%------------------------------------------------------------------------------
% File     : ITP127^1 : TPTP v8.2.0. Released v7.5.0.
% Domain   : Interactive Theorem Proving
% Problem  : Sledgehammer Monomorphic_Monad problem prob_2789__7122292_1
% Version  : Especial.
% English  :

% Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
%          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source   : [Des21]
% Names    : Monomorphic_Monad/prob_2789__7122292_1 [Des21]

% Status   : Theorem
% Rating   : 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0
% Syntax   : Number of formulae    :  353 ( 116 unt;  37 typ;   0 def)
%            Number of atoms       :  769 ( 436 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 2537 (  60   ~;   9   |;  23   &;2121   @)
%                                         (   0 <=>; 324  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :  702 ( 702   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   35 (  32 usr;   4 con; 0-3 aty)
%            Number of variables   : 1106 (  82   ^;1003   !;  21   ?;1106   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Sledgehammer 2021-02-23 15:37:01.423
%------------------------------------------------------------------------------
% Could-be-implicit typings (5)
thf(ty_n_t__Countable____Set____Type__Ocset_It__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_J,type,
    counta191869203tT_a_m: $tType ).

thf(ty_n_t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
    monomo197243225tT_a_m: $tType ).

thf(ty_n_t__Countable____Set____Type__Ocset_Itf__c_J,type,
    countable_Set_cset_c: $tType ).

thf(ty_n_tf__m,type,
    m: $tType ).

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

% Explicit typings (32)
thf(sy_c_Countable__Set__Type_Ocin_001tf__c,type,
    countable_Set_cin_c: c > countable_Set_cset_c > $o ).

thf(sy_c_Countable__Set__Type_Ocinsert_001tf__c,type,
    counta472291938sert_c: c > countable_Set_cset_c > countable_Set_cset_c ).

thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c,type,
    comp_M864375327_a_m_c: ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > ( c > monomo197243225tT_a_m ) > c > monomo197243225tT_a_m ).

thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c_001tf__c,type,
    comp_M1062614966_m_c_c: ( monomo197243225tT_a_m > c ) > ( c > monomo197243225tT_a_m ) > c > c ).

thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
    comp_M1944986301tT_a_m: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m > m ).

thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001tf__c,type,
    comp_M750374444_m_m_c: ( monomo197243225tT_a_m > m ) > ( c > monomo197243225tT_a_m ) > c > m ).

thf(sy_c_Fun_Ocomp_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001tf__m,type,
    comp_M750374454_m_m_m: ( monomo197243225tT_a_m > m ) > ( m > monomo197243225tT_a_m ) > m > m ).

thf(sy_c_Fun_Ocomp_001tf__c_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c,type,
    comp_c1772230468_a_m_c: ( c > monomo197243225tT_a_m ) > ( c > c ) > c > monomo197243225tT_a_m ).

thf(sy_c_Fun_Ocomp_001tf__c_001tf__c_001tf__c,type,
    comp_c_c_c: ( c > c ) > ( c > c ) > c > c ).

thf(sy_c_Fun_Ocomp_001tf__c_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
    comp_c997395372tT_a_m: ( c > m ) > ( monomo197243225tT_a_m > c ) > monomo197243225tT_a_m > m ).

thf(sy_c_Fun_Ocomp_001tf__c_001tf__m_001tf__c,type,
    comp_c_m_c: ( c > m ) > ( c > c ) > c > m ).

thf(sy_c_Fun_Ocomp_001tf__c_001tf__m_001tf__m,type,
    comp_c_m_m: ( c > m ) > ( m > c ) > m > m ).

thf(sy_c_Fun_Ocomp_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__c,type,
    comp_m1038691662_a_m_c: ( m > monomo197243225tT_a_m ) > ( c > m ) > c > monomo197243225tT_a_m ).

thf(sy_c_Fun_Ocomp_001tf__m_001tf__c_001tf__c,type,
    comp_m_c_c: ( m > c ) > ( c > m ) > c > c ).

thf(sy_c_Fun_Ocomp_001tf__m_001tf__m_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J,type,
    comp_m263856566tT_a_m: ( m > m ) > ( monomo197243225tT_a_m > m ) > monomo197243225tT_a_m > m ).

thf(sy_c_Fun_Ocomp_001tf__m_001tf__m_001tf__c,type,
    comp_m_m_c: ( m > m ) > ( c > m ) > c > m ).

thf(sy_c_Fun_Ocomp_001tf__m_001tf__m_001tf__m,type,
    comp_m_m_m: ( m > m ) > ( m > m ) > m > m ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
    minus_1646763425cset_c: countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).

thf(sy_c_If_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
    if_Cou1542198912cset_c: $o > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).

thf(sy_c_If_001tf__c,type,
    if_c: $o > c > c > c ).

thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_Ocset__nondetM__base_Oaltc__nondet_001t__Monomorphic____Monad____Mirabelle____yhgbvxlbev__OnondetT_Itf__a_Mtf__m_J_001tf__m_001tf__a,type,
    monomo2081011572_m_m_a: ( counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m ) > counta191869203tT_a_m > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).

thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_Ocset__nondetM__base_Oaltc__nondet_001tf__c_001tf__m_001tf__a,type,
    monomo463139869_c_m_a: ( countable_Set_cset_c > ( c > m ) > m ) > countable_Set_cset_c > ( c > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).

thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_OnondetT_ONondetT_001tf__m_001tf__a,type,
    monomo412532791tT_m_a: m > monomo197243225tT_a_m ).

thf(sy_c_Monomorphic__Monad__Mirabelle__yhgbvxlbev_OnondetT_Orun__nondet_001tf__a_001tf__m,type,
    monomo624345106et_a_m: monomo197243225tT_a_m > m ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
    bot_bo1320844070cset_c: countable_Set_cset_c ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
    ord_le1587667814cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Countable____Set____Type__Ocset_Itf__c_J_J,type,
    ord_le1376176871cset_c: ( $o > countable_Set_cset_c ) > ( $o > countable_Set_cset_c ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
    ord_le15364698cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).

thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Countable____Set____Type__Ocset_Itf__c_J,type,
    order_1683649299cset_c: ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).

thf(sy_v_f____,type,
    f: c > monomo197243225tT_a_m ).

thf(sy_v_mergec,type,
    mergec: countable_Set_cset_c > ( c > m ) > m ).

thf(sy_v_x____,type,
    x: c ).

% Relevant facts (310)
thf(fact_0_mergec__single,axiom,
    ! [X: c,F: c > m] :
      ( ( mergec @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) @ F )
      = ( F @ X ) ) ).

% mergec_single
thf(fact_1_cset__nondetM__base_Oaltc__nondet_Ocong,axiom,
    monomo463139869_c_m_a = monomo463139869_c_m_a ).

% cset_nondetM_base.altc_nondet.cong
thf(fact_2_cinsert__absorb2,axiom,
    ! [X: c,A: countable_Set_cset_c] :
      ( ( counta472291938sert_c @ X @ ( counta472291938sert_c @ X @ A ) )
      = ( counta472291938sert_c @ X @ A ) ) ).

% cinsert_absorb2
thf(fact_3_cdoubleton__eq__iff,axiom,
    ! [A2: c,B: c,C: c,D: c] :
      ( ( ( counta472291938sert_c @ A2 @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
        = ( counta472291938sert_c @ C @ ( counta472291938sert_c @ D @ bot_bo1320844070cset_c ) ) )
      = ( ( ( A2 = C )
          & ( B = D ) )
        | ( ( A2 = D )
          & ( B = C ) ) ) ) ).

% cdoubleton_eq_iff
thf(fact_4_csingleton__inject,axiom,
    ! [A2: c,B: c] :
      ( ( ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c )
        = ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
     => ( A2 = B ) ) ).

% csingleton_inject
thf(fact_5_cinsert__not__cempty,axiom,
    ! [A2: c,A: countable_Set_cset_c] :
      ( ( counta472291938sert_c @ A2 @ A )
     != bot_bo1320844070cset_c ) ).

% cinsert_not_cempty
thf(fact_6_cinsert__commute,axiom,
    ! [X: c,Y: c,A: countable_Set_cset_c] :
      ( ( counta472291938sert_c @ X @ ( counta472291938sert_c @ Y @ A ) )
      = ( counta472291938sert_c @ Y @ ( counta472291938sert_c @ X @ A ) ) ) ).

% cinsert_commute
thf(fact_7_run__altc__nondet,axiom,
    ! [A: countable_Set_cset_c,F: c > monomo197243225tT_a_m] :
      ( ( monomo624345106et_a_m @ ( monomo463139869_c_m_a @ mergec @ A @ F ) )
      = ( mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F ) ) ) ).

% run_altc_nondet
thf(fact_8_nondetT_Oexpand,axiom,
    ! [NondetT: monomo197243225tT_a_m,NondetT2: monomo197243225tT_a_m] :
      ( ( ( monomo624345106et_a_m @ NondetT )
        = ( monomo624345106et_a_m @ NondetT2 ) )
     => ( NondetT = NondetT2 ) ) ).

% nondetT.expand
thf(fact_9_cset__nondetM__base_Orun__altc__nondet,axiom,
    ! [Mergec: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m,A: counta191869203tT_a_m,F: monomo197243225tT_a_m > monomo197243225tT_a_m] :
      ( ( monomo624345106et_a_m @ ( monomo2081011572_m_m_a @ Mergec @ A @ F ) )
      = ( Mergec @ A @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ F ) ) ) ).

% cset_nondetM_base.run_altc_nondet
thf(fact_10_cset__nondetM__base_Orun__altc__nondet,axiom,
    ! [Mergec: countable_Set_cset_c > ( c > m ) > m,A: countable_Set_cset_c,F: c > monomo197243225tT_a_m] :
      ( ( monomo624345106et_a_m @ ( monomo463139869_c_m_a @ Mergec @ A @ F ) )
      = ( Mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F ) ) ) ).

% cset_nondetM_base.run_altc_nondet
thf(fact_11_altc__nondet__def,axiom,
    ! [A: countable_Set_cset_c,F: c > monomo197243225tT_a_m] :
      ( ( monomo463139869_c_m_a @ mergec @ A @ F )
      = ( monomo412532791tT_m_a @ ( mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F ) ) ) ) ).

% altc_nondet_def
thf(fact_12_comp__apply,axiom,
    ( comp_M1944986301tT_a_m
    = ( ^ [F2: monomo197243225tT_a_m > m,G: monomo197243225tT_a_m > monomo197243225tT_a_m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_apply
thf(fact_13_comp__apply,axiom,
    ( comp_m263856566tT_a_m
    = ( ^ [F2: m > m,G: monomo197243225tT_a_m > m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_apply
thf(fact_14_comp__apply,axiom,
    ( comp_m_m_c
    = ( ^ [F2: m > m,G: c > m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_apply
thf(fact_15_comp__apply,axiom,
    ( comp_c1772230468_a_m_c
    = ( ^ [F2: c > monomo197243225tT_a_m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_apply
thf(fact_16_comp__apply,axiom,
    ( comp_c_m_c
    = ( ^ [F2: c > m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_apply
thf(fact_17_comp__apply,axiom,
    ( comp_M750374444_m_m_c
    = ( ^ [F2: monomo197243225tT_a_m > m,G: c > monomo197243225tT_a_m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_apply
thf(fact_18_cset__nondetM__base_Oaltc__nondet__def,axiom,
    ( monomo2081011572_m_m_a
    = ( ^ [Mergec2: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m,A3: counta191869203tT_a_m,F2: monomo197243225tT_a_m > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( Mergec2 @ A3 @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ F2 ) ) ) ) ) ).

% cset_nondetM_base.altc_nondet_def
thf(fact_19_cset__nondetM__base_Oaltc__nondet__def,axiom,
    ( monomo463139869_c_m_a
    = ( ^ [Mergec2: countable_Set_cset_c > ( c > m ) > m,A3: countable_Set_cset_c,F2: c > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( Mergec2 @ A3 @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ F2 ) ) ) ) ) ).

% cset_nondetM_base.altc_nondet_def
thf(fact_20_comp__def,axiom,
    ( comp_M1944986301tT_a_m
    = ( ^ [F2: monomo197243225tT_a_m > m,G: monomo197243225tT_a_m > monomo197243225tT_a_m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_def
thf(fact_21_comp__def,axiom,
    ( comp_m263856566tT_a_m
    = ( ^ [F2: m > m,G: monomo197243225tT_a_m > m,X2: monomo197243225tT_a_m] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_def
thf(fact_22_comp__def,axiom,
    ( comp_m_m_c
    = ( ^ [F2: m > m,G: c > m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_def
thf(fact_23_comp__def,axiom,
    ( comp_c1772230468_a_m_c
    = ( ^ [F2: c > monomo197243225tT_a_m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_def
thf(fact_24_comp__def,axiom,
    ( comp_c_m_c
    = ( ^ [F2: c > m,G: c > c,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_def
thf(fact_25_comp__def,axiom,
    ( comp_M750374444_m_m_c
    = ( ^ [F2: monomo197243225tT_a_m > m,G: c > monomo197243225tT_a_m,X2: c] : ( F2 @ ( G @ X2 ) ) ) ) ).

% comp_def
thf(fact_26_comp__assoc,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,H: c > c] :
      ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ G2 ) @ H )
      = ( comp_M750374444_m_m_c @ F @ ( comp_c1772230468_a_m_c @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_27_comp__assoc,axiom,
    ! [F: m > m,G2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m] :
      ( ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ F @ G2 ) @ H )
      = ( comp_m_m_c @ F @ ( comp_M750374444_m_m_c @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_28_comp__assoc,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m] :
      ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ G2 ) @ H )
      = ( comp_M750374444_m_m_c @ F @ ( comp_M864375327_a_m_c @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_29_comp__assoc,axiom,
    ! [F: m > m,G2: m > m,H: c > m] :
      ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
      = ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_30_comp__assoc,axiom,
    ! [F: c > m,G2: m > c,H: c > m] :
      ( ( comp_m_m_c @ ( comp_c_m_m @ F @ G2 ) @ H )
      = ( comp_c_m_c @ F @ ( comp_m_c_c @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_31_comp__assoc,axiom,
    ! [F: m > m,G2: c > m,H: c > c] :
      ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
      = ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_32_comp__assoc,axiom,
    ! [F: c > m,G2: c > c,H: c > c] :
      ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
      = ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_33_comp__assoc,axiom,
    ! [F: m > m,G2: c > m,H: monomo197243225tT_a_m > c] :
      ( ( comp_c997395372tT_a_m @ ( comp_m_m_c @ F @ G2 ) @ H )
      = ( comp_m263856566tT_a_m @ F @ ( comp_c997395372tT_a_m @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_34_comp__assoc,axiom,
    ! [F: c > m,G2: monomo197243225tT_a_m > c,H: c > monomo197243225tT_a_m] :
      ( ( comp_M750374444_m_m_c @ ( comp_c997395372tT_a_m @ F @ G2 ) @ H )
      = ( comp_c_m_c @ F @ ( comp_M1062614966_m_c_c @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_35_comp__assoc,axiom,
    ! [F: m > m,G2: m > m,H: monomo197243225tT_a_m > m] :
      ( ( comp_m263856566tT_a_m @ ( comp_m_m_m @ F @ G2 ) @ H )
      = ( comp_m263856566tT_a_m @ F @ ( comp_m263856566tT_a_m @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_36_comp__eq__dest,axiom,
    ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m,V: c] :
      ( ( ( comp_M750374444_m_m_c @ A2 @ B )
        = ( comp_M750374444_m_m_c @ C @ D ) )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_37_comp__eq__dest,axiom,
    ! [A2: m > m,B: c > m,C: m > m,D: c > m,V: c] :
      ( ( ( comp_m_m_c @ A2 @ B )
        = ( comp_m_m_c @ C @ D ) )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_38_comp__eq__dest,axiom,
    ! [A2: m > m,B: c > m,C: c > m,D: c > c,V: c] :
      ( ( ( comp_m_m_c @ A2 @ B )
        = ( comp_c_m_c @ C @ D ) )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_39_comp__eq__dest,axiom,
    ! [A2: c > m,B: c > c,C: m > m,D: c > m,V: c] :
      ( ( ( comp_c_m_c @ A2 @ B )
        = ( comp_m_m_c @ C @ D ) )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_40_comp__eq__dest,axiom,
    ! [A2: c > m,B: c > c,C: c > m,D: c > c,V: c] :
      ( ( ( comp_c_m_c @ A2 @ B )
        = ( comp_c_m_c @ C @ D ) )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_41_comp__eq__dest,axiom,
    ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: m > m,D: c > m,V: c] :
      ( ( ( comp_M750374444_m_m_c @ A2 @ B )
        = ( comp_m_m_c @ C @ D ) )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_42_comp__eq__dest,axiom,
    ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m,D: c > c,V: c] :
      ( ( ( comp_M750374444_m_m_c @ A2 @ B )
        = ( comp_c_m_c @ C @ D ) )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_43_comp__eq__dest,axiom,
    ! [A2: m > m,B: monomo197243225tT_a_m > m,C: m > m,D: monomo197243225tT_a_m > m,V: monomo197243225tT_a_m] :
      ( ( ( comp_m263856566tT_a_m @ A2 @ B )
        = ( comp_m263856566tT_a_m @ C @ D ) )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_44_comp__eq__dest,axiom,
    ! [A2: m > m,B: c > m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m,V: c] :
      ( ( ( comp_m_m_c @ A2 @ B )
        = ( comp_M750374444_m_m_c @ C @ D ) )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_45_comp__eq__dest,axiom,
    ! [A2: c > monomo197243225tT_a_m,B: c > c,C: c > monomo197243225tT_a_m,D: c > c,V: c] :
      ( ( ( comp_c1772230468_a_m_c @ A2 @ B )
        = ( comp_c1772230468_a_m_c @ C @ D ) )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_46_comp__eq__elim,axiom,
    ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m] :
      ( ( ( comp_M750374444_m_m_c @ A2 @ B )
        = ( comp_M750374444_m_m_c @ C @ D ) )
     => ! [V2: c] :
          ( ( A2 @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_47_comp__eq__elim,axiom,
    ! [A2: m > m,B: c > m,C: m > m,D: c > m] :
      ( ( ( comp_m_m_c @ A2 @ B )
        = ( comp_m_m_c @ C @ D ) )
     => ! [V2: c] :
          ( ( A2 @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_48_comp__eq__elim,axiom,
    ! [A2: m > m,B: c > m,C: c > m,D: c > c] :
      ( ( ( comp_m_m_c @ A2 @ B )
        = ( comp_c_m_c @ C @ D ) )
     => ! [V2: c] :
          ( ( A2 @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_49_comp__eq__elim,axiom,
    ! [A2: c > m,B: c > c,C: m > m,D: c > m] :
      ( ( ( comp_c_m_c @ A2 @ B )
        = ( comp_m_m_c @ C @ D ) )
     => ! [V2: c] :
          ( ( A2 @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_50_comp__eq__elim,axiom,
    ! [A2: c > m,B: c > c,C: c > m,D: c > c] :
      ( ( ( comp_c_m_c @ A2 @ B )
        = ( comp_c_m_c @ C @ D ) )
     => ! [V2: c] :
          ( ( A2 @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_51_comp__eq__elim,axiom,
    ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: m > m,D: c > m] :
      ( ( ( comp_M750374444_m_m_c @ A2 @ B )
        = ( comp_m_m_c @ C @ D ) )
     => ! [V2: c] :
          ( ( A2 @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_52_comp__eq__elim,axiom,
    ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m,D: c > c] :
      ( ( ( comp_M750374444_m_m_c @ A2 @ B )
        = ( comp_c_m_c @ C @ D ) )
     => ! [V2: c] :
          ( ( A2 @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_53_comp__eq__elim,axiom,
    ! [A2: m > m,B: monomo197243225tT_a_m > m,C: m > m,D: monomo197243225tT_a_m > m] :
      ( ( ( comp_m263856566tT_a_m @ A2 @ B )
        = ( comp_m263856566tT_a_m @ C @ D ) )
     => ! [V2: monomo197243225tT_a_m] :
          ( ( A2 @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_54_comp__eq__elim,axiom,
    ! [A2: m > m,B: c > m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m] :
      ( ( ( comp_m_m_c @ A2 @ B )
        = ( comp_M750374444_m_m_c @ C @ D ) )
     => ! [V2: c] :
          ( ( A2 @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_55_comp__eq__elim,axiom,
    ! [A2: c > monomo197243225tT_a_m,B: c > c,C: c > monomo197243225tT_a_m,D: c > c] :
      ( ( ( comp_c1772230468_a_m_c @ A2 @ B )
        = ( comp_c1772230468_a_m_c @ C @ D ) )
     => ! [V2: c] :
          ( ( A2 @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_56_comp__cong,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,F3: monomo197243225tT_a_m > m,G3: c > monomo197243225tT_a_m,X3: c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( F3 @ ( G3 @ X3 ) ) )
     => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
        = ( comp_M750374444_m_m_c @ F3 @ G3 @ X3 ) ) ) ).

% comp_cong
thf(fact_57_comp__cong,axiom,
    ! [F: m > m,G2: c > m,X: c,F3: m > m,G3: c > m,X3: c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( F3 @ ( G3 @ X3 ) ) )
     => ( ( comp_m_m_c @ F @ G2 @ X )
        = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).

% comp_cong
thf(fact_58_comp__cong,axiom,
    ! [F: m > m,G2: c > m,X: c,F3: c > m,G3: c > c,X3: c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( F3 @ ( G3 @ X3 ) ) )
     => ( ( comp_m_m_c @ F @ G2 @ X )
        = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).

% comp_cong
thf(fact_59_comp__cong,axiom,
    ! [F: c > m,G2: c > c,X: c,F3: m > m,G3: c > m,X3: c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( F3 @ ( G3 @ X3 ) ) )
     => ( ( comp_c_m_c @ F @ G2 @ X )
        = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).

% comp_cong
thf(fact_60_comp__cong,axiom,
    ! [F: c > m,G2: c > c,X: c,F3: c > m,G3: c > c,X3: c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( F3 @ ( G3 @ X3 ) ) )
     => ( ( comp_c_m_c @ F @ G2 @ X )
        = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).

% comp_cong
thf(fact_61_comp__cong,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,F3: m > m,G3: c > m,X3: c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( F3 @ ( G3 @ X3 ) ) )
     => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
        = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).

% comp_cong
thf(fact_62_comp__cong,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,F3: c > m,G3: c > c,X3: c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( F3 @ ( G3 @ X3 ) ) )
     => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
        = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).

% comp_cong
thf(fact_63_comp__cong,axiom,
    ! [F: m > m,G2: monomo197243225tT_a_m > m,X: monomo197243225tT_a_m,F3: m > m,G3: c > m,X3: c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( F3 @ ( G3 @ X3 ) ) )
     => ( ( comp_m263856566tT_a_m @ F @ G2 @ X )
        = ( comp_m_m_c @ F3 @ G3 @ X3 ) ) ) ).

% comp_cong
thf(fact_64_comp__cong,axiom,
    ! [F: m > m,G2: monomo197243225tT_a_m > m,X: monomo197243225tT_a_m,F3: c > m,G3: c > c,X3: c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( F3 @ ( G3 @ X3 ) ) )
     => ( ( comp_m263856566tT_a_m @ F @ G2 @ X )
        = ( comp_c_m_c @ F3 @ G3 @ X3 ) ) ) ).

% comp_cong
thf(fact_65_comp__cong,axiom,
    ! [F: m > m,G2: c > m,X: c,F3: monomo197243225tT_a_m > m,G3: c > monomo197243225tT_a_m,X3: c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( F3 @ ( G3 @ X3 ) ) )
     => ( ( comp_m_m_c @ F @ G2 @ X )
        = ( comp_M750374444_m_m_c @ F3 @ G3 @ X3 ) ) ) ).

% comp_cong
thf(fact_66_comp__eq__dest__lhs,axiom,
    ! [A2: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,V: monomo197243225tT_a_m] :
      ( ( ( comp_M1944986301tT_a_m @ A2 @ B )
        = C )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_67_comp__eq__dest__lhs,axiom,
    ! [A2: m > m,B: monomo197243225tT_a_m > m,C: monomo197243225tT_a_m > m,V: monomo197243225tT_a_m] :
      ( ( ( comp_m263856566tT_a_m @ A2 @ B )
        = C )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_68_comp__eq__dest__lhs,axiom,
    ! [A2: m > m,B: c > m,C: c > m,V: c] :
      ( ( ( comp_m_m_c @ A2 @ B )
        = C )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_69_comp__eq__dest__lhs,axiom,
    ! [A2: c > monomo197243225tT_a_m,B: c > c,C: c > monomo197243225tT_a_m,V: c] :
      ( ( ( comp_c1772230468_a_m_c @ A2 @ B )
        = C )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_70_comp__eq__dest__lhs,axiom,
    ! [A2: c > m,B: c > c,C: c > m,V: c] :
      ( ( ( comp_c_m_c @ A2 @ B )
        = C )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_71_comp__eq__dest__lhs,axiom,
    ! [A2: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m,V: c] :
      ( ( ( comp_M750374444_m_m_c @ A2 @ B )
        = C )
     => ( ( A2 @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_72_comp__apply__eq,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,H: monomo197243225tT_a_m > m,K: c > monomo197243225tT_a_m] :
      ( ( ( F @ ( G2 @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
        = ( comp_M750374444_m_m_c @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_73_comp__apply__eq,axiom,
    ! [F: m > m,G2: c > m,X: c,H: m > m,K: c > m] :
      ( ( ( F @ ( G2 @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_m_m_c @ F @ G2 @ X )
        = ( comp_m_m_c @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_74_comp__apply__eq,axiom,
    ! [F: m > m,G2: c > m,X: c,H: c > m,K: c > c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_m_m_c @ F @ G2 @ X )
        = ( comp_c_m_c @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_75_comp__apply__eq,axiom,
    ! [F: c > m,G2: c > c,X: c,H: m > m,K: c > m] :
      ( ( ( F @ ( G2 @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_c_m_c @ F @ G2 @ X )
        = ( comp_m_m_c @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_76_comp__apply__eq,axiom,
    ! [F: c > m,G2: c > c,X: c,H: c > m,K: c > c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_c_m_c @ F @ G2 @ X )
        = ( comp_c_m_c @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_77_comp__apply__eq,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,H: m > m,K: c > m] :
      ( ( ( F @ ( G2 @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
        = ( comp_m_m_c @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_78_comp__apply__eq,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,X: c,H: c > m,K: c > c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_M750374444_m_m_c @ F @ G2 @ X )
        = ( comp_c_m_c @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_79_comp__apply__eq,axiom,
    ! [F: m > m,G2: monomo197243225tT_a_m > m,X: monomo197243225tT_a_m,H: m > m,K: monomo197243225tT_a_m > m] :
      ( ( ( F @ ( G2 @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_m263856566tT_a_m @ F @ G2 @ X )
        = ( comp_m263856566tT_a_m @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_80_comp__apply__eq,axiom,
    ! [F: m > m,G2: c > m,X: c,H: monomo197243225tT_a_m > m,K: c > monomo197243225tT_a_m] :
      ( ( ( F @ ( G2 @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_m_m_c @ F @ G2 @ X )
        = ( comp_M750374444_m_m_c @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_81_comp__apply__eq,axiom,
    ! [F: c > monomo197243225tT_a_m,G2: c > c,X: c,H: c > monomo197243225tT_a_m,K: c > c] :
      ( ( ( F @ ( G2 @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_c1772230468_a_m_c @ F @ G2 @ X )
        = ( comp_c1772230468_a_m_c @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_82_nondetT_Oinject,axiom,
    ! [X: m,Ya: m] :
      ( ( ( monomo412532791tT_m_a @ X )
        = ( monomo412532791tT_m_a @ Ya ) )
      = ( X = Ya ) ) ).

% nondetT.inject
thf(fact_83_nondetT_Ocollapse,axiom,
    ! [NondetT: monomo197243225tT_a_m] :
      ( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ NondetT ) )
      = NondetT ) ).

% nondetT.collapse
thf(fact_84_nondetT_Oexhaust,axiom,
    ! [Y: monomo197243225tT_a_m] :
      ~ ! [X4: m] :
          ( Y
         != ( monomo412532791tT_m_a @ X4 ) ) ).

% nondetT.exhaust
thf(fact_85_nondetT_Oinduct,axiom,
    ! [P: monomo197243225tT_a_m > $o,NondetT: monomo197243225tT_a_m] :
      ( ! [Xa: m] : ( P @ ( monomo412532791tT_m_a @ Xa ) )
     => ( P @ NondetT ) ) ).

% nondetT.induct
thf(fact_86_nondetT_Oexhaust__sel,axiom,
    ! [NondetT: monomo197243225tT_a_m] :
      ( NondetT
      = ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ NondetT ) ) ) ).

% nondetT.exhaust_sel
thf(fact_87_nondetT_Osel,axiom,
    ! [X: m] :
      ( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ X ) )
      = X ) ).

% nondetT.sel
thf(fact_88_rewriteR__comp__comp2,axiom,
    ! [G2: c > monomo197243225tT_a_m,H: c > c,R1: monomo197243225tT_a_m > monomo197243225tT_a_m,R2: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m,L: monomo197243225tT_a_m > m] :
      ( ( ( comp_c1772230468_a_m_c @ G2 @ H )
        = ( comp_M864375327_a_m_c @ R1 @ R2 ) )
     => ( ( ( comp_M1944986301tT_a_m @ F @ R1 )
          = L )
       => ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ G2 ) @ H )
          = ( comp_M750374444_m_m_c @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_89_rewriteR__comp__comp2,axiom,
    ! [G2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,R1: c > monomo197243225tT_a_m,R2: c > c,F: monomo197243225tT_a_m > m,L: c > m] :
      ( ( ( comp_M864375327_a_m_c @ G2 @ H )
        = ( comp_c1772230468_a_m_c @ R1 @ R2 ) )
     => ( ( ( comp_M750374444_m_m_c @ F @ R1 )
          = L )
       => ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ G2 ) @ H )
          = ( comp_c_m_c @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_90_rewriteR__comp__comp2,axiom,
    ! [G2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m,R1: monomo197243225tT_a_m > m,R2: c > monomo197243225tT_a_m,F: m > m,L: monomo197243225tT_a_m > m] :
      ( ( ( comp_M750374444_m_m_c @ G2 @ H )
        = ( comp_M750374444_m_m_c @ R1 @ R2 ) )
     => ( ( ( comp_m263856566tT_a_m @ F @ R1 )
          = L )
       => ( ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ F @ G2 ) @ H )
          = ( comp_M750374444_m_m_c @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_91_rewriteR__comp__comp2,axiom,
    ! [G2: c > c,H: c > c,R1: m > c,R2: c > m,F: c > m,L: m > m] :
      ( ( ( comp_c_c_c @ G2 @ H )
        = ( comp_m_c_c @ R1 @ R2 ) )
     => ( ( ( comp_c_m_m @ F @ R1 )
          = L )
       => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
          = ( comp_m_m_c @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_92_rewriteR__comp__comp2,axiom,
    ! [G2: m > c,H: c > m,R1: c > c,R2: c > c,F: c > m,L: c > m] :
      ( ( ( comp_m_c_c @ G2 @ H )
        = ( comp_c_c_c @ R1 @ R2 ) )
     => ( ( ( comp_c_m_c @ F @ R1 )
          = L )
       => ( ( comp_m_m_c @ ( comp_c_m_m @ F @ G2 ) @ H )
          = ( comp_c_m_c @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_93_rewriteR__comp__comp2,axiom,
    ! [G2: c > c,H: c > c,R1: c > c,R2: c > c,F: c > m,L: c > m] :
      ( ( ( comp_c_c_c @ G2 @ H )
        = ( comp_c_c_c @ R1 @ R2 ) )
     => ( ( ( comp_c_m_c @ F @ R1 )
          = L )
       => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
          = ( comp_c_m_c @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_94_rewriteR__comp__comp2,axiom,
    ! [G2: m > m,H: c > m,R1: m > m,R2: c > m,F: m > m,L: m > m] :
      ( ( ( comp_m_m_c @ G2 @ H )
        = ( comp_m_m_c @ R1 @ R2 ) )
     => ( ( ( comp_m_m_m @ F @ R1 )
          = L )
       => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
          = ( comp_m_m_c @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_95_rewriteR__comp__comp2,axiom,
    ! [G2: m > m,H: c > m,R1: c > m,R2: c > c,F: m > m,L: c > m] :
      ( ( ( comp_m_m_c @ G2 @ H )
        = ( comp_c_m_c @ R1 @ R2 ) )
     => ( ( ( comp_m_m_c @ F @ R1 )
          = L )
       => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
          = ( comp_c_m_c @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_96_rewriteR__comp__comp2,axiom,
    ! [G2: c > m,H: c > c,R1: m > m,R2: c > m,F: m > m,L: m > m] :
      ( ( ( comp_c_m_c @ G2 @ H )
        = ( comp_m_m_c @ R1 @ R2 ) )
     => ( ( ( comp_m_m_m @ F @ R1 )
          = L )
       => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
          = ( comp_m_m_c @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_97_rewriteR__comp__comp2,axiom,
    ! [G2: c > m,H: c > c,R1: c > m,R2: c > c,F: m > m,L: c > m] :
      ( ( ( comp_c_m_c @ G2 @ H )
        = ( comp_c_m_c @ R1 @ R2 ) )
     => ( ( ( comp_m_m_c @ F @ R1 )
          = L )
       => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
          = ( comp_c_m_c @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_98_rewriteL__comp__comp2,axiom,
    ! [F: m > m,G2: monomo197243225tT_a_m > m,L1: monomo197243225tT_a_m > m,L2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,R: c > monomo197243225tT_a_m] :
      ( ( ( comp_m263856566tT_a_m @ F @ G2 )
        = ( comp_M1944986301tT_a_m @ L1 @ L2 ) )
     => ( ( ( comp_M864375327_a_m_c @ L2 @ H )
          = R )
       => ( ( comp_m_m_c @ F @ ( comp_M750374444_m_m_c @ G2 @ H ) )
          = ( comp_M750374444_m_m_c @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_99_rewriteL__comp__comp2,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: monomo197243225tT_a_m > monomo197243225tT_a_m,L1: m > m,L2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m,R: c > m] :
      ( ( ( comp_M1944986301tT_a_m @ F @ G2 )
        = ( comp_m263856566tT_a_m @ L1 @ L2 ) )
     => ( ( ( comp_M750374444_m_m_c @ L2 @ H )
          = R )
       => ( ( comp_M750374444_m_m_c @ F @ ( comp_M864375327_a_m_c @ G2 @ H ) )
          = ( comp_m_m_c @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_100_rewriteL__comp__comp2,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,L1: monomo197243225tT_a_m > m,L2: c > monomo197243225tT_a_m,H: c > c,R: c > monomo197243225tT_a_m] :
      ( ( ( comp_M750374444_m_m_c @ F @ G2 )
        = ( comp_M750374444_m_m_c @ L1 @ L2 ) )
     => ( ( ( comp_c1772230468_a_m_c @ L2 @ H )
          = R )
       => ( ( comp_M750374444_m_m_c @ F @ ( comp_c1772230468_a_m_c @ G2 @ H ) )
          = ( comp_M750374444_m_m_c @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_101_rewriteL__comp__comp2,axiom,
    ! [F: m > m,G2: m > m,L1: c > m,L2: m > c,H: c > m,R: c > c] :
      ( ( ( comp_m_m_m @ F @ G2 )
        = ( comp_c_m_m @ L1 @ L2 ) )
     => ( ( ( comp_m_c_c @ L2 @ H )
          = R )
       => ( ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) )
          = ( comp_c_m_c @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_102_rewriteL__comp__comp2,axiom,
    ! [F: m > m,G2: m > m,L1: m > m,L2: m > m,H: c > m,R: c > m] :
      ( ( ( comp_m_m_m @ F @ G2 )
        = ( comp_m_m_m @ L1 @ L2 ) )
     => ( ( ( comp_m_m_c @ L2 @ H )
          = R )
       => ( ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) )
          = ( comp_m_m_c @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_103_rewriteL__comp__comp2,axiom,
    ! [F: c > m,G2: m > c,L1: m > m,L2: m > m,H: c > m,R: c > m] :
      ( ( ( comp_c_m_m @ F @ G2 )
        = ( comp_m_m_m @ L1 @ L2 ) )
     => ( ( ( comp_m_m_c @ L2 @ H )
          = R )
       => ( ( comp_c_m_c @ F @ ( comp_m_c_c @ G2 @ H ) )
          = ( comp_m_m_c @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_104_rewriteL__comp__comp2,axiom,
    ! [F: m > m,G2: c > m,L1: m > m,L2: c > m,H: c > c,R: c > m] :
      ( ( ( comp_m_m_c @ F @ G2 )
        = ( comp_m_m_c @ L1 @ L2 ) )
     => ( ( ( comp_c_m_c @ L2 @ H )
          = R )
       => ( ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
          = ( comp_m_m_c @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_105_rewriteL__comp__comp2,axiom,
    ! [F: m > m,G2: c > m,L1: c > m,L2: c > c,H: c > c,R: c > c] :
      ( ( ( comp_m_m_c @ F @ G2 )
        = ( comp_c_m_c @ L1 @ L2 ) )
     => ( ( ( comp_c_c_c @ L2 @ H )
          = R )
       => ( ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
          = ( comp_c_m_c @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_106_rewriteL__comp__comp2,axiom,
    ! [F: c > m,G2: c > c,L1: m > m,L2: c > m,H: c > c,R: c > m] :
      ( ( ( comp_c_m_c @ F @ G2 )
        = ( comp_m_m_c @ L1 @ L2 ) )
     => ( ( ( comp_c_m_c @ L2 @ H )
          = R )
       => ( ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) )
          = ( comp_m_m_c @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_107_rewriteL__comp__comp2,axiom,
    ! [F: c > m,G2: c > c,L1: c > m,L2: c > c,H: c > c,R: c > c] :
      ( ( ( comp_c_m_c @ F @ G2 )
        = ( comp_c_m_c @ L1 @ L2 ) )
     => ( ( ( comp_c_c_c @ L2 @ H )
          = R )
       => ( ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) )
          = ( comp_c_m_c @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_108_rewriteR__comp__comp,axiom,
    ! [G2: c > monomo197243225tT_a_m,H: c > c,R: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
      ( ( ( comp_c1772230468_a_m_c @ G2 @ H )
        = R )
     => ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ G2 ) @ H )
        = ( comp_M750374444_m_m_c @ F @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_109_rewriteR__comp__comp,axiom,
    ! [G2: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m,R: c > m,F: m > m] :
      ( ( ( comp_M750374444_m_m_c @ G2 @ H )
        = R )
     => ( ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ F @ G2 ) @ H )
        = ( comp_m_m_c @ F @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_110_rewriteR__comp__comp,axiom,
    ! [G2: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,R: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
      ( ( ( comp_M864375327_a_m_c @ G2 @ H )
        = R )
     => ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ G2 ) @ H )
        = ( comp_M750374444_m_m_c @ F @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_111_rewriteR__comp__comp,axiom,
    ! [G2: m > c,H: c > m,R: c > c,F: c > m] :
      ( ( ( comp_m_c_c @ G2 @ H )
        = R )
     => ( ( comp_m_m_c @ ( comp_c_m_m @ F @ G2 ) @ H )
        = ( comp_c_m_c @ F @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_112_rewriteR__comp__comp,axiom,
    ! [G2: c > c,H: c > c,R: c > c,F: c > m] :
      ( ( ( comp_c_c_c @ G2 @ H )
        = R )
     => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ G2 ) @ H )
        = ( comp_c_m_c @ F @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_113_rewriteR__comp__comp,axiom,
    ! [G2: m > m,H: c > m,R: c > m,F: m > m] :
      ( ( ( comp_m_m_c @ G2 @ H )
        = R )
     => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ G2 ) @ H )
        = ( comp_m_m_c @ F @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_114_rewriteR__comp__comp,axiom,
    ! [G2: c > m,H: c > c,R: c > m,F: m > m] :
      ( ( ( comp_c_m_c @ G2 @ H )
        = R )
     => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ G2 ) @ H )
        = ( comp_m_m_c @ F @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_115_rewriteR__comp__comp,axiom,
    ! [G2: c > m,H: monomo197243225tT_a_m > c,R: monomo197243225tT_a_m > m,F: m > m] :
      ( ( ( comp_c997395372tT_a_m @ G2 @ H )
        = R )
     => ( ( comp_c997395372tT_a_m @ ( comp_m_m_c @ F @ G2 ) @ H )
        = ( comp_m263856566tT_a_m @ F @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_116_rewriteR__comp__comp,axiom,
    ! [G2: monomo197243225tT_a_m > c,H: c > monomo197243225tT_a_m,R: c > c,F: c > m] :
      ( ( ( comp_M1062614966_m_c_c @ G2 @ H )
        = R )
     => ( ( comp_M750374444_m_m_c @ ( comp_c997395372tT_a_m @ F @ G2 ) @ H )
        = ( comp_c_m_c @ F @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_117_rewriteR__comp__comp,axiom,
    ! [G2: m > monomo197243225tT_a_m,H: c > m,R: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
      ( ( ( comp_m1038691662_a_m_c @ G2 @ H )
        = R )
     => ( ( comp_m_m_c @ ( comp_M750374454_m_m_m @ F @ G2 ) @ H )
        = ( comp_M750374444_m_m_c @ F @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_118_rewriteL__comp__comp,axiom,
    ! [F: m > m,G2: monomo197243225tT_a_m > m,L: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m] :
      ( ( ( comp_m263856566tT_a_m @ F @ G2 )
        = L )
     => ( ( comp_m_m_c @ F @ ( comp_M750374444_m_m_c @ G2 @ H ) )
        = ( comp_M750374444_m_m_c @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_119_rewriteL__comp__comp,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: c > monomo197243225tT_a_m,L: c > m,H: c > c] :
      ( ( ( comp_M750374444_m_m_c @ F @ G2 )
        = L )
     => ( ( comp_M750374444_m_m_c @ F @ ( comp_c1772230468_a_m_c @ G2 @ H ) )
        = ( comp_c_m_c @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_120_rewriteL__comp__comp,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: monomo197243225tT_a_m > monomo197243225tT_a_m,L: monomo197243225tT_a_m > m,H: c > monomo197243225tT_a_m] :
      ( ( ( comp_M1944986301tT_a_m @ F @ G2 )
        = L )
     => ( ( comp_M750374444_m_m_c @ F @ ( comp_M864375327_a_m_c @ G2 @ H ) )
        = ( comp_M750374444_m_m_c @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_121_rewriteL__comp__comp,axiom,
    ! [F: m > m,G2: m > m,L: m > m,H: c > m] :
      ( ( ( comp_m_m_m @ F @ G2 )
        = L )
     => ( ( comp_m_m_c @ F @ ( comp_m_m_c @ G2 @ H ) )
        = ( comp_m_m_c @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_122_rewriteL__comp__comp,axiom,
    ! [F: c > m,G2: m > c,L: m > m,H: c > m] :
      ( ( ( comp_c_m_m @ F @ G2 )
        = L )
     => ( ( comp_c_m_c @ F @ ( comp_m_c_c @ G2 @ H ) )
        = ( comp_m_m_c @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_123_rewriteL__comp__comp,axiom,
    ! [F: m > m,G2: c > m,L: c > m,H: c > c] :
      ( ( ( comp_m_m_c @ F @ G2 )
        = L )
     => ( ( comp_m_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
        = ( comp_c_m_c @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_124_rewriteL__comp__comp,axiom,
    ! [F: c > m,G2: c > c,L: c > m,H: c > c] :
      ( ( ( comp_c_m_c @ F @ G2 )
        = L )
     => ( ( comp_c_m_c @ F @ ( comp_c_c_c @ G2 @ H ) )
        = ( comp_c_m_c @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_125_rewriteL__comp__comp,axiom,
    ! [F: m > monomo197243225tT_a_m,G2: c > m,L: c > monomo197243225tT_a_m,H: c > c] :
      ( ( ( comp_m1038691662_a_m_c @ F @ G2 )
        = L )
     => ( ( comp_m1038691662_a_m_c @ F @ ( comp_c_m_c @ G2 @ H ) )
        = ( comp_c1772230468_a_m_c @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_126_rewriteL__comp__comp,axiom,
    ! [F: monomo197243225tT_a_m > m,G2: m > monomo197243225tT_a_m,L: m > m,H: c > m] :
      ( ( ( comp_M750374454_m_m_m @ F @ G2 )
        = L )
     => ( ( comp_M750374444_m_m_c @ F @ ( comp_m1038691662_a_m_c @ G2 @ H ) )
        = ( comp_m_m_c @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_127_rewriteL__comp__comp,axiom,
    ! [F: m > m,G2: m > m,L: m > m,H: monomo197243225tT_a_m > m] :
      ( ( ( comp_m_m_m @ F @ G2 )
        = L )
     => ( ( comp_m263856566tT_a_m @ F @ ( comp_m263856566tT_a_m @ G2 @ H ) )
        = ( comp_m263856566tT_a_m @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_128_type__copy__map__cong0,axiom,
    ! [M: c > monomo197243225tT_a_m,G2: c > c,X: c,N: monomo197243225tT_a_m > monomo197243225tT_a_m,H: c > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
      ( ( ( M @ ( G2 @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ M ) @ G2 @ X )
        = ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_129_type__copy__map__cong0,axiom,
    ! [M: monomo197243225tT_a_m > monomo197243225tT_a_m,G2: c > monomo197243225tT_a_m,X: c,N: c > monomo197243225tT_a_m,H: c > c,F: monomo197243225tT_a_m > m] :
      ( ( ( M @ ( G2 @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ F @ M ) @ G2 @ X )
        = ( comp_c_m_c @ ( comp_M750374444_m_m_c @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_130_type__copy__map__cong0,axiom,
    ! [M: m > m,G2: c > m,X: c,N: c > m,H: c > c,F: m > m] :
      ( ( ( M @ ( G2 @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_m_m_c @ ( comp_m_m_m @ F @ M ) @ G2 @ X )
        = ( comp_c_m_c @ ( comp_m_m_c @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_131_type__copy__map__cong0,axiom,
    ! [M: m > c,G2: c > m,X: c,N: c > c,H: c > c,F: c > m] :
      ( ( ( M @ ( G2 @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_m_m_c @ ( comp_c_m_m @ F @ M ) @ G2 @ X )
        = ( comp_c_m_c @ ( comp_c_m_c @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_132_type__copy__map__cong0,axiom,
    ! [M: c > m,G2: c > c,X: c,N: m > m,H: c > m,F: m > m] :
      ( ( ( M @ ( G2 @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ M ) @ G2 @ X )
        = ( comp_m_m_c @ ( comp_m_m_m @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_133_type__copy__map__cong0,axiom,
    ! [M: c > m,G2: c > c,X: c,N: c > m,H: c > c,F: m > m] :
      ( ( ( M @ ( G2 @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_c_m_c @ ( comp_m_m_c @ F @ M ) @ G2 @ X )
        = ( comp_c_m_c @ ( comp_m_m_c @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_134_type__copy__map__cong0,axiom,
    ! [M: c > c,G2: c > c,X: c,N: m > c,H: c > m,F: c > m] :
      ( ( ( M @ ( G2 @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ M ) @ G2 @ X )
        = ( comp_m_m_c @ ( comp_c_m_m @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_135_type__copy__map__cong0,axiom,
    ! [M: c > c,G2: c > c,X: c,N: c > c,H: c > c,F: c > m] :
      ( ( ( M @ ( G2 @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_c_m_c @ ( comp_c_m_c @ F @ M ) @ G2 @ X )
        = ( comp_c_m_c @ ( comp_c_m_c @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_136_type__copy__map__cong0,axiom,
    ! [M: c > m,G2: monomo197243225tT_a_m > c,X: monomo197243225tT_a_m,N: m > m,H: monomo197243225tT_a_m > m,F: m > m] :
      ( ( ( M @ ( G2 @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_c997395372tT_a_m @ ( comp_m_m_c @ F @ M ) @ G2 @ X )
        = ( comp_m263856566tT_a_m @ ( comp_m_m_m @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_137_type__copy__map__cong0,axiom,
    ! [M: c > c,G2: monomo197243225tT_a_m > c,X: monomo197243225tT_a_m,N: m > c,H: monomo197243225tT_a_m > m,F: c > m] :
      ( ( ( M @ ( G2 @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_c997395372tT_a_m @ ( comp_c_m_c @ F @ M ) @ G2 @ X )
        = ( comp_m263856566tT_a_m @ ( comp_c_m_m @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_138_fun_Omap__comp,axiom,
    ! [G2: m > m,F: monomo197243225tT_a_m > m,V: c > monomo197243225tT_a_m] :
      ( ( comp_m_m_c @ G2 @ ( comp_M750374444_m_m_c @ F @ V ) )
      = ( comp_M750374444_m_m_c @ ( comp_m263856566tT_a_m @ G2 @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_139_fun_Omap__comp,axiom,
    ! [G2: monomo197243225tT_a_m > m,F: c > monomo197243225tT_a_m,V: c > c] :
      ( ( comp_M750374444_m_m_c @ G2 @ ( comp_c1772230468_a_m_c @ F @ V ) )
      = ( comp_c_m_c @ ( comp_M750374444_m_m_c @ G2 @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_140_fun_Omap__comp,axiom,
    ! [G2: monomo197243225tT_a_m > m,F: monomo197243225tT_a_m > monomo197243225tT_a_m,V: c > monomo197243225tT_a_m] :
      ( ( comp_M750374444_m_m_c @ G2 @ ( comp_M864375327_a_m_c @ F @ V ) )
      = ( comp_M750374444_m_m_c @ ( comp_M1944986301tT_a_m @ G2 @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_141_fun_Omap__comp,axiom,
    ! [G2: m > m,F: m > m,V: c > m] :
      ( ( comp_m_m_c @ G2 @ ( comp_m_m_c @ F @ V ) )
      = ( comp_m_m_c @ ( comp_m_m_m @ G2 @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_142_fun_Omap__comp,axiom,
    ! [G2: m > m,F: c > m,V: c > c] :
      ( ( comp_m_m_c @ G2 @ ( comp_c_m_c @ F @ V ) )
      = ( comp_c_m_c @ ( comp_m_m_c @ G2 @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_143_fun_Omap__comp,axiom,
    ! [G2: c > m,F: m > c,V: c > m] :
      ( ( comp_c_m_c @ G2 @ ( comp_m_c_c @ F @ V ) )
      = ( comp_m_m_c @ ( comp_c_m_m @ G2 @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_144_fun_Omap__comp,axiom,
    ! [G2: c > m,F: c > c,V: c > c] :
      ( ( comp_c_m_c @ G2 @ ( comp_c_c_c @ F @ V ) )
      = ( comp_c_m_c @ ( comp_c_m_c @ G2 @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_145_fun_Omap__comp,axiom,
    ! [G2: m > monomo197243225tT_a_m,F: c > m,V: c > c] :
      ( ( comp_m1038691662_a_m_c @ G2 @ ( comp_c_m_c @ F @ V ) )
      = ( comp_c1772230468_a_m_c @ ( comp_m1038691662_a_m_c @ G2 @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_146_fun_Omap__comp,axiom,
    ! [G2: monomo197243225tT_a_m > m,F: m > monomo197243225tT_a_m,V: c > m] :
      ( ( comp_M750374444_m_m_c @ G2 @ ( comp_m1038691662_a_m_c @ F @ V ) )
      = ( comp_m_m_c @ ( comp_M750374454_m_m_m @ G2 @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_147_fun_Omap__comp,axiom,
    ! [G2: m > m,F: c > m,V: monomo197243225tT_a_m > c] :
      ( ( comp_m263856566tT_a_m @ G2 @ ( comp_c997395372tT_a_m @ F @ V ) )
      = ( comp_c997395372tT_a_m @ ( comp_m_m_c @ G2 @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_148_function__factors__left,axiom,
    ! [G2: monomo197243225tT_a_m > monomo197243225tT_a_m,F: monomo197243225tT_a_m > m] :
      ( ( ! [X2: monomo197243225tT_a_m,Y2: monomo197243225tT_a_m] :
            ( ( ( G2 @ X2 )
              = ( G2 @ Y2 ) )
           => ( ( F @ X2 )
              = ( F @ Y2 ) ) ) )
      = ( ? [H2: monomo197243225tT_a_m > m] :
            ( F
            = ( comp_M1944986301tT_a_m @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_149_function__factors__left,axiom,
    ! [G2: monomo197243225tT_a_m > m,F: monomo197243225tT_a_m > m] :
      ( ( ! [X2: monomo197243225tT_a_m,Y2: monomo197243225tT_a_m] :
            ( ( ( G2 @ X2 )
              = ( G2 @ Y2 ) )
           => ( ( F @ X2 )
              = ( F @ Y2 ) ) ) )
      = ( ? [H2: m > m] :
            ( F
            = ( comp_m263856566tT_a_m @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_150_function__factors__left,axiom,
    ! [G2: c > m,F: c > m] :
      ( ( ! [X2: c,Y2: c] :
            ( ( ( G2 @ X2 )
              = ( G2 @ Y2 ) )
           => ( ( F @ X2 )
              = ( F @ Y2 ) ) ) )
      = ( ? [H2: m > m] :
            ( F
            = ( comp_m_m_c @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_151_function__factors__left,axiom,
    ! [G2: c > c,F: c > monomo197243225tT_a_m] :
      ( ( ! [X2: c,Y2: c] :
            ( ( ( G2 @ X2 )
              = ( G2 @ Y2 ) )
           => ( ( F @ X2 )
              = ( F @ Y2 ) ) ) )
      = ( ? [H2: c > monomo197243225tT_a_m] :
            ( F
            = ( comp_c1772230468_a_m_c @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_152_function__factors__left,axiom,
    ! [G2: c > c,F: c > m] :
      ( ( ! [X2: c,Y2: c] :
            ( ( ( G2 @ X2 )
              = ( G2 @ Y2 ) )
           => ( ( F @ X2 )
              = ( F @ Y2 ) ) ) )
      = ( ? [H2: c > m] :
            ( F
            = ( comp_c_m_c @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_153_function__factors__left,axiom,
    ! [G2: c > monomo197243225tT_a_m,F: c > m] :
      ( ( ! [X2: c,Y2: c] :
            ( ( ( G2 @ X2 )
              = ( G2 @ Y2 ) )
           => ( ( F @ X2 )
              = ( F @ Y2 ) ) ) )
      = ( ? [H2: monomo197243225tT_a_m > m] :
            ( F
            = ( comp_M750374444_m_m_c @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_154_function__factors__right,axiom,
    ! [G2: monomo197243225tT_a_m > m,F: monomo197243225tT_a_m > m] :
      ( ( ! [X2: monomo197243225tT_a_m] :
          ? [Y2: monomo197243225tT_a_m] :
            ( ( G2 @ Y2 )
            = ( F @ X2 ) ) )
      = ( ? [H2: monomo197243225tT_a_m > monomo197243225tT_a_m] :
            ( F
            = ( comp_M1944986301tT_a_m @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_155_function__factors__right,axiom,
    ! [G2: m > m,F: monomo197243225tT_a_m > m] :
      ( ( ! [X2: monomo197243225tT_a_m] :
          ? [Y2: m] :
            ( ( G2 @ Y2 )
            = ( F @ X2 ) ) )
      = ( ? [H2: monomo197243225tT_a_m > m] :
            ( F
            = ( comp_m263856566tT_a_m @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_156_function__factors__right,axiom,
    ! [G2: m > m,F: c > m] :
      ( ( ! [X2: c] :
          ? [Y2: m] :
            ( ( G2 @ Y2 )
            = ( F @ X2 ) ) )
      = ( ? [H2: c > m] :
            ( F
            = ( comp_m_m_c @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_157_function__factors__right,axiom,
    ! [G2: c > monomo197243225tT_a_m,F: c > monomo197243225tT_a_m] :
      ( ( ! [X2: c] :
          ? [Y2: c] :
            ( ( G2 @ Y2 )
            = ( F @ X2 ) ) )
      = ( ? [H2: c > c] :
            ( F
            = ( comp_c1772230468_a_m_c @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_158_function__factors__right,axiom,
    ! [G2: c > m,F: c > m] :
      ( ( ! [X2: c] :
          ? [Y2: c] :
            ( ( G2 @ Y2 )
            = ( F @ X2 ) ) )
      = ( ? [H2: c > c] :
            ( F
            = ( comp_c_m_c @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_159_function__factors__right,axiom,
    ! [G2: monomo197243225tT_a_m > m,F: c > m] :
      ( ( ! [X2: c] :
          ? [Y2: monomo197243225tT_a_m] :
            ( ( G2 @ Y2 )
            = ( F @ X2 ) ) )
      = ( ? [H2: c > monomo197243225tT_a_m] :
            ( F
            = ( comp_M750374444_m_m_c @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_160_cinsert__cDiff__single,axiom,
    ! [A2: c,A: countable_Set_cset_c] :
      ( ( counta472291938sert_c @ A2 @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) )
      = ( counta472291938sert_c @ A2 @ A ) ) ).

% cinsert_cDiff_single
thf(fact_161_cDiff__idemp,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ B2 )
      = ( minus_1646763425cset_c @ A @ B2 ) ) ).

% cDiff_idemp
thf(fact_162_cDiff__cancel,axiom,
    ! [A: countable_Set_cset_c] :
      ( ( minus_1646763425cset_c @ A @ A )
      = bot_bo1320844070cset_c ) ).

% cDiff_cancel
thf(fact_163_cDiff__cempty,axiom,
    ! [A: countable_Set_cset_c] :
      ( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
      = A ) ).

% cDiff_cempty
thf(fact_164_cempty__cDiff,axiom,
    ! [A: countable_Set_cset_c] :
      ( ( minus_1646763425cset_c @ bot_bo1320844070cset_c @ A )
      = bot_bo1320844070cset_c ) ).

% cempty_cDiff
thf(fact_165_cDiff__cinsert,axiom,
    ! [A: countable_Set_cset_c,A2: c,B2: countable_Set_cset_c] :
      ( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ B2 ) )
      = ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) ) ).

% cDiff_cinsert
thf(fact_166_cDiff__cinsert2,axiom,
    ! [A: countable_Set_cset_c,A2: c,B2: countable_Set_cset_c] :
      ( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ B2 ) )
      = ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) @ B2 ) ) ).

% cDiff_cinsert2
thf(fact_167_cDiff__single__cinsert,axiom,
    ! [A: countable_Set_cset_c,X: c,B2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) @ B2 )
     => ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) ) ) ).

% cDiff_single_cinsert
thf(fact_168_cinsert__cDiff,axiom,
    ! [A2: c,A: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ A2 @ A )
     => ( ( counta472291938sert_c @ A2 @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) ) )
        = A ) ) ).

% cinsert_cDiff
thf(fact_169_order__refl,axiom,
    ! [X: countable_Set_cset_c] : ( ord_le15364698cset_c @ X @ X ) ).

% order_refl
thf(fact_170_csubset__antisym,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A @ B2 )
     => ( ( ord_le15364698cset_c @ B2 @ A )
       => ( A = B2 ) ) ) ).

% csubset_antisym
thf(fact_171_all__not__cin__conv,axiom,
    ! [A: countable_Set_cset_c] :
      ( ( ! [X2: c] :
            ~ ( countable_Set_cin_c @ X2 @ A ) )
      = ( A = bot_bo1320844070cset_c ) ) ).

% all_not_cin_conv
thf(fact_172_cempty__iff,axiom,
    ! [C: c] :
      ~ ( countable_Set_cin_c @ C @ bot_bo1320844070cset_c ) ).

% cempty_iff
thf(fact_173_cinsert__iff,axiom,
    ! [A2: c,B: c,A: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ A ) )
      = ( ( A2 = B )
        | ( countable_Set_cin_c @ A2 @ A ) ) ) ).

% cinsert_iff
thf(fact_174_cinsertCI,axiom,
    ! [A2: c,B2: countable_Set_cset_c,B: c] :
      ( ( ~ ( countable_Set_cin_c @ A2 @ B2 )
       => ( A2 = B ) )
     => ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ B2 ) ) ) ).

% cinsertCI
thf(fact_175_csubsetI,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ! [X4: c] :
          ( ( countable_Set_cin_c @ X4 @ A )
         => ( countable_Set_cin_c @ X4 @ B2 ) )
     => ( ord_le15364698cset_c @ A @ B2 ) ) ).

% csubsetI
thf(fact_176_cempty__fsubsetI,axiom,
    ! [X: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ X ) ).

% cempty_fsubsetI
thf(fact_177_csubset__cempty,axiom,
    ! [A: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
      = ( A = bot_bo1320844070cset_c ) ) ).

% csubset_cempty
thf(fact_178_cDiff__iff,axiom,
    ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
      = ( ( countable_Set_cin_c @ C @ A )
        & ~ ( countable_Set_cin_c @ C @ B2 ) ) ) ).

% cDiff_iff
thf(fact_179_cDiffI,axiom,
    ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ C @ A )
     => ( ~ ( countable_Set_cin_c @ C @ B2 )
       => ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) ) ) ) ).

% cDiffI
thf(fact_180_cinsert__csubset,axiom,
    ! [X: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
      = ( ( countable_Set_cin_c @ X @ B2 )
        & ( ord_le15364698cset_c @ A @ B2 ) ) ) ).

% cinsert_csubset
thf(fact_181_cinsert__cDiff1,axiom,
    ! [X: c,B2: countable_Set_cset_c,A: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ X @ B2 )
     => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
        = ( minus_1646763425cset_c @ A @ B2 ) ) ) ).

% cinsert_cDiff1
thf(fact_182_csubset__cinsert,axiom,
    ! [X: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ~ ( countable_Set_cin_c @ X @ A )
     => ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) )
        = ( ord_le15364698cset_c @ A @ B2 ) ) ) ).

% csubset_cinsert
thf(fact_183_dual__order_Oantisym,axiom,
    ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ B @ A2 )
     => ( ( ord_le15364698cset_c @ A2 @ B )
       => ( A2 = B ) ) ) ).

% dual_order.antisym
thf(fact_184_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : Y3 = Z )
    = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ B3 @ A4 )
          & ( ord_le15364698cset_c @ A4 @ B3 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_185_dual__order_Otrans,axiom,
    ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ B @ A2 )
     => ( ( ord_le15364698cset_c @ C @ B )
       => ( ord_le15364698cset_c @ C @ A2 ) ) ) ).

% dual_order.trans
thf(fact_186_dual__order_Orefl,axiom,
    ! [A2: countable_Set_cset_c] : ( ord_le15364698cset_c @ A2 @ A2 ) ).

% dual_order.refl
thf(fact_187_order__trans,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ X @ Y )
     => ( ( ord_le15364698cset_c @ Y @ Z2 )
       => ( ord_le15364698cset_c @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_188_order__class_Oorder_Oantisym,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ B )
     => ( ( ord_le15364698cset_c @ B @ A2 )
       => ( A2 = B ) ) ) ).

% order_class.order.antisym
thf(fact_189_ord__le__eq__trans,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ B )
     => ( ( B = C )
       => ( ord_le15364698cset_c @ A2 @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_190_ord__eq__le__trans,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( A2 = B )
     => ( ( ord_le15364698cset_c @ B @ C )
       => ( ord_le15364698cset_c @ A2 @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_191_order__class_Oorder_Oeq__iff,axiom,
    ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : Y3 = Z )
    = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ A4 @ B3 )
          & ( ord_le15364698cset_c @ B3 @ A4 ) ) ) ) ).

% order_class.order.eq_iff
thf(fact_192_antisym__conv,axiom,
    ! [Y: countable_Set_cset_c,X: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ Y @ X )
     => ( ( ord_le15364698cset_c @ X @ Y )
        = ( X = Y ) ) ) ).

% antisym_conv
thf(fact_193_eqcelem__imp__iff,axiom,
    ! [X: c,Y: c,A: countable_Set_cset_c] :
      ( ( X = Y )
     => ( ( countable_Set_cin_c @ X @ A )
        = ( countable_Set_cin_c @ Y @ A ) ) ) ).

% eqcelem_imp_iff
thf(fact_194_cset__eq__csubset,axiom,
    ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : Y3 = Z )
    = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ A3 @ B4 )
          & ( ord_le15364698cset_c @ B4 @ A3 ) ) ) ) ).

% cset_eq_csubset
thf(fact_195_order_Otrans,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ B )
     => ( ( ord_le15364698cset_c @ B @ C )
       => ( ord_le15364698cset_c @ A2 @ C ) ) ) ).

% order.trans
thf(fact_196_eqcset__imp__iff,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,X: c] :
      ( ( A = B2 )
     => ( ( countable_Set_cin_c @ X @ A )
        = ( countable_Set_cin_c @ X @ B2 ) ) ) ).

% eqcset_imp_iff
thf(fact_197_eq__refl,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( X = Y )
     => ( ord_le15364698cset_c @ X @ Y ) ) ).

% eq_refl
thf(fact_198_if__split__cin2,axiom,
    ! [A2: c,Q: $o,X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ A2 @ ( if_Cou1542198912cset_c @ Q @ X @ Y ) )
      = ( ( Q
         => ( countable_Set_cin_c @ A2 @ X ) )
        & ( ~ Q
         => ( countable_Set_cin_c @ A2 @ Y ) ) ) ) ).

% if_split_cin2
thf(fact_199_if__split__cin1,axiom,
    ! [Q: $o,X: c,Y: c,B: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ ( if_c @ Q @ X @ Y ) @ B )
      = ( ( Q
         => ( countable_Set_cin_c @ X @ B ) )
        & ( ~ Q
         => ( countable_Set_cin_c @ Y @ B ) ) ) ) ).

% if_split_cin1
thf(fact_200_eq__cmem__trans,axiom,
    ! [A2: c,B: c,A: countable_Set_cset_c] :
      ( ( A2 = B )
     => ( ( countable_Set_cin_c @ B @ A )
       => ( countable_Set_cin_c @ A2 @ A ) ) ) ).

% eq_cmem_trans
thf(fact_201_csubset__trans,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A @ B2 )
     => ( ( ord_le15364698cset_c @ B2 @ C2 )
       => ( ord_le15364698cset_c @ A @ C2 ) ) ) ).

% csubset_trans
thf(fact_202_csubset__refl,axiom,
    ! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ) ).

% csubset_refl
thf(fact_203_cequalityD2,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( A = B2 )
     => ( ord_le15364698cset_c @ B2 @ A ) ) ).

% cequalityD2
thf(fact_204_cequalityD1,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( A = B2 )
     => ( ord_le15364698cset_c @ A @ B2 ) ) ).

% cequalityD1
thf(fact_205_cequalityCE,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C: c] :
      ( ( A = B2 )
     => ( ( ( countable_Set_cin_c @ C @ A )
         => ~ ( countable_Set_cin_c @ C @ B2 ) )
       => ~ ( ~ ( countable_Set_cin_c @ C @ A )
           => ( countable_Set_cin_c @ C @ B2 ) ) ) ) ).

% cequalityCE
thf(fact_206_antisym,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ X @ Y )
     => ( ( ord_le15364698cset_c @ Y @ X )
       => ( X = Y ) ) ) ).

% antisym
thf(fact_207_cequalityE,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( A = B2 )
     => ~ ( ( ord_le15364698cset_c @ A @ B2 )
         => ~ ( ord_le15364698cset_c @ B2 @ A ) ) ) ).

% cequalityE
thf(fact_208_eq__iff,axiom,
    ( ( ^ [Y3: countable_Set_cset_c,Z: countable_Set_cset_c] : Y3 = Z )
    = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ X2 @ Y2 )
          & ( ord_le15364698cset_c @ Y2 @ X2 ) ) ) ) ).

% eq_iff
thf(fact_209_csubsetD,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C: c] :
      ( ( ord_le15364698cset_c @ A @ B2 )
     => ( ( countable_Set_cin_c @ C @ A )
       => ( countable_Set_cin_c @ C @ B2 ) ) ) ).

% csubsetD
thf(fact_210_cset__eqI,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ! [X4: c] :
          ( ( countable_Set_cin_c @ X4 @ A )
          = ( countable_Set_cin_c @ X4 @ B2 ) )
     => ( A = B2 ) ) ).

% cset_eqI
thf(fact_211_cin__mono,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,X: c] :
      ( ( ord_le15364698cset_c @ A @ B2 )
     => ( ( countable_Set_cin_c @ X @ A )
       => ( countable_Set_cin_c @ X @ B2 ) ) ) ).

% cin_mono
thf(fact_212_ord__le__eq__subst,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le15364698cset_c @ X4 @ Y4 )
             => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le15364698cset_c @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_213_ord__eq__le__subst,axiom,
    ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le15364698cset_c @ B @ C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le15364698cset_c @ X4 @ Y4 )
             => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le15364698cset_c @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_214_order__subst2,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ B )
     => ( ( ord_le15364698cset_c @ ( F @ B ) @ C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le15364698cset_c @ X4 @ Y4 )
             => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le15364698cset_c @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_215_order__subst1,axiom,
    ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ ( F @ B ) )
     => ( ( ord_le15364698cset_c @ B @ C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le15364698cset_c @ X4 @ Y4 )
             => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le15364698cset_c @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_216_equals__cemptyI,axiom,
    ! [A: countable_Set_cset_c] :
      ( ! [Y4: c] :
          ~ ( countable_Set_cin_c @ Y4 @ A )
     => ( A = bot_bo1320844070cset_c ) ) ).

% equals_cemptyI
thf(fact_217_equals__cemptyD,axiom,
    ! [A: countable_Set_cset_c,A2: c] :
      ( ( A = bot_bo1320844070cset_c )
     => ~ ( countable_Set_cin_c @ A2 @ A ) ) ).

% equals_cemptyD
thf(fact_218_ex__cin__conv,axiom,
    ! [A: countable_Set_cset_c] :
      ( ( ? [X2: c] : ( countable_Set_cin_c @ X2 @ A ) )
      = ( A != bot_bo1320844070cset_c ) ) ).

% ex_cin_conv
thf(fact_219_cemptyE,axiom,
    ! [A2: c] :
      ~ ( countable_Set_cin_c @ A2 @ bot_bo1320844070cset_c ) ).

% cemptyE
thf(fact_220_mk__disjoint__cinsert,axiom,
    ! [A2: c,A: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ A2 @ A )
     => ? [B5: countable_Set_cset_c] :
          ( ( A
            = ( counta472291938sert_c @ A2 @ B5 ) )
          & ~ ( countable_Set_cin_c @ A2 @ B5 ) ) ) ).

% mk_disjoint_cinsert
thf(fact_221_cinsert__absorb,axiom,
    ! [A2: c,A: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ A2 @ A )
     => ( ( counta472291938sert_c @ A2 @ A )
        = A ) ) ).

% cinsert_absorb
thf(fact_222_cinsert__ident,axiom,
    ! [X: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ~ ( countable_Set_cin_c @ X @ A )
     => ( ~ ( countable_Set_cin_c @ X @ B2 )
       => ( ( ( counta472291938sert_c @ X @ A )
            = ( counta472291938sert_c @ X @ B2 ) )
          = ( A = B2 ) ) ) ) ).

% cinsert_ident
thf(fact_223_set__cinsert,axiom,
    ! [X: c,A: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ X @ A )
     => ~ ! [B5: countable_Set_cset_c] :
            ( ( A
              = ( counta472291938sert_c @ X @ B5 ) )
           => ( countable_Set_cin_c @ X @ B5 ) ) ) ).

% set_cinsert
thf(fact_224_cinsertI2,axiom,
    ! [A2: c,B2: countable_Set_cset_c,B: c] :
      ( ( countable_Set_cin_c @ A2 @ B2 )
     => ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ B2 ) ) ) ).

% cinsertI2
thf(fact_225_cinsertI1,axiom,
    ! [A2: c,B2: countable_Set_cset_c] : ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ A2 @ B2 ) ) ).

% cinsertI1
thf(fact_226_cinsertE,axiom,
    ! [A2: c,B: c,A: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ A2 @ ( counta472291938sert_c @ B @ A ) )
     => ( ( A2 != B )
       => ( countable_Set_cin_c @ A2 @ A ) ) ) ).

% cinsertE
thf(fact_227_bot_Oextremum__uniqueI,axiom,
    ! [A2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ bot_bo1320844070cset_c )
     => ( A2 = bot_bo1320844070cset_c ) ) ).

% bot.extremum_uniqueI
thf(fact_228_bot_Oextremum__unique,axiom,
    ! [A2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ bot_bo1320844070cset_c )
      = ( A2 = bot_bo1320844070cset_c ) ) ).

% bot.extremum_unique
thf(fact_229_bot_Oextremum,axiom,
    ! [A2: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A2 ) ).

% bot.extremum
thf(fact_230_cDiffD2,axiom,
    ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
     => ~ ( countable_Set_cin_c @ C @ B2 ) ) ).

% cDiffD2
thf(fact_231_cDiffD1,axiom,
    ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
     => ( countable_Set_cin_c @ C @ A ) ) ).

% cDiffD1
thf(fact_232_cDiffE,axiom,
    ! [C: c,A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ A @ B2 ) )
     => ~ ( ( countable_Set_cin_c @ C @ A )
         => ( countable_Set_cin_c @ C @ B2 ) ) ) ).

% cDiffE
thf(fact_233_csubset__cinsertI2,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,B: c] :
      ( ( ord_le15364698cset_c @ A @ B2 )
     => ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ B2 ) ) ) ).

% csubset_cinsertI2
thf(fact_234_csubset__cinsertI,axiom,
    ! [B2: countable_Set_cset_c,A2: c] : ( ord_le15364698cset_c @ B2 @ ( counta472291938sert_c @ A2 @ B2 ) ) ).

% csubset_cinsertI
thf(fact_235_cinsert__mono,axiom,
    ! [C2: countable_Set_cset_c,D2: countable_Set_cset_c,A2: c] :
      ( ( ord_le15364698cset_c @ C2 @ D2 )
     => ( ord_le15364698cset_c @ ( counta472291938sert_c @ A2 @ C2 ) @ ( counta472291938sert_c @ A2 @ D2 ) ) ) ).

% cinsert_mono
thf(fact_236_cDiff__csubset,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] : ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ A ) ).

% cDiff_csubset
thf(fact_237_double__cDiff,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A @ B2 )
     => ( ( ord_le15364698cset_c @ B2 @ C2 )
       => ( ( minus_1646763425cset_c @ B2 @ ( minus_1646763425cset_c @ C2 @ A ) )
          = A ) ) ) ).

% double_cDiff
thf(fact_238_cminus__mono,axiom,
    ! [A: countable_Set_cset_c,C2: countable_Set_cset_c,D2: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A @ C2 )
     => ( ( ord_le15364698cset_c @ D2 @ B2 )
       => ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B2 ) @ ( minus_1646763425cset_c @ C2 @ D2 ) ) ) ) ).

% cminus_mono
thf(fact_239_csubset__cinsert__iff,axiom,
    ! [A: countable_Set_cset_c,X: c,B2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) )
      = ( ( ( countable_Set_cin_c @ X @ A )
         => ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) @ B2 ) )
        & ( ~ ( countable_Set_cin_c @ X @ A )
         => ( ord_le15364698cset_c @ A @ B2 ) ) ) ) ).

% csubset_cinsert_iff
thf(fact_240_csingleton__iff,axiom,
    ! [B: c,A2: c] :
      ( ( countable_Set_cin_c @ B @ ( counta472291938sert_c @ A2 @ bot_bo1320844070cset_c ) )
      = ( B = A2 ) ) ).

% csingleton_iff
thf(fact_241_cinsert__cDiff__if,axiom,
    ! [X: c,B2: countable_Set_cset_c,A: countable_Set_cset_c] :
      ( ( ( countable_Set_cin_c @ X @ B2 )
       => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
          = ( minus_1646763425cset_c @ A @ B2 ) ) )
      & ( ~ ( countable_Set_cin_c @ X @ B2 )
       => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ B2 )
          = ( counta472291938sert_c @ X @ ( minus_1646763425cset_c @ A @ B2 ) ) ) ) ) ).

% cinsert_cDiff_if
thf(fact_242_csubset__csingletonD,axiom,
    ! [A: countable_Set_cset_c,X: c] :
      ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) )
     => ( ( A = bot_bo1320844070cset_c )
        | ( A
          = ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) ) ) ).

% csubset_csingletonD
thf(fact_243_cDiff__cinsert__absorb,axiom,
    ! [X: c,A: countable_Set_cset_c] :
      ( ~ ( countable_Set_cin_c @ X @ A )
     => ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ X @ A ) @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) )
        = A ) ) ).

% cDiff_cinsert_absorb
thf(fact_244_cpsubset__finsert__iff,axiom,
    ! [A: countable_Set_cset_c,X: c,B2: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A @ ( counta472291938sert_c @ X @ B2 ) )
      = ( ( ( countable_Set_cin_c @ X @ B2 )
         => ( ord_le1587667814cset_c @ A @ B2 ) )
        & ( ~ ( countable_Set_cin_c @ X @ B2 )
         => ( ( ( countable_Set_cin_c @ X @ A )
             => ( ord_le1587667814cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ X @ bot_bo1320844070cset_c ) ) @ B2 ) )
            & ( ~ ( countable_Set_cin_c @ X @ A )
             => ( ord_le15364698cset_c @ A @ B2 ) ) ) ) ) ) ).

% cpsubset_finsert_iff
thf(fact_245_Greatest__equality,axiom,
    ! [P: countable_Set_cset_c > $o,X: countable_Set_cset_c] :
      ( ( P @ X )
     => ( ! [Y4: countable_Set_cset_c] :
            ( ( P @ Y4 )
           => ( ord_le15364698cset_c @ Y4 @ X ) )
       => ( ( order_1683649299cset_c @ P )
          = X ) ) ) ).

% Greatest_equality
thf(fact_246_GreatestI2__order,axiom,
    ! [P: countable_Set_cset_c > $o,X: countable_Set_cset_c,Q: countable_Set_cset_c > $o] :
      ( ( P @ X )
     => ( ! [Y4: countable_Set_cset_c] :
            ( ( P @ Y4 )
           => ( ord_le15364698cset_c @ Y4 @ X ) )
       => ( ! [X4: countable_Set_cset_c] :
              ( ( P @ X4 )
             => ( ! [Y5: countable_Set_cset_c] :
                    ( ( P @ Y5 )
                   => ( ord_le15364698cset_c @ Y5 @ X4 ) )
               => ( Q @ X4 ) ) )
         => ( Q @ ( order_1683649299cset_c @ P ) ) ) ) ) ).

% GreatestI2_order
thf(fact_247_le__rel__bool__arg__iff,axiom,
    ( ord_le1376176871cset_c
    = ( ^ [X5: $o > countable_Set_cset_c,Y6: $o > countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ ( X5 @ $false ) @ ( Y6 @ $false ) )
          & ( ord_le15364698cset_c @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).

% le_rel_bool_arg_iff
thf(fact_248_ord__eq__less__subst,axiom,
    ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le1587667814cset_c @ B @ C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le1587667814cset_c @ X4 @ Y4 )
             => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_249_ord__less__eq__subst,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le1587667814cset_c @ X4 @ Y4 )
             => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_250_order__less__subst1,axiom,
    ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ ( F @ B ) )
     => ( ( ord_le1587667814cset_c @ B @ C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le1587667814cset_c @ X4 @ Y4 )
             => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_251_order__less__subst2,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ B )
     => ( ( ord_le1587667814cset_c @ ( F @ B ) @ C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le1587667814cset_c @ X4 @ Y4 )
             => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_252_order_Oasym,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ B )
     => ~ ( ord_le1587667814cset_c @ B @ A2 ) ) ).

% order.asym
thf(fact_253_cpsubset__trans,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A @ B2 )
     => ( ( ord_le1587667814cset_c @ B2 @ C2 )
       => ( ord_le1587667814cset_c @ A @ C2 ) ) ) ).

% cpsubset_trans
thf(fact_254_less__imp__neq,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ X @ Y )
     => ( X != Y ) ) ).

% less_imp_neq
thf(fact_255_less__asym,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ X @ Y )
     => ~ ( ord_le1587667814cset_c @ Y @ X ) ) ).

% less_asym
thf(fact_256_less__asym_H,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ B )
     => ~ ( ord_le1587667814cset_c @ B @ A2 ) ) ).

% less_asym'
thf(fact_257_less__trans,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ X @ Y )
     => ( ( ord_le1587667814cset_c @ Y @ Z2 )
       => ( ord_le1587667814cset_c @ X @ Z2 ) ) ) ).

% less_trans
thf(fact_258_less__irrefl,axiom,
    ! [X: countable_Set_cset_c] :
      ~ ( ord_le1587667814cset_c @ X @ X ) ).

% less_irrefl
thf(fact_259_ord__eq__less__trans,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( A2 = B )
     => ( ( ord_le1587667814cset_c @ B @ C )
       => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).

% ord_eq_less_trans
thf(fact_260_ord__less__eq__trans,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ B )
     => ( ( B = C )
       => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).

% ord_less_eq_trans
thf(fact_261_dual__order_Oasym,axiom,
    ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ B @ A2 )
     => ~ ( ord_le1587667814cset_c @ A2 @ B ) ) ).

% dual_order.asym
thf(fact_262_less__imp__not__eq,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ X @ Y )
     => ( X != Y ) ) ).

% less_imp_not_eq
thf(fact_263_less__not__sym,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ X @ Y )
     => ~ ( ord_le1587667814cset_c @ Y @ X ) ) ).

% less_not_sym
thf(fact_264_less__imp__not__eq2,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ X @ Y )
     => ( Y != X ) ) ).

% less_imp_not_eq2
thf(fact_265_less__imp__triv,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,P: $o] :
      ( ( ord_le1587667814cset_c @ X @ Y )
     => ( ( ord_le1587667814cset_c @ Y @ X )
       => P ) ) ).

% less_imp_triv
thf(fact_266_dual__order_Oirrefl,axiom,
    ! [A2: countable_Set_cset_c] :
      ~ ( ord_le1587667814cset_c @ A2 @ A2 ) ).

% dual_order.irrefl
thf(fact_267_order_Ostrict__trans,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ B )
     => ( ( ord_le1587667814cset_c @ B @ C )
       => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).

% order.strict_trans
thf(fact_268_less__imp__not__less,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ X @ Y )
     => ~ ( ord_le1587667814cset_c @ Y @ X ) ) ).

% less_imp_not_less
thf(fact_269_dual__order_Ostrict__trans,axiom,
    ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ B @ A2 )
     => ( ( ord_le1587667814cset_c @ C @ B )
       => ( ord_le1587667814cset_c @ C @ A2 ) ) ) ).

% dual_order.strict_trans
thf(fact_270_order_Ostrict__implies__not__eq,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ B )
     => ( A2 != B ) ) ).

% order.strict_implies_not_eq
thf(fact_271_dual__order_Ostrict__implies__not__eq,axiom,
    ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ B @ A2 )
     => ( A2 != B ) ) ).

% dual_order.strict_implies_not_eq
thf(fact_272_leD,axiom,
    ! [Y: countable_Set_cset_c,X: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ Y @ X )
     => ~ ( ord_le1587667814cset_c @ X @ Y ) ) ).

% leD
thf(fact_273_le__less,axiom,
    ( ord_le15364698cset_c
    = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
          ( ( ord_le1587667814cset_c @ X2 @ Y2 )
          | ( X2 = Y2 ) ) ) ) ).

% le_less
thf(fact_274_less__le,axiom,
    ( ord_le1587667814cset_c
    = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ X2 @ Y2 )
          & ( X2 != Y2 ) ) ) ) ).

% less_le
thf(fact_275_order__le__less__subst1,axiom,
    ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ ( F @ B ) )
     => ( ( ord_le1587667814cset_c @ B @ C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le1587667814cset_c @ X4 @ Y4 )
             => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_276_order__le__less__subst2,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ B )
     => ( ( ord_le1587667814cset_c @ ( F @ B ) @ C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le15364698cset_c @ X4 @ Y4 )
             => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_277_order__less__le__subst1,axiom,
    ! [A2: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ ( F @ B ) )
     => ( ( ord_le15364698cset_c @ B @ C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le15364698cset_c @ X4 @ Y4 )
             => ( ord_le15364698cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le1587667814cset_c @ A2 @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_278_order__less__le__subst2,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,F: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ B )
     => ( ( ord_le15364698cset_c @ ( F @ B ) @ C )
       => ( ! [X4: countable_Set_cset_c,Y4: countable_Set_cset_c] :
              ( ( ord_le1587667814cset_c @ X4 @ Y4 )
             => ( ord_le1587667814cset_c @ ( F @ X4 ) @ ( F @ Y4 ) ) )
         => ( ord_le1587667814cset_c @ ( F @ A2 ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_279_le__neq__trans,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ B )
     => ( ( A2 != B )
       => ( ord_le1587667814cset_c @ A2 @ B ) ) ) ).

% le_neq_trans
thf(fact_280_antisym__conv1,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ~ ( ord_le1587667814cset_c @ X @ Y )
     => ( ( ord_le15364698cset_c @ X @ Y )
        = ( X = Y ) ) ) ).

% antisym_conv1
thf(fact_281_antisym__conv2,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ X @ Y )
     => ( ( ~ ( ord_le1587667814cset_c @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv2
thf(fact_282_less__imp__le,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ X @ Y )
     => ( ord_le15364698cset_c @ X @ Y ) ) ).

% less_imp_le
thf(fact_283_le__less__trans,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ X @ Y )
     => ( ( ord_le1587667814cset_c @ Y @ Z2 )
       => ( ord_le1587667814cset_c @ X @ Z2 ) ) ) ).

% le_less_trans
thf(fact_284_less__le__trans,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c,Z2: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ X @ Y )
     => ( ( ord_le15364698cset_c @ Y @ Z2 )
       => ( ord_le1587667814cset_c @ X @ Z2 ) ) ) ).

% less_le_trans
thf(fact_285_le__imp__less__or__eq,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ X @ Y )
     => ( ( ord_le1587667814cset_c @ X @ Y )
        | ( X = Y ) ) ) ).

% le_imp_less_or_eq
thf(fact_286_less__le__not__le,axiom,
    ( ord_le1587667814cset_c
    = ( ^ [X2: countable_Set_cset_c,Y2: countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ X2 @ Y2 )
          & ~ ( ord_le15364698cset_c @ Y2 @ X2 ) ) ) ) ).

% less_le_not_le
thf(fact_287_order_Ostrict__trans1,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A2 @ B )
     => ( ( ord_le1587667814cset_c @ B @ C )
       => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).

% order.strict_trans1
thf(fact_288_order_Ostrict__trans2,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ B )
     => ( ( ord_le15364698cset_c @ B @ C )
       => ( ord_le1587667814cset_c @ A2 @ C ) ) ) ).

% order.strict_trans2
thf(fact_289_order_Oorder__iff__strict,axiom,
    ( ord_le15364698cset_c
    = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
          ( ( ord_le1587667814cset_c @ A4 @ B3 )
          | ( A4 = B3 ) ) ) ) ).

% order.order_iff_strict
thf(fact_290_order_Ostrict__iff__order,axiom,
    ( ord_le1587667814cset_c
    = ( ^ [A4: countable_Set_cset_c,B3: countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ A4 @ B3 )
          & ( A4 != B3 ) ) ) ) ).

% order.strict_iff_order
thf(fact_291_dual__order_Ostrict__trans1,axiom,
    ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ B @ A2 )
     => ( ( ord_le1587667814cset_c @ C @ B )
       => ( ord_le1587667814cset_c @ C @ A2 ) ) ) ).

% dual_order.strict_trans1
thf(fact_292_dual__order_Ostrict__trans2,axiom,
    ! [B: countable_Set_cset_c,A2: countable_Set_cset_c,C: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ B @ A2 )
     => ( ( ord_le15364698cset_c @ C @ B )
       => ( ord_le1587667814cset_c @ C @ A2 ) ) ) ).

% dual_order.strict_trans2
thf(fact_293_order_Ostrict__implies__order,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A2 @ B )
     => ( ord_le15364698cset_c @ A2 @ B ) ) ).

% order.strict_implies_order
thf(fact_294_dual__order_Oorder__iff__strict,axiom,
    ( ord_le15364698cset_c
    = ( ^ [B3: countable_Set_cset_c,A4: countable_Set_cset_c] :
          ( ( ord_le1587667814cset_c @ B3 @ A4 )
          | ( A4 = B3 ) ) ) ) ).

% dual_order.order_iff_strict
thf(fact_295_dual__order_Ostrict__iff__order,axiom,
    ( ord_le1587667814cset_c
    = ( ^ [B3: countable_Set_cset_c,A4: countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ B3 @ A4 )
          & ( A4 != B3 ) ) ) ) ).

% dual_order.strict_iff_order
thf(fact_296_dual__order_Ostrict__implies__order,axiom,
    ! [B: countable_Set_cset_c,A2: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ B @ A2 )
     => ( ord_le15364698cset_c @ B @ A2 ) ) ).

% dual_order.strict_implies_order
thf(fact_297_order_Onot__eq__order__implies__strict,axiom,
    ! [A2: countable_Set_cset_c,B: countable_Set_cset_c] :
      ( ( A2 != B )
     => ( ( ord_le15364698cset_c @ A2 @ B )
       => ( ord_le1587667814cset_c @ A2 @ B ) ) ) ).

% order.not_eq_order_implies_strict
thf(fact_298_bot_Oextremum__strict,axiom,
    ! [A2: countable_Set_cset_c] :
      ~ ( ord_le1587667814cset_c @ A2 @ bot_bo1320844070cset_c ) ).

% bot.extremum_strict
thf(fact_299_bot_Onot__eq__extremum,axiom,
    ! [A2: countable_Set_cset_c] :
      ( ( A2 != bot_bo1320844070cset_c )
      = ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A2 ) ) ).

% bot.not_eq_extremum
thf(fact_300_cpsubsetD,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C: c] :
      ( ( ord_le1587667814cset_c @ A @ B2 )
     => ( ( countable_Set_cin_c @ C @ A )
       => ( countable_Set_cin_c @ C @ B2 ) ) ) ).

% cpsubsetD
thf(fact_301_not__cpsubset__cempty,axiom,
    ! [A: countable_Set_cset_c] :
      ~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ) ).

% not_cpsubset_cempty
thf(fact_302_cpsubset__eq,axiom,
    ( ord_le1587667814cset_c
    = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ A3 @ B4 )
          & ( A3 != B4 ) ) ) ) ).

% cpsubset_eq
thf(fact_303_less__cset__def,axiom,
    ( ord_le1587667814cset_c
    = ( ^ [Xs: countable_Set_cset_c,Ys: countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ Xs @ Ys )
          & ( Xs != Ys ) ) ) ) ).

% less_cset_def
thf(fact_304_cpsubset__imp__fsubset,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A @ B2 )
     => ( ord_le15364698cset_c @ A @ B2 ) ) ).

% cpsubset_imp_fsubset
thf(fact_305_cpsubset__csubset__trans,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A @ B2 )
     => ( ( ord_le15364698cset_c @ B2 @ C2 )
       => ( ord_le1587667814cset_c @ A @ C2 ) ) ) ).

% cpsubset_csubset_trans
thf(fact_306_csubset__cpsubset__trans,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c,C2: countable_Set_cset_c] :
      ( ( ord_le15364698cset_c @ A @ B2 )
     => ( ( ord_le1587667814cset_c @ B2 @ C2 )
       => ( ord_le1587667814cset_c @ A @ C2 ) ) ) ).

% csubset_cpsubset_trans
thf(fact_307_csubset__not__fsubset__eq,axiom,
    ( ord_le1587667814cset_c
    = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
          ( ( ord_le15364698cset_c @ A3 @ B4 )
          & ~ ( ord_le15364698cset_c @ B4 @ A3 ) ) ) ) ).

% csubset_not_fsubset_eq
thf(fact_308_csubset__iff__pfsubset__eq,axiom,
    ( ord_le15364698cset_c
    = ( ^ [A3: countable_Set_cset_c,B4: countable_Set_cset_c] :
          ( ( ord_le1587667814cset_c @ A3 @ B4 )
          | ( A3 = B4 ) ) ) ) ).

% csubset_iff_pfsubset_eq
thf(fact_309_cpsubset__imp__ex__fmem,axiom,
    ! [A: countable_Set_cset_c,B2: countable_Set_cset_c] :
      ( ( ord_le1587667814cset_c @ A @ B2 )
     => ? [B6: c] : ( countable_Set_cin_c @ B6 @ ( minus_1646763425cset_c @ B2 @ A ) ) ) ).

% cpsubset_imp_ex_fmem

% Helper facts (5)
thf(help_If_2_1_If_001tf__c_T,axiom,
    ! [X: c,Y: c] :
      ( ( if_c @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001tf__c_T,axiom,
    ! [X: c,Y: c] :
      ( ( if_c @ $true @ X @ Y )
      = X ) ).

thf(help_If_3_1_If_001t__Countable____Set____Type__Ocset_Itf__c_J_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__Countable____Set____Type__Ocset_Itf__c_J_T,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( if_Cou1542198912cset_c @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Countable____Set____Type__Ocset_Itf__c_J_T,axiom,
    ! [X: countable_Set_cset_c,Y: countable_Set_cset_c] :
      ( ( if_Cou1542198912cset_c @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ f )
    = ( f @ x ) ) ).

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