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

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : Separation_Logic_Unbounded/0003_FixedPoint/prob_00994_030071__6960144_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1474 ( 410 unt; 191 typ;   0 def)
%            Number of atoms       : 4514 ( 794 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives : 10805 ( 273   ~;  40   |; 171   &;8324   @)
%                                         (   0 <=>;1997  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Number of types       :   16 (  15 usr)
%            Number of type conns  : 7364 (7364   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  179 ( 176 usr;  14 con; 0-4 aty)
%            Number of variables   : 3507 ( 315   ^;3159   !;  33   ?;3507   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 16:05:44.159
%------------------------------------------------------------------------------
% Could-be-implicit typings (15)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_J,type,
    set_Pr2676350728994116295_set_a: $tType ).

thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_J,type,
    set_Su1130066786674581787_set_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J_J,type,
    set_c_4840651787527498510et_a_o: $tType ).

thf(ty_n_t__Set__Oset_It__Option__Ooption_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_J,type,
    set_option_c_d_set_a: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_J,type,
    set_set_c_d_set_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J,type,
    set_c_d_set_a_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    set_e_f_set_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    set_c_d_set_a: $tType ).

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

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

thf(ty_n_tf__f,type,
    f: $tType ).

thf(ty_n_tf__e,type,
    e: $tType ).

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

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

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

% Explicit typings (176)
thf(sy_c_Complete__Lattices_OSup__class_OSup_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J,type,
    comple5290581719055393889et_a_o: set_c_d_set_a_o > ( ( c > d ) > set_a ) > $o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    comple3834726295627996700_set_a: set_c_d_set_a > ( c > d ) > set_a ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    comple139064028104612508_set_a: set_e_f_set_a > ( e > f ) > set_a ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    comple6131501996466690428_set_a: set_set_c_d_set_a > set_c_d_set_a ).

thf(sy_c_Complete__Partial__Order_Occpo_Oadmissible_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    comple1957918121334358780_set_a: ( set_c_d_set_a > ( c > d ) > set_a ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Complete__Partial__Order_Occpo_Oadmissible_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    comple7485627890665750396_set_a: ( set_e_f_set_a > ( e > f ) > set_a ) > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( e > f ) > set_a ) > $o ) > $o ).

thf(sy_c_Complete__Partial__Order_Occpo__class_Ofixp_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    comple2361085228800170300_set_a: ( ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > ( c > d ) > set_a ).

thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    condit6926915774301931483_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > set_c_d_set_a > $o ).

thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    condit3231253506778547291_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > set_e_f_set_a > $o ).

thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    condit9007271454129256903_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > set_c_d_set_a > $o ).

thf(sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    condit5311609186605872711_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > set_e_f_set_a > $o ).

thf(sy_c_Conditionally__Complete__Lattices_Opreordering__bdd_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    condit5292637031048566470_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Conditionally__Complete__Lattices_Opreordering__bdd_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    condit1596974763525182278_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > $o ).

thf(sy_c_Conditionally__Complete__Lattices_Opreordering__bdd_Obdd_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    condit8154225043310684324_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > set_c_d_set_a > $o ).

thf(sy_c_Conditionally__Complete__Lattices_Opreordering__bdd_Obdd_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    condit4458562775787300132_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > set_e_f_set_a > $o ).

thf(sy_c_Finite__Set_Ofinite_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    finite3330819693523053784_set_a: set_c_d_set_a > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    finite1740182815655637662_set_a: set_option_c_d_set_a > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    finite2397556900044337168_set_a: set_Pr2676350728994116295_set_a > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    finite457288119118821432_set_a: set_set_c_d_set_a > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__a_J,type,
    finite_finite_set_a: set_set_a > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    finite5989733633321134460_set_a: set_Su1130066786674581787_set_a > $o ).

thf(sy_c_FixedPoint_Ologic_OInf_001tf__c_001tf__d_001tf__a,type,
    inf_c_d_a: set_c_d_set_a > ( c > d ) > set_a ).

thf(sy_c_FixedPoint_Ologic_OInf_001tf__e_001tf__f_001tf__a,type,
    inf_e_f_a: set_e_f_set_a > ( e > f ) > set_a ).

thf(sy_c_FixedPoint_Ologic_OSup_001tf__c_001tf__d_001tf__a,type,
    sup_c_d_a: set_c_d_set_a > ( c > d ) > set_a ).

thf(sy_c_FixedPoint_Ologic_OSup_001tf__e_001tf__f_001tf__a,type,
    sup_e_f_a: set_e_f_set_a > ( e > f ) > set_a ).

thf(sy_c_FixedPoint_Ologic_Oempty__interp_001_062_Itf__c_Mtf__d_J_001tf__a,type,
    empty_interp_c_d_a: ( c > d ) > set_a ).

thf(sy_c_FixedPoint_Ologic_Oempty__interp_001_062_Itf__e_Mtf__f_J_001tf__a,type,
    empty_interp_e_f_a: ( e > f ) > set_a ).

thf(sy_c_FixedPoint_Ologic_Ofull__interp_001tf__c_001tf__d_001tf__a,type,
    full_interp_c_d_a: ( c > d ) > set_a ).

thf(sy_c_FixedPoint_Ologic_Ofull__interp_001tf__e_001tf__f_001tf__a,type,
    full_interp_e_f_a: ( e > f ) > set_a ).

thf(sy_c_FixedPoint_Ologic_Oinf_001tf__c_001tf__d_001tf__a,type,
    inf_c_d_a2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a ).

thf(sy_c_FixedPoint_Ologic_Oinf_001tf__e_001tf__f_001tf__a,type,
    inf_e_f_a2: ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > ( e > f ) > set_a ).

thf(sy_c_FixedPoint_Ologic_Oless_001tf__c_001tf__d_001tf__a,type,
    less_c_d_a: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ).

thf(sy_c_FixedPoint_Ologic_Oless_001tf__e_001tf__f_001tf__a,type,
    less_e_f_a: ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ).

thf(sy_c_FixedPoint_Ologic_Omonotonic_001tf__c_001tf__d_001tf__a,type,
    monotonic_c_d_a: ( ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > $o ).

thf(sy_c_FixedPoint_Ologic_Omonotonic_001tf__e_001tf__f_001tf__a,type,
    monotonic_e_f_a: ( ( ( e > f ) > set_a ) > ( e > f ) > set_a ) > $o ).

thf(sy_c_FixedPoint_Ologic_Oset__closure__property_001tf__a_001tf__c_001tf__d,type,
    set_cl2807270042661212426_a_c_d: ( a > a > set_a ) > ( ( c > d ) > set_a ) > $o ).

thf(sy_c_FixedPoint_Ologic_Oset__closure__property_001tf__a_001tf__e_001tf__f,type,
    set_cl6455730915570636170_a_e_f: ( a > a > set_a ) > ( ( e > f ) > set_a ) > $o ).

thf(sy_c_FixedPoint_Ologic_Osmaller__interp_001tf__c_001tf__d_001tf__a,type,
    smaller_interp_c_d_a: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ).

thf(sy_c_FixedPoint_Ologic_Osmaller__interp_001tf__e_001tf__f_001tf__a,type,
    smaller_interp_e_f_a: ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J,type,
    monoto6135324833271912870et_a_o: set_c_d_set_a > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Fun_Omonotone__on_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    monoto2937423850181994535_set_a: set_c_d_set_a > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    monoto8465133619513386151_set_a: set_c_d_set_a > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( e > f ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    monoto6642458133393520519_set_a: set_c_d_set_a > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( set_c_d_set_a > set_c_d_set_a > $o ) > ( ( ( c > d ) > set_a ) > set_c_d_set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_001t__Set__Oset_Itf__a_J,type,
    monoto6316088450447394390_set_a: set_c_d_set_a > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( set_a > set_a > $o ) > ( ( ( c > d ) > set_a ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J,type,
    monoto947098964958182694et_a_o: set_e_f_set_a > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ) > ( ( ( e > f ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Fun_Omonotone__on_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    monoto247478589472066471_set_a: set_e_f_set_a > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( e > f ) > set_a ) > ( c > d ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    monoto5775188358803458087_set_a: set_e_f_set_a > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( e > f ) > set_a ) > ( e > f ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    monoto7716863510275742471_set_a: set_e_f_set_a > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( set_c_d_set_a > set_c_d_set_a > $o ) > ( ( ( e > f ) > set_a ) > set_c_d_set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_001t__Set__Oset_Itf__a_J,type,
    monoto2776068642243291606_set_a: set_e_f_set_a > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( set_a > set_a > $o ) > ( ( ( e > f ) > set_a ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    monoto5673664640695304391_set_a: set_set_c_d_set_a > ( set_c_d_set_a > set_c_d_set_a > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( set_c_d_set_a > ( c > d ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    monoto4733996707696316455_set_a: set_set_c_d_set_a > ( set_c_d_set_a > set_c_d_set_a > $o ) > ( set_c_d_set_a > set_c_d_set_a > $o ) > ( set_c_d_set_a > set_c_d_set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_001t__Set__Oset_Itf__a_J,type,
    monoto9091215303422693110_set_a: set_set_c_d_set_a > ( set_c_d_set_a > set_c_d_set_a > $o ) > ( set_a > set_a > $o ) > ( set_c_d_set_a > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Set__Oset_Itf__a_J_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    monoto2748056057003999288_set_a: set_set_a > ( set_a > set_a > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( set_a > ( c > d ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Set__Oset_Itf__a_J_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    monoto8275765826335390904_set_a: set_set_a > ( set_a > set_a > $o ) > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( set_a > ( e > f ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Set__Oset_Itf__a_J_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    monoto7894950695950633880_set_a: set_set_a > ( set_a > set_a > $o ) > ( set_c_d_set_a > set_c_d_set_a > $o ) > ( set_a > set_c_d_set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Set__Oset_Itf__a_J_001t__Set__Oset_Itf__a_J,type,
    monoto7172710143293369831_set_a: set_set_a > ( set_a > set_a > $o ) > ( set_a > set_a > $o ) > ( set_a > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001tf__a_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J,type,
    monoto466107916892698775et_a_o: set_a > ( a > a > $o ) > ( ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ) > ( a > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Fun_Omonotone__on_001tf__a_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    monoto2502030104860647832_set_a: set_a > ( a > a > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( a > ( c > d ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001tf__a_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    monoto8029739874192039448_set_a: set_a > ( a > a > $o ) > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( a > ( e > f ) > set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001tf__a_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    monoto4999900198720154872_set_a: set_a > ( a > a > $o ) > ( set_c_d_set_a > set_c_d_set_a > $o ) > ( a > set_c_d_set_a ) > $o ).

thf(sy_c_Fun_Omonotone__on_001tf__a_001t__Set__Oset_Itf__a_J,type,
    monotone_on_a_set_a: set_a > ( a > a > $o ) > ( set_a > set_a > $o ) > ( a > set_a ) > $o ).

thf(sy_c_Groups_Ocomm__monoid_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    comm_m5313561445344189892_set_a: ( set_c_d_set_a > set_c_d_set_a > set_c_d_set_a ) > set_c_d_set_a > $o ).

thf(sy_c_Groups_Ominus__class_Ominus_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    minus_6165026464846083862_set_a: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    minus_1665977719694084726_set_a: set_c_d_set_a > set_c_d_set_a > set_c_d_set_a ).

thf(sy_c_Groups_Omonoid_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    monoid_set_c_d_set_a: ( set_c_d_set_a > set_c_d_set_a > set_c_d_set_a ) > set_c_d_set_a > $o ).

thf(sy_c_If_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    if_e_f_set_a: $o > ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > ( e > f ) > set_a ).

thf(sy_c_Inductive_Ocomplete__lattice_Ogfp_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    comple4132920576971123013_set_a: ( set_c_d_set_a > ( c > d ) > set_a ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > ( c > d ) > set_a ).

thf(sy_c_Inductive_Ocomplete__lattice_Ogfp_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    comple437258309447738821_set_a: ( set_e_f_set_a > ( e > f ) > set_a ) > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( e > f ) > set_a ) > ( e > f ) > set_a ) > ( e > f ) > set_a ).

thf(sy_c_Inductive_Ocomplete__lattice_Olfp_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    comple5961674822413889664_set_a: ( set_c_d_set_a > ( c > d ) > set_a ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > ( c > d ) > set_a ).

thf(sy_c_Inductive_Ocomplete__lattice_Olfp_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    comple2266012554890505472_set_a: ( set_e_f_set_a > ( e > f ) > set_a ) > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( e > f ) > set_a ) > ( e > f ) > set_a ) > ( e > f ) > set_a ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    inf_inf_c_d_set_a: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    inf_in754637537901350525_set_a: set_c_d_set_a > set_c_d_set_a > set_c_d_set_a ).

thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    semila3717735699007493233_set_a: ( set_c_d_set_a > set_c_d_set_a > set_c_d_set_a ) > set_c_d_set_a > $o ).

thf(sy_c_Lattices_Osemilattice__neutr__order_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    semila6957839794703059165_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    semila2050215183435169853_set_a: ( set_c_d_set_a > set_c_d_set_a > set_c_d_set_a ) > set_c_d_set_a > ( set_c_d_set_a > set_c_d_set_a > $o ) > ( set_c_d_set_a > set_c_d_set_a > $o ) > $o ).

thf(sy_c_Lattices_Osemilattice__order_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    semila1630236661048524575_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    sup_sup_c_d_set_a: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    sup_su3175602471750379875_set_a: set_c_d_set_a > set_c_d_set_a > set_c_d_set_a ).

thf(sy_c_Lattices__Big_Osemilattice__inf_OInf__fin_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    lattic1898000229760699588_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > set_c_d_set_a > ( c > d ) > set_a ).

thf(sy_c_Lattices__Big_Osemilattice__order__set_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    lattic1995125144389820681_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J,type,
    bot_bo919924463001950746et_a_o: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J,type,
    bot_bot_c_d_set_a_o: ( ( c > d ) > set_a ) > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    bot_bot_c_d_set_a: ( c > d ) > set_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    bot_bo738396921950161403_set_a: set_c_d_set_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    bot_bo750607107412379259_set_a: set_e_f_set_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
    bot_bot_set_a: set_a ).

thf(sy_c_Orderings_Oord_OLeast_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    least_c_d_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > $o ) > ( c > d ) > set_a ).

thf(sy_c_Orderings_Oord_OLeast_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    least_e_f_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( e > f ) > set_a ) > $o ) > ( e > f ) > set_a ).

thf(sy_c_Orderings_Oord_Omax_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    max_c_d_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a ).

thf(sy_c_Orderings_Oord_Omax_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    max_e_f_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > ( e > f ) > set_a ).

thf(sy_c_Orderings_Oord_Omin_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    min_c_d_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a ).

thf(sy_c_Orderings_Oord_Omin_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    min_e_f_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > ( e > f ) > set_a ).

thf(sy_c_Orderings_Oord__class_Oless_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J,type,
    ord_le5853012546958565978et_a_o: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J,type,
    ord_less_c_d_set_a_o: ( ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    ord_less_c_d_set_a: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    ord_less_e_f_set_a: ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    ord_le3685282097655362107_set_a: set_c_d_set_a > set_c_d_set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_I_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    ord_le3697492283117579963_set_a: set_e_f_set_a > set_e_f_set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_J,type,
    ord_le7529600783926193563_set_a: set_set_c_d_set_a > set_set_c_d_set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
    ord_less_set_set_a: set_set_a > set_set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
    ord_less_set_a: set_a > set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J,type,
    ord_le1832228425591547726et_a_o: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J,type,
    ord_le961293222253252206et_a_o: ( ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J,type,
    ord_le6228063065474434894et_a_o: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    ord_le8464990428230162895_set_a: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    ord_le4769328160706778703_set_a: ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_M_062_It__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_M_Eo_J_J,type,
    ord_le5545401091215412046et_a_o: ( set_c_d_set_a > set_c_d_set_a > $o ) > ( set_c_d_set_a > set_c_d_set_a > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_Itf__a_J_M_062_It__Set__Oset_Itf__a_J_M_Eo_J_J,type,
    ord_le6897189994354892814et_a_o: ( set_a > set_a > $o ) > ( set_a > set_a > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    ord_le5982164083705284911_set_a: set_c_d_set_a > set_c_d_set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    ord_le5994374269167502767_set_a: set_e_f_set_a > set_e_f_set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_J,type,
    ord_le7272806397018272911_set_a: set_set_c_d_set_a > set_set_c_d_set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
    ord_le3724670747650509150_set_a: set_set_a > set_set_a > $o ).

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

thf(sy_c_Orderings_Oorder_OGreatest_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    greatest_c_d_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > $o ) > ( c > d ) > set_a ).

thf(sy_c_Orderings_Oorder_OGreatest_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    greatest_e_f_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( ( e > f ) > set_a ) > $o ) > ( e > f ) > set_a ).

thf(sy_c_Orderings_Oordering_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    ordering_c_d_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Orderings_Oordering__top_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    orderi5785346111247480928_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( c > d ) > set_a ) > $o ).

thf(sy_c_Orderings_Oordering__top_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    orderi13773357969974208_set_a: ( set_c_d_set_a > set_c_d_set_a > $o ) > ( set_c_d_set_a > set_c_d_set_a > $o ) > set_c_d_set_a > $o ).

thf(sy_c_Orderings_Opartial__preordering_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J,type,
    partia8378609006112419556et_a_o: ( ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ) > $o ).

thf(sy_c_Orderings_Opartial__preordering_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    partia701112543150332005_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Orderings_Opartial__preordering_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    partia6228822312481723621_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > $o ).

thf(sy_c_Orderings_Opartial__preordering_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    partia1270112395057131461_set_a: ( set_c_d_set_a > set_c_d_set_a > $o ) > $o ).

thf(sy_c_Orderings_Opartial__preordering_001t__Set__Oset_Itf__a_J,type,
    partia6602192050731689876_set_a: ( set_a > set_a > $o ) > $o ).

thf(sy_c_Orderings_Opreordering_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    preord7021486942077351306_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J,type,
    top_to5121151994761190654et_a_o: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J,type,
    top_top_c_d_set_a_o: ( ( c > d ) > set_a ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J,type,
    top_top_e_f_set_a_o: ( ( e > f ) > set_a ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    top_top_c_d_set_a: ( c > d ) > set_a ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    top_top_e_f_set_a: ( e > f ) > set_a ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_M_Eo_J,type,
    top_to6119605859643668830et_a_o: set_c_d_set_a > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Set__Oset_Itf__a_J_M_Eo_J,type,
    top_top_set_a_o: set_a > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_Itf__a_M_Eo_J,type,
    top_top_a_o: a > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
    top_top_o: $o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    top_to4267977599310771935_set_a: set_c_d_set_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    top_to4280187784772989791_set_a: set_e_f_set_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_J,type,
    top_to1333438998097461157_set_a: set_option_c_d_set_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_J,type,
    top_to3895570120271872023_set_a: set_Pr2676350728994116295_set_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_J,type,
    top_to5717711934741766719_set_a: set_set_c_d_set_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
    top_top_set_set_a: set_set_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_J,type,
    top_to279427854467338187_set_a: set_Su1130066786674581787_set_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
    top_top_set_a: set_a ).

thf(sy_c_Relation_Oantisymp__on_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_J,type,
    antisy3644999338385500379et_a_o: set_c_4840651787527498510et_a_o > ( ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ) > $o ).

thf(sy_c_Relation_Oantisymp__on_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    antisy1518167394357443548_set_a: set_c_d_set_a > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > $o ).

thf(sy_c_Relation_Oantisymp__on_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    antisy7045877163688835164_set_a: set_e_f_set_a > ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > $o ).

thf(sy_c_Relation_Oantisymp__on_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    antisy2568922457103120188_set_a: set_set_c_d_set_a > ( set_c_d_set_a > set_c_d_set_a > $o ) > $o ).

thf(sy_c_Relation_Oantisymp__on_001t__Set__Oset_Itf__a_J,type,
    antisymp_on_set_a: set_set_a > ( set_a > set_a > $o ) > $o ).

thf(sy_c_Relation_Oantisymp__on_001tf__a,type,
    antisymp_on_a: set_a > ( a > a > $o ) > $o ).

thf(sy_c_Set_OCollect_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    collect_c_d_set_a: ( ( ( c > d ) > set_a ) > $o ) > set_c_d_set_a ).

thf(sy_c_Set_OCollect_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    collect_e_f_set_a: ( ( ( e > f ) > set_a ) > $o ) > set_e_f_set_a ).

thf(sy_c_Set_OCollect_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    collec3354561713582630522_set_a: ( set_c_d_set_a > $o ) > set_set_c_d_set_a ).

thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__a_J,type,
    collect_set_a: ( set_a > $o ) > set_set_a ).

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

thf(sy_c_Set_Oimage_001_062_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_M_Eo_J_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    image_8552787320881293370_set_a: ( ( ( ( c > d ) > set_a ) > $o ) > set_c_d_set_a ) > set_c_d_set_a_o > set_set_c_d_set_a ).

thf(sy_c_Set_Oimage_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    image_5710119992958135237_set_a: ( ( ( c > d ) > set_a ) > ( c > d ) > set_a ) > set_c_d_set_a > set_c_d_set_a ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    image_5418612861375423429_set_a: ( set_c_d_set_a > set_c_d_set_a ) > set_set_c_d_set_a > set_set_c_d_set_a ).

thf(sy_c_Set_Oinsert_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    insert_c_d_set_a: ( ( c > d ) > set_a ) > set_c_d_set_a > set_c_d_set_a ).

thf(sy_c_Set_Ois__singleton_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    is_sin6979784932356128547_set_a: set_c_d_set_a > $o ).

thf(sy_c_Set__Interval_Oord_OatLeastAtMost_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_at2224545791267470424_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > set_c_d_set_a ).

thf(sy_c_Set__Interval_Oord_OatLeastAtMost_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_at7752255560598862040_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > set_e_f_set_a ).

thf(sy_c_Set__Interval_Oord_OatLeastLessThan_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_at2139306834251651636_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > set_c_d_set_a ).

thf(sy_c_Set__Interval_Oord_OatLeast_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_at4358065015900363374_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( c > d ) > set_a ) > set_c_d_set_a ).

thf(sy_c_Set__Interval_Oord_OatLeast_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_at662402748376979182_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( e > f ) > set_a ) > set_e_f_set_a ).

thf(sy_c_Set__Interval_Oord_OatMost_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_atMost_c_d_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( c > d ) > set_a ) > set_c_d_set_a ).

thf(sy_c_Set__Interval_Oord_OatMost_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_atMost_e_f_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( e > f ) > set_a ) > set_e_f_set_a ).

thf(sy_c_Set__Interval_Oord_OgreaterThanAtMost_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_gr4053032598485390707_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > set_c_d_set_a ).

thf(sy_c_Set__Interval_Oord_OgreaterThanLessThan_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_gr2245648953767368143_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > set_c_d_set_a ).

thf(sy_c_Set__Interval_Oord_OgreaterThan_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_gr5532796609634356233_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( c > d ) > set_a ) > set_c_d_set_a ).

thf(sy_c_Set__Interval_Oord_OlessThan_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_le5418582716766741598_set_a: ( ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o ) > ( ( c > d ) > set_a ) > set_c_d_set_a ).

thf(sy_c_Set__Interval_Oord_OlessThan_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    set_le1722920449243357406_set_a: ( ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o ) > ( ( e > f ) > set_a ) > set_e_f_set_a ).

thf(sy_c_member_001_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J,type,
    member_c_d_set_a: ( ( c > d ) > set_a ) > set_c_d_set_a > $o ).

thf(sy_c_member_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J,type,
    member_e_f_set_a: ( ( e > f ) > set_a ) > set_e_f_set_a > $o ).

thf(sy_c_member_001t__Set__Oset_I_062_I_062_Itf__c_Mtf__d_J_Mt__Set__Oset_Itf__a_J_J_J,type,
    member_set_c_d_set_a: set_c_d_set_a > set_set_c_d_set_a > $o ).

thf(sy_c_member_001t__Set__Oset_Itf__a_J,type,
    member_set_a: set_a > set_set_a > $o ).

thf(sy_c_member_001tf__a,type,
    member_a: a > set_a > $o ).

thf(sy_v_S,type,
    s: a > a > set_a ).

thf(sy_v_f,type,
    f2: ( ( c > d ) > set_a ) > ( c > d ) > set_a ).

% Relevant facts (1279)
thf(fact_0_assms_I1_J,axiom,
    monotonic_c_d_a @ f2 ).

% assms(1)
thf(fact_1_mono__same,axiom,
    ( monotonic_e_f_a
    = ( monoto5775188358803458087_set_a @ top_to4280187784772989791_set_a @ ord_le4769328160706778703_set_a @ ord_le4769328160706778703_set_a ) ) ).

% mono_same
thf(fact_2_mono__same,axiom,
    ( monotonic_c_d_a
    = ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a ) ) ).

% mono_same
thf(fact_3_order__class_OmonoD,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_le8464990428230162895_set_a @ X @ Y )
       => ( ord_le8464990428230162895_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoD
thf(fact_4_order__class_OmonoD,axiom,
    ! [F: set_a > set_a,X: set_a,Y: set_a] :
      ( ( monoto7172710143293369831_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_less_eq_set_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoD
thf(fact_5_order__class_OmonoD,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto6316088450447394390_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le8464990428230162895_set_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoD
thf(fact_6_order__class_OmonoD,axiom,
    ! [F: set_a > ( c > d ) > set_a,X: set_a,Y: set_a] :
      ( ( monoto2748056057003999288_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_less_eq_set_a @ X @ Y )
       => ( ord_le8464990428230162895_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoD
thf(fact_7_order__class_OmonoD,axiom,
    ! [F: set_a > ( e > f ) > set_a,X: set_a,Y: set_a] :
      ( ( monoto8275765826335390904_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( ord_less_eq_set_a @ X @ Y )
       => ( ord_le4769328160706778703_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoD
thf(fact_8_order__class_OmonoD,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto2776068642243291606_set_a @ top_to4280187784772989791_set_a @ ord_le4769328160706778703_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le4769328160706778703_set_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoD
thf(fact_9_order__class_OmonoD,axiom,
    ! [F: set_c_d_set_a > set_a,X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( monoto9091215303422693110_set_a @ top_to5717711934741766719_set_a @ ord_le5982164083705284911_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoD
thf(fact_10_order__class_OmonoD,axiom,
    ! [F: set_a > set_c_d_set_a,X: set_a,Y: set_a] :
      ( ( monoto7894950695950633880_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( ord_less_eq_set_a @ X @ Y )
       => ( ord_le5982164083705284911_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoD
thf(fact_11_order__class_OmonoD,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto8465133619513386151_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( ord_le8464990428230162895_set_a @ X @ Y )
       => ( ord_le4769328160706778703_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoD
thf(fact_12_order__class_OmonoD,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ ord_le4769328160706778703_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_le4769328160706778703_set_a @ X @ Y )
       => ( ord_le8464990428230162895_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoD
thf(fact_13_order__class_OmonoE,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_le8464990428230162895_set_a @ X @ Y )
       => ( ord_le8464990428230162895_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoE
thf(fact_14_order__class_OmonoE,axiom,
    ! [F: set_a > set_a,X: set_a,Y: set_a] :
      ( ( monoto7172710143293369831_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_less_eq_set_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoE
thf(fact_15_order__class_OmonoE,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto6316088450447394390_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le8464990428230162895_set_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoE
thf(fact_16_order__class_OmonoE,axiom,
    ! [F: set_a > ( c > d ) > set_a,X: set_a,Y: set_a] :
      ( ( monoto2748056057003999288_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_less_eq_set_a @ X @ Y )
       => ( ord_le8464990428230162895_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoE
thf(fact_17_order__class_OmonoE,axiom,
    ! [F: set_a > ( e > f ) > set_a,X: set_a,Y: set_a] :
      ( ( monoto8275765826335390904_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( ord_less_eq_set_a @ X @ Y )
       => ( ord_le4769328160706778703_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoE
thf(fact_18_order__class_OmonoE,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto2776068642243291606_set_a @ top_to4280187784772989791_set_a @ ord_le4769328160706778703_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le4769328160706778703_set_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoE
thf(fact_19_order__class_OmonoE,axiom,
    ! [F: set_c_d_set_a > set_a,X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( monoto9091215303422693110_set_a @ top_to5717711934741766719_set_a @ ord_le5982164083705284911_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoE
thf(fact_20_order__class_OmonoE,axiom,
    ! [F: set_a > set_c_d_set_a,X: set_a,Y: set_a] :
      ( ( monoto7894950695950633880_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( ord_less_eq_set_a @ X @ Y )
       => ( ord_le5982164083705284911_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoE
thf(fact_21_order__class_OmonoE,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto8465133619513386151_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( ord_le8464990428230162895_set_a @ X @ Y )
       => ( ord_le4769328160706778703_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoE
thf(fact_22_order__class_OmonoE,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ ord_le4769328160706778703_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_le4769328160706778703_set_a @ X @ Y )
       => ( ord_le8464990428230162895_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.monoE
thf(fact_23_order__class_OmonoI,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
         => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% order_class.monoI
thf(fact_24_order__class_OmonoI,axiom,
    ! [F: set_a > set_a] :
      ( ! [X2: set_a,Y2: set_a] :
          ( ( ord_less_eq_set_a @ X2 @ Y2 )
         => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto7172710143293369831_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_less_eq_set_a @ F ) ) ).

% order_class.monoI
thf(fact_25_order__class_OmonoI,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
         => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto6316088450447394390_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_less_eq_set_a @ F ) ) ).

% order_class.monoI
thf(fact_26_order__class_OmonoI,axiom,
    ! [F: set_a > ( c > d ) > set_a] :
      ( ! [X2: set_a,Y2: set_a] :
          ( ( ord_less_eq_set_a @ X2 @ Y2 )
         => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto2748056057003999288_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% order_class.monoI
thf(fact_27_order__class_OmonoI,axiom,
    ! [F: set_a > ( e > f ) > set_a] :
      ( ! [X2: set_a,Y2: set_a] :
          ( ( ord_less_eq_set_a @ X2 @ Y2 )
         => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto8275765826335390904_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% order_class.monoI
thf(fact_28_order__class_OmonoI,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_a] :
      ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
         => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto2776068642243291606_set_a @ top_to4280187784772989791_set_a @ ord_le4769328160706778703_set_a @ ord_less_eq_set_a @ F ) ) ).

% order_class.monoI
thf(fact_29_order__class_OmonoI,axiom,
    ! [F: set_c_d_set_a > set_a] :
      ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ X2 @ Y2 )
         => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto9091215303422693110_set_a @ top_to5717711934741766719_set_a @ ord_le5982164083705284911_set_a @ ord_less_eq_set_a @ F ) ) ).

% order_class.monoI
thf(fact_30_order__class_OmonoI,axiom,
    ! [F: set_a > set_c_d_set_a] :
      ( ! [X2: set_a,Y2: set_a] :
          ( ( ord_less_eq_set_a @ X2 @ Y2 )
         => ( ord_le5982164083705284911_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto7894950695950633880_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le5982164083705284911_set_a @ F ) ) ).

% order_class.monoI
thf(fact_31_order__class_OmonoI,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( e > f ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
         => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto8465133619513386151_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% order_class.monoI
thf(fact_32_order__class_OmonoI,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( c > d ) > set_a] :
      ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
         => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ ord_le4769328160706778703_set_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% order_class.monoI
thf(fact_33_order__class_Omono__imp__mono__on,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( monoto2937423850181994535_set_a @ A @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% order_class.mono_imp_mono_on
thf(fact_34_order__class_Omono__imp__mono__on,axiom,
    ! [F: set_a > set_a,A: set_set_a] :
      ( ( monoto7172710143293369831_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_less_eq_set_a @ F )
     => ( monoto7172710143293369831_set_a @ A @ ord_less_eq_set_a @ ord_less_eq_set_a @ F ) ) ).

% order_class.mono_imp_mono_on
thf(fact_35_order__class_Omono__imp__mono__on,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_a,A: set_c_d_set_a] :
      ( ( monoto6316088450447394390_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_less_eq_set_a @ F )
     => ( monoto6316088450447394390_set_a @ A @ ord_le8464990428230162895_set_a @ ord_less_eq_set_a @ F ) ) ).

% order_class.mono_imp_mono_on
thf(fact_36_order__class_Omono__imp__mono__on,axiom,
    ! [F: set_a > ( c > d ) > set_a,A: set_set_a] :
      ( ( monoto2748056057003999288_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( monoto2748056057003999288_set_a @ A @ ord_less_eq_set_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% order_class.mono_imp_mono_on
thf(fact_37_order__class_Omono__imp__mono__on,axiom,
    ! [F: set_a > ( e > f ) > set_a,A: set_set_a] :
      ( ( monoto8275765826335390904_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le4769328160706778703_set_a @ F )
     => ( monoto8275765826335390904_set_a @ A @ ord_less_eq_set_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% order_class.mono_imp_mono_on
thf(fact_38_order__class_Omono__imp__mono__on,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_a,A: set_e_f_set_a] :
      ( ( monoto2776068642243291606_set_a @ top_to4280187784772989791_set_a @ ord_le4769328160706778703_set_a @ ord_less_eq_set_a @ F )
     => ( monoto2776068642243291606_set_a @ A @ ord_le4769328160706778703_set_a @ ord_less_eq_set_a @ F ) ) ).

% order_class.mono_imp_mono_on
thf(fact_39_order__class_Omono__imp__mono__on,axiom,
    ! [F: set_c_d_set_a > set_a,A: set_set_c_d_set_a] :
      ( ( monoto9091215303422693110_set_a @ top_to5717711934741766719_set_a @ ord_le5982164083705284911_set_a @ ord_less_eq_set_a @ F )
     => ( monoto9091215303422693110_set_a @ A @ ord_le5982164083705284911_set_a @ ord_less_eq_set_a @ F ) ) ).

% order_class.mono_imp_mono_on
thf(fact_40_order__class_Omono__imp__mono__on,axiom,
    ! [F: set_a > set_c_d_set_a,A: set_set_a] :
      ( ( monoto7894950695950633880_set_a @ top_top_set_set_a @ ord_less_eq_set_a @ ord_le5982164083705284911_set_a @ F )
     => ( monoto7894950695950633880_set_a @ A @ ord_less_eq_set_a @ ord_le5982164083705284911_set_a @ F ) ) ).

% order_class.mono_imp_mono_on
thf(fact_41_order__class_Omono__imp__mono__on,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,A: set_c_d_set_a] :
      ( ( monoto8465133619513386151_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le4769328160706778703_set_a @ F )
     => ( monoto8465133619513386151_set_a @ A @ ord_le8464990428230162895_set_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% order_class.mono_imp_mono_on
thf(fact_42_order__class_Omono__imp__mono__on,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,A: set_e_f_set_a] :
      ( ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ ord_le4769328160706778703_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( monoto247478589472066471_set_a @ A @ ord_le4769328160706778703_set_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% order_class.mono_imp_mono_on
thf(fact_43_UNIV__I,axiom,
    ! [X: a] : ( member_a @ X @ top_top_set_a ) ).

% UNIV_I
thf(fact_44_UNIV__I,axiom,
    ! [X: set_c_d_set_a] : ( member_set_c_d_set_a @ X @ top_to5717711934741766719_set_a ) ).

% UNIV_I
thf(fact_45_UNIV__I,axiom,
    ! [X: set_a] : ( member_set_a @ X @ top_top_set_set_a ) ).

% UNIV_I
thf(fact_46_UNIV__I,axiom,
    ! [X: ( e > f ) > set_a] : ( member_e_f_set_a @ X @ top_to4280187784772989791_set_a ) ).

% UNIV_I
thf(fact_47_UNIV__I,axiom,
    ! [X: ( c > d ) > set_a] : ( member_c_d_set_a @ X @ top_to4267977599310771935_set_a ) ).

% UNIV_I
thf(fact_48_iso__tuple__UNIV__I,axiom,
    ! [X: a] : ( member_a @ X @ top_top_set_a ) ).

% iso_tuple_UNIV_I
thf(fact_49_iso__tuple__UNIV__I,axiom,
    ! [X: set_c_d_set_a] : ( member_set_c_d_set_a @ X @ top_to5717711934741766719_set_a ) ).

% iso_tuple_UNIV_I
thf(fact_50_iso__tuple__UNIV__I,axiom,
    ! [X: set_a] : ( member_set_a @ X @ top_top_set_set_a ) ).

% iso_tuple_UNIV_I
thf(fact_51_iso__tuple__UNIV__I,axiom,
    ! [X: ( e > f ) > set_a] : ( member_e_f_set_a @ X @ top_to4280187784772989791_set_a ) ).

% iso_tuple_UNIV_I
thf(fact_52_iso__tuple__UNIV__I,axiom,
    ! [X: ( c > d ) > set_a] : ( member_c_d_set_a @ X @ top_to4267977599310771935_set_a ) ).

% iso_tuple_UNIV_I
thf(fact_53_top__apply,axiom,
    ( top_top_c_d_set_a_o
    = ( ^ [X3: ( c > d ) > set_a] : top_top_o ) ) ).

% top_apply
thf(fact_54_top__apply,axiom,
    ( top_top_c_d_set_a
    = ( ^ [X3: c > d] : top_top_set_a ) ) ).

% top_apply
thf(fact_55_preorder__class_Oorder__refl,axiom,
    ! [X: set_c_d_set_a] : ( ord_le5982164083705284911_set_a @ X @ X ) ).

% preorder_class.order_refl
thf(fact_56_preorder__class_Oorder__refl,axiom,
    ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) ).

% preorder_class.order_refl
thf(fact_57_preorder__class_Oorder__refl,axiom,
    ! [X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] : ( ord_le1832228425591547726et_a_o @ X @ X ) ).

% preorder_class.order_refl
thf(fact_58_preorder__class_Oorder__refl,axiom,
    ! [X: ( e > f ) > set_a] : ( ord_le4769328160706778703_set_a @ X @ X ) ).

% preorder_class.order_refl
thf(fact_59_preorder__class_Oorder__refl,axiom,
    ! [X: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ X @ X ) ).

% preorder_class.order_refl
thf(fact_60_preorder__class_Odual__order_Orefl,axiom,
    ! [A2: set_c_d_set_a] : ( ord_le5982164083705284911_set_a @ A2 @ A2 ) ).

% preorder_class.dual_order.refl
thf(fact_61_preorder__class_Odual__order_Orefl,axiom,
    ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).

% preorder_class.dual_order.refl
thf(fact_62_preorder__class_Odual__order_Orefl,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] : ( ord_le1832228425591547726et_a_o @ A2 @ A2 ) ).

% preorder_class.dual_order.refl
thf(fact_63_preorder__class_Odual__order_Orefl,axiom,
    ! [A2: ( e > f ) > set_a] : ( ord_le4769328160706778703_set_a @ A2 @ A2 ) ).

% preorder_class.dual_order.refl
thf(fact_64_preorder__class_Odual__order_Orefl,axiom,
    ! [A2: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ A2 @ A2 ) ).

% preorder_class.dual_order.refl
thf(fact_65_local_OmonoD,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_c_d_set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto6642458133393520519_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( smaller_interp_c_d_a @ X @ Y )
       => ( ord_le5982164083705284911_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoD
thf(fact_66_local_OmonoD,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto6316088450447394390_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_less_eq_set_a @ F )
     => ( ( smaller_interp_c_d_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoD
thf(fact_67_local_OmonoD,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto6135324833271912870et_a_o @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le1832228425591547726et_a_o @ F )
     => ( ( smaller_interp_c_d_a @ X @ Y )
       => ( ord_le1832228425591547726et_a_o @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoD
thf(fact_68_local_OmonoD,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto8465133619513386151_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( smaller_interp_c_d_a @ X @ Y )
       => ( ord_le4769328160706778703_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoD
thf(fact_69_local_OmonoD,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( smaller_interp_e_f_a @ X @ Y )
       => ( ord_le8464990428230162895_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoD
thf(fact_70_local_OmonoD,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_c_d_set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto7716863510275742471_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( smaller_interp_e_f_a @ X @ Y )
       => ( ord_le5982164083705284911_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoD
thf(fact_71_local_OmonoD,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto2776068642243291606_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_less_eq_set_a @ F )
     => ( ( smaller_interp_e_f_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoD
thf(fact_72_local_OmonoD,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto947098964958182694et_a_o @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le1832228425591547726et_a_o @ F )
     => ( ( smaller_interp_e_f_a @ X @ Y )
       => ( ord_le1832228425591547726et_a_o @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoD
thf(fact_73_local_OmonoD,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( e > f ) > set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto5775188358803458087_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( smaller_interp_e_f_a @ X @ Y )
       => ( ord_le4769328160706778703_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoD
thf(fact_74_local_OmonoD,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( smaller_interp_c_d_a @ X @ Y )
       => ( ord_le8464990428230162895_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoD
thf(fact_75_local_OmonoE,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_c_d_set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto6642458133393520519_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( smaller_interp_c_d_a @ X @ Y )
       => ( ord_le5982164083705284911_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoE
thf(fact_76_local_OmonoE,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto6316088450447394390_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_less_eq_set_a @ F )
     => ( ( smaller_interp_c_d_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoE
thf(fact_77_local_OmonoE,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto6135324833271912870et_a_o @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le1832228425591547726et_a_o @ F )
     => ( ( smaller_interp_c_d_a @ X @ Y )
       => ( ord_le1832228425591547726et_a_o @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoE
thf(fact_78_local_OmonoE,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto8465133619513386151_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( smaller_interp_c_d_a @ X @ Y )
       => ( ord_le4769328160706778703_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoE
thf(fact_79_local_OmonoE,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( smaller_interp_e_f_a @ X @ Y )
       => ( ord_le8464990428230162895_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoE
thf(fact_80_local_OmonoE,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_c_d_set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto7716863510275742471_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( smaller_interp_e_f_a @ X @ Y )
       => ( ord_le5982164083705284911_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoE
thf(fact_81_local_OmonoE,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto2776068642243291606_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_less_eq_set_a @ F )
     => ( ( smaller_interp_e_f_a @ X @ Y )
       => ( ord_less_eq_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoE
thf(fact_82_local_OmonoE,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto947098964958182694et_a_o @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le1832228425591547726et_a_o @ F )
     => ( ( smaller_interp_e_f_a @ X @ Y )
       => ( ord_le1832228425591547726et_a_o @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoE
thf(fact_83_local_OmonoE,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( e > f ) > set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto5775188358803458087_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( smaller_interp_e_f_a @ X @ Y )
       => ( ord_le4769328160706778703_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoE
thf(fact_84_local_OmonoE,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( smaller_interp_c_d_a @ X @ Y )
       => ( ord_le8464990428230162895_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.monoE
thf(fact_85_smaller__interp__def,axiom,
    ( smaller_interp_c_d_a
    = ( ^ [Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
        ! [S: c > d] : ( ord_less_eq_set_a @ ( Delta @ S ) @ ( Delta2 @ S ) ) ) ) ).

% smaller_interp_def
thf(fact_86_smaller__interp__def,axiom,
    ( smaller_interp_e_f_a
    = ( ^ [Delta: ( e > f ) > set_a,Delta2: ( e > f ) > set_a] :
        ! [S: e > f] : ( ord_less_eq_set_a @ ( Delta @ S ) @ ( Delta2 @ S ) ) ) ) ).

% smaller_interp_def
thf(fact_87_smaller__interp__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ A2 @ B )
     => ( ( smaller_interp_c_d_a @ B @ C )
       => ( smaller_interp_c_d_a @ A2 @ C ) ) ) ).

% smaller_interp_trans
thf(fact_88_smaller__interp__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ A2 @ B )
     => ( ( smaller_interp_e_f_a @ B @ C )
       => ( smaller_interp_e_f_a @ A2 @ C ) ) ) ).

% smaller_interp_trans
thf(fact_89_smaller__interp__antisym,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ A2 @ B )
     => ( ( smaller_interp_c_d_a @ B @ A2 )
       => ( A2 = B ) ) ) ).

% smaller_interp_antisym
thf(fact_90_smaller__interp__antisym,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ A2 @ B )
     => ( ( smaller_interp_e_f_a @ B @ A2 )
       => ( A2 = B ) ) ) ).

% smaller_interp_antisym
thf(fact_91_smaller__interpI,axiom,
    ! [Delta3: ( c > d ) > set_a,Delta4: ( c > d ) > set_a] :
      ( ! [S2: c > d,X2: a] :
          ( ( member_a @ X2 @ ( Delta3 @ S2 ) )
         => ( member_a @ X2 @ ( Delta4 @ S2 ) ) )
     => ( smaller_interp_c_d_a @ Delta3 @ Delta4 ) ) ).

% smaller_interpI
thf(fact_92_smaller__interpI,axiom,
    ! [Delta3: ( e > f ) > set_a,Delta4: ( e > f ) > set_a] :
      ( ! [S2: e > f,X2: a] :
          ( ( member_a @ X2 @ ( Delta3 @ S2 ) )
         => ( member_a @ X2 @ ( Delta4 @ S2 ) ) )
     => ( smaller_interp_e_f_a @ Delta3 @ Delta4 ) ) ).

% smaller_interpI
thf(fact_93_local_Oorder__trans,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ X @ Y )
     => ( ( smaller_interp_c_d_a @ Y @ Z )
       => ( smaller_interp_c_d_a @ X @ Z ) ) ) ).

% local.order_trans
thf(fact_94_local_Oorder__trans,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a,Z: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ X @ Y )
     => ( ( smaller_interp_e_f_a @ Y @ Z )
       => ( smaller_interp_e_f_a @ X @ Z ) ) ) ).

% local.order_trans
thf(fact_95_local_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: ( c > d ) > set_a,Z2: ( c > d ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [X3: ( c > d ) > set_a,Y4: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ X3 @ Y4 )
          & ( smaller_interp_c_d_a @ Y4 @ X3 ) ) ) ) ).

% local.order_eq_iff
thf(fact_96_local_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: ( e > f ) > set_a,Z2: ( e > f ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [X3: ( e > f ) > set_a,Y4: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ X3 @ Y4 )
          & ( smaller_interp_e_f_a @ Y4 @ X3 ) ) ) ) ).

% local.order_eq_iff
thf(fact_97_local_Oorder__antisym,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ X @ Y )
     => ( ( smaller_interp_c_d_a @ Y @ X )
       => ( X = Y ) ) ) ).

% local.order_antisym
thf(fact_98_local_Oorder__antisym,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ X @ Y )
     => ( ( smaller_interp_e_f_a @ Y @ X )
       => ( X = Y ) ) ) ).

% local.order_antisym
thf(fact_99_local_Oord__le__eq__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ A2 @ B )
     => ( ( B = C )
       => ( smaller_interp_c_d_a @ A2 @ C ) ) ) ).

% local.ord_le_eq_trans
thf(fact_100_local_Oord__le__eq__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ A2 @ B )
     => ( ( B = C )
       => ( smaller_interp_e_f_a @ A2 @ C ) ) ) ).

% local.ord_le_eq_trans
thf(fact_101_local_Oord__eq__le__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( A2 = B )
     => ( ( smaller_interp_c_d_a @ B @ C )
       => ( smaller_interp_c_d_a @ A2 @ C ) ) ) ).

% local.ord_eq_le_trans
thf(fact_102_local_Oord__eq__le__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( A2 = B )
     => ( ( smaller_interp_e_f_a @ B @ C )
       => ( smaller_interp_e_f_a @ A2 @ C ) ) ) ).

% local.ord_eq_le_trans
thf(fact_103_local_Oeq__refl,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( X = Y )
     => ( smaller_interp_c_d_a @ X @ Y ) ) ).

% local.eq_refl
thf(fact_104_local_Oeq__refl,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( X = Y )
     => ( smaller_interp_e_f_a @ X @ Y ) ) ).

% local.eq_refl
thf(fact_105_local_Oantisym__conv,axiom,
    ! [Y: ( c > d ) > set_a,X: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ Y @ X )
     => ( ( smaller_interp_c_d_a @ X @ Y )
        = ( X = Y ) ) ) ).

% local.antisym_conv
thf(fact_106_local_Oantisym__conv,axiom,
    ! [Y: ( e > f ) > set_a,X: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ Y @ X )
     => ( ( smaller_interp_e_f_a @ X @ Y )
        = ( X = Y ) ) ) ).

% local.antisym_conv
thf(fact_107_local_Oorder_Oeq__iff,axiom,
    ( ( ^ [Y3: ( c > d ) > set_a,Z2: ( c > d ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ A3 @ B2 )
          & ( smaller_interp_c_d_a @ B2 @ A3 ) ) ) ) ).

% local.order.eq_iff
thf(fact_108_local_Oorder_Oeq__iff,axiom,
    ( ( ^ [Y3: ( e > f ) > set_a,Z2: ( e > f ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ A3 @ B2 )
          & ( smaller_interp_e_f_a @ B2 @ A3 ) ) ) ) ).

% local.order.eq_iff
thf(fact_109_local_Odual__order_Otrans,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ B @ A2 )
     => ( ( smaller_interp_c_d_a @ C @ B )
       => ( smaller_interp_c_d_a @ C @ A2 ) ) ) ).

% local.dual_order.trans
thf(fact_110_local_Odual__order_Otrans,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ B @ A2 )
     => ( ( smaller_interp_e_f_a @ C @ B )
       => ( smaller_interp_e_f_a @ C @ A2 ) ) ) ).

% local.dual_order.trans
thf(fact_111_local_Odual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: ( c > d ) > set_a,Z2: ( c > d ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ B2 @ A3 )
          & ( smaller_interp_c_d_a @ A3 @ B2 ) ) ) ) ).

% local.dual_order.eq_iff
thf(fact_112_local_Odual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: ( e > f ) > set_a,Z2: ( e > f ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ B2 @ A3 )
          & ( smaller_interp_e_f_a @ A3 @ B2 ) ) ) ) ).

% local.dual_order.eq_iff
thf(fact_113_local_Odual__order_Oantisym,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ B @ A2 )
     => ( ( smaller_interp_c_d_a @ A2 @ B )
       => ( A2 = B ) ) ) ).

% local.dual_order.antisym
thf(fact_114_local_Odual__order_Oantisym,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ B @ A2 )
     => ( ( smaller_interp_e_f_a @ A2 @ B )
       => ( A2 = B ) ) ) ).

% local.dual_order.antisym
thf(fact_115_monotonicI,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( e > f ) > set_a] :
      ( ! [Delta5: ( e > f ) > set_a,Delta6: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ Delta5 @ Delta6 )
         => ( smaller_interp_e_f_a @ ( F @ Delta5 ) @ ( F @ Delta6 ) ) )
     => ( monotonic_e_f_a @ F ) ) ).

% monotonicI
thf(fact_116_monotonicI,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [Delta5: ( c > d ) > set_a,Delta6: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ Delta5 @ Delta6 )
         => ( smaller_interp_c_d_a @ ( F @ Delta5 ) @ ( F @ Delta6 ) ) )
     => ( monotonic_c_d_a @ F ) ) ).

% monotonicI
thf(fact_117_monotonic__def,axiom,
    ( monotonic_e_f_a
    = ( ^ [F2: ( ( e > f ) > set_a ) > ( e > f ) > set_a] :
        ! [Delta: ( e > f ) > set_a,Delta2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ Delta @ Delta2 )
         => ( smaller_interp_e_f_a @ ( F2 @ Delta ) @ ( F2 @ Delta2 ) ) ) ) ) ).

% monotonic_def
thf(fact_118_monotonic__def,axiom,
    ( monotonic_c_d_a
    = ( ^ [F2: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
        ! [Delta: ( c > d ) > set_a,Delta2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ Delta @ Delta2 )
         => ( smaller_interp_c_d_a @ ( F2 @ Delta ) @ ( F2 @ Delta2 ) ) ) ) ) ).

% monotonic_def
thf(fact_119_local_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( monoto6642458133393520519_set_a @ A @ smaller_interp_c_d_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto6642458133393520519_set_a @ B3 @ smaller_interp_c_d_a @ ord_le5982164083705284911_set_a @ F ) ) ) ).

% local.mono_on_subset
thf(fact_120_local_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_a,B3: set_c_d_set_a] :
      ( ( monoto6316088450447394390_set_a @ A @ smaller_interp_c_d_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto6316088450447394390_set_a @ B3 @ smaller_interp_c_d_a @ ord_less_eq_set_a @ F ) ) ) ).

% local.mono_on_subset
thf(fact_121_local_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B3: set_c_d_set_a] :
      ( ( monoto6135324833271912870et_a_o @ A @ smaller_interp_c_d_a @ ord_le1832228425591547726et_a_o @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto6135324833271912870et_a_o @ B3 @ smaller_interp_c_d_a @ ord_le1832228425591547726et_a_o @ F ) ) ) ).

% local.mono_on_subset
thf(fact_122_local_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,B3: set_c_d_set_a] :
      ( ( monoto8465133619513386151_set_a @ A @ smaller_interp_c_d_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto8465133619513386151_set_a @ B3 @ smaller_interp_c_d_a @ ord_le4769328160706778703_set_a @ F ) ) ) ).

% local.mono_on_subset
thf(fact_123_local_Omono__on__subset,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,B3: set_e_f_set_a] :
      ( ( monoto247478589472066471_set_a @ A @ smaller_interp_e_f_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_le5994374269167502767_set_a @ B3 @ A )
       => ( monoto247478589472066471_set_a @ B3 @ smaller_interp_e_f_a @ ord_le8464990428230162895_set_a @ F ) ) ) ).

% local.mono_on_subset
thf(fact_124_local_Omono__on__subset,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > set_c_d_set_a,B3: set_e_f_set_a] :
      ( ( monoto7716863510275742471_set_a @ A @ smaller_interp_e_f_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( ord_le5994374269167502767_set_a @ B3 @ A )
       => ( monoto7716863510275742471_set_a @ B3 @ smaller_interp_e_f_a @ ord_le5982164083705284911_set_a @ F ) ) ) ).

% local.mono_on_subset
thf(fact_125_local_Omono__on__subset,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > set_a,B3: set_e_f_set_a] :
      ( ( monoto2776068642243291606_set_a @ A @ smaller_interp_e_f_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le5994374269167502767_set_a @ B3 @ A )
       => ( monoto2776068642243291606_set_a @ B3 @ smaller_interp_e_f_a @ ord_less_eq_set_a @ F ) ) ) ).

% local.mono_on_subset
thf(fact_126_local_Omono__on__subset,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B3: set_e_f_set_a] :
      ( ( monoto947098964958182694et_a_o @ A @ smaller_interp_e_f_a @ ord_le1832228425591547726et_a_o @ F )
     => ( ( ord_le5994374269167502767_set_a @ B3 @ A )
       => ( monoto947098964958182694et_a_o @ B3 @ smaller_interp_e_f_a @ ord_le1832228425591547726et_a_o @ F ) ) ) ).

% local.mono_on_subset
thf(fact_127_local_Omono__on__subset,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( e > f ) > set_a,B3: set_e_f_set_a] :
      ( ( monoto5775188358803458087_set_a @ A @ smaller_interp_e_f_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( ord_le5994374269167502767_set_a @ B3 @ A )
       => ( monoto5775188358803458087_set_a @ B3 @ smaller_interp_e_f_a @ ord_le4769328160706778703_set_a @ F ) ) ) ).

% local.mono_on_subset
thf(fact_128_local_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B3: set_c_d_set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ smaller_interp_c_d_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto2937423850181994535_set_a @ B3 @ smaller_interp_c_d_a @ ord_le8464990428230162895_set_a @ F ) ) ) ).

% local.mono_on_subset
thf(fact_129_local_Omono__onI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_c_d_set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( smaller_interp_c_d_a @ R @ S2 )
             => ( ord_le5982164083705284911_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto6642458133393520519_set_a @ A @ smaller_interp_c_d_a @ ord_le5982164083705284911_set_a @ F ) ) ).

% local.mono_onI
thf(fact_130_local_Omono__onI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( smaller_interp_c_d_a @ R @ S2 )
             => ( ord_less_eq_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto6316088450447394390_set_a @ A @ smaller_interp_c_d_a @ ord_less_eq_set_a @ F ) ) ).

% local.mono_onI
thf(fact_131_local_Omono__onI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( smaller_interp_c_d_a @ R @ S2 )
             => ( ord_le1832228425591547726et_a_o @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto6135324833271912870et_a_o @ A @ smaller_interp_c_d_a @ ord_le1832228425591547726et_a_o @ F ) ) ).

% local.mono_onI
thf(fact_132_local_Omono__onI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( smaller_interp_c_d_a @ R @ S2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto8465133619513386151_set_a @ A @ smaller_interp_c_d_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% local.mono_onI
thf(fact_133_local_Omono__onI,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a] :
      ( ! [R: ( e > f ) > set_a,S2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ R @ A )
         => ( ( member_e_f_set_a @ S2 @ A )
           => ( ( smaller_interp_e_f_a @ R @ S2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto247478589472066471_set_a @ A @ smaller_interp_e_f_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% local.mono_onI
thf(fact_134_local_Omono__onI,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > set_c_d_set_a] :
      ( ! [R: ( e > f ) > set_a,S2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ R @ A )
         => ( ( member_e_f_set_a @ S2 @ A )
           => ( ( smaller_interp_e_f_a @ R @ S2 )
             => ( ord_le5982164083705284911_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto7716863510275742471_set_a @ A @ smaller_interp_e_f_a @ ord_le5982164083705284911_set_a @ F ) ) ).

% local.mono_onI
thf(fact_135_local_Omono__onI,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > set_a] :
      ( ! [R: ( e > f ) > set_a,S2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ R @ A )
         => ( ( member_e_f_set_a @ S2 @ A )
           => ( ( smaller_interp_e_f_a @ R @ S2 )
             => ( ord_less_eq_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto2776068642243291606_set_a @ A @ smaller_interp_e_f_a @ ord_less_eq_set_a @ F ) ) ).

% local.mono_onI
thf(fact_136_local_Omono__onI,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ! [R: ( e > f ) > set_a,S2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ R @ A )
         => ( ( member_e_f_set_a @ S2 @ A )
           => ( ( smaller_interp_e_f_a @ R @ S2 )
             => ( ord_le1832228425591547726et_a_o @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto947098964958182694et_a_o @ A @ smaller_interp_e_f_a @ ord_le1832228425591547726et_a_o @ F ) ) ).

% local.mono_onI
thf(fact_137_local_Omono__onI,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( e > f ) > set_a] :
      ( ! [R: ( e > f ) > set_a,S2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ R @ A )
         => ( ( member_e_f_set_a @ S2 @ A )
           => ( ( smaller_interp_e_f_a @ R @ S2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto5775188358803458087_set_a @ A @ smaller_interp_e_f_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% local.mono_onI
thf(fact_138_local_Omono__onI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( smaller_interp_c_d_a @ R @ S2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto2937423850181994535_set_a @ A @ smaller_interp_c_d_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% local.mono_onI
thf(fact_139_local_Omono__onD,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_c_d_set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto6642458133393520519_set_a @ A @ smaller_interp_c_d_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( smaller_interp_c_d_a @ R2 @ S3 )
           => ( ord_le5982164083705284911_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.mono_onD
thf(fact_140_local_Omono__onD,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto6316088450447394390_set_a @ A @ smaller_interp_c_d_a @ ord_less_eq_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( smaller_interp_c_d_a @ R2 @ S3 )
           => ( ord_less_eq_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.mono_onD
thf(fact_141_local_Omono__onD,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto6135324833271912870et_a_o @ A @ smaller_interp_c_d_a @ ord_le1832228425591547726et_a_o @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( smaller_interp_c_d_a @ R2 @ S3 )
           => ( ord_le1832228425591547726et_a_o @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.mono_onD
thf(fact_142_local_Omono__onD,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto8465133619513386151_set_a @ A @ smaller_interp_c_d_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( smaller_interp_c_d_a @ R2 @ S3 )
           => ( ord_le4769328160706778703_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.mono_onD
thf(fact_143_local_Omono__onD,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,R2: ( e > f ) > set_a,S3: ( e > f ) > set_a] :
      ( ( monoto247478589472066471_set_a @ A @ smaller_interp_e_f_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( member_e_f_set_a @ R2 @ A )
       => ( ( member_e_f_set_a @ S3 @ A )
         => ( ( smaller_interp_e_f_a @ R2 @ S3 )
           => ( ord_le8464990428230162895_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.mono_onD
thf(fact_144_local_Omono__onD,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > set_c_d_set_a,R2: ( e > f ) > set_a,S3: ( e > f ) > set_a] :
      ( ( monoto7716863510275742471_set_a @ A @ smaller_interp_e_f_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( member_e_f_set_a @ R2 @ A )
       => ( ( member_e_f_set_a @ S3 @ A )
         => ( ( smaller_interp_e_f_a @ R2 @ S3 )
           => ( ord_le5982164083705284911_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.mono_onD
thf(fact_145_local_Omono__onD,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > set_a,R2: ( e > f ) > set_a,S3: ( e > f ) > set_a] :
      ( ( monoto2776068642243291606_set_a @ A @ smaller_interp_e_f_a @ ord_less_eq_set_a @ F )
     => ( ( member_e_f_set_a @ R2 @ A )
       => ( ( member_e_f_set_a @ S3 @ A )
         => ( ( smaller_interp_e_f_a @ R2 @ S3 )
           => ( ord_less_eq_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.mono_onD
thf(fact_146_local_Omono__onD,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,R2: ( e > f ) > set_a,S3: ( e > f ) > set_a] :
      ( ( monoto947098964958182694et_a_o @ A @ smaller_interp_e_f_a @ ord_le1832228425591547726et_a_o @ F )
     => ( ( member_e_f_set_a @ R2 @ A )
       => ( ( member_e_f_set_a @ S3 @ A )
         => ( ( smaller_interp_e_f_a @ R2 @ S3 )
           => ( ord_le1832228425591547726et_a_o @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.mono_onD
thf(fact_147_local_Omono__onD,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( e > f ) > set_a,R2: ( e > f ) > set_a,S3: ( e > f ) > set_a] :
      ( ( monoto5775188358803458087_set_a @ A @ smaller_interp_e_f_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( member_e_f_set_a @ R2 @ A )
       => ( ( member_e_f_set_a @ S3 @ A )
         => ( ( smaller_interp_e_f_a @ R2 @ S3 )
           => ( ord_le4769328160706778703_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.mono_onD
thf(fact_148_local_Omono__onD,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ smaller_interp_c_d_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( smaller_interp_c_d_a @ R2 @ S3 )
           => ( ord_le8464990428230162895_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.mono_onD
thf(fact_149_local_Omono__imp__mono__on,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_c_d_set_a,A: set_c_d_set_a] :
      ( ( monoto6642458133393520519_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le5982164083705284911_set_a @ F )
     => ( monoto6642458133393520519_set_a @ A @ smaller_interp_c_d_a @ ord_le5982164083705284911_set_a @ F ) ) ).

% local.mono_imp_mono_on
thf(fact_150_local_Omono__imp__mono__on,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_a,A: set_c_d_set_a] :
      ( ( monoto6316088450447394390_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_less_eq_set_a @ F )
     => ( monoto6316088450447394390_set_a @ A @ smaller_interp_c_d_a @ ord_less_eq_set_a @ F ) ) ).

% local.mono_imp_mono_on
thf(fact_151_local_Omono__imp__mono__on,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A: set_c_d_set_a] :
      ( ( monoto6135324833271912870et_a_o @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le1832228425591547726et_a_o @ F )
     => ( monoto6135324833271912870et_a_o @ A @ smaller_interp_c_d_a @ ord_le1832228425591547726et_a_o @ F ) ) ).

% local.mono_imp_mono_on
thf(fact_152_local_Omono__imp__mono__on,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,A: set_c_d_set_a] :
      ( ( monoto8465133619513386151_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le4769328160706778703_set_a @ F )
     => ( monoto8465133619513386151_set_a @ A @ smaller_interp_c_d_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% local.mono_imp_mono_on
thf(fact_153_local_Omono__imp__mono__on,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,A: set_e_f_set_a] :
      ( ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le8464990428230162895_set_a @ F )
     => ( monoto247478589472066471_set_a @ A @ smaller_interp_e_f_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% local.mono_imp_mono_on
thf(fact_154_local_Omono__imp__mono__on,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_c_d_set_a,A: set_e_f_set_a] :
      ( ( monoto7716863510275742471_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le5982164083705284911_set_a @ F )
     => ( monoto7716863510275742471_set_a @ A @ smaller_interp_e_f_a @ ord_le5982164083705284911_set_a @ F ) ) ).

% local.mono_imp_mono_on
thf(fact_155_local_Omono__imp__mono__on,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_a,A: set_e_f_set_a] :
      ( ( monoto2776068642243291606_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_less_eq_set_a @ F )
     => ( monoto2776068642243291606_set_a @ A @ smaller_interp_e_f_a @ ord_less_eq_set_a @ F ) ) ).

% local.mono_imp_mono_on
thf(fact_156_local_Omono__imp__mono__on,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A: set_e_f_set_a] :
      ( ( monoto947098964958182694et_a_o @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le1832228425591547726et_a_o @ F )
     => ( monoto947098964958182694et_a_o @ A @ smaller_interp_e_f_a @ ord_le1832228425591547726et_a_o @ F ) ) ).

% local.mono_imp_mono_on
thf(fact_157_local_Omono__imp__mono__on,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( e > f ) > set_a,A: set_e_f_set_a] :
      ( ( monoto5775188358803458087_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le4769328160706778703_set_a @ F )
     => ( monoto5775188358803458087_set_a @ A @ smaller_interp_e_f_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% local.mono_imp_mono_on
thf(fact_158_local_Omono__imp__mono__on,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le8464990428230162895_set_a @ F )
     => ( monoto2937423850181994535_set_a @ A @ smaller_interp_c_d_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% local.mono_imp_mono_on
thf(fact_159_local_OmonoI,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_c_d_set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ X2 @ Y2 )
         => ( ord_le5982164083705284911_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto6642458133393520519_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le5982164083705284911_set_a @ F ) ) ).

% local.monoI
thf(fact_160_local_OmonoI,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ X2 @ Y2 )
         => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto6316088450447394390_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_less_eq_set_a @ F ) ) ).

% local.monoI
thf(fact_161_local_OmonoI,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ X2 @ Y2 )
         => ( ord_le1832228425591547726et_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto6135324833271912870et_a_o @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le1832228425591547726et_a_o @ F ) ) ).

% local.monoI
thf(fact_162_local_OmonoI,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( e > f ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ X2 @ Y2 )
         => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto8465133619513386151_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% local.monoI
thf(fact_163_local_OmonoI,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( c > d ) > set_a] :
      ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ X2 @ Y2 )
         => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% local.monoI
thf(fact_164_local_OmonoI,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_c_d_set_a] :
      ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ X2 @ Y2 )
         => ( ord_le5982164083705284911_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto7716863510275742471_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le5982164083705284911_set_a @ F ) ) ).

% local.monoI
thf(fact_165_local_OmonoI,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_a] :
      ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ X2 @ Y2 )
         => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto2776068642243291606_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_less_eq_set_a @ F ) ) ).

% local.monoI
thf(fact_166_local_OmonoI,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ X2 @ Y2 )
         => ( ord_le1832228425591547726et_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto947098964958182694et_a_o @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le1832228425591547726et_a_o @ F ) ) ).

% local.monoI
thf(fact_167_local_OmonoI,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( e > f ) > set_a] :
      ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ X2 @ Y2 )
         => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto5775188358803458087_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% local.monoI
thf(fact_168_local_OmonoI,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ X2 @ Y2 )
         => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% local.monoI
thf(fact_169_local_Oorder_Orefl,axiom,
    ! [A2: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ A2 @ A2 ) ).

% local.order.refl
thf(fact_170_local_Oorder_Orefl,axiom,
    ! [A2: ( e > f ) > set_a] : ( smaller_interp_e_f_a @ A2 @ A2 ) ).

% local.order.refl
thf(fact_171_local_Oorder__refl,axiom,
    ! [X: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ X @ X ) ).

% local.order_refl
thf(fact_172_local_Oorder__refl,axiom,
    ! [X: ( e > f ) > set_a] : ( smaller_interp_e_f_a @ X @ X ) ).

% local.order_refl
thf(fact_173_smaller__interp__refl,axiom,
    ! [Delta3: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ Delta3 @ Delta3 ) ).

% smaller_interp_refl
thf(fact_174_smaller__interp__refl,axiom,
    ! [Delta3: ( e > f ) > set_a] : ( smaller_interp_e_f_a @ Delta3 @ Delta3 ) ).

% smaller_interp_refl
thf(fact_175_local_OGreatestI2__order,axiom,
    ! [P: ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a,Q: ( ( c > d ) > set_a ) > $o] :
      ( ( P @ X )
     => ( ! [Y2: ( c > d ) > set_a] :
            ( ( P @ Y2 )
           => ( smaller_interp_c_d_a @ Y2 @ X ) )
       => ( ! [X2: ( c > d ) > set_a] :
              ( ( P @ X2 )
             => ( ! [Y5: ( c > d ) > set_a] :
                    ( ( P @ Y5 )
                   => ( smaller_interp_c_d_a @ Y5 @ X2 ) )
               => ( Q @ X2 ) ) )
         => ( Q @ ( greatest_c_d_set_a @ smaller_interp_c_d_a @ P ) ) ) ) ) ).

% local.GreatestI2_order
thf(fact_176_local_OGreatestI2__order,axiom,
    ! [P: ( ( e > f ) > set_a ) > $o,X: ( e > f ) > set_a,Q: ( ( e > f ) > set_a ) > $o] :
      ( ( P @ X )
     => ( ! [Y2: ( e > f ) > set_a] :
            ( ( P @ Y2 )
           => ( smaller_interp_e_f_a @ Y2 @ X ) )
       => ( ! [X2: ( e > f ) > set_a] :
              ( ( P @ X2 )
             => ( ! [Y5: ( e > f ) > set_a] :
                    ( ( P @ Y5 )
                   => ( smaller_interp_e_f_a @ Y5 @ X2 ) )
               => ( Q @ X2 ) ) )
         => ( Q @ ( greatest_e_f_set_a @ smaller_interp_e_f_a @ P ) ) ) ) ) ).

% local.GreatestI2_order
thf(fact_177_local_OGreatest__equality,axiom,
    ! [P: ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a] :
      ( ( P @ X )
     => ( ! [Y2: ( c > d ) > set_a] :
            ( ( P @ Y2 )
           => ( smaller_interp_c_d_a @ Y2 @ X ) )
       => ( ( greatest_c_d_set_a @ smaller_interp_c_d_a @ P )
          = X ) ) ) ).

% local.Greatest_equality
thf(fact_178_local_OGreatest__equality,axiom,
    ! [P: ( ( e > f ) > set_a ) > $o,X: ( e > f ) > set_a] :
      ( ( P @ X )
     => ( ! [Y2: ( e > f ) > set_a] :
            ( ( P @ Y2 )
           => ( smaller_interp_e_f_a @ Y2 @ X ) )
       => ( ( greatest_e_f_set_a @ smaller_interp_e_f_a @ P )
          = X ) ) ) ).

% local.Greatest_equality
thf(fact_179_top__set__def,axiom,
    ( top_to5717711934741766719_set_a
    = ( collec3354561713582630522_set_a @ top_to6119605859643668830et_a_o ) ) ).

% top_set_def
thf(fact_180_top__set__def,axiom,
    ( top_top_set_set_a
    = ( collect_set_a @ top_top_set_a_o ) ) ).

% top_set_def
thf(fact_181_top__set__def,axiom,
    ( top_to4280187784772989791_set_a
    = ( collect_e_f_set_a @ top_top_e_f_set_a_o ) ) ).

% top_set_def
thf(fact_182_top__set__def,axiom,
    ( top_to4267977599310771935_set_a
    = ( collect_c_d_set_a @ top_top_c_d_set_a_o ) ) ).

% top_set_def
thf(fact_183_subset__UNIV,axiom,
    ! [A: set_set_c_d_set_a] : ( ord_le7272806397018272911_set_a @ A @ top_to5717711934741766719_set_a ) ).

% subset_UNIV
thf(fact_184_subset__UNIV,axiom,
    ! [A: set_set_a] : ( ord_le3724670747650509150_set_a @ A @ top_top_set_set_a ) ).

% subset_UNIV
thf(fact_185_subset__UNIV,axiom,
    ! [A: set_e_f_set_a] : ( ord_le5994374269167502767_set_a @ A @ top_to4280187784772989791_set_a ) ).

% subset_UNIV
thf(fact_186_subset__UNIV,axiom,
    ! [A: set_a] : ( ord_less_eq_set_a @ A @ top_top_set_a ) ).

% subset_UNIV
thf(fact_187_subset__UNIV,axiom,
    ! [A: set_c_d_set_a] : ( ord_le5982164083705284911_set_a @ A @ top_to4267977599310771935_set_a ) ).

% subset_UNIV
thf(fact_188_monotone__on__subset,axiom,
    ! [A: set_c_d_set_a,Orda: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Ordb: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B3: set_c_d_set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ Orda @ Ordb @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto2937423850181994535_set_a @ B3 @ Orda @ Ordb @ F ) ) ) ).

% monotone_on_subset
thf(fact_189_mem__Collect__eq,axiom,
    ! [A2: a,P: a > $o] :
      ( ( member_a @ A2 @ ( collect_a @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_190_mem__Collect__eq,axiom,
    ! [A2: set_c_d_set_a,P: set_c_d_set_a > $o] :
      ( ( member_set_c_d_set_a @ A2 @ ( collec3354561713582630522_set_a @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_191_mem__Collect__eq,axiom,
    ! [A2: ( c > d ) > set_a,P: ( ( c > d ) > set_a ) > $o] :
      ( ( member_c_d_set_a @ A2 @ ( collect_c_d_set_a @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_192_Collect__mem__eq,axiom,
    ! [A: set_a] :
      ( ( collect_a
        @ ^ [X3: a] : ( member_a @ X3 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_193_Collect__mem__eq,axiom,
    ! [A: set_set_c_d_set_a] :
      ( ( collec3354561713582630522_set_a
        @ ^ [X3: set_c_d_set_a] : ( member_set_c_d_set_a @ X3 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_194_Collect__mem__eq,axiom,
    ! [A: set_c_d_set_a] :
      ( ( collect_c_d_set_a
        @ ^ [X3: ( c > d ) > set_a] : ( member_c_d_set_a @ X3 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_195_Collect__cong,axiom,
    ! [P: ( ( c > d ) > set_a ) > $o,Q: ( ( c > d ) > set_a ) > $o] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( P @ X2 )
          = ( Q @ X2 ) )
     => ( ( collect_c_d_set_a @ P )
        = ( collect_c_d_set_a @ Q ) ) ) ).

% Collect_cong
thf(fact_196_order__antisym__conv,axiom,
    ! [Y: set_c_d_set_a,X: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ Y @ X )
     => ( ( ord_le5982164083705284911_set_a @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_197_order__antisym__conv,axiom,
    ! [Y: set_a,X: set_a] :
      ( ( ord_less_eq_set_a @ Y @ X )
     => ( ( ord_less_eq_set_a @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_198_order__antisym__conv,axiom,
    ! [Y: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ Y @ X )
     => ( ( ord_le1832228425591547726et_a_o @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_199_order__antisym__conv,axiom,
    ! [Y: ( e > f ) > set_a,X: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ Y @ X )
     => ( ( ord_le4769328160706778703_set_a @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_200_order__antisym__conv,axiom,
    ! [Y: ( c > d ) > set_a,X: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ Y @ X )
     => ( ( ord_le8464990428230162895_set_a @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_201_ord__le__eq__subst,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_202_ord__le__eq__subst,axiom,
    ! [A2: set_a,B: set_a,F: set_a > set_a,C: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_203_ord__le__eq__subst,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > set_a,C: set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_204_ord__le__eq__subst,axiom,
    ! [A2: set_a,B: set_a,F: set_a > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_205_ord__le__eq__subst,axiom,
    ! [A2: set_a,B: set_a,F: set_a > ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4769328160706778703_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_206_ord__le__eq__subst,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,F: ( ( e > f ) > set_a ) > set_a,C: set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_207_ord__le__eq__subst,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > set_a,C: set_a] :
      ( ( ord_le5982164083705284911_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le5982164083705284911_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_208_ord__le__eq__subst,axiom,
    ! [A2: set_a,B: set_a,F: set_a > set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le5982164083705284911_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le5982164083705284911_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_209_ord__le__eq__subst,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4769328160706778703_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_210_ord__le__eq__subst,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_211_ord__eq__le__subst,axiom,
    ! [A2: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_212_ord__eq__le__subst,axiom,
    ! [A2: set_a,F: set_a > set_a,B: set_a,C: set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_213_ord__eq__le__subst,axiom,
    ! [A2: set_a,F: ( ( c > d ) > set_a ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_214_ord__eq__le__subst,axiom,
    ! [A2: ( c > d ) > set_a,F: set_a > ( c > d ) > set_a,B: set_a,C: set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_215_ord__eq__le__subst,axiom,
    ! [A2: ( e > f ) > set_a,F: set_a > ( e > f ) > set_a,B: set_a,C: set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4769328160706778703_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_216_ord__eq__le__subst,axiom,
    ! [A2: set_a,F: ( ( e > f ) > set_a ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le4769328160706778703_set_a @ B @ C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_217_ord__eq__le__subst,axiom,
    ! [A2: set_a,F: set_c_d_set_a > set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le5982164083705284911_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le5982164083705284911_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_218_ord__eq__le__subst,axiom,
    ! [A2: set_c_d_set_a,F: set_a > set_c_d_set_a,B: set_a,C: set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le5982164083705284911_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le5982164083705284911_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_219_ord__eq__le__subst,axiom,
    ! [A2: ( e > f ) > set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4769328160706778703_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_220_ord__eq__le__subst,axiom,
    ! [A2: ( c > d ) > set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le4769328160706778703_set_a @ B @ C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_221_order__eq__refl,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( X = Y )
     => ( ord_le5982164083705284911_set_a @ X @ Y ) ) ).

% order_eq_refl
thf(fact_222_order__eq__refl,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( X = Y )
     => ( ord_less_eq_set_a @ X @ Y ) ) ).

% order_eq_refl
thf(fact_223_order__eq__refl,axiom,
    ! [X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( X = Y )
     => ( ord_le1832228425591547726et_a_o @ X @ Y ) ) ).

% order_eq_refl
thf(fact_224_order__eq__refl,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( X = Y )
     => ( ord_le4769328160706778703_set_a @ X @ Y ) ) ).

% order_eq_refl
thf(fact_225_order__eq__refl,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( X = Y )
     => ( ord_le8464990428230162895_set_a @ X @ Y ) ) ).

% order_eq_refl
thf(fact_226_order__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ord_le8464990428230162895_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_227_order__subst2,axiom,
    ! [A2: set_a,B: set_a,F: set_a > set_a,C: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_228_order__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > set_a,C: set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_229_order__subst2,axiom,
    ! [A2: set_a,B: set_a,F: set_a > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_le8464990428230162895_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_230_order__subst2,axiom,
    ! [A2: set_a,B: set_a,F: set_a > ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_le4769328160706778703_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4769328160706778703_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_231_order__subst2,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,F: ( ( e > f ) > set_a ) > set_a,C: set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ B )
     => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_232_order__subst2,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > set_a,C: set_a] :
      ( ( ord_le5982164083705284911_set_a @ A2 @ B )
     => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le5982164083705284911_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_233_order__subst2,axiom,
    ! [A2: set_a,B: set_a,F: set_a > set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_le5982164083705284911_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le5982164083705284911_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le5982164083705284911_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_234_order__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ord_le4769328160706778703_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4769328160706778703_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_235_order__subst2,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ B )
     => ( ( ord_le8464990428230162895_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_236_order__subst1,axiom,
    ! [A2: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_237_order__subst1,axiom,
    ! [A2: set_a,F: set_a > set_a,B: set_a,C: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_238_order__subst1,axiom,
    ! [A2: ( c > d ) > set_a,F: set_a > ( c > d ) > set_a,B: set_a,C: set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_239_order__subst1,axiom,
    ! [A2: set_a,F: ( ( c > d ) > set_a ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_eq_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_240_order__subst1,axiom,
    ! [A2: set_a,F: ( ( e > f ) > set_a ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_less_eq_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le4769328160706778703_set_a @ B @ C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_241_order__subst1,axiom,
    ! [A2: ( e > f ) > set_a,F: set_a > ( e > f ) > set_a,B: set_a,C: set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4769328160706778703_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_242_order__subst1,axiom,
    ! [A2: set_c_d_set_a,F: set_a > set_c_d_set_a,B: set_a,C: set_a] :
      ( ( ord_le5982164083705284911_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le5982164083705284911_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le5982164083705284911_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_243_order__subst1,axiom,
    ! [A2: set_a,F: set_c_d_set_a > set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_less_eq_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le5982164083705284911_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le5982164083705284911_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_244_order__subst1,axiom,
    ! [A2: ( c > d ) > set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le4769328160706778703_set_a @ B @ C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le8464990428230162895_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_245_order__subst1,axiom,
    ! [A2: ( e > f ) > set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4769328160706778703_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_246_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_c_d_set_a,Z2: set_c_d_set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: set_c_d_set_a,B2: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ A3 @ B2 )
          & ( ord_le5982164083705284911_set_a @ B2 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_247_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_a,Z2: set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: set_a,B2: set_a] :
          ( ( ord_less_eq_set_a @ A3 @ B2 )
          & ( ord_less_eq_set_a @ B2 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_248_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Z2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] : ( Y3 = Z2 ) )
    = ( ^ [A3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le1832228425591547726et_a_o @ A3 @ B2 )
          & ( ord_le1832228425591547726et_a_o @ B2 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_249_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: ( e > f ) > set_a,Z2: ( e > f ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ A3 @ B2 )
          & ( ord_le4769328160706778703_set_a @ B2 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_250_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: ( c > d ) > set_a,Z2: ( c > d ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ A3 @ B2 )
          & ( ord_le8464990428230162895_set_a @ B2 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_251_antisym,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A2 @ B )
     => ( ( ord_le5982164083705284911_set_a @ B @ A2 )
       => ( A2 = B ) ) ) ).

% antisym
thf(fact_252_antisym,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_less_eq_set_a @ B @ A2 )
       => ( A2 = B ) ) ) ).

% antisym
thf(fact_253_antisym,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ A2 @ B )
     => ( ( ord_le1832228425591547726et_a_o @ B @ A2 )
       => ( A2 = B ) ) ) ).

% antisym
thf(fact_254_antisym,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ B )
     => ( ( ord_le4769328160706778703_set_a @ B @ A2 )
       => ( A2 = B ) ) ) ).

% antisym
thf(fact_255_antisym,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ord_le8464990428230162895_set_a @ B @ A2 )
       => ( A2 = B ) ) ) ).

% antisym
thf(fact_256_preorder__class_Odual__order_Otrans,axiom,
    ! [B: set_c_d_set_a,A2: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ B @ A2 )
     => ( ( ord_le5982164083705284911_set_a @ C @ B )
       => ( ord_le5982164083705284911_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.trans
thf(fact_257_preorder__class_Odual__order_Otrans,axiom,
    ! [B: set_a,A2: set_a,C: set_a] :
      ( ( ord_less_eq_set_a @ B @ A2 )
     => ( ( ord_less_eq_set_a @ C @ B )
       => ( ord_less_eq_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.trans
thf(fact_258_preorder__class_Odual__order_Otrans,axiom,
    ! [B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,C: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ B @ A2 )
     => ( ( ord_le1832228425591547726et_a_o @ C @ B )
       => ( ord_le1832228425591547726et_a_o @ C @ A2 ) ) ) ).

% preorder_class.dual_order.trans
thf(fact_259_preorder__class_Odual__order_Otrans,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ B @ A2 )
     => ( ( ord_le4769328160706778703_set_a @ C @ B )
       => ( ord_le4769328160706778703_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.trans
thf(fact_260_preorder__class_Odual__order_Otrans,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ B @ A2 )
     => ( ( ord_le8464990428230162895_set_a @ C @ B )
       => ( ord_le8464990428230162895_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.trans
thf(fact_261_order__class_Odual__order_Oantisym,axiom,
    ! [B: set_c_d_set_a,A2: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ B @ A2 )
     => ( ( ord_le5982164083705284911_set_a @ A2 @ B )
       => ( A2 = B ) ) ) ).

% order_class.dual_order.antisym
thf(fact_262_order__class_Odual__order_Oantisym,axiom,
    ! [B: set_a,A2: set_a] :
      ( ( ord_less_eq_set_a @ B @ A2 )
     => ( ( ord_less_eq_set_a @ A2 @ B )
       => ( A2 = B ) ) ) ).

% order_class.dual_order.antisym
thf(fact_263_order__class_Odual__order_Oantisym,axiom,
    ! [B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ B @ A2 )
     => ( ( ord_le1832228425591547726et_a_o @ A2 @ B )
       => ( A2 = B ) ) ) ).

% order_class.dual_order.antisym
thf(fact_264_order__class_Odual__order_Oantisym,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ B @ A2 )
     => ( ( ord_le4769328160706778703_set_a @ A2 @ B )
       => ( A2 = B ) ) ) ).

% order_class.dual_order.antisym
thf(fact_265_order__class_Odual__order_Oantisym,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ B @ A2 )
     => ( ( ord_le8464990428230162895_set_a @ A2 @ B )
       => ( A2 = B ) ) ) ).

% order_class.dual_order.antisym
thf(fact_266_order__class_Odual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: set_c_d_set_a,Z2: set_c_d_set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: set_c_d_set_a,B2: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ B2 @ A3 )
          & ( ord_le5982164083705284911_set_a @ A3 @ B2 ) ) ) ) ).

% order_class.dual_order.eq_iff
thf(fact_267_order__class_Odual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: set_a,Z2: set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: set_a,B2: set_a] :
          ( ( ord_less_eq_set_a @ B2 @ A3 )
          & ( ord_less_eq_set_a @ A3 @ B2 ) ) ) ) ).

% order_class.dual_order.eq_iff
thf(fact_268_order__class_Odual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Z2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] : ( Y3 = Z2 ) )
    = ( ^ [A3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le1832228425591547726et_a_o @ B2 @ A3 )
          & ( ord_le1832228425591547726et_a_o @ A3 @ B2 ) ) ) ) ).

% order_class.dual_order.eq_iff
thf(fact_269_order__class_Odual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: ( e > f ) > set_a,Z2: ( e > f ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ B2 @ A3 )
          & ( ord_le4769328160706778703_set_a @ A3 @ B2 ) ) ) ) ).

% order_class.dual_order.eq_iff
thf(fact_270_order__class_Odual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: ( c > d ) > set_a,Z2: ( c > d ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ B2 @ A3 )
          & ( ord_le8464990428230162895_set_a @ A3 @ B2 ) ) ) ) ).

% order_class.dual_order.eq_iff
thf(fact_271_preorder__class_Oorder__trans,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a,Z: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ X @ Y )
     => ( ( ord_le5982164083705284911_set_a @ Y @ Z )
       => ( ord_le5982164083705284911_set_a @ X @ Z ) ) ) ).

% preorder_class.order_trans
thf(fact_272_preorder__class_Oorder__trans,axiom,
    ! [X: set_a,Y: set_a,Z: set_a] :
      ( ( ord_less_eq_set_a @ X @ Y )
     => ( ( ord_less_eq_set_a @ Y @ Z )
       => ( ord_less_eq_set_a @ X @ Z ) ) ) ).

% preorder_class.order_trans
thf(fact_273_preorder__class_Oorder__trans,axiom,
    ! [X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Z: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ X @ Y )
     => ( ( ord_le1832228425591547726et_a_o @ Y @ Z )
       => ( ord_le1832228425591547726et_a_o @ X @ Z ) ) ) ).

% preorder_class.order_trans
thf(fact_274_preorder__class_Oorder__trans,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a,Z: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ X @ Y )
     => ( ( ord_le4769328160706778703_set_a @ Y @ Z )
       => ( ord_le4769328160706778703_set_a @ X @ Z ) ) ) ).

% preorder_class.order_trans
thf(fact_275_preorder__class_Oorder__trans,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ Y )
     => ( ( ord_le8464990428230162895_set_a @ Y @ Z )
       => ( ord_le8464990428230162895_set_a @ X @ Z ) ) ) ).

% preorder_class.order_trans
thf(fact_276_preorder__class_Oorder_Otrans,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A2 @ B )
     => ( ( ord_le5982164083705284911_set_a @ B @ C )
       => ( ord_le5982164083705284911_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.trans
thf(fact_277_preorder__class_Oorder_Otrans,axiom,
    ! [A2: set_a,B: set_a,C: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.trans
thf(fact_278_preorder__class_Oorder_Otrans,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,C: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ A2 @ B )
     => ( ( ord_le1832228425591547726et_a_o @ B @ C )
       => ( ord_le1832228425591547726et_a_o @ A2 @ C ) ) ) ).

% preorder_class.order.trans
thf(fact_279_preorder__class_Oorder_Otrans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ B )
     => ( ( ord_le4769328160706778703_set_a @ B @ C )
       => ( ord_le4769328160706778703_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.trans
thf(fact_280_preorder__class_Oorder_Otrans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ord_le8464990428230162895_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.trans
thf(fact_281_order__class_Oorder__antisym,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ X @ Y )
     => ( ( ord_le5982164083705284911_set_a @ Y @ X )
       => ( X = Y ) ) ) ).

% order_class.order_antisym
thf(fact_282_order__class_Oorder__antisym,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( ord_less_eq_set_a @ X @ Y )
     => ( ( ord_less_eq_set_a @ Y @ X )
       => ( X = Y ) ) ) ).

% order_class.order_antisym
thf(fact_283_order__class_Oorder__antisym,axiom,
    ! [X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ X @ Y )
     => ( ( ord_le1832228425591547726et_a_o @ Y @ X )
       => ( X = Y ) ) ) ).

% order_class.order_antisym
thf(fact_284_order__class_Oorder__antisym,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ X @ Y )
     => ( ( ord_le4769328160706778703_set_a @ Y @ X )
       => ( X = Y ) ) ) ).

% order_class.order_antisym
thf(fact_285_order__class_Oorder__antisym,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ Y )
     => ( ( ord_le8464990428230162895_set_a @ Y @ X )
       => ( X = Y ) ) ) ).

% order_class.order_antisym
thf(fact_286_ord__class_Oord__le__eq__trans,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A2 @ B )
     => ( ( B = C )
       => ( ord_le5982164083705284911_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_le_eq_trans
thf(fact_287_ord__class_Oord__le__eq__trans,axiom,
    ! [A2: set_a,B: set_a,C: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( B = C )
       => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_le_eq_trans
thf(fact_288_ord__class_Oord__le__eq__trans,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,C: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ A2 @ B )
     => ( ( B = C )
       => ( ord_le1832228425591547726et_a_o @ A2 @ C ) ) ) ).

% ord_class.ord_le_eq_trans
thf(fact_289_ord__class_Oord__le__eq__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ B )
     => ( ( B = C )
       => ( ord_le4769328160706778703_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_le_eq_trans
thf(fact_290_ord__class_Oord__le__eq__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( B = C )
       => ( ord_le8464990428230162895_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_le_eq_trans
thf(fact_291_ord__class_Oord__eq__le__trans,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( A2 = B )
     => ( ( ord_le5982164083705284911_set_a @ B @ C )
       => ( ord_le5982164083705284911_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_eq_le_trans
thf(fact_292_ord__class_Oord__eq__le__trans,axiom,
    ! [A2: set_a,B: set_a,C: set_a] :
      ( ( A2 = B )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_eq_le_trans
thf(fact_293_ord__class_Oord__eq__le__trans,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,C: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( A2 = B )
     => ( ( ord_le1832228425591547726et_a_o @ B @ C )
       => ( ord_le1832228425591547726et_a_o @ A2 @ C ) ) ) ).

% ord_class.ord_eq_le_trans
thf(fact_294_ord__class_Oord__eq__le__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( A2 = B )
     => ( ( ord_le4769328160706778703_set_a @ B @ C )
       => ( ord_le4769328160706778703_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_eq_le_trans
thf(fact_295_ord__class_Oord__eq__le__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( A2 = B )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ord_le8464990428230162895_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_eq_le_trans
thf(fact_296_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_c_d_set_a,Z2: set_c_d_set_a] : ( Y3 = Z2 ) )
    = ( ^ [X3: set_c_d_set_a,Y4: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ X3 @ Y4 )
          & ( ord_le5982164083705284911_set_a @ Y4 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_297_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_a,Z2: set_a] : ( Y3 = Z2 ) )
    = ( ^ [X3: set_a,Y4: set_a] :
          ( ( ord_less_eq_set_a @ X3 @ Y4 )
          & ( ord_less_eq_set_a @ Y4 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_298_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Z2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] : ( Y3 = Z2 ) )
    = ( ^ [X3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y4: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le1832228425591547726et_a_o @ X3 @ Y4 )
          & ( ord_le1832228425591547726et_a_o @ Y4 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_299_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: ( e > f ) > set_a,Z2: ( e > f ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [X3: ( e > f ) > set_a,Y4: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ X3 @ Y4 )
          & ( ord_le4769328160706778703_set_a @ Y4 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_300_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: ( c > d ) > set_a,Z2: ( c > d ) > set_a] : ( Y3 = Z2 ) )
    = ( ^ [X3: ( c > d ) > set_a,Y4: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ X3 @ Y4 )
          & ( ord_le8464990428230162895_set_a @ Y4 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_301_UNIV__witness,axiom,
    ? [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).

% UNIV_witness
thf(fact_302_UNIV__witness,axiom,
    ? [X2: set_c_d_set_a] : ( member_set_c_d_set_a @ X2 @ top_to5717711934741766719_set_a ) ).

% UNIV_witness
thf(fact_303_UNIV__witness,axiom,
    ? [X2: set_a] : ( member_set_a @ X2 @ top_top_set_set_a ) ).

% UNIV_witness
thf(fact_304_UNIV__witness,axiom,
    ? [X2: ( e > f ) > set_a] : ( member_e_f_set_a @ X2 @ top_to4280187784772989791_set_a ) ).

% UNIV_witness
thf(fact_305_UNIV__witness,axiom,
    ? [X2: ( c > d ) > set_a] : ( member_c_d_set_a @ X2 @ top_to4267977599310771935_set_a ) ).

% UNIV_witness
thf(fact_306_UNIV__eq__I,axiom,
    ! [A: set_a] :
      ( ! [X2: a] : ( member_a @ X2 @ A )
     => ( top_top_set_a = A ) ) ).

% UNIV_eq_I
thf(fact_307_UNIV__eq__I,axiom,
    ! [A: set_set_c_d_set_a] :
      ( ! [X2: set_c_d_set_a] : ( member_set_c_d_set_a @ X2 @ A )
     => ( top_to5717711934741766719_set_a = A ) ) ).

% UNIV_eq_I
thf(fact_308_UNIV__eq__I,axiom,
    ! [A: set_set_a] :
      ( ! [X2: set_a] : ( member_set_a @ X2 @ A )
     => ( top_top_set_set_a = A ) ) ).

% UNIV_eq_I
thf(fact_309_UNIV__eq__I,axiom,
    ! [A: set_e_f_set_a] :
      ( ! [X2: ( e > f ) > set_a] : ( member_e_f_set_a @ X2 @ A )
     => ( top_to4280187784772989791_set_a = A ) ) ).

% UNIV_eq_I
thf(fact_310_UNIV__eq__I,axiom,
    ! [A: set_c_d_set_a] :
      ( ! [X2: ( c > d ) > set_a] : ( member_c_d_set_a @ X2 @ A )
     => ( top_to4267977599310771935_set_a = A ) ) ).

% UNIV_eq_I
thf(fact_311_monotone__on__def,axiom,
    ( monoto2937423850181994535_set_a
    = ( ^ [A4: set_c_d_set_a,Orda2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Ordb2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F2: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
        ! [X3: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X3 @ A4 )
         => ! [Y4: ( c > d ) > set_a] :
              ( ( member_c_d_set_a @ Y4 @ A4 )
             => ( ( Orda2 @ X3 @ Y4 )
               => ( Ordb2 @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) ) ) ) ) ) ).

% monotone_on_def
thf(fact_312_monotone__onI,axiom,
    ! [A: set_c_d_set_a,Orda: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Ordb: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X2 @ A )
         => ( ( member_c_d_set_a @ Y2 @ A )
           => ( ( Orda @ X2 @ Y2 )
             => ( Ordb @ ( F @ X2 ) @ ( F @ Y2 ) ) ) ) )
     => ( monoto2937423850181994535_set_a @ A @ Orda @ Ordb @ F ) ) ).

% monotone_onI
thf(fact_313_monotone__onD,axiom,
    ! [A: set_c_d_set_a,Orda: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Ordb: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ Orda @ Ordb @ F )
     => ( ( member_c_d_set_a @ X @ A )
       => ( ( member_c_d_set_a @ Y @ A )
         => ( ( Orda @ X @ Y )
           => ( Ordb @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ) ).

% monotone_onD
thf(fact_314_order__top__class_Otop_Oextremum__uniqueI,axiom,
    ! [A2: set_set_c_d_set_a] :
      ( ( ord_le7272806397018272911_set_a @ top_to5717711934741766719_set_a @ A2 )
     => ( A2 = top_to5717711934741766719_set_a ) ) ).

% order_top_class.top.extremum_uniqueI
thf(fact_315_order__top__class_Otop_Oextremum__uniqueI,axiom,
    ! [A2: set_set_a] :
      ( ( ord_le3724670747650509150_set_a @ top_top_set_set_a @ A2 )
     => ( A2 = top_top_set_set_a ) ) ).

% order_top_class.top.extremum_uniqueI
thf(fact_316_order__top__class_Otop_Oextremum__uniqueI,axiom,
    ! [A2: set_e_f_set_a] :
      ( ( ord_le5994374269167502767_set_a @ top_to4280187784772989791_set_a @ A2 )
     => ( A2 = top_to4280187784772989791_set_a ) ) ).

% order_top_class.top.extremum_uniqueI
thf(fact_317_order__top__class_Otop_Oextremum__uniqueI,axiom,
    ! [A2: ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le961293222253252206et_a_o @ top_top_c_d_set_a_o @ A2 )
     => ( A2 = top_top_c_d_set_a_o ) ) ).

% order_top_class.top.extremum_uniqueI
thf(fact_318_order__top__class_Otop_Oextremum__uniqueI,axiom,
    ! [A2: set_a] :
      ( ( ord_less_eq_set_a @ top_top_set_a @ A2 )
     => ( A2 = top_top_set_a ) ) ).

% order_top_class.top.extremum_uniqueI
thf(fact_319_order__top__class_Otop_Oextremum__uniqueI,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ top_to5121151994761190654et_a_o @ A2 )
     => ( A2 = top_to5121151994761190654et_a_o ) ) ).

% order_top_class.top.extremum_uniqueI
thf(fact_320_order__top__class_Otop_Oextremum__uniqueI,axiom,
    ! [A2: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ top_top_e_f_set_a @ A2 )
     => ( A2 = top_top_e_f_set_a ) ) ).

% order_top_class.top.extremum_uniqueI
thf(fact_321_order__top__class_Otop_Oextremum__uniqueI,axiom,
    ! [A2: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ top_to4267977599310771935_set_a @ A2 )
     => ( A2 = top_to4267977599310771935_set_a ) ) ).

% order_top_class.top.extremum_uniqueI
thf(fact_322_order__top__class_Otop_Oextremum__uniqueI,axiom,
    ! [A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ top_top_c_d_set_a @ A2 )
     => ( A2 = top_top_c_d_set_a ) ) ).

% order_top_class.top.extremum_uniqueI
thf(fact_323_order__top__class_Otop_Oextremum__unique,axiom,
    ! [A2: set_set_c_d_set_a] :
      ( ( ord_le7272806397018272911_set_a @ top_to5717711934741766719_set_a @ A2 )
      = ( A2 = top_to5717711934741766719_set_a ) ) ).

% order_top_class.top.extremum_unique
thf(fact_324_order__top__class_Otop_Oextremum__unique,axiom,
    ! [A2: set_set_a] :
      ( ( ord_le3724670747650509150_set_a @ top_top_set_set_a @ A2 )
      = ( A2 = top_top_set_set_a ) ) ).

% order_top_class.top.extremum_unique
thf(fact_325_order__top__class_Otop_Oextremum__unique,axiom,
    ! [A2: set_e_f_set_a] :
      ( ( ord_le5994374269167502767_set_a @ top_to4280187784772989791_set_a @ A2 )
      = ( A2 = top_to4280187784772989791_set_a ) ) ).

% order_top_class.top.extremum_unique
thf(fact_326_order__top__class_Otop_Oextremum__unique,axiom,
    ! [A2: ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le961293222253252206et_a_o @ top_top_c_d_set_a_o @ A2 )
      = ( A2 = top_top_c_d_set_a_o ) ) ).

% order_top_class.top.extremum_unique
thf(fact_327_order__top__class_Otop_Oextremum__unique,axiom,
    ! [A2: set_a] :
      ( ( ord_less_eq_set_a @ top_top_set_a @ A2 )
      = ( A2 = top_top_set_a ) ) ).

% order_top_class.top.extremum_unique
thf(fact_328_order__top__class_Otop_Oextremum__unique,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ top_to5121151994761190654et_a_o @ A2 )
      = ( A2 = top_to5121151994761190654et_a_o ) ) ).

% order_top_class.top.extremum_unique
thf(fact_329_order__top__class_Otop_Oextremum__unique,axiom,
    ! [A2: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ top_top_e_f_set_a @ A2 )
      = ( A2 = top_top_e_f_set_a ) ) ).

% order_top_class.top.extremum_unique
thf(fact_330_order__top__class_Otop_Oextremum__unique,axiom,
    ! [A2: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ top_to4267977599310771935_set_a @ A2 )
      = ( A2 = top_to4267977599310771935_set_a ) ) ).

% order_top_class.top.extremum_unique
thf(fact_331_order__top__class_Otop_Oextremum__unique,axiom,
    ! [A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ top_top_c_d_set_a @ A2 )
      = ( A2 = top_top_c_d_set_a ) ) ).

% order_top_class.top.extremum_unique
thf(fact_332_order__top__class_Otop__greatest,axiom,
    ! [A2: set_set_c_d_set_a] : ( ord_le7272806397018272911_set_a @ A2 @ top_to5717711934741766719_set_a ) ).

% order_top_class.top_greatest
thf(fact_333_order__top__class_Otop__greatest,axiom,
    ! [A2: set_set_a] : ( ord_le3724670747650509150_set_a @ A2 @ top_top_set_set_a ) ).

% order_top_class.top_greatest
thf(fact_334_order__top__class_Otop__greatest,axiom,
    ! [A2: set_e_f_set_a] : ( ord_le5994374269167502767_set_a @ A2 @ top_to4280187784772989791_set_a ) ).

% order_top_class.top_greatest
thf(fact_335_order__top__class_Otop__greatest,axiom,
    ! [A2: ( ( c > d ) > set_a ) > $o] : ( ord_le961293222253252206et_a_o @ A2 @ top_top_c_d_set_a_o ) ).

% order_top_class.top_greatest
thf(fact_336_order__top__class_Otop__greatest,axiom,
    ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ top_top_set_a ) ).

% order_top_class.top_greatest
thf(fact_337_order__top__class_Otop__greatest,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] : ( ord_le1832228425591547726et_a_o @ A2 @ top_to5121151994761190654et_a_o ) ).

% order_top_class.top_greatest
thf(fact_338_order__top__class_Otop__greatest,axiom,
    ! [A2: ( e > f ) > set_a] : ( ord_le4769328160706778703_set_a @ A2 @ top_top_e_f_set_a ) ).

% order_top_class.top_greatest
thf(fact_339_order__top__class_Otop__greatest,axiom,
    ! [A2: set_c_d_set_a] : ( ord_le5982164083705284911_set_a @ A2 @ top_to4267977599310771935_set_a ) ).

% order_top_class.top_greatest
thf(fact_340_order__top__class_Otop__greatest,axiom,
    ! [A2: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ A2 @ top_top_c_d_set_a ) ).

% order_top_class.top_greatest
thf(fact_341_ord__class_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B3: set_c_d_set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto2937423850181994535_set_a @ B3 @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F ) ) ) ).

% ord_class.mono_on_subset
thf(fact_342_ord__class_Omono__on__subset,axiom,
    ! [A: set_set_a,F: set_a > set_a,B3: set_set_a] :
      ( ( monoto7172710143293369831_set_a @ A @ ord_less_eq_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le3724670747650509150_set_a @ B3 @ A )
       => ( monoto7172710143293369831_set_a @ B3 @ ord_less_eq_set_a @ ord_less_eq_set_a @ F ) ) ) ).

% ord_class.mono_on_subset
thf(fact_343_ord__class_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_a,B3: set_c_d_set_a] :
      ( ( monoto6316088450447394390_set_a @ A @ ord_le8464990428230162895_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto6316088450447394390_set_a @ B3 @ ord_le8464990428230162895_set_a @ ord_less_eq_set_a @ F ) ) ) ).

% ord_class.mono_on_subset
thf(fact_344_ord__class_Omono__on__subset,axiom,
    ! [A: set_set_a,F: set_a > ( c > d ) > set_a,B3: set_set_a] :
      ( ( monoto2748056057003999288_set_a @ A @ ord_less_eq_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_le3724670747650509150_set_a @ B3 @ A )
       => ( monoto2748056057003999288_set_a @ B3 @ ord_less_eq_set_a @ ord_le8464990428230162895_set_a @ F ) ) ) ).

% ord_class.mono_on_subset
thf(fact_345_ord__class_Omono__on__subset,axiom,
    ! [A: set_set_a,F: set_a > ( e > f ) > set_a,B3: set_set_a] :
      ( ( monoto8275765826335390904_set_a @ A @ ord_less_eq_set_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( ord_le3724670747650509150_set_a @ B3 @ A )
       => ( monoto8275765826335390904_set_a @ B3 @ ord_less_eq_set_a @ ord_le4769328160706778703_set_a @ F ) ) ) ).

% ord_class.mono_on_subset
thf(fact_346_ord__class_Omono__on__subset,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > set_a,B3: set_e_f_set_a] :
      ( ( monoto2776068642243291606_set_a @ A @ ord_le4769328160706778703_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le5994374269167502767_set_a @ B3 @ A )
       => ( monoto2776068642243291606_set_a @ B3 @ ord_le4769328160706778703_set_a @ ord_less_eq_set_a @ F ) ) ) ).

% ord_class.mono_on_subset
thf(fact_347_ord__class_Omono__on__subset,axiom,
    ! [A: set_set_c_d_set_a,F: set_c_d_set_a > set_a,B3: set_set_c_d_set_a] :
      ( ( monoto9091215303422693110_set_a @ A @ ord_le5982164083705284911_set_a @ ord_less_eq_set_a @ F )
     => ( ( ord_le7272806397018272911_set_a @ B3 @ A )
       => ( monoto9091215303422693110_set_a @ B3 @ ord_le5982164083705284911_set_a @ ord_less_eq_set_a @ F ) ) ) ).

% ord_class.mono_on_subset
thf(fact_348_ord__class_Omono__on__subset,axiom,
    ! [A: set_set_a,F: set_a > set_c_d_set_a,B3: set_set_a] :
      ( ( monoto7894950695950633880_set_a @ A @ ord_less_eq_set_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( ord_le3724670747650509150_set_a @ B3 @ A )
       => ( monoto7894950695950633880_set_a @ B3 @ ord_less_eq_set_a @ ord_le5982164083705284911_set_a @ F ) ) ) ).

% ord_class.mono_on_subset
thf(fact_349_ord__class_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,B3: set_c_d_set_a] :
      ( ( monoto8465133619513386151_set_a @ A @ ord_le8464990428230162895_set_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto8465133619513386151_set_a @ B3 @ ord_le8464990428230162895_set_a @ ord_le4769328160706778703_set_a @ F ) ) ) ).

% ord_class.mono_on_subset
thf(fact_350_ord__class_Omono__on__subset,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,B3: set_e_f_set_a] :
      ( ( monoto247478589472066471_set_a @ A @ ord_le4769328160706778703_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_le5994374269167502767_set_a @ B3 @ A )
       => ( monoto247478589472066471_set_a @ B3 @ ord_le4769328160706778703_set_a @ ord_le8464990428230162895_set_a @ F ) ) ) ).

% ord_class.mono_on_subset
thf(fact_351_ord__class_Omono__onI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( ord_le8464990428230162895_set_a @ R @ S2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto2937423850181994535_set_a @ A @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% ord_class.mono_onI
thf(fact_352_ord__class_Omono__onI,axiom,
    ! [A: set_set_a,F: set_a > set_a] :
      ( ! [R: set_a,S2: set_a] :
          ( ( member_set_a @ R @ A )
         => ( ( member_set_a @ S2 @ A )
           => ( ( ord_less_eq_set_a @ R @ S2 )
             => ( ord_less_eq_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto7172710143293369831_set_a @ A @ ord_less_eq_set_a @ ord_less_eq_set_a @ F ) ) ).

% ord_class.mono_onI
thf(fact_353_ord__class_Omono__onI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( ord_le8464990428230162895_set_a @ R @ S2 )
             => ( ord_less_eq_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto6316088450447394390_set_a @ A @ ord_le8464990428230162895_set_a @ ord_less_eq_set_a @ F ) ) ).

% ord_class.mono_onI
thf(fact_354_ord__class_Omono__onI,axiom,
    ! [A: set_set_a,F: set_a > ( c > d ) > set_a] :
      ( ! [R: set_a,S2: set_a] :
          ( ( member_set_a @ R @ A )
         => ( ( member_set_a @ S2 @ A )
           => ( ( ord_less_eq_set_a @ R @ S2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto2748056057003999288_set_a @ A @ ord_less_eq_set_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% ord_class.mono_onI
thf(fact_355_ord__class_Omono__onI,axiom,
    ! [A: set_set_a,F: set_a > ( e > f ) > set_a] :
      ( ! [R: set_a,S2: set_a] :
          ( ( member_set_a @ R @ A )
         => ( ( member_set_a @ S2 @ A )
           => ( ( ord_less_eq_set_a @ R @ S2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto8275765826335390904_set_a @ A @ ord_less_eq_set_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% ord_class.mono_onI
thf(fact_356_ord__class_Omono__onI,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > set_a] :
      ( ! [R: ( e > f ) > set_a,S2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ R @ A )
         => ( ( member_e_f_set_a @ S2 @ A )
           => ( ( ord_le4769328160706778703_set_a @ R @ S2 )
             => ( ord_less_eq_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto2776068642243291606_set_a @ A @ ord_le4769328160706778703_set_a @ ord_less_eq_set_a @ F ) ) ).

% ord_class.mono_onI
thf(fact_357_ord__class_Omono__onI,axiom,
    ! [A: set_set_c_d_set_a,F: set_c_d_set_a > set_a] :
      ( ! [R: set_c_d_set_a,S2: set_c_d_set_a] :
          ( ( member_set_c_d_set_a @ R @ A )
         => ( ( member_set_c_d_set_a @ S2 @ A )
           => ( ( ord_le5982164083705284911_set_a @ R @ S2 )
             => ( ord_less_eq_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto9091215303422693110_set_a @ A @ ord_le5982164083705284911_set_a @ ord_less_eq_set_a @ F ) ) ).

% ord_class.mono_onI
thf(fact_358_ord__class_Omono__onI,axiom,
    ! [A: set_set_a,F: set_a > set_c_d_set_a] :
      ( ! [R: set_a,S2: set_a] :
          ( ( member_set_a @ R @ A )
         => ( ( member_set_a @ S2 @ A )
           => ( ( ord_less_eq_set_a @ R @ S2 )
             => ( ord_le5982164083705284911_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto7894950695950633880_set_a @ A @ ord_less_eq_set_a @ ord_le5982164083705284911_set_a @ F ) ) ).

% ord_class.mono_onI
thf(fact_359_ord__class_Omono__onI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( ord_le8464990428230162895_set_a @ R @ S2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto8465133619513386151_set_a @ A @ ord_le8464990428230162895_set_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% ord_class.mono_onI
thf(fact_360_ord__class_Omono__onI,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a] :
      ( ! [R: ( e > f ) > set_a,S2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ R @ A )
         => ( ( member_e_f_set_a @ S2 @ A )
           => ( ( ord_le4769328160706778703_set_a @ R @ S2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto247478589472066471_set_a @ A @ ord_le4769328160706778703_set_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% ord_class.mono_onI
thf(fact_361_ord__class_Omono__onD,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( ord_le8464990428230162895_set_a @ R2 @ S3 )
           => ( ord_le8464990428230162895_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord_class.mono_onD
thf(fact_362_ord__class_Omono__onD,axiom,
    ! [A: set_set_a,F: set_a > set_a,R2: set_a,S3: set_a] :
      ( ( monoto7172710143293369831_set_a @ A @ ord_less_eq_set_a @ ord_less_eq_set_a @ F )
     => ( ( member_set_a @ R2 @ A )
       => ( ( member_set_a @ S3 @ A )
         => ( ( ord_less_eq_set_a @ R2 @ S3 )
           => ( ord_less_eq_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord_class.mono_onD
thf(fact_363_ord__class_Omono__onD,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto6316088450447394390_set_a @ A @ ord_le8464990428230162895_set_a @ ord_less_eq_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( ord_le8464990428230162895_set_a @ R2 @ S3 )
           => ( ord_less_eq_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord_class.mono_onD
thf(fact_364_ord__class_Omono__onD,axiom,
    ! [A: set_set_a,F: set_a > ( c > d ) > set_a,R2: set_a,S3: set_a] :
      ( ( monoto2748056057003999288_set_a @ A @ ord_less_eq_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( member_set_a @ R2 @ A )
       => ( ( member_set_a @ S3 @ A )
         => ( ( ord_less_eq_set_a @ R2 @ S3 )
           => ( ord_le8464990428230162895_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord_class.mono_onD
thf(fact_365_ord__class_Omono__onD,axiom,
    ! [A: set_set_a,F: set_a > ( e > f ) > set_a,R2: set_a,S3: set_a] :
      ( ( monoto8275765826335390904_set_a @ A @ ord_less_eq_set_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( member_set_a @ R2 @ A )
       => ( ( member_set_a @ S3 @ A )
         => ( ( ord_less_eq_set_a @ R2 @ S3 )
           => ( ord_le4769328160706778703_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord_class.mono_onD
thf(fact_366_ord__class_Omono__onD,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > set_a,R2: ( e > f ) > set_a,S3: ( e > f ) > set_a] :
      ( ( monoto2776068642243291606_set_a @ A @ ord_le4769328160706778703_set_a @ ord_less_eq_set_a @ F )
     => ( ( member_e_f_set_a @ R2 @ A )
       => ( ( member_e_f_set_a @ S3 @ A )
         => ( ( ord_le4769328160706778703_set_a @ R2 @ S3 )
           => ( ord_less_eq_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord_class.mono_onD
thf(fact_367_ord__class_Omono__onD,axiom,
    ! [A: set_set_c_d_set_a,F: set_c_d_set_a > set_a,R2: set_c_d_set_a,S3: set_c_d_set_a] :
      ( ( monoto9091215303422693110_set_a @ A @ ord_le5982164083705284911_set_a @ ord_less_eq_set_a @ F )
     => ( ( member_set_c_d_set_a @ R2 @ A )
       => ( ( member_set_c_d_set_a @ S3 @ A )
         => ( ( ord_le5982164083705284911_set_a @ R2 @ S3 )
           => ( ord_less_eq_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord_class.mono_onD
thf(fact_368_ord__class_Omono__onD,axiom,
    ! [A: set_set_a,F: set_a > set_c_d_set_a,R2: set_a,S3: set_a] :
      ( ( monoto7894950695950633880_set_a @ A @ ord_less_eq_set_a @ ord_le5982164083705284911_set_a @ F )
     => ( ( member_set_a @ R2 @ A )
       => ( ( member_set_a @ S3 @ A )
         => ( ( ord_less_eq_set_a @ R2 @ S3 )
           => ( ord_le5982164083705284911_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord_class.mono_onD
thf(fact_369_ord__class_Omono__onD,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto8465133619513386151_set_a @ A @ ord_le8464990428230162895_set_a @ ord_le4769328160706778703_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( ord_le8464990428230162895_set_a @ R2 @ S3 )
           => ( ord_le4769328160706778703_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord_class.mono_onD
thf(fact_370_ord__class_Omono__onD,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,R2: ( e > f ) > set_a,S3: ( e > f ) > set_a] :
      ( ( monoto247478589472066471_set_a @ A @ ord_le4769328160706778703_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( member_e_f_set_a @ R2 @ A )
       => ( ( member_e_f_set_a @ S3 @ A )
         => ( ( ord_le4769328160706778703_set_a @ R2 @ S3 )
           => ( ord_le8464990428230162895_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord_class.mono_onD
thf(fact_371_ord_Omono__on__subset,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > ( c > d ) > set_a,B3: set_a] :
      ( ( monoto2502030104860647832_set_a @ A @ Less_eq @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_less_eq_set_a @ B3 @ A )
       => ( monoto2502030104860647832_set_a @ B3 @ Less_eq @ ord_le8464990428230162895_set_a @ F ) ) ) ).

% ord.mono_on_subset
thf(fact_372_ord_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( monoto6642458133393520519_set_a @ A @ Less_eq @ ord_le5982164083705284911_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto6642458133393520519_set_a @ B3 @ Less_eq @ ord_le5982164083705284911_set_a @ F ) ) ) ).

% ord.mono_on_subset
thf(fact_373_ord_Omono__on__subset,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > set_c_d_set_a,B3: set_a] :
      ( ( monoto4999900198720154872_set_a @ A @ Less_eq @ ord_le5982164083705284911_set_a @ F )
     => ( ( ord_less_eq_set_a @ B3 @ A )
       => ( monoto4999900198720154872_set_a @ B3 @ Less_eq @ ord_le5982164083705284911_set_a @ F ) ) ) ).

% ord.mono_on_subset
thf(fact_374_ord_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > set_a,B3: set_c_d_set_a] :
      ( ( monoto6316088450447394390_set_a @ A @ Less_eq @ ord_less_eq_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto6316088450447394390_set_a @ B3 @ Less_eq @ ord_less_eq_set_a @ F ) ) ) ).

% ord.mono_on_subset
thf(fact_375_ord_Omono__on__subset,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > set_a,B3: set_a] :
      ( ( monotone_on_a_set_a @ A @ Less_eq @ ord_less_eq_set_a @ F )
     => ( ( ord_less_eq_set_a @ B3 @ A )
       => ( monotone_on_a_set_a @ B3 @ Less_eq @ ord_less_eq_set_a @ F ) ) ) ).

% ord.mono_on_subset
thf(fact_376_ord_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B3: set_c_d_set_a] :
      ( ( monoto6135324833271912870et_a_o @ A @ Less_eq @ ord_le1832228425591547726et_a_o @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto6135324833271912870et_a_o @ B3 @ Less_eq @ ord_le1832228425591547726et_a_o @ F ) ) ) ).

% ord.mono_on_subset
thf(fact_377_ord_Omono__on__subset,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B3: set_a] :
      ( ( monoto466107916892698775et_a_o @ A @ Less_eq @ ord_le1832228425591547726et_a_o @ F )
     => ( ( ord_less_eq_set_a @ B3 @ A )
       => ( monoto466107916892698775et_a_o @ B3 @ Less_eq @ ord_le1832228425591547726et_a_o @ F ) ) ) ).

% ord.mono_on_subset
thf(fact_378_ord_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,B3: set_c_d_set_a] :
      ( ( monoto8465133619513386151_set_a @ A @ Less_eq @ ord_le4769328160706778703_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto8465133619513386151_set_a @ B3 @ Less_eq @ ord_le4769328160706778703_set_a @ F ) ) ) ).

% ord.mono_on_subset
thf(fact_379_ord_Omono__on__subset,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > ( e > f ) > set_a,B3: set_a] :
      ( ( monoto8029739874192039448_set_a @ A @ Less_eq @ ord_le4769328160706778703_set_a @ F )
     => ( ( ord_less_eq_set_a @ B3 @ A )
       => ( monoto8029739874192039448_set_a @ B3 @ Less_eq @ ord_le4769328160706778703_set_a @ F ) ) ) ).

% ord.mono_on_subset
thf(fact_380_ord_Omono__on__subset,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B3: set_c_d_set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ Less_eq @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( monoto2937423850181994535_set_a @ B3 @ Less_eq @ ord_le8464990428230162895_set_a @ F ) ) ) ).

% ord.mono_on_subset
thf(fact_381_ord_Omono__on__def,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ Less_eq @ ord_le8464990428230162895_set_a @ F )
      = ( ! [R3: ( c > d ) > set_a,S: ( c > d ) > set_a] :
            ( ( ( member_c_d_set_a @ R3 @ A )
              & ( member_c_d_set_a @ S @ A )
              & ( Less_eq @ R3 @ S ) )
           => ( ord_le8464990428230162895_set_a @ ( F @ R3 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_382_ord_Omono__on__def,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > set_a] :
      ( ( monotone_on_a_set_a @ A @ Less_eq @ ord_less_eq_set_a @ F )
      = ( ! [R3: a,S: a] :
            ( ( ( member_a @ R3 @ A )
              & ( member_a @ S @ A )
              & ( Less_eq @ R3 @ S ) )
           => ( ord_less_eq_set_a @ ( F @ R3 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_383_ord_Omono__on__def,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > ( c > d ) > set_a] :
      ( ( monoto2502030104860647832_set_a @ A @ Less_eq @ ord_le8464990428230162895_set_a @ F )
      = ( ! [R3: a,S: a] :
            ( ( ( member_a @ R3 @ A )
              & ( member_a @ S @ A )
              & ( Less_eq @ R3 @ S ) )
           => ( ord_le8464990428230162895_set_a @ ( F @ R3 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_384_ord_Omono__on__def,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > ( e > f ) > set_a] :
      ( ( monoto8029739874192039448_set_a @ A @ Less_eq @ ord_le4769328160706778703_set_a @ F )
      = ( ! [R3: a,S: a] :
            ( ( ( member_a @ R3 @ A )
              & ( member_a @ S @ A )
              & ( Less_eq @ R3 @ S ) )
           => ( ord_le4769328160706778703_set_a @ ( F @ R3 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_385_ord_Omono__on__def,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > set_c_d_set_a] :
      ( ( monoto4999900198720154872_set_a @ A @ Less_eq @ ord_le5982164083705284911_set_a @ F )
      = ( ! [R3: a,S: a] :
            ( ( ( member_a @ R3 @ A )
              & ( member_a @ S @ A )
              & ( Less_eq @ R3 @ S ) )
           => ( ord_le5982164083705284911_set_a @ ( F @ R3 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_386_ord_Omono__on__def,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > set_a] :
      ( ( monoto6316088450447394390_set_a @ A @ Less_eq @ ord_less_eq_set_a @ F )
      = ( ! [R3: ( c > d ) > set_a,S: ( c > d ) > set_a] :
            ( ( ( member_c_d_set_a @ R3 @ A )
              & ( member_c_d_set_a @ S @ A )
              & ( Less_eq @ R3 @ S ) )
           => ( ord_less_eq_set_a @ ( F @ R3 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_387_ord_Omono__on__def,axiom,
    ! [A: set_set_c_d_set_a,Less_eq: set_c_d_set_a > set_c_d_set_a > $o,F: set_c_d_set_a > set_a] :
      ( ( monoto9091215303422693110_set_a @ A @ Less_eq @ ord_less_eq_set_a @ F )
      = ( ! [R3: set_c_d_set_a,S: set_c_d_set_a] :
            ( ( ( member_set_c_d_set_a @ R3 @ A )
              & ( member_set_c_d_set_a @ S @ A )
              & ( Less_eq @ R3 @ S ) )
           => ( ord_less_eq_set_a @ ( F @ R3 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_388_ord_Omono__on__def,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a] :
      ( ( monoto8465133619513386151_set_a @ A @ Less_eq @ ord_le4769328160706778703_set_a @ F )
      = ( ! [R3: ( c > d ) > set_a,S: ( c > d ) > set_a] :
            ( ( ( member_c_d_set_a @ R3 @ A )
              & ( member_c_d_set_a @ S @ A )
              & ( Less_eq @ R3 @ S ) )
           => ( ord_le4769328160706778703_set_a @ ( F @ R3 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_389_ord_Omono__on__def,axiom,
    ! [A: set_set_c_d_set_a,Less_eq: set_c_d_set_a > set_c_d_set_a > $o,F: set_c_d_set_a > ( c > d ) > set_a] :
      ( ( monoto5673664640695304391_set_a @ A @ Less_eq @ ord_le8464990428230162895_set_a @ F )
      = ( ! [R3: set_c_d_set_a,S: set_c_d_set_a] :
            ( ( ( member_set_c_d_set_a @ R3 @ A )
              & ( member_set_c_d_set_a @ S @ A )
              & ( Less_eq @ R3 @ S ) )
           => ( ord_le8464990428230162895_set_a @ ( F @ R3 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_390_ord_Omono__on__def,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > set_c_d_set_a] :
      ( ( monoto6642458133393520519_set_a @ A @ Less_eq @ ord_le5982164083705284911_set_a @ F )
      = ( ! [R3: ( c > d ) > set_a,S: ( c > d ) > set_a] :
            ( ( ( member_c_d_set_a @ R3 @ A )
              & ( member_c_d_set_a @ S @ A )
              & ( Less_eq @ R3 @ S ) )
           => ( ord_le5982164083705284911_set_a @ ( F @ R3 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_391_ord_Omono__onI,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( Less_eq @ R @ S2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto2937423850181994535_set_a @ A @ Less_eq @ ord_le8464990428230162895_set_a @ F ) ) ).

% ord.mono_onI
thf(fact_392_ord_Omono__onI,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > set_a] :
      ( ! [R: a,S2: a] :
          ( ( member_a @ R @ A )
         => ( ( member_a @ S2 @ A )
           => ( ( Less_eq @ R @ S2 )
             => ( ord_less_eq_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monotone_on_a_set_a @ A @ Less_eq @ ord_less_eq_set_a @ F ) ) ).

% ord.mono_onI
thf(fact_393_ord_Omono__onI,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > ( c > d ) > set_a] :
      ( ! [R: a,S2: a] :
          ( ( member_a @ R @ A )
         => ( ( member_a @ S2 @ A )
           => ( ( Less_eq @ R @ S2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto2502030104860647832_set_a @ A @ Less_eq @ ord_le8464990428230162895_set_a @ F ) ) ).

% ord.mono_onI
thf(fact_394_ord_Omono__onI,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > ( e > f ) > set_a] :
      ( ! [R: a,S2: a] :
          ( ( member_a @ R @ A )
         => ( ( member_a @ S2 @ A )
           => ( ( Less_eq @ R @ S2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto8029739874192039448_set_a @ A @ Less_eq @ ord_le4769328160706778703_set_a @ F ) ) ).

% ord.mono_onI
thf(fact_395_ord_Omono__onI,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > set_c_d_set_a] :
      ( ! [R: a,S2: a] :
          ( ( member_a @ R @ A )
         => ( ( member_a @ S2 @ A )
           => ( ( Less_eq @ R @ S2 )
             => ( ord_le5982164083705284911_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto4999900198720154872_set_a @ A @ Less_eq @ ord_le5982164083705284911_set_a @ F ) ) ).

% ord.mono_onI
thf(fact_396_ord_Omono__onI,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( Less_eq @ R @ S2 )
             => ( ord_less_eq_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto6316088450447394390_set_a @ A @ Less_eq @ ord_less_eq_set_a @ F ) ) ).

% ord.mono_onI
thf(fact_397_ord_Omono__onI,axiom,
    ! [A: set_set_c_d_set_a,Less_eq: set_c_d_set_a > set_c_d_set_a > $o,F: set_c_d_set_a > set_a] :
      ( ! [R: set_c_d_set_a,S2: set_c_d_set_a] :
          ( ( member_set_c_d_set_a @ R @ A )
         => ( ( member_set_c_d_set_a @ S2 @ A )
           => ( ( Less_eq @ R @ S2 )
             => ( ord_less_eq_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto9091215303422693110_set_a @ A @ Less_eq @ ord_less_eq_set_a @ F ) ) ).

% ord.mono_onI
thf(fact_398_ord_Omono__onI,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( Less_eq @ R @ S2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto8465133619513386151_set_a @ A @ Less_eq @ ord_le4769328160706778703_set_a @ F ) ) ).

% ord.mono_onI
thf(fact_399_ord_Omono__onI,axiom,
    ! [A: set_set_c_d_set_a,Less_eq: set_c_d_set_a > set_c_d_set_a > $o,F: set_c_d_set_a > ( c > d ) > set_a] :
      ( ! [R: set_c_d_set_a,S2: set_c_d_set_a] :
          ( ( member_set_c_d_set_a @ R @ A )
         => ( ( member_set_c_d_set_a @ S2 @ A )
           => ( ( Less_eq @ R @ S2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto5673664640695304391_set_a @ A @ Less_eq @ ord_le8464990428230162895_set_a @ F ) ) ).

% ord.mono_onI
thf(fact_400_ord_Omono__onI,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > set_c_d_set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( Less_eq @ R @ S2 )
             => ( ord_le5982164083705284911_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto6642458133393520519_set_a @ A @ Less_eq @ ord_le5982164083705284911_set_a @ F ) ) ).

% ord.mono_onI
thf(fact_401_ord_Omono__onD,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ Less_eq @ ord_le8464990428230162895_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( Less_eq @ R2 @ S3 )
           => ( ord_le8464990428230162895_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_402_ord_Omono__onD,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > set_a,R2: a,S3: a] :
      ( ( monotone_on_a_set_a @ A @ Less_eq @ ord_less_eq_set_a @ F )
     => ( ( member_a @ R2 @ A )
       => ( ( member_a @ S3 @ A )
         => ( ( Less_eq @ R2 @ S3 )
           => ( ord_less_eq_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_403_ord_Omono__onD,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > ( c > d ) > set_a,R2: a,S3: a] :
      ( ( monoto2502030104860647832_set_a @ A @ Less_eq @ ord_le8464990428230162895_set_a @ F )
     => ( ( member_a @ R2 @ A )
       => ( ( member_a @ S3 @ A )
         => ( ( Less_eq @ R2 @ S3 )
           => ( ord_le8464990428230162895_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_404_ord_Omono__onD,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > ( e > f ) > set_a,R2: a,S3: a] :
      ( ( monoto8029739874192039448_set_a @ A @ Less_eq @ ord_le4769328160706778703_set_a @ F )
     => ( ( member_a @ R2 @ A )
       => ( ( member_a @ S3 @ A )
         => ( ( Less_eq @ R2 @ S3 )
           => ( ord_le4769328160706778703_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_405_ord_Omono__onD,axiom,
    ! [A: set_a,Less_eq: a > a > $o,F: a > set_c_d_set_a,R2: a,S3: a] :
      ( ( monoto4999900198720154872_set_a @ A @ Less_eq @ ord_le5982164083705284911_set_a @ F )
     => ( ( member_a @ R2 @ A )
       => ( ( member_a @ S3 @ A )
         => ( ( Less_eq @ R2 @ S3 )
           => ( ord_le5982164083705284911_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_406_ord_Omono__onD,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto6316088450447394390_set_a @ A @ Less_eq @ ord_less_eq_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( Less_eq @ R2 @ S3 )
           => ( ord_less_eq_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_407_ord_Omono__onD,axiom,
    ! [A: set_set_c_d_set_a,Less_eq: set_c_d_set_a > set_c_d_set_a > $o,F: set_c_d_set_a > set_a,R2: set_c_d_set_a,S3: set_c_d_set_a] :
      ( ( monoto9091215303422693110_set_a @ A @ Less_eq @ ord_less_eq_set_a @ F )
     => ( ( member_set_c_d_set_a @ R2 @ A )
       => ( ( member_set_c_d_set_a @ S3 @ A )
         => ( ( Less_eq @ R2 @ S3 )
           => ( ord_less_eq_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_408_ord_Omono__onD,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto8465133619513386151_set_a @ A @ Less_eq @ ord_le4769328160706778703_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( Less_eq @ R2 @ S3 )
           => ( ord_le4769328160706778703_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_409_ord_Omono__onD,axiom,
    ! [A: set_set_c_d_set_a,Less_eq: set_c_d_set_a > set_c_d_set_a > $o,F: set_c_d_set_a > ( c > d ) > set_a,R2: set_c_d_set_a,S3: set_c_d_set_a] :
      ( ( monoto5673664640695304391_set_a @ A @ Less_eq @ ord_le8464990428230162895_set_a @ F )
     => ( ( member_set_c_d_set_a @ R2 @ A )
       => ( ( member_set_c_d_set_a @ S3 @ A )
         => ( ( Less_eq @ R2 @ S3 )
           => ( ord_le8464990428230162895_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_410_ord_Omono__onD,axiom,
    ! [A: set_c_d_set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > set_c_d_set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto6642458133393520519_set_a @ A @ Less_eq @ ord_le5982164083705284911_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( Less_eq @ R2 @ S3 )
           => ( ord_le5982164083705284911_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_411_le__fun__def,axiom,
    ( ord_le1832228425591547726et_a_o
    = ( ^ [F2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,G: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
        ! [X3: ( c > d ) > set_a] : ( ord_le961293222253252206et_a_o @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).

% le_fun_def
thf(fact_412_le__fun__def,axiom,
    ( ord_le4769328160706778703_set_a
    = ( ^ [F2: ( e > f ) > set_a,G: ( e > f ) > set_a] :
        ! [X3: e > f] : ( ord_less_eq_set_a @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).

% le_fun_def
thf(fact_413_le__fun__def,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [F2: ( c > d ) > set_a,G: ( c > d ) > set_a] :
        ! [X3: c > d] : ( ord_less_eq_set_a @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).

% le_fun_def
thf(fact_414_le__funI,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,G2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ! [X2: ( c > d ) > set_a] : ( ord_le961293222253252206et_a_o @ ( F @ X2 ) @ ( G2 @ X2 ) )
     => ( ord_le1832228425591547726et_a_o @ F @ G2 ) ) ).

% le_funI
thf(fact_415_le__funI,axiom,
    ! [F: ( e > f ) > set_a,G2: ( e > f ) > set_a] :
      ( ! [X2: e > f] : ( ord_less_eq_set_a @ ( F @ X2 ) @ ( G2 @ X2 ) )
     => ( ord_le4769328160706778703_set_a @ F @ G2 ) ) ).

% le_funI
thf(fact_416_le__funI,axiom,
    ! [F: ( c > d ) > set_a,G2: ( c > d ) > set_a] :
      ( ! [X2: c > d] : ( ord_less_eq_set_a @ ( F @ X2 ) @ ( G2 @ X2 ) )
     => ( ord_le8464990428230162895_set_a @ F @ G2 ) ) ).

% le_funI
thf(fact_417_le__funE,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,G2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a] :
      ( ( ord_le1832228425591547726et_a_o @ F @ G2 )
     => ( ord_le961293222253252206et_a_o @ ( F @ X ) @ ( G2 @ X ) ) ) ).

% le_funE
thf(fact_418_le__funE,axiom,
    ! [F: ( e > f ) > set_a,G2: ( e > f ) > set_a,X: e > f] :
      ( ( ord_le4769328160706778703_set_a @ F @ G2 )
     => ( ord_less_eq_set_a @ ( F @ X ) @ ( G2 @ X ) ) ) ).

% le_funE
thf(fact_419_le__funE,axiom,
    ! [F: ( c > d ) > set_a,G2: ( c > d ) > set_a,X: c > d] :
      ( ( ord_le8464990428230162895_set_a @ F @ G2 )
     => ( ord_less_eq_set_a @ ( F @ X ) @ ( G2 @ X ) ) ) ).

% le_funE
thf(fact_420_le__funD,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,G2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a] :
      ( ( ord_le1832228425591547726et_a_o @ F @ G2 )
     => ( ord_le961293222253252206et_a_o @ ( F @ X ) @ ( G2 @ X ) ) ) ).

% le_funD
thf(fact_421_le__funD,axiom,
    ! [F: ( e > f ) > set_a,G2: ( e > f ) > set_a,X: e > f] :
      ( ( ord_le4769328160706778703_set_a @ F @ G2 )
     => ( ord_less_eq_set_a @ ( F @ X ) @ ( G2 @ X ) ) ) ).

% le_funD
thf(fact_422_le__funD,axiom,
    ! [F: ( c > d ) > set_a,G2: ( c > d ) > set_a,X: c > d] :
      ( ( ord_le8464990428230162895_set_a @ F @ G2 )
     => ( ord_less_eq_set_a @ ( F @ X ) @ ( G2 @ X ) ) ) ).

% le_funD
thf(fact_423_monotoneI,axiom,
    ! [Orda: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Ordb: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( Orda @ X2 @ Y2 )
         => ( Ordb @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ Orda @ Ordb @ F ) ) ).

% monotoneI
thf(fact_424_monotoneD,axiom,
    ! [Orda: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Ordb: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ Orda @ Ordb @ F )
     => ( ( Orda @ X @ Y )
       => ( Ordb @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% monotoneD
thf(fact_425_local_OLeast1I,axiom,
    ! [P: ( ( c > d ) > set_a ) > $o] :
      ( ? [X4: ( c > d ) > set_a] :
          ( ( P @ X4 )
          & ! [Y2: ( c > d ) > set_a] :
              ( ( P @ Y2 )
             => ( smaller_interp_c_d_a @ X4 @ Y2 ) )
          & ! [Y2: ( c > d ) > set_a] :
              ( ( ( P @ Y2 )
                & ! [Ya: ( c > d ) > set_a] :
                    ( ( P @ Ya )
                   => ( smaller_interp_c_d_a @ Y2 @ Ya ) ) )
             => ( Y2 = X4 ) ) )
     => ( P @ ( least_c_d_set_a @ smaller_interp_c_d_a @ P ) ) ) ).

% local.Least1I
thf(fact_426_local_OLeast1I,axiom,
    ! [P: ( ( e > f ) > set_a ) > $o] :
      ( ? [X4: ( e > f ) > set_a] :
          ( ( P @ X4 )
          & ! [Y2: ( e > f ) > set_a] :
              ( ( P @ Y2 )
             => ( smaller_interp_e_f_a @ X4 @ Y2 ) )
          & ! [Y2: ( e > f ) > set_a] :
              ( ( ( P @ Y2 )
                & ! [Ya: ( e > f ) > set_a] :
                    ( ( P @ Ya )
                   => ( smaller_interp_e_f_a @ Y2 @ Ya ) ) )
             => ( Y2 = X4 ) ) )
     => ( P @ ( least_e_f_set_a @ smaller_interp_e_f_a @ P ) ) ) ).

% local.Least1I
thf(fact_427_local_OLeast1__le,axiom,
    ! [P: ( ( c > d ) > set_a ) > $o,Z: ( c > d ) > set_a] :
      ( ? [X4: ( c > d ) > set_a] :
          ( ( P @ X4 )
          & ! [Y2: ( c > d ) > set_a] :
              ( ( P @ Y2 )
             => ( smaller_interp_c_d_a @ X4 @ Y2 ) )
          & ! [Y2: ( c > d ) > set_a] :
              ( ( ( P @ Y2 )
                & ! [Ya: ( c > d ) > set_a] :
                    ( ( P @ Ya )
                   => ( smaller_interp_c_d_a @ Y2 @ Ya ) ) )
             => ( Y2 = X4 ) ) )
     => ( ( P @ Z )
       => ( smaller_interp_c_d_a @ ( least_c_d_set_a @ smaller_interp_c_d_a @ P ) @ Z ) ) ) ).

% local.Least1_le
thf(fact_428_local_OLeast1__le,axiom,
    ! [P: ( ( e > f ) > set_a ) > $o,Z: ( e > f ) > set_a] :
      ( ? [X4: ( e > f ) > set_a] :
          ( ( P @ X4 )
          & ! [Y2: ( e > f ) > set_a] :
              ( ( P @ Y2 )
             => ( smaller_interp_e_f_a @ X4 @ Y2 ) )
          & ! [Y2: ( e > f ) > set_a] :
              ( ( ( P @ Y2 )
                & ! [Ya: ( e > f ) > set_a] :
                    ( ( P @ Ya )
                   => ( smaller_interp_e_f_a @ Y2 @ Ya ) ) )
             => ( Y2 = X4 ) ) )
     => ( ( P @ Z )
       => ( smaller_interp_e_f_a @ ( least_e_f_set_a @ smaller_interp_e_f_a @ P ) @ Z ) ) ) ).

% local.Least1_le
thf(fact_429_local_OLeastI2__order,axiom,
    ! [P: ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a,Q: ( ( c > d ) > set_a ) > $o] :
      ( ( P @ X )
     => ( ! [Y2: ( c > d ) > set_a] :
            ( ( P @ Y2 )
           => ( smaller_interp_c_d_a @ X @ Y2 ) )
       => ( ! [X2: ( c > d ) > set_a] :
              ( ( P @ X2 )
             => ( ! [Y5: ( c > d ) > set_a] :
                    ( ( P @ Y5 )
                   => ( smaller_interp_c_d_a @ X2 @ Y5 ) )
               => ( Q @ X2 ) ) )
         => ( Q @ ( least_c_d_set_a @ smaller_interp_c_d_a @ P ) ) ) ) ) ).

% local.LeastI2_order
thf(fact_430_local_OLeastI2__order,axiom,
    ! [P: ( ( e > f ) > set_a ) > $o,X: ( e > f ) > set_a,Q: ( ( e > f ) > set_a ) > $o] :
      ( ( P @ X )
     => ( ! [Y2: ( e > f ) > set_a] :
            ( ( P @ Y2 )
           => ( smaller_interp_e_f_a @ X @ Y2 ) )
       => ( ! [X2: ( e > f ) > set_a] :
              ( ( P @ X2 )
             => ( ! [Y5: ( e > f ) > set_a] :
                    ( ( P @ Y5 )
                   => ( smaller_interp_e_f_a @ X2 @ Y5 ) )
               => ( Q @ X2 ) ) )
         => ( Q @ ( least_e_f_set_a @ smaller_interp_e_f_a @ P ) ) ) ) ) ).

% local.LeastI2_order
thf(fact_431_local_OLeast__equality,axiom,
    ! [P: ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a] :
      ( ( P @ X )
     => ( ! [Y2: ( c > d ) > set_a] :
            ( ( P @ Y2 )
           => ( smaller_interp_c_d_a @ X @ Y2 ) )
       => ( ( least_c_d_set_a @ smaller_interp_c_d_a @ P )
          = X ) ) ) ).

% local.Least_equality
thf(fact_432_local_OLeast__equality,axiom,
    ! [P: ( ( e > f ) > set_a ) > $o,X: ( e > f ) > set_a] :
      ( ( P @ X )
     => ( ! [Y2: ( e > f ) > set_a] :
            ( ( P @ Y2 )
           => ( smaller_interp_e_f_a @ X @ Y2 ) )
       => ( ( least_e_f_set_a @ smaller_interp_e_f_a @ P )
          = X ) ) ) ).

% local.Least_equality
thf(fact_433_local_Omax__def,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ( smaller_interp_c_d_a @ A2 @ B )
       => ( ( max_c_d_set_a @ smaller_interp_c_d_a @ A2 @ B )
          = B ) )
      & ( ~ ( smaller_interp_c_d_a @ A2 @ B )
       => ( ( max_c_d_set_a @ smaller_interp_c_d_a @ A2 @ B )
          = A2 ) ) ) ).

% local.max_def
thf(fact_434_local_Omax__def,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( ( smaller_interp_e_f_a @ A2 @ B )
       => ( ( max_e_f_set_a @ smaller_interp_e_f_a @ A2 @ B )
          = B ) )
      & ( ~ ( smaller_interp_e_f_a @ A2 @ B )
       => ( ( max_e_f_set_a @ smaller_interp_e_f_a @ A2 @ B )
          = A2 ) ) ) ).

% local.max_def
thf(fact_435_local_Omin__def,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ( smaller_interp_c_d_a @ A2 @ B )
       => ( ( min_c_d_set_a @ smaller_interp_c_d_a @ A2 @ B )
          = A2 ) )
      & ( ~ ( smaller_interp_c_d_a @ A2 @ B )
       => ( ( min_c_d_set_a @ smaller_interp_c_d_a @ A2 @ B )
          = B ) ) ) ).

% local.min_def
thf(fact_436_local_Omin__def,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( ( smaller_interp_e_f_a @ A2 @ B )
       => ( ( min_e_f_set_a @ smaller_interp_e_f_a @ A2 @ B )
          = A2 ) )
      & ( ~ ( smaller_interp_e_f_a @ A2 @ B )
       => ( ( min_e_f_set_a @ smaller_interp_e_f_a @ A2 @ B )
          = B ) ) ) ).

% local.min_def
thf(fact_437_local_Oorder_Opartial__preordering__axioms,axiom,
    partia701112543150332005_set_a @ smaller_interp_c_d_a ).

% local.order.partial_preordering_axioms
thf(fact_438_local_Oorder_Opartial__preordering__axioms,axiom,
    partia6228822312481723621_set_a @ smaller_interp_e_f_a ).

% local.order.partial_preordering_axioms
thf(fact_439_assms_I3_J,axiom,
    ! [Delta3: ( c > d ) > set_a] :
      ( ( set_cl2807270042661212426_a_c_d @ s @ Delta3 )
     => ( set_cl2807270042661212426_a_c_d @ s @ ( f2 @ Delta3 ) ) ) ).

% assms(3)
thf(fact_440_local_Oantisymp__on__le,axiom,
    ! [A: set_c_d_set_a] : ( antisy1518167394357443548_set_a @ A @ smaller_interp_c_d_a ) ).

% local.antisymp_on_le
thf(fact_441_local_Oantisymp__on__le,axiom,
    ! [A: set_e_f_set_a] : ( antisy7045877163688835164_set_a @ A @ smaller_interp_e_f_a ) ).

% local.antisymp_on_le
thf(fact_442_local_Obdd__above_OE,axiom,
    ! [A: set_e_f_set_a] :
      ( ( condit3231253506778547291_set_a @ smaller_interp_e_f_a @ A )
     => ~ ! [M: ( e > f ) > set_a] :
            ~ ! [X4: ( e > f ) > set_a] :
                ( ( member_e_f_set_a @ X4 @ A )
               => ( smaller_interp_e_f_a @ X4 @ M ) ) ) ).

% local.bdd_above.E
thf(fact_443_local_Obdd__above_OE,axiom,
    ! [A: set_c_d_set_a] :
      ( ( condit6926915774301931483_set_a @ smaller_interp_c_d_a @ A )
     => ~ ! [M: ( c > d ) > set_a] :
            ~ ! [X4: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ X4 @ A )
               => ( smaller_interp_c_d_a @ X4 @ M ) ) ) ).

% local.bdd_above.E
thf(fact_444_local_Obdd__above__def,axiom,
    ! [A: set_e_f_set_a] :
      ( ( condit3231253506778547291_set_a @ smaller_interp_e_f_a @ A )
      = ( ? [M2: ( e > f ) > set_a] :
          ! [X3: ( e > f ) > set_a] :
            ( ( member_e_f_set_a @ X3 @ A )
           => ( smaller_interp_e_f_a @ X3 @ M2 ) ) ) ) ).

% local.bdd_above_def
thf(fact_445_local_Obdd__above__def,axiom,
    ! [A: set_c_d_set_a] :
      ( ( condit6926915774301931483_set_a @ smaller_interp_c_d_a @ A )
      = ( ? [M2: ( c > d ) > set_a] :
          ! [X3: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X3 @ A )
           => ( smaller_interp_c_d_a @ X3 @ M2 ) ) ) ) ).

% local.bdd_above_def
thf(fact_446_set__closure__property__instantiate,axiom,
    ! [S4: a > a > set_a,Delta3: ( c > d ) > set_a,A2: a,S3: c > d,B: a,X: a] :
      ( ( set_cl2807270042661212426_a_c_d @ S4 @ Delta3 )
     => ( ( member_a @ A2 @ ( Delta3 @ S3 ) )
       => ( ( member_a @ B @ ( Delta3 @ S3 ) )
         => ( ( member_a @ X @ ( S4 @ A2 @ B ) )
           => ( member_a @ X @ ( Delta3 @ S3 ) ) ) ) ) ) ).

% set_closure_property_instantiate
thf(fact_447_set__closure__property__instantiate,axiom,
    ! [S4: a > a > set_a,Delta3: ( e > f ) > set_a,A2: a,S3: e > f,B: a,X: a] :
      ( ( set_cl6455730915570636170_a_e_f @ S4 @ Delta3 )
     => ( ( member_a @ A2 @ ( Delta3 @ S3 ) )
       => ( ( member_a @ B @ ( Delta3 @ S3 ) )
         => ( ( member_a @ X @ ( S4 @ A2 @ B ) )
           => ( member_a @ X @ ( Delta3 @ S3 ) ) ) ) ) ) ).

% set_closure_property_instantiate
thf(fact_448_set__closure__property__def,axiom,
    ( set_cl2807270042661212426_a_c_d
    = ( ^ [S5: a > a > set_a,Delta: ( c > d ) > set_a] :
        ! [A3: a,B2: a,S: c > d] :
          ( ( ( member_a @ A3 @ ( Delta @ S ) )
            & ( member_a @ B2 @ ( Delta @ S ) ) )
         => ( ord_less_eq_set_a @ ( S5 @ A3 @ B2 ) @ ( Delta @ S ) ) ) ) ) ).

% set_closure_property_def
thf(fact_449_set__closure__property__def,axiom,
    ( set_cl6455730915570636170_a_e_f
    = ( ^ [S5: a > a > set_a,Delta: ( e > f ) > set_a] :
        ! [A3: a,B2: a,S: e > f] :
          ( ( ( member_a @ A3 @ ( Delta @ S ) )
            & ( member_a @ B2 @ ( Delta @ S ) ) )
         => ( ord_less_eq_set_a @ ( S5 @ A3 @ B2 ) @ ( Delta @ S ) ) ) ) ) ).

% set_closure_property_def
thf(fact_450_set__closure__propertyI,axiom,
    ! [Delta3: ( c > d ) > set_a,S4: a > a > set_a] :
      ( ! [A5: a,B4: a,S2: c > d] :
          ( ( ( member_a @ A5 @ ( Delta3 @ S2 ) )
            & ( member_a @ B4 @ ( Delta3 @ S2 ) ) )
         => ( ord_less_eq_set_a @ ( S4 @ A5 @ B4 ) @ ( Delta3 @ S2 ) ) )
     => ( set_cl2807270042661212426_a_c_d @ S4 @ Delta3 ) ) ).

% set_closure_propertyI
thf(fact_451_set__closure__propertyI,axiom,
    ! [Delta3: ( e > f ) > set_a,S4: a > a > set_a] :
      ( ! [A5: a,B4: a,S2: e > f] :
          ( ( ( member_a @ A5 @ ( Delta3 @ S2 ) )
            & ( member_a @ B4 @ ( Delta3 @ S2 ) ) )
         => ( ord_less_eq_set_a @ ( S4 @ A5 @ B4 ) @ ( Delta3 @ S2 ) ) )
     => ( set_cl6455730915570636170_a_e_f @ S4 @ Delta3 ) ) ).

% set_closure_propertyI
thf(fact_452_local_Obdd__above__mono,axiom,
    ! [B3: set_e_f_set_a,A: set_e_f_set_a] :
      ( ( condit3231253506778547291_set_a @ smaller_interp_e_f_a @ B3 )
     => ( ( ord_le5994374269167502767_set_a @ A @ B3 )
       => ( condit3231253506778547291_set_a @ smaller_interp_e_f_a @ A ) ) ) ).

% local.bdd_above_mono
thf(fact_453_local_Obdd__above__mono,axiom,
    ! [B3: set_c_d_set_a,A: set_c_d_set_a] :
      ( ( condit6926915774301931483_set_a @ smaller_interp_c_d_a @ B3 )
     => ( ( ord_le5982164083705284911_set_a @ A @ B3 )
       => ( condit6926915774301931483_set_a @ smaller_interp_c_d_a @ A ) ) ) ).

% local.bdd_above_mono
thf(fact_454_subsetI,axiom,
    ! [A: set_set_c_d_set_a,B3: set_set_c_d_set_a] :
      ( ! [X2: set_c_d_set_a] :
          ( ( member_set_c_d_set_a @ X2 @ A )
         => ( member_set_c_d_set_a @ X2 @ B3 ) )
     => ( ord_le7272806397018272911_set_a @ A @ B3 ) ) ).

% subsetI
thf(fact_455_subsetI,axiom,
    ! [A: set_a,B3: set_a] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_a @ X2 @ B3 ) )
     => ( ord_less_eq_set_a @ A @ B3 ) ) ).

% subsetI
thf(fact_456_subsetI,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X2 @ A )
         => ( member_c_d_set_a @ X2 @ B3 ) )
     => ( ord_le5982164083705284911_set_a @ A @ B3 ) ) ).

% subsetI
thf(fact_457_subset__antisym,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A @ B3 )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( A = B3 ) ) ) ).

% subset_antisym
thf(fact_458_subset__antisym,axiom,
    ! [A: set_a,B3: set_a] :
      ( ( ord_less_eq_set_a @ A @ B3 )
     => ( ( ord_less_eq_set_a @ B3 @ A )
       => ( A = B3 ) ) ) ).

% subset_antisym
thf(fact_459_top1I,axiom,
    ! [X: ( c > d ) > set_a] : ( top_top_c_d_set_a_o @ X ) ).

% top1I
thf(fact_460_local_Obdd__above__top,axiom,
    ! [A: set_e_f_set_a] : ( condit3231253506778547291_set_a @ smaller_interp_e_f_a @ A ) ).

% local.bdd_above_top
thf(fact_461_local_Obdd__above__top,axiom,
    ! [A: set_c_d_set_a] : ( condit6926915774301931483_set_a @ smaller_interp_c_d_a @ A ) ).

% local.bdd_above_top
thf(fact_462_local_Obdd__aboveI,axiom,
    ! [A: set_e_f_set_a,M3: ( e > f ) > set_a] :
      ( ! [X2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ X2 @ A )
         => ( smaller_interp_e_f_a @ X2 @ M3 ) )
     => ( condit3231253506778547291_set_a @ smaller_interp_e_f_a @ A ) ) ).

% local.bdd_aboveI
thf(fact_463_local_Obdd__aboveI,axiom,
    ! [A: set_c_d_set_a,M3: ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X2 @ A )
         => ( smaller_interp_c_d_a @ X2 @ M3 ) )
     => ( condit6926915774301931483_set_a @ smaller_interp_c_d_a @ A ) ) ).

% local.bdd_aboveI
thf(fact_464_in__mono,axiom,
    ! [A: set_set_c_d_set_a,B3: set_set_c_d_set_a,X: set_c_d_set_a] :
      ( ( ord_le7272806397018272911_set_a @ A @ B3 )
     => ( ( member_set_c_d_set_a @ X @ A )
       => ( member_set_c_d_set_a @ X @ B3 ) ) ) ).

% in_mono
thf(fact_465_in__mono,axiom,
    ! [A: set_a,B3: set_a,X: a] :
      ( ( ord_less_eq_set_a @ A @ B3 )
     => ( ( member_a @ X @ A )
       => ( member_a @ X @ B3 ) ) ) ).

% in_mono
thf(fact_466_in__mono,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a,X: ( c > d ) > set_a] :
      ( ( ord_le5982164083705284911_set_a @ A @ B3 )
     => ( ( member_c_d_set_a @ X @ A )
       => ( member_c_d_set_a @ X @ B3 ) ) ) ).

% in_mono
thf(fact_467_subsetD,axiom,
    ! [A: set_set_c_d_set_a,B3: set_set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le7272806397018272911_set_a @ A @ B3 )
     => ( ( member_set_c_d_set_a @ C @ A )
       => ( member_set_c_d_set_a @ C @ B3 ) ) ) ).

% subsetD
thf(fact_468_subsetD,axiom,
    ! [A: set_a,B3: set_a,C: a] :
      ( ( ord_less_eq_set_a @ A @ B3 )
     => ( ( member_a @ C @ A )
       => ( member_a @ C @ B3 ) ) ) ).

% subsetD
thf(fact_469_subsetD,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a,C: ( c > d ) > set_a] :
      ( ( ord_le5982164083705284911_set_a @ A @ B3 )
     => ( ( member_c_d_set_a @ C @ A )
       => ( member_c_d_set_a @ C @ B3 ) ) ) ).

% subsetD
thf(fact_470_equalityE,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( A = B3 )
     => ~ ( ( ord_le5982164083705284911_set_a @ A @ B3 )
         => ~ ( ord_le5982164083705284911_set_a @ B3 @ A ) ) ) ).

% equalityE
thf(fact_471_equalityE,axiom,
    ! [A: set_a,B3: set_a] :
      ( ( A = B3 )
     => ~ ( ( ord_less_eq_set_a @ A @ B3 )
         => ~ ( ord_less_eq_set_a @ B3 @ A ) ) ) ).

% equalityE
thf(fact_472_subset__eq,axiom,
    ( ord_le7272806397018272911_set_a
    = ( ^ [A4: set_set_c_d_set_a,B5: set_set_c_d_set_a] :
        ! [X3: set_c_d_set_a] :
          ( ( member_set_c_d_set_a @ X3 @ A4 )
         => ( member_set_c_d_set_a @ X3 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_473_subset__eq,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A4: set_a,B5: set_a] :
        ! [X3: a] :
          ( ( member_a @ X3 @ A4 )
         => ( member_a @ X3 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_474_subset__eq,axiom,
    ( ord_le5982164083705284911_set_a
    = ( ^ [A4: set_c_d_set_a,B5: set_c_d_set_a] :
        ! [X3: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X3 @ A4 )
         => ( member_c_d_set_a @ X3 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_475_equalityD1,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( A = B3 )
     => ( ord_le5982164083705284911_set_a @ A @ B3 ) ) ).

% equalityD1
thf(fact_476_equalityD1,axiom,
    ! [A: set_a,B3: set_a] :
      ( ( A = B3 )
     => ( ord_less_eq_set_a @ A @ B3 ) ) ).

% equalityD1
thf(fact_477_equalityD2,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( A = B3 )
     => ( ord_le5982164083705284911_set_a @ B3 @ A ) ) ).

% equalityD2
thf(fact_478_equalityD2,axiom,
    ! [A: set_a,B3: set_a] :
      ( ( A = B3 )
     => ( ord_less_eq_set_a @ B3 @ A ) ) ).

% equalityD2
thf(fact_479_subset__iff,axiom,
    ( ord_le7272806397018272911_set_a
    = ( ^ [A4: set_set_c_d_set_a,B5: set_set_c_d_set_a] :
        ! [T: set_c_d_set_a] :
          ( ( member_set_c_d_set_a @ T @ A4 )
         => ( member_set_c_d_set_a @ T @ B5 ) ) ) ) ).

% subset_iff
thf(fact_480_subset__iff,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A4: set_a,B5: set_a] :
        ! [T: a] :
          ( ( member_a @ T @ A4 )
         => ( member_a @ T @ B5 ) ) ) ) ).

% subset_iff
thf(fact_481_subset__iff,axiom,
    ( ord_le5982164083705284911_set_a
    = ( ^ [A4: set_c_d_set_a,B5: set_c_d_set_a] :
        ! [T: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ T @ A4 )
         => ( member_c_d_set_a @ T @ B5 ) ) ) ) ).

% subset_iff
thf(fact_482_subset__refl,axiom,
    ! [A: set_c_d_set_a] : ( ord_le5982164083705284911_set_a @ A @ A ) ).

% subset_refl
thf(fact_483_subset__refl,axiom,
    ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) ).

% subset_refl
thf(fact_484_Collect__mono,axiom,
    ! [P: ( ( c > d ) > set_a ) > $o,Q: ( ( c > d ) > set_a ) > $o] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( P @ X2 )
         => ( Q @ X2 ) )
     => ( ord_le5982164083705284911_set_a @ ( collect_c_d_set_a @ P ) @ ( collect_c_d_set_a @ Q ) ) ) ).

% Collect_mono
thf(fact_485_Collect__mono,axiom,
    ! [P: a > $o,Q: a > $o] :
      ( ! [X2: a] :
          ( ( P @ X2 )
         => ( Q @ X2 ) )
     => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).

% Collect_mono
thf(fact_486_subset__trans,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a,C2: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A @ B3 )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ C2 )
       => ( ord_le5982164083705284911_set_a @ A @ C2 ) ) ) ).

% subset_trans
thf(fact_487_subset__trans,axiom,
    ! [A: set_a,B3: set_a,C2: set_a] :
      ( ( ord_less_eq_set_a @ A @ B3 )
     => ( ( ord_less_eq_set_a @ B3 @ C2 )
       => ( ord_less_eq_set_a @ A @ C2 ) ) ) ).

% subset_trans
thf(fact_488_set__eq__subset,axiom,
    ( ( ^ [Y3: set_c_d_set_a,Z2: set_c_d_set_a] : ( Y3 = Z2 ) )
    = ( ^ [A4: set_c_d_set_a,B5: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ A4 @ B5 )
          & ( ord_le5982164083705284911_set_a @ B5 @ A4 ) ) ) ) ).

% set_eq_subset
thf(fact_489_set__eq__subset,axiom,
    ( ( ^ [Y3: set_a,Z2: set_a] : ( Y3 = Z2 ) )
    = ( ^ [A4: set_a,B5: set_a] :
          ( ( ord_less_eq_set_a @ A4 @ B5 )
          & ( ord_less_eq_set_a @ B5 @ A4 ) ) ) ) ).

% set_eq_subset
thf(fact_490_Collect__mono__iff,axiom,
    ! [P: ( ( c > d ) > set_a ) > $o,Q: ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le5982164083705284911_set_a @ ( collect_c_d_set_a @ P ) @ ( collect_c_d_set_a @ Q ) )
      = ( ! [X3: ( c > d ) > set_a] :
            ( ( P @ X3 )
           => ( Q @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_491_Collect__mono__iff,axiom,
    ! [P: a > $o,Q: a > $o] :
      ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
      = ( ! [X3: a] :
            ( ( P @ X3 )
           => ( Q @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_492_partial__preordering__def,axiom,
    ( partia701112543150332005_set_a
    = ( ^ [Less_eq2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ! [A3: ( c > d ) > set_a] : ( Less_eq2 @ A3 @ A3 )
          & ! [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a,C3: ( c > d ) > set_a] :
              ( ( Less_eq2 @ A3 @ B2 )
             => ( ( Less_eq2 @ B2 @ C3 )
               => ( Less_eq2 @ A3 @ C3 ) ) ) ) ) ) ).

% partial_preordering_def
thf(fact_493_partial__preordering_Otrans,axiom,
    ! [Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( partia701112543150332005_set_a @ Less_eq )
     => ( ( Less_eq @ A2 @ B )
       => ( ( Less_eq @ B @ C )
         => ( Less_eq @ A2 @ C ) ) ) ) ).

% partial_preordering.trans
thf(fact_494_partial__preordering_Ointro,axiom,
    ! [Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ! [A5: ( c > d ) > set_a] : ( Less_eq @ A5 @ A5 )
     => ( ! [A5: ( c > d ) > set_a,B4: ( c > d ) > set_a,C4: ( c > d ) > set_a] :
            ( ( Less_eq @ A5 @ B4 )
           => ( ( Less_eq @ B4 @ C4 )
             => ( Less_eq @ A5 @ C4 ) ) )
       => ( partia701112543150332005_set_a @ Less_eq ) ) ) ).

% partial_preordering.intro
thf(fact_495_partial__preordering_Orefl,axiom,
    ! [Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A2: ( c > d ) > set_a] :
      ( ( partia701112543150332005_set_a @ Less_eq )
     => ( Less_eq @ A2 @ A2 ) ) ).

% partial_preordering.refl
thf(fact_496_ord_Omin_Ocong,axiom,
    min_e_f_set_a = min_e_f_set_a ).

% ord.min.cong
thf(fact_497_ord_Omax_Ocong,axiom,
    max_e_f_set_a = max_e_f_set_a ).

% ord.max.cong
thf(fact_498_ord_Omin__def,axiom,
    ( min_e_f_set_a
    = ( ^ [Less_eq2: ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o,A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] : ( if_e_f_set_a @ ( Less_eq2 @ A3 @ B2 ) @ A3 @ B2 ) ) ) ).

% ord.min_def
thf(fact_499_ord_Omax__def,axiom,
    ( max_e_f_set_a
    = ( ^ [Less_eq2: ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o,A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] : ( if_e_f_set_a @ ( Less_eq2 @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).

% ord.max_def
thf(fact_500_preorder__class_Oorder_Opartial__preordering__axioms,axiom,
    partia1270112395057131461_set_a @ ord_le5982164083705284911_set_a ).

% preorder_class.order.partial_preordering_axioms
thf(fact_501_preorder__class_Oorder_Opartial__preordering__axioms,axiom,
    partia6602192050731689876_set_a @ ord_less_eq_set_a ).

% preorder_class.order.partial_preordering_axioms
thf(fact_502_preorder__class_Oorder_Opartial__preordering__axioms,axiom,
    partia8378609006112419556et_a_o @ ord_le1832228425591547726et_a_o ).

% preorder_class.order.partial_preordering_axioms
thf(fact_503_preorder__class_Oorder_Opartial__preordering__axioms,axiom,
    partia6228822312481723621_set_a @ ord_le4769328160706778703_set_a ).

% preorder_class.order.partial_preordering_axioms
thf(fact_504_preorder__class_Oorder_Opartial__preordering__axioms,axiom,
    partia701112543150332005_set_a @ ord_le8464990428230162895_set_a ).

% preorder_class.order.partial_preordering_axioms
thf(fact_505_local_Obdd__above__primitive__def,axiom,
    ( ( condit3231253506778547291_set_a @ smaller_interp_e_f_a )
    = ( condit4458562775787300132_set_a @ smaller_interp_e_f_a ) ) ).

% local.bdd_above_primitive_def
thf(fact_506_local_Obdd__above__primitive__def,axiom,
    ( ( condit6926915774301931483_set_a @ smaller_interp_c_d_a )
    = ( condit8154225043310684324_set_a @ smaller_interp_c_d_a ) ) ).

% local.bdd_above_primitive_def
thf(fact_507_top__empty__eq,axiom,
    ( top_top_a_o
    = ( ^ [X3: a] : ( member_a @ X3 @ top_top_set_a ) ) ) ).

% top_empty_eq
thf(fact_508_top__empty__eq,axiom,
    ( top_to6119605859643668830et_a_o
    = ( ^ [X3: set_c_d_set_a] : ( member_set_c_d_set_a @ X3 @ top_to5717711934741766719_set_a ) ) ) ).

% top_empty_eq
thf(fact_509_top__empty__eq,axiom,
    ( top_top_set_a_o
    = ( ^ [X3: set_a] : ( member_set_a @ X3 @ top_top_set_set_a ) ) ) ).

% top_empty_eq
thf(fact_510_top__empty__eq,axiom,
    ( top_top_e_f_set_a_o
    = ( ^ [X3: ( e > f ) > set_a] : ( member_e_f_set_a @ X3 @ top_to4280187784772989791_set_a ) ) ) ).

% top_empty_eq
thf(fact_511_top__empty__eq,axiom,
    ( top_top_c_d_set_a_o
    = ( ^ [X3: ( c > d ) > set_a] : ( member_c_d_set_a @ X3 @ top_to4267977599310771935_set_a ) ) ) ).

% top_empty_eq
thf(fact_512_antisymp__on__subset,axiom,
    ! [A: set_c_d_set_a,R4: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B3: set_c_d_set_a] :
      ( ( antisy1518167394357443548_set_a @ A @ R4 )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ A )
       => ( antisy1518167394357443548_set_a @ B3 @ R4 ) ) ) ).

% antisymp_on_subset
thf(fact_513_antisymp__on__subset,axiom,
    ! [A: set_a,R4: a > a > $o,B3: set_a] :
      ( ( antisymp_on_a @ A @ R4 )
     => ( ( ord_less_eq_set_a @ B3 @ A )
       => ( antisymp_on_a @ B3 @ R4 ) ) ) ).

% antisymp_on_subset
thf(fact_514_antisympD,axiom,
    ! [R4: set_c_d_set_a > set_c_d_set_a > $o,X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( antisy2568922457103120188_set_a @ top_to5717711934741766719_set_a @ R4 )
     => ( ( R4 @ X @ Y )
       => ( ( R4 @ Y @ X )
         => ( X = Y ) ) ) ) ).

% antisympD
thf(fact_515_antisympD,axiom,
    ! [R4: set_a > set_a > $o,X: set_a,Y: set_a] :
      ( ( antisymp_on_set_a @ top_top_set_set_a @ R4 )
     => ( ( R4 @ X @ Y )
       => ( ( R4 @ Y @ X )
         => ( X = Y ) ) ) ) ).

% antisympD
thf(fact_516_antisympD,axiom,
    ! [R4: ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( antisy7045877163688835164_set_a @ top_to4280187784772989791_set_a @ R4 )
     => ( ( R4 @ X @ Y )
       => ( ( R4 @ Y @ X )
         => ( X = Y ) ) ) ) ).

% antisympD
thf(fact_517_antisympD,axiom,
    ! [R4: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( antisy1518167394357443548_set_a @ top_to4267977599310771935_set_a @ R4 )
     => ( ( R4 @ X @ Y )
       => ( ( R4 @ Y @ X )
         => ( X = Y ) ) ) ) ).

% antisympD
thf(fact_518_antisympI,axiom,
    ! [R4: set_c_d_set_a > set_c_d_set_a > $o] :
      ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
          ( ( R4 @ X2 @ Y2 )
         => ( ( R4 @ Y2 @ X2 )
           => ( X2 = Y2 ) ) )
     => ( antisy2568922457103120188_set_a @ top_to5717711934741766719_set_a @ R4 ) ) ).

% antisympI
thf(fact_519_antisympI,axiom,
    ! [R4: set_a > set_a > $o] :
      ( ! [X2: set_a,Y2: set_a] :
          ( ( R4 @ X2 @ Y2 )
         => ( ( R4 @ Y2 @ X2 )
           => ( X2 = Y2 ) ) )
     => ( antisymp_on_set_a @ top_top_set_set_a @ R4 ) ) ).

% antisympI
thf(fact_520_antisympI,axiom,
    ! [R4: ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o] :
      ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
          ( ( R4 @ X2 @ Y2 )
         => ( ( R4 @ Y2 @ X2 )
           => ( X2 = Y2 ) ) )
     => ( antisy7045877163688835164_set_a @ top_to4280187784772989791_set_a @ R4 ) ) ).

% antisympI
thf(fact_521_antisympI,axiom,
    ! [R4: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( R4 @ X2 @ Y2 )
         => ( ( R4 @ Y2 @ X2 )
           => ( X2 = Y2 ) ) )
     => ( antisy1518167394357443548_set_a @ top_to4267977599310771935_set_a @ R4 ) ) ).

% antisympI
thf(fact_522_antisymp__equality,axiom,
    ( antisy2568922457103120188_set_a @ top_to5717711934741766719_set_a
    @ ^ [Y3: set_c_d_set_a,Z2: set_c_d_set_a] : ( Y3 = Z2 ) ) ).

% antisymp_equality
thf(fact_523_antisymp__equality,axiom,
    ( antisymp_on_set_a @ top_top_set_set_a
    @ ^ [Y3: set_a,Z2: set_a] : ( Y3 = Z2 ) ) ).

% antisymp_equality
thf(fact_524_antisymp__equality,axiom,
    ( antisy7045877163688835164_set_a @ top_to4280187784772989791_set_a
    @ ^ [Y3: ( e > f ) > set_a,Z2: ( e > f ) > set_a] : ( Y3 = Z2 ) ) ).

% antisymp_equality
thf(fact_525_antisymp__equality,axiom,
    ( antisy1518167394357443548_set_a @ top_to4267977599310771935_set_a
    @ ^ [Y3: ( c > d ) > set_a,Z2: ( c > d ) > set_a] : ( Y3 = Z2 ) ) ).

% antisymp_equality
thf(fact_526_antisymp__less__eq,axiom,
    ! [R2: set_c_d_set_a > set_c_d_set_a > $o,S3: set_c_d_set_a > set_c_d_set_a > $o] :
      ( ( ord_le5545401091215412046et_a_o @ R2 @ S3 )
     => ( ( antisy2568922457103120188_set_a @ top_to5717711934741766719_set_a @ S3 )
       => ( antisy2568922457103120188_set_a @ top_to5717711934741766719_set_a @ R2 ) ) ) ).

% antisymp_less_eq
thf(fact_527_antisymp__less__eq,axiom,
    ! [R2: set_a > set_a > $o,S3: set_a > set_a > $o] :
      ( ( ord_le6897189994354892814et_a_o @ R2 @ S3 )
     => ( ( antisymp_on_set_a @ top_top_set_set_a @ S3 )
       => ( antisymp_on_set_a @ top_top_set_set_a @ R2 ) ) ) ).

% antisymp_less_eq
thf(fact_528_antisymp__less__eq,axiom,
    ! [R2: ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o,S3: ( ( e > f ) > set_a ) > ( ( e > f ) > set_a ) > $o] :
      ( ( ord_le6228063065474434894et_a_o @ R2 @ S3 )
     => ( ( antisy7045877163688835164_set_a @ top_to4280187784772989791_set_a @ S3 )
       => ( antisy7045877163688835164_set_a @ top_to4280187784772989791_set_a @ R2 ) ) ) ).

% antisymp_less_eq
thf(fact_529_antisymp__less__eq,axiom,
    ! [R2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,S3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ R2 @ S3 )
     => ( ( antisy1518167394357443548_set_a @ top_to4267977599310771935_set_a @ S3 )
       => ( antisy1518167394357443548_set_a @ top_to4267977599310771935_set_a @ R2 ) ) ) ).

% antisymp_less_eq
thf(fact_530_order__class_Oantisymp__on__le,axiom,
    ! [A: set_set_c_d_set_a] : ( antisy2568922457103120188_set_a @ A @ ord_le5982164083705284911_set_a ) ).

% order_class.antisymp_on_le
thf(fact_531_order__class_Oantisymp__on__le,axiom,
    ! [A: set_set_a] : ( antisymp_on_set_a @ A @ ord_less_eq_set_a ) ).

% order_class.antisymp_on_le
thf(fact_532_order__class_Oantisymp__on__le,axiom,
    ! [A: set_c_4840651787527498510et_a_o] : ( antisy3644999338385500379et_a_o @ A @ ord_le1832228425591547726et_a_o ) ).

% order_class.antisymp_on_le
thf(fact_533_order__class_Oantisymp__on__le,axiom,
    ! [A: set_e_f_set_a] : ( antisy7045877163688835164_set_a @ A @ ord_le4769328160706778703_set_a ) ).

% order_class.antisymp_on_le
thf(fact_534_order__class_Oantisymp__on__le,axiom,
    ! [A: set_c_d_set_a] : ( antisy1518167394357443548_set_a @ A @ ord_le8464990428230162895_set_a ) ).

% order_class.antisymp_on_le
thf(fact_535_local_Odual__order_Onot__eq__order__implies__strict,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( A2 != B )
     => ( ( smaller_interp_c_d_a @ B @ A2 )
       => ( less_c_d_a @ B @ A2 ) ) ) ).

% local.dual_order.not_eq_order_implies_strict
thf(fact_536_local_Odual__order_Onot__eq__order__implies__strict,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( A2 != B )
     => ( ( smaller_interp_e_f_a @ B @ A2 )
       => ( less_e_f_a @ B @ A2 ) ) ) ).

% local.dual_order.not_eq_order_implies_strict
thf(fact_537_local_Odual__order_Oorder__iff__strict,axiom,
    ( smaller_interp_c_d_a
    = ( ^ [B2: ( c > d ) > set_a,A3: ( c > d ) > set_a] :
          ( ( less_c_d_a @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% local.dual_order.order_iff_strict
thf(fact_538_local_Odual__order_Oorder__iff__strict,axiom,
    ( smaller_interp_e_f_a
    = ( ^ [B2: ( e > f ) > set_a,A3: ( e > f ) > set_a] :
          ( ( less_e_f_a @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% local.dual_order.order_iff_strict
thf(fact_539_local_Odual__order_Ostrict__iff__not,axiom,
    ( less_c_d_a
    = ( ^ [B2: ( c > d ) > set_a,A3: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ B2 @ A3 )
          & ~ ( smaller_interp_c_d_a @ A3 @ B2 ) ) ) ) ).

% local.dual_order.strict_iff_not
thf(fact_540_local_Odual__order_Ostrict__iff__not,axiom,
    ( less_e_f_a
    = ( ^ [B2: ( e > f ) > set_a,A3: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ B2 @ A3 )
          & ~ ( smaller_interp_e_f_a @ A3 @ B2 ) ) ) ) ).

% local.dual_order.strict_iff_not
thf(fact_541_local_Odual__order_Ostrict__iff__order,axiom,
    ( less_c_d_a
    = ( ^ [B2: ( c > d ) > set_a,A3: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% local.dual_order.strict_iff_order
thf(fact_542_local_Odual__order_Ostrict__iff__order,axiom,
    ( less_e_f_a
    = ( ^ [B2: ( e > f ) > set_a,A3: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% local.dual_order.strict_iff_order
thf(fact_543_local_Odual__order_Ostrict__implies__order,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( less_c_d_a @ B @ A2 )
     => ( smaller_interp_c_d_a @ B @ A2 ) ) ).

% local.dual_order.strict_implies_order
thf(fact_544_local_Odual__order_Ostrict__implies__order,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a] :
      ( ( less_e_f_a @ B @ A2 )
     => ( smaller_interp_e_f_a @ B @ A2 ) ) ).

% local.dual_order.strict_implies_order
thf(fact_545_local_Odual__order_Ostrict__trans1,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ B @ A2 )
     => ( ( less_c_d_a @ C @ B )
       => ( less_c_d_a @ C @ A2 ) ) ) ).

% local.dual_order.strict_trans1
thf(fact_546_local_Odual__order_Ostrict__trans1,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ B @ A2 )
     => ( ( less_e_f_a @ C @ B )
       => ( less_e_f_a @ C @ A2 ) ) ) ).

% local.dual_order.strict_trans1
thf(fact_547_local_Odual__order_Ostrict__trans2,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( less_c_d_a @ B @ A2 )
     => ( ( smaller_interp_c_d_a @ C @ B )
       => ( less_c_d_a @ C @ A2 ) ) ) ).

% local.dual_order.strict_trans2
thf(fact_548_local_Odual__order_Ostrict__trans2,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( less_e_f_a @ B @ A2 )
     => ( ( smaller_interp_e_f_a @ C @ B )
       => ( less_e_f_a @ C @ A2 ) ) ) ).

% local.dual_order.strict_trans2
thf(fact_549_local_Oorder_Oorder__iff__strict,axiom,
    ( smaller_interp_c_d_a
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( less_c_d_a @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% local.order.order_iff_strict
thf(fact_550_local_Oorder_Oorder__iff__strict,axiom,
    ( smaller_interp_e_f_a
    = ( ^ [A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] :
          ( ( less_e_f_a @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% local.order.order_iff_strict
thf(fact_551_local_Oorder_Ostrict__iff__not,axiom,
    ( less_c_d_a
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ A3 @ B2 )
          & ~ ( smaller_interp_c_d_a @ B2 @ A3 ) ) ) ) ).

% local.order.strict_iff_not
thf(fact_552_local_Oorder_Ostrict__iff__not,axiom,
    ( less_e_f_a
    = ( ^ [A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ A3 @ B2 )
          & ~ ( smaller_interp_e_f_a @ B2 @ A3 ) ) ) ) ).

% local.order.strict_iff_not
thf(fact_553_local_Oorder_Ostrict__implies__order,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( less_c_d_a @ A2 @ B )
     => ( smaller_interp_c_d_a @ A2 @ B ) ) ).

% local.order.strict_implies_order
thf(fact_554_local_Oorder_Ostrict__implies__order,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( less_e_f_a @ A2 @ B )
     => ( smaller_interp_e_f_a @ A2 @ B ) ) ).

% local.order.strict_implies_order
thf(fact_555_local_Oorder_Ostrict__trans1,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ A2 @ B )
     => ( ( less_c_d_a @ B @ C )
       => ( less_c_d_a @ A2 @ C ) ) ) ).

% local.order.strict_trans1
thf(fact_556_local_Oorder_Ostrict__trans1,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ A2 @ B )
     => ( ( less_e_f_a @ B @ C )
       => ( less_e_f_a @ A2 @ C ) ) ) ).

% local.order.strict_trans1
thf(fact_557_local_Oorder_Ostrict__trans2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( less_c_d_a @ A2 @ B )
     => ( ( smaller_interp_c_d_a @ B @ C )
       => ( less_c_d_a @ A2 @ C ) ) ) ).

% local.order.strict_trans2
thf(fact_558_local_Oorder_Ostrict__trans2,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( less_e_f_a @ A2 @ B )
     => ( ( smaller_interp_e_f_a @ B @ C )
       => ( less_e_f_a @ A2 @ C ) ) ) ).

% local.order.strict_trans2
thf(fact_559_local_Oantisym__conv1,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ~ ( less_c_d_a @ X @ Y )
     => ( ( smaller_interp_c_d_a @ X @ Y )
        = ( X = Y ) ) ) ).

% local.antisym_conv1
thf(fact_560_local_Oantisym__conv1,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ~ ( less_e_f_a @ X @ Y )
     => ( ( smaller_interp_e_f_a @ X @ Y )
        = ( X = Y ) ) ) ).

% local.antisym_conv1
thf(fact_561_local_Oantisym__conv2,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ X @ Y )
     => ( ( ~ ( less_c_d_a @ X @ Y ) )
        = ( X = Y ) ) ) ).

% local.antisym_conv2
thf(fact_562_local_Oantisym__conv2,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ X @ Y )
     => ( ( ~ ( less_e_f_a @ X @ Y ) )
        = ( X = Y ) ) ) ).

% local.antisym_conv2
thf(fact_563_local_OleD,axiom,
    ! [Y: ( c > d ) > set_a,X: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ Y @ X )
     => ~ ( less_c_d_a @ X @ Y ) ) ).

% local.leD
thf(fact_564_local_OleD,axiom,
    ! [Y: ( e > f ) > set_a,X: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ Y @ X )
     => ~ ( less_e_f_a @ X @ Y ) ) ).

% local.leD
thf(fact_565_local_Ole__imp__less__or__eq,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ X @ Y )
     => ( ( less_c_d_a @ X @ Y )
        | ( X = Y ) ) ) ).

% local.le_imp_less_or_eq
thf(fact_566_local_Ole__imp__less__or__eq,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ X @ Y )
     => ( ( less_e_f_a @ X @ Y )
        | ( X = Y ) ) ) ).

% local.le_imp_less_or_eq
thf(fact_567_local_Ole__less,axiom,
    ( smaller_interp_c_d_a
    = ( ^ [X3: ( c > d ) > set_a,Y4: ( c > d ) > set_a] :
          ( ( less_c_d_a @ X3 @ Y4 )
          | ( X3 = Y4 ) ) ) ) ).

% local.le_less
thf(fact_568_local_Ole__less,axiom,
    ( smaller_interp_e_f_a
    = ( ^ [X3: ( e > f ) > set_a,Y4: ( e > f ) > set_a] :
          ( ( less_e_f_a @ X3 @ Y4 )
          | ( X3 = Y4 ) ) ) ) ).

% local.le_less
thf(fact_569_local_Ole__less__trans,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ X @ Y )
     => ( ( less_c_d_a @ Y @ Z )
       => ( less_c_d_a @ X @ Z ) ) ) ).

% local.le_less_trans
thf(fact_570_local_Ole__less__trans,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a,Z: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ X @ Y )
     => ( ( less_e_f_a @ Y @ Z )
       => ( less_e_f_a @ X @ Z ) ) ) ).

% local.le_less_trans
thf(fact_571_local_Ole__neq__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ A2 @ B )
     => ( ( A2 != B )
       => ( less_c_d_a @ A2 @ B ) ) ) ).

% local.le_neq_trans
thf(fact_572_local_Ole__neq__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ A2 @ B )
     => ( ( A2 != B )
       => ( less_e_f_a @ A2 @ B ) ) ) ).

% local.le_neq_trans
thf(fact_573_less__def,axiom,
    ( less_c_d_a
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% less_def
thf(fact_574_less__def,axiom,
    ( less_e_f_a
    = ( ^ [A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% less_def
thf(fact_575_local_Oless__imp__le,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( less_c_d_a @ X @ Y )
     => ( smaller_interp_c_d_a @ X @ Y ) ) ).

% local.less_imp_le
thf(fact_576_local_Oless__imp__le,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( less_e_f_a @ X @ Y )
     => ( smaller_interp_e_f_a @ X @ Y ) ) ).

% local.less_imp_le
thf(fact_577_local_Oless__le,axiom,
    ( less_c_d_a
    = ( ^ [X3: ( c > d ) > set_a,Y4: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ X3 @ Y4 )
          & ( X3 != Y4 ) ) ) ) ).

% local.less_le
thf(fact_578_local_Oless__le,axiom,
    ( less_e_f_a
    = ( ^ [X3: ( e > f ) > set_a,Y4: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ X3 @ Y4 )
          & ( X3 != Y4 ) ) ) ) ).

% local.less_le
thf(fact_579_local_Oless__le__not__le,axiom,
    ( less_c_d_a
    = ( ^ [X3: ( c > d ) > set_a,Y4: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ X3 @ Y4 )
          & ~ ( smaller_interp_c_d_a @ Y4 @ X3 ) ) ) ) ).

% local.less_le_not_le
thf(fact_580_local_Oless__le__not__le,axiom,
    ( less_e_f_a
    = ( ^ [X3: ( e > f ) > set_a,Y4: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ X3 @ Y4 )
          & ~ ( smaller_interp_e_f_a @ Y4 @ X3 ) ) ) ) ).

% local.less_le_not_le
thf(fact_581_local_Oless__le__trans,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( less_c_d_a @ X @ Y )
     => ( ( smaller_interp_c_d_a @ Y @ Z )
       => ( less_c_d_a @ X @ Z ) ) ) ).

% local.less_le_trans
thf(fact_582_local_Oless__le__trans,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a,Z: ( e > f ) > set_a] :
      ( ( less_e_f_a @ X @ Y )
     => ( ( smaller_interp_e_f_a @ Y @ Z )
       => ( less_e_f_a @ X @ Z ) ) ) ).

% local.less_le_trans
thf(fact_583_local_Oneq__le__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( A2 != B )
     => ( ( smaller_interp_c_d_a @ A2 @ B )
       => ( less_c_d_a @ A2 @ B ) ) ) ).

% local.neq_le_trans
thf(fact_584_local_Oneq__le__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( A2 != B )
     => ( ( smaller_interp_e_f_a @ A2 @ B )
       => ( less_e_f_a @ A2 @ B ) ) ) ).

% local.neq_le_trans
thf(fact_585_local_Onless__le,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ~ ( less_c_d_a @ A2 @ B ) )
      = ( ~ ( smaller_interp_c_d_a @ A2 @ B )
        | ( A2 = B ) ) ) ).

% local.nless_le
thf(fact_586_local_Onless__le,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( ~ ( less_e_f_a @ A2 @ B ) )
      = ( ~ ( smaller_interp_e_f_a @ A2 @ B )
        | ( A2 = B ) ) ) ).

% local.nless_le
thf(fact_587_local_Oantisymp__on__less,axiom,
    ! [A: set_c_d_set_a] : ( antisy1518167394357443548_set_a @ A @ less_c_d_a ) ).

% local.antisymp_on_less
thf(fact_588_local_Oantisymp__on__less,axiom,
    ! [A: set_e_f_set_a] : ( antisy7045877163688835164_set_a @ A @ less_e_f_a ) ).

% local.antisymp_on_less
thf(fact_589_predicate2I,axiom,
    ! [P: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Q: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( P @ X2 @ Y2 )
         => ( Q @ X2 @ Y2 ) )
     => ( ord_le1832228425591547726et_a_o @ P @ Q ) ) ).

% predicate2I
thf(fact_590_assms_I2_J,axiom,
    set_cl6455730915570636170_a_e_f @ s @ empty_interp_e_f_a ).

% assms(2)
thf(fact_591_predicate2D,axiom,
    ! [P: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Q: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_le1832228425591547726et_a_o @ P @ Q )
     => ( ( P @ X @ Y )
       => ( Q @ X @ Y ) ) ) ).

% predicate2D
thf(fact_592_rev__predicate2D,axiom,
    ! [P: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Q: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( P @ X @ Y )
     => ( ( ord_le1832228425591547726et_a_o @ P @ Q )
       => ( Q @ X @ Y ) ) ) ).

% rev_predicate2D
thf(fact_593_antisymp__onD,axiom,
    ! [A: set_a,R4: a > a > $o,X: a,Y: a] :
      ( ( antisymp_on_a @ A @ R4 )
     => ( ( member_a @ X @ A )
       => ( ( member_a @ Y @ A )
         => ( ( R4 @ X @ Y )
           => ( ( R4 @ Y @ X )
             => ( X = Y ) ) ) ) ) ) ).

% antisymp_onD
thf(fact_594_antisymp__onD,axiom,
    ! [A: set_set_c_d_set_a,R4: set_c_d_set_a > set_c_d_set_a > $o,X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( antisy2568922457103120188_set_a @ A @ R4 )
     => ( ( member_set_c_d_set_a @ X @ A )
       => ( ( member_set_c_d_set_a @ Y @ A )
         => ( ( R4 @ X @ Y )
           => ( ( R4 @ Y @ X )
             => ( X = Y ) ) ) ) ) ) ).

% antisymp_onD
thf(fact_595_antisymp__onD,axiom,
    ! [A: set_c_d_set_a,R4: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( antisy1518167394357443548_set_a @ A @ R4 )
     => ( ( member_c_d_set_a @ X @ A )
       => ( ( member_c_d_set_a @ Y @ A )
         => ( ( R4 @ X @ Y )
           => ( ( R4 @ Y @ X )
             => ( X = Y ) ) ) ) ) ) ).

% antisymp_onD
thf(fact_596_antisymp__onI,axiom,
    ! [A: set_a,R4: a > a > $o] :
      ( ! [X2: a,Y2: a] :
          ( ( member_a @ X2 @ A )
         => ( ( member_a @ Y2 @ A )
           => ( ( R4 @ X2 @ Y2 )
             => ( ( R4 @ Y2 @ X2 )
               => ( X2 = Y2 ) ) ) ) )
     => ( antisymp_on_a @ A @ R4 ) ) ).

% antisymp_onI
thf(fact_597_antisymp__onI,axiom,
    ! [A: set_set_c_d_set_a,R4: set_c_d_set_a > set_c_d_set_a > $o] :
      ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
          ( ( member_set_c_d_set_a @ X2 @ A )
         => ( ( member_set_c_d_set_a @ Y2 @ A )
           => ( ( R4 @ X2 @ Y2 )
             => ( ( R4 @ Y2 @ X2 )
               => ( X2 = Y2 ) ) ) ) )
     => ( antisy2568922457103120188_set_a @ A @ R4 ) ) ).

% antisymp_onI
thf(fact_598_antisymp__onI,axiom,
    ! [A: set_c_d_set_a,R4: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X2 @ A )
         => ( ( member_c_d_set_a @ Y2 @ A )
           => ( ( R4 @ X2 @ Y2 )
             => ( ( R4 @ Y2 @ X2 )
               => ( X2 = Y2 ) ) ) ) )
     => ( antisy1518167394357443548_set_a @ A @ R4 ) ) ).

% antisymp_onI
thf(fact_599_antisymp__on__def,axiom,
    ( antisy1518167394357443548_set_a
    = ( ^ [A4: set_c_d_set_a,R5: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
        ! [X3: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X3 @ A4 )
         => ! [Y4: ( c > d ) > set_a] :
              ( ( member_c_d_set_a @ Y4 @ A4 )
             => ( ( R5 @ X3 @ Y4 )
               => ( ( R5 @ Y4 @ X3 )
                 => ( X3 = Y4 ) ) ) ) ) ) ) ).

% antisymp_on_def
thf(fact_600_local_Ostrict__mono__mono,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_c_d_set_a] :
      ( ( monoto6642458133393520519_set_a @ top_to4267977599310771935_set_a @ less_c_d_a @ ord_le3685282097655362107_set_a @ F )
     => ( monoto6642458133393520519_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le5982164083705284911_set_a @ F ) ) ).

% local.strict_mono_mono
thf(fact_601_local_Ostrict__mono__mono,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_a] :
      ( ( monoto6316088450447394390_set_a @ top_to4267977599310771935_set_a @ less_c_d_a @ ord_less_set_a @ F )
     => ( monoto6316088450447394390_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_less_eq_set_a @ F ) ) ).

% local.strict_mono_mono
thf(fact_602_local_Ostrict__mono__mono,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( monoto6135324833271912870et_a_o @ top_to4267977599310771935_set_a @ less_c_d_a @ ord_le5853012546958565978et_a_o @ F )
     => ( monoto6135324833271912870et_a_o @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le1832228425591547726et_a_o @ F ) ) ).

% local.strict_mono_mono
thf(fact_603_local_Ostrict__mono__mono,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( e > f ) > set_a] :
      ( ( monoto8465133619513386151_set_a @ top_to4267977599310771935_set_a @ less_c_d_a @ ord_less_e_f_set_a @ F )
     => ( monoto8465133619513386151_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% local.strict_mono_mono
thf(fact_604_local_Ostrict__mono__mono,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( c > d ) > set_a] :
      ( ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ less_e_f_a @ ord_less_c_d_set_a @ F )
     => ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% local.strict_mono_mono
thf(fact_605_local_Ostrict__mono__mono,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_c_d_set_a] :
      ( ( monoto7716863510275742471_set_a @ top_to4280187784772989791_set_a @ less_e_f_a @ ord_le3685282097655362107_set_a @ F )
     => ( monoto7716863510275742471_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le5982164083705284911_set_a @ F ) ) ).

% local.strict_mono_mono
thf(fact_606_local_Ostrict__mono__mono,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_a] :
      ( ( monoto2776068642243291606_set_a @ top_to4280187784772989791_set_a @ less_e_f_a @ ord_less_set_a @ F )
     => ( monoto2776068642243291606_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_less_eq_set_a @ F ) ) ).

% local.strict_mono_mono
thf(fact_607_local_Ostrict__mono__mono,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( monoto947098964958182694et_a_o @ top_to4280187784772989791_set_a @ less_e_f_a @ ord_le5853012546958565978et_a_o @ F )
     => ( monoto947098964958182694et_a_o @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le1832228425591547726et_a_o @ F ) ) ).

% local.strict_mono_mono
thf(fact_608_local_Ostrict__mono__mono,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( e > f ) > set_a] :
      ( ( monoto5775188358803458087_set_a @ top_to4280187784772989791_set_a @ less_e_f_a @ ord_less_e_f_set_a @ F )
     => ( monoto5775188358803458087_set_a @ top_to4280187784772989791_set_a @ smaller_interp_e_f_a @ ord_le4769328160706778703_set_a @ F ) ) ).

% local.strict_mono_mono
thf(fact_609_local_Ostrict__mono__mono,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ less_c_d_a @ ord_less_c_d_set_a @ F )
     => ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% local.strict_mono_mono
thf(fact_610_local_Obdd__above_Opreordering__bdd__axioms,axiom,
    condit1596974763525182278_set_a @ smaller_interp_e_f_a @ less_e_f_a ).

% local.bdd_above.preordering_bdd_axioms
thf(fact_611_local_Obdd__above_Opreordering__bdd__axioms,axiom,
    condit5292637031048566470_set_a @ smaller_interp_c_d_a @ less_c_d_a ).

% local.bdd_above.preordering_bdd_axioms
thf(fact_612_local_Ostrict__monoI,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( c > d ) > set_a] :
      ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
          ( ( less_e_f_a @ X2 @ Y2 )
         => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ less_e_f_a @ ord_less_c_d_set_a @ F ) ) ).

% local.strict_monoI
thf(fact_613_local_Ostrict__monoI,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_c_d_set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( less_c_d_a @ X2 @ Y2 )
         => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto6642458133393520519_set_a @ top_to4267977599310771935_set_a @ less_c_d_a @ ord_le3685282097655362107_set_a @ F ) ) ).

% local.strict_monoI
thf(fact_614_local_Ostrict__monoI,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_c_d_set_a] :
      ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
          ( ( less_e_f_a @ X2 @ Y2 )
         => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto7716863510275742471_set_a @ top_to4280187784772989791_set_a @ less_e_f_a @ ord_le3685282097655362107_set_a @ F ) ) ).

% local.strict_monoI
thf(fact_615_local_Ostrict__monoI,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( less_c_d_a @ X2 @ Y2 )
         => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ less_c_d_a @ ord_less_c_d_set_a @ F ) ) ).

% local.strict_monoI
thf(fact_616_local_Ostrict__monoD,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto247478589472066471_set_a @ top_to4280187784772989791_set_a @ less_e_f_a @ ord_less_c_d_set_a @ F )
     => ( ( less_e_f_a @ X @ Y )
       => ( ord_less_c_d_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.strict_monoD
thf(fact_617_local_Ostrict__monoD,axiom,
    ! [F: ( ( c > d ) > set_a ) > set_c_d_set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto6642458133393520519_set_a @ top_to4267977599310771935_set_a @ less_c_d_a @ ord_le3685282097655362107_set_a @ F )
     => ( ( less_c_d_a @ X @ Y )
       => ( ord_le3685282097655362107_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.strict_monoD
thf(fact_618_local_Ostrict__monoD,axiom,
    ! [F: ( ( e > f ) > set_a ) > set_c_d_set_a,X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( monoto7716863510275742471_set_a @ top_to4280187784772989791_set_a @ less_e_f_a @ ord_le3685282097655362107_set_a @ F )
     => ( ( less_e_f_a @ X @ Y )
       => ( ord_le3685282097655362107_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.strict_monoD
thf(fact_619_local_Ostrict__monoD,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ less_c_d_a @ ord_less_c_d_set_a @ F )
     => ( ( less_c_d_a @ X @ Y )
       => ( ord_less_c_d_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% local.strict_monoD
thf(fact_620_local_Obdd__below__mono,axiom,
    ! [B3: set_e_f_set_a,A: set_e_f_set_a] :
      ( ( condit5311609186605872711_set_a @ smaller_interp_e_f_a @ B3 )
     => ( ( ord_le5994374269167502767_set_a @ A @ B3 )
       => ( condit5311609186605872711_set_a @ smaller_interp_e_f_a @ A ) ) ) ).

% local.bdd_below_mono
thf(fact_621_local_Obdd__below__mono,axiom,
    ! [B3: set_c_d_set_a,A: set_c_d_set_a] :
      ( ( condit9007271454129256903_set_a @ smaller_interp_c_d_a @ B3 )
     => ( ( ord_le5982164083705284911_set_a @ A @ B3 )
       => ( condit9007271454129256903_set_a @ smaller_interp_c_d_a @ A ) ) ) ).

% local.bdd_below_mono
thf(fact_622_test__axiom__inf,axiom,
    ! [A: set_e_f_set_a,Z: ( e > f ) > set_a] :
      ( ! [X2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ X2 @ A )
         => ( smaller_interp_e_f_a @ Z @ X2 ) )
     => ( smaller_interp_e_f_a @ Z @ ( inf_e_f_a @ A ) ) ) ).

% test_axiom_inf
thf(fact_623_test__axiom__inf,axiom,
    ! [A: set_c_d_set_a,Z: ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X2 @ A )
         => ( smaller_interp_c_d_a @ Z @ X2 ) )
     => ( smaller_interp_c_d_a @ Z @ ( inf_c_d_a @ A ) ) ) ).

% test_axiom_inf
thf(fact_624_local_Ole__Inf__iff,axiom,
    ! [B: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( smaller_interp_c_d_a @ B @ ( inf_c_d_a @ A ) )
      = ( ! [X3: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X3 @ A )
           => ( smaller_interp_c_d_a @ B @ X3 ) ) ) ) ).

% local.le_Inf_iff
thf(fact_625_local_Ole__Inf__iff,axiom,
    ! [B: ( e > f ) > set_a,A: set_e_f_set_a] :
      ( ( smaller_interp_e_f_a @ B @ ( inf_e_f_a @ A ) )
      = ( ! [X3: ( e > f ) > set_a] :
            ( ( member_e_f_set_a @ X3 @ A )
           => ( smaller_interp_e_f_a @ B @ X3 ) ) ) ) ).

% local.le_Inf_iff
thf(fact_626_local_OInf__mono,axiom,
    ! [B3: set_e_f_set_a,A: set_e_f_set_a] :
      ( ! [B4: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ B4 @ B3 )
         => ? [X4: ( e > f ) > set_a] :
              ( ( member_e_f_set_a @ X4 @ A )
              & ( smaller_interp_e_f_a @ X4 @ B4 ) ) )
     => ( smaller_interp_e_f_a @ ( inf_e_f_a @ A ) @ ( inf_e_f_a @ B3 ) ) ) ).

% local.Inf_mono
thf(fact_627_local_OInf__mono,axiom,
    ! [B3: set_c_d_set_a,A: set_c_d_set_a] :
      ( ! [B4: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ B4 @ B3 )
         => ? [X4: ( c > d ) > set_a] :
              ( ( member_c_d_set_a @ X4 @ A )
              & ( smaller_interp_c_d_a @ X4 @ B4 ) ) )
     => ( smaller_interp_c_d_a @ ( inf_c_d_a @ A ) @ ( inf_c_d_a @ B3 ) ) ) ).

% local.Inf_mono
thf(fact_628_local_OInf__lower2,axiom,
    ! [U: ( e > f ) > set_a,A: set_e_f_set_a,V: ( e > f ) > set_a] :
      ( ( member_e_f_set_a @ U @ A )
     => ( ( smaller_interp_e_f_a @ U @ V )
       => ( smaller_interp_e_f_a @ ( inf_e_f_a @ A ) @ V ) ) ) ).

% local.Inf_lower2
thf(fact_629_local_OInf__lower2,axiom,
    ! [U: ( c > d ) > set_a,A: set_c_d_set_a,V: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ U @ A )
     => ( ( smaller_interp_c_d_a @ U @ V )
       => ( smaller_interp_c_d_a @ ( inf_c_d_a @ A ) @ V ) ) ) ).

% local.Inf_lower2
thf(fact_630_local_OInf__lower,axiom,
    ! [X: ( e > f ) > set_a,A: set_e_f_set_a] :
      ( ( member_e_f_set_a @ X @ A )
     => ( smaller_interp_e_f_a @ ( inf_e_f_a @ A ) @ X ) ) ).

% local.Inf_lower
thf(fact_631_local_OInf__lower,axiom,
    ! [X: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( member_c_d_set_a @ X @ A )
     => ( smaller_interp_c_d_a @ ( inf_c_d_a @ A ) @ X ) ) ).

% local.Inf_lower
thf(fact_632_local_OInf__eqI,axiom,
    ! [A: set_e_f_set_a,X: ( e > f ) > set_a] :
      ( ! [I: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ I @ A )
         => ( smaller_interp_e_f_a @ X @ I ) )
     => ( ! [Y2: ( e > f ) > set_a] :
            ( ! [I2: ( e > f ) > set_a] :
                ( ( member_e_f_set_a @ I2 @ A )
               => ( smaller_interp_e_f_a @ Y2 @ I2 ) )
           => ( smaller_interp_e_f_a @ Y2 @ X ) )
       => ( ( inf_e_f_a @ A )
          = X ) ) ) ).

% local.Inf_eqI
thf(fact_633_local_OInf__eqI,axiom,
    ! [A: set_c_d_set_a,X: ( c > d ) > set_a] :
      ( ! [I: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ I @ A )
         => ( smaller_interp_c_d_a @ X @ I ) )
     => ( ! [Y2: ( c > d ) > set_a] :
            ( ! [I2: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ I2 @ A )
               => ( smaller_interp_c_d_a @ Y2 @ I2 ) )
           => ( smaller_interp_c_d_a @ Y2 @ X ) )
       => ( ( inf_c_d_a @ A )
          = X ) ) ) ).

% local.Inf_eqI
thf(fact_634_test__axiom__sup,axiom,
    ! [A: set_e_f_set_a,Z: ( e > f ) > set_a] :
      ( ! [X2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ X2 @ A )
         => ( smaller_interp_e_f_a @ X2 @ Z ) )
     => ( smaller_interp_e_f_a @ ( sup_e_f_a @ A ) @ Z ) ) ).

% test_axiom_sup
thf(fact_635_test__axiom__sup,axiom,
    ! [A: set_c_d_set_a,Z: ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X2 @ A )
         => ( smaller_interp_c_d_a @ X2 @ Z ) )
     => ( smaller_interp_c_d_a @ ( sup_c_d_a @ A ) @ Z ) ) ).

% test_axiom_sup
thf(fact_636_local_OSup__upper2,axiom,
    ! [U: ( e > f ) > set_a,A: set_e_f_set_a,V: ( e > f ) > set_a] :
      ( ( member_e_f_set_a @ U @ A )
     => ( ( smaller_interp_e_f_a @ V @ U )
       => ( smaller_interp_e_f_a @ V @ ( sup_e_f_a @ A ) ) ) ) ).

% local.Sup_upper2
thf(fact_637_local_OSup__upper2,axiom,
    ! [U: ( c > d ) > set_a,A: set_c_d_set_a,V: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ U @ A )
     => ( ( smaller_interp_c_d_a @ V @ U )
       => ( smaller_interp_c_d_a @ V @ ( sup_c_d_a @ A ) ) ) ) ).

% local.Sup_upper2
thf(fact_638_local_OSup__upper,axiom,
    ! [X: ( e > f ) > set_a,A: set_e_f_set_a] :
      ( ( member_e_f_set_a @ X @ A )
     => ( smaller_interp_e_f_a @ X @ ( sup_e_f_a @ A ) ) ) ).

% local.Sup_upper
thf(fact_639_local_OSup__upper,axiom,
    ! [X: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( member_c_d_set_a @ X @ A )
     => ( smaller_interp_c_d_a @ X @ ( sup_c_d_a @ A ) ) ) ).

% local.Sup_upper
thf(fact_640_local_OSup__mono,axiom,
    ! [A: set_e_f_set_a,B3: set_e_f_set_a] :
      ( ! [A5: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ A5 @ A )
         => ? [X4: ( e > f ) > set_a] :
              ( ( member_e_f_set_a @ X4 @ B3 )
              & ( smaller_interp_e_f_a @ A5 @ X4 ) ) )
     => ( smaller_interp_e_f_a @ ( sup_e_f_a @ A ) @ ( sup_e_f_a @ B3 ) ) ) ).

% local.Sup_mono
thf(fact_641_local_OSup__mono,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ! [A5: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ A5 @ A )
         => ? [X4: ( c > d ) > set_a] :
              ( ( member_c_d_set_a @ X4 @ B3 )
              & ( smaller_interp_c_d_a @ A5 @ X4 ) ) )
     => ( smaller_interp_c_d_a @ ( sup_c_d_a @ A ) @ ( sup_c_d_a @ B3 ) ) ) ).

% local.Sup_mono
thf(fact_642_local_OSup__le__iff,axiom,
    ! [A: set_c_d_set_a,B: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ ( sup_c_d_a @ A ) @ B )
      = ( ! [X3: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X3 @ A )
           => ( smaller_interp_c_d_a @ X3 @ B ) ) ) ) ).

% local.Sup_le_iff
thf(fact_643_local_OSup__le__iff,axiom,
    ! [A: set_e_f_set_a,B: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ ( sup_e_f_a @ A ) @ B )
      = ( ! [X3: ( e > f ) > set_a] :
            ( ( member_e_f_set_a @ X3 @ A )
           => ( smaller_interp_e_f_a @ X3 @ B ) ) ) ) ).

% local.Sup_le_iff
thf(fact_644_local_OSup__eqI,axiom,
    ! [A: set_e_f_set_a,X: ( e > f ) > set_a] :
      ( ! [Y2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ Y2 @ A )
         => ( smaller_interp_e_f_a @ Y2 @ X ) )
     => ( ! [Y2: ( e > f ) > set_a] :
            ( ! [Z3: ( e > f ) > set_a] :
                ( ( member_e_f_set_a @ Z3 @ A )
               => ( smaller_interp_e_f_a @ Z3 @ Y2 ) )
           => ( smaller_interp_e_f_a @ X @ Y2 ) )
       => ( ( sup_e_f_a @ A )
          = X ) ) ) ).

% local.Sup_eqI
thf(fact_645_local_OSup__eqI,axiom,
    ! [A: set_c_d_set_a,X: ( c > d ) > set_a] :
      ( ! [Y2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ Y2 @ A )
         => ( smaller_interp_c_d_a @ Y2 @ X ) )
     => ( ! [Y2: ( c > d ) > set_a] :
            ( ! [Z3: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ Z3 @ A )
               => ( smaller_interp_c_d_a @ Z3 @ Y2 ) )
           => ( smaller_interp_c_d_a @ X @ Y2 ) )
       => ( ( sup_c_d_a @ A )
          = X ) ) ) ).

% local.Sup_eqI
thf(fact_646_local_Otop__unique,axiom,
    ! [A2: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ full_interp_c_d_a @ A2 )
      = ( A2 = full_interp_c_d_a ) ) ).

% local.top_unique
thf(fact_647_local_Otop__unique,axiom,
    ! [A2: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ full_interp_e_f_a @ A2 )
      = ( A2 = full_interp_e_f_a ) ) ).

% local.top_unique
thf(fact_648_local_Otop__le,axiom,
    ! [A2: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ full_interp_c_d_a @ A2 )
     => ( A2 = full_interp_c_d_a ) ) ).

% local.top_le
thf(fact_649_local_Otop__le,axiom,
    ! [A2: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ full_interp_e_f_a @ A2 )
     => ( A2 = full_interp_e_f_a ) ) ).

% local.top_le
thf(fact_650_local_Otop__greatest,axiom,
    ! [A2: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ A2 @ full_interp_c_d_a ) ).

% local.top_greatest
thf(fact_651_local_Otop__greatest,axiom,
    ! [A2: ( e > f ) > set_a] : ( smaller_interp_e_f_a @ A2 @ full_interp_e_f_a ) ).

% local.top_greatest
thf(fact_652_smaller__full,axiom,
    ! [X: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ X @ full_interp_c_d_a ) ).

% smaller_full
thf(fact_653_smaller__full,axiom,
    ! [X: ( e > f ) > set_a] : ( smaller_interp_e_f_a @ X @ full_interp_e_f_a ) ).

% smaller_full
thf(fact_654_local_Odual__order_Oasym,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( less_c_d_a @ B @ A2 )
     => ~ ( less_c_d_a @ A2 @ B ) ) ).

% local.dual_order.asym
thf(fact_655_local_Odual__order_Oasym,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a] :
      ( ( less_e_f_a @ B @ A2 )
     => ~ ( less_e_f_a @ A2 @ B ) ) ).

% local.dual_order.asym
thf(fact_656_local_Odual__order_Ostrict__implies__not__eq,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( less_c_d_a @ B @ A2 )
     => ( A2 != B ) ) ).

% local.dual_order.strict_implies_not_eq
thf(fact_657_local_Odual__order_Ostrict__implies__not__eq,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a] :
      ( ( less_e_f_a @ B @ A2 )
     => ( A2 != B ) ) ).

% local.dual_order.strict_implies_not_eq
thf(fact_658_local_Odual__order_Ostrict__trans,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( less_c_d_a @ B @ A2 )
     => ( ( less_c_d_a @ C @ B )
       => ( less_c_d_a @ C @ A2 ) ) ) ).

% local.dual_order.strict_trans
thf(fact_659_local_Odual__order_Ostrict__trans,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( less_e_f_a @ B @ A2 )
     => ( ( less_e_f_a @ C @ B )
       => ( less_e_f_a @ C @ A2 ) ) ) ).

% local.dual_order.strict_trans
thf(fact_660_local_Oorder_Oasym,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( less_c_d_a @ A2 @ B )
     => ~ ( less_c_d_a @ B @ A2 ) ) ).

% local.order.asym
thf(fact_661_local_Oorder_Oasym,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( less_e_f_a @ A2 @ B )
     => ~ ( less_e_f_a @ B @ A2 ) ) ).

% local.order.asym
thf(fact_662_local_Oorder_Oirrefl,axiom,
    ! [A2: ( c > d ) > set_a] :
      ~ ( less_c_d_a @ A2 @ A2 ) ).

% local.order.irrefl
thf(fact_663_local_Oorder_Oirrefl,axiom,
    ! [A2: ( e > f ) > set_a] :
      ~ ( less_e_f_a @ A2 @ A2 ) ).

% local.order.irrefl
thf(fact_664_local_Oorder_Ostrict__implies__not__eq,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( less_c_d_a @ A2 @ B )
     => ( A2 != B ) ) ).

% local.order.strict_implies_not_eq
thf(fact_665_local_Oorder_Ostrict__implies__not__eq,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( less_e_f_a @ A2 @ B )
     => ( A2 != B ) ) ).

% local.order.strict_implies_not_eq
thf(fact_666_local_Oorder_Ostrict__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( less_c_d_a @ A2 @ B )
     => ( ( less_c_d_a @ B @ C )
       => ( less_c_d_a @ A2 @ C ) ) ) ).

% local.order.strict_trans
thf(fact_667_local_Oorder_Ostrict__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( less_e_f_a @ A2 @ B )
     => ( ( less_e_f_a @ B @ C )
       => ( less_e_f_a @ A2 @ C ) ) ) ).

% local.order.strict_trans
thf(fact_668_local_Oless__asym,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( less_c_d_a @ X @ Y )
     => ~ ( less_c_d_a @ Y @ X ) ) ).

% local.less_asym
thf(fact_669_local_Oless__asym,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( less_e_f_a @ X @ Y )
     => ~ ( less_e_f_a @ Y @ X ) ) ).

% local.less_asym
thf(fact_670_local_Oless__asym_H,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( less_c_d_a @ A2 @ B )
     => ~ ( less_c_d_a @ B @ A2 ) ) ).

% local.less_asym'
thf(fact_671_local_Oless__asym_H,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( less_e_f_a @ A2 @ B )
     => ~ ( less_e_f_a @ B @ A2 ) ) ).

% local.less_asym'
thf(fact_672_local_Oless__imp__neq,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( less_c_d_a @ X @ Y )
     => ( X != Y ) ) ).

% local.less_imp_neq
thf(fact_673_local_Oless__imp__neq,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( less_e_f_a @ X @ Y )
     => ( X != Y ) ) ).

% local.less_imp_neq
thf(fact_674_local_Oless__imp__not__eq,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( less_c_d_a @ X @ Y )
     => ( X != Y ) ) ).

% local.less_imp_not_eq
thf(fact_675_local_Oless__imp__not__eq,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( less_e_f_a @ X @ Y )
     => ( X != Y ) ) ).

% local.less_imp_not_eq
thf(fact_676_local_Oless__imp__not__eq2,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( less_c_d_a @ X @ Y )
     => ( Y != X ) ) ).

% local.less_imp_not_eq2
thf(fact_677_local_Oless__imp__not__eq2,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( less_e_f_a @ X @ Y )
     => ( Y != X ) ) ).

% local.less_imp_not_eq2
thf(fact_678_local_Oless__imp__not__less,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( less_c_d_a @ X @ Y )
     => ~ ( less_c_d_a @ Y @ X ) ) ).

% local.less_imp_not_less
thf(fact_679_local_Oless__imp__not__less,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( less_e_f_a @ X @ Y )
     => ~ ( less_e_f_a @ Y @ X ) ) ).

% local.less_imp_not_less
thf(fact_680_local_Oless__imp__triv,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,P: $o] :
      ( ( less_c_d_a @ X @ Y )
     => ( ( less_c_d_a @ Y @ X )
       => P ) ) ).

% local.less_imp_triv
thf(fact_681_local_Oless__imp__triv,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a,P: $o] :
      ( ( less_e_f_a @ X @ Y )
     => ( ( less_e_f_a @ Y @ X )
       => P ) ) ).

% local.less_imp_triv
thf(fact_682_local_Oless__irrefl,axiom,
    ! [X: ( c > d ) > set_a] :
      ~ ( less_c_d_a @ X @ X ) ).

% local.less_irrefl
thf(fact_683_local_Oless__irrefl,axiom,
    ! [X: ( e > f ) > set_a] :
      ~ ( less_e_f_a @ X @ X ) ).

% local.less_irrefl
thf(fact_684_local_Oless__not__sym,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( less_c_d_a @ X @ Y )
     => ~ ( less_c_d_a @ Y @ X ) ) ).

% local.less_not_sym
thf(fact_685_local_Oless__not__sym,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( less_e_f_a @ X @ Y )
     => ~ ( less_e_f_a @ Y @ X ) ) ).

% local.less_not_sym
thf(fact_686_local_Oless__trans,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( less_c_d_a @ X @ Y )
     => ( ( less_c_d_a @ Y @ Z )
       => ( less_c_d_a @ X @ Z ) ) ) ).

% local.less_trans
thf(fact_687_local_Oless__trans,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a,Z: ( e > f ) > set_a] :
      ( ( less_e_f_a @ X @ Y )
     => ( ( less_e_f_a @ Y @ Z )
       => ( less_e_f_a @ X @ Z ) ) ) ).

% local.less_trans
thf(fact_688_local_Oord__eq__less__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( A2 = B )
     => ( ( less_c_d_a @ B @ C )
       => ( less_c_d_a @ A2 @ C ) ) ) ).

% local.ord_eq_less_trans
thf(fact_689_local_Oord__eq__less__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( A2 = B )
     => ( ( less_e_f_a @ B @ C )
       => ( less_e_f_a @ A2 @ C ) ) ) ).

% local.ord_eq_less_trans
thf(fact_690_local_Oord__less__eq__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( less_c_d_a @ A2 @ B )
     => ( ( B = C )
       => ( less_c_d_a @ A2 @ C ) ) ) ).

% local.ord_less_eq_trans
thf(fact_691_local_Oord__less__eq__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( less_e_f_a @ A2 @ B )
     => ( ( B = C )
       => ( less_e_f_a @ A2 @ C ) ) ) ).

% local.ord_less_eq_trans
thf(fact_692_local_Oless__top,axiom,
    ! [A2: ( e > f ) > set_a] :
      ( ( A2 != full_interp_e_f_a )
      = ( less_e_f_a @ A2 @ full_interp_e_f_a ) ) ).

% local.less_top
thf(fact_693_local_Oless__top,axiom,
    ! [A2: ( c > d ) > set_a] :
      ( ( A2 != full_interp_c_d_a )
      = ( less_c_d_a @ A2 @ full_interp_c_d_a ) ) ).

% local.less_top
thf(fact_694_local_Onot__top__less,axiom,
    ! [A2: ( e > f ) > set_a] :
      ~ ( less_e_f_a @ full_interp_e_f_a @ A2 ) ).

% local.not_top_less
thf(fact_695_local_Onot__top__less,axiom,
    ! [A2: ( c > d ) > set_a] :
      ~ ( less_c_d_a @ full_interp_c_d_a @ A2 ) ).

% local.not_top_less
thf(fact_696_set__closure__prop__empty__all_I2_J,axiom,
    ! [S4: a > a > set_a] : ( set_cl2807270042661212426_a_c_d @ S4 @ full_interp_c_d_a ) ).

% set_closure_prop_empty_all(2)
thf(fact_697_set__closure__prop__empty__all_I2_J,axiom,
    ! [S4: a > a > set_a] : ( set_cl6455730915570636170_a_e_f @ S4 @ full_interp_e_f_a ) ).

% set_closure_prop_empty_all(2)
thf(fact_698_smaller__empty,axiom,
    ! [X: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ empty_interp_c_d_a @ X ) ).

% smaller_empty
thf(fact_699_smaller__empty,axiom,
    ! [X: ( e > f ) > set_a] : ( smaller_interp_e_f_a @ empty_interp_e_f_a @ X ) ).

% smaller_empty
thf(fact_700_local_Ole__bot,axiom,
    ! [A2: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ A2 @ empty_interp_c_d_a )
     => ( A2 = empty_interp_c_d_a ) ) ).

% local.le_bot
thf(fact_701_local_Ole__bot,axiom,
    ! [A2: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ A2 @ empty_interp_e_f_a )
     => ( A2 = empty_interp_e_f_a ) ) ).

% local.le_bot
thf(fact_702_local_Obot__unique,axiom,
    ! [A2: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ A2 @ empty_interp_c_d_a )
      = ( A2 = empty_interp_c_d_a ) ) ).

% local.bot_unique
thf(fact_703_local_Obot__unique,axiom,
    ! [A2: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ A2 @ empty_interp_e_f_a )
      = ( A2 = empty_interp_e_f_a ) ) ).

% local.bot_unique
thf(fact_704_local_Obot__least,axiom,
    ! [A2: ( c > d ) > set_a] : ( smaller_interp_c_d_a @ empty_interp_c_d_a @ A2 ) ).

% local.bot_least
thf(fact_705_local_Obot__least,axiom,
    ! [A2: ( e > f ) > set_a] : ( smaller_interp_e_f_a @ empty_interp_e_f_a @ A2 ) ).

% local.bot_least
thf(fact_706_local_Onot__less__bot,axiom,
    ! [A2: ( c > d ) > set_a] :
      ~ ( less_c_d_a @ A2 @ empty_interp_c_d_a ) ).

% local.not_less_bot
thf(fact_707_local_Onot__less__bot,axiom,
    ! [A2: ( e > f ) > set_a] :
      ~ ( less_e_f_a @ A2 @ empty_interp_e_f_a ) ).

% local.not_less_bot
thf(fact_708_local_Obot__less,axiom,
    ! [A2: ( c > d ) > set_a] :
      ( ( A2 != empty_interp_c_d_a )
      = ( less_c_d_a @ empty_interp_c_d_a @ A2 ) ) ).

% local.bot_less
thf(fact_709_local_Obot__less,axiom,
    ! [A2: ( e > f ) > set_a] :
      ( ( A2 != empty_interp_e_f_a )
      = ( less_e_f_a @ empty_interp_e_f_a @ A2 ) ) ).

% local.bot_less
thf(fact_710_local_Obdd__below__def,axiom,
    ! [A: set_e_f_set_a] :
      ( ( condit5311609186605872711_set_a @ smaller_interp_e_f_a @ A )
      = ( ? [M2: ( e > f ) > set_a] :
          ! [X3: ( e > f ) > set_a] :
            ( ( member_e_f_set_a @ X3 @ A )
           => ( smaller_interp_e_f_a @ M2 @ X3 ) ) ) ) ).

% local.bdd_below_def
thf(fact_711_local_Obdd__below__def,axiom,
    ! [A: set_c_d_set_a] :
      ( ( condit9007271454129256903_set_a @ smaller_interp_c_d_a @ A )
      = ( ? [M2: ( c > d ) > set_a] :
          ! [X3: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X3 @ A )
           => ( smaller_interp_c_d_a @ M2 @ X3 ) ) ) ) ).

% local.bdd_below_def
thf(fact_712_local_Obdd__below_OE,axiom,
    ! [A: set_e_f_set_a] :
      ( ( condit5311609186605872711_set_a @ smaller_interp_e_f_a @ A )
     => ~ ! [M: ( e > f ) > set_a] :
            ~ ! [X4: ( e > f ) > set_a] :
                ( ( member_e_f_set_a @ X4 @ A )
               => ( smaller_interp_e_f_a @ M @ X4 ) ) ) ).

% local.bdd_below.E
thf(fact_713_local_Obdd__below_OE,axiom,
    ! [A: set_c_d_set_a] :
      ( ( condit9007271454129256903_set_a @ smaller_interp_c_d_a @ A )
     => ~ ! [M: ( c > d ) > set_a] :
            ~ ! [X4: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ X4 @ A )
               => ( smaller_interp_c_d_a @ M @ X4 ) ) ) ).

% local.bdd_below.E
thf(fact_714_local_OInf__superset__mono,axiom,
    ! [B3: set_c_d_set_a,A: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ B3 @ A )
     => ( smaller_interp_c_d_a @ ( inf_c_d_a @ A ) @ ( inf_c_d_a @ B3 ) ) ) ).

% local.Inf_superset_mono
thf(fact_715_local_OInf__superset__mono,axiom,
    ! [B3: set_e_f_set_a,A: set_e_f_set_a] :
      ( ( ord_le5994374269167502767_set_a @ B3 @ A )
     => ( smaller_interp_e_f_a @ ( inf_e_f_a @ A ) @ ( inf_e_f_a @ B3 ) ) ) ).

% local.Inf_superset_mono
thf(fact_716_local_OSup__subset__mono,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A @ B3 )
     => ( smaller_interp_c_d_a @ ( sup_c_d_a @ A ) @ ( sup_c_d_a @ B3 ) ) ) ).

% local.Sup_subset_mono
thf(fact_717_local_OSup__subset__mono,axiom,
    ! [A: set_e_f_set_a,B3: set_e_f_set_a] :
      ( ( ord_le5994374269167502767_set_a @ A @ B3 )
     => ( smaller_interp_e_f_a @ ( sup_e_f_a @ A ) @ ( sup_e_f_a @ B3 ) ) ) ).

% local.Sup_subset_mono
thf(fact_718_set__closure__prop__empty__all_I1_J,axiom,
    ! [S4: a > a > set_a] : ( set_cl2807270042661212426_a_c_d @ S4 @ empty_interp_c_d_a ) ).

% set_closure_prop_empty_all(1)
thf(fact_719_set__closure__prop__empty__all_I1_J,axiom,
    ! [S4: a > a > set_a] : ( set_cl6455730915570636170_a_e_f @ S4 @ empty_interp_e_f_a ) ).

% set_closure_prop_empty_all(1)
thf(fact_720_local_Ostrict__mono__onD,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,R2: ( e > f ) > set_a,S3: ( e > f ) > set_a] :
      ( ( monoto247478589472066471_set_a @ A @ less_e_f_a @ ord_less_c_d_set_a @ F )
     => ( ( member_e_f_set_a @ R2 @ A )
       => ( ( member_e_f_set_a @ S3 @ A )
         => ( ( less_e_f_a @ R2 @ S3 )
           => ( ord_less_c_d_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.strict_mono_onD
thf(fact_721_local_Ostrict__mono__onD,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_c_d_set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto6642458133393520519_set_a @ A @ less_c_d_a @ ord_le3685282097655362107_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( less_c_d_a @ R2 @ S3 )
           => ( ord_le3685282097655362107_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.strict_mono_onD
thf(fact_722_local_Ostrict__mono__onD,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > set_c_d_set_a,R2: ( e > f ) > set_a,S3: ( e > f ) > set_a] :
      ( ( monoto7716863510275742471_set_a @ A @ less_e_f_a @ ord_le3685282097655362107_set_a @ F )
     => ( ( member_e_f_set_a @ R2 @ A )
       => ( ( member_e_f_set_a @ S3 @ A )
         => ( ( less_e_f_a @ R2 @ S3 )
           => ( ord_le3685282097655362107_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.strict_mono_onD
thf(fact_723_local_Ostrict__mono__onD,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ less_c_d_a @ ord_less_c_d_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( less_c_d_a @ R2 @ S3 )
           => ( ord_less_c_d_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% local.strict_mono_onD
thf(fact_724_local_Ostrict__mono__onI,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a] :
      ( ! [R: ( e > f ) > set_a,S2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ R @ A )
         => ( ( member_e_f_set_a @ S2 @ A )
           => ( ( less_e_f_a @ R @ S2 )
             => ( ord_less_c_d_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto247478589472066471_set_a @ A @ less_e_f_a @ ord_less_c_d_set_a @ F ) ) ).

% local.strict_mono_onI
thf(fact_725_local_Ostrict__mono__onI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_c_d_set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( less_c_d_a @ R @ S2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto6642458133393520519_set_a @ A @ less_c_d_a @ ord_le3685282097655362107_set_a @ F ) ) ).

% local.strict_mono_onI
thf(fact_726_local_Ostrict__mono__onI,axiom,
    ! [A: set_e_f_set_a,F: ( ( e > f ) > set_a ) > set_c_d_set_a] :
      ( ! [R: ( e > f ) > set_a,S2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ R @ A )
         => ( ( member_e_f_set_a @ S2 @ A )
           => ( ( less_e_f_a @ R @ S2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto7716863510275742471_set_a @ A @ less_e_f_a @ ord_le3685282097655362107_set_a @ F ) ) ).

% local.strict_mono_onI
thf(fact_727_local_Ostrict__mono__onI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( less_c_d_a @ R @ S2 )
             => ( ord_less_c_d_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto2937423850181994535_set_a @ A @ less_c_d_a @ ord_less_c_d_set_a @ F ) ) ).

% local.strict_mono_onI
thf(fact_728_psubsetI,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A @ B3 )
     => ( ( A != B3 )
       => ( ord_le3685282097655362107_set_a @ A @ B3 ) ) ) ).

% psubsetI
thf(fact_729_psubsetI,axiom,
    ! [A: set_a,B3: set_a] :
      ( ( ord_less_eq_set_a @ A @ B3 )
     => ( ( A != B3 )
       => ( ord_less_set_a @ A @ B3 ) ) ) ).

% psubsetI
thf(fact_730_local_OSup__bot__conv_I1_J,axiom,
    ! [A: set_c_d_set_a] :
      ( ( ( sup_c_d_a @ A )
        = empty_interp_c_d_a )
      = ( ! [X3: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X3 @ A )
           => ( X3 = empty_interp_c_d_a ) ) ) ) ).

% local.Sup_bot_conv(1)
thf(fact_731_local_OSup__bot__conv_I1_J,axiom,
    ! [A: set_e_f_set_a] :
      ( ( ( sup_e_f_a @ A )
        = empty_interp_e_f_a )
      = ( ! [X3: ( e > f ) > set_a] :
            ( ( member_e_f_set_a @ X3 @ A )
           => ( X3 = empty_interp_e_f_a ) ) ) ) ).

% local.Sup_bot_conv(1)
thf(fact_732_local_OSup__bot__conv_I2_J,axiom,
    ! [A: set_c_d_set_a] :
      ( ( empty_interp_c_d_a
        = ( sup_c_d_a @ A ) )
      = ( ! [X3: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X3 @ A )
           => ( X3 = empty_interp_c_d_a ) ) ) ) ).

% local.Sup_bot_conv(2)
thf(fact_733_local_OSup__bot__conv_I2_J,axiom,
    ! [A: set_e_f_set_a] :
      ( ( empty_interp_e_f_a
        = ( sup_e_f_a @ A ) )
      = ( ! [X3: ( e > f ) > set_a] :
            ( ( member_e_f_set_a @ X3 @ A )
           => ( X3 = empty_interp_e_f_a ) ) ) ) ).

% local.Sup_bot_conv(2)
thf(fact_734_local_OSup__UNIV,axiom,
    ( ( sup_e_f_a @ top_to4280187784772989791_set_a )
    = full_interp_e_f_a ) ).

% local.Sup_UNIV
thf(fact_735_local_OSup__UNIV,axiom,
    ( ( sup_c_d_a @ top_to4267977599310771935_set_a )
    = full_interp_c_d_a ) ).

% local.Sup_UNIV
thf(fact_736_local_Olfp__lowerbound,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,A: ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ ( F @ A ) @ A )
     => ( smaller_interp_c_d_a @ ( comple5961674822413889664_set_a @ inf_c_d_a @ smaller_interp_c_d_a @ F ) @ A ) ) ).

% local.lfp_lowerbound
thf(fact_737_local_Olfp__lowerbound,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( e > f ) > set_a,A: ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ ( F @ A ) @ A )
     => ( smaller_interp_e_f_a @ ( comple2266012554890505472_set_a @ inf_e_f_a @ smaller_interp_e_f_a @ F ) @ A ) ) ).

% local.lfp_lowerbound
thf(fact_738_local_Olfp__greatest,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,A: ( c > d ) > set_a] :
      ( ! [U2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ ( F @ U2 ) @ U2 )
         => ( smaller_interp_c_d_a @ A @ U2 ) )
     => ( smaller_interp_c_d_a @ A @ ( comple5961674822413889664_set_a @ inf_c_d_a @ smaller_interp_c_d_a @ F ) ) ) ).

% local.lfp_greatest
thf(fact_739_local_Olfp__greatest,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( e > f ) > set_a,A: ( e > f ) > set_a] :
      ( ! [U2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ ( F @ U2 ) @ U2 )
         => ( smaller_interp_e_f_a @ A @ U2 ) )
     => ( smaller_interp_e_f_a @ A @ ( comple2266012554890505472_set_a @ inf_e_f_a @ smaller_interp_e_f_a @ F ) ) ) ).

% local.lfp_greatest
thf(fact_740_local_Ogfp__upperbound,axiom,
    ! [X5: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ( smaller_interp_c_d_a @ X5 @ ( F @ X5 ) )
     => ( smaller_interp_c_d_a @ X5 @ ( comple4132920576971123013_set_a @ sup_c_d_a @ smaller_interp_c_d_a @ F ) ) ) ).

% local.gfp_upperbound
thf(fact_741_local_Ogfp__upperbound,axiom,
    ! [X5: ( e > f ) > set_a,F: ( ( e > f ) > set_a ) > ( e > f ) > set_a] :
      ( ( smaller_interp_e_f_a @ X5 @ ( F @ X5 ) )
     => ( smaller_interp_e_f_a @ X5 @ ( comple437258309447738821_set_a @ sup_e_f_a @ smaller_interp_e_f_a @ F ) ) ) ).

% local.gfp_upperbound
thf(fact_742_local_Ogfp__least,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X5: ( c > d ) > set_a] :
      ( ! [U2: ( c > d ) > set_a] :
          ( ( smaller_interp_c_d_a @ U2 @ ( F @ U2 ) )
         => ( smaller_interp_c_d_a @ U2 @ X5 ) )
     => ( smaller_interp_c_d_a @ ( comple4132920576971123013_set_a @ sup_c_d_a @ smaller_interp_c_d_a @ F ) @ X5 ) ) ).

% local.gfp_least
thf(fact_743_local_Ogfp__least,axiom,
    ! [F: ( ( e > f ) > set_a ) > ( e > f ) > set_a,X5: ( e > f ) > set_a] :
      ( ! [U2: ( e > f ) > set_a] :
          ( ( smaller_interp_e_f_a @ U2 @ ( F @ U2 ) )
         => ( smaller_interp_e_f_a @ U2 @ X5 ) )
     => ( smaller_interp_e_f_a @ ( comple437258309447738821_set_a @ sup_e_f_a @ smaller_interp_e_f_a @ F ) @ X5 ) ) ).

% local.gfp_least
thf(fact_744_local_Obdd__below__bot,axiom,
    ! [A: set_e_f_set_a] : ( condit5311609186605872711_set_a @ smaller_interp_e_f_a @ A ) ).

% local.bdd_below_bot
thf(fact_745_local_Obdd__below__bot,axiom,
    ! [A: set_c_d_set_a] : ( condit9007271454129256903_set_a @ smaller_interp_c_d_a @ A ) ).

% local.bdd_below_bot
thf(fact_746_local_Obdd__belowI,axiom,
    ! [A: set_e_f_set_a,M4: ( e > f ) > set_a] :
      ( ! [X2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ X2 @ A )
         => ( smaller_interp_e_f_a @ M4 @ X2 ) )
     => ( condit5311609186605872711_set_a @ smaller_interp_e_f_a @ A ) ) ).

% local.bdd_belowI
thf(fact_747_local_Obdd__belowI,axiom,
    ! [A: set_c_d_set_a,M4: ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X2 @ A )
         => ( smaller_interp_c_d_a @ M4 @ X2 ) )
     => ( condit9007271454129256903_set_a @ smaller_interp_c_d_a @ A ) ) ).

% local.bdd_belowI
thf(fact_748_local_Obdd__below_OI,axiom,
    ! [A: set_e_f_set_a,M3: ( e > f ) > set_a] :
      ( ! [X2: ( e > f ) > set_a] :
          ( ( member_e_f_set_a @ X2 @ A )
         => ( smaller_interp_e_f_a @ M3 @ X2 ) )
     => ( condit5311609186605872711_set_a @ smaller_interp_e_f_a @ A ) ) ).

% local.bdd_below.I
thf(fact_749_local_Obdd__below_OI,axiom,
    ! [A: set_c_d_set_a,M3: ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X2 @ A )
         => ( smaller_interp_c_d_a @ M3 @ X2 ) )
     => ( condit9007271454129256903_set_a @ smaller_interp_c_d_a @ A ) ) ).

% local.bdd_below.I
thf(fact_750_local_OInf__UNIV,axiom,
    ( ( inf_c_d_a @ top_to4267977599310771935_set_a )
    = empty_interp_c_d_a ) ).

% local.Inf_UNIV
thf(fact_751_local_OInf__UNIV,axiom,
    ( ( inf_e_f_a @ top_to4280187784772989791_set_a )
    = empty_interp_e_f_a ) ).

% local.Inf_UNIV
thf(fact_752_local_Omin__top2,axiom,
    ! [X: ( c > d ) > set_a] :
      ( ( min_c_d_set_a @ smaller_interp_c_d_a @ X @ full_interp_c_d_a )
      = X ) ).

% local.min_top2
thf(fact_753_local_Omin__top2,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( min_e_f_set_a @ smaller_interp_e_f_a @ X @ full_interp_e_f_a )
      = X ) ).

% local.min_top2
thf(fact_754_local_Omin__top,axiom,
    ! [X: ( c > d ) > set_a] :
      ( ( min_c_d_set_a @ smaller_interp_c_d_a @ full_interp_c_d_a @ X )
      = X ) ).

% local.min_top
thf(fact_755_local_Omin__top,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( min_e_f_set_a @ smaller_interp_e_f_a @ full_interp_e_f_a @ X )
      = X ) ).

% local.min_top
thf(fact_756_local_Omax__top2,axiom,
    ! [X: ( c > d ) > set_a] :
      ( ( max_c_d_set_a @ smaller_interp_c_d_a @ X @ full_interp_c_d_a )
      = full_interp_c_d_a ) ).

% local.max_top2
thf(fact_757_local_Omax__top2,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( max_e_f_set_a @ smaller_interp_e_f_a @ X @ full_interp_e_f_a )
      = full_interp_e_f_a ) ).

% local.max_top2
thf(fact_758_local_Omax__top,axiom,
    ! [X: ( c > d ) > set_a] :
      ( ( max_c_d_set_a @ smaller_interp_c_d_a @ full_interp_c_d_a @ X )
      = full_interp_c_d_a ) ).

% local.max_top
thf(fact_759_local_Omax__top,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( max_e_f_set_a @ smaller_interp_e_f_a @ full_interp_e_f_a @ X )
      = full_interp_e_f_a ) ).

% local.max_top
thf(fact_760_local_Omin__bot2,axiom,
    ! [X: ( c > d ) > set_a] :
      ( ( min_c_d_set_a @ smaller_interp_c_d_a @ X @ empty_interp_c_d_a )
      = empty_interp_c_d_a ) ).

% local.min_bot2
thf(fact_761_local_Omin__bot2,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( min_e_f_set_a @ smaller_interp_e_f_a @ X @ empty_interp_e_f_a )
      = empty_interp_e_f_a ) ).

% local.min_bot2
thf(fact_762_local_Omin__bot,axiom,
    ! [X: ( c > d ) > set_a] :
      ( ( min_c_d_set_a @ smaller_interp_c_d_a @ empty_interp_c_d_a @ X )
      = empty_interp_c_d_a ) ).

% local.min_bot
thf(fact_763_local_Omin__bot,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( min_e_f_set_a @ smaller_interp_e_f_a @ empty_interp_e_f_a @ X )
      = empty_interp_e_f_a ) ).

% local.min_bot
thf(fact_764_local_Omax__bot2,axiom,
    ! [X: ( c > d ) > set_a] :
      ( ( max_c_d_set_a @ smaller_interp_c_d_a @ X @ empty_interp_c_d_a )
      = X ) ).

% local.max_bot2
thf(fact_765_local_Omax__bot2,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( max_e_f_set_a @ smaller_interp_e_f_a @ X @ empty_interp_e_f_a )
      = X ) ).

% local.max_bot2
thf(fact_766_local_Omax__bot,axiom,
    ! [X: ( c > d ) > set_a] :
      ( ( max_c_d_set_a @ smaller_interp_c_d_a @ empty_interp_c_d_a @ X )
      = X ) ).

% local.max_bot
thf(fact_767_local_Omax__bot,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( max_e_f_set_a @ smaller_interp_e_f_a @ empty_interp_e_f_a @ X )
      = X ) ).

% local.max_bot
thf(fact_768_order__class_Oless__imp__neq,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ X @ Y )
     => ( X != Y ) ) ).

% order_class.less_imp_neq
thf(fact_769_order__class_Oless__imp__neq,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ X @ Y )
     => ( X != Y ) ) ).

% order_class.less_imp_neq
thf(fact_770_preorder__class_Oorder_Oasym,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ~ ( ord_less_c_d_set_a @ B @ A2 ) ) ).

% preorder_class.order.asym
thf(fact_771_preorder__class_Oorder_Oasym,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ~ ( ord_le3685282097655362107_set_a @ B @ A2 ) ) ).

% preorder_class.order.asym
thf(fact_772_ord__class_Oord__eq__less__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( A2 = B )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ord_less_c_d_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_eq_less_trans
thf(fact_773_ord__class_Oord__eq__less__trans,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( A2 = B )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ord_le3685282097655362107_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_eq_less_trans
thf(fact_774_ord__class_Oord__less__eq__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( B = C )
       => ( ord_less_c_d_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_less_eq_trans
thf(fact_775_ord__class_Oord__less__eq__trans,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( B = C )
       => ( ord_le3685282097655362107_set_a @ A2 @ C ) ) ) ).

% ord_class.ord_less_eq_trans
thf(fact_776_preorder__class_Odual__order_Oasym,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ B @ A2 )
     => ~ ( ord_less_c_d_set_a @ A2 @ B ) ) ).

% preorder_class.dual_order.asym
thf(fact_777_preorder__class_Odual__order_Oasym,axiom,
    ! [B: set_c_d_set_a,A2: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ B @ A2 )
     => ~ ( ord_le3685282097655362107_set_a @ A2 @ B ) ) ).

% preorder_class.dual_order.asym
thf(fact_778_preorder__class_Odual__order_Oirrefl,axiom,
    ! [A2: ( c > d ) > set_a] :
      ~ ( ord_less_c_d_set_a @ A2 @ A2 ) ).

% preorder_class.dual_order.irrefl
thf(fact_779_preorder__class_Odual__order_Oirrefl,axiom,
    ! [A2: set_c_d_set_a] :
      ~ ( ord_le3685282097655362107_set_a @ A2 @ A2 ) ).

% preorder_class.dual_order.irrefl
thf(fact_780_preorder__class_Oorder_Ostrict__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ord_less_c_d_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans
thf(fact_781_preorder__class_Oorder_Ostrict__trans,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ord_le3685282097655362107_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans
thf(fact_782_preorder__class_Odual__order_Ostrict__trans,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ B @ A2 )
     => ( ( ord_less_c_d_set_a @ C @ B )
       => ( ord_less_c_d_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans
thf(fact_783_preorder__class_Odual__order_Ostrict__trans,axiom,
    ! [B: set_c_d_set_a,A2: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ B @ A2 )
     => ( ( ord_le3685282097655362107_set_a @ C @ B )
       => ( ord_le3685282097655362107_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans
thf(fact_784_order__class_Oorder_Ostrict__implies__not__eq,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( A2 != B ) ) ).

% order_class.order.strict_implies_not_eq
thf(fact_785_order__class_Oorder_Ostrict__implies__not__eq,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( A2 != B ) ) ).

% order_class.order.strict_implies_not_eq
thf(fact_786_order__class_Odual__order_Ostrict__implies__not__eq,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ B @ A2 )
     => ( A2 != B ) ) ).

% order_class.dual_order.strict_implies_not_eq
thf(fact_787_order__class_Odual__order_Ostrict__implies__not__eq,axiom,
    ! [B: set_c_d_set_a,A2: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ B @ A2 )
     => ( A2 != B ) ) ).

% order_class.dual_order.strict_implies_not_eq
thf(fact_788_order__less__asym,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ X @ Y )
     => ~ ( ord_less_c_d_set_a @ Y @ X ) ) ).

% order_less_asym
thf(fact_789_order__less__asym,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ X @ Y )
     => ~ ( ord_le3685282097655362107_set_a @ Y @ X ) ) ).

% order_less_asym
thf(fact_790_order__less__asym_H,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ~ ( ord_less_c_d_set_a @ B @ A2 ) ) ).

% order_less_asym'
thf(fact_791_order__less__asym_H,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ~ ( ord_le3685282097655362107_set_a @ B @ A2 ) ) ).

% order_less_asym'
thf(fact_792_order__less__trans,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ X @ Y )
     => ( ( ord_less_c_d_set_a @ Y @ Z )
       => ( ord_less_c_d_set_a @ X @ Z ) ) ) ).

% order_less_trans
thf(fact_793_order__less__trans,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a,Z: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ X @ Y )
     => ( ( ord_le3685282097655362107_set_a @ Y @ Z )
       => ( ord_le3685282097655362107_set_a @ X @ Z ) ) ) ).

% order_less_trans
thf(fact_794_ord__eq__less__subst,axiom,
    ! [A2: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_795_ord__eq__less__subst,axiom,
    ! [A2: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_c_d_set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_796_ord__eq__less__subst,axiom,
    ! [A2: ( c > d ) > set_a,F: set_c_d_set_a > ( c > d ) > set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_797_ord__eq__less__subst,axiom,
    ! [A2: set_c_d_set_a,F: set_c_d_set_a > set_c_d_set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_798_ord__less__eq__subst,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_799_ord__less__eq__subst,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_800_ord__less__eq__subst,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_801_ord__less__eq__subst,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_802_order__less__irrefl,axiom,
    ! [X: ( c > d ) > set_a] :
      ~ ( ord_less_c_d_set_a @ X @ X ) ).

% order_less_irrefl
thf(fact_803_order__less__irrefl,axiom,
    ! [X: set_c_d_set_a] :
      ~ ( ord_le3685282097655362107_set_a @ X @ X ) ).

% order_less_irrefl
thf(fact_804_order__less__subst1,axiom,
    ! [A2: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_805_order__less__subst1,axiom,
    ! [A2: ( c > d ) > set_a,F: set_c_d_set_a > ( c > d ) > set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_806_order__less__subst1,axiom,
    ! [A2: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_c_d_set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_807_order__less__subst1,axiom,
    ! [A2: set_c_d_set_a,F: set_c_d_set_a > set_c_d_set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_808_order__less__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( ord_less_c_d_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_809_order__less__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( ord_le3685282097655362107_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_810_order__less__subst2,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( ord_less_c_d_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_811_order__less__subst2,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( ord_le3685282097655362107_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_812_order__less__not__sym,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ X @ Y )
     => ~ ( ord_less_c_d_set_a @ Y @ X ) ) ).

% order_less_not_sym
thf(fact_813_order__less__not__sym,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ X @ Y )
     => ~ ( ord_le3685282097655362107_set_a @ Y @ X ) ) ).

% order_less_not_sym
thf(fact_814_order__less__imp__triv,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,P: $o] :
      ( ( ord_less_c_d_set_a @ X @ Y )
     => ( ( ord_less_c_d_set_a @ Y @ X )
       => P ) ) ).

% order_less_imp_triv
thf(fact_815_order__less__imp__triv,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a,P: $o] :
      ( ( ord_le3685282097655362107_set_a @ X @ Y )
     => ( ( ord_le3685282097655362107_set_a @ Y @ X )
       => P ) ) ).

% order_less_imp_triv
thf(fact_816_order__less__imp__not__eq,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ X @ Y )
     => ( X != Y ) ) ).

% order_less_imp_not_eq
thf(fact_817_order__less__imp__not__eq,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ X @ Y )
     => ( X != Y ) ) ).

% order_less_imp_not_eq
thf(fact_818_order__less__imp__not__eq2,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ X @ Y )
     => ( Y != X ) ) ).

% order_less_imp_not_eq2
thf(fact_819_order__less__imp__not__eq2,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ X @ Y )
     => ( Y != X ) ) ).

% order_less_imp_not_eq2
thf(fact_820_order__less__imp__not__less,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ X @ Y )
     => ~ ( ord_less_c_d_set_a @ Y @ X ) ) ).

% order_less_imp_not_less
thf(fact_821_order__less__imp__not__less,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ X @ Y )
     => ~ ( ord_le3685282097655362107_set_a @ Y @ X ) ) ).

% order_less_imp_not_less
thf(fact_822_order__class_OleD,axiom,
    ! [Y: set_c_d_set_a,X: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ Y @ X )
     => ~ ( ord_le3685282097655362107_set_a @ X @ Y ) ) ).

% order_class.leD
thf(fact_823_order__class_OleD,axiom,
    ! [Y: set_a,X: set_a] :
      ( ( ord_less_eq_set_a @ Y @ X )
     => ~ ( ord_less_set_a @ X @ Y ) ) ).

% order_class.leD
thf(fact_824_order__class_OleD,axiom,
    ! [Y: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ Y @ X )
     => ~ ( ord_le5853012546958565978et_a_o @ X @ Y ) ) ).

% order_class.leD
thf(fact_825_order__class_OleD,axiom,
    ! [Y: ( e > f ) > set_a,X: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ Y @ X )
     => ~ ( ord_less_e_f_set_a @ X @ Y ) ) ).

% order_class.leD
thf(fact_826_order__class_OleD,axiom,
    ! [Y: ( c > d ) > set_a,X: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ Y @ X )
     => ~ ( ord_less_c_d_set_a @ X @ Y ) ) ).

% order_class.leD
thf(fact_827_order__class_Onless__le,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a] :
      ( ( ~ ( ord_le3685282097655362107_set_a @ A2 @ B ) )
      = ( ~ ( ord_le5982164083705284911_set_a @ A2 @ B )
        | ( A2 = B ) ) ) ).

% order_class.nless_le
thf(fact_828_order__class_Onless__le,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( ~ ( ord_less_set_a @ A2 @ B ) )
      = ( ~ ( ord_less_eq_set_a @ A2 @ B )
        | ( A2 = B ) ) ) ).

% order_class.nless_le
thf(fact_829_order__class_Onless__le,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ~ ( ord_le5853012546958565978et_a_o @ A2 @ B ) )
      = ( ~ ( ord_le1832228425591547726et_a_o @ A2 @ B )
        | ( A2 = B ) ) ) ).

% order_class.nless_le
thf(fact_830_order__class_Onless__le,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( ~ ( ord_less_e_f_set_a @ A2 @ B ) )
      = ( ~ ( ord_le4769328160706778703_set_a @ A2 @ B )
        | ( A2 = B ) ) ) ).

% order_class.nless_le
thf(fact_831_order__class_Onless__le,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ~ ( ord_less_c_d_set_a @ A2 @ B ) )
      = ( ~ ( ord_le8464990428230162895_set_a @ A2 @ B )
        | ( A2 = B ) ) ) ).

% order_class.nless_le
thf(fact_832_order__class_Oantisym__conv1,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ~ ( ord_le3685282097655362107_set_a @ X @ Y )
     => ( ( ord_le5982164083705284911_set_a @ X @ Y )
        = ( X = Y ) ) ) ).

% order_class.antisym_conv1
thf(fact_833_order__class_Oantisym__conv1,axiom,
    ! [X: set_a,Y: set_a] :
      ( ~ ( ord_less_set_a @ X @ Y )
     => ( ( ord_less_eq_set_a @ X @ Y )
        = ( X = Y ) ) ) ).

% order_class.antisym_conv1
thf(fact_834_order__class_Oantisym__conv1,axiom,
    ! [X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ~ ( ord_le5853012546958565978et_a_o @ X @ Y )
     => ( ( ord_le1832228425591547726et_a_o @ X @ Y )
        = ( X = Y ) ) ) ).

% order_class.antisym_conv1
thf(fact_835_order__class_Oantisym__conv1,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ~ ( ord_less_e_f_set_a @ X @ Y )
     => ( ( ord_le4769328160706778703_set_a @ X @ Y )
        = ( X = Y ) ) ) ).

% order_class.antisym_conv1
thf(fact_836_order__class_Oantisym__conv1,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ~ ( ord_less_c_d_set_a @ X @ Y )
     => ( ( ord_le8464990428230162895_set_a @ X @ Y )
        = ( X = Y ) ) ) ).

% order_class.antisym_conv1
thf(fact_837_order__class_Oantisym__conv2,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ X @ Y )
     => ( ( ~ ( ord_le3685282097655362107_set_a @ X @ Y ) )
        = ( X = Y ) ) ) ).

% order_class.antisym_conv2
thf(fact_838_order__class_Oantisym__conv2,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( ord_less_eq_set_a @ X @ Y )
     => ( ( ~ ( ord_less_set_a @ X @ Y ) )
        = ( X = Y ) ) ) ).

% order_class.antisym_conv2
thf(fact_839_order__class_Oantisym__conv2,axiom,
    ! [X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ X @ Y )
     => ( ( ~ ( ord_le5853012546958565978et_a_o @ X @ Y ) )
        = ( X = Y ) ) ) ).

% order_class.antisym_conv2
thf(fact_840_order__class_Oantisym__conv2,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ X @ Y )
     => ( ( ~ ( ord_less_e_f_set_a @ X @ Y ) )
        = ( X = Y ) ) ) ).

% order_class.antisym_conv2
thf(fact_841_order__class_Oantisym__conv2,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ Y )
     => ( ( ~ ( ord_less_c_d_set_a @ X @ Y ) )
        = ( X = Y ) ) ) ).

% order_class.antisym_conv2
thf(fact_842_preorder__class_Oless__le__not__le,axiom,
    ( ord_le3685282097655362107_set_a
    = ( ^ [X3: set_c_d_set_a,Y4: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ X3 @ Y4 )
          & ~ ( ord_le5982164083705284911_set_a @ Y4 @ X3 ) ) ) ) ).

% preorder_class.less_le_not_le
thf(fact_843_preorder__class_Oless__le__not__le,axiom,
    ( ord_less_set_a
    = ( ^ [X3: set_a,Y4: set_a] :
          ( ( ord_less_eq_set_a @ X3 @ Y4 )
          & ~ ( ord_less_eq_set_a @ Y4 @ X3 ) ) ) ) ).

% preorder_class.less_le_not_le
thf(fact_844_preorder__class_Oless__le__not__le,axiom,
    ( ord_le5853012546958565978et_a_o
    = ( ^ [X3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y4: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le1832228425591547726et_a_o @ X3 @ Y4 )
          & ~ ( ord_le1832228425591547726et_a_o @ Y4 @ X3 ) ) ) ) ).

% preorder_class.less_le_not_le
thf(fact_845_preorder__class_Oless__le__not__le,axiom,
    ( ord_less_e_f_set_a
    = ( ^ [X3: ( e > f ) > set_a,Y4: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ X3 @ Y4 )
          & ~ ( ord_le4769328160706778703_set_a @ Y4 @ X3 ) ) ) ) ).

% preorder_class.less_le_not_le
thf(fact_846_preorder__class_Oless__le__not__le,axiom,
    ( ord_less_c_d_set_a
    = ( ^ [X3: ( c > d ) > set_a,Y4: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ X3 @ Y4 )
          & ~ ( ord_le8464990428230162895_set_a @ Y4 @ X3 ) ) ) ) ).

% preorder_class.less_le_not_le
thf(fact_847_order__class_Oorder_Oorder__iff__strict,axiom,
    ( ord_le5982164083705284911_set_a
    = ( ^ [A3: set_c_d_set_a,B2: set_c_d_set_a] :
          ( ( ord_le3685282097655362107_set_a @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% order_class.order.order_iff_strict
thf(fact_848_order__class_Oorder_Oorder__iff__strict,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A3: set_a,B2: set_a] :
          ( ( ord_less_set_a @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% order_class.order.order_iff_strict
thf(fact_849_order__class_Oorder_Oorder__iff__strict,axiom,
    ( ord_le1832228425591547726et_a_o
    = ( ^ [A3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le5853012546958565978et_a_o @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% order_class.order.order_iff_strict
thf(fact_850_order__class_Oorder_Oorder__iff__strict,axiom,
    ( ord_le4769328160706778703_set_a
    = ( ^ [A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] :
          ( ( ord_less_e_f_set_a @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% order_class.order.order_iff_strict
thf(fact_851_order__class_Oorder_Oorder__iff__strict,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( ord_less_c_d_set_a @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% order_class.order.order_iff_strict
thf(fact_852_order__class_Oorder_Ostrict__iff__order,axiom,
    ( ord_le3685282097655362107_set_a
    = ( ^ [A3: set_c_d_set_a,B2: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% order_class.order.strict_iff_order
thf(fact_853_order__class_Oorder_Ostrict__iff__order,axiom,
    ( ord_less_set_a
    = ( ^ [A3: set_a,B2: set_a] :
          ( ( ord_less_eq_set_a @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% order_class.order.strict_iff_order
thf(fact_854_order__class_Oorder_Ostrict__iff__order,axiom,
    ( ord_le5853012546958565978et_a_o
    = ( ^ [A3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le1832228425591547726et_a_o @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% order_class.order.strict_iff_order
thf(fact_855_order__class_Oorder_Ostrict__iff__order,axiom,
    ( ord_less_e_f_set_a
    = ( ^ [A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% order_class.order.strict_iff_order
thf(fact_856_order__class_Oorder_Ostrict__iff__order,axiom,
    ( ord_less_c_d_set_a
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% order_class.order.strict_iff_order
thf(fact_857_preorder__class_Oorder_Ostrict__trans1,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A2 @ B )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ord_le3685282097655362107_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans1
thf(fact_858_preorder__class_Oorder_Ostrict__trans1,axiom,
    ! [A2: set_a,B: set_a,C: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_less_set_a @ B @ C )
       => ( ord_less_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans1
thf(fact_859_preorder__class_Oorder_Ostrict__trans1,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,C: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ A2 @ B )
     => ( ( ord_le5853012546958565978et_a_o @ B @ C )
       => ( ord_le5853012546958565978et_a_o @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans1
thf(fact_860_preorder__class_Oorder_Ostrict__trans1,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ B )
     => ( ( ord_less_e_f_set_a @ B @ C )
       => ( ord_less_e_f_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans1
thf(fact_861_preorder__class_Oorder_Ostrict__trans1,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ord_less_c_d_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans1
thf(fact_862_preorder__class_Oorder_Ostrict__trans2,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( ord_le5982164083705284911_set_a @ B @ C )
       => ( ord_le3685282097655362107_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans2
thf(fact_863_preorder__class_Oorder_Ostrict__trans2,axiom,
    ! [A2: set_a,B: set_a,C: set_a] :
      ( ( ord_less_set_a @ A2 @ B )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ord_less_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans2
thf(fact_864_preorder__class_Oorder_Ostrict__trans2,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,C: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le5853012546958565978et_a_o @ A2 @ B )
     => ( ( ord_le1832228425591547726et_a_o @ B @ C )
       => ( ord_le5853012546958565978et_a_o @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans2
thf(fact_865_preorder__class_Oorder_Ostrict__trans2,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_less_e_f_set_a @ A2 @ B )
     => ( ( ord_le4769328160706778703_set_a @ B @ C )
       => ( ord_less_e_f_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans2
thf(fact_866_preorder__class_Oorder_Ostrict__trans2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ord_less_c_d_set_a @ A2 @ C ) ) ) ).

% preorder_class.order.strict_trans2
thf(fact_867_preorder__class_Oorder_Ostrict__iff__not,axiom,
    ( ord_le3685282097655362107_set_a
    = ( ^ [A3: set_c_d_set_a,B2: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ A3 @ B2 )
          & ~ ( ord_le5982164083705284911_set_a @ B2 @ A3 ) ) ) ) ).

% preorder_class.order.strict_iff_not
thf(fact_868_preorder__class_Oorder_Ostrict__iff__not,axiom,
    ( ord_less_set_a
    = ( ^ [A3: set_a,B2: set_a] :
          ( ( ord_less_eq_set_a @ A3 @ B2 )
          & ~ ( ord_less_eq_set_a @ B2 @ A3 ) ) ) ) ).

% preorder_class.order.strict_iff_not
thf(fact_869_preorder__class_Oorder_Ostrict__iff__not,axiom,
    ( ord_le5853012546958565978et_a_o
    = ( ^ [A3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le1832228425591547726et_a_o @ A3 @ B2 )
          & ~ ( ord_le1832228425591547726et_a_o @ B2 @ A3 ) ) ) ) ).

% preorder_class.order.strict_iff_not
thf(fact_870_preorder__class_Oorder_Ostrict__iff__not,axiom,
    ( ord_less_e_f_set_a
    = ( ^ [A3: ( e > f ) > set_a,B2: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ A3 @ B2 )
          & ~ ( ord_le4769328160706778703_set_a @ B2 @ A3 ) ) ) ) ).

% preorder_class.order.strict_iff_not
thf(fact_871_preorder__class_Oorder_Ostrict__iff__not,axiom,
    ( ord_less_c_d_set_a
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ A3 @ B2 )
          & ~ ( ord_le8464990428230162895_set_a @ B2 @ A3 ) ) ) ) ).

% preorder_class.order.strict_iff_not
thf(fact_872_order__class_Odual__order_Oorder__iff__strict,axiom,
    ( ord_le5982164083705284911_set_a
    = ( ^ [B2: set_c_d_set_a,A3: set_c_d_set_a] :
          ( ( ord_le3685282097655362107_set_a @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% order_class.dual_order.order_iff_strict
thf(fact_873_order__class_Odual__order_Oorder__iff__strict,axiom,
    ( ord_less_eq_set_a
    = ( ^ [B2: set_a,A3: set_a] :
          ( ( ord_less_set_a @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% order_class.dual_order.order_iff_strict
thf(fact_874_order__class_Odual__order_Oorder__iff__strict,axiom,
    ( ord_le1832228425591547726et_a_o
    = ( ^ [B2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le5853012546958565978et_a_o @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% order_class.dual_order.order_iff_strict
thf(fact_875_order__class_Odual__order_Oorder__iff__strict,axiom,
    ( ord_le4769328160706778703_set_a
    = ( ^ [B2: ( e > f ) > set_a,A3: ( e > f ) > set_a] :
          ( ( ord_less_e_f_set_a @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% order_class.dual_order.order_iff_strict
thf(fact_876_order__class_Odual__order_Oorder__iff__strict,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [B2: ( c > d ) > set_a,A3: ( c > d ) > set_a] :
          ( ( ord_less_c_d_set_a @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% order_class.dual_order.order_iff_strict
thf(fact_877_order__class_Odual__order_Ostrict__iff__order,axiom,
    ( ord_le3685282097655362107_set_a
    = ( ^ [B2: set_c_d_set_a,A3: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% order_class.dual_order.strict_iff_order
thf(fact_878_order__class_Odual__order_Ostrict__iff__order,axiom,
    ( ord_less_set_a
    = ( ^ [B2: set_a,A3: set_a] :
          ( ( ord_less_eq_set_a @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% order_class.dual_order.strict_iff_order
thf(fact_879_order__class_Odual__order_Ostrict__iff__order,axiom,
    ( ord_le5853012546958565978et_a_o
    = ( ^ [B2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le1832228425591547726et_a_o @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% order_class.dual_order.strict_iff_order
thf(fact_880_order__class_Odual__order_Ostrict__iff__order,axiom,
    ( ord_less_e_f_set_a
    = ( ^ [B2: ( e > f ) > set_a,A3: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% order_class.dual_order.strict_iff_order
thf(fact_881_order__class_Odual__order_Ostrict__iff__order,axiom,
    ( ord_less_c_d_set_a
    = ( ^ [B2: ( c > d ) > set_a,A3: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% order_class.dual_order.strict_iff_order
thf(fact_882_preorder__class_Odual__order_Ostrict__trans1,axiom,
    ! [B: set_c_d_set_a,A2: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ B @ A2 )
     => ( ( ord_le3685282097655362107_set_a @ C @ B )
       => ( ord_le3685282097655362107_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans1
thf(fact_883_preorder__class_Odual__order_Ostrict__trans1,axiom,
    ! [B: set_a,A2: set_a,C: set_a] :
      ( ( ord_less_eq_set_a @ B @ A2 )
     => ( ( ord_less_set_a @ C @ B )
       => ( ord_less_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans1
thf(fact_884_preorder__class_Odual__order_Ostrict__trans1,axiom,
    ! [B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,C: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ B @ A2 )
     => ( ( ord_le5853012546958565978et_a_o @ C @ B )
       => ( ord_le5853012546958565978et_a_o @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans1
thf(fact_885_preorder__class_Odual__order_Ostrict__trans1,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ B @ A2 )
     => ( ( ord_less_e_f_set_a @ C @ B )
       => ( ord_less_e_f_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans1
thf(fact_886_preorder__class_Odual__order_Ostrict__trans1,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ B @ A2 )
     => ( ( ord_less_c_d_set_a @ C @ B )
       => ( ord_less_c_d_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans1
thf(fact_887_preorder__class_Odual__order_Ostrict__trans2,axiom,
    ! [B: set_c_d_set_a,A2: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ B @ A2 )
     => ( ( ord_le5982164083705284911_set_a @ C @ B )
       => ( ord_le3685282097655362107_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans2
thf(fact_888_preorder__class_Odual__order_Ostrict__trans2,axiom,
    ! [B: set_a,A2: set_a,C: set_a] :
      ( ( ord_less_set_a @ B @ A2 )
     => ( ( ord_less_eq_set_a @ C @ B )
       => ( ord_less_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans2
thf(fact_889_preorder__class_Odual__order_Ostrict__trans2,axiom,
    ! [B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,C: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le5853012546958565978et_a_o @ B @ A2 )
     => ( ( ord_le1832228425591547726et_a_o @ C @ B )
       => ( ord_le5853012546958565978et_a_o @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans2
thf(fact_890_preorder__class_Odual__order_Ostrict__trans2,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_less_e_f_set_a @ B @ A2 )
     => ( ( ord_le4769328160706778703_set_a @ C @ B )
       => ( ord_less_e_f_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans2
thf(fact_891_preorder__class_Odual__order_Ostrict__trans2,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ B @ A2 )
     => ( ( ord_le8464990428230162895_set_a @ C @ B )
       => ( ord_less_c_d_set_a @ C @ A2 ) ) ) ).

% preorder_class.dual_order.strict_trans2
thf(fact_892_preorder__class_Odual__order_Ostrict__iff__not,axiom,
    ( ord_le3685282097655362107_set_a
    = ( ^ [B2: set_c_d_set_a,A3: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ B2 @ A3 )
          & ~ ( ord_le5982164083705284911_set_a @ A3 @ B2 ) ) ) ) ).

% preorder_class.dual_order.strict_iff_not
thf(fact_893_preorder__class_Odual__order_Ostrict__iff__not,axiom,
    ( ord_less_set_a
    = ( ^ [B2: set_a,A3: set_a] :
          ( ( ord_less_eq_set_a @ B2 @ A3 )
          & ~ ( ord_less_eq_set_a @ A3 @ B2 ) ) ) ) ).

% preorder_class.dual_order.strict_iff_not
thf(fact_894_preorder__class_Odual__order_Ostrict__iff__not,axiom,
    ( ord_le5853012546958565978et_a_o
    = ( ^ [B2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le1832228425591547726et_a_o @ B2 @ A3 )
          & ~ ( ord_le1832228425591547726et_a_o @ A3 @ B2 ) ) ) ) ).

% preorder_class.dual_order.strict_iff_not
thf(fact_895_preorder__class_Odual__order_Ostrict__iff__not,axiom,
    ( ord_less_e_f_set_a
    = ( ^ [B2: ( e > f ) > set_a,A3: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ B2 @ A3 )
          & ~ ( ord_le4769328160706778703_set_a @ A3 @ B2 ) ) ) ) ).

% preorder_class.dual_order.strict_iff_not
thf(fact_896_preorder__class_Odual__order_Ostrict__iff__not,axiom,
    ( ord_less_c_d_set_a
    = ( ^ [B2: ( c > d ) > set_a,A3: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ B2 @ A3 )
          & ~ ( ord_le8464990428230162895_set_a @ A3 @ B2 ) ) ) ) ).

% preorder_class.dual_order.strict_iff_not
thf(fact_897_preorder__class_Oorder_Ostrict__implies__order,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ord_le5982164083705284911_set_a @ A2 @ B ) ) ).

% preorder_class.order.strict_implies_order
thf(fact_898_preorder__class_Oorder_Ostrict__implies__order,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( ord_less_set_a @ A2 @ B )
     => ( ord_less_eq_set_a @ A2 @ B ) ) ).

% preorder_class.order.strict_implies_order
thf(fact_899_preorder__class_Oorder_Ostrict__implies__order,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le5853012546958565978et_a_o @ A2 @ B )
     => ( ord_le1832228425591547726et_a_o @ A2 @ B ) ) ).

% preorder_class.order.strict_implies_order
thf(fact_900_preorder__class_Oorder_Ostrict__implies__order,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( ord_less_e_f_set_a @ A2 @ B )
     => ( ord_le4769328160706778703_set_a @ A2 @ B ) ) ).

% preorder_class.order.strict_implies_order
thf(fact_901_preorder__class_Oorder_Ostrict__implies__order,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ord_le8464990428230162895_set_a @ A2 @ B ) ) ).

% preorder_class.order.strict_implies_order
thf(fact_902_preorder__class_Odual__order_Ostrict__implies__order,axiom,
    ! [B: set_c_d_set_a,A2: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ B @ A2 )
     => ( ord_le5982164083705284911_set_a @ B @ A2 ) ) ).

% preorder_class.dual_order.strict_implies_order
thf(fact_903_preorder__class_Odual__order_Ostrict__implies__order,axiom,
    ! [B: set_a,A2: set_a] :
      ( ( ord_less_set_a @ B @ A2 )
     => ( ord_less_eq_set_a @ B @ A2 ) ) ).

% preorder_class.dual_order.strict_implies_order
thf(fact_904_preorder__class_Odual__order_Ostrict__implies__order,axiom,
    ! [B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le5853012546958565978et_a_o @ B @ A2 )
     => ( ord_le1832228425591547726et_a_o @ B @ A2 ) ) ).

% preorder_class.dual_order.strict_implies_order
thf(fact_905_preorder__class_Odual__order_Ostrict__implies__order,axiom,
    ! [B: ( e > f ) > set_a,A2: ( e > f ) > set_a] :
      ( ( ord_less_e_f_set_a @ B @ A2 )
     => ( ord_le4769328160706778703_set_a @ B @ A2 ) ) ).

% preorder_class.dual_order.strict_implies_order
thf(fact_906_preorder__class_Odual__order_Ostrict__implies__order,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ B @ A2 )
     => ( ord_le8464990428230162895_set_a @ B @ A2 ) ) ).

% preorder_class.dual_order.strict_implies_order
thf(fact_907_order__le__less,axiom,
    ( ord_le5982164083705284911_set_a
    = ( ^ [X3: set_c_d_set_a,Y4: set_c_d_set_a] :
          ( ( ord_le3685282097655362107_set_a @ X3 @ Y4 )
          | ( X3 = Y4 ) ) ) ) ).

% order_le_less
thf(fact_908_order__le__less,axiom,
    ( ord_less_eq_set_a
    = ( ^ [X3: set_a,Y4: set_a] :
          ( ( ord_less_set_a @ X3 @ Y4 )
          | ( X3 = Y4 ) ) ) ) ).

% order_le_less
thf(fact_909_order__le__less,axiom,
    ( ord_le1832228425591547726et_a_o
    = ( ^ [X3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y4: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le5853012546958565978et_a_o @ X3 @ Y4 )
          | ( X3 = Y4 ) ) ) ) ).

% order_le_less
thf(fact_910_order__le__less,axiom,
    ( ord_le4769328160706778703_set_a
    = ( ^ [X3: ( e > f ) > set_a,Y4: ( e > f ) > set_a] :
          ( ( ord_less_e_f_set_a @ X3 @ Y4 )
          | ( X3 = Y4 ) ) ) ) ).

% order_le_less
thf(fact_911_order__le__less,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [X3: ( c > d ) > set_a,Y4: ( c > d ) > set_a] :
          ( ( ord_less_c_d_set_a @ X3 @ Y4 )
          | ( X3 = Y4 ) ) ) ) ).

% order_le_less
thf(fact_912_order__less__le,axiom,
    ( ord_le3685282097655362107_set_a
    = ( ^ [X3: set_c_d_set_a,Y4: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ X3 @ Y4 )
          & ( X3 != Y4 ) ) ) ) ).

% order_less_le
thf(fact_913_order__less__le,axiom,
    ( ord_less_set_a
    = ( ^ [X3: set_a,Y4: set_a] :
          ( ( ord_less_eq_set_a @ X3 @ Y4 )
          & ( X3 != Y4 ) ) ) ) ).

% order_less_le
thf(fact_914_order__less__le,axiom,
    ( ord_le5853012546958565978et_a_o
    = ( ^ [X3: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y4: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le1832228425591547726et_a_o @ X3 @ Y4 )
          & ( X3 != Y4 ) ) ) ) ).

% order_less_le
thf(fact_915_order__less__le,axiom,
    ( ord_less_e_f_set_a
    = ( ^ [X3: ( e > f ) > set_a,Y4: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ X3 @ Y4 )
          & ( X3 != Y4 ) ) ) ) ).

% order_less_le
thf(fact_916_order__less__le,axiom,
    ( ord_less_c_d_set_a
    = ( ^ [X3: ( c > d ) > set_a,Y4: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ X3 @ Y4 )
          & ( X3 != Y4 ) ) ) ) ).

% order_less_le
thf(fact_917_order__less__imp__le,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ X @ Y )
     => ( ord_le5982164083705284911_set_a @ X @ Y ) ) ).

% order_less_imp_le
thf(fact_918_order__less__imp__le,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( ord_less_set_a @ X @ Y )
     => ( ord_less_eq_set_a @ X @ Y ) ) ).

% order_less_imp_le
thf(fact_919_order__less__imp__le,axiom,
    ! [X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le5853012546958565978et_a_o @ X @ Y )
     => ( ord_le1832228425591547726et_a_o @ X @ Y ) ) ).

% order_less_imp_le
thf(fact_920_order__less__imp__le,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( ord_less_e_f_set_a @ X @ Y )
     => ( ord_le4769328160706778703_set_a @ X @ Y ) ) ).

% order_less_imp_le
thf(fact_921_order__less__imp__le,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ X @ Y )
     => ( ord_le8464990428230162895_set_a @ X @ Y ) ) ).

% order_less_imp_le
thf(fact_922_order__le__neq__trans,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A2 @ B )
     => ( ( A2 != B )
       => ( ord_le3685282097655362107_set_a @ A2 @ B ) ) ) ).

% order_le_neq_trans
thf(fact_923_order__le__neq__trans,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( A2 != B )
       => ( ord_less_set_a @ A2 @ B ) ) ) ).

% order_le_neq_trans
thf(fact_924_order__le__neq__trans,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ A2 @ B )
     => ( ( A2 != B )
       => ( ord_le5853012546958565978et_a_o @ A2 @ B ) ) ) ).

% order_le_neq_trans
thf(fact_925_order__le__neq__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ B )
     => ( ( A2 != B )
       => ( ord_less_e_f_set_a @ A2 @ B ) ) ) ).

% order_le_neq_trans
thf(fact_926_order__le__neq__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( A2 != B )
       => ( ord_less_c_d_set_a @ A2 @ B ) ) ) ).

% order_le_neq_trans
thf(fact_927_order__neq__le__trans,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a] :
      ( ( A2 != B )
     => ( ( ord_le5982164083705284911_set_a @ A2 @ B )
       => ( ord_le3685282097655362107_set_a @ A2 @ B ) ) ) ).

% order_neq_le_trans
thf(fact_928_order__neq__le__trans,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( A2 != B )
     => ( ( ord_less_eq_set_a @ A2 @ B )
       => ( ord_less_set_a @ A2 @ B ) ) ) ).

% order_neq_le_trans
thf(fact_929_order__neq__le__trans,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( A2 != B )
     => ( ( ord_le1832228425591547726et_a_o @ A2 @ B )
       => ( ord_le5853012546958565978et_a_o @ A2 @ B ) ) ) ).

% order_neq_le_trans
thf(fact_930_order__neq__le__trans,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a] :
      ( ( A2 != B )
     => ( ( ord_le4769328160706778703_set_a @ A2 @ B )
       => ( ord_less_e_f_set_a @ A2 @ B ) ) ) ).

% order_neq_le_trans
thf(fact_931_order__neq__le__trans,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( A2 != B )
     => ( ( ord_le8464990428230162895_set_a @ A2 @ B )
       => ( ord_less_c_d_set_a @ A2 @ B ) ) ) ).

% order_neq_le_trans
thf(fact_932_order__le__less__trans,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a,Z: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ X @ Y )
     => ( ( ord_le3685282097655362107_set_a @ Y @ Z )
       => ( ord_le3685282097655362107_set_a @ X @ Z ) ) ) ).

% order_le_less_trans
thf(fact_933_order__le__less__trans,axiom,
    ! [X: set_a,Y: set_a,Z: set_a] :
      ( ( ord_less_eq_set_a @ X @ Y )
     => ( ( ord_less_set_a @ Y @ Z )
       => ( ord_less_set_a @ X @ Z ) ) ) ).

% order_le_less_trans
thf(fact_934_order__le__less__trans,axiom,
    ! [X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Z: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ X @ Y )
     => ( ( ord_le5853012546958565978et_a_o @ Y @ Z )
       => ( ord_le5853012546958565978et_a_o @ X @ Z ) ) ) ).

% order_le_less_trans
thf(fact_935_order__le__less__trans,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a,Z: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ X @ Y )
     => ( ( ord_less_e_f_set_a @ Y @ Z )
       => ( ord_less_e_f_set_a @ X @ Z ) ) ) ).

% order_le_less_trans
thf(fact_936_order__le__less__trans,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ Y )
     => ( ( ord_less_c_d_set_a @ Y @ Z )
       => ( ord_less_c_d_set_a @ X @ Z ) ) ) ).

% order_le_less_trans
thf(fact_937_order__less__le__trans,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a,Z: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ X @ Y )
     => ( ( ord_le5982164083705284911_set_a @ Y @ Z )
       => ( ord_le3685282097655362107_set_a @ X @ Z ) ) ) ).

% order_less_le_trans
thf(fact_938_order__less__le__trans,axiom,
    ! [X: set_a,Y: set_a,Z: set_a] :
      ( ( ord_less_set_a @ X @ Y )
     => ( ( ord_less_eq_set_a @ Y @ Z )
       => ( ord_less_set_a @ X @ Z ) ) ) ).

% order_less_le_trans
thf(fact_939_order__less__le__trans,axiom,
    ! [X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Z: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le5853012546958565978et_a_o @ X @ Y )
     => ( ( ord_le1832228425591547726et_a_o @ Y @ Z )
       => ( ord_le5853012546958565978et_a_o @ X @ Z ) ) ) ).

% order_less_le_trans
thf(fact_940_order__less__le__trans,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a,Z: ( e > f ) > set_a] :
      ( ( ord_less_e_f_set_a @ X @ Y )
     => ( ( ord_le4769328160706778703_set_a @ Y @ Z )
       => ( ord_less_e_f_set_a @ X @ Z ) ) ) ).

% order_less_le_trans
thf(fact_941_order__less__le__trans,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ X @ Y )
     => ( ( ord_le8464990428230162895_set_a @ Y @ Z )
       => ( ord_less_c_d_set_a @ X @ Z ) ) ) ).

% order_less_le_trans
thf(fact_942_order__le__less__subst1,axiom,
    ! [A2: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_943_order__le__less__subst1,axiom,
    ! [A2: ( c > d ) > set_a,F: set_c_d_set_a > ( c > d ) > set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_944_order__le__less__subst1,axiom,
    ! [A2: set_c_d_set_a,F: ( ( c > d ) > set_a ) > set_c_d_set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le5982164083705284911_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_945_order__le__less__subst1,axiom,
    ! [A2: set_c_d_set_a,F: set_c_d_set_a > set_c_d_set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_946_order__le__less__subst1,axiom,
    ! [A2: set_a,F: ( ( c > d ) > set_a ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_eq_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_947_order__le__less__subst1,axiom,
    ! [A2: set_a,F: set_c_d_set_a > set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_less_eq_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_948_order__le__less__subst1,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le1832228425591547726et_a_o @ A2 @ ( F @ B ) )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_le5853012546958565978et_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le5853012546958565978et_a_o @ A2 @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_949_order__le__less__subst1,axiom,
    ! [A2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: set_c_d_set_a > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le1832228425591547726et_a_o @ A2 @ ( F @ B ) )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_le5853012546958565978et_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le5853012546958565978et_a_o @ A2 @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_950_order__le__less__subst1,axiom,
    ! [A2: ( e > f ) > set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_c_d_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_less_e_f_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_e_f_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_951_order__le__less__subst1,axiom,
    ! [A2: ( e > f ) > set_a,F: set_c_d_set_a > ( e > f ) > set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le3685282097655362107_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_less_e_f_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_e_f_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_952_order__le__less__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ord_less_c_d_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_953_order__le__less__subst2,axiom,
    ! [A2: set_a,B: set_a,F: set_a > set_a,C: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_less_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_954_order__le__less__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > set_a,C: set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ord_less_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_955_order__le__less__subst2,axiom,
    ! [A2: set_a,B: set_a,F: set_a > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_less_c_d_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_956_order__le__less__subst2,axiom,
    ! [A2: set_a,B: set_a,F: set_a > ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_less_e_f_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_e_f_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_957_order__le__less__subst2,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,F: ( ( e > f ) > set_a ) > set_a,C: set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ B )
     => ( ( ord_less_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_958_order__le__less__subst2,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > set_a,C: set_a] :
      ( ( ord_le5982164083705284911_set_a @ A2 @ B )
     => ( ( ord_less_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le5982164083705284911_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_959_order__le__less__subst2,axiom,
    ! [A2: set_a,B: set_a,F: set_a > set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_le3685282097655362107_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le5982164083705284911_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_960_order__le__less__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ord_less_e_f_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_e_f_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_961_order__le__less__subst2,axiom,
    ! [A2: ( e > f ) > set_a,B: ( e > f ) > set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ A2 @ B )
     => ( ( ord_less_c_d_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_962_order__less__le__subst1,axiom,
    ! [A2: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_963_order__less__le__subst1,axiom,
    ! [A2: set_a,F: set_a > set_a,B: set_a,C: set_a] :
      ( ( ord_less_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_964_order__less__le__subst1,axiom,
    ! [A2: set_a,F: ( ( c > d ) > set_a ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_965_order__less__le__subst1,axiom,
    ! [A2: ( c > d ) > set_a,F: set_a > ( c > d ) > set_a,B: set_a,C: set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_966_order__less__le__subst1,axiom,
    ! [A2: ( e > f ) > set_a,F: set_a > ( e > f ) > set_a,B: set_a,C: set_a] :
      ( ( ord_less_e_f_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_e_f_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_967_order__less__le__subst1,axiom,
    ! [A2: set_a,F: ( ( e > f ) > set_a ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_less_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le4769328160706778703_set_a @ B @ C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_968_order__less__le__subst1,axiom,
    ! [A2: set_a,F: set_c_d_set_a > set_a,B: set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_less_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le5982164083705284911_set_a @ B @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le5982164083705284911_set_a @ X2 @ Y2 )
             => ( ord_less_eq_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_969_order__less__le__subst1,axiom,
    ! [A2: set_c_d_set_a,F: set_a > set_c_d_set_a,B: set_a,C: set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_less_eq_set_a @ B @ C )
       => ( ! [X2: set_a,Y2: set_a] :
              ( ( ord_less_eq_set_a @ X2 @ Y2 )
             => ( ord_le5982164083705284911_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_970_order__less__le__subst1,axiom,
    ! [A2: ( e > f ) > set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_e_f_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le8464990428230162895_set_a @ B @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ord_le4769328160706778703_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_e_f_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_971_order__less__le__subst1,axiom,
    ! [A2: ( c > d ) > set_a,F: ( ( e > f ) > set_a ) > ( c > d ) > set_a,B: ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ ( F @ B ) )
     => ( ( ord_le4769328160706778703_set_a @ B @ C )
       => ( ! [X2: ( e > f ) > set_a,Y2: ( e > f ) > set_a] :
              ( ( ord_le4769328160706778703_set_a @ X2 @ Y2 )
             => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_972_order__less__le__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( ord_le8464990428230162895_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_973_order__less__le__subst2,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( ord_le8464990428230162895_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_c_d_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_974_order__less__le__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( ord_le5982164083705284911_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_975_order__less__le__subst2,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > set_c_d_set_a,C: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( ord_le5982164083705284911_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_le3685282097655362107_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3685282097655362107_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_976_order__less__le__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > set_a,C: set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_977_order__less__le__subst2,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > set_a,C: set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_978_order__less__le__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,C: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( ord_le1832228425591547726et_a_o @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_le5853012546958565978et_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le5853012546958565978et_a_o @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_979_order__less__le__subst2,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,C: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( ord_le1832228425591547726et_a_o @ ( F @ B ) @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_le5853012546958565978et_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le5853012546958565978et_a_o @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_980_order__less__le__subst2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_less_c_d_set_a @ A2 @ B )
     => ( ( ord_le4769328160706778703_set_a @ ( F @ B ) @ C )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( ord_less_c_d_set_a @ X2 @ Y2 )
             => ( ord_less_e_f_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_e_f_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_981_order__less__le__subst2,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a,F: set_c_d_set_a > ( e > f ) > set_a,C: ( e > f ) > set_a] :
      ( ( ord_le3685282097655362107_set_a @ A2 @ B )
     => ( ( ord_le4769328160706778703_set_a @ ( F @ B ) @ C )
       => ( ! [X2: set_c_d_set_a,Y2: set_c_d_set_a] :
              ( ( ord_le3685282097655362107_set_a @ X2 @ Y2 )
             => ( ord_less_e_f_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_less_e_f_set_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_982_order__le__imp__less__or__eq,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ X @ Y )
     => ( ( ord_le3685282097655362107_set_a @ X @ Y )
        | ( X = Y ) ) ) ).

% order_le_imp_less_or_eq
thf(fact_983_order__le__imp__less__or__eq,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( ord_less_eq_set_a @ X @ Y )
     => ( ( ord_less_set_a @ X @ Y )
        | ( X = Y ) ) ) ).

% order_le_imp_less_or_eq
thf(fact_984_order__le__imp__less__or__eq,axiom,
    ! [X: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Y: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le1832228425591547726et_a_o @ X @ Y )
     => ( ( ord_le5853012546958565978et_a_o @ X @ Y )
        | ( X = Y ) ) ) ).

% order_le_imp_less_or_eq
thf(fact_985_order__le__imp__less__or__eq,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( ord_le4769328160706778703_set_a @ X @ Y )
     => ( ( ord_less_e_f_set_a @ X @ Y )
        | ( X = Y ) ) ) ).

% order_le_imp_less_or_eq
thf(fact_986_order__le__imp__less__or__eq,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ Y )
     => ( ( ord_less_c_d_set_a @ X @ Y )
        | ( X = Y ) ) ) ).

% order_le_imp_less_or_eq
thf(fact_987_order__top__class_Otop_Oextremum__strict,axiom,
    ! [A2: set_set_c_d_set_a] :
      ~ ( ord_le7529600783926193563_set_a @ top_to5717711934741766719_set_a @ A2 ) ).

% order_top_class.top.extremum_strict
thf(fact_988_order__top__class_Otop_Oextremum__strict,axiom,
    ! [A2: set_set_a] :
      ~ ( ord_less_set_set_a @ top_top_set_set_a @ A2 ) ).

% order_top_class.top.extremum_strict
thf(fact_989_order__top__class_Otop_Oextremum__strict,axiom,
    ! [A2: set_e_f_set_a] :
      ~ ( ord_le3697492283117579963_set_a @ top_to4280187784772989791_set_a @ A2 ) ).

% order_top_class.top.extremum_strict
thf(fact_990_order__top__class_Otop_Oextremum__strict,axiom,
    ! [A2: ( ( c > d ) > set_a ) > $o] :
      ~ ( ord_less_c_d_set_a_o @ top_top_c_d_set_a_o @ A2 ) ).

% order_top_class.top.extremum_strict
thf(fact_991_order__top__class_Otop_Oextremum__strict,axiom,
    ! [A2: ( c > d ) > set_a] :
      ~ ( ord_less_c_d_set_a @ top_top_c_d_set_a @ A2 ) ).

% order_top_class.top.extremum_strict
thf(fact_992_order__top__class_Otop_Oextremum__strict,axiom,
    ! [A2: set_c_d_set_a] :
      ~ ( ord_le3685282097655362107_set_a @ top_to4267977599310771935_set_a @ A2 ) ).

% order_top_class.top.extremum_strict
thf(fact_993_order__top__class_Otop_Onot__eq__extremum,axiom,
    ! [A2: set_set_c_d_set_a] :
      ( ( A2 != top_to5717711934741766719_set_a )
      = ( ord_le7529600783926193563_set_a @ A2 @ top_to5717711934741766719_set_a ) ) ).

% order_top_class.top.not_eq_extremum
thf(fact_994_order__top__class_Otop_Onot__eq__extremum,axiom,
    ! [A2: set_set_a] :
      ( ( A2 != top_top_set_set_a )
      = ( ord_less_set_set_a @ A2 @ top_top_set_set_a ) ) ).

% order_top_class.top.not_eq_extremum
thf(fact_995_order__top__class_Otop_Onot__eq__extremum,axiom,
    ! [A2: set_e_f_set_a] :
      ( ( A2 != top_to4280187784772989791_set_a )
      = ( ord_le3697492283117579963_set_a @ A2 @ top_to4280187784772989791_set_a ) ) ).

% order_top_class.top.not_eq_extremum
thf(fact_996_order__top__class_Otop_Onot__eq__extremum,axiom,
    ! [A2: ( ( c > d ) > set_a ) > $o] :
      ( ( A2 != top_top_c_d_set_a_o )
      = ( ord_less_c_d_set_a_o @ A2 @ top_top_c_d_set_a_o ) ) ).

% order_top_class.top.not_eq_extremum
thf(fact_997_order__top__class_Otop_Onot__eq__extremum,axiom,
    ! [A2: ( c > d ) > set_a] :
      ( ( A2 != top_top_c_d_set_a )
      = ( ord_less_c_d_set_a @ A2 @ top_top_c_d_set_a ) ) ).

% order_top_class.top.not_eq_extremum
thf(fact_998_order__top__class_Otop_Onot__eq__extremum,axiom,
    ! [A2: set_c_d_set_a] :
      ( ( A2 != top_to4267977599310771935_set_a )
      = ( ord_le3685282097655362107_set_a @ A2 @ top_to4267977599310771935_set_a ) ) ).

% order_top_class.top.not_eq_extremum
thf(fact_999_psubsetE,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A @ B3 )
     => ~ ( ( ord_le5982164083705284911_set_a @ A @ B3 )
         => ( ord_le5982164083705284911_set_a @ B3 @ A ) ) ) ).

% psubsetE
thf(fact_1000_psubsetE,axiom,
    ! [A: set_a,B3: set_a] :
      ( ( ord_less_set_a @ A @ B3 )
     => ~ ( ( ord_less_eq_set_a @ A @ B3 )
         => ( ord_less_eq_set_a @ B3 @ A ) ) ) ).

% psubsetE
thf(fact_1001_psubset__eq,axiom,
    ( ord_le3685282097655362107_set_a
    = ( ^ [A4: set_c_d_set_a,B5: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ A4 @ B5 )
          & ( A4 != B5 ) ) ) ) ).

% psubset_eq
thf(fact_1002_psubset__eq,axiom,
    ( ord_less_set_a
    = ( ^ [A4: set_a,B5: set_a] :
          ( ( ord_less_eq_set_a @ A4 @ B5 )
          & ( A4 != B5 ) ) ) ) ).

% psubset_eq
thf(fact_1003_psubset__imp__subset,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A @ B3 )
     => ( ord_le5982164083705284911_set_a @ A @ B3 ) ) ).

% psubset_imp_subset
thf(fact_1004_psubset__imp__subset,axiom,
    ! [A: set_a,B3: set_a] :
      ( ( ord_less_set_a @ A @ B3 )
     => ( ord_less_eq_set_a @ A @ B3 ) ) ).

% psubset_imp_subset
thf(fact_1005_psubset__subset__trans,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a,C2: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A @ B3 )
     => ( ( ord_le5982164083705284911_set_a @ B3 @ C2 )
       => ( ord_le3685282097655362107_set_a @ A @ C2 ) ) ) ).

% psubset_subset_trans
thf(fact_1006_psubset__subset__trans,axiom,
    ! [A: set_a,B3: set_a,C2: set_a] :
      ( ( ord_less_set_a @ A @ B3 )
     => ( ( ord_less_eq_set_a @ B3 @ C2 )
       => ( ord_less_set_a @ A @ C2 ) ) ) ).

% psubset_subset_trans
thf(fact_1007_subset__not__subset__eq,axiom,
    ( ord_le3685282097655362107_set_a
    = ( ^ [A4: set_c_d_set_a,B5: set_c_d_set_a] :
          ( ( ord_le5982164083705284911_set_a @ A4 @ B5 )
          & ~ ( ord_le5982164083705284911_set_a @ B5 @ A4 ) ) ) ) ).

% subset_not_subset_eq
thf(fact_1008_subset__not__subset__eq,axiom,
    ( ord_less_set_a
    = ( ^ [A4: set_a,B5: set_a] :
          ( ( ord_less_eq_set_a @ A4 @ B5 )
          & ~ ( ord_less_eq_set_a @ B5 @ A4 ) ) ) ) ).

% subset_not_subset_eq
thf(fact_1009_subset__psubset__trans,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a,C2: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A @ B3 )
     => ( ( ord_le3685282097655362107_set_a @ B3 @ C2 )
       => ( ord_le3685282097655362107_set_a @ A @ C2 ) ) ) ).

% subset_psubset_trans
thf(fact_1010_subset__psubset__trans,axiom,
    ! [A: set_a,B3: set_a,C2: set_a] :
      ( ( ord_less_eq_set_a @ A @ B3 )
     => ( ( ord_less_set_a @ B3 @ C2 )
       => ( ord_less_set_a @ A @ C2 ) ) ) ).

% subset_psubset_trans
thf(fact_1011_subset__iff__psubset__eq,axiom,
    ( ord_le5982164083705284911_set_a
    = ( ^ [A4: set_c_d_set_a,B5: set_c_d_set_a] :
          ( ( ord_le3685282097655362107_set_a @ A4 @ B5 )
          | ( A4 = B5 ) ) ) ) ).

% subset_iff_psubset_eq
thf(fact_1012_subset__iff__psubset__eq,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A4: set_a,B5: set_a] :
          ( ( ord_less_set_a @ A4 @ B5 )
          | ( A4 = B5 ) ) ) ) ).

% subset_iff_psubset_eq
thf(fact_1013_less__fun__def,axiom,
    ( ord_le5853012546958565978et_a_o
    = ( ^ [F2: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,G: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o] :
          ( ( ord_le1832228425591547726et_a_o @ F2 @ G )
          & ~ ( ord_le1832228425591547726et_a_o @ G @ F2 ) ) ) ) ).

% less_fun_def
thf(fact_1014_less__fun__def,axiom,
    ( ord_less_e_f_set_a
    = ( ^ [F2: ( e > f ) > set_a,G: ( e > f ) > set_a] :
          ( ( ord_le4769328160706778703_set_a @ F2 @ G )
          & ~ ( ord_le4769328160706778703_set_a @ G @ F2 ) ) ) ) ).

% less_fun_def
thf(fact_1015_less__fun__def,axiom,
    ( ord_less_c_d_set_a
    = ( ^ [F2: ( c > d ) > set_a,G: ( c > d ) > set_a] :
          ( ( ord_le8464990428230162895_set_a @ F2 @ G )
          & ~ ( ord_le8464990428230162895_set_a @ G @ F2 ) ) ) ) ).

% less_fun_def
thf(fact_1016_ord_Ostrict__mono__onD,axiom,
    ! [A: set_a,Less: a > a > $o,F: a > set_c_d_set_a,R2: a,S3: a] :
      ( ( monoto4999900198720154872_set_a @ A @ Less @ ord_le3685282097655362107_set_a @ F )
     => ( ( member_a @ R2 @ A )
       => ( ( member_a @ S3 @ A )
         => ( ( Less @ R2 @ S3 )
           => ( ord_le3685282097655362107_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.strict_mono_onD
thf(fact_1017_ord_Ostrict__mono__onD,axiom,
    ! [A: set_set_c_d_set_a,Less: set_c_d_set_a > set_c_d_set_a > $o,F: set_c_d_set_a > set_c_d_set_a,R2: set_c_d_set_a,S3: set_c_d_set_a] :
      ( ( monoto4733996707696316455_set_a @ A @ Less @ ord_le3685282097655362107_set_a @ F )
     => ( ( member_set_c_d_set_a @ R2 @ A )
       => ( ( member_set_c_d_set_a @ S3 @ A )
         => ( ( Less @ R2 @ S3 )
           => ( ord_le3685282097655362107_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.strict_mono_onD
thf(fact_1018_ord_Ostrict__mono__onD,axiom,
    ! [A: set_c_d_set_a,Less: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ Less @ ord_less_c_d_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( Less @ R2 @ S3 )
           => ( ord_less_c_d_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord.strict_mono_onD
thf(fact_1019_ord_Ostrict__mono__onI,axiom,
    ! [A: set_c_d_set_a,Less: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( Less @ R @ S2 )
             => ( ord_less_c_d_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto2937423850181994535_set_a @ A @ Less @ ord_less_c_d_set_a @ F ) ) ).

% ord.strict_mono_onI
thf(fact_1020_ord_Ostrict__mono__on__def,axiom,
    ! [A: set_c_d_set_a,Less: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ Less @ ord_less_c_d_set_a @ F )
      = ( ! [R3: ( c > d ) > set_a,S: ( c > d ) > set_a] :
            ( ( ( member_c_d_set_a @ R3 @ A )
              & ( member_c_d_set_a @ S @ A )
              & ( Less @ R3 @ S ) )
           => ( ord_less_c_d_set_a @ ( F @ R3 ) @ ( F @ S ) ) ) ) ) ).

% ord.strict_mono_on_def
thf(fact_1021_ord__class_Ostrict__mono__onD,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,R2: ( c > d ) > set_a,S3: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ A @ ord_less_c_d_set_a @ ord_less_c_d_set_a @ F )
     => ( ( member_c_d_set_a @ R2 @ A )
       => ( ( member_c_d_set_a @ S3 @ A )
         => ( ( ord_less_c_d_set_a @ R2 @ S3 )
           => ( ord_less_c_d_set_a @ ( F @ R2 ) @ ( F @ S3 ) ) ) ) ) ) ).

% ord_class.strict_mono_onD
thf(fact_1022_ord__class_Ostrict__mono__onI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [R: ( c > d ) > set_a,S2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ R @ A )
         => ( ( member_c_d_set_a @ S2 @ A )
           => ( ( ord_less_c_d_set_a @ R @ S2 )
             => ( ord_less_c_d_set_a @ ( F @ R ) @ ( F @ S2 ) ) ) ) )
     => ( monoto2937423850181994535_set_a @ A @ ord_less_c_d_set_a @ ord_less_c_d_set_a @ F ) ) ).

% ord_class.strict_mono_onI
thf(fact_1023_order__class_Ostrict__monoD,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_less_c_d_set_a @ ord_less_c_d_set_a @ F )
     => ( ( ord_less_c_d_set_a @ X @ Y )
       => ( ord_less_c_d_set_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% order_class.strict_monoD
thf(fact_1024_order__class_Ostrict__monoI,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
          ( ( ord_less_c_d_set_a @ X2 @ Y2 )
         => ( ord_less_c_d_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_less_c_d_set_a @ ord_less_c_d_set_a @ F ) ) ).

% order_class.strict_monoI
thf(fact_1025_order__class_Ostrict__mono__mono,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_less_c_d_set_a @ ord_less_c_d_set_a @ F )
     => ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F ) ) ).

% order_class.strict_mono_mono
thf(fact_1026_local_OatLeast__eq__UNIV__iff,axiom,
    ! [X: ( c > d ) > set_a] :
      ( ( ( set_at4358065015900363374_set_a @ smaller_interp_c_d_a @ X )
        = top_to4267977599310771935_set_a )
      = ( X = empty_interp_c_d_a ) ) ).

% local.atLeast_eq_UNIV_iff
thf(fact_1027_local_OatLeast__eq__UNIV__iff,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( ( set_at662402748376979182_set_a @ smaller_interp_e_f_a @ X )
        = top_to4280187784772989791_set_a )
      = ( X = empty_interp_e_f_a ) ) ).

% local.atLeast_eq_UNIV_iff
thf(fact_1028_local_OatMost__eq__UNIV__iff,axiom,
    ! [X: ( c > d ) > set_a] :
      ( ( ( set_atMost_c_d_set_a @ smaller_interp_c_d_a @ X )
        = top_to4267977599310771935_set_a )
      = ( X = full_interp_c_d_a ) ) ).

% local.atMost_eq_UNIV_iff
thf(fact_1029_preorder__class_Obdd__above_Opreordering__bdd__axioms,axiom,
    condit5292637031048566470_set_a @ ord_le8464990428230162895_set_a @ ord_less_c_d_set_a ).

% preorder_class.bdd_above.preordering_bdd_axioms
thf(fact_1030_local_OatLeastAtMost__eq__UNIV__iff,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ( set_at2224545791267470424_set_a @ smaller_interp_c_d_a @ X @ Y )
        = top_to4267977599310771935_set_a )
      = ( ( X = empty_interp_c_d_a )
        & ( Y = full_interp_c_d_a ) ) ) ).

% local.atLeastAtMost_eq_UNIV_iff
thf(fact_1031_local_OatLeastAtMost__eq__UNIV__iff,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( ( set_at7752255560598862040_set_a @ smaller_interp_e_f_a @ X @ Y )
        = top_to4280187784772989791_set_a )
      = ( ( X = empty_interp_e_f_a )
        & ( Y = full_interp_e_f_a ) ) ) ).

% local.atLeastAtMost_eq_UNIV_iff
thf(fact_1032_local_OatLeastAtMost__iff,axiom,
    ! [I3: ( c > d ) > set_a,L: ( c > d ) > set_a,U: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ I3 @ ( set_at2224545791267470424_set_a @ smaller_interp_c_d_a @ L @ U ) )
      = ( ( smaller_interp_c_d_a @ L @ I3 )
        & ( smaller_interp_c_d_a @ I3 @ U ) ) ) ).

% local.atLeastAtMost_iff
thf(fact_1033_local_OatLeast__iff,axiom,
    ! [I3: ( c > d ) > set_a,K: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ I3 @ ( set_at4358065015900363374_set_a @ smaller_interp_c_d_a @ K ) )
      = ( smaller_interp_c_d_a @ K @ I3 ) ) ).

% local.atLeast_iff
thf(fact_1034_local_OatMost__iff,axiom,
    ! [I3: ( c > d ) > set_a,K: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ I3 @ ( set_atMost_c_d_set_a @ smaller_interp_c_d_a @ K ) )
      = ( smaller_interp_c_d_a @ I3 @ K ) ) ).

% local.atMost_iff
thf(fact_1035_local_OInf__atMost,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( inf_e_f_a @ ( set_atMost_e_f_set_a @ smaller_interp_e_f_a @ X ) )
      = empty_interp_e_f_a ) ).

% local.Inf_atMost
thf(fact_1036_psubsetD,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a,C: ( c > d ) > set_a] :
      ( ( ord_le3685282097655362107_set_a @ A @ B3 )
     => ( ( member_c_d_set_a @ C @ A )
       => ( member_c_d_set_a @ C @ B3 ) ) ) ).

% psubsetD
thf(fact_1037_preorder__class_Oorder_Opreordering__axioms,axiom,
    preord7021486942077351306_set_a @ ord_le8464990428230162895_set_a @ ord_less_c_d_set_a ).

% preorder_class.order.preordering_axioms
thf(fact_1038_order__class_Oorder_Oordering__axioms,axiom,
    ordering_c_d_set_a @ ord_le8464990428230162895_set_a @ ord_less_c_d_set_a ).

% order_class.order.ordering_axioms
thf(fact_1039_order__top__class_Otop_Oordering__top__axioms,axiom,
    orderi13773357969974208_set_a @ ord_le5982164083705284911_set_a @ ord_le3685282097655362107_set_a @ top_to4267977599310771935_set_a ).

% order_top_class.top.ordering_top_axioms
thf(fact_1040_order__top__class_Otop_Oordering__top__axioms,axiom,
    orderi5785346111247480928_set_a @ ord_le8464990428230162895_set_a @ ord_less_c_d_set_a @ top_top_c_d_set_a ).

% order_top_class.top.ordering_top_axioms
thf(fact_1041_preordering__bdd_OE,axiom,
    ! [Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Less: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A: set_c_d_set_a] :
      ( ( condit5292637031048566470_set_a @ Less_eq @ Less )
     => ( ( condit8154225043310684324_set_a @ Less_eq @ A )
       => ~ ! [M: ( c > d ) > set_a] :
              ~ ! [X4: ( c > d ) > set_a] :
                  ( ( member_c_d_set_a @ X4 @ A )
                 => ( Less_eq @ X4 @ M ) ) ) ) ).

% preordering_bdd.E
thf(fact_1042_preordering__bdd_OI,axiom,
    ! [Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Less: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,A: set_c_d_set_a,M3: ( c > d ) > set_a] :
      ( ( condit5292637031048566470_set_a @ Less_eq @ Less )
     => ( ! [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ A )
           => ( Less_eq @ X2 @ M3 ) )
       => ( condit8154225043310684324_set_a @ Less_eq @ A ) ) ) ).

% preordering_bdd.I
thf(fact_1043_local_OInf__atMostLessThan,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( less_e_f_a @ full_interp_e_f_a @ X )
     => ( ( inf_e_f_a @ ( set_le1722920449243357406_set_a @ less_e_f_a @ X ) )
        = empty_interp_e_f_a ) ) ).

% local.Inf_atMostLessThan
thf(fact_1044_empty__interp__def,axiom,
    ( empty_interp_e_f_a
    = ( ^ [S: e > f] : bot_bot_set_a ) ) ).

% empty_interp_def
thf(fact_1045_local_OInf__less__eq,axiom,
    ! [A: set_c_d_set_a,U: ( c > d ) > set_a] :
      ( ! [V2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ V2 @ A )
         => ( smaller_interp_c_d_a @ V2 @ U ) )
     => ( ( A != bot_bo738396921950161403_set_a )
       => ( smaller_interp_c_d_a @ ( inf_c_d_a @ A ) @ U ) ) ) ).

% local.Inf_less_eq
thf(fact_1046_local_Oless__eq__Sup,axiom,
    ! [A: set_c_d_set_a,U: ( c > d ) > set_a] :
      ( ! [V2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ V2 @ A )
         => ( smaller_interp_c_d_a @ U @ V2 ) )
     => ( ( A != bot_bo738396921950161403_set_a )
       => ( smaller_interp_c_d_a @ U @ ( sup_c_d_a @ A ) ) ) ) ).

% local.less_eq_Sup
thf(fact_1047_empty__iff,axiom,
    ! [C: ( c > d ) > set_a] :
      ~ ( member_c_d_set_a @ C @ bot_bo738396921950161403_set_a ) ).

% empty_iff
thf(fact_1048_all__not__in__conv,axiom,
    ! [A: set_c_d_set_a] :
      ( ( ! [X3: ( c > d ) > set_a] :
            ~ ( member_c_d_set_a @ X3 @ A ) )
      = ( A = bot_bo738396921950161403_set_a ) ) ).

% all_not_in_conv
thf(fact_1049_IntI,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ A )
     => ( ( member_c_d_set_a @ C @ B3 )
       => ( member_c_d_set_a @ C @ ( inf_in754637537901350525_set_a @ A @ B3 ) ) ) ) ).

% IntI
thf(fact_1050_Int__iff,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ ( inf_in754637537901350525_set_a @ A @ B3 ) )
      = ( ( member_c_d_set_a @ C @ A )
        & ( member_c_d_set_a @ C @ B3 ) ) ) ).

% Int_iff
thf(fact_1051_Int__UNIV,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ( inf_in754637537901350525_set_a @ A @ B3 )
        = top_to4267977599310771935_set_a )
      = ( ( A = top_to4267977599310771935_set_a )
        & ( B3 = top_to4267977599310771935_set_a ) ) ) ).

% Int_UNIV
thf(fact_1052_local_OgreaterThan__iff,axiom,
    ! [I3: ( c > d ) > set_a,K: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ I3 @ ( set_gr5532796609634356233_set_a @ less_c_d_a @ K ) )
      = ( less_c_d_a @ K @ I3 ) ) ).

% local.greaterThan_iff
thf(fact_1053_local_OlessThan__iff,axiom,
    ! [I3: ( c > d ) > set_a,K: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ I3 @ ( set_le5418582716766741598_set_a @ less_c_d_a @ K ) )
      = ( less_c_d_a @ I3 @ K ) ) ).

% local.lessThan_iff
thf(fact_1054_sup__empty,axiom,
    ( ( sup_e_f_a @ bot_bo750607107412379259_set_a )
    = empty_interp_e_f_a ) ).

% sup_empty
thf(fact_1055_local_OatLeastLessThan__iff,axiom,
    ! [I3: ( c > d ) > set_a,L: ( c > d ) > set_a,U: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ I3 @ ( set_at2139306834251651636_set_a @ smaller_interp_c_d_a @ less_c_d_a @ L @ U ) )
      = ( ( smaller_interp_c_d_a @ L @ I3 )
        & ( less_c_d_a @ I3 @ U ) ) ) ).

% local.atLeastLessThan_iff
thf(fact_1056_order__bot__class_Obot_Oextremum__uniqueI,axiom,
    ! [A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ bot_bot_c_d_set_a )
     => ( A2 = bot_bot_c_d_set_a ) ) ).

% order_bot_class.bot.extremum_uniqueI
thf(fact_1057_order__bot__class_Obot_Oextremum__unique,axiom,
    ! [A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ bot_bot_c_d_set_a )
      = ( A2 = bot_bot_c_d_set_a ) ) ).

% order_bot_class.bot.extremum_unique
thf(fact_1058_order__bot__class_Obot_Oextremum,axiom,
    ! [A2: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ bot_bot_c_d_set_a @ A2 ) ).

% order_bot_class.bot.extremum
thf(fact_1059_Int__UNIV__right,axiom,
    ! [A: set_c_d_set_a] :
      ( ( inf_in754637537901350525_set_a @ A @ top_to4267977599310771935_set_a )
      = A ) ).

% Int_UNIV_right
thf(fact_1060_Int__UNIV__left,axiom,
    ! [B3: set_c_d_set_a] :
      ( ( inf_in754637537901350525_set_a @ top_to4267977599310771935_set_a @ B3 )
      = B3 ) ).

% Int_UNIV_left
thf(fact_1061_Int__Collect__mono,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a,P: ( ( c > d ) > set_a ) > $o,Q: ( ( c > d ) > set_a ) > $o] :
      ( ( ord_le5982164083705284911_set_a @ A @ B3 )
     => ( ! [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ A )
           => ( ( P @ X2 )
             => ( Q @ X2 ) ) )
       => ( ord_le5982164083705284911_set_a @ ( inf_in754637537901350525_set_a @ A @ ( collect_c_d_set_a @ P ) ) @ ( inf_in754637537901350525_set_a @ B3 @ ( collect_c_d_set_a @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_1062_IntE,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ ( inf_in754637537901350525_set_a @ A @ B3 ) )
     => ~ ( ( member_c_d_set_a @ C @ A )
         => ~ ( member_c_d_set_a @ C @ B3 ) ) ) ).

% IntE
thf(fact_1063_IntD1,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ ( inf_in754637537901350525_set_a @ A @ B3 ) )
     => ( member_c_d_set_a @ C @ A ) ) ).

% IntD1
thf(fact_1064_IntD2,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ ( inf_in754637537901350525_set_a @ A @ B3 ) )
     => ( member_c_d_set_a @ C @ B3 ) ) ).

% IntD2
thf(fact_1065_emptyE,axiom,
    ! [A2: ( c > d ) > set_a] :
      ~ ( member_c_d_set_a @ A2 @ bot_bo738396921950161403_set_a ) ).

% emptyE
thf(fact_1066_equals0D,axiom,
    ! [A: set_c_d_set_a,A2: ( c > d ) > set_a] :
      ( ( A = bot_bo738396921950161403_set_a )
     => ~ ( member_c_d_set_a @ A2 @ A ) ) ).

% equals0D
thf(fact_1067_equals0I,axiom,
    ! [A: set_c_d_set_a] :
      ( ! [Y2: ( c > d ) > set_a] :
          ~ ( member_c_d_set_a @ Y2 @ A )
     => ( A = bot_bo738396921950161403_set_a ) ) ).

% equals0I
thf(fact_1068_Int__emptyI,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X2 @ A )
         => ~ ( member_c_d_set_a @ X2 @ B3 ) )
     => ( ( inf_in754637537901350525_set_a @ A @ B3 )
        = bot_bo738396921950161403_set_a ) ) ).

% Int_emptyI
thf(fact_1069_ex__in__conv,axiom,
    ! [A: set_c_d_set_a] :
      ( ( ? [X3: ( c > d ) > set_a] : ( member_c_d_set_a @ X3 @ A ) )
      = ( A != bot_bo738396921950161403_set_a ) ) ).

% ex_in_conv
thf(fact_1070_disjoint__iff,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ( inf_in754637537901350525_set_a @ A @ B3 )
        = bot_bo738396921950161403_set_a )
      = ( ! [X3: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X3 @ A )
           => ~ ( member_c_d_set_a @ X3 @ B3 ) ) ) ) ).

% disjoint_iff
thf(fact_1071_empty__not__UNIV,axiom,
    bot_bo738396921950161403_set_a != top_to4267977599310771935_set_a ).

% empty_not_UNIV
thf(fact_1072_monotone__on__empty,axiom,
    ! [Orda: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,Ordb: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] : ( monoto2937423850181994535_set_a @ bot_bo738396921950161403_set_a @ Orda @ Ordb @ F ) ).

% monotone_on_empty
thf(fact_1073_semilattice__inf__class_Omono__inf,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,A: ( c > d ) > set_a,B3: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ord_le8464990428230162895_set_a @ ( F @ ( inf_inf_c_d_set_a @ A @ B3 ) ) @ ( inf_inf_c_d_set_a @ ( F @ A ) @ ( F @ B3 ) ) ) ) ).

% semilattice_inf_class.mono_inf
thf(fact_1074_local_OgreaterThanLessThan__iff,axiom,
    ! [I3: ( c > d ) > set_a,L: ( c > d ) > set_a,U: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ I3 @ ( set_gr2245648953767368143_set_a @ less_c_d_a @ L @ U ) )
      = ( ( less_c_d_a @ L @ I3 )
        & ( less_c_d_a @ I3 @ U ) ) ) ).

% local.greaterThanLessThan_iff
thf(fact_1075_local_OgreaterThanAtMost__iff,axiom,
    ! [I3: ( c > d ) > set_a,L: ( c > d ) > set_a,U: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ I3 @ ( set_gr4053032598485390707_set_a @ smaller_interp_c_d_a @ less_c_d_a @ L @ U ) )
      = ( ( less_c_d_a @ L @ I3 )
        & ( smaller_interp_c_d_a @ I3 @ U ) ) ) ).

% local.greaterThanAtMost_iff
thf(fact_1076_bot__empty__eq,axiom,
    ( bot_bot_c_d_set_a_o
    = ( ^ [X3: ( c > d ) > set_a] : ( member_c_d_set_a @ X3 @ bot_bo738396921950161403_set_a ) ) ) ).

% bot_empty_eq
thf(fact_1077_antisym__bot,axiom,
    antisy1518167394357443548_set_a @ top_to4267977599310771935_set_a @ bot_bo919924463001950746et_a_o ).

% antisym_bot
thf(fact_1078_ord_OatLeastAtMost__iff,axiom,
    ! [I3: ( c > d ) > set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,L: ( c > d ) > set_a,U: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ I3 @ ( set_at2224545791267470424_set_a @ Less_eq @ L @ U ) )
      = ( ( Less_eq @ L @ I3 )
        & ( Less_eq @ I3 @ U ) ) ) ).

% ord.atLeastAtMost_iff
thf(fact_1079_ord_OatLeast__iff,axiom,
    ! [I3: ( c > d ) > set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,K: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ I3 @ ( set_at4358065015900363374_set_a @ Less_eq @ K ) )
      = ( Less_eq @ K @ I3 ) ) ).

% ord.atLeast_iff
thf(fact_1080_ord_OatMost__iff,axiom,
    ! [I3: ( c > d ) > set_a,Less_eq: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > $o,K: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ I3 @ ( set_atMost_c_d_set_a @ Less_eq @ K ) )
      = ( Less_eq @ I3 @ K ) ) ).

% ord.atMost_iff
thf(fact_1081_bounded__semilattice__inf__top__class_Oinf__top__left,axiom,
    ! [X: set_c_d_set_a] :
      ( ( inf_in754637537901350525_set_a @ top_to4267977599310771935_set_a @ X )
      = X ) ).

% bounded_semilattice_inf_top_class.inf_top_left
thf(fact_1082_bounded__semilattice__inf__top__class_Oinf__top__right,axiom,
    ! [X: set_c_d_set_a] :
      ( ( inf_in754637537901350525_set_a @ X @ top_to4267977599310771935_set_a )
      = X ) ).

% bounded_semilattice_inf_top_class.inf_top_right
thf(fact_1083_bounded__semilattice__inf__top__class_Oinf__eq__top__iff,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ( inf_in754637537901350525_set_a @ X @ Y )
        = top_to4267977599310771935_set_a )
      = ( ( X = top_to4267977599310771935_set_a )
        & ( Y = top_to4267977599310771935_set_a ) ) ) ).

% bounded_semilattice_inf_top_class.inf_eq_top_iff
thf(fact_1084_bounded__semilattice__inf__top__class_Otop__eq__inf__iff,axiom,
    ! [X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( top_to4267977599310771935_set_a
        = ( inf_in754637537901350525_set_a @ X @ Y ) )
      = ( ( X = top_to4267977599310771935_set_a )
        & ( Y = top_to4267977599310771935_set_a ) ) ) ).

% bounded_semilattice_inf_top_class.top_eq_inf_iff
thf(fact_1085_semilattice__inf__class_Oinf_Obounded__iff,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ ( inf_inf_c_d_set_a @ B @ C ) )
      = ( ( ord_le8464990428230162895_set_a @ A2 @ B )
        & ( ord_le8464990428230162895_set_a @ A2 @ C ) ) ) ).

% semilattice_inf_class.inf.bounded_iff
thf(fact_1086_semilattice__inf__class_Ole__inf__iff,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ ( inf_inf_c_d_set_a @ Y @ Z ) )
      = ( ( ord_le8464990428230162895_set_a @ X @ Y )
        & ( ord_le8464990428230162895_set_a @ X @ Z ) ) ) ).

% semilattice_inf_class.le_inf_iff
thf(fact_1087_bounded__semilattice__inf__top__class_Oinf__top_Oright__neutral,axiom,
    ! [A2: set_c_d_set_a] :
      ( ( inf_in754637537901350525_set_a @ A2 @ top_to4267977599310771935_set_a )
      = A2 ) ).

% bounded_semilattice_inf_top_class.inf_top.right_neutral
thf(fact_1088_bounded__semilattice__inf__top__class_Oinf__top_Oneutr__eq__iff,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a] :
      ( ( top_to4267977599310771935_set_a
        = ( inf_in754637537901350525_set_a @ A2 @ B ) )
      = ( ( A2 = top_to4267977599310771935_set_a )
        & ( B = top_to4267977599310771935_set_a ) ) ) ).

% bounded_semilattice_inf_top_class.inf_top.neutr_eq_iff
thf(fact_1089_bounded__semilattice__inf__top__class_Oinf__top_Oleft__neutral,axiom,
    ! [A2: set_c_d_set_a] :
      ( ( inf_in754637537901350525_set_a @ top_to4267977599310771935_set_a @ A2 )
      = A2 ) ).

% bounded_semilattice_inf_top_class.inf_top.left_neutral
thf(fact_1090_bounded__semilattice__inf__top__class_Oinf__top_Oeq__neutr__iff,axiom,
    ! [A2: set_c_d_set_a,B: set_c_d_set_a] :
      ( ( ( inf_in754637537901350525_set_a @ A2 @ B )
        = top_to4267977599310771935_set_a )
      = ( ( A2 = top_to4267977599310771935_set_a )
        & ( B = top_to4267977599310771935_set_a ) ) ) ).

% bounded_semilattice_inf_top_class.inf_top.eq_neutr_iff
thf(fact_1091_lattice__class_Oinf__sup__ord_I2_J,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ ( inf_inf_c_d_set_a @ X @ Y ) @ Y ) ).

% lattice_class.inf_sup_ord(2)
thf(fact_1092_lattice__class_Oinf__sup__ord_I1_J,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ ( inf_inf_c_d_set_a @ X @ Y ) @ X ) ).

% lattice_class.inf_sup_ord(1)
thf(fact_1093_semilattice__inf__class_Oinf__le1,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ ( inf_inf_c_d_set_a @ X @ Y ) @ X ) ).

% semilattice_inf_class.inf_le1
thf(fact_1094_semilattice__inf__class_Oinf__le2,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ ( inf_inf_c_d_set_a @ X @ Y ) @ Y ) ).

% semilattice_inf_class.inf_le2
thf(fact_1095_semilattice__inf__class_Ole__infE,axiom,
    ! [X: ( c > d ) > set_a,A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ ( inf_inf_c_d_set_a @ A2 @ B ) )
     => ~ ( ( ord_le8464990428230162895_set_a @ X @ A2 )
         => ~ ( ord_le8464990428230162895_set_a @ X @ B ) ) ) ).

% semilattice_inf_class.le_infE
thf(fact_1096_semilattice__inf__class_Ole__infI,axiom,
    ! [X: ( c > d ) > set_a,A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ A2 )
     => ( ( ord_le8464990428230162895_set_a @ X @ B )
       => ( ord_le8464990428230162895_set_a @ X @ ( inf_inf_c_d_set_a @ A2 @ B ) ) ) ) ).

% semilattice_inf_class.le_infI
thf(fact_1097_semilattice__inf__class_Oinf__mono,axiom,
    ! [A2: ( c > d ) > set_a,C: ( c > d ) > set_a,B: ( c > d ) > set_a,D: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ C )
     => ( ( ord_le8464990428230162895_set_a @ B @ D )
       => ( ord_le8464990428230162895_set_a @ ( inf_inf_c_d_set_a @ A2 @ B ) @ ( inf_inf_c_d_set_a @ C @ D ) ) ) ) ).

% semilattice_inf_class.inf_mono
thf(fact_1098_semilattice__inf__class_Ole__infI1,axiom,
    ! [A2: ( c > d ) > set_a,X: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ X )
     => ( ord_le8464990428230162895_set_a @ ( inf_inf_c_d_set_a @ A2 @ B ) @ X ) ) ).

% semilattice_inf_class.le_infI1
thf(fact_1099_semilattice__inf__class_Ole__infI2,axiom,
    ! [B: ( c > d ) > set_a,X: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ B @ X )
     => ( ord_le8464990428230162895_set_a @ ( inf_inf_c_d_set_a @ A2 @ B ) @ X ) ) ).

% semilattice_inf_class.le_infI2
thf(fact_1100_semilattice__inf__class_Oinf_OorderE,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( A2
        = ( inf_inf_c_d_set_a @ A2 @ B ) ) ) ).

% semilattice_inf_class.inf.orderE
thf(fact_1101_semilattice__inf__class_Oinf_OorderI,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( A2
        = ( inf_inf_c_d_set_a @ A2 @ B ) )
     => ( ord_le8464990428230162895_set_a @ A2 @ B ) ) ).

% semilattice_inf_class.inf.orderI
thf(fact_1102_semilattice__inf__class_Oinf__unique,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ ( F @ X2 @ Y2 ) @ X2 )
     => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ ( F @ X2 @ Y2 ) @ Y2 )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a,Z4: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ X2 @ Y2 )
             => ( ( ord_le8464990428230162895_set_a @ X2 @ Z4 )
               => ( ord_le8464990428230162895_set_a @ X2 @ ( F @ Y2 @ Z4 ) ) ) )
         => ( ( inf_inf_c_d_set_a @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% semilattice_inf_class.inf_unique
thf(fact_1103_semilattice__inf__class_Ole__iff__inf,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [X3: ( c > d ) > set_a,Y4: ( c > d ) > set_a] :
          ( ( inf_inf_c_d_set_a @ X3 @ Y4 )
          = X3 ) ) ) ).

% semilattice_inf_class.le_iff_inf
thf(fact_1104_semilattice__inf__class_Oinf_Oabsorb1,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( inf_inf_c_d_set_a @ A2 @ B )
        = A2 ) ) ).

% semilattice_inf_class.inf.absorb1
thf(fact_1105_semilattice__inf__class_Oinf_Oabsorb2,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ B @ A2 )
     => ( ( inf_inf_c_d_set_a @ A2 @ B )
        = B ) ) ).

% semilattice_inf_class.inf.absorb2
thf(fact_1106_semilattice__inf__class_Oinf__absorb1,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ Y )
     => ( ( inf_inf_c_d_set_a @ X @ Y )
        = X ) ) ).

% semilattice_inf_class.inf_absorb1
thf(fact_1107_semilattice__inf__class_Oinf__absorb2,axiom,
    ! [Y: ( c > d ) > set_a,X: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ Y @ X )
     => ( ( inf_inf_c_d_set_a @ X @ Y )
        = Y ) ) ).

% semilattice_inf_class.inf_absorb2
thf(fact_1108_semilattice__inf__class_Oinf_OboundedE,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ ( inf_inf_c_d_set_a @ B @ C ) )
     => ~ ( ( ord_le8464990428230162895_set_a @ A2 @ B )
         => ~ ( ord_le8464990428230162895_set_a @ A2 @ C ) ) ) ).

% semilattice_inf_class.inf.boundedE
thf(fact_1109_semilattice__inf__class_Oinf_OboundedI,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( ord_le8464990428230162895_set_a @ A2 @ C )
       => ( ord_le8464990428230162895_set_a @ A2 @ ( inf_inf_c_d_set_a @ B @ C ) ) ) ) ).

% semilattice_inf_class.inf.boundedI
thf(fact_1110_semilattice__inf__class_Oinf__greatest,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ Y )
     => ( ( ord_le8464990428230162895_set_a @ X @ Z )
       => ( ord_le8464990428230162895_set_a @ X @ ( inf_inf_c_d_set_a @ Y @ Z ) ) ) ) ).

% semilattice_inf_class.inf_greatest
thf(fact_1111_semilattice__inf__class_Oinf_Oorder__iff,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( A3
          = ( inf_inf_c_d_set_a @ A3 @ B2 ) ) ) ) ).

% semilattice_inf_class.inf.order_iff
thf(fact_1112_semilattice__inf__class_Oinf_Ocobounded1,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ ( inf_inf_c_d_set_a @ A2 @ B ) @ A2 ) ).

% semilattice_inf_class.inf.cobounded1
thf(fact_1113_semilattice__inf__class_Oinf_Ocobounded2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ ( inf_inf_c_d_set_a @ A2 @ B ) @ B ) ).

% semilattice_inf_class.inf.cobounded2
thf(fact_1114_semilattice__inf__class_Oinf_Oabsorb__iff1,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( inf_inf_c_d_set_a @ A3 @ B2 )
          = A3 ) ) ) ).

% semilattice_inf_class.inf.absorb_iff1
thf(fact_1115_semilattice__inf__class_Oinf_Oabsorb__iff2,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [B2: ( c > d ) > set_a,A3: ( c > d ) > set_a] :
          ( ( inf_inf_c_d_set_a @ A3 @ B2 )
          = B2 ) ) ) ).

% semilattice_inf_class.inf.absorb_iff2
thf(fact_1116_semilattice__inf__class_Oinf_OcoboundedI1,axiom,
    ! [A2: ( c > d ) > set_a,C: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ C )
     => ( ord_le8464990428230162895_set_a @ ( inf_inf_c_d_set_a @ A2 @ B ) @ C ) ) ).

% semilattice_inf_class.inf.coboundedI1
thf(fact_1117_semilattice__inf__class_Oinf_OcoboundedI2,axiom,
    ! [B: ( c > d ) > set_a,C: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ B @ C )
     => ( ord_le8464990428230162895_set_a @ ( inf_inf_c_d_set_a @ A2 @ B ) @ C ) ) ).

% semilattice_inf_class.inf.coboundedI2
thf(fact_1118_local_Omono__inf,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,A: ( c > d ) > set_a,B3: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ smaller_interp_c_d_a @ ord_le8464990428230162895_set_a @ F )
     => ( ord_le8464990428230162895_set_a @ ( F @ ( inf_c_d_a2 @ A @ B3 ) ) @ ( inf_inf_c_d_set_a @ ( F @ A ) @ ( F @ B3 ) ) ) ) ).

% local.mono_inf
thf(fact_1119__092_060open_062set__closure__property_AS_A_ISup__class_OSup_A_123_125_J_092_060close_062,axiom,
    set_cl2807270042661212426_a_c_d @ s @ ( comple3834726295627996700_set_a @ bot_bo738396921950161403_set_a ) ).

% \<open>set_closure_property S (Sup_class.Sup {})\<close>
thf(fact_1120__092_060open_062set__closure__property_AS_A_ISup__class_OSup_A_123_125_J_092_060close_062,axiom,
    set_cl6455730915570636170_a_e_f @ s @ ( comple139064028104612508_set_a @ bot_bo750607107412379259_set_a ) ).

% \<open>set_closure_property S (Sup_class.Sup {})\<close>
thf(fact_1121_insert__iff,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( member_c_d_set_a @ A2 @ ( insert_c_d_set_a @ B @ A ) )
      = ( ( A2 = B )
        | ( member_c_d_set_a @ A2 @ A ) ) ) ).

% insert_iff
thf(fact_1122_insertCI,axiom,
    ! [A2: ( c > d ) > set_a,B3: set_c_d_set_a,B: ( c > d ) > set_a] :
      ( ( ~ ( member_c_d_set_a @ A2 @ B3 )
       => ( A2 = B ) )
     => ( member_c_d_set_a @ A2 @ ( insert_c_d_set_a @ B @ B3 ) ) ) ).

% insertCI
thf(fact_1123_singletonI,axiom,
    ! [A2: ( c > d ) > set_a] : ( member_c_d_set_a @ A2 @ ( insert_c_d_set_a @ A2 @ bot_bo738396921950161403_set_a ) ) ).

% singletonI
thf(fact_1124_insert__subset,axiom,
    ! [X: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ ( insert_c_d_set_a @ X @ A ) @ B3 )
      = ( ( member_c_d_set_a @ X @ B3 )
        & ( ord_le5982164083705284911_set_a @ A @ B3 ) ) ) ).

% insert_subset
thf(fact_1125_Int__insert__left__if0,axiom,
    ! [A2: ( c > d ) > set_a,C2: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ~ ( member_c_d_set_a @ A2 @ C2 )
     => ( ( inf_in754637537901350525_set_a @ ( insert_c_d_set_a @ A2 @ B3 ) @ C2 )
        = ( inf_in754637537901350525_set_a @ B3 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_1126_Int__insert__left__if1,axiom,
    ! [A2: ( c > d ) > set_a,C2: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ A2 @ C2 )
     => ( ( inf_in754637537901350525_set_a @ ( insert_c_d_set_a @ A2 @ B3 ) @ C2 )
        = ( insert_c_d_set_a @ A2 @ ( inf_in754637537901350525_set_a @ B3 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1127_Int__insert__right__if0,axiom,
    ! [A2: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ~ ( member_c_d_set_a @ A2 @ A )
     => ( ( inf_in754637537901350525_set_a @ A @ ( insert_c_d_set_a @ A2 @ B3 ) )
        = ( inf_in754637537901350525_set_a @ A @ B3 ) ) ) ).

% Int_insert_right_if0
thf(fact_1128_Int__insert__right__if1,axiom,
    ! [A2: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ A2 @ A )
     => ( ( inf_in754637537901350525_set_a @ A @ ( insert_c_d_set_a @ A2 @ B3 ) )
        = ( insert_c_d_set_a @ A2 @ ( inf_in754637537901350525_set_a @ A @ B3 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1129_local_Oinf__bot__left,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( inf_e_f_a2 @ empty_interp_e_f_a @ X )
      = empty_interp_e_f_a ) ).

% local.inf_bot_left
thf(fact_1130_local_Oinf__bot__right,axiom,
    ! [X: ( e > f ) > set_a] :
      ( ( inf_e_f_a2 @ X @ empty_interp_e_f_a )
      = empty_interp_e_f_a ) ).

% local.inf_bot_right
thf(fact_1131_insert__disjoint_I1_J,axiom,
    ! [A2: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ( inf_in754637537901350525_set_a @ ( insert_c_d_set_a @ A2 @ A ) @ B3 )
        = bot_bo738396921950161403_set_a )
      = ( ~ ( member_c_d_set_a @ A2 @ B3 )
        & ( ( inf_in754637537901350525_set_a @ A @ B3 )
          = bot_bo738396921950161403_set_a ) ) ) ).

% insert_disjoint(1)
thf(fact_1132_insert__disjoint_I2_J,axiom,
    ! [A2: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( bot_bo738396921950161403_set_a
        = ( inf_in754637537901350525_set_a @ ( insert_c_d_set_a @ A2 @ A ) @ B3 ) )
      = ( ~ ( member_c_d_set_a @ A2 @ B3 )
        & ( bot_bo738396921950161403_set_a
          = ( inf_in754637537901350525_set_a @ A @ B3 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1133_disjoint__insert_I1_J,axiom,
    ! [B3: set_c_d_set_a,A2: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( ( inf_in754637537901350525_set_a @ B3 @ ( insert_c_d_set_a @ A2 @ A ) )
        = bot_bo738396921950161403_set_a )
      = ( ~ ( member_c_d_set_a @ A2 @ B3 )
        & ( ( inf_in754637537901350525_set_a @ B3 @ A )
          = bot_bo738396921950161403_set_a ) ) ) ).

% disjoint_insert(1)
thf(fact_1134_disjoint__insert_I2_J,axiom,
    ! [A: set_c_d_set_a,B: ( c > d ) > set_a,B3: set_c_d_set_a] :
      ( ( bot_bo738396921950161403_set_a
        = ( inf_in754637537901350525_set_a @ A @ ( insert_c_d_set_a @ B @ B3 ) ) )
      = ( ~ ( member_c_d_set_a @ B @ A )
        & ( bot_bo738396921950161403_set_a
          = ( inf_in754637537901350525_set_a @ A @ B3 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1135_singletonD,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ B @ ( insert_c_d_set_a @ A2 @ bot_bo738396921950161403_set_a ) )
     => ( B = A2 ) ) ).

% singletonD
thf(fact_1136_singleton__iff,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ B @ ( insert_c_d_set_a @ A2 @ bot_bo738396921950161403_set_a ) )
      = ( B = A2 ) ) ).

% singleton_iff
thf(fact_1137_mk__disjoint__insert,axiom,
    ! [A2: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( member_c_d_set_a @ A2 @ A )
     => ? [B6: set_c_d_set_a] :
          ( ( A
            = ( insert_c_d_set_a @ A2 @ B6 ) )
          & ~ ( member_c_d_set_a @ A2 @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_1138_insert__eq__iff,axiom,
    ! [A2: ( c > d ) > set_a,A: set_c_d_set_a,B: ( c > d ) > set_a,B3: set_c_d_set_a] :
      ( ~ ( member_c_d_set_a @ A2 @ A )
     => ( ~ ( member_c_d_set_a @ B @ B3 )
       => ( ( ( insert_c_d_set_a @ A2 @ A )
            = ( insert_c_d_set_a @ B @ B3 ) )
          = ( ( ( A2 = B )
             => ( A = B3 ) )
            & ( ( A2 != B )
             => ? [C5: set_c_d_set_a] :
                  ( ( A
                    = ( insert_c_d_set_a @ B @ C5 ) )
                  & ~ ( member_c_d_set_a @ B @ C5 )
                  & ( B3
                    = ( insert_c_d_set_a @ A2 @ C5 ) )
                  & ~ ( member_c_d_set_a @ A2 @ C5 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1139_insert__absorb,axiom,
    ! [A2: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( member_c_d_set_a @ A2 @ A )
     => ( ( insert_c_d_set_a @ A2 @ A )
        = A ) ) ).

% insert_absorb
thf(fact_1140_insert__ident,axiom,
    ! [X: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ~ ( member_c_d_set_a @ X @ A )
     => ( ~ ( member_c_d_set_a @ X @ B3 )
       => ( ( ( insert_c_d_set_a @ X @ A )
            = ( insert_c_d_set_a @ X @ B3 ) )
          = ( A = B3 ) ) ) ) ).

% insert_ident
thf(fact_1141_Set_Oset__insert,axiom,
    ! [X: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( member_c_d_set_a @ X @ A )
     => ~ ! [B6: set_c_d_set_a] :
            ( ( A
              = ( insert_c_d_set_a @ X @ B6 ) )
           => ( member_c_d_set_a @ X @ B6 ) ) ) ).

% Set.set_insert
thf(fact_1142_insertI2,axiom,
    ! [A2: ( c > d ) > set_a,B3: set_c_d_set_a,B: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ A2 @ B3 )
     => ( member_c_d_set_a @ A2 @ ( insert_c_d_set_a @ B @ B3 ) ) ) ).

% insertI2
thf(fact_1143_insertI1,axiom,
    ! [A2: ( c > d ) > set_a,B3: set_c_d_set_a] : ( member_c_d_set_a @ A2 @ ( insert_c_d_set_a @ A2 @ B3 ) ) ).

% insertI1
thf(fact_1144_insertE,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( member_c_d_set_a @ A2 @ ( insert_c_d_set_a @ B @ A ) )
     => ( ( A2 != B )
       => ( member_c_d_set_a @ A2 @ A ) ) ) ).

% insertE
thf(fact_1145_subset__insert,axiom,
    ! [X: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ~ ( member_c_d_set_a @ X @ A )
     => ( ( ord_le5982164083705284911_set_a @ A @ ( insert_c_d_set_a @ X @ B3 ) )
        = ( ord_le5982164083705284911_set_a @ A @ B3 ) ) ) ).

% subset_insert
thf(fact_1146_cSup__eq__maximum,axiom,
    ! [Z: ( c > d ) > set_a,X5: set_c_d_set_a] :
      ( ( member_c_d_set_a @ Z @ X5 )
     => ( ! [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ X5 )
           => ( ord_le8464990428230162895_set_a @ X2 @ Z ) )
       => ( ( comple3834726295627996700_set_a @ X5 )
          = Z ) ) ) ).

% cSup_eq_maximum
thf(fact_1147_Int__insert__right,axiom,
    ! [A2: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ( member_c_d_set_a @ A2 @ A )
       => ( ( inf_in754637537901350525_set_a @ A @ ( insert_c_d_set_a @ A2 @ B3 ) )
          = ( insert_c_d_set_a @ A2 @ ( inf_in754637537901350525_set_a @ A @ B3 ) ) ) )
      & ( ~ ( member_c_d_set_a @ A2 @ A )
       => ( ( inf_in754637537901350525_set_a @ A @ ( insert_c_d_set_a @ A2 @ B3 ) )
          = ( inf_in754637537901350525_set_a @ A @ B3 ) ) ) ) ).

% Int_insert_right
thf(fact_1148_Int__insert__left,axiom,
    ! [A2: ( c > d ) > set_a,C2: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ( member_c_d_set_a @ A2 @ C2 )
       => ( ( inf_in754637537901350525_set_a @ ( insert_c_d_set_a @ A2 @ B3 ) @ C2 )
          = ( insert_c_d_set_a @ A2 @ ( inf_in754637537901350525_set_a @ B3 @ C2 ) ) ) )
      & ( ~ ( member_c_d_set_a @ A2 @ C2 )
       => ( ( inf_in754637537901350525_set_a @ ( insert_c_d_set_a @ A2 @ B3 ) @ C2 )
          = ( inf_in754637537901350525_set_a @ B3 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_1149_insert__UNIV,axiom,
    ! [X: ( c > d ) > set_a] :
      ( ( insert_c_d_set_a @ X @ top_to4267977599310771935_set_a )
      = top_to4267977599310771935_set_a ) ).

% insert_UNIV
thf(fact_1150_cSup__least,axiom,
    ! [X5: set_c_d_set_a,Z: ( c > d ) > set_a] :
      ( ( X5 != bot_bo738396921950161403_set_a )
     => ( ! [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ X5 )
           => ( ord_le8464990428230162895_set_a @ X2 @ Z ) )
       => ( ord_le8464990428230162895_set_a @ ( comple3834726295627996700_set_a @ X5 ) @ Z ) ) ) ).

% cSup_least
thf(fact_1151_cSup__eq__non__empty,axiom,
    ! [X5: set_c_d_set_a,A2: ( c > d ) > set_a] :
      ( ( X5 != bot_bo738396921950161403_set_a )
     => ( ! [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ X5 )
           => ( ord_le8464990428230162895_set_a @ X2 @ A2 ) )
       => ( ! [Y2: ( c > d ) > set_a] :
              ( ! [X4: ( c > d ) > set_a] :
                  ( ( member_c_d_set_a @ X4 @ X5 )
                 => ( ord_le8464990428230162895_set_a @ X4 @ Y2 ) )
             => ( ord_le8464990428230162895_set_a @ A2 @ Y2 ) )
         => ( ( comple3834726295627996700_set_a @ X5 )
            = A2 ) ) ) ) ).

% cSup_eq_non_empty
thf(fact_1152_complete__lattice__class_OSup__UNIV,axiom,
    ( ( comple6131501996466690428_set_a @ top_to5717711934741766719_set_a )
    = top_to4267977599310771935_set_a ) ).

% complete_lattice_class.Sup_UNIV
thf(fact_1153_complete__lattice__class_OSup__UNIV,axiom,
    ( ( comple3834726295627996700_set_a @ top_to4267977599310771935_set_a )
    = top_top_c_d_set_a ) ).

% complete_lattice_class.Sup_UNIV
thf(fact_1154_Union__UNIV,axiom,
    ( ( comple6131501996466690428_set_a @ top_to5717711934741766719_set_a )
    = top_to4267977599310771935_set_a ) ).

% Union_UNIV
thf(fact_1155_bounded__semilattice__inf__top__class_Oinf__top_Osemilattice__neutr__order__axioms,axiom,
    semila2050215183435169853_set_a @ inf_in754637537901350525_set_a @ top_to4267977599310771935_set_a @ ord_le5982164083705284911_set_a @ ord_le3685282097655362107_set_a ).

% bounded_semilattice_inf_top_class.inf_top.semilattice_neutr_order_axioms
thf(fact_1156_bounded__semilattice__inf__top__class_Oinf__top_Osemilattice__neutr__order__axioms,axiom,
    semila6957839794703059165_set_a @ inf_inf_c_d_set_a @ top_top_c_d_set_a @ ord_le8464990428230162895_set_a @ ord_less_c_d_set_a ).

% bounded_semilattice_inf_top_class.inf_top.semilattice_neutr_order_axioms
thf(fact_1157_complete__lattice__class_OSup__eqI,axiom,
    ! [A: set_c_d_set_a,X: ( c > d ) > set_a] :
      ( ! [Y2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ Y2 @ A )
         => ( ord_le8464990428230162895_set_a @ Y2 @ X ) )
     => ( ! [Y2: ( c > d ) > set_a] :
            ( ! [Z3: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ Z3 @ A )
               => ( ord_le8464990428230162895_set_a @ Z3 @ Y2 ) )
           => ( ord_le8464990428230162895_set_a @ X @ Y2 ) )
       => ( ( comple3834726295627996700_set_a @ A )
          = X ) ) ) ).

% complete_lattice_class.Sup_eqI
thf(fact_1158_complete__lattice__class_OSup__mono,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ! [A5: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ A5 @ A )
         => ? [X4: ( c > d ) > set_a] :
              ( ( member_c_d_set_a @ X4 @ B3 )
              & ( ord_le8464990428230162895_set_a @ A5 @ X4 ) ) )
     => ( ord_le8464990428230162895_set_a @ ( comple3834726295627996700_set_a @ A ) @ ( comple3834726295627996700_set_a @ B3 ) ) ) ).

% complete_lattice_class.Sup_mono
thf(fact_1159_complete__lattice__class_OSup__least,axiom,
    ! [A: set_c_d_set_a,Z: ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X2 @ A )
         => ( ord_le8464990428230162895_set_a @ X2 @ Z ) )
     => ( ord_le8464990428230162895_set_a @ ( comple3834726295627996700_set_a @ A ) @ Z ) ) ).

% complete_lattice_class.Sup_least
thf(fact_1160_complete__lattice__class_OSup__upper,axiom,
    ! [X: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( member_c_d_set_a @ X @ A )
     => ( ord_le8464990428230162895_set_a @ X @ ( comple3834726295627996700_set_a @ A ) ) ) ).

% complete_lattice_class.Sup_upper
thf(fact_1161_complete__lattice__class_OSup__le__iff,axiom,
    ! [A: set_c_d_set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ ( comple3834726295627996700_set_a @ A ) @ B )
      = ( ! [X3: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X3 @ A )
           => ( ord_le8464990428230162895_set_a @ X3 @ B ) ) ) ) ).

% complete_lattice_class.Sup_le_iff
thf(fact_1162_complete__lattice__class_OSup__upper2,axiom,
    ! [U: ( c > d ) > set_a,A: set_c_d_set_a,V: ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ U @ A )
     => ( ( ord_le8464990428230162895_set_a @ V @ U )
       => ( ord_le8464990428230162895_set_a @ V @ ( comple3834726295627996700_set_a @ A ) ) ) ) ).

% complete_lattice_class.Sup_upper2
thf(fact_1163_complete__lattice__class_Oless__eq__Sup,axiom,
    ! [A: set_c_d_set_a,U: ( c > d ) > set_a] :
      ( ! [V2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ V2 @ A )
         => ( ord_le8464990428230162895_set_a @ U @ V2 ) )
     => ( ( A != bot_bo738396921950161403_set_a )
       => ( ord_le8464990428230162895_set_a @ U @ ( comple3834726295627996700_set_a @ A ) ) ) ) ).

% complete_lattice_class.less_eq_Sup
thf(fact_1164_complete__lattice__class_OSup__subset__mono,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A @ B3 )
     => ( ord_le8464990428230162895_set_a @ ( comple3834726295627996700_set_a @ A ) @ ( comple3834726295627996700_set_a @ B3 ) ) ) ).

% complete_lattice_class.Sup_subset_mono
thf(fact_1165_complete__lattice__class_OSup__inter__less__eq,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] : ( ord_le8464990428230162895_set_a @ ( comple3834726295627996700_set_a @ ( inf_in754637537901350525_set_a @ A @ B3 ) ) @ ( inf_inf_c_d_set_a @ ( comple3834726295627996700_set_a @ A ) @ ( comple3834726295627996700_set_a @ B3 ) ) ) ).

% complete_lattice_class.Sup_inter_less_eq
thf(fact_1166_set__closure__property__admissible,axiom,
    ! [S4: a > a > set_a] : ( comple1957918121334358780_set_a @ comple3834726295627996700_set_a @ ord_le8464990428230162895_set_a @ ( set_cl2807270042661212426_a_c_d @ S4 ) ) ).

% set_closure_property_admissible
thf(fact_1167_set__closure__property__admissible,axiom,
    ! [S4: a > a > set_a] : ( comple7485627890665750396_set_a @ comple139064028104612508_set_a @ ord_le4769328160706778703_set_a @ ( set_cl6455730915570636170_a_e_f @ S4 ) ) ).

% set_closure_property_admissible
thf(fact_1168_Diff__iff,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ ( minus_1665977719694084726_set_a @ A @ B3 ) )
      = ( ( member_c_d_set_a @ C @ A )
        & ~ ( member_c_d_set_a @ C @ B3 ) ) ) ).

% Diff_iff
thf(fact_1169_DiffI,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ A )
     => ( ~ ( member_c_d_set_a @ C @ B3 )
       => ( member_c_d_set_a @ C @ ( minus_1665977719694084726_set_a @ A @ B3 ) ) ) ) ).

% DiffI
thf(fact_1170_insert__Diff1,axiom,
    ! [X: ( c > d ) > set_a,B3: set_c_d_set_a,A: set_c_d_set_a] :
      ( ( member_c_d_set_a @ X @ B3 )
     => ( ( minus_1665977719694084726_set_a @ ( insert_c_d_set_a @ X @ A ) @ B3 )
        = ( minus_1665977719694084726_set_a @ A @ B3 ) ) ) ).

% insert_Diff1
thf(fact_1171_Diff__insert0,axiom,
    ! [X: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ~ ( member_c_d_set_a @ X @ A )
     => ( ( minus_1665977719694084726_set_a @ A @ ( insert_c_d_set_a @ X @ B3 ) )
        = ( minus_1665977719694084726_set_a @ A @ B3 ) ) ) ).

% Diff_insert0
thf(fact_1172_Diff__UNIV,axiom,
    ! [A: set_c_d_set_a] :
      ( ( minus_1665977719694084726_set_a @ A @ top_to4267977599310771935_set_a )
      = bot_bo738396921950161403_set_a ) ).

% Diff_UNIV
thf(fact_1173_insert__Diff__if,axiom,
    ! [X: ( c > d ) > set_a,B3: set_c_d_set_a,A: set_c_d_set_a] :
      ( ( ( member_c_d_set_a @ X @ B3 )
       => ( ( minus_1665977719694084726_set_a @ ( insert_c_d_set_a @ X @ A ) @ B3 )
          = ( minus_1665977719694084726_set_a @ A @ B3 ) ) )
      & ( ~ ( member_c_d_set_a @ X @ B3 )
       => ( ( minus_1665977719694084726_set_a @ ( insert_c_d_set_a @ X @ A ) @ B3 )
          = ( insert_c_d_set_a @ X @ ( minus_1665977719694084726_set_a @ A @ B3 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1174_Diff__insert__absorb,axiom,
    ! [X: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ~ ( member_c_d_set_a @ X @ A )
     => ( ( minus_1665977719694084726_set_a @ ( insert_c_d_set_a @ X @ A ) @ ( insert_c_d_set_a @ X @ bot_bo738396921950161403_set_a ) )
        = A ) ) ).

% Diff_insert_absorb
thf(fact_1175_insert__Diff,axiom,
    ! [A2: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( member_c_d_set_a @ A2 @ A )
     => ( ( insert_c_d_set_a @ A2 @ ( minus_1665977719694084726_set_a @ A @ ( insert_c_d_set_a @ A2 @ bot_bo738396921950161403_set_a ) ) )
        = A ) ) ).

% insert_Diff
thf(fact_1176_subset__Diff__insert,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a,X: ( c > d ) > set_a,C2: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A @ ( minus_1665977719694084726_set_a @ B3 @ ( insert_c_d_set_a @ X @ C2 ) ) )
      = ( ( ord_le5982164083705284911_set_a @ A @ ( minus_1665977719694084726_set_a @ B3 @ C2 ) )
        & ~ ( member_c_d_set_a @ X @ A ) ) ) ).

% subset_Diff_insert
thf(fact_1177_psubset__imp__ex__mem,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A @ B3 )
     => ? [B4: ( c > d ) > set_a] : ( member_c_d_set_a @ B4 @ ( minus_1665977719694084726_set_a @ B3 @ A ) ) ) ).

% psubset_imp_ex_mem
thf(fact_1178_DiffD2,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ ( minus_1665977719694084726_set_a @ A @ B3 ) )
     => ~ ( member_c_d_set_a @ C @ B3 ) ) ).

% DiffD2
thf(fact_1179_DiffD1,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ ( minus_1665977719694084726_set_a @ A @ B3 ) )
     => ( member_c_d_set_a @ C @ A ) ) ).

% DiffD1
thf(fact_1180_DiffE,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ ( minus_1665977719694084726_set_a @ A @ B3 ) )
     => ~ ( ( member_c_d_set_a @ C @ A )
         => ( member_c_d_set_a @ C @ B3 ) ) ) ).

% DiffE
thf(fact_1181_subset__insert__iff,axiom,
    ! [A: set_c_d_set_a,X: ( c > d ) > set_a,B3: set_c_d_set_a] :
      ( ( ord_le5982164083705284911_set_a @ A @ ( insert_c_d_set_a @ X @ B3 ) )
      = ( ( ( member_c_d_set_a @ X @ A )
         => ( ord_le5982164083705284911_set_a @ ( minus_1665977719694084726_set_a @ A @ ( insert_c_d_set_a @ X @ bot_bo738396921950161403_set_a ) ) @ B3 ) )
        & ( ~ ( member_c_d_set_a @ X @ A )
         => ( ord_le5982164083705284911_set_a @ A @ B3 ) ) ) ) ).

% subset_insert_iff
thf(fact_1182_psubset__insert__iff,axiom,
    ! [A: set_c_d_set_a,X: ( c > d ) > set_a,B3: set_c_d_set_a] :
      ( ( ord_le3685282097655362107_set_a @ A @ ( insert_c_d_set_a @ X @ B3 ) )
      = ( ( ( member_c_d_set_a @ X @ B3 )
         => ( ord_le3685282097655362107_set_a @ A @ B3 ) )
        & ( ~ ( member_c_d_set_a @ X @ B3 )
         => ( ( ( member_c_d_set_a @ X @ A )
             => ( ord_le3685282097655362107_set_a @ ( minus_1665977719694084726_set_a @ A @ ( insert_c_d_set_a @ X @ bot_bo738396921950161403_set_a ) ) @ B3 ) )
            & ( ~ ( member_c_d_set_a @ X @ A )
             => ( ord_le5982164083705284911_set_a @ A @ B3 ) ) ) ) ) ) ).

% psubset_insert_iff
thf(fact_1183_semilattice__inf__class_OInf__fin_Osemilattice__order__set__axioms,axiom,
    lattic1995125144389820681_set_a @ inf_inf_c_d_set_a @ ord_le8464990428230162895_set_a @ ord_less_c_d_set_a ).

% semilattice_inf_class.Inf_fin.semilattice_order_set_axioms
thf(fact_1184_bounded__semilattice__inf__top__class_Oinf__top_Osemilattice__neutr__axioms,axiom,
    semila3717735699007493233_set_a @ inf_in754637537901350525_set_a @ top_to4267977599310771935_set_a ).

% bounded_semilattice_inf_top_class.inf_top.semilattice_neutr_axioms
thf(fact_1185_bounded__semilattice__inf__top__class_Oinf__top_Omonoid__axioms,axiom,
    monoid_set_c_d_set_a @ inf_in754637537901350525_set_a @ top_to4267977599310771935_set_a ).

% bounded_semilattice_inf_top_class.inf_top.monoid_axioms
thf(fact_1186_diff__shunt__var,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ( minus_6165026464846083862_set_a @ X @ Y )
        = bot_bot_c_d_set_a )
      = ( ord_le8464990428230162895_set_a @ X @ Y ) ) ).

% diff_shunt_var
thf(fact_1187_boolean__algebra_Oconj__one__right,axiom,
    ! [X: set_c_d_set_a] :
      ( ( inf_in754637537901350525_set_a @ X @ top_to4267977599310771935_set_a )
      = X ) ).

% boolean_algebra.conj_one_right
thf(fact_1188_image__eqI,axiom,
    ! [B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_c_d_set_a @ X @ A )
       => ( member_c_d_set_a @ B @ ( image_5710119992958135237_set_a @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_1189_complete__lattice__class_OSUP__eq,axiom,
    ! [A: set_c_d_set_a,B3: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,G2: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [I: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ I @ A )
         => ? [X4: ( c > d ) > set_a] :
              ( ( member_c_d_set_a @ X4 @ B3 )
              & ( ord_le8464990428230162895_set_a @ ( F @ I ) @ ( G2 @ X4 ) ) ) )
     => ( ! [J: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ J @ B3 )
           => ? [X4: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ X4 @ A )
                & ( ord_le8464990428230162895_set_a @ ( G2 @ J ) @ ( F @ X4 ) ) ) )
       => ( ( comple3834726295627996700_set_a @ ( image_5710119992958135237_set_a @ F @ A ) )
          = ( comple3834726295627996700_set_a @ ( image_5710119992958135237_set_a @ G2 @ B3 ) ) ) ) ) ).

% complete_lattice_class.SUP_eq
thf(fact_1190_rev__image__eqI,axiom,
    ! [X: ( c > d ) > set_a,A: set_c_d_set_a,B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ X @ A )
     => ( ( B
          = ( F @ X ) )
       => ( member_c_d_set_a @ B @ ( image_5710119992958135237_set_a @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_1191_imageI,axiom,
    ! [X: ( c > d ) > set_a,A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ( member_c_d_set_a @ X @ A )
     => ( member_c_d_set_a @ ( F @ X ) @ ( image_5710119992958135237_set_a @ F @ A ) ) ) ).

% imageI
thf(fact_1192_surjD,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ( image_5710119992958135237_set_a @ F @ top_to4267977599310771935_set_a )
        = top_to4267977599310771935_set_a )
     => ? [X2: ( c > d ) > set_a] :
          ( Y
          = ( F @ X2 ) ) ) ).

% surjD
thf(fact_1193_surjE,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ( image_5710119992958135237_set_a @ F @ top_to4267977599310771935_set_a )
        = top_to4267977599310771935_set_a )
     => ~ ! [X2: ( c > d ) > set_a] :
            ( Y
           != ( F @ X2 ) ) ) ).

% surjE
thf(fact_1194_surjI,axiom,
    ! [G2: ( ( c > d ) > set_a ) > ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( G2 @ ( F @ X2 ) )
          = X2 )
     => ( ( image_5710119992958135237_set_a @ G2 @ top_to4267977599310771935_set_a )
        = top_to4267977599310771935_set_a ) ) ).

% surjI
thf(fact_1195_rangeI,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a] : ( member_c_d_set_a @ ( F @ X ) @ ( image_5710119992958135237_set_a @ F @ top_to4267977599310771935_set_a ) ) ).

% rangeI
thf(fact_1196_surj__def,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ( ( image_5710119992958135237_set_a @ F @ top_to4267977599310771935_set_a )
        = top_to4267977599310771935_set_a )
      = ( ! [Y4: ( c > d ) > set_a] :
          ? [X3: ( c > d ) > set_a] :
            ( Y4
            = ( F @ X3 ) ) ) ) ).

% surj_def
thf(fact_1197_range__eqI,axiom,
    ! [B: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a] :
      ( ( B
        = ( F @ X ) )
     => ( member_c_d_set_a @ B @ ( image_5710119992958135237_set_a @ F @ top_to4267977599310771935_set_a ) ) ) ).

% range_eqI
thf(fact_1198_image__subsetI,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B3: set_c_d_set_a] :
      ( ! [X2: ( c > d ) > set_a] :
          ( ( member_c_d_set_a @ X2 @ A )
         => ( member_c_d_set_a @ ( F @ X2 ) @ B3 ) )
     => ( ord_le5982164083705284911_set_a @ ( image_5710119992958135237_set_a @ F @ A ) @ B3 ) ) ).

% image_subsetI
thf(fact_1199_range__subsetD,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,B3: set_c_d_set_a,I3: ( c > d ) > set_a] :
      ( ( ord_le5982164083705284911_set_a @ ( image_5710119992958135237_set_a @ F @ top_to4267977599310771935_set_a ) @ B3 )
     => ( member_c_d_set_a @ ( F @ I3 ) @ B3 ) ) ).

% range_subsetD
thf(fact_1200_bounded__semilattice__inf__top__class_Oinf__top_Ocomm__monoid__axioms,axiom,
    comm_m5313561445344189892_set_a @ inf_in754637537901350525_set_a @ top_to4267977599310771935_set_a ).

% bounded_semilattice_inf_top_class.inf_top.comm_monoid_axioms
thf(fact_1201_cSUP__least,axiom,
    ! [A: set_c_d_set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,M3: ( c > d ) > set_a] :
      ( ( A != bot_bo738396921950161403_set_a )
     => ( ! [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ A )
           => ( ord_le8464990428230162895_set_a @ ( F @ X2 ) @ M3 ) )
       => ( ord_le8464990428230162895_set_a @ ( comple3834726295627996700_set_a @ ( image_5710119992958135237_set_a @ F @ A ) ) @ M3 ) ) ) ).

% cSUP_least
thf(fact_1202_complete__lattice__class_OSUP__eq__iff,axiom,
    ! [I4: set_c_d_set_a,C: ( c > d ) > set_a,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ( I4 != bot_bo738396921950161403_set_a )
     => ( ! [I: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ I @ I4 )
           => ( ord_le8464990428230162895_set_a @ C @ ( F @ I ) ) )
       => ( ( ( comple3834726295627996700_set_a @ ( image_5710119992958135237_set_a @ F @ I4 ) )
            = C )
          = ( ! [X3: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ X3 @ I4 )
               => ( ( F @ X3 )
                  = C ) ) ) ) ) ) ).

% complete_lattice_class.SUP_eq_iff
thf(fact_1203_Sup__SUP__eq,axiom,
    ( comple5290581719055393889et_a_o
    = ( ^ [S5: set_c_d_set_a_o,X3: ( c > d ) > set_a] : ( member_c_d_set_a @ X3 @ ( comple6131501996466690428_set_a @ ( image_8552787320881293370_set_a @ collect_c_d_set_a @ S5 ) ) ) ) ) ).

% Sup_SUP_eq
thf(fact_1204_in__image__insert__iff,axiom,
    ! [B3: set_set_c_d_set_a,X: ( c > d ) > set_a,A: set_c_d_set_a] :
      ( ! [C6: set_c_d_set_a] :
          ( ( member_set_c_d_set_a @ C6 @ B3 )
         => ~ ( member_c_d_set_a @ X @ C6 ) )
     => ( ( member_set_c_d_set_a @ A @ ( image_5418612861375423429_set_a @ ( insert_c_d_set_a @ X ) @ B3 ) )
        = ( ( member_c_d_set_a @ X @ A )
          & ( member_set_c_d_set_a @ ( minus_1665977719694084726_set_a @ A @ ( insert_c_d_set_a @ X @ bot_bo738396921950161403_set_a ) ) @ B3 ) ) ) ) ).

% in_image_insert_iff
thf(fact_1205_is__singletonI_H,axiom,
    ! [A: set_c_d_set_a] :
      ( ( A != bot_bo738396921950161403_set_a )
     => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ A )
           => ( ( member_c_d_set_a @ Y2 @ A )
             => ( X2 = Y2 ) ) )
       => ( is_sin6979784932356128547_set_a @ A ) ) ) ).

% is_singletonI'
thf(fact_1206_semilattice__inf__class_Oinf_Osemilattice__order__axioms,axiom,
    semila1630236661048524575_set_a @ inf_inf_c_d_set_a @ ord_le8464990428230162895_set_a @ ord_less_c_d_set_a ).

% semilattice_inf_class.inf.semilattice_order_axioms
thf(fact_1207_fixp__induct,axiom,
    ! [P: ( ( c > d ) > set_a ) > $o,F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ( comple1957918121334358780_set_a @ comple3834726295627996700_set_a @ ord_le8464990428230162895_set_a @ P )
     => ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F )
       => ( ( P @ ( comple3834726295627996700_set_a @ bot_bo738396921950161403_set_a ) )
         => ( ! [X2: ( c > d ) > set_a] :
                ( ( P @ X2 )
               => ( P @ ( F @ X2 ) ) )
           => ( P @ ( comple2361085228800170300_set_a @ F ) ) ) ) ) ) ).

% fixp_induct
thf(fact_1208_local_Ofinite__Inf__in,axiom,
    ! [A: set_c_d_set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( A != bot_bo738396921950161403_set_a )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] :
              ( ( member_c_d_set_a @ X2 @ A )
             => ( ( member_c_d_set_a @ Y2 @ A )
               => ( member_c_d_set_a @ ( inf_c_d_a2 @ X2 @ Y2 ) @ A ) ) )
         => ( member_c_d_set_a @ ( inf_c_d_a @ A ) @ A ) ) ) ) ).

% local.finite_Inf_in
thf(fact_1209_local_Ofinite__has__maximal2,axiom,
    ! [A: set_c_d_set_a,A2: ( c > d ) > set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( member_c_d_set_a @ A2 @ A )
       => ? [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ A )
            & ( smaller_interp_c_d_a @ A2 @ X2 )
            & ! [Xa: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ Xa @ A )
               => ( ( smaller_interp_c_d_a @ X2 @ Xa )
                 => ( X2 = Xa ) ) ) ) ) ) ).

% local.finite_has_maximal2
thf(fact_1210_local_Ofinite__has__minimal2,axiom,
    ! [A: set_c_d_set_a,A2: ( c > d ) > set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( member_c_d_set_a @ A2 @ A )
       => ? [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ A )
            & ( smaller_interp_c_d_a @ X2 @ A2 )
            & ! [Xa: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ Xa @ A )
               => ( ( smaller_interp_c_d_a @ Xa @ X2 )
                 => ( X2 = Xa ) ) ) ) ) ) ).

% local.finite_has_minimal2
thf(fact_1211_le__cSup__finite,axiom,
    ! [X5: set_c_d_set_a,X: ( c > d ) > set_a] :
      ( ( finite3330819693523053784_set_a @ X5 )
     => ( ( member_c_d_set_a @ X @ X5 )
       => ( ord_le8464990428230162895_set_a @ X @ ( comple3834726295627996700_set_a @ X5 ) ) ) ) ).

% le_cSup_finite
thf(fact_1212_fixp__unfold,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( comple2361085228800170300_set_a @ F )
        = ( F @ ( comple2361085228800170300_set_a @ F ) ) ) ) ).

% fixp_unfold
thf(fact_1213_fixp__lowerbound,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ( ord_le8464990428230162895_set_a @ ( F @ Z ) @ Z )
       => ( ord_le8464990428230162895_set_a @ ( comple2361085228800170300_set_a @ F ) @ Z ) ) ) ).

% fixp_lowerbound
thf(fact_1214_finite__remove__induct,axiom,
    ! [B3: set_c_d_set_a,P: set_c_d_set_a > $o] :
      ( ( finite3330819693523053784_set_a @ B3 )
     => ( ( P @ bot_bo738396921950161403_set_a )
       => ( ! [A6: set_c_d_set_a] :
              ( ( finite3330819693523053784_set_a @ A6 )
             => ( ( A6 != bot_bo738396921950161403_set_a )
               => ( ( ord_le5982164083705284911_set_a @ A6 @ B3 )
                 => ( ! [X4: ( c > d ) > set_a] :
                        ( ( member_c_d_set_a @ X4 @ A6 )
                       => ( P @ ( minus_1665977719694084726_set_a @ A6 @ ( insert_c_d_set_a @ X4 @ bot_bo738396921950161403_set_a ) ) ) )
                   => ( P @ A6 ) ) ) ) )
         => ( P @ B3 ) ) ) ) ).

% finite_remove_induct
thf(fact_1215_finite__Plus__UNIV__iff,axiom,
    ( ( finite5989733633321134460_set_a @ top_to279427854467338187_set_a )
    = ( ( finite3330819693523053784_set_a @ top_to4267977599310771935_set_a )
      & ( finite3330819693523053784_set_a @ top_to4267977599310771935_set_a ) ) ) ).

% finite_Plus_UNIV_iff
thf(fact_1216_order__class_Ofinite__has__minimal2,axiom,
    ! [A: set_c_d_set_a,A2: ( c > d ) > set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( member_c_d_set_a @ A2 @ A )
       => ? [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ A )
            & ( ord_le8464990428230162895_set_a @ X2 @ A2 )
            & ! [Xa: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ Xa @ A )
               => ( ( ord_le8464990428230162895_set_a @ Xa @ X2 )
                 => ( X2 = Xa ) ) ) ) ) ) ).

% order_class.finite_has_minimal2
thf(fact_1217_order__class_Ofinite__has__maximal2,axiom,
    ! [A: set_c_d_set_a,A2: ( c > d ) > set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( member_c_d_set_a @ A2 @ A )
       => ? [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ A )
            & ( ord_le8464990428230162895_set_a @ A2 @ X2 )
            & ! [Xa: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ Xa @ A )
               => ( ( ord_le8464990428230162895_set_a @ X2 @ Xa )
                 => ( X2 = Xa ) ) ) ) ) ) ).

% order_class.finite_has_maximal2
thf(fact_1218_finite__prod,axiom,
    ( ( finite2397556900044337168_set_a @ top_to3895570120271872023_set_a )
    = ( ( finite3330819693523053784_set_a @ top_to4267977599310771935_set_a )
      & ( finite3330819693523053784_set_a @ top_to4267977599310771935_set_a ) ) ) ).

% finite_prod
thf(fact_1219_finite__Prod__UNIV,axiom,
    ( ( finite3330819693523053784_set_a @ top_to4267977599310771935_set_a )
   => ( ( finite3330819693523053784_set_a @ top_to4267977599310771935_set_a )
     => ( finite2397556900044337168_set_a @ top_to3895570120271872023_set_a ) ) ) ).

% finite_Prod_UNIV
thf(fact_1220_ex__new__if__finite,axiom,
    ! [A: set_c_d_set_a] :
      ( ~ ( finite3330819693523053784_set_a @ top_to4267977599310771935_set_a )
     => ( ( finite3330819693523053784_set_a @ A )
       => ? [A5: ( c > d ) > set_a] :
            ~ ( member_c_d_set_a @ A5 @ A ) ) ) ).

% ex_new_if_finite
thf(fact_1221_order__class_Ofinite__has__minimal,axiom,
    ! [A: set_c_d_set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( A != bot_bo738396921950161403_set_a )
       => ? [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ A )
            & ! [Xa: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ Xa @ A )
               => ( ( ord_le8464990428230162895_set_a @ Xa @ X2 )
                 => ( X2 = Xa ) ) ) ) ) ) ).

% order_class.finite_has_minimal
thf(fact_1222_order__class_Ofinite__has__maximal,axiom,
    ! [A: set_c_d_set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( A != bot_bo738396921950161403_set_a )
       => ? [X2: ( c > d ) > set_a] :
            ( ( member_c_d_set_a @ X2 @ A )
            & ! [Xa: ( c > d ) > set_a] :
                ( ( member_c_d_set_a @ Xa @ A )
               => ( ( ord_le8464990428230162895_set_a @ X2 @ Xa )
                 => ( X2 = Xa ) ) ) ) ) ) ).

% order_class.finite_has_maximal
thf(fact_1223_Finite__Set_Ofinite__set,axiom,
    ( ( finite457288119118821432_set_a @ top_to5717711934741766719_set_a )
    = ( finite3330819693523053784_set_a @ top_to4267977599310771935_set_a ) ) ).

% Finite_Set.finite_set
thf(fact_1224_finite__subset__induct,axiom,
    ! [F3: set_c_d_set_a,A: set_c_d_set_a,P: set_c_d_set_a > $o] :
      ( ( finite3330819693523053784_set_a @ F3 )
     => ( ( ord_le5982164083705284911_set_a @ F3 @ A )
       => ( ( P @ bot_bo738396921950161403_set_a )
         => ( ! [A5: ( c > d ) > set_a,F4: set_c_d_set_a] :
                ( ( finite3330819693523053784_set_a @ F4 )
               => ( ( member_c_d_set_a @ A5 @ A )
                 => ( ~ ( member_c_d_set_a @ A5 @ F4 )
                   => ( ( P @ F4 )
                     => ( P @ ( insert_c_d_set_a @ A5 @ F4 ) ) ) ) ) )
           => ( P @ F3 ) ) ) ) ) ).

% finite_subset_induct
thf(fact_1225_finite__subset__induct_H,axiom,
    ! [F3: set_c_d_set_a,A: set_c_d_set_a,P: set_c_d_set_a > $o] :
      ( ( finite3330819693523053784_set_a @ F3 )
     => ( ( ord_le5982164083705284911_set_a @ F3 @ A )
       => ( ( P @ bot_bo738396921950161403_set_a )
         => ( ! [A5: ( c > d ) > set_a,F4: set_c_d_set_a] :
                ( ( finite3330819693523053784_set_a @ F4 )
               => ( ( member_c_d_set_a @ A5 @ A )
                 => ( ( ord_le5982164083705284911_set_a @ F4 @ A )
                   => ( ~ ( member_c_d_set_a @ A5 @ F4 )
                     => ( ( P @ F4 )
                       => ( P @ ( insert_c_d_set_a @ A5 @ F4 ) ) ) ) ) ) )
           => ( P @ F3 ) ) ) ) ) ).

% finite_subset_induct'
thf(fact_1226_finite__fun__UNIVD2,axiom,
    ( ( finite3330819693523053784_set_a @ top_to4267977599310771935_set_a )
   => ( finite_finite_set_a @ top_top_set_set_a ) ) ).

% finite_fun_UNIVD2
thf(fact_1227_remove__induct,axiom,
    ! [P: set_c_d_set_a > $o,B3: set_c_d_set_a] :
      ( ( P @ bot_bo738396921950161403_set_a )
     => ( ( ~ ( finite3330819693523053784_set_a @ B3 )
         => ( P @ B3 ) )
       => ( ! [A6: set_c_d_set_a] :
              ( ( finite3330819693523053784_set_a @ A6 )
             => ( ( A6 != bot_bo738396921950161403_set_a )
               => ( ( ord_le5982164083705284911_set_a @ A6 @ B3 )
                 => ( ! [X4: ( c > d ) > set_a] :
                        ( ( member_c_d_set_a @ X4 @ A6 )
                       => ( P @ ( minus_1665977719694084726_set_a @ A6 @ ( insert_c_d_set_a @ X4 @ bot_bo738396921950161403_set_a ) ) ) )
                   => ( P @ A6 ) ) ) ) )
         => ( P @ B3 ) ) ) ) ).

% remove_induct
thf(fact_1228_finite__option__UNIV,axiom,
    ( ( finite1740182815655637662_set_a @ top_to1333438998097461157_set_a )
    = ( finite3330819693523053784_set_a @ top_to4267977599310771935_set_a ) ) ).

% finite_option_UNIV
thf(fact_1229_local_OInf__fin_Oremove,axiom,
    ! [A: set_c_d_set_a,X: ( c > d ) > set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( member_c_d_set_a @ X @ A )
       => ( ( ( ( minus_1665977719694084726_set_a @ A @ ( insert_c_d_set_a @ X @ bot_bo738396921950161403_set_a ) )
              = bot_bo738396921950161403_set_a )
           => ( ( lattic1898000229760699588_set_a @ inf_c_d_a2 @ A )
              = X ) )
          & ( ( ( minus_1665977719694084726_set_a @ A @ ( insert_c_d_set_a @ X @ bot_bo738396921950161403_set_a ) )
             != bot_bo738396921950161403_set_a )
           => ( ( lattic1898000229760699588_set_a @ inf_c_d_a2 @ A )
              = ( inf_c_d_a2 @ X @ ( lattic1898000229760699588_set_a @ inf_c_d_a2 @ ( minus_1665977719694084726_set_a @ A @ ( insert_c_d_set_a @ X @ bot_bo738396921950161403_set_a ) ) ) ) ) ) ) ) ) ).

% local.Inf_fin.remove
thf(fact_1230_local_OInf__fin_Oin__idem,axiom,
    ! [A: set_c_d_set_a,X: ( c > d ) > set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( member_c_d_set_a @ X @ A )
       => ( ( inf_c_d_a2 @ X @ ( lattic1898000229760699588_set_a @ inf_c_d_a2 @ A ) )
          = ( lattic1898000229760699588_set_a @ inf_c_d_a2 @ A ) ) ) ) ).

% local.Inf_fin.in_idem
thf(fact_1231_local_OInf__fin_OcoboundedI,axiom,
    ! [A: set_c_d_set_a,A2: ( c > d ) > set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( member_c_d_set_a @ A2 @ A )
       => ( smaller_interp_c_d_a @ ( lattic1898000229760699588_set_a @ inf_c_d_a2 @ A ) @ A2 ) ) ) ).

% local.Inf_fin.coboundedI
thf(fact_1232_local_OInf__fin_OboundedI,axiom,
    ! [A: set_c_d_set_a,X: ( c > d ) > set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( A != bot_bo738396921950161403_set_a )
       => ( ! [A5: ( c > d ) > set_a] :
              ( ( member_c_d_set_a @ A5 @ A )
             => ( smaller_interp_c_d_a @ X @ A5 ) )
         => ( smaller_interp_c_d_a @ X @ ( lattic1898000229760699588_set_a @ inf_c_d_a2 @ A ) ) ) ) ) ).

% local.Inf_fin.boundedI
thf(fact_1233_local_OInf__fin_OboundedE,axiom,
    ! [A: set_c_d_set_a,X: ( c > d ) > set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( A != bot_bo738396921950161403_set_a )
       => ( ( smaller_interp_c_d_a @ X @ ( lattic1898000229760699588_set_a @ inf_c_d_a2 @ A ) )
         => ! [A7: ( c > d ) > set_a] :
              ( ( member_c_d_set_a @ A7 @ A )
             => ( smaller_interp_c_d_a @ X @ A7 ) ) ) ) ) ).

% local.Inf_fin.boundedE
thf(fact_1234_local_OInf__fin_Oinsert__not__elem,axiom,
    ! [A: set_c_d_set_a,X: ( c > d ) > set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ~ ( member_c_d_set_a @ X @ A )
       => ( ( A != bot_bo738396921950161403_set_a )
         => ( ( lattic1898000229760699588_set_a @ inf_c_d_a2 @ ( insert_c_d_set_a @ X @ A ) )
            = ( inf_c_d_a2 @ X @ ( lattic1898000229760699588_set_a @ inf_c_d_a2 @ A ) ) ) ) ) ) ).

% local.Inf_fin.insert_not_elem
thf(fact_1235_local_OInf__fin_Oclosed,axiom,
    ! [A: set_c_d_set_a] :
      ( ( finite3330819693523053784_set_a @ A )
     => ( ( A != bot_bo738396921950161403_set_a )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] : ( member_c_d_set_a @ ( inf_c_d_a2 @ X2 @ Y2 ) @ ( insert_c_d_set_a @ X2 @ ( insert_c_d_set_a @ Y2 @ bot_bo738396921950161403_set_a ) ) )
         => ( member_c_d_set_a @ ( lattic1898000229760699588_set_a @ inf_c_d_a2 @ A ) @ A ) ) ) ) ).

% local.Inf_fin.closed
thf(fact_1236_Un__iff,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ ( sup_su3175602471750379875_set_a @ A @ B3 ) )
      = ( ( member_c_d_set_a @ C @ A )
        | ( member_c_d_set_a @ C @ B3 ) ) ) ).

% Un_iff
thf(fact_1237_UnCI,axiom,
    ! [C: ( c > d ) > set_a,B3: set_c_d_set_a,A: set_c_d_set_a] :
      ( ( ~ ( member_c_d_set_a @ C @ B3 )
       => ( member_c_d_set_a @ C @ A ) )
     => ( member_c_d_set_a @ C @ ( sup_su3175602471750379875_set_a @ A @ B3 ) ) ) ).

% UnCI
thf(fact_1238_semilattice__sup__class_Ole__sup__iff,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ ( sup_sup_c_d_set_a @ X @ Y ) @ Z )
      = ( ( ord_le8464990428230162895_set_a @ X @ Z )
        & ( ord_le8464990428230162895_set_a @ Y @ Z ) ) ) ).

% semilattice_sup_class.le_sup_iff
thf(fact_1239_semilattice__sup__class_Osup_Obounded__iff,axiom,
    ! [B: ( c > d ) > set_a,C: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ ( sup_sup_c_d_set_a @ B @ C ) @ A2 )
      = ( ( ord_le8464990428230162895_set_a @ B @ A2 )
        & ( ord_le8464990428230162895_set_a @ C @ A2 ) ) ) ).

% semilattice_sup_class.sup.bounded_iff
thf(fact_1240_bounded__lattice__top__class_Osup__top__left,axiom,
    ! [X: set_c_d_set_a] :
      ( ( sup_su3175602471750379875_set_a @ top_to4267977599310771935_set_a @ X )
      = top_to4267977599310771935_set_a ) ).

% bounded_lattice_top_class.sup_top_left
thf(fact_1241_bounded__lattice__top__class_Osup__top__right,axiom,
    ! [X: set_c_d_set_a] :
      ( ( sup_su3175602471750379875_set_a @ X @ top_to4267977599310771935_set_a )
      = top_to4267977599310771935_set_a ) ).

% bounded_lattice_top_class.sup_top_right
thf(fact_1242_boolean__algebra_Odisj__one__left,axiom,
    ! [X: set_c_d_set_a] :
      ( ( sup_su3175602471750379875_set_a @ top_to4267977599310771935_set_a @ X )
      = top_to4267977599310771935_set_a ) ).

% boolean_algebra.disj_one_left
thf(fact_1243_boolean__algebra_Odisj__one__right,axiom,
    ! [X: set_c_d_set_a] :
      ( ( sup_su3175602471750379875_set_a @ X @ top_to4267977599310771935_set_a )
      = top_to4267977599310771935_set_a ) ).

% boolean_algebra.disj_one_right
thf(fact_1244_Un__UNIV__right,axiom,
    ! [A: set_c_d_set_a] :
      ( ( sup_su3175602471750379875_set_a @ A @ top_to4267977599310771935_set_a )
      = top_to4267977599310771935_set_a ) ).

% Un_UNIV_right
thf(fact_1245_Un__UNIV__left,axiom,
    ! [B3: set_c_d_set_a] :
      ( ( sup_su3175602471750379875_set_a @ top_to4267977599310771935_set_a @ B3 )
      = top_to4267977599310771935_set_a ) ).

% Un_UNIV_left
thf(fact_1246_boolean__algebra_Ocomplement__unique,axiom,
    ! [A2: set_c_d_set_a,X: set_c_d_set_a,Y: set_c_d_set_a] :
      ( ( ( inf_in754637537901350525_set_a @ A2 @ X )
        = bot_bo738396921950161403_set_a )
     => ( ( ( sup_su3175602471750379875_set_a @ A2 @ X )
          = top_to4267977599310771935_set_a )
       => ( ( ( inf_in754637537901350525_set_a @ A2 @ Y )
            = bot_bo738396921950161403_set_a )
         => ( ( ( sup_su3175602471750379875_set_a @ A2 @ Y )
              = top_to4267977599310771935_set_a )
           => ( X = Y ) ) ) ) ) ).

% boolean_algebra.complement_unique
thf(fact_1247_semilattice__sup__class_Omono__sup,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( c > d ) > set_a,A: ( c > d ) > set_a,B3: ( c > d ) > set_a] :
      ( ( monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ F )
     => ( ord_le8464990428230162895_set_a @ ( sup_sup_c_d_set_a @ ( F @ A ) @ ( F @ B3 ) ) @ ( F @ ( sup_sup_c_d_set_a @ A @ B3 ) ) ) ) ).

% semilattice_sup_class.mono_sup
thf(fact_1248_UnI2,axiom,
    ! [C: ( c > d ) > set_a,B3: set_c_d_set_a,A: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ B3 )
     => ( member_c_d_set_a @ C @ ( sup_su3175602471750379875_set_a @ A @ B3 ) ) ) ).

% UnI2
thf(fact_1249_UnI1,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ A )
     => ( member_c_d_set_a @ C @ ( sup_su3175602471750379875_set_a @ A @ B3 ) ) ) ).

% UnI1
thf(fact_1250_UnE,axiom,
    ! [C: ( c > d ) > set_a,A: set_c_d_set_a,B3: set_c_d_set_a] :
      ( ( member_c_d_set_a @ C @ ( sup_su3175602471750379875_set_a @ A @ B3 ) )
     => ( ~ ( member_c_d_set_a @ C @ A )
       => ( member_c_d_set_a @ C @ B3 ) ) ) ).

% UnE
thf(fact_1251_semilattice__sup__class_Osup_OcoboundedI2,axiom,
    ! [C: ( c > d ) > set_a,B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ C @ B )
     => ( ord_le8464990428230162895_set_a @ C @ ( sup_sup_c_d_set_a @ A2 @ B ) ) ) ).

% semilattice_sup_class.sup.coboundedI2
thf(fact_1252_semilattice__sup__class_Osup_OcoboundedI1,axiom,
    ! [C: ( c > d ) > set_a,A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ C @ A2 )
     => ( ord_le8464990428230162895_set_a @ C @ ( sup_sup_c_d_set_a @ A2 @ B ) ) ) ).

% semilattice_sup_class.sup.coboundedI1
thf(fact_1253_semilattice__sup__class_Osup_Oabsorb__iff2,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [A3: ( c > d ) > set_a,B2: ( c > d ) > set_a] :
          ( ( sup_sup_c_d_set_a @ A3 @ B2 )
          = B2 ) ) ) ).

% semilattice_sup_class.sup.absorb_iff2
thf(fact_1254_semilattice__sup__class_Osup_Oabsorb__iff1,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [B2: ( c > d ) > set_a,A3: ( c > d ) > set_a] :
          ( ( sup_sup_c_d_set_a @ A3 @ B2 )
          = A3 ) ) ) ).

% semilattice_sup_class.sup.absorb_iff1
thf(fact_1255_semilattice__sup__class_Osup_Ocobounded2,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ B @ ( sup_sup_c_d_set_a @ A2 @ B ) ) ).

% semilattice_sup_class.sup.cobounded2
thf(fact_1256_semilattice__sup__class_Osup_Ocobounded1,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ A2 @ ( sup_sup_c_d_set_a @ A2 @ B ) ) ).

% semilattice_sup_class.sup.cobounded1
thf(fact_1257_semilattice__sup__class_Osup_Oorder__iff,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [B2: ( c > d ) > set_a,A3: ( c > d ) > set_a] :
          ( A3
          = ( sup_sup_c_d_set_a @ A3 @ B2 ) ) ) ) ).

% semilattice_sup_class.sup.order_iff
thf(fact_1258_semilattice__sup__class_Osup_OboundedI,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a,C: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ B @ A2 )
     => ( ( ord_le8464990428230162895_set_a @ C @ A2 )
       => ( ord_le8464990428230162895_set_a @ ( sup_sup_c_d_set_a @ B @ C ) @ A2 ) ) ) ).

% semilattice_sup_class.sup.boundedI
thf(fact_1259_semilattice__sup__class_Osup_OboundedE,axiom,
    ! [B: ( c > d ) > set_a,C: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ ( sup_sup_c_d_set_a @ B @ C ) @ A2 )
     => ~ ( ( ord_le8464990428230162895_set_a @ B @ A2 )
         => ~ ( ord_le8464990428230162895_set_a @ C @ A2 ) ) ) ).

% semilattice_sup_class.sup.boundedE
thf(fact_1260_semilattice__sup__class_Osup__absorb2,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ Y )
     => ( ( sup_sup_c_d_set_a @ X @ Y )
        = Y ) ) ).

% semilattice_sup_class.sup_absorb2
thf(fact_1261_semilattice__sup__class_Osup__absorb1,axiom,
    ! [Y: ( c > d ) > set_a,X: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ Y @ X )
     => ( ( sup_sup_c_d_set_a @ X @ Y )
        = X ) ) ).

% semilattice_sup_class.sup_absorb1
thf(fact_1262_semilattice__sup__class_Osup_Oabsorb2,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ B )
     => ( ( sup_sup_c_d_set_a @ A2 @ B )
        = B ) ) ).

% semilattice_sup_class.sup.absorb2
thf(fact_1263_semilattice__sup__class_Osup_Oabsorb1,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ B @ A2 )
     => ( ( sup_sup_c_d_set_a @ A2 @ B )
        = A2 ) ) ).

% semilattice_sup_class.sup.absorb1
thf(fact_1264_semilattice__sup__class_Osup__unique,axiom,
    ! [F: ( ( c > d ) > set_a ) > ( ( c > d ) > set_a ) > ( c > d ) > set_a,X: ( c > d ) > set_a,Y: ( c > d ) > set_a] :
      ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ X2 @ ( F @ X2 @ Y2 ) )
     => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ Y2 @ ( F @ X2 @ Y2 ) )
       => ( ! [X2: ( c > d ) > set_a,Y2: ( c > d ) > set_a,Z4: ( c > d ) > set_a] :
              ( ( ord_le8464990428230162895_set_a @ Y2 @ X2 )
             => ( ( ord_le8464990428230162895_set_a @ Z4 @ X2 )
               => ( ord_le8464990428230162895_set_a @ ( F @ Y2 @ Z4 ) @ X2 ) ) )
         => ( ( sup_sup_c_d_set_a @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% semilattice_sup_class.sup_unique
thf(fact_1265_semilattice__sup__class_Osup_OorderI,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( A2
        = ( sup_sup_c_d_set_a @ A2 @ B ) )
     => ( ord_le8464990428230162895_set_a @ B @ A2 ) ) ).

% semilattice_sup_class.sup.orderI
thf(fact_1266_semilattice__sup__class_Osup_OorderE,axiom,
    ! [B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ B @ A2 )
     => ( A2
        = ( sup_sup_c_d_set_a @ A2 @ B ) ) ) ).

% semilattice_sup_class.sup.orderE
thf(fact_1267_semilattice__sup__class_Ole__iff__sup,axiom,
    ( ord_le8464990428230162895_set_a
    = ( ^ [X3: ( c > d ) > set_a,Y4: ( c > d ) > set_a] :
          ( ( sup_sup_c_d_set_a @ X3 @ Y4 )
          = Y4 ) ) ) ).

% semilattice_sup_class.le_iff_sup
thf(fact_1268_semilattice__sup__class_Osup__least,axiom,
    ! [Y: ( c > d ) > set_a,X: ( c > d ) > set_a,Z: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ Y @ X )
     => ( ( ord_le8464990428230162895_set_a @ Z @ X )
       => ( ord_le8464990428230162895_set_a @ ( sup_sup_c_d_set_a @ Y @ Z ) @ X ) ) ) ).

% semilattice_sup_class.sup_least
thf(fact_1269_semilattice__sup__class_Osup__mono,axiom,
    ! [A2: ( c > d ) > set_a,C: ( c > d ) > set_a,B: ( c > d ) > set_a,D: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ C )
     => ( ( ord_le8464990428230162895_set_a @ B @ D )
       => ( ord_le8464990428230162895_set_a @ ( sup_sup_c_d_set_a @ A2 @ B ) @ ( sup_sup_c_d_set_a @ C @ D ) ) ) ) ).

% semilattice_sup_class.sup_mono
thf(fact_1270_semilattice__sup__class_Osup_Omono,axiom,
    ! [C: ( c > d ) > set_a,A2: ( c > d ) > set_a,D: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ C @ A2 )
     => ( ( ord_le8464990428230162895_set_a @ D @ B )
       => ( ord_le8464990428230162895_set_a @ ( sup_sup_c_d_set_a @ C @ D ) @ ( sup_sup_c_d_set_a @ A2 @ B ) ) ) ) ).

% semilattice_sup_class.sup.mono
thf(fact_1271_semilattice__sup__class_Ole__supI2,axiom,
    ! [X: ( c > d ) > set_a,B: ( c > d ) > set_a,A2: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ B )
     => ( ord_le8464990428230162895_set_a @ X @ ( sup_sup_c_d_set_a @ A2 @ B ) ) ) ).

% semilattice_sup_class.le_supI2
thf(fact_1272_semilattice__sup__class_Ole__supI1,axiom,
    ! [X: ( c > d ) > set_a,A2: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ X @ A2 )
     => ( ord_le8464990428230162895_set_a @ X @ ( sup_sup_c_d_set_a @ A2 @ B ) ) ) ).

% semilattice_sup_class.le_supI1
thf(fact_1273_semilattice__sup__class_Osup__ge2,axiom,
    ! [Y: ( c > d ) > set_a,X: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ Y @ ( sup_sup_c_d_set_a @ X @ Y ) ) ).

% semilattice_sup_class.sup_ge2
thf(fact_1274_semilattice__sup__class_Osup__ge1,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ X @ ( sup_sup_c_d_set_a @ X @ Y ) ) ).

% semilattice_sup_class.sup_ge1
thf(fact_1275_semilattice__sup__class_Ole__supI,axiom,
    ! [A2: ( c > d ) > set_a,X: ( c > d ) > set_a,B: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ A2 @ X )
     => ( ( ord_le8464990428230162895_set_a @ B @ X )
       => ( ord_le8464990428230162895_set_a @ ( sup_sup_c_d_set_a @ A2 @ B ) @ X ) ) ) ).

% semilattice_sup_class.le_supI
thf(fact_1276_semilattice__sup__class_Ole__supE,axiom,
    ! [A2: ( c > d ) > set_a,B: ( c > d ) > set_a,X: ( c > d ) > set_a] :
      ( ( ord_le8464990428230162895_set_a @ ( sup_sup_c_d_set_a @ A2 @ B ) @ X )
     => ~ ( ( ord_le8464990428230162895_set_a @ A2 @ X )
         => ~ ( ord_le8464990428230162895_set_a @ B @ X ) ) ) ).

% semilattice_sup_class.le_supE
thf(fact_1277_lattice__class_Oinf__sup__ord_I3_J,axiom,
    ! [X: ( c > d ) > set_a,Y: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ X @ ( sup_sup_c_d_set_a @ X @ Y ) ) ).

% lattice_class.inf_sup_ord(3)
thf(fact_1278_lattice__class_Oinf__sup__ord_I4_J,axiom,
    ! [Y: ( c > d ) > set_a,X: ( c > d ) > set_a] : ( ord_le8464990428230162895_set_a @ Y @ ( sup_sup_c_d_set_a @ X @ Y ) ) ).

% lattice_class.inf_sup_ord(4)

% Helper facts (3)
thf(help_If_3_1_If_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_T,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( if_e_f_set_a @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001_062_I_062_Itf__e_Mtf__f_J_Mt__Set__Oset_Itf__a_J_J_T,axiom,
    ! [X: ( e > f ) > set_a,Y: ( e > f ) > set_a] :
      ( ( if_e_f_set_a @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    monoto2937423850181994535_set_a @ top_to4267977599310771935_set_a @ ord_le8464990428230162895_set_a @ ord_le8464990428230162895_set_a @ f2 ).

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