
        = ( minus_7668950675640249231_a1_a2 @ A2 @ B2 ) ) ) ).

% insert_Diff1
thf(fact_1107_insert__Diff1,axiom,
    ! [X2: mapping_c1_set_c2,B2: set_ma7306327908849618074set_c2,A2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ X2 @ B2 )
     => ( ( minus_4895843051822776563set_c2 @ ( insert88652402460333204set_c2 @ X2 @ A2 ) @ B2 )
        = ( minus_4895843051822776563set_c2 @ A2 @ B2 ) ) ) ).

% insert_Diff1
thf(fact_1108_insert__Diff1,axiom,
    ! [X2: mapping_b1_set_b2,B2: set_ma6254658672695423900set_b2,A2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ X2 @ B2 )
     => ( ( minus_3844173815668582389set_b2 @ ( insert5864948013431823510set_b2 @ X2 @ A2 ) @ B2 )
        = ( minus_3844173815668582389set_b2 @ A2 @ B2 ) ) ) ).

% insert_Diff1
thf(fact_1109_Diff__insert0,axiom,
    ! [X2: b2,A2: set_b2,B2: set_b2] :
      ( ~ ( member_b2 @ X2 @ A2 )
     => ( ( minus_minus_set_b2 @ A2 @ ( insert_b2 @ X2 @ B2 ) )
        = ( minus_minus_set_b2 @ A2 @ B2 ) ) ) ).

% Diff_insert0
thf(fact_1110_Diff__insert0,axiom,
    ! [X2: c2,A2: set_c2,B2: set_c2] :
      ( ~ ( member_c2 @ X2 @ A2 )
     => ( ( minus_minus_set_c2 @ A2 @ ( insert_c2 @ X2 @ B2 ) )
        = ( minus_minus_set_c2 @ A2 @ B2 ) ) ) ).

% Diff_insert0
thf(fact_1111_Diff__insert0,axiom,
    ! [X2: nat,A2: set_nat,B2: set_nat] :
      ( ~ ( member_nat @ X2 @ A2 )
     => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ B2 ) )
        = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).

% Diff_insert0
thf(fact_1112_Diff__insert0,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B2: set_Pr9202269149784407460_c1_c2] :
      ( ~ ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( minus_7665148276959638667_c1_c2 @ A2 @ ( insert7158109610518197396_c1_c2 @ X2 @ B2 ) )
        = ( minus_7665148276959638667_c1_c2 @ A2 @ B2 ) ) ) ).

% Diff_insert0
thf(fact_1113_Diff__insert0,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B2: set_Pr4592484330697324838_b1_b2] :
      ( ~ ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ( minus_3055363457872556045_b1_b2 @ A2 @ ( insert7793476323617067286_b1_b2 @ X2 @ B2 ) )
        = ( minus_3055363457872556045_b1_b2 @ A2 @ B2 ) ) ) ).

% Diff_insert0
thf(fact_1114_Diff__insert0,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B2: set_Pr9206071548465018024_a1_a2] :
      ( ~ ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ( minus_7668950675640249231_a1_a2 @ A2 @ ( insert8428843036715937176_a1_a2 @ X2 @ B2 ) )
        = ( minus_7668950675640249231_a1_a2 @ A2 @ B2 ) ) ) ).

% Diff_insert0
thf(fact_1115_Diff__insert0,axiom,
    ! [X2: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2,B2: set_ma7306327908849618074set_c2] :
      ( ~ ( member341037065618468219set_c2 @ X2 @ A2 )
     => ( ( minus_4895843051822776563set_c2 @ A2 @ ( insert88652402460333204set_c2 @ X2 @ B2 ) )
        = ( minus_4895843051822776563set_c2 @ A2 @ B2 ) ) ) ).

% Diff_insert0
thf(fact_1116_Diff__insert0,axiom,
    ! [X2: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2,B2: set_ma6254658672695423900set_b2] :
      ( ~ ( member6117332676589958525set_b2 @ X2 @ A2 )
     => ( ( minus_3844173815668582389set_b2 @ A2 @ ( insert5864948013431823510set_b2 @ X2 @ B2 ) )
        = ( minus_3844173815668582389set_b2 @ A2 @ B2 ) ) ) ).

% Diff_insert0
thf(fact_1117_less__prod__simps,axiom,
    ! [Leq_a: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,Less_a: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,Less_b: ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o,X1: b1 > option_set_b2,X22: c1 > option_set_c2,Y1: b1 > option_set_b2,Y2: c1 > option_set_c2] :
      ( ( contai8407464508621859084set_c2 @ Leq_a @ Less_a @ Less_b @ ( produc890782565133688235set_c2 @ X1 @ X22 ) @ ( produc890782565133688235set_c2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Less_b @ X22 @ Y2 ) ) ) ) ).

% less_prod_simps
thf(fact_1118_less__prod__simps,axiom,
    ! [Leq_a: mapping_b1_set_b2 > mapping_b1_set_b2 > $o,Less_a: mapping_b1_set_b2 > mapping_b1_set_b2 > $o,Less_b: mapping_c1_set_c2 > mapping_c1_set_c2 > $o,X1: mapping_b1_set_b2,X22: mapping_c1_set_c2,Y1: mapping_b1_set_b2,Y2: mapping_c1_set_c2] :
      ( ( contai6005974929653906500set_c2 @ Leq_a @ Less_a @ Less_b @ ( produc1212179418963815907set_c2 @ X1 @ X22 ) @ ( produc1212179418963815907set_c2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Less_b @ X22 @ Y2 ) ) ) ) ).

% less_prod_simps
thf(fact_1119_less__prod__simps,axiom,
    ! [Leq_a: ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o,Less_a: ( c1 > option_set_c2 ) > ( c1 > option_set_c2 ) > $o,Less_b: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,X1: c1 > option_set_c2,X22: b1 > option_set_b2,Y1: c1 > option_set_c2,Y2: b1 > option_set_b2] :
      ( ( contai2799764470782511372set_b2 @ Leq_a @ Less_a @ Less_b @ ( produc4506454564149116331set_b2 @ X1 @ X22 ) @ ( produc4506454564149116331set_b2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Less_b @ X22 @ Y2 ) ) ) ) ).

% less_prod_simps
thf(fact_1120_less__prod__simps,axiom,
    ! [Leq_a: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,Less_a: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,Less_b: ( b1 > option_set_b2 ) > ( b1 > option_set_b2 ) > $o,X1: b1 > option_set_b2,X22: b1 > option_set_b2,Y1: b1 > option_set_b2,Y2: b1 > option_set_b2] :
      ( ( contai2668647468241185550set_b2 @ Leq_a @ Less_a @ Less_b @ ( produc4375337561607790509set_b2 @ X1 @ X22 ) @ ( produc4375337561607790509set_b2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Less_b @ X22 @ Y2 ) ) ) ) ).

% less_prod_simps
thf(fact_1121_less__prod__simps,axiom,
    ! [Leq_a: c1 > c1 > $o,Less_a: c1 > c1 > $o,Less_b: c2 > c2 > $o,X1: c1,X22: c2,Y1: c1,Y2: c2] :
      ( ( contai1115268768815788637_c1_c2 @ Leq_a @ Less_a @ Less_b @ ( product_Pair_c1_c2 @ X1 @ X22 ) @ ( product_Pair_c1_c2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Less_b @ X22 @ Y2 ) ) ) ) ).

% less_prod_simps
thf(fact_1122_less__prod__simps,axiom,
    ! [Leq_a: b1 > b1 > $o,Less_a: b1 > b1 > $o,Less_b: b2 > b2 > $o,X1: b1,X22: b2,Y1: b1,Y2: b2] :
      ( ( contai1750917769420709727_b1_b2 @ Leq_a @ Less_a @ Less_b @ ( product_Pair_b1_b2 @ X1 @ X22 ) @ ( product_Pair_b1_b2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Less_b @ X22 @ Y2 ) ) ) ) ).

% less_prod_simps
thf(fact_1123_less__prod__simps,axiom,
    ! [Leq_a: a1 > a1 > $o,Less_a: a1 > a1 > $o,Less_b: a2 > a2 > $o,X1: a1,X22: a2,Y1: a1,Y2: a2] :
      ( ( contai2386566770025630817_a1_a2 @ Leq_a @ Less_a @ Less_b @ ( product_Pair_a1_a2 @ X1 @ X22 ) @ ( product_Pair_a1_a2 @ Y1 @ Y2 ) )
      = ( ( Less_a @ X1 @ Y1 )
        | ( ( Leq_a @ X1 @ Y1 )
          & ( Less_b @ X22 @ Y2 ) ) ) ) ).

% less_prod_simps
thf(fact_1124_insert__Diff__single,axiom,
    ! [A: b2,A2: set_b2] :
      ( ( insert_b2 @ A @ ( minus_minus_set_b2 @ A2 @ ( insert_b2 @ A @ bot_bot_set_b2 ) ) )
      = ( insert_b2 @ A @ A2 ) ) ).

% insert_Diff_single
thf(fact_1125_insert__Diff__single,axiom,
    ! [A: c2,A2: set_c2] :
      ( ( insert_c2 @ A @ ( minus_minus_set_c2 @ A2 @ ( insert_c2 @ A @ bot_bot_set_c2 ) ) )
      = ( insert_c2 @ A @ A2 ) ) ).

% insert_Diff_single
thf(fact_1126_insert__Diff__single,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
      = ( insert_nat @ A @ A2 ) ) ).

% insert_Diff_single
thf(fact_1127_set__diff__eq,axiom,
    ( minus_7665148276959638667_c1_c2
    = ( ^ [A6: set_Pr9202269149784407460_c1_c2,B6: set_Pr9202269149784407460_c1_c2] :
          ( collec5229596525471704495_c1_c2
          @ ^ [X: product_prod_c1_c2] :
              ( ( member1440383022217085037_c1_c2 @ X @ A6 )
              & ~ ( member1440383022217085037_c1_c2 @ X @ B6 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1128_set__diff__eq,axiom,
    ( minus_3055363457872556045_b1_b2
    = ( ^ [A6: set_Pr4592484330697324838_b1_b2,B6: set_Pr4592484330697324838_b1_b2] :
          ( collec5864963238570574385_b1_b2
          @ ^ [X: product_prod_b1_b2] :
              ( ( member2075749735315954927_b1_b2 @ X @ A6 )
              & ~ ( member2075749735315954927_b1_b2 @ X @ B6 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1129_set__diff__eq,axiom,
    ( minus_7668950675640249231_a1_a2
    = ( ^ [A6: set_Pr9206071548465018024_a1_a2,B6: set_Pr9206071548465018024_a1_a2] :
          ( collec6500329951669444275_a1_a2
          @ ^ [X: product_prod_a1_a2] :
              ( ( member2711116448414824817_a1_a2 @ X @ A6 )
              & ~ ( member2711116448414824817_a1_a2 @ X @ B6 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1130_set__diff__eq,axiom,
    ( minus_4895843051822776563set_c2
    = ( ^ [A6: set_ma7306327908849618074set_c2,B6: set_ma7306327908849618074set_c2] :
          ( collec787794305286987193set_c2
          @ ^ [X: mapping_c1_set_c2] :
              ( ( member341037065618468219set_c2 @ X @ A6 )
              & ~ ( member341037065618468219set_c2 @ X @ B6 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1131_set__diff__eq,axiom,
    ( minus_3844173815668582389set_b2
    = ( ^ [A6: set_ma6254658672695423900set_b2,B6: set_ma6254658672695423900set_b2] :
          ( collec6564089916258477499set_b2
          @ ^ [X: mapping_b1_set_b2] :
              ( ( member6117332676589958525set_b2 @ X @ A6 )
              & ~ ( member6117332676589958525set_b2 @ X @ B6 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1132_set__diff__eq,axiom,
    ( minus_minus_set_nat
    = ( ^ [A6: set_nat,B6: set_nat] :
          ( collect_nat
          @ ^ [X: nat] :
              ( ( member_nat @ X @ A6 )
              & ~ ( member_nat @ X @ B6 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1133_set__diff__eq,axiom,
    ( minus_minus_set_c2
    = ( ^ [A6: set_c2,B6: set_c2] :
          ( collect_c2
          @ ^ [X: c2] :
              ( ( member_c2 @ X @ A6 )
              & ~ ( member_c2 @ X @ B6 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1134_set__diff__eq,axiom,
    ( minus_minus_set_b2
    = ( ^ [A6: set_b2,B6: set_b2] :
          ( collect_b2
          @ ^ [X: b2] :
              ( ( member_b2 @ X @ A6 )
              & ~ ( member_b2 @ X @ B6 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1135_DiffD2,axiom,
    ! [C: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ C @ ( minus_7665148276959638667_c1_c2 @ A2 @ B2 ) )
     => ~ ( member1440383022217085037_c1_c2 @ C @ B2 ) ) ).

% DiffD2
thf(fact_1136_DiffD2,axiom,
    ! [C: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ C @ ( minus_3055363457872556045_b1_b2 @ A2 @ B2 ) )
     => ~ ( member2075749735315954927_b1_b2 @ C @ B2 ) ) ).

% DiffD2
thf(fact_1137_DiffD2,axiom,
    ! [C: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ C @ ( minus_7668950675640249231_a1_a2 @ A2 @ B2 ) )
     => ~ ( member2711116448414824817_a1_a2 @ C @ B2 ) ) ).

% DiffD2
thf(fact_1138_DiffD2,axiom,
    ! [C: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2,B2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ C @ ( minus_4895843051822776563set_c2 @ A2 @ B2 ) )
     => ~ ( member341037065618468219set_c2 @ C @ B2 ) ) ).

% DiffD2
thf(fact_1139_DiffD2,axiom,
    ! [C: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2,B2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ C @ ( minus_3844173815668582389set_b2 @ A2 @ B2 ) )
     => ~ ( member6117332676589958525set_b2 @ C @ B2 ) ) ).

% DiffD2
thf(fact_1140_DiffD1,axiom,
    ! [C: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ C @ ( minus_7665148276959638667_c1_c2 @ A2 @ B2 ) )
     => ( member1440383022217085037_c1_c2 @ C @ A2 ) ) ).

% DiffD1
thf(fact_1141_DiffD1,axiom,
    ! [C: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ C @ ( minus_3055363457872556045_b1_b2 @ A2 @ B2 ) )
     => ( member2075749735315954927_b1_b2 @ C @ A2 ) ) ).

% DiffD1
thf(fact_1142_DiffD1,axiom,
    ! [C: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ C @ ( minus_7668950675640249231_a1_a2 @ A2 @ B2 ) )
     => ( member2711116448414824817_a1_a2 @ C @ A2 ) ) ).

% DiffD1
thf(fact_1143_DiffD1,axiom,
    ! [C: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2,B2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ C @ ( minus_4895843051822776563set_c2 @ A2 @ B2 ) )
     => ( member341037065618468219set_c2 @ C @ A2 ) ) ).

% DiffD1
thf(fact_1144_DiffD1,axiom,
    ! [C: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2,B2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ C @ ( minus_3844173815668582389set_b2 @ A2 @ B2 ) )
     => ( member6117332676589958525set_b2 @ C @ A2 ) ) ).

% DiffD1
thf(fact_1145_DiffE,axiom,
    ! [C: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2,B2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ C @ ( minus_7665148276959638667_c1_c2 @ A2 @ B2 ) )
     => ~ ( ( member1440383022217085037_c1_c2 @ C @ A2 )
         => ( member1440383022217085037_c1_c2 @ C @ B2 ) ) ) ).

% DiffE
thf(fact_1146_DiffE,axiom,
    ! [C: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2,B2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ C @ ( minus_3055363457872556045_b1_b2 @ A2 @ B2 ) )
     => ~ ( ( member2075749735315954927_b1_b2 @ C @ A2 )
         => ( member2075749735315954927_b1_b2 @ C @ B2 ) ) ) ).

% DiffE
thf(fact_1147_DiffE,axiom,
    ! [C: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2,B2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ C @ ( minus_7668950675640249231_a1_a2 @ A2 @ B2 ) )
     => ~ ( ( member2711116448414824817_a1_a2 @ C @ A2 )
         => ( member2711116448414824817_a1_a2 @ C @ B2 ) ) ) ).

% DiffE
thf(fact_1148_DiffE,axiom,
    ! [C: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2,B2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ C @ ( minus_4895843051822776563set_c2 @ A2 @ B2 ) )
     => ~ ( ( member341037065618468219set_c2 @ C @ A2 )
         => ( member341037065618468219set_c2 @ C @ B2 ) ) ) ).

% DiffE
thf(fact_1149_DiffE,axiom,
    ! [C: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2,B2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ C @ ( minus_3844173815668582389set_b2 @ A2 @ B2 ) )
     => ~ ( ( member6117332676589958525set_b2 @ C @ A2 )
         => ( member6117332676589958525set_b2 @ C @ B2 ) ) ) ).

% DiffE
thf(fact_1150_h__out__alt__def,axiom,
    ! [M4: fsm_c1_c2_nat,Q2: c1,X2: c2] :
      ( ( h_out_c1_c2_nat @ M4 @ ( product_Pair_c1_c2 @ Q2 @ X2 ) )
      = ( collect_nat
        @ ^ [Uu: nat] :
          ? [T: produc3241757979290108727nat_c1] :
            ( ( Uu
              = ( product_fst_nat_c1 @ ( produc7336435173887311145nat_c1 @ ( produc270200811892208669nat_c1 @ T ) ) ) )
            & ( member3128768103774925024nat_c1 @ T @ ( transi2084939702413591072c2_nat @ M4 ) )
            & ( ( produc4276822746176773595nat_c1 @ T )
              = Q2 )
            & ( ( produc7565652559555057131nat_c1 @ ( produc270200811892208669nat_c1 @ T ) )
              = X2 ) ) ) ) ).

% h_out_alt_def
thf(fact_1151_h__out__alt__def,axiom,
    ! [M4: fsm_c1_c2_c2,Q2: c1,X2: c2] :
      ( ( h_out_c1_c2_c2 @ M4 @ ( product_Pair_c1_c2 @ Q2 @ X2 ) )
      = ( collect_c2
        @ ^ [Uu: c2] :
          ? [T: produc2542824572670609817_c2_c1] :
            ( ( Uu
              = ( product_fst_c2_c1 @ ( produc5489181492457034123_c2_c1 @ ( produc5050033203791246591_c2_c1 @ T ) ) ) )
            & ( member8472636576389039298_c2_c1 @ T @ ( transitions_c1_c2_c2 @ M4 ) )
            & ( ( produc961655714375637949_c2_c1 @ T )
              = Q2 )
            & ( ( produc8421445729417850189_c2_c1 @ ( produc5050033203791246591_c2_c1 @ T ) )
              = X2 ) ) ) ) ).

% h_out_alt_def
thf(fact_1152_h__out__alt__def,axiom,
    ! [M4: fsm_c1_c2_b2,Q2: c1,X2: c2] :
      ( ( h_out_c1_c2_b2 @ M4 @ ( product_Pair_c1_c2 @ Q2 @ X2 ) )
      = ( collect_b2
        @ ^ [Uu: b2] :
          ? [T: produc2995545231740769754_b2_c1] :
            ( ( Uu
              = ( product_fst_b2_c1 @ ( produc6124830493062020812_b2_c1 @ ( produc2399362773292650944_b2_c1 @ T ) ) ) )
            & ( member8925357235459199235_b2_c1 @ T @ ( transitions_c1_c2_b2 @ M4 ) )
            & ( ( produc7534357320731818110_b2_c1 @ T )
              = Q2 )
            & ( ( produc9057094730022836878_b2_c1 @ ( produc2399362773292650944_b2_c1 @ T ) )
              = X2 ) ) ) ) ).

% h_out_alt_def
thf(fact_1153_h__out__alt__def,axiom,
    ! [M4: fsm_b1_b2_nat,Q2: b1,X2: b2] :
      ( ( h_out_b1_b2_nat @ M4 @ ( product_Pair_b1_b2 @ Q2 @ X2 ) )
      = ( collect_nat
        @ ^ [Uu: nat] :
          ? [T: produc3104264649751066808nat_b1] :
            ( ( Uu
              = ( product_fst_nat_b1 @ ( produc3396204299756358121nat_b1 @ ( produc5537737292678728094nat_b1 @ T ) ) ) )
            & ( member2991274774235883105nat_b1 @ T @ ( transi2454530297511208738b2_nat @ M4 ) )
            & ( ( produc320987190108517212nat_b1 @ T )
              = Q2 )
            & ( ( produc3625421685424104107nat_b1 @ ( produc5537737292678728094nat_b1 @ T ) )
              = X2 ) ) ) ) ).

% h_out_alt_def
thf(fact_1154_h__out__alt__def,axiom,
    ! [M4: fsm_b1_b2_c2,Q2: b1,X2: b2] :
      ( ( h_out_b1_b2_c2 @ M4 @ ( product_Pair_b1_b2 @ Q2 @ X2 ) )
      = ( collect_c2
        @ ^ [Uu: c2] :
          ? [T: produc7422474658093489946_c2_b1] :
            ( ( Uu
              = ( product_fst_c2_b1 @ ( produc8592423287667002571_c2_b1 @ ( produc7839628770475960960_c2_b1 @ T ) ) ) )
            & ( member4128914624957143619_c2_b1 @ T @ ( transitions_b1_b2_c2 @ M4 ) )
            & ( ( produc3751251281060352318_c2_b1 @ T )
              = Q2 )
            & ( ( produc2301315487773042829_c2_b1 @ ( produc7839628770475960960_c2_b1 @ T ) )
              = X2 ) ) ) ) ).

% h_out_alt_def
thf(fact_1155_h__out__alt__def,axiom,
    ! [M4: fsm_b1_b2_b2,Q2: b1,X2: b2] :
      ( ( h_out_b1_b2_b2 @ M4 @ ( product_Pair_b1_b2 @ Q2 @ X2 ) )
      = ( collect_b2
        @ ^ [Uu: b2] :
          ? [T: produc7875195317163649883_b2_b1] :
            ( ( Uu
              = ( product_fst_b2_b1 @ ( produc4700251417213452_b2_b1 @ ( produc5188958339977365313_b2_b1 @ T ) ) ) )
            & ( member4581635284027303556_b2_b1 @ T @ ( transitions_b1_b2_b2 @ M4 ) )
            & ( ( produc1100580850561756671_b2_b1 @ T )
              = Q2 )
            & ( ( produc2936964488378029518_b2_b1 @ ( produc5188958339977365313_b2_b1 @ T ) )
              = X2 ) ) ) ) ).

% h_out_alt_def
thf(fact_1156_h__out__alt__def,axiom,
    ! [M4: fsm_a1_a2_nat,Q2: a1,X2: a2] :
      ( ( h_out_a1_a2_nat @ M4 @ ( product_Pair_a1_a2 @ Q2 @ X2 ) )
      = ( collect_nat
        @ ^ [Uu: nat] :
          ? [T: produc2966771320212024889nat_a1] :
            ( ( Uu
              = ( product_fst_nat_a1 @ ( produc8679345462480180905nat_a1 @ ( produc1581901736610471711nat_a1 @ T ) ) ) )
            & ( member2853781444696841186nat_a1 @ T @ ( transi2824120892608826404a2_nat @ M4 ) )
            & ( ( produc5588523670895036637nat_a1 @ T )
              = Q2 )
            & ( ( produc8908562848147926891nat_a1 @ ( produc1581901736610471711nat_a1 @ T ) )
              = X2 ) ) ) ) ).

% h_out_alt_def
thf(fact_1157_h__out__alt__def,axiom,
    ! [M4: fsm_a1_a2_c2,Q2: a1,X2: a2] :
      ( ( h_out_a1_a2_c2 @ M4 @ ( product_Pair_a1_a2 @ Q2 @ X2 ) )
      = ( collect_c2
        @ ^ [Uu: c2] :
          ? [T: produc3078752706661594267_c2_a1] :
            ( ( Uu
              = ( product_fst_c2_a1 @ ( produc2472293046022195211_c2_a1 @ ( produc1405852300305899521_c2_a1 @ T ) ) ) )
            & ( member9008564710380023748_c2_a1 @ T @ ( transitions_a1_a2_c2 @ M4 ) )
            & ( ( produc6540846847745066687_c2_a1 @ T )
              = Q2 )
            & ( ( produc5404557282983011277_c2_a1 @ ( produc1405852300305899521_c2_a1 @ T ) )
              = X2 ) ) ) ) ).

% h_out_alt_def
thf(fact_1158_h__out__alt__def,axiom,
    ! [M4: fsm_a1_a2_b2,Q2: a1,X2: a2] :
      ( ( h_out_a1_a2_b2 @ M4 @ ( product_Pair_a1_a2 @ Q2 @ X2 ) )
      = ( collect_b2
        @ ^ [Uu: b2] :
          ? [T: produc3531473365731754204_b2_a1] :
            ( ( Uu
              = ( product_fst_b2_a1 @ ( produc3107942046627181900_b2_a1 @ ( produc7978553906662079682_b2_a1 @ T ) ) ) )
            & ( member237913332595407877_b2_a1 @ T @ ( transitions_a1_a2_b2 @ M4 ) )
            & ( ( produc3890176417246471040_b2_a1 @ T )
              = Q2 )
            & ( ( produc6040206283587997966_b2_a1 @ ( produc7978553906662079682_b2_a1 @ T ) )
              = X2 ) ) ) ) ).

% h_out_alt_def
thf(fact_1159_h__out__alt__def,axiom,
    ! [M4: fsm_ma3562454073340529286c2_nat,Q2: mapping_b1_set_b2,X2: mapping_c1_set_c2] :
      ( ( h_out_6598019409568368631c2_nat @ M4 @ ( produc1212179418963815907set_c2 @ Q2 @ X2 ) )
      = ( collect_nat
        @ ^ [Uu: nat] :
          ? [T: produc5623429682246142959set_b2] :
            ( ( Uu
              = ( produc8741527518219369531set_b2 @ ( produc5142812559059572012set_b2 @ ( produc2294650927625083477set_b2 @ T ) ) ) )
            & ( member3857524843657475480set_b2 @ T @ ( transi1170656512200261639c2_nat @ M4 ) )
            & ( ( produc2478237369292639251set_b2 @ T )
              = Q2 )
            & ( ( produc5923294967876517358set_b2 @ ( produc2294650927625083477set_b2 @ T ) )
              = X2 ) ) ) ) ).

% h_out_alt_def
thf(fact_1160_insert__Diff__if,axiom,
    ! [X2: b2,B2: set_b2,A2: set_b2] :
      ( ( ( member_b2 @ X2 @ B2 )
       => ( ( minus_minus_set_b2 @ ( insert_b2 @ X2 @ A2 ) @ B2 )
          = ( minus_minus_set_b2 @ A2 @ B2 ) ) )
      & ( ~ ( member_b2 @ X2 @ B2 )
       => ( ( minus_minus_set_b2 @ ( insert_b2 @ X2 @ A2 ) @ B2 )
          = ( insert_b2 @ X2 @ ( minus_minus_set_b2 @ A2 @ B2 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1161_insert__Diff__if,axiom,
    ! [X2: c2,B2: set_c2,A2: set_c2] :
      ( ( ( member_c2 @ X2 @ B2 )
       => ( ( minus_minus_set_c2 @ ( insert_c2 @ X2 @ A2 ) @ B2 )
          = ( minus_minus_set_c2 @ A2 @ B2 ) ) )
      & ( ~ ( member_c2 @ X2 @ B2 )
       => ( ( minus_minus_set_c2 @ ( insert_c2 @ X2 @ A2 ) @ B2 )
          = ( insert_c2 @ X2 @ ( minus_minus_set_c2 @ A2 @ B2 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1162_insert__Diff__if,axiom,
    ! [X2: nat,B2: set_nat,A2: set_nat] :
      ( ( ( member_nat @ X2 @ B2 )
       => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A2 ) @ B2 )
          = ( minus_minus_set_nat @ A2 @ B2 ) ) )
      & ( ~ ( member_nat @ X2 @ B2 )
       => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A2 ) @ B2 )
          = ( insert_nat @ X2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1163_insert__Diff__if,axiom,
    ! [X2: product_prod_c1_c2,B2: set_Pr9202269149784407460_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( ( member1440383022217085037_c1_c2 @ X2 @ B2 )
       => ( ( minus_7665148276959638667_c1_c2 @ ( insert7158109610518197396_c1_c2 @ X2 @ A2 ) @ B2 )
          = ( minus_7665148276959638667_c1_c2 @ A2 @ B2 ) ) )
      & ( ~ ( member1440383022217085037_c1_c2 @ X2 @ B2 )
       => ( ( minus_7665148276959638667_c1_c2 @ ( insert7158109610518197396_c1_c2 @ X2 @ A2 ) @ B2 )
          = ( insert7158109610518197396_c1_c2 @ X2 @ ( minus_7665148276959638667_c1_c2 @ A2 @ B2 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1164_insert__Diff__if,axiom,
    ! [X2: product_prod_b1_b2,B2: set_Pr4592484330697324838_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( ( member2075749735315954927_b1_b2 @ X2 @ B2 )
       => ( ( minus_3055363457872556045_b1_b2 @ ( insert7793476323617067286_b1_b2 @ X2 @ A2 ) @ B2 )
          = ( minus_3055363457872556045_b1_b2 @ A2 @ B2 ) ) )
      & ( ~ ( member2075749735315954927_b1_b2 @ X2 @ B2 )
       => ( ( minus_3055363457872556045_b1_b2 @ ( insert7793476323617067286_b1_b2 @ X2 @ A2 ) @ B2 )
          = ( insert7793476323617067286_b1_b2 @ X2 @ ( minus_3055363457872556045_b1_b2 @ A2 @ B2 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1165_insert__Diff__if,axiom,
    ! [X2: product_prod_a1_a2,B2: set_Pr9206071548465018024_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( ( member2711116448414824817_a1_a2 @ X2 @ B2 )
       => ( ( minus_7668950675640249231_a1_a2 @ ( insert8428843036715937176_a1_a2 @ X2 @ A2 ) @ B2 )
          = ( minus_7668950675640249231_a1_a2 @ A2 @ B2 ) ) )
      & ( ~ ( member2711116448414824817_a1_a2 @ X2 @ B2 )
       => ( ( minus_7668950675640249231_a1_a2 @ ( insert8428843036715937176_a1_a2 @ X2 @ A2 ) @ B2 )
          = ( insert8428843036715937176_a1_a2 @ X2 @ ( minus_7668950675640249231_a1_a2 @ A2 @ B2 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1166_insert__Diff__if,axiom,
    ! [X2: mapping_c1_set_c2,B2: set_ma7306327908849618074set_c2,A2: set_ma7306327908849618074set_c2] :
      ( ( ( member341037065618468219set_c2 @ X2 @ B2 )
       => ( ( minus_4895843051822776563set_c2 @ ( insert88652402460333204set_c2 @ X2 @ A2 ) @ B2 )
          = ( minus_4895843051822776563set_c2 @ A2 @ B2 ) ) )
      & ( ~ ( member341037065618468219set_c2 @ X2 @ B2 )
       => ( ( minus_4895843051822776563set_c2 @ ( insert88652402460333204set_c2 @ X2 @ A2 ) @ B2 )
          = ( insert88652402460333204set_c2 @ X2 @ ( minus_4895843051822776563set_c2 @ A2 @ B2 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1167_insert__Diff__if,axiom,
    ! [X2: mapping_b1_set_b2,B2: set_ma6254658672695423900set_b2,A2: set_ma6254658672695423900set_b2] :
      ( ( ( member6117332676589958525set_b2 @ X2 @ B2 )
       => ( ( minus_3844173815668582389set_b2 @ ( insert5864948013431823510set_b2 @ X2 @ A2 ) @ B2 )
          = ( minus_3844173815668582389set_b2 @ A2 @ B2 ) ) )
      & ( ~ ( member6117332676589958525set_b2 @ X2 @ B2 )
       => ( ( minus_3844173815668582389set_b2 @ ( insert5864948013431823510set_b2 @ X2 @ A2 ) @ B2 )
          = ( insert5864948013431823510set_b2 @ X2 @ ( minus_3844173815668582389set_b2 @ A2 @ B2 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1168_finite__snd__helper,axiom,
    ! [Xs2: set_Pr2267770373837101659_c2_c2,Q2: c1,P2: c2] :
      ( ( finite921781255737873084_c2_c2 @ Xs2 )
     => ( finite_finite_c2
        @ ( collect_c2
          @ ^ [Z: c2] : ( member4649867262780390844_c2_c2 @ ( produc7786241149486573599_c2_c2 @ ( product_Pair_c1_c2 @ Q2 @ P2 ) @ Z ) @ Xs2 ) ) ) ) ).

% finite_snd_helper
thf(fact_1169_finite__snd__helper,axiom,
    ! [Xs2: set_Pr308655985248614684_c2_b2,Q2: c1,P2: c2] :
      ( ( finite921498968231756285_c2_b2 @ Xs2 )
     => ( finite_finite_b2
        @ ( collect_b2
          @ ^ [Z: b2] : ( member4649584975274274045_c2_b2 @ ( produc7786241149486508000_c2_b2 @ ( product_Pair_c1_c2 @ Q2 @ P2 ) @ Z ) @ Xs2 ) ) ) ) ).

% finite_snd_helper
thf(fact_1170_finite__snd__helper,axiom,
    ! [Xs2: set_Pr2824962942362912377c2_nat,Q2: c1,P2: c2] :
      ( ( finite3440685243065785306c2_nat @ Xs2 )
     => ( finite_finite_nat
        @ ( collect_nat
          @ ^ [Z: nat] : ( member4264303227967407834c2_nat @ ( produc6479004527688444733c2_nat @ ( product_Pair_c1_c2 @ Q2 @ P2 ) @ Z ) @ Xs2 ) ) ) ) ).

% finite_snd_helper
thf(fact_1171_finite__snd__helper,axiom,
    ! [Xs2: set_Pr5605561542190788829_b2_c2,Q2: b1,P2: b2] :
      ( ( finite6216809810777508414_b2_c2 @ Xs2 )
     => ( finite_finite_c2
        @ ( collect_c2
          @ ^ [Z: c2] : ( member721523780965250366_b2_c2 @ ( produc3857897667671433121_b2_c2 @ ( product_Pair_b1_b2 @ Q2 @ P2 ) @ Z ) @ Xs2 ) ) ) ) ).

% finite_snd_helper
thf(fact_1172_finite__snd__helper,axiom,
    ! [Xs2: set_Pr3646447153602301854_b2_b2,Q2: b1,P2: b2] :
      ( ( finite6216527523271391615_b2_b2 @ Xs2 )
     => ( finite_finite_b2
        @ ( collect_b2
          @ ^ [Z: b2] : ( member721241493459133567_b2_b2 @ ( produc3857897667671367522_b2_b2 @ ( product_Pair_b1_b2 @ Q2 @ P2 ) @ Z ) @ Xs2 ) ) ) ) ).

% finite_snd_helper
thf(fact_1173_finite__snd__helper,axiom,
    ! [Xs2: set_Pr6819770292282554875b2_nat,Q2: b1,P2: b2] :
      ( ( finite4261596373372629084b2_nat @ Xs2 )
     => ( finite_finite_nat
        @ ( collect_nat
          @ ^ [Z: nat] : ( member5085214358274251612b2_nat @ ( produc7299915657995288511b2_nat @ ( product_Pair_b1_b2 @ Q2 @ P2 ) @ Z ) @ Xs2 ) ) ) ) ).

% finite_snd_helper
thf(fact_1174_finite__snd__helper,axiom,
    ! [Xs2: set_Pr8943352710544475999_a2_c2,Q2: a1,P2: a2] :
      ( ( finite2288466328962367936_a2_c2 @ Xs2 )
     => ( finite_finite_c2
        @ ( collect_c2
          @ ^ [Z: c2] : ( member6016552336004885696_a2_c2 @ ( produc9152926222711068451_a2_c2 @ ( product_Pair_a1_a2 @ Q2 @ P2 ) @ Z ) @ Xs2 ) ) ) ) ).

% finite_snd_helper
thf(fact_1175_finite__snd__helper,axiom,
    ! [Xs2: set_Pr6984238321955989024_a2_b2,Q2: a1,P2: a2] :
      ( ( finite2288184041456251137_a2_b2 @ Xs2 )
     => ( finite_finite_b2
        @ ( collect_b2
          @ ^ [Z: b2] : ( member6016270048498768897_a2_b2 @ ( produc9152926222711002852_a2_b2 @ ( product_Pair_a1_a2 @ Q2 @ P2 ) @ Z ) @ Xs2 ) ) ) ) ).

% finite_snd_helper
thf(fact_1176_finite__snd__helper,axiom,
    ! [Xs2: set_Pr1591205605347421565a2_nat,Q2: a1,P2: a2] :
      ( ( finite5082507503679472862a2_nat @ Xs2 )
     => ( finite_finite_nat
        @ ( collect_nat
          @ ^ [Z: nat] : ( member5906125488581095390a2_nat @ ( produc8120826788302132289a2_nat @ ( product_Pair_a1_a2 @ Q2 @ P2 ) @ Z ) @ Xs2 ) ) ) ) ).

% finite_snd_helper
thf(fact_1177_finite__snd__helper,axiom,
    ! [Xs2: set_Pr8355152109431543362_c2_c2,Q2: mapping_b1_set_b2,P2: mapping_c1_set_c2] :
      ( ( finite8055457123860967971_c2_c2 @ Xs2 )
     => ( finite_finite_c2
        @ ( collect_c2
          @ ^ [Z: c2] : ( member4770052056032943395_c2_c2 @ ( produc8088469960754206598_c2_c2 @ ( produc1212179418963815907set_c2 @ Q2 @ P2 ) @ Z ) @ Xs2 ) ) ) ) ).

% finite_snd_helper
thf(fact_1178_h__out_Osimps,axiom,
    ! [M4: fsm_c1_c2_nat,Q2: c1,X2: c2] :
      ( ( h_out_c1_c2_nat @ M4 @ ( product_Pair_c1_c2 @ Q2 @ X2 ) )
      = ( collect_nat
        @ ^ [Y6: nat] :
          ? [Q5: c1] : ( member3128768103774925024nat_c1 @ ( produc312663335071628783nat_c1 @ Q2 @ ( produc97587416969510103nat_c1 @ X2 @ ( product_Pair_nat_c1 @ Y6 @ Q5 ) ) ) @ ( transi2084939702413591072c2_nat @ M4 ) ) ) ) ).

% h_out.simps
thf(fact_1179_h__out_Osimps,axiom,
    ! [M4: fsm_c1_c2_c2,Q2: c1,X2: c2] :
      ( ( h_out_c1_c2_c2 @ M4 @ ( product_Pair_c1_c2 @ Q2 @ X2 ) )
      = ( collect_c2
        @ ^ [Y6: c2] :
          ? [Q5: c1] : ( member8472636576389039298_c2_c1 @ ( produc7456726006540687825_c2_c1 @ Q2 @ ( produc7668360288004781625_c2_c1 @ X2 @ ( product_Pair_c2_c1 @ Y6 @ Q5 ) ) ) @ ( transitions_c1_c2_c2 @ M4 ) ) ) ) ).

% h_out.simps
thf(fact_1180_h__out_Osimps,axiom,
    ! [M4: fsm_c1_c2_b2,Q2: c1,X2: c2] :
      ( ( h_out_c1_c2_b2 @ M4 @ ( product_Pair_c1_c2 @ Q2 @ X2 ) )
      = ( collect_b2
        @ ^ [Y6: b2] :
          ? [Q5: c1] : ( member8925357235459199235_b2_c1 @ ( produc4806055576042092178_b2_c1 @ Q2 @ ( produc8304009288609768314_b2_c1 @ X2 @ ( product_Pair_b2_c1 @ Y6 @ Q5 ) ) ) @ ( transitions_c1_c2_b2 @ M4 ) ) ) ) ).

% h_out.simps
thf(fact_1181_h__out_Osimps,axiom,
    ! [M4: fsm_b1_b2_nat,Q2: b1,X2: b2] :
      ( ( h_out_b1_b2_nat @ M4 @ ( product_Pair_b1_b2 @ Q2 @ X2 ) )
      = ( collect_nat
        @ ^ [Y6: nat] :
          ? [Q5: b1] : ( member2991274774235883105nat_b1 @ ( produc5580199815858148208nat_b1 @ Q2 @ ( produc5380728579693332887nat_b1 @ X2 @ ( product_Pair_nat_b1 @ Y6 @ Q5 ) ) ) @ ( transi2454530297511208738b2_nat @ M4 ) ) ) ) ).

% h_out.simps
thf(fact_1182_h__out_Osimps,axiom,
    ! [M4: fsm_b1_b2_c2,Q2: b1,X2: b2] :
      ( ( h_out_b1_b2_c2 @ M4 @ ( product_Pair_b1_b2 @ Q2 @ X2 ) )
      = ( collect_c2
        @ ^ [Y6: c2] :
          ? [Q5: b1] : ( member4128914624957143619_c2_b1 @ ( produc1022949536370626386_c2_b1 @ Q2 @ ( produc1548230046359974265_c2_b1 @ X2 @ ( product_Pair_c2_b1 @ Y6 @ Q5 ) ) ) @ ( transitions_b1_b2_c2 @ M4 ) ) ) ) ).

% h_out.simps
thf(fact_1183_h__out_Osimps,axiom,
    ! [M4: fsm_b1_b2_b2,Q2: b1,X2: b2] :
      ( ( h_out_b1_b2_b2 @ M4 @ ( product_Pair_b1_b2 @ Q2 @ X2 ) )
      = ( collect_b2
        @ ^ [Y6: b2] :
          ? [Q5: b1] : ( member4581635284027303556_b2_b1 @ ( produc7595651142726806547_b2_b1 @ Q2 @ ( produc2183879046964960954_b2_b1 @ X2 @ ( product_Pair_b2_b1 @ Y6 @ Q5 ) ) ) @ ( transitions_b1_b2_b2 @ M4 ) ) ) ) ).

% h_out.simps
thf(fact_1184_h__out_Osimps,axiom,
    ! [M4: fsm_a1_a2_nat,Q2: a1,X2: a2] :
      ( ( h_out_a1_a2_nat @ M4 @ ( product_Pair_a1_a2 @ Q2 @ X2 ) )
      = ( collect_nat
        @ ^ [Y6: nat] :
          ? [Q5: a1] : ( member2853781444696841186nat_a1 @ ( produc1624364259789891825nat_a1 @ Q2 @ ( produc1440497705562379863nat_a1 @ X2 @ ( product_Pair_nat_a1 @ Y6 @ Q5 ) ) ) @ ( transi2824120892608826404a2_nat @ M4 ) ) ) ) ).

% h_out.simps
thf(fact_1185_h__out_Osimps,axiom,
    ! [M4: fsm_a1_a2_c2,Q2: a1,X2: a2] :
      ( ( h_out_a1_a2_c2 @ M4 @ ( product_Pair_a1_a2 @ Q2 @ X2 ) )
      = ( collect_c2
        @ ^ [Y6: c2] :
          ? [Q5: a1] : ( member9008564710380023748_c2_a1 @ ( produc3812545103055340755_c2_a1 @ Q2 @ ( produc4651471841569942713_c2_a1 @ X2 @ ( product_Pair_c2_a1 @ Y6 @ Q5 ) ) ) @ ( transitions_a1_a2_c2 @ M4 ) ) ) ) ).

% h_out.simps
thf(fact_1186_h__out_Osimps,axiom,
    ! [M4: fsm_a1_a2_b2,Q2: a1,X2: a2] :
      ( ( h_out_a1_a2_b2 @ M4 @ ( product_Pair_a1_a2 @ Q2 @ X2 ) )
      = ( collect_b2
        @ ^ [Y6: b2] :
          ? [Q5: a1] : ( member237913332595407877_b2_a1 @ ( produc1161874672556745108_b2_a1 @ Q2 @ ( produc5287120842174929402_b2_a1 @ X2 @ ( product_Pair_b2_a1 @ Y6 @ Q5 ) ) ) @ ( transitions_a1_a2_b2 @ M4 ) ) ) ) ).

% h_out.simps
thf(fact_1187_h__out_Osimps,axiom,
    ! [M4: fsm_ma3562454073340529286c2_nat,Q2: mapping_b1_set_b2,X2: mapping_c1_set_c2] :
      ( ( h_out_6598019409568368631c2_nat @ M4 @ ( produc1212179418963815907set_c2 @ Q2 @ X2 ) )
      = ( collect_nat
        @ ^ [Y6: nat] :
          ? [Q5: mapping_b1_set_b2] : ( member3857524843657475480set_b2 @ ( produc3698891015744838695set_b2 @ Q2 @ ( produc9076999002715555034set_b2 @ X2 @ ( produc198978297537896015set_b2 @ Y6 @ Q5 ) ) ) @ ( transi1170656512200261639c2_nat @ M4 ) ) ) ) ).

% h_out.simps
thf(fact_1188_h__out_Oelims,axiom,
    ! [X2: fsm_c1_c2_nat,Xa2: product_prod_c1_c2,Y5: set_nat] :
      ( ( ( h_out_c1_c2_nat @ X2 @ Xa2 )
        = Y5 )
     => ~ ! [Q3: c1,X3: c2] :
            ( ( Xa2
              = ( product_Pair_c1_c2 @ Q3 @ X3 ) )
           => ( Y5
             != ( collect_nat
                @ ^ [Y6: nat] :
                  ? [Q5: c1] : ( member3128768103774925024nat_c1 @ ( produc312663335071628783nat_c1 @ Q3 @ ( produc97587416969510103nat_c1 @ X3 @ ( product_Pair_nat_c1 @ Y6 @ Q5 ) ) ) @ ( transi2084939702413591072c2_nat @ X2 ) ) ) ) ) ) ).

% h_out.elims
thf(fact_1189_h__out_Oelims,axiom,
    ! [X2: fsm_c1_c2_c2,Xa2: product_prod_c1_c2,Y5: set_c2] :
      ( ( ( h_out_c1_c2_c2 @ X2 @ Xa2 )
        = Y5 )
     => ~ ! [Q3: c1,X3: c2] :
            ( ( Xa2
              = ( product_Pair_c1_c2 @ Q3 @ X3 ) )
           => ( Y5
             != ( collect_c2
                @ ^ [Y6: c2] :
                  ? [Q5: c1] : ( member8472636576389039298_c2_c1 @ ( produc7456726006540687825_c2_c1 @ Q3 @ ( produc7668360288004781625_c2_c1 @ X3 @ ( product_Pair_c2_c1 @ Y6 @ Q5 ) ) ) @ ( transitions_c1_c2_c2 @ X2 ) ) ) ) ) ) ).

% h_out.elims
thf(fact_1190_h__out_Oelims,axiom,
    ! [X2: fsm_c1_c2_b2,Xa2: product_prod_c1_c2,Y5: set_b2] :
      ( ( ( h_out_c1_c2_b2 @ X2 @ Xa2 )
        = Y5 )
     => ~ ! [Q3: c1,X3: c2] :
            ( ( Xa2
              = ( product_Pair_c1_c2 @ Q3 @ X3 ) )
           => ( Y5
             != ( collect_b2
                @ ^ [Y6: b2] :
                  ? [Q5: c1] : ( member8925357235459199235_b2_c1 @ ( produc4806055576042092178_b2_c1 @ Q3 @ ( produc8304009288609768314_b2_c1 @ X3 @ ( product_Pair_b2_c1 @ Y6 @ Q5 ) ) ) @ ( transitions_c1_c2_b2 @ X2 ) ) ) ) ) ) ).

% h_out.elims
thf(fact_1191_h__out_Oelims,axiom,
    ! [X2: fsm_b1_b2_nat,Xa2: product_prod_b1_b2,Y5: set_nat] :
      ( ( ( h_out_b1_b2_nat @ X2 @ Xa2 )
        = Y5 )
     => ~ ! [Q3: b1,X3: b2] :
            ( ( Xa2
              = ( product_Pair_b1_b2 @ Q3 @ X3 ) )
           => ( Y5
             != ( collect_nat
                @ ^ [Y6: nat] :
                  ? [Q5: b1] : ( member2991274774235883105nat_b1 @ ( produc5580199815858148208nat_b1 @ Q3 @ ( produc5380728579693332887nat_b1 @ X3 @ ( product_Pair_nat_b1 @ Y6 @ Q5 ) ) ) @ ( transi2454530297511208738b2_nat @ X2 ) ) ) ) ) ) ).

% h_out.elims
thf(fact_1192_h__out_Oelims,axiom,
    ! [X2: fsm_b1_b2_c2,Xa2: product_prod_b1_b2,Y5: set_c2] :
      ( ( ( h_out_b1_b2_c2 @ X2 @ Xa2 )
        = Y5 )
     => ~ ! [Q3: b1,X3: b2] :
            ( ( Xa2
              = ( product_Pair_b1_b2 @ Q3 @ X3 ) )
           => ( Y5
             != ( collect_c2
                @ ^ [Y6: c2] :
                  ? [Q5: b1] : ( member4128914624957143619_c2_b1 @ ( produc1022949536370626386_c2_b1 @ Q3 @ ( produc1548230046359974265_c2_b1 @ X3 @ ( product_Pair_c2_b1 @ Y6 @ Q5 ) ) ) @ ( transitions_b1_b2_c2 @ X2 ) ) ) ) ) ) ).

% h_out.elims
thf(fact_1193_h__out_Oelims,axiom,
    ! [X2: fsm_b1_b2_b2,Xa2: product_prod_b1_b2,Y5: set_b2] :
      ( ( ( h_out_b1_b2_b2 @ X2 @ Xa2 )
        = Y5 )
     => ~ ! [Q3: b1,X3: b2] :
            ( ( Xa2
              = ( product_Pair_b1_b2 @ Q3 @ X3 ) )
           => ( Y5
             != ( collect_b2
                @ ^ [Y6: b2] :
                  ? [Q5: b1] : ( member4581635284027303556_b2_b1 @ ( produc7595651142726806547_b2_b1 @ Q3 @ ( produc2183879046964960954_b2_b1 @ X3 @ ( product_Pair_b2_b1 @ Y6 @ Q5 ) ) ) @ ( transitions_b1_b2_b2 @ X2 ) ) ) ) ) ) ).

% h_out.elims
thf(fact_1194_h__out_Oelims,axiom,
    ! [X2: fsm_a1_a2_nat,Xa2: product_prod_a1_a2,Y5: set_nat] :
      ( ( ( h_out_a1_a2_nat @ X2 @ Xa2 )
        = Y5 )
     => ~ ! [Q3: a1,X3: a2] :
            ( ( Xa2
              = ( product_Pair_a1_a2 @ Q3 @ X3 ) )
           => ( Y5
             != ( collect_nat
                @ ^ [Y6: nat] :
                  ? [Q5: a1] : ( member2853781444696841186nat_a1 @ ( produc1624364259789891825nat_a1 @ Q3 @ ( produc1440497705562379863nat_a1 @ X3 @ ( product_Pair_nat_a1 @ Y6 @ Q5 ) ) ) @ ( transi2824120892608826404a2_nat @ X2 ) ) ) ) ) ) ).

% h_out.elims
thf(fact_1195_h__out_Oelims,axiom,
    ! [X2: fsm_a1_a2_c2,Xa2: product_prod_a1_a2,Y5: set_c2] :
      ( ( ( h_out_a1_a2_c2 @ X2 @ Xa2 )
        = Y5 )
     => ~ ! [Q3: a1,X3: a2] :
            ( ( Xa2
              = ( product_Pair_a1_a2 @ Q3 @ X3 ) )
           => ( Y5
             != ( collect_c2
                @ ^ [Y6: c2] :
                  ? [Q5: a1] : ( member9008564710380023748_c2_a1 @ ( produc3812545103055340755_c2_a1 @ Q3 @ ( produc4651471841569942713_c2_a1 @ X3 @ ( product_Pair_c2_a1 @ Y6 @ Q5 ) ) ) @ ( transitions_a1_a2_c2 @ X2 ) ) ) ) ) ) ).

% h_out.elims
thf(fact_1196_h__out_Oelims,axiom,
    ! [X2: fsm_a1_a2_b2,Xa2: product_prod_a1_a2,Y5: set_b2] :
      ( ( ( h_out_a1_a2_b2 @ X2 @ Xa2 )
        = Y5 )
     => ~ ! [Q3: a1,X3: a2] :
            ( ( Xa2
              = ( product_Pair_a1_a2 @ Q3 @ X3 ) )
           => ( Y5
             != ( collect_b2
                @ ^ [Y6: b2] :
                  ? [Q5: a1] : ( member237913332595407877_b2_a1 @ ( produc1161874672556745108_b2_a1 @ Q3 @ ( produc5287120842174929402_b2_a1 @ X3 @ ( product_Pair_b2_a1 @ Y6 @ Q5 ) ) ) @ ( transitions_a1_a2_b2 @ X2 ) ) ) ) ) ) ).

% h_out.elims
thf(fact_1197_h__out_Oelims,axiom,
    ! [X2: fsm_ma3562454073340529286c2_nat,Xa2: produc4061897789176782763set_c2,Y5: set_nat] :
      ( ( ( h_out_6598019409568368631c2_nat @ X2 @ Xa2 )
        = Y5 )
     => ~ ! [Q3: mapping_b1_set_b2,X3: mapping_c1_set_c2] :
            ( ( Xa2
              = ( produc1212179418963815907set_c2 @ Q3 @ X3 ) )
           => ( Y5
             != ( collect_nat
                @ ^ [Y6: nat] :
                  ? [Q5: mapping_b1_set_b2] : ( member3857524843657475480set_b2 @ ( produc3698891015744838695set_b2 @ Q3 @ ( produc9076999002715555034set_b2 @ X3 @ ( produc198978297537896015set_b2 @ Y6 @ Q5 ) ) ) @ ( transi1170656512200261639c2_nat @ X2 ) ) ) ) ) ) ).

% h_out.elims
thf(fact_1198_in__image__insert__iff,axiom,
    ! [B2: set_se1646440499870488708_c1_c2,X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ! [C8: set_Pr9202269149784407460_c1_c2] :
          ( ( member5405957699526441805_c1_c2 @ C8 @ B2 )
         => ~ ( member1440383022217085037_c1_c2 @ X2 @ C8 ) )
     => ( ( member5405957699526441805_c1_c2 @ A2 @ ( image_4069597477799417477_c1_c2 @ ( insert7158109610518197396_c1_c2 @ X2 ) @ B2 ) )
        = ( ( member1440383022217085037_c1_c2 @ X2 @ A2 )
          & ( member5405957699526441805_c1_c2 @ ( minus_7665148276959638667_c1_c2 @ A2 @ ( insert7158109610518197396_c1_c2 @ X2 @ bot_bo745477178175700496_c1_c2 ) ) @ B2 ) ) ) ) ).

% in_image_insert_iff
thf(fact_1199_in__image__insert__iff,axiom,
    ! [B2: set_se4998383558405042950_b1_b2,X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ! [C8: set_Pr4592484330697324838_b1_b2] :
          ( ( member796172880439359183_b1_b2 @ C8 @ B2 )
         => ~ ( member2075749735315954927_b1_b2 @ X2 @ C8 ) )
     => ( ( member796172880439359183_b1_b2 @ A2 @ ( image_2322887115139085829_b1_b2 @ ( insert7793476323617067286_b1_b2 @ X2 ) @ B2 ) )
        = ( ( member2075749735315954927_b1_b2 @ X2 @ A2 )
          & ( member796172880439359183_b1_b2 @ ( minus_3055363457872556045_b1_b2 @ A2 @ ( insert7793476323617067286_b1_b2 @ X2 @ bot_bo5359064395943393682_b1_b2 ) ) @ B2 ) ) ) ) ).

% in_image_insert_iff
thf(fact_1200_in__image__insert__iff,axiom,
    ! [B2: set_se8350326616939597192_a1_a2,X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ! [C8: set_Pr9206071548465018024_a1_a2] :
          ( ( member5409760098207052369_a1_a2 @ C8 @ B2 )
         => ~ ( member2711116448414824817_a1_a2 @ X2 @ C8 ) )
     => ( ( member5409760098207052369_a1_a2 @ A2 @ ( image_576176752478754181_a1_a2 @ ( insert8428843036715937176_a1_a2 @ X2 ) @ B2 ) )
        = ( ( member2711116448414824817_a1_a2 @ X2 @ A2 )
          & ( member5409760098207052369_a1_a2 @ ( minus_7668950675640249231_a1_a2 @ A2 @ ( insert8428843036715937176_a1_a2 @ X2 @ bot_bo749279576856311060_a1_a2 ) ) @ B2 ) ) ) ) ).

% in_image_insert_iff
thf(fact_1201_in__image__insert__iff,axiom,
    ! [B2: set_se755747229750772688set_c2,X2: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2] :
      ( ! [C8: set_ma7306327908849618074set_c2] :
          ( ( member2994778624228093873set_c2 @ C8 @ B2 )
         => ~ ( member341037065618468219set_c2 @ X2 @ C8 ) )
     => ( ( member2994778624228093873set_c2 @ A2 @ ( image_8300128395462491579set_c2 @ ( insert88652402460333204set_c2 @ X2 ) @ B2 ) )
        = ( ( member341037065618468219set_c2 @ X2 @ A2 )
          & ( member2994778624228093873set_c2 @ ( minus_4895843051822776563set_c2 @ A2 @ ( insert88652402460333204set_c2 @ X2 @ bot_bo7584170878874662190set_c2 ) ) @ B2 ) ) ) ) ).

% in_image_insert_iff
thf(fact_1202_in__image__insert__iff,axiom,
    ! [B2: set_se6628959053713443282set_b2,X2: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2] :
      ( ! [C8: set_ma6254658672695423900set_b2] :
          ( ( member1943109388073899699set_b2 @ C8 @ B2 )
         => ~ ( member6117332676589958525set_b2 @ X2 @ C8 ) )
     => ( ( member1943109388073899699set_b2 @ A2 @ ( image_1104638922923574975set_b2 @ ( insert5864948013431823510set_b2 @ X2 ) @ B2 ) )
        = ( ( member6117332676589958525set_b2 @ X2 @ A2 )
          & ( member1943109388073899699set_b2 @ ( minus_3844173815668582389set_b2 @ A2 @ ( insert5864948013431823510set_b2 @ X2 @ bot_bo6532501642720468016set_b2 ) ) @ B2 ) ) ) ) ).

% in_image_insert_iff
thf(fact_1203_in__image__insert__iff,axiom,
    ! [B2: set_set_b2,X2: b2,A2: set_b2] :
      ( ! [C8: set_b2] :
          ( ( member_set_b2 @ C8 @ B2 )
         => ~ ( member_b2 @ X2 @ C8 ) )
     => ( ( member_set_b2 @ A2 @ ( image_set_b2_set_b2 @ ( insert_b2 @ X2 ) @ B2 ) )
        = ( ( member_b2 @ X2 @ A2 )
          & ( member_set_b2 @ ( minus_minus_set_b2 @ A2 @ ( insert_b2 @ X2 @ bot_bot_set_b2 ) ) @ B2 ) ) ) ) ).

% in_image_insert_iff
thf(fact_1204_in__image__insert__iff,axiom,
    ! [B2: set_set_c2,X2: c2,A2: set_c2] :
      ( ! [C8: set_c2] :
          ( ( member_set_c2 @ C8 @ B2 )
         => ~ ( member_c2 @ X2 @ C8 ) )
     => ( ( member_set_c2 @ A2 @ ( image_set_c2_set_c2 @ ( insert_c2 @ X2 ) @ B2 ) )
        = ( ( member_c2 @ X2 @ A2 )
          & ( member_set_c2 @ ( minus_minus_set_c2 @ A2 @ ( insert_c2 @ X2 @ bot_bot_set_c2 ) ) @ B2 ) ) ) ) ).

% in_image_insert_iff
thf(fact_1205_in__image__insert__iff,axiom,
    ! [B2: set_set_nat,X2: nat,A2: set_nat] :
      ( ! [C8: set_nat] :
          ( ( member_set_nat @ C8 @ B2 )
         => ~ ( member_nat @ X2 @ C8 ) )
     => ( ( member_set_nat @ A2 @ ( image_7916887816326733075et_nat @ ( insert_nat @ X2 ) @ B2 ) )
        = ( ( member_nat @ X2 @ A2 )
          & ( member_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B2 ) ) ) ) ).

% in_image_insert_iff
thf(fact_1206_Diff__insert__absorb,axiom,
    ! [X2: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ~ ( member1440383022217085037_c1_c2 @ X2 @ A2 )
     => ( ( minus_7665148276959638667_c1_c2 @ ( insert7158109610518197396_c1_c2 @ X2 @ A2 ) @ ( insert7158109610518197396_c1_c2 @ X2 @ bot_bo745477178175700496_c1_c2 ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1207_Diff__insert__absorb,axiom,
    ! [X2: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ~ ( member2075749735315954927_b1_b2 @ X2 @ A2 )
     => ( ( minus_3055363457872556045_b1_b2 @ ( insert7793476323617067286_b1_b2 @ X2 @ A2 ) @ ( insert7793476323617067286_b1_b2 @ X2 @ bot_bo5359064395943393682_b1_b2 ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1208_Diff__insert__absorb,axiom,
    ! [X2: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ~ ( member2711116448414824817_a1_a2 @ X2 @ A2 )
     => ( ( minus_7668950675640249231_a1_a2 @ ( insert8428843036715937176_a1_a2 @ X2 @ A2 ) @ ( insert8428843036715937176_a1_a2 @ X2 @ bot_bo749279576856311060_a1_a2 ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1209_Diff__insert__absorb,axiom,
    ! [X2: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2] :
      ( ~ ( member341037065618468219set_c2 @ X2 @ A2 )
     => ( ( minus_4895843051822776563set_c2 @ ( insert88652402460333204set_c2 @ X2 @ A2 ) @ ( insert88652402460333204set_c2 @ X2 @ bot_bo7584170878874662190set_c2 ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1210_Diff__insert__absorb,axiom,
    ! [X2: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2] :
      ( ~ ( member6117332676589958525set_b2 @ X2 @ A2 )
     => ( ( minus_3844173815668582389set_b2 @ ( insert5864948013431823510set_b2 @ X2 @ A2 ) @ ( insert5864948013431823510set_b2 @ X2 @ bot_bo6532501642720468016set_b2 ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1211_Diff__insert__absorb,axiom,
    ! [X2: b2,A2: set_b2] :
      ( ~ ( member_b2 @ X2 @ A2 )
     => ( ( minus_minus_set_b2 @ ( insert_b2 @ X2 @ A2 ) @ ( insert_b2 @ X2 @ bot_bot_set_b2 ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1212_Diff__insert__absorb,axiom,
    ! [X2: c2,A2: set_c2] :
      ( ~ ( member_c2 @ X2 @ A2 )
     => ( ( minus_minus_set_c2 @ ( insert_c2 @ X2 @ A2 ) @ ( insert_c2 @ X2 @ bot_bot_set_c2 ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1213_Diff__insert__absorb,axiom,
    ! [X2: nat,A2: set_nat] :
      ( ~ ( member_nat @ X2 @ A2 )
     => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A2 ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1214_Diff__insert2,axiom,
    ! [A2: set_b2,A: b2,B2: set_b2] :
      ( ( minus_minus_set_b2 @ A2 @ ( insert_b2 @ A @ B2 ) )
      = ( minus_minus_set_b2 @ ( minus_minus_set_b2 @ A2 @ ( insert_b2 @ A @ bot_bot_set_b2 ) ) @ B2 ) ) ).

% Diff_insert2
thf(fact_1215_Diff__insert2,axiom,
    ! [A2: set_c2,A: c2,B2: set_c2] :
      ( ( minus_minus_set_c2 @ A2 @ ( insert_c2 @ A @ B2 ) )
      = ( minus_minus_set_c2 @ ( minus_minus_set_c2 @ A2 @ ( insert_c2 @ A @ bot_bot_set_c2 ) ) @ B2 ) ) ).

% Diff_insert2
thf(fact_1216_Diff__insert2,axiom,
    ! [A2: set_nat,A: nat,B2: set_nat] :
      ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
      = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B2 ) ) ).

% Diff_insert2
thf(fact_1217_insert__Diff,axiom,
    ! [A: product_prod_c1_c2,A2: set_Pr9202269149784407460_c1_c2] :
      ( ( member1440383022217085037_c1_c2 @ A @ A2 )
     => ( ( insert7158109610518197396_c1_c2 @ A @ ( minus_7665148276959638667_c1_c2 @ A2 @ ( insert7158109610518197396_c1_c2 @ A @ bot_bo745477178175700496_c1_c2 ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1218_insert__Diff,axiom,
    ! [A: product_prod_b1_b2,A2: set_Pr4592484330697324838_b1_b2] :
      ( ( member2075749735315954927_b1_b2 @ A @ A2 )
     => ( ( insert7793476323617067286_b1_b2 @ A @ ( minus_3055363457872556045_b1_b2 @ A2 @ ( insert7793476323617067286_b1_b2 @ A @ bot_bo5359064395943393682_b1_b2 ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1219_insert__Diff,axiom,
    ! [A: product_prod_a1_a2,A2: set_Pr9206071548465018024_a1_a2] :
      ( ( member2711116448414824817_a1_a2 @ A @ A2 )
     => ( ( insert8428843036715937176_a1_a2 @ A @ ( minus_7668950675640249231_a1_a2 @ A2 @ ( insert8428843036715937176_a1_a2 @ A @ bot_bo749279576856311060_a1_a2 ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1220_insert__Diff,axiom,
    ! [A: mapping_c1_set_c2,A2: set_ma7306327908849618074set_c2] :
      ( ( member341037065618468219set_c2 @ A @ A2 )
     => ( ( insert88652402460333204set_c2 @ A @ ( minus_4895843051822776563set_c2 @ A2 @ ( insert88652402460333204set_c2 @ A @ bot_bo7584170878874662190set_c2 ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1221_insert__Diff,axiom,
    ! [A: mapping_b1_set_b2,A2: set_ma6254658672695423900set_b2] :
      ( ( member6117332676589958525set_b2 @ A @ A2 )
     => ( ( insert5864948013431823510set_b2 @ A @ ( minus_3844173815668582389set_b2 @ A2 @ ( insert5864948013431823510set_b2 @ A @ bot_bo6532501642720468016set_b2 ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1222_insert__Diff,axiom,
    ! [A: b2,A2: set_b2] :
      ( ( member_b2 @ A @ A2 )
     => ( ( insert_b2 @ A @ ( minus_minus_set_b2 @ A2 @ ( insert_b2 @ A @ bot_bot_set_b2 ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1223_insert__Diff,axiom,
    ! [A: c2,A2: set_c2] :
      ( ( member_c2 @ A @ A2 )
     => ( ( insert_c2 @ A @ ( minus_minus_set_c2 @ A2 @ ( insert_c2 @ A @ bot_bot_set_c2 ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1224_insert__Diff,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( member_nat @ A @ A2 )
     => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1225_Diff__insert,axiom,
    ! [A2: set_b2,A: b2,B2: set_b2] :
      ( ( minus_minus_set_b2 @ A2 @ ( insert_b2 @ A @ B2 ) )
      = ( minus_minus_set_b2 @ ( minus_minus_set_b2 @ A2 @ B2 ) @ ( insert_b2 @ A @ bot_bot_set_b2 ) ) ) ).

% Diff_insert
thf(fact_1226_Diff__insert,axiom,
    ! [A2: set_c2,A: c2,B2: set_c2] :
      ( ( minus_minus_set_c2 @ A2 @ ( insert_c2 @ A @ B2 ) )
      = ( minus_minus_set_c2 @ ( minus_minus_set_c2 @ A2 @ B2 ) @ ( insert_c2 @ A @ bot_bot_set_c2 ) ) ) ).

% Diff_insert
thf(fact_1227_Diff__insert,axiom,
    ! [A2: set_nat,A: nat,B2: set_nat] :
      ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
      = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).

% Diff_insert
thf(fact_1228_Set_Oremove__def,axiom,
    ( remove_b2
    = ( ^ [X: b2,A6: set_b2] : ( minus_minus_set_b2 @ A6 @ ( insert_b2 @ X @ bot_bot_set_b2 ) ) ) ) ).

% Set.remove_def
thf(fact_1229_Set_Oremove__def,axiom,
    ( remove_c2
    = ( ^ [X: c2,A6: set_c2] : ( minus_minus_set_c2 @ A6 @ ( insert_c2 @ X @ bot_bot_set_c2 ) ) ) ) ).

% Set.remove_def
thf(fact_1230_Set_Oremove__def,axiom,
    ( remove_nat
    = ( ^ [X: nat,A6: set_nat] : ( minus_minus_set_nat @ A6 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).

% Set.remove_def
thf(fact_1231_finite__Diff__insert,axiom,
    ! [A2: set_b2,A: b2,B2: set_b2] :
      ( ( finite_finite_b2 @ ( minus_minus_set_b2 @ A2 @ ( insert_b2 @ A @ B2 ) ) )
      = ( finite_finite_b2 @ ( minus_minus_set_b2 @ A2 @ B2 ) ) ) ).

% finite_Diff_insert
thf(fact_1232_finite__Diff__insert,axiom,
    ! [A2: set_c2,A: c2,B2: set_c2] :
      ( ( finite_finite_c2 @ ( minus_minus_set_c2 @ A2 @ ( insert_c2 @ A @ B2 ) ) )
      = ( finite_finite_c2 @ ( minus_minus_set_c2 @ A2 @ B2 ) ) ) ).

% finite_Diff_insert
thf(fact_1233_finite__Diff__insert,axiom,
    ! [A2: set_nat,A: nat,B2: set_nat] :
      ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) ) )
      = ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).

% finite_Diff_insert
thf(fact_1234_finite__Collect__bounded__ex,axiom,
    ! [P: c2 > $o,Q: c2 > c2 > $o] :
      ( ( finite_finite_c2 @ ( collect_c2 @ P ) )
     => ( ( finite_finite_c2
          @ ( collect_c2
            @ ^ [X: c2] :
              ? [Y6: c2] :
                ( ( P @ Y6 )
                & ( Q @ X @ Y6 ) ) ) )
        = ( ! [Y6: c2] :
              ( ( P @ Y6 )
             => ( finite_finite_c2
                @ ( collect_c2
                  @ ^ [X: c2] : ( Q @ X @ Y6 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_1235_finite__Collect__bounded__ex,axiom,
    ! [P: c2 > $o,Q: b2 > c2 > $o] :
      ( ( finite_finite_c2 @ ( collect_c2 @ P ) )
     => ( ( finite_finite_b2
          @ ( collect_b2
            @ ^ [X: b2] :
              ? [Y6: c2] :
                ( ( P @ Y6 )
                & ( Q @ X @ Y6 ) ) ) )
        = ( ! [Y6: c2] :
              ( ( P @ Y6 )
             => ( finite_finite_b2
                @ ( collect_b2
                  @ ^ [X: b2] : ( Q @ X @ Y6 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_1236_finite__Collect__bounded__ex,axiom,
    ! [P: b2 > $o,Q: c2 > b2 > $o] :
      ( ( finite_finite_b2 @ ( collect_b2 @ P ) )
     => ( ( finite_finite_c2
          @ ( collect_c2
            @ ^ [X: c2] :
              ? [Y6: b2] :
                ( ( P @ Y6 )
                & ( Q @ X @ Y6 ) ) ) )
        = ( ! [Y6: b2] :
              ( ( P @ Y6 )
             => ( finite_finite_c2
                @ ( collect_c2
                  @ ^ [X: c2] : ( Q @ X @ Y6 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_1237_finite__Collect__bounded__ex,axiom,
    ! [P: b2 > $o,Q: b2 > b2 > $o] :
      ( ( finite_finite_b2 @ ( collect_b2 @ P ) )
     => ( ( finite_finite_b2
          @ ( collect_b2
            @ ^ [X: b2] :
              ? [Y6: b2] :
                ( ( P @ Y6 )
                & ( Q @ X @ Y6 ) ) ) )
        = ( ! [Y6: b2] :
              ( ( P @ Y6 )
             => ( finite_finite_b2
                @ ( collect_b2
                  @ ^ [X: b2] : ( Q @ X @ Y6 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_1238_finite__Collect__bounded__ex,axiom,
    ! [P: c2 > $o,Q: nat > c2 > $o] :
      ( ( finite_finite_c2 @ ( collect_c2 @ P ) )
     => ( ( finite_finite_nat
          @ ( collect_nat
            @ ^ [X: nat] :
              ? [Y6: c2] :
                ( ( P @ Y6 )
                & ( Q @ X @ Y6 ) ) ) )
        = ( ! [Y6: c2] :
              ( ( P @ Y6 )
             => ( finite_finite_nat
                @ ( collect_nat
                  @ ^ [X: nat] : ( Q @ X @ Y6 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_1239_finite__Collect__bounded__ex,axiom,
    ! [P: b2 > $o,Q: nat > b2 > $o] :
      ( ( finite_finite_b2 @ ( collect_b2 @ P ) )
     => ( ( finite_finite_nat
          @ ( collect_nat
            @ ^ [X: nat] :
              ? [Y6: b2] :
                ( ( P @ Y6 )
                & ( Q @ X @ Y6 ) ) ) )
        = ( ! [Y6: b2] :
              ( ( P @ Y6 )
             => ( finite_finite_nat
                @ ( collect_nat
                  @ ^ [X: nat] : ( Q @ X @ Y6 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_1240_finite__Collect__bounded__ex,axiom,
    ! [P: nat > $o,Q: c2 > nat > $o] :
      ( ( finite_finite_nat @ ( collect_nat @ P ) )
     => ( ( finite_finite_c2
          @ ( collect_c2
            @ ^ [X: c2] :
              ? [Y6: nat] :
                ( ( P @ Y6 )
                & ( Q @ X @ Y6 ) ) ) )
        = ( ! [Y6: nat] :
              ( ( P @ Y6 )
             => ( finite_finite_c2
                @ ( collect_c2
                  @ ^ [X: c2] : ( Q @ X @ Y6 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_1241_finite__Collect__bounded__ex,axiom,
    ! [P: nat > $o,Q: b2 > nat > $o] :
      ( ( finite_finite_nat @ ( collect_nat @ P ) )
     => ( ( finite_finite_b2
          @ ( collect_b2
            @ ^ [X: b2] :
              ? [Y6: nat] :
                ( ( P @ Y6 )
                & ( Q @ X @ Y6 ) ) ) )
        = ( ! [Y6: nat] :
              ( ( P @ Y6 )
             => ( finite_finite_b2
                @ ( collect_b2
                  @ ^ [X: b2] : ( Q @ X @ Y6 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_1242_finite__Collect__bounded__ex,axiom,
    ! [P: nat > $o,Q: nat > nat > $o] :
      ( ( finite_finite_nat @ ( collect_nat @ P ) )
     => ( ( finite_finite_nat
          @ ( collect_nat
            @ ^ [X: nat] :
              ? [Y6: nat] :
                ( ( P @ Y6 )
                & ( Q @ X @ Y6 ) ) ) )
        = ( ! [Y6: nat] :
              ( ( P @ Y6 )
             => ( finite_finite_nat
                @ ( collect_nat
                  @ ^ [X: nat] : ( Q @ X @ Y6 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_1243_finite__insert,axiom,
    ! [A: b2,A2: set_b2] :
      ( ( finite_finite_b2 @ ( insert_b2 @ A @ A2 ) )
      = ( finite_finite_b2 @ A2 ) ) ).

% finite_insert
thf(fact_1244_finite__insert,axiom,
    ! [A: c2,A2: set_c2] :
      ( ( finite_finite_c2 @ ( insert_c2 @ A @ A2 ) )
      = ( finite_finite_c2 @ A2 ) ) ).

% finite_insert
thf(fact_1245_finite__insert,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( finite_finite_nat @ ( insert_nat @ A @ A2 ) )
      = ( finite_finite_nat @ A2 ) ) ).

% finite_insert
thf(fact_1246_finite__imageI,axiom,
    ! [F5: set_Pr9206071548465018024_a1_a2,H: product_prod_a1_a2 > product_prod_b1_b2] :
      ( ( finite9152749144624424049_a1_a2 @ F5 )
     => ( finite8517382431525554159_b1_b2 @ ( image_1398015525354814723_b1_b2 @ H @ F5 ) ) ) ).

% finite_imageI
thf(fact_1247_finite__imageI,axiom,
    ! [F5: set_Pr9206071548465018024_a1_a2,H: product_prod_a1_a2 > product_prod_c1_c2] :
      ( ( finite9152749144624424049_a1_a2 @ F5 )
     => ( finite7882015718426684269_c1_c2 @ ( image_762648812255944833_c1_c2 @ H @ F5 ) ) ) ).

% finite_imageI
thf(fact_1248_finite__imageI,axiom,
    ! [F5: set_Pr9202269149784407460_c1_c2,H: product_prod_c1_c2 > mapping_c1_set_c2] :
      ( ( finite7882015718426684269_c1_c2 @ F5 )
     => ( finite5621885356302860923set_c2 @ ( image_5984881132562613603set_c2 @ H @ F5 ) ) ) ).

% finite_imageI
thf(fact_1249_finite__imageI,axiom,
    ! [F5: set_Pr4592484330697324838_b1_b2,H: product_prod_b1_b2 > mapping_b1_set_b2] :
      ( ( finite8517382431525554159_b1_b2 @ F5 )
     => ( finite2174808930419575421set_b2 @ ( image_6686293874852392167set_b2 @ H @ F5 ) ) ) ).

% finite_imageI
thf(fact_1250_finite__imageI,axiom,
    ! [F5: set_Pr1660683266160182027set_c2,H: produc4061897789176782763set_c2 > produc4061897789176782763set_c2] :
      ( ( finite199606665216627796set_c2 @ F5 )
     => ( finite199606665216627796set_c2 @ ( image_7945144516369962181set_c2 @ H @ F5 ) ) ) ).

% finite_imageI
thf(fact_1251_finite__imageI,axiom,
    ! [F5: set_nat,H: nat > nat] :
      ( ( finite_finite_nat @ F5 )
     => ( finite_finite_nat @ ( image_nat_nat2 @ H @ F5 ) ) ) ).

% finite_imageI
thf(fact_1252_infinite__remove,axiom,
    ! [S3: set_b2,A: b2] :
      ( ~ ( finite_finite_b2 @ S3 )
     => ~ ( finite_finite_b2 @ ( minus_minus_set_b2 @ S3 @ ( insert_b2 @ A @ bot_bot_set_b2 ) ) ) ) ).

% infinite_remove
thf(fact_1253_infinite__remove,axiom,
    ! [S3: set_c2,A: c2] :
      ( ~ ( finite_finite_c2 @ S3 )
     => ~ ( finite_finite_c2 @ ( minus_minus_set_c2 @ S3 @ ( insert_c2 @ A @ bot_bot_set_c2 ) ) ) ) ).

% infinite_remove
thf(fact_1254_infinite__remove,axiom,
    ! [S3: set_nat,A: nat] :
      ( ~ ( finite_finite_nat @ S3 )
     => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).

% infinite_remove
thf(fact_1255_infinite__coinduct,axiom,
    ! [X5: set_b2 > $o,A2: set_b2] :
      ( ( X5 @ A2 )
     => ( ! [A7: set_b2] :
            ( ( X5 @ A7 )
           => ? [X4: b2] :
                ( ( member_b2 @ X4 @ A7 )
                & ( ( X5 @ ( minus_minus_set_b2 @ A7 @ ( insert_b2 @ X4 @ bot_bot_set_b2 ) ) )
                  | ~ ( finite_finite_b2 @ ( minus_minus_set_b2 @ A7 @ ( insert_b2 @ X4 @ bot_bot_set_b2 ) ) ) ) ) )
       => ~ ( finite_finite_b2 @ A2 ) ) ) ).

% infinite_coinduct
thf(fact_1256_infinite__coinduct,axiom,
    ! [X5: set_c2 > $o,A2: set_c2] :
      ( ( X5 @ A2 )
     => ( ! [A7: set_c2] :
            ( ( X5 @ A7 )
           => ? [X4: c2] :
                ( ( member_c2 @ X4 @ A7 )
                & ( ( X5 @ ( minus_minus_set_c2 @ A7 @ ( insert_c2 @ X4 @ bot_bot_set_c2 ) ) )
                  | ~ ( finite_finite_c2 @ ( minus_minus_set_c2 @ A7 @ ( insert_c2 @ X4 @ bot_bot_set_c2 ) ) ) ) ) )
       => ~ ( finite_finite_c2 @ A2 ) ) ) ).

% infinite_coinduct
thf(fact_1257_infinite__coinduct,axiom,
    ! [X5: set_nat > $o,A2: set_nat] :
      ( ( X5 @ A2 )
     => ( ! [A7: set_nat] :
            ( ( X5 @ A7 )
           => ? [X4: nat] :
                ( ( member_nat @ X4 @ A7 )
                & ( ( X5 @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) )
                  | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ) )
       => ~ ( finite_finite_nat @ A2 ) ) ) ).

% infinite_coinduct
thf(fact_1258_finite__empty__induct,axiom,
    ! [A2: set_Pr9202269149784407460_c1_c2,P: set_Pr9202269149784407460_c1_c2 > $o] :
      ( ( finite7882015718426684269_c1_c2 @ A2 )
     => ( ( P @ A2 )
       => ( ! [A4: product_prod_c1_c2,A7: set_Pr9202269149784407460_c1_c2] :
              ( ( finite7882015718426684269_c1_c2 @ A7 )
             => ( ( member1440383022217085037_c1_c2 @ A4 @ A7 )
               => ( ( P @ A7 )
                 => ( P @ ( minus_7665148276959638667_c1_c2 @ A7 @ ( insert7158109610518197396_c1_c2 @ A4 @ bot_bo745477178175700496_c1_c2 ) ) ) ) ) )
         => ( P @ bot_bo745477178175700496_c1_c2 ) ) ) ) ).

% finite_empty_induct
thf(fact_1259_finite__empty__induct,axiom,
    ! [A2: set_Pr4592484330697324838_b1_b2,P: set_Pr4592484330697324838_b1_b2 > $o] :
      ( ( finite8517382431525554159_b1_b2 @ A2 )
     => ( ( P @ A2 )
       => ( ! [A4: product_prod_b1_b2,A7: set_Pr4592484330697324838_b1_b2] :
              ( ( finite8517382431525554159_b1_b2 @ A7 )
             => ( ( member2075749735315954927_b1_b2 @ A4 @ A7 )
               => ( ( P @ A7 )
                 => ( P @ ( minus_3055363457872556045_b1_b2 @ A7 @ ( insert7793476323617067286_b1_b2 @ A4 @ bot_bo5359064395943393682_b1_b2 ) ) ) ) ) )
         => ( P @ bot_bo5359064395943393682_b1_b2 ) ) ) ) ).

% finite_empty_induct
thf(fact_1260_finite__empty__induct,axiom,
    ! [A2: set_Pr9206071548465018024_a1_a2,P: set_Pr9206071548465018024_a1_a2 > $o] :
      ( ( finite9152749144624424049_a1_a2 @ A2 )
     => ( ( P @ A2 )
       => ( ! [A4: product_prod_a1_a2,A7: set_Pr9206071548465018024_a1_a2] :
              ( ( finite9152749144624424049_a1_a2 @ A7 )
             => ( ( member2711116448414824817_a1_a2 @ A4 @ A7 )
               => ( ( P @ A7 )
                 => ( P @ ( minus_7668950675640249231_a1_a2 @ A7 @ ( insert8428843036715937176_a1_a2 @ A4 @ bot_bo749279576856311060_a1_a2 ) ) ) ) ) )
         => ( P @ bot_bo749279576856311060_a1_a2 ) ) ) ) ).

% finite_empty_induct
thf(fact_1261_finite__empty__induct,axiom,
    ! [A2: set_ma7306327908849618074set_c2,P: set_ma7306327908849618074set_c2 > $o] :
      ( ( finite5621885356302860923set_c2 @ A2 )
     => ( ( P @ A2 )
       => ( ! [A4: mapping_c1_set_c2,A7: set_ma7306327908849618074set_c2] :
              ( ( finite5621885356302860923set_c2 @ A7 )
             => ( ( member341037065618468219set_c2 @ A4 @ A7 )
               => ( ( P @ A7 )
                 => ( P @ ( minus_4895843051822776563set_c2 @ A7 @ ( insert88652402460333204set_c2 @ A4 @ bot_bo7584170878874662190set_c2 ) ) ) ) ) )
         => ( P @ bot_bo7584170878874662190set_c2 ) ) ) ) ).

% finite_empty_induct
thf(fact_1262_finite__empty__induct,axiom,
    ! [A2: set_ma6254658672695423900set_b2,P: set_ma6254658672695423900set_b2 > $o] :
      ( ( finite2174808930419575421set_b2 @ A2 )
     => ( ( P @ A2 )
       => ( ! [A4: mapping_b1_set_b2,A7: set_ma6254658672695423900set_b2] :
              ( ( finite2174808930419575421set_b2 @ A7 )
             => ( ( member6117332676589958525set_b2 @ A4 @ A7 )
               => ( ( P @ A7 )
                 => ( P @ ( minus_3844173815668582389set_b2 @ A7 @ ( insert5864948013431823510set_b2 @ A4 @ bot_bo6532501642720468016set_b2 ) ) ) ) ) )
         => ( P @ bot_bo6532501642720468016set_b2 ) ) ) ) ).

% finite_empty_induct
thf(fact_1263_finite__empty__induct,axiom,
    ! [A2: set_b2,P: set_b2 > $o] :
      ( ( finite_finite_b2 @ A2 )
     => ( ( P @ A2 )
       => ( ! [A4: b2,A7: set_b2] :
              ( ( finite_finite_b2 @ A7 )
             => ( ( member_b2 @ A4 @ A7 )
               => ( ( P @ A7 )
                 => ( P @ ( minus_minus_set_b2 @ A7 @ ( insert_b2 @ A4 @ bot_bot_set_b2 ) ) ) ) ) )
         => ( P @ bot_bot_set_b2 ) ) ) ) ).

% finite_empty_induct
thf(fact_1264_finite__empty__induct,axiom,
    ! [A2: set_c2,P: set_c2 > $o] :
      ( ( finite_finite_c2 @ A2 )
     => ( ( P @ A2 )
       => ( ! [A4: c2,A7: set_c2] :
              ( ( finite_finite_c2 @ A7 )
             => ( ( member_c2 @ A4 @ A7 )
               => ( ( P @ A7 )
                 => ( P @ ( minus_minus_set_c2 @ A7 @ ( insert_c2 @ A4 @ bot_bot_set_c2 ) ) ) ) ) )
         => ( P @ bot_bot_set_c2 ) ) ) ) ).

% finite_empty_induct
thf(fact_1265_finite__empty__induct,axiom,
    ! [A2: set_nat,P: set_nat > $o] :
      ( ( finite_finite_nat @ A2 )
     => ( ( P @ A2 )
       => ( ! [A4: nat,A7: set_nat] :
              ( ( finite_finite_nat @ A7 )
             => ( ( member_nat @ A4 @ A7 )
               => ( ( P @ A7 )
                 => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ A4 @ bot_bot_set_nat ) ) ) ) ) )
         => ( P @ bot_bot_set_nat ) ) ) ) ).

% finite_empty_induct
thf(fact_1266_finite__Collect__disjI,axiom,
    ! [P: c2 > $o,Q: c2 > $o] :
      ( ( finite_finite_c2
        @ ( collect_c2
          @ ^ [X: c2] :
              ( ( P @ X )
              | ( Q @ X ) ) ) )
      = ( ( finite_finite_c2 @ ( collect_c2 @ P ) )
        & ( finite_finite_c2 @ ( collect_c2 @ Q ) ) ) ) ).

% finite_Collect_disjI
thf(fact_1267_finite__Collect__disjI,axiom,
    ! [P: b2 > $o,Q: b2 > $o] :
      ( ( finite_finite_b2
        @ ( collect_b2
          @ ^ [X: b2] :
              ( ( P @ X )
              | ( Q @ X ) ) ) )
      = ( ( finite_finite_b2 @ ( collect_b2 @ P ) )
        & ( finite_finite_b2 @ ( collect_b2 @ Q ) ) ) ) ).

% finite_Collect_disjI
thf(fact_1268_finite__Collect__disjI,axiom,
    ! [P: nat > $o,Q: nat > $o] :
      ( ( finite_finite_nat
        @ ( collect_nat
          @ ^ [X: nat] :
              ( ( P @ X )
              | ( Q @ X ) ) ) )
      = ( ( finite_finite_nat @ ( collect_nat @ P ) )
        & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).

% finite_Collect_disjI
thf(fact_1269_finite__Collect__conjI,axiom,
    ! [P: c2 > $o,Q: c2 > $o] :
      ( ( ( finite_finite_c2 @ ( collect_c2 @ P ) )
        | ( finite_finite_c2 @ ( collect_c2 @ Q ) ) )
     => ( finite_finite_c2
        @ ( collect_c2
          @ ^ [X: c2] :
              ( ( P @ X )
              & ( Q @ X ) ) ) ) ) ).

% finite_Collect_conjI
thf(fact_1270_finite__Collect__conjI,axiom,
    ! [P: b2 > $o,Q: b2 > $o] :
      ( ( ( finite_finite_b2 @ ( collect_b2 @ P ) )
        | ( finite_finite_b2 @ ( collect_b2 @ Q ) ) )
     => ( finite_finite_b2
        @ ( collect_b2
          @ ^ [X: b2] :
              ( ( P @ X )
              & ( Q @ X ) ) ) ) ) ).

% finite_Collect_conjI
thf(fact_1271_finite__Collect__conjI,axiom,
    ! [P: nat > $o,Q: nat > $o] :
      ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
        | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
     => ( finite_finite_nat
        @ ( collect_nat
          @ ^ [X: nat] :
              ( ( P @ X )
              & ( Q @ X ) ) ) ) ) ).

% finite_Collect_conjI
thf(fact_1272_finite__Collect__le__nat,axiom,
    ! [K: nat] :
      ( finite_finite_nat
      @ ( collect_nat
        @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).

% finite_Collect_le_nat
thf(fact_1273_size_H__char__eq__0,axiom,
    ( size_char
    = ( ^ [C3: char] : zero_zero_nat ) ) ).

% size'_char_eq_0

% Helper facts (9)
thf(help_If_2_1_If_001t__Set__Oset_Itf__a2_J_T,axiom,
    ! [X2: set_a2,Y5: set_a2] :
      ( ( if_set_a2 @ $false @ X2 @ Y5 )
      = Y5 ) ).

thf(help_If_1_1_If_001t__Set__Oset_Itf__a2_J_T,axiom,
    ! [X2: set_a2,Y5: set_a2] :
      ( ( if_set_a2 @ $true @ X2 @ Y5 )
      = X2 ) ).

thf(help_If_2_1_If_001t__Set__Oset_Itf__b2_J_T,axiom,
    ! [X2: set_b2,Y5: set_b2] :
      ( ( if_set_b2 @ $false @ X2 @ Y5 )
      = Y5 ) ).

thf(help_If_1_1_If_001t__Set__Oset_Itf__b2_J_T,axiom,
    ! [X2: set_b2,Y5: set_b2] :
      ( ( if_set_b2 @ $true @ X2 @ Y5 )
      = X2 ) ).

thf(help_If_2_1_If_001t__Set__Oset_Itf__c2_J_T,axiom,
    ! [X2: set_c2,Y5: set_c2] :
      ( ( if_set_c2 @ $false @ X2 @ Y5 )
      = Y5 ) ).

thf(help_If_1_1_If_001t__Set__Oset_Itf__c2_J_T,axiom,
    ! [X2: set_c2,Y5: set_c2] :
      ( ( if_set_c2 @ $true @ X2 @ Y5 )
      = X2 ) ).

thf(help_If_3_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
    ! [X2: set_nat,Y5: set_nat] :
      ( ( if_set_nat @ $false @ X2 @ Y5 )
      = Y5 ) ).

thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
    ! [X2: set_nat,Y5: set_nat] :
      ( ( if_set_nat @ $true @ X2 @ Y5 )
      = X2 ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( produc890782565133688235set_c2 @ ( set_as_map_b1_b2 @ ( image_1398015525354814723_b1_b2 @ f1 @ ( set_RB6720226376580087827_a1_a2 @ t ) ) ) @ ( set_as_map_c1_c2 @ ( image_762648812255944833_c1_c2 @ f2 @ ( set_RB6720226376580087827_a1_a2 @ t ) ) ) )
    = ( case_o989950291820459046_order
      @ ( abort_2778816509743918716set_c2 @ ( literal2 @ $false @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $false @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $true @ $true @ $true @ $false @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $false @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
        @ ^ [Uu: product_unit] : ( produc890782565133688235set_c2 @ ( set_as_map_b1_b2 @ ( image_1398015525354814723_b1_b2 @ f1 @ ( set_RB6720226376580087827_a1_a2 @ t ) ) ) @ ( set_as_map_c1_c2 @ ( image_762648812255944833_c1_c2 @ f2 @ ( set_RB6720226376580087827_a1_a2 @ t ) ) ) ) )
      @ ^ [X: product_prod_a1_a2 > product_prod_a1_a2 > order] :
          ( produc890782565133688235set_c2
          @ ( lookup_b1_set_b2
            @ ( produc4038274906788240847set_c2
              @ ( rBT_fo5132325507301440204set_c2
                @ ^ [Kv: product_prod_a1_a2] :
                    ( produc4732439310506902963set_c2
                    @ ^ [M1: mapping_b1_set_b2,M2: mapping_c1_set_c2] :
                        ( produc1212179418963815907set_c2
                        @ ( produc6418488838319782393set_b2
                          @ ^ [Y6: b1,Z: b2] :
                              ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ Y6 @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M1 )
                              @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ Y6 @ ( insert_b2 @ Z @ Zs ) @ M1 )
                              @ ( lookup_b1_set_b2 @ M1 @ Y6 ) )
                          @ ( f1 @ Kv ) )
                        @ ( produc4822369076420559349set_c2
                          @ ^ [Y6: c1,Z: c2] :
                              ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ Y6 @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M2 )
                              @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ Y6 @ ( insert_c2 @ Z @ Zs ) @ M2 )
                              @ ( lookup_c1_set_c2 @ M2 @ Y6 ) )
                          @ ( f2 @ Kv ) ) ) )
                @ t
                @ ( produc1212179418963815907set_c2 @ empty_b1_set_b2 @ empty_c1_set_c2 ) ) ) )
          @ ( lookup_c1_set_c2
            @ ( produc6032943676959796241set_c2
              @ ( rBT_fo5132325507301440204set_c2
                @ ^ [Kv: product_prod_a1_a2] :
                    ( produc4732439310506902963set_c2
                    @ ^ [M1: mapping_b1_set_b2,M2: mapping_c1_set_c2] :
                        ( produc1212179418963815907set_c2
                        @ ( produc6418488838319782393set_b2
                          @ ^ [Y6: b1,Z: b2] :
                              ( case_o3420813927363517980set_b2 @ ( update_b1_set_b2 @ Y6 @ ( insert_b2 @ Z @ bot_bot_set_b2 ) @ M1 )
                              @ ^ [Zs: set_b2] : ( update_b1_set_b2 @ Y6 @ ( insert_b2 @ Z @ Zs ) @ M1 )
                              @ ( lookup_b1_set_b2 @ M1 @ Y6 ) )
                          @ ( f1 @ Kv ) )
                        @ ( produc4822369076420559349set_c2
                          @ ^ [Y6: c1,Z: c2] :
                              ( case_o4190434630649893849set_c2 @ ( update_c1_set_c2 @ Y6 @ ( insert_c2 @ Z @ bot_bot_set_c2 ) @ M2 )
                              @ ^ [Zs: set_c2] : ( update_c1_set_c2 @ Y6 @ ( insert_c2 @ Z @ Zs ) @ M2 )
                              @ ( lookup_c1_set_c2 @ M2 @ Y6 ) )
                          @ ( f2 @ Kv ) ) ) )
                @ t
                @ ( produc1212179418963815907set_c2 @ empty_b1_set_b2 @ empty_c1_set_c2 ) ) ) ) )
      @ ( contai3539521610808799152_order @ collec5371428610649875267_a1_a2 ) ) ) ).

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