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

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : Risk_Free_Lending/0000_Risk_Free_Lending/prob_01382_044015__6001088_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1401 ( 734 unt; 123 typ;   0 def)
%            Number of atoms       : 3181 (1393 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 9368 ( 185   ~;  73   |; 137   &;7922   @)
%                                         (   0 <=>;1051  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Number of types       :   10 (   9 usr)
%            Number of type conns  :  416 ( 416   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  117 ( 114 usr;  17 con; 0-3 aty)
%            Number of variables   : 3319 ( 326   ^;2959   !;  34   ?;3319   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 15:57:50.820
%------------------------------------------------------------------------------
% Could-be-implicit typings (9)
thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mt__Real__Oreal_J_J,type,
    set_nat_real: $tType ).

thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J,type,
    set_complex: $tType ).

thf(ty_n_t__Risk____Free____Lending__Oaccount,type,
    risk_Free_account: $tType ).

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

thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
    set_int: $tType ).

thf(ty_n_t__Complex__Ocomplex,type,
    complex: $tType ).

thf(ty_n_t__Real__Oreal,type,
    real: $tType ).

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

thf(ty_n_t__Int__Oint,type,
    int: $tType ).

% Explicit typings (114)
thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
    finite3207457112153483333omplex: set_complex > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
    finite_finite_int: set_int > $o ).

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

thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
    abs_abs_int: int > int ).

thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
    abs_abs_real: real > real ).

thf(sy_c_Groups_Ominus__class_Ominus_001_062_I_062_It__Nat__Onat_Mt__Real__Oreal_J_M_Eo_J,type,
    minus_930488207635846619real_o: ( ( nat > real ) > $o ) > ( ( nat > real ) > $o ) > ( nat > real ) > $o ).

thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Complex__Ocomplex_M_Eo_J,type,
    minus_8727706125548526216plex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).

thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Int__Oint_M_Eo_J,type,
    minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).

thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Nat__Onat_M_Eo_J,type,
    minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex,type,
    minus_minus_complex: complex > complex > complex ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
    minus_minus_int: int > int > int ).

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

thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
    minus_minus_real: real > real > real ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Risk____Free____Lending__Oaccount,type,
    minus_4846202936726426316ccount: risk_Free_account > risk_Free_account > risk_Free_account ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Real__Oreal_J_J,type,
    minus_3492551254948764970t_real: set_nat_real > set_nat_real > set_nat_real ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
    minus_811609699411566653omplex: set_complex > set_complex > set_complex ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
    minus_minus_set_int: set_int > set_int > set_int ).

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

thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex,type,
    one_one_complex: complex ).

thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
    one_one_int: int ).

thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
    one_one_nat: nat ).

thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
    one_one_real: real ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex,type,
    plus_plus_complex: complex > complex > complex ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
    plus_plus_int: int > int > int ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
    plus_plus_nat: nat > nat > nat ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
    plus_plus_real: real > real > real ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Risk____Free____Lending__Oaccount,type,
    plus_p1863581527469039996ccount: risk_Free_account > risk_Free_account > risk_Free_account ).

thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex,type,
    times_times_complex: complex > complex > complex ).

thf(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint,type,
    times_times_int: int > int > int ).

thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
    times_times_nat: nat > nat > nat ).

thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal,type,
    times_times_real: real > real > real ).

thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
    uminus_uminus_real: real > real ).

thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Risk____Free____Lending__Oaccount,type,
    uminus3377898441596595772ccount: risk_Free_account > risk_Free_account ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex,type,
    zero_zero_complex: complex ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
    zero_zero_int: int ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
    zero_zero_nat: nat ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
    zero_zero_real: real ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Risk____Free____Lending__Oaccount,type,
    zero_z1425366712893667068ccount: risk_Free_account ).

thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
    groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).

thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Nat__Onat,type,
    groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).

thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Real__Oreal,type,
    groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).

thf(sy_c_If_001t__Real__Oreal,type,
    if_real: $o > real > real > real ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Nat__Onat_Mt__Real__Oreal_J_M_Eo_J,type,
    sup_sup_nat_real_o: ( ( nat > real ) > $o ) > ( ( nat > real ) > $o ) > ( nat > real ) > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Complex__Ocomplex_M_Eo_J,type,
    sup_sup_complex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Int__Oint_M_Eo_J,type,
    sup_sup_int_o: ( int > $o ) > ( int > $o ) > int > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_Eo_J,type,
    sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
    sup_sup_int: int > int > int ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
    sup_sup_nat: nat > nat > nat ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Real__Oreal,type,
    sup_sup_real: real > real > real ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Real__Oreal_J_J,type,
    sup_sup_set_nat_real: set_nat_real > set_nat_real > set_nat_real ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Complex__Ocomplex_J,type,
    sup_sup_set_complex: set_complex > set_complex > set_complex ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
    sup_sup_set_int: set_int > set_int > set_int ).

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

thf(sy_c_Nat_OSuc,type,
    suc: nat > nat ).

thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
    neg_nu6511756317524482435omplex: complex > complex ).

thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
    neg_nu3811975205180677377ec_int: int > int ).

thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
    neg_nu6075765906172075777c_real: real > real ).

thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
    neg_nu8557863876264182079omplex: complex > complex ).

thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
    neg_nu5851722552734809277nc_int: int > int ).

thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
    neg_nu8295874005876285629c_real: real > real ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
    ord_less_int: int > int > $o ).

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

thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
    ord_less_real: real > real > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Risk____Free____Lending__Oaccount,type,
    ord_le2131251472502387783ccount: risk_Free_account > risk_Free_account > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
    ord_less_set_nat: set_nat > set_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Nat__Onat_Mt__Real__Oreal_J_M_Eo_J,type,
    ord_le7676461544873280788real_o: ( ( nat > real ) > $o ) > ( ( nat > real ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_Eo_J,type,
    ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
    ord_less_eq_int: int > int > $o ).

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

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
    ord_less_eq_real: real > real > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Risk____Free____Lending__Oaccount,type,
    ord_le4245800335709223507ccount: risk_Free_account > risk_Free_account > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Real__Oreal_J_J,type,
    ord_le2908806416726583473t_real: set_nat_real > set_nat_real > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Complex__Ocomplex_J,type,
    ord_le211207098394363844omplex: set_complex > set_complex > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
    ord_less_eq_set_int: set_int > set_int > $o ).

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

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_It__Nat__Onat_Mt__Real__Oreal_J_M_Eo_J,type,
    top_top_nat_real_o: ( nat > real ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Complex__Ocomplex_M_Eo_J,type,
    top_top_complex_o: complex > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Int__Oint_M_Eo_J,type,
    top_top_int_o: int > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
    top_top_nat_o: nat > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Real__Oreal_J_J,type,
    top_top_set_nat_real: set_nat_real ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Complex__Ocomplex_J,type,
    top_top_set_complex: set_complex ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Int__Oint_J,type,
    top_top_set_int: set_int ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
    top_top_set_nat: set_nat ).

thf(sy_c_Ordinal__Arithmetic_Ofin__support_001t__Real__Oreal_001t__Nat__Onat,type,
    ordina1579063754167848977al_nat: real > set_nat > set_nat_real ).

thf(sy_c_Ordinal__Arithmetic_Osupport_001t__Real__Oreal_001t__Nat__Onat,type,
    ordina7525502726642723294al_nat: real > set_nat > ( nat > real ) > set_nat ).

thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex,type,
    power_power_complex: complex > nat > complex ).

thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
    power_power_nat: nat > nat > nat ).

thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
    power_power_real: real > nat > real ).

thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
    real_V1022390504157884413omplex: complex > real ).

thf(sy_c_Risk__Free__Lending_Oaccount_OAbs__account,type,
    risk_F5458100604530014700ccount: ( nat > real ) > risk_Free_account ).

thf(sy_c_Risk__Free__Lending_Oaccount_ORep__account,type,
    risk_F170160801229183585ccount: risk_Free_account > nat > real ).

thf(sy_c_Risk__Free__Lending_Ocash__reserve,type,
    risk_F1914734008469130493eserve: risk_Free_account > real ).

thf(sy_c_Risk__Free__Lending_Ojust__cash,type,
    risk_Free_just_cash: real > risk_Free_account ).

thf(sy_c_Risk__Free__Lending_Onet__asset__value,type,
    risk_F2906766666041932210_value: risk_Free_account > real ).

thf(sy_c_Risk__Free__Lending_Oreturn__loans,type,
    risk_F2121631595377017831_loans: ( nat > real ) > risk_Free_account > risk_Free_account ).

thf(sy_c_Risk__Free__Lending_Oshortest__period,type,
    risk_F4612863212915232279period: risk_Free_account > nat ).

thf(sy_c_Risk__Free__Lending_Ostrictly__solvent,type,
    risk_F1636578016437888323olvent: risk_Free_account > $o ).

thf(sy_c_Risk__Free__Lending_Oupdate__account,type,
    risk_F444380041991734328ccount: ( nat > real ) > real > risk_Free_account > risk_Free_account ).

thf(sy_c_Risk__Free__Lending_Ovalid__transfer,type,
    risk_F1023690899723030139ansfer: risk_Free_account > risk_Free_account > $o ).

thf(sy_c_Set_OCollect_001_062_It__Nat__Onat_Mt__Real__Oreal_J,type,
    collect_nat_real: ( ( nat > real ) > $o ) > set_nat_real ).

thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
    collect_complex: ( complex > $o ) > set_complex ).

thf(sy_c_Set_OCollect_001t__Int__Oint,type,
    collect_int: ( int > $o ) > set_int ).

thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
    set_ord_atMost_nat: nat > set_nat ).

thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
    artanh_real: real > real ).

thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
    ln_ln_real: real > real ).

thf(sy_c_Typedef_Otype__definition_001t__Risk____Free____Lending__Oaccount_001_062_It__Nat__Onat_Mt__Real__Oreal_J,type,
    type_d8982087200295354172t_real: ( risk_Free_account > nat > real ) > ( ( nat > real ) > risk_Free_account ) > set_nat_real > $o ).

thf(sy_c_member_001_062_It__Nat__Onat_Mt__Real__Oreal_J,type,
    member_nat_real: ( nat > real ) > set_nat_real > $o ).

thf(sy_c_member_001t__Complex__Ocomplex,type,
    member_complex: complex > set_complex > $o ).

thf(sy_c_member_001t__Int__Oint,type,
    member_int: int > set_int > $o ).

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

thf(sy_v__092_060alpha_062,type,
    alpha: risk_Free_account ).

thf(sy_v__092_060beta_062,type,
    beta: risk_Free_account ).

thf(sy_v__092_060rho_062,type,
    rho: nat > real ).

% Relevant facts (1274)
thf(fact_0__092_060open_062_092_060pi_062_A_092_060beta_062_A_092_060in_062_Afin__support_A0_AUNIV_092_060close_062,axiom,
    member_nat_real @ ( risk_F170160801229183585ccount @ beta ) @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) ).

% \<open>\<pi> \<beta> \<in> fin_support 0 UNIV\<close>
thf(fact_1__092_060open_062_092_060pi_062_A_092_060alpha_062_A_092_060in_062_Afin__support_A0_AUNIV_092_060close_062,axiom,
    member_nat_real @ ( risk_F170160801229183585ccount @ alpha ) @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) ).

% \<open>\<pi> \<alpha> \<in> fin_support 0 UNIV\<close>
thf(fact_2__092_060open_062support_A0_AUNIV_A_I_092_060lambda_062n_O_A_I1_A_N_A_092_060rho_062_An_J_A_K_A_092_060pi_062_A_092_060beta_062_An_J_A_092_060subseteq_062_Asupport_A0_AUNIV_A_I_092_060pi_062_A_092_060beta_062_J_092_060close_062,axiom,
    ( ord_less_eq_set_nat
    @ ( ordina7525502726642723294al_nat @ zero_zero_real @ top_top_set_nat
      @ ^ [N: nat] : ( times_times_real @ ( minus_minus_real @ one_one_real @ ( rho @ N ) ) @ ( risk_F170160801229183585ccount @ beta @ N ) ) )
    @ ( ordina7525502726642723294al_nat @ zero_zero_real @ top_top_set_nat @ ( risk_F170160801229183585ccount @ beta ) ) ) ).

% \<open>support 0 UNIV (\<lambda>n. (1 - \<rho> n) * \<pi> \<beta> n) \<subseteq> support 0 UNIV (\<pi> \<beta>)\<close>
thf(fact_3__092_060open_062support_A0_AUNIV_A_I_092_060lambda_062n_O_A_I1_A_N_A_092_060rho_062_An_J_A_K_A_092_060pi_062_A_092_060alpha_062_An_J_A_092_060subseteq_062_Asupport_A0_AUNIV_A_I_092_060pi_062_A_092_060alpha_062_J_092_060close_062,axiom,
    ( ord_less_eq_set_nat
    @ ( ordina7525502726642723294al_nat @ zero_zero_real @ top_top_set_nat
      @ ^ [N: nat] : ( times_times_real @ ( minus_minus_real @ one_one_real @ ( rho @ N ) ) @ ( risk_F170160801229183585ccount @ alpha @ N ) ) )
    @ ( ordina7525502726642723294al_nat @ zero_zero_real @ top_top_set_nat @ ( risk_F170160801229183585ccount @ alpha ) ) ) ).

% \<open>support 0 UNIV (\<lambda>n. (1 - \<rho> n) * \<pi> \<alpha> n) \<subseteq> support 0 UNIV (\<pi> \<alpha>)\<close>
thf(fact_4__092_060open_062support_A0_AUNIV_A_I_092_060lambda_062n_O_A_I1_A_N_A_092_060rho_062_An_J_A_K_A_I_092_060pi_062_A_092_060alpha_062_An_A_L_A_092_060pi_062_A_092_060beta_062_An_J_J_A_092_060subseteq_062_Asupport_A0_AUNIV_A_I_092_060pi_062_A_092_060alpha_062_J_A_092_060union_062_Asupport_A0_AUNIV_A_I_092_060pi_062_A_092_060beta_062_J_092_060close_062,axiom,
    ( ord_less_eq_set_nat
    @ ( ordina7525502726642723294al_nat @ zero_zero_real @ top_top_set_nat
      @ ^ [N: nat] : ( times_times_real @ ( minus_minus_real @ one_one_real @ ( rho @ N ) ) @ ( plus_plus_real @ ( risk_F170160801229183585ccount @ alpha @ N ) @ ( risk_F170160801229183585ccount @ beta @ N ) ) ) )
    @ ( sup_sup_set_nat @ ( ordina7525502726642723294al_nat @ zero_zero_real @ top_top_set_nat @ ( risk_F170160801229183585ccount @ alpha ) ) @ ( ordina7525502726642723294al_nat @ zero_zero_real @ top_top_set_nat @ ( risk_F170160801229183585ccount @ beta ) ) ) ) ).

% \<open>support 0 UNIV (\<lambda>n. (1 - \<rho> n) * (\<pi> \<alpha> n + \<pi> \<beta> n)) \<subseteq> support 0 UNIV (\<pi> \<alpha>) \<union> support 0 UNIV (\<pi> \<beta>)\<close>
thf(fact_5_Rep__account,axiom,
    ! [X: risk_Free_account] : ( member_nat_real @ ( risk_F170160801229183585ccount @ X ) @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) ) ).

% Rep_account
thf(fact_6_Rep__account__cases,axiom,
    ! [Y: nat > real] :
      ( ( member_nat_real @ Y @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) )
     => ~ ! [X2: risk_Free_account] :
            ( Y
           != ( risk_F170160801229183585ccount @ X2 ) ) ) ).

% Rep_account_cases
thf(fact_7_Rep__account__induct,axiom,
    ! [Y: nat > real,P: ( nat > real ) > $o] :
      ( ( member_nat_real @ Y @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) )
     => ( ! [X2: risk_Free_account] : ( P @ ( risk_F170160801229183585ccount @ X2 ) )
       => ( P @ Y ) ) ) ).

% Rep_account_induct
thf(fact_8_Rep__account__inject,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ( risk_F170160801229183585ccount @ X )
        = ( risk_F170160801229183585ccount @ Y ) )
      = ( X = Y ) ) ).

% Rep_account_inject
thf(fact_9_diff__numeral__special_I9_J,axiom,
    ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
    = zero_zero_complex ) ).

% diff_numeral_special(9)
thf(fact_10_diff__numeral__special_I9_J,axiom,
    ( ( minus_minus_real @ one_one_real @ one_one_real )
    = zero_zero_real ) ).

% diff_numeral_special(9)
thf(fact_11_diff__numeral__special_I9_J,axiom,
    ( ( minus_minus_int @ one_one_int @ one_one_int )
    = zero_zero_int ) ).

% diff_numeral_special(9)
thf(fact_12_mult__cancel__left1,axiom,
    ! [C: complex,B: complex] :
      ( ( C
        = ( times_times_complex @ C @ B ) )
      = ( ( C = zero_zero_complex )
        | ( B = one_one_complex ) ) ) ).

% mult_cancel_left1
thf(fact_13_mult__cancel__left1,axiom,
    ! [C: real,B: real] :
      ( ( C
        = ( times_times_real @ C @ B ) )
      = ( ( C = zero_zero_real )
        | ( B = one_one_real ) ) ) ).

% mult_cancel_left1
thf(fact_14_mult__cancel__left1,axiom,
    ! [C: int,B: int] :
      ( ( C
        = ( times_times_int @ C @ B ) )
      = ( ( C = zero_zero_int )
        | ( B = one_one_int ) ) ) ).

% mult_cancel_left1
thf(fact_15_mult__cancel__left2,axiom,
    ! [C: complex,A: complex] :
      ( ( ( times_times_complex @ C @ A )
        = C )
      = ( ( C = zero_zero_complex )
        | ( A = one_one_complex ) ) ) ).

% mult_cancel_left2
thf(fact_16_mult__cancel__left2,axiom,
    ! [C: real,A: real] :
      ( ( ( times_times_real @ C @ A )
        = C )
      = ( ( C = zero_zero_real )
        | ( A = one_one_real ) ) ) ).

% mult_cancel_left2
thf(fact_17_mult__cancel__left2,axiom,
    ! [C: int,A: int] :
      ( ( ( times_times_int @ C @ A )
        = C )
      = ( ( C = zero_zero_int )
        | ( A = one_one_int ) ) ) ).

% mult_cancel_left2
thf(fact_18_mult__cancel__right1,axiom,
    ! [C: complex,B: complex] :
      ( ( C
        = ( times_times_complex @ B @ C ) )
      = ( ( C = zero_zero_complex )
        | ( B = one_one_complex ) ) ) ).

% mult_cancel_right1
thf(fact_19_mult__cancel__right1,axiom,
    ! [C: real,B: real] :
      ( ( C
        = ( times_times_real @ B @ C ) )
      = ( ( C = zero_zero_real )
        | ( B = one_one_real ) ) ) ).

% mult_cancel_right1
thf(fact_20_mult__cancel__right1,axiom,
    ! [C: int,B: int] :
      ( ( C
        = ( times_times_int @ B @ C ) )
      = ( ( C = zero_zero_int )
        | ( B = one_one_int ) ) ) ).

% mult_cancel_right1
thf(fact_21_mult__cancel__right2,axiom,
    ! [A: complex,C: complex] :
      ( ( ( times_times_complex @ A @ C )
        = C )
      = ( ( C = zero_zero_complex )
        | ( A = one_one_complex ) ) ) ).

% mult_cancel_right2
thf(fact_22_mult__cancel__right2,axiom,
    ! [A: real,C: real] :
      ( ( ( times_times_real @ A @ C )
        = C )
      = ( ( C = zero_zero_real )
        | ( A = one_one_real ) ) ) ).

% mult_cancel_right2
thf(fact_23_mult__cancel__right2,axiom,
    ! [A: int,C: int] :
      ( ( ( times_times_int @ A @ C )
        = C )
      = ( ( C = zero_zero_int )
        | ( A = one_one_int ) ) ) ).

% mult_cancel_right2
thf(fact_24_Rep__account__return__loans,axiom,
    ! [Rho: nat > real,Alpha: risk_Free_account] :
      ( ( risk_F170160801229183585ccount @ ( risk_F2121631595377017831_loans @ Rho @ Alpha ) )
      = ( ^ [N: nat] : ( times_times_real @ ( minus_minus_real @ one_one_real @ ( Rho @ N ) ) @ ( risk_F170160801229183585ccount @ Alpha @ N ) ) ) ) ).

% Rep_account_return_loans
thf(fact_25_mult_Oright__neutral,axiom,
    ! [A: complex] :
      ( ( times_times_complex @ A @ one_one_complex )
      = A ) ).

% mult.right_neutral
thf(fact_26_mult_Oright__neutral,axiom,
    ! [A: real] :
      ( ( times_times_real @ A @ one_one_real )
      = A ) ).

% mult.right_neutral
thf(fact_27_mult_Oright__neutral,axiom,
    ! [A: int] :
      ( ( times_times_int @ A @ one_one_int )
      = A ) ).

% mult.right_neutral
thf(fact_28_mult_Oright__neutral,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ A @ one_one_nat )
      = A ) ).

% mult.right_neutral
thf(fact_29_mult__1,axiom,
    ! [A: complex] :
      ( ( times_times_complex @ one_one_complex @ A )
      = A ) ).

% mult_1
thf(fact_30_mult__1,axiom,
    ! [A: real] :
      ( ( times_times_real @ one_one_real @ A )
      = A ) ).

% mult_1
thf(fact_31_mult__1,axiom,
    ! [A: int] :
      ( ( times_times_int @ one_one_int @ A )
      = A ) ).

% mult_1
thf(fact_32_mult__1,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ one_one_nat @ A )
      = A ) ).

% mult_1
thf(fact_33_diff__self,axiom,
    ! [A: real] :
      ( ( minus_minus_real @ A @ A )
      = zero_zero_real ) ).

% diff_self
thf(fact_34_diff__self,axiom,
    ! [A: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ A @ A )
      = zero_z1425366712893667068ccount ) ).

% diff_self
thf(fact_35_diff__self,axiom,
    ! [A: int] :
      ( ( minus_minus_int @ A @ A )
      = zero_zero_int ) ).

% diff_self
thf(fact_36_diff__self,axiom,
    ! [A: complex] :
      ( ( minus_minus_complex @ A @ A )
      = zero_zero_complex ) ).

% diff_self
thf(fact_37_diff__0__right,axiom,
    ! [A: real] :
      ( ( minus_minus_real @ A @ zero_zero_real )
      = A ) ).

% diff_0_right
thf(fact_38_diff__0__right,axiom,
    ! [A: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ A @ zero_z1425366712893667068ccount )
      = A ) ).

% diff_0_right
thf(fact_39_diff__0__right,axiom,
    ! [A: int] :
      ( ( minus_minus_int @ A @ zero_zero_int )
      = A ) ).

% diff_0_right
thf(fact_40_diff__0__right,axiom,
    ! [A: complex] :
      ( ( minus_minus_complex @ A @ zero_zero_complex )
      = A ) ).

% diff_0_right
thf(fact_41_zero__diff,axiom,
    ! [A: nat] :
      ( ( minus_minus_nat @ zero_zero_nat @ A )
      = zero_zero_nat ) ).

% zero_diff
thf(fact_42_diff__zero,axiom,
    ! [A: real] :
      ( ( minus_minus_real @ A @ zero_zero_real )
      = A ) ).

% diff_zero
thf(fact_43_diff__zero,axiom,
    ! [A: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ A @ zero_z1425366712893667068ccount )
      = A ) ).

% diff_zero
thf(fact_44_diff__zero,axiom,
    ! [A: int] :
      ( ( minus_minus_int @ A @ zero_zero_int )
      = A ) ).

% diff_zero
thf(fact_45_diff__zero,axiom,
    ! [A: nat] :
      ( ( minus_minus_nat @ A @ zero_zero_nat )
      = A ) ).

% diff_zero
thf(fact_46_diff__zero,axiom,
    ! [A: complex] :
      ( ( minus_minus_complex @ A @ zero_zero_complex )
      = A ) ).

% diff_zero
thf(fact_47_add__left__cancel,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
      = ( B = C ) ) ).

% add_left_cancel
thf(fact_48_add__left__cancel,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ( plus_p1863581527469039996ccount @ A @ B )
        = ( plus_p1863581527469039996ccount @ A @ C ) )
      = ( B = C ) ) ).

% add_left_cancel
thf(fact_49_add__left__cancel,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
      = ( B = C ) ) ).

% add_left_cancel
thf(fact_50_add__left__cancel,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ( plus_plus_int @ A @ B )
        = ( plus_plus_int @ A @ C ) )
      = ( B = C ) ) ).

% add_left_cancel
thf(fact_51_add__left__cancel,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( ( plus_plus_complex @ A @ B )
        = ( plus_plus_complex @ A @ C ) )
      = ( B = C ) ) ).

% add_left_cancel
thf(fact_52_add__right__cancel,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ( plus_plus_real @ B @ A )
        = ( plus_plus_real @ C @ A ) )
      = ( B = C ) ) ).

% add_right_cancel
thf(fact_53_add__right__cancel,axiom,
    ! [B: risk_Free_account,A: risk_Free_account,C: risk_Free_account] :
      ( ( ( plus_p1863581527469039996ccount @ B @ A )
        = ( plus_p1863581527469039996ccount @ C @ A ) )
      = ( B = C ) ) ).

% add_right_cancel
thf(fact_54_add__right__cancel,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ( plus_plus_nat @ B @ A )
        = ( plus_plus_nat @ C @ A ) )
      = ( B = C ) ) ).

% add_right_cancel
thf(fact_55_add__right__cancel,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ( plus_plus_int @ B @ A )
        = ( plus_plus_int @ C @ A ) )
      = ( B = C ) ) ).

% add_right_cancel
thf(fact_56_add__right__cancel,axiom,
    ! [B: complex,A: complex,C: complex] :
      ( ( ( plus_plus_complex @ B @ A )
        = ( plus_plus_complex @ C @ A ) )
      = ( B = C ) ) ).

% add_right_cancel
thf(fact_57_le__zero__eq,axiom,
    ! [N2: nat] :
      ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
      = ( N2 = zero_zero_nat ) ) ).

% le_zero_eq
thf(fact_58_mult__cancel__right,axiom,
    ! [A: complex,C: complex,B: complex] :
      ( ( ( times_times_complex @ A @ C )
        = ( times_times_complex @ B @ C ) )
      = ( ( C = zero_zero_complex )
        | ( A = B ) ) ) ).

% mult_cancel_right
thf(fact_59_mult__cancel__right,axiom,
    ! [A: real,C: real,B: real] :
      ( ( ( times_times_real @ A @ C )
        = ( times_times_real @ B @ C ) )
      = ( ( C = zero_zero_real )
        | ( A = B ) ) ) ).

% mult_cancel_right
thf(fact_60_mult__cancel__right,axiom,
    ! [A: int,C: int,B: int] :
      ( ( ( times_times_int @ A @ C )
        = ( times_times_int @ B @ C ) )
      = ( ( C = zero_zero_int )
        | ( A = B ) ) ) ).

% mult_cancel_right
thf(fact_61_mult__cancel__right,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ( times_times_nat @ A @ C )
        = ( times_times_nat @ B @ C ) )
      = ( ( C = zero_zero_nat )
        | ( A = B ) ) ) ).

% mult_cancel_right
thf(fact_62_mult__cancel__left,axiom,
    ! [C: complex,A: complex,B: complex] :
      ( ( ( times_times_complex @ C @ A )
        = ( times_times_complex @ C @ B ) )
      = ( ( C = zero_zero_complex )
        | ( A = B ) ) ) ).

% mult_cancel_left
thf(fact_63_mult__cancel__left,axiom,
    ! [C: real,A: real,B: real] :
      ( ( ( times_times_real @ C @ A )
        = ( times_times_real @ C @ B ) )
      = ( ( C = zero_zero_real )
        | ( A = B ) ) ) ).

% mult_cancel_left
thf(fact_64_mult__cancel__left,axiom,
    ! [C: int,A: int,B: int] :
      ( ( ( times_times_int @ C @ A )
        = ( times_times_int @ C @ B ) )
      = ( ( C = zero_zero_int )
        | ( A = B ) ) ) ).

% mult_cancel_left
thf(fact_65_mult__cancel__left,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ( times_times_nat @ C @ A )
        = ( times_times_nat @ C @ B ) )
      = ( ( C = zero_zero_nat )
        | ( A = B ) ) ) ).

% mult_cancel_left
thf(fact_66_mult__eq__0__iff,axiom,
    ! [A: complex,B: complex] :
      ( ( ( times_times_complex @ A @ B )
        = zero_zero_complex )
      = ( ( A = zero_zero_complex )
        | ( B = zero_zero_complex ) ) ) ).

% mult_eq_0_iff
thf(fact_67_mult__eq__0__iff,axiom,
    ! [A: real,B: real] :
      ( ( ( times_times_real @ A @ B )
        = zero_zero_real )
      = ( ( A = zero_zero_real )
        | ( B = zero_zero_real ) ) ) ).

% mult_eq_0_iff
thf(fact_68_mult__eq__0__iff,axiom,
    ! [A: int,B: int] :
      ( ( ( times_times_int @ A @ B )
        = zero_zero_int )
      = ( ( A = zero_zero_int )
        | ( B = zero_zero_int ) ) ) ).

% mult_eq_0_iff
thf(fact_69_mult__eq__0__iff,axiom,
    ! [A: nat,B: nat] :
      ( ( ( times_times_nat @ A @ B )
        = zero_zero_nat )
      = ( ( A = zero_zero_nat )
        | ( B = zero_zero_nat ) ) ) ).

% mult_eq_0_iff
thf(fact_70_mult__zero__right,axiom,
    ! [A: complex] :
      ( ( times_times_complex @ A @ zero_zero_complex )
      = zero_zero_complex ) ).

% mult_zero_right
thf(fact_71_mult__zero__right,axiom,
    ! [A: real] :
      ( ( times_times_real @ A @ zero_zero_real )
      = zero_zero_real ) ).

% mult_zero_right
thf(fact_72_mult__zero__right,axiom,
    ! [A: int] :
      ( ( times_times_int @ A @ zero_zero_int )
      = zero_zero_int ) ).

% mult_zero_right
thf(fact_73_mult__zero__right,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ A @ zero_zero_nat )
      = zero_zero_nat ) ).

% mult_zero_right
thf(fact_74_mult__zero__left,axiom,
    ! [A: complex] :
      ( ( times_times_complex @ zero_zero_complex @ A )
      = zero_zero_complex ) ).

% mult_zero_left
thf(fact_75_mult__zero__left,axiom,
    ! [A: real] :
      ( ( times_times_real @ zero_zero_real @ A )
      = zero_zero_real ) ).

% mult_zero_left
thf(fact_76_mult__zero__left,axiom,
    ! [A: int] :
      ( ( times_times_int @ zero_zero_int @ A )
      = zero_zero_int ) ).

% mult_zero_left
thf(fact_77_mult__zero__left,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ zero_zero_nat @ A )
      = zero_zero_nat ) ).

% mult_zero_left
thf(fact_78_add__le__cancel__left,axiom,
    ! [C: risk_Free_account,A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ C @ A ) @ ( plus_p1863581527469039996ccount @ C @ B ) )
      = ( ord_le4245800335709223507ccount @ A @ B ) ) ).

% add_le_cancel_left
thf(fact_79_add__le__cancel__left,axiom,
    ! [C: real,A: real,B: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
      = ( ord_less_eq_real @ A @ B ) ) ).

% add_le_cancel_left
thf(fact_80_add__le__cancel__left,axiom,
    ! [C: int,A: int,B: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
      = ( ord_less_eq_int @ A @ B ) ) ).

% add_le_cancel_left
thf(fact_81_add__le__cancel__left,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
      = ( ord_less_eq_nat @ A @ B ) ) ).

% add_le_cancel_left
thf(fact_82_add__le__cancel__right,axiom,
    ! [A: risk_Free_account,C: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ ( plus_p1863581527469039996ccount @ B @ C ) )
      = ( ord_le4245800335709223507ccount @ A @ B ) ) ).

% add_le_cancel_right
thf(fact_83_add__le__cancel__right,axiom,
    ! [A: real,C: real,B: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
      = ( ord_less_eq_real @ A @ B ) ) ).

% add_le_cancel_right
thf(fact_84_add__le__cancel__right,axiom,
    ! [A: int,C: int,B: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
      = ( ord_less_eq_int @ A @ B ) ) ).

% add_le_cancel_right
thf(fact_85_add__le__cancel__right,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
      = ( ord_less_eq_nat @ A @ B ) ) ).

% add_le_cancel_right
thf(fact_86_add__0,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ zero_zero_real @ A )
      = A ) ).

% add_0
thf(fact_87_add__0,axiom,
    ! [A: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ zero_z1425366712893667068ccount @ A )
      = A ) ).

% add_0
thf(fact_88_add__0,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ zero_zero_nat @ A )
      = A ) ).

% add_0
thf(fact_89_add__0,axiom,
    ! [A: int] :
      ( ( plus_plus_int @ zero_zero_int @ A )
      = A ) ).

% add_0
thf(fact_90_add__0,axiom,
    ! [A: complex] :
      ( ( plus_plus_complex @ zero_zero_complex @ A )
      = A ) ).

% add_0
thf(fact_91_zero__eq__add__iff__both__eq__0,axiom,
    ! [X: nat,Y: nat] :
      ( ( zero_zero_nat
        = ( plus_plus_nat @ X @ Y ) )
      = ( ( X = zero_zero_nat )
        & ( Y = zero_zero_nat ) ) ) ).

% zero_eq_add_iff_both_eq_0
thf(fact_92_add__eq__0__iff__both__eq__0,axiom,
    ! [X: nat,Y: nat] :
      ( ( ( plus_plus_nat @ X @ Y )
        = zero_zero_nat )
      = ( ( X = zero_zero_nat )
        & ( Y = zero_zero_nat ) ) ) ).

% add_eq_0_iff_both_eq_0
thf(fact_93_add__cancel__right__right,axiom,
    ! [A: real,B: real] :
      ( ( A
        = ( plus_plus_real @ A @ B ) )
      = ( B = zero_zero_real ) ) ).

% add_cancel_right_right
thf(fact_94_add__cancel__right__right,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( A
        = ( plus_p1863581527469039996ccount @ A @ B ) )
      = ( B = zero_z1425366712893667068ccount ) ) ).

% add_cancel_right_right
thf(fact_95_add__cancel__right__right,axiom,
    ! [A: nat,B: nat] :
      ( ( A
        = ( plus_plus_nat @ A @ B ) )
      = ( B = zero_zero_nat ) ) ).

% add_cancel_right_right
thf(fact_96_add__cancel__right__right,axiom,
    ! [A: int,B: int] :
      ( ( A
        = ( plus_plus_int @ A @ B ) )
      = ( B = zero_zero_int ) ) ).

% add_cancel_right_right
thf(fact_97_add__cancel__right__right,axiom,
    ! [A: complex,B: complex] :
      ( ( A
        = ( plus_plus_complex @ A @ B ) )
      = ( B = zero_zero_complex ) ) ).

% add_cancel_right_right
thf(fact_98_add__cancel__right__left,axiom,
    ! [A: real,B: real] :
      ( ( A
        = ( plus_plus_real @ B @ A ) )
      = ( B = zero_zero_real ) ) ).

% add_cancel_right_left
thf(fact_99_add__cancel__right__left,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( A
        = ( plus_p1863581527469039996ccount @ B @ A ) )
      = ( B = zero_z1425366712893667068ccount ) ) ).

% add_cancel_right_left
thf(fact_100_add__cancel__right__left,axiom,
    ! [A: nat,B: nat] :
      ( ( A
        = ( plus_plus_nat @ B @ A ) )
      = ( B = zero_zero_nat ) ) ).

% add_cancel_right_left
thf(fact_101_add__cancel__right__left,axiom,
    ! [A: int,B: int] :
      ( ( A
        = ( plus_plus_int @ B @ A ) )
      = ( B = zero_zero_int ) ) ).

% add_cancel_right_left
thf(fact_102_add__cancel__right__left,axiom,
    ! [A: complex,B: complex] :
      ( ( A
        = ( plus_plus_complex @ B @ A ) )
      = ( B = zero_zero_complex ) ) ).

% add_cancel_right_left
thf(fact_103_add__cancel__left__right,axiom,
    ! [A: real,B: real] :
      ( ( ( plus_plus_real @ A @ B )
        = A )
      = ( B = zero_zero_real ) ) ).

% add_cancel_left_right
thf(fact_104_add__cancel__left__right,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ( plus_p1863581527469039996ccount @ A @ B )
        = A )
      = ( B = zero_z1425366712893667068ccount ) ) ).

% add_cancel_left_right
thf(fact_105_add__cancel__left__right,axiom,
    ! [A: nat,B: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = A )
      = ( B = zero_zero_nat ) ) ).

% add_cancel_left_right
thf(fact_106_add__cancel__left__right,axiom,
    ! [A: int,B: int] :
      ( ( ( plus_plus_int @ A @ B )
        = A )
      = ( B = zero_zero_int ) ) ).

% add_cancel_left_right
thf(fact_107_add__cancel__left__right,axiom,
    ! [A: complex,B: complex] :
      ( ( ( plus_plus_complex @ A @ B )
        = A )
      = ( B = zero_zero_complex ) ) ).

% add_cancel_left_right
thf(fact_108_add__cancel__left__left,axiom,
    ! [B: real,A: real] :
      ( ( ( plus_plus_real @ B @ A )
        = A )
      = ( B = zero_zero_real ) ) ).

% add_cancel_left_left
thf(fact_109_add__cancel__left__left,axiom,
    ! [B: risk_Free_account,A: risk_Free_account] :
      ( ( ( plus_p1863581527469039996ccount @ B @ A )
        = A )
      = ( B = zero_z1425366712893667068ccount ) ) ).

% add_cancel_left_left
thf(fact_110_add__cancel__left__left,axiom,
    ! [B: nat,A: nat] :
      ( ( ( plus_plus_nat @ B @ A )
        = A )
      = ( B = zero_zero_nat ) ) ).

% add_cancel_left_left
thf(fact_111_add__cancel__left__left,axiom,
    ! [B: int,A: int] :
      ( ( ( plus_plus_int @ B @ A )
        = A )
      = ( B = zero_zero_int ) ) ).

% add_cancel_left_left
thf(fact_112_add__cancel__left__left,axiom,
    ! [B: complex,A: complex] :
      ( ( ( plus_plus_complex @ B @ A )
        = A )
      = ( B = zero_zero_complex ) ) ).

% add_cancel_left_left
thf(fact_113_double__zero__sym,axiom,
    ! [A: real] :
      ( ( zero_zero_real
        = ( plus_plus_real @ A @ A ) )
      = ( A = zero_zero_real ) ) ).

% double_zero_sym
thf(fact_114_double__zero__sym,axiom,
    ! [A: int] :
      ( ( zero_zero_int
        = ( plus_plus_int @ A @ A ) )
      = ( A = zero_zero_int ) ) ).

% double_zero_sym
thf(fact_115_add_Oright__neutral,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ) ).

% add.right_neutral
thf(fact_116_add_Oright__neutral,axiom,
    ! [A: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ A @ zero_z1425366712893667068ccount )
      = A ) ).

% add.right_neutral
thf(fact_117_add_Oright__neutral,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ A @ zero_zero_nat )
      = A ) ).

% add.right_neutral
thf(fact_118_add_Oright__neutral,axiom,
    ! [A: int] :
      ( ( plus_plus_int @ A @ zero_zero_int )
      = A ) ).

% add.right_neutral
thf(fact_119_add_Oright__neutral,axiom,
    ! [A: complex] :
      ( ( plus_plus_complex @ A @ zero_zero_complex )
      = A ) ).

% add.right_neutral
thf(fact_120_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
    ! [A: real] :
      ( ( minus_minus_real @ A @ A )
      = zero_zero_real ) ).

% cancel_comm_monoid_add_class.diff_cancel
thf(fact_121_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
    ! [A: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ A @ A )
      = zero_z1425366712893667068ccount ) ).

% cancel_comm_monoid_add_class.diff_cancel
thf(fact_122_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
    ! [A: int] :
      ( ( minus_minus_int @ A @ A )
      = zero_zero_int ) ).

% cancel_comm_monoid_add_class.diff_cancel
thf(fact_123_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
    ! [A: nat] :
      ( ( minus_minus_nat @ A @ A )
      = zero_zero_nat ) ).

% cancel_comm_monoid_add_class.diff_cancel
thf(fact_124_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
    ! [A: complex] :
      ( ( minus_minus_complex @ A @ A )
      = zero_zero_complex ) ).

% cancel_comm_monoid_add_class.diff_cancel
thf(fact_125_add__diff__cancel__right_H,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
      = A ) ).

% add_diff_cancel_right'
thf(fact_126_add__diff__cancel__right_H,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ B )
      = A ) ).

% add_diff_cancel_right'
thf(fact_127_add__diff__cancel__right_H,axiom,
    ! [A: int,B: int] :
      ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
      = A ) ).

% add_diff_cancel_right'
thf(fact_128_add__diff__cancel__right_H,axiom,
    ! [A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
      = A ) ).

% add_diff_cancel_right'
thf(fact_129_add__diff__cancel__right_H,axiom,
    ! [A: complex,B: complex] :
      ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
      = A ) ).

% add_diff_cancel_right'
thf(fact_130_add__diff__cancel__right,axiom,
    ! [A: real,C: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
      = ( minus_minus_real @ A @ B ) ) ).

% add_diff_cancel_right
thf(fact_131_add__diff__cancel__right,axiom,
    ! [A: risk_Free_account,C: risk_Free_account,B: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ ( plus_p1863581527469039996ccount @ B @ C ) )
      = ( minus_4846202936726426316ccount @ A @ B ) ) ).

% add_diff_cancel_right
thf(fact_132_add__diff__cancel__right,axiom,
    ! [A: int,C: int,B: int] :
      ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
      = ( minus_minus_int @ A @ B ) ) ).

% add_diff_cancel_right
thf(fact_133_add__diff__cancel__right,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
      = ( minus_minus_nat @ A @ B ) ) ).

% add_diff_cancel_right
thf(fact_134_add__diff__cancel__right,axiom,
    ! [A: complex,C: complex,B: complex] :
      ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ C ) )
      = ( minus_minus_complex @ A @ B ) ) ).

% add_diff_cancel_right
thf(fact_135_mem__Collect__eq,axiom,
    ! [A: nat > real,P: ( nat > real ) > $o] :
      ( ( member_nat_real @ A @ ( collect_nat_real @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_136_mem__Collect__eq,axiom,
    ! [A: nat,P: nat > $o] :
      ( ( member_nat @ A @ ( collect_nat @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_137_mem__Collect__eq,axiom,
    ! [A: int,P: int > $o] :
      ( ( member_int @ A @ ( collect_int @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_138_mem__Collect__eq,axiom,
    ! [A: complex,P: complex > $o] :
      ( ( member_complex @ A @ ( collect_complex @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_139_Collect__mem__eq,axiom,
    ! [A2: set_nat_real] :
      ( ( collect_nat_real
        @ ^ [X3: nat > real] : ( member_nat_real @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_140_Collect__mem__eq,axiom,
    ! [A2: set_nat] :
      ( ( collect_nat
        @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_141_Collect__mem__eq,axiom,
    ! [A2: set_int] :
      ( ( collect_int
        @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_142_Collect__mem__eq,axiom,
    ! [A2: set_complex] :
      ( ( collect_complex
        @ ^ [X3: complex] : ( member_complex @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_143_Collect__cong,axiom,
    ! [P: nat > $o,Q: nat > $o] :
      ( ! [X2: nat] :
          ( ( P @ X2 )
          = ( Q @ X2 ) )
     => ( ( collect_nat @ P )
        = ( collect_nat @ Q ) ) ) ).

% Collect_cong
thf(fact_144_Collect__cong,axiom,
    ! [P: int > $o,Q: int > $o] :
      ( ! [X2: int] :
          ( ( P @ X2 )
          = ( Q @ X2 ) )
     => ( ( collect_int @ P )
        = ( collect_int @ Q ) ) ) ).

% Collect_cong
thf(fact_145_Collect__cong,axiom,
    ! [P: complex > $o,Q: complex > $o] :
      ( ! [X2: complex] :
          ( ( P @ X2 )
          = ( Q @ X2 ) )
     => ( ( collect_complex @ P )
        = ( collect_complex @ Q ) ) ) ).

% Collect_cong
thf(fact_146_add__diff__cancel__left_H,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
      = B ) ).

% add_diff_cancel_left'
thf(fact_147_add__diff__cancel__left_H,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ A )
      = B ) ).

% add_diff_cancel_left'
thf(fact_148_add__diff__cancel__left_H,axiom,
    ! [A: int,B: int] :
      ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
      = B ) ).

% add_diff_cancel_left'
thf(fact_149_add__diff__cancel__left_H,axiom,
    ! [A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
      = B ) ).

% add_diff_cancel_left'
thf(fact_150_add__diff__cancel__left_H,axiom,
    ! [A: complex,B: complex] :
      ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ A )
      = B ) ).

% add_diff_cancel_left'
thf(fact_151_add__diff__cancel__left,axiom,
    ! [C: real,A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
      = ( minus_minus_real @ A @ B ) ) ).

% add_diff_cancel_left
thf(fact_152_add__diff__cancel__left,axiom,
    ! [C: risk_Free_account,A: risk_Free_account,B: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ ( plus_p1863581527469039996ccount @ C @ A ) @ ( plus_p1863581527469039996ccount @ C @ B ) )
      = ( minus_4846202936726426316ccount @ A @ B ) ) ).

% add_diff_cancel_left
thf(fact_153_add__diff__cancel__left,axiom,
    ! [C: int,A: int,B: int] :
      ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
      = ( minus_minus_int @ A @ B ) ) ).

% add_diff_cancel_left
thf(fact_154_add__diff__cancel__left,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
      = ( minus_minus_nat @ A @ B ) ) ).

% add_diff_cancel_left
thf(fact_155_add__diff__cancel__left,axiom,
    ! [C: complex,A: complex,B: complex] :
      ( ( minus_minus_complex @ ( plus_plus_complex @ C @ A ) @ ( plus_plus_complex @ C @ B ) )
      = ( minus_minus_complex @ A @ B ) ) ).

% add_diff_cancel_left
thf(fact_156_diff__add__cancel,axiom,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
      = A ) ).

% diff_add_cancel
thf(fact_157_diff__add__cancel,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ ( minus_4846202936726426316ccount @ A @ B ) @ B )
      = A ) ).

% diff_add_cancel
thf(fact_158_diff__add__cancel,axiom,
    ! [A: int,B: int] :
      ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
      = A ) ).

% diff_add_cancel
thf(fact_159_diff__add__cancel,axiom,
    ! [A: complex,B: complex] :
      ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ B )
      = A ) ).

% diff_add_cancel
thf(fact_160_add__diff__cancel,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
      = A ) ).

% add_diff_cancel
thf(fact_161_add__diff__cancel,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ B )
      = A ) ).

% add_diff_cancel
thf(fact_162_add__diff__cancel,axiom,
    ! [A: int,B: int] :
      ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
      = A ) ).

% add_diff_cancel
thf(fact_163_add__diff__cancel,axiom,
    ! [A: complex,B: complex] :
      ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
      = A ) ).

% add_diff_cancel
thf(fact_164_Rep__account__zero,axiom,
    ( ( risk_F170160801229183585ccount @ zero_z1425366712893667068ccount )
    = ( ^ [Uu: nat] : zero_zero_real ) ) ).

% Rep_account_zero
thf(fact_165_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [A: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
      = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).

% zero_le_double_add_iff_zero_le_single_add
thf(fact_166_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [A: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
      = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).

% zero_le_double_add_iff_zero_le_single_add
thf(fact_167_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [A: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
      = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).

% double_add_le_zero_iff_single_add_le_zero
thf(fact_168_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [A: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
      = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).

% double_add_le_zero_iff_single_add_le_zero
thf(fact_169_le__add__same__cancel2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ ( plus_p1863581527469039996ccount @ B @ A ) )
      = ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ B ) ) ).

% le_add_same_cancel2
thf(fact_170_le__add__same__cancel2,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
      = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).

% le_add_same_cancel2
thf(fact_171_le__add__same__cancel2,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
      = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).

% le_add_same_cancel2
thf(fact_172_le__add__same__cancel2,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
      = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).

% le_add_same_cancel2
thf(fact_173_le__add__same__cancel1,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ ( plus_p1863581527469039996ccount @ A @ B ) )
      = ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ B ) ) ).

% le_add_same_cancel1
thf(fact_174_le__add__same__cancel1,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
      = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).

% le_add_same_cancel1
thf(fact_175_le__add__same__cancel1,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
      = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).

% le_add_same_cancel1
thf(fact_176_le__add__same__cancel1,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
      = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).

% le_add_same_cancel1
thf(fact_177_add__le__same__cancel2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ B )
      = ( ord_le4245800335709223507ccount @ A @ zero_z1425366712893667068ccount ) ) ).

% add_le_same_cancel2
thf(fact_178_add__le__same__cancel2,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
      = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).

% add_le_same_cancel2
thf(fact_179_add__le__same__cancel2,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
      = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).

% add_le_same_cancel2
thf(fact_180_add__le__same__cancel2,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
      = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).

% add_le_same_cancel2
thf(fact_181_add__le__same__cancel1,axiom,
    ! [B: risk_Free_account,A: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ B @ A ) @ B )
      = ( ord_le4245800335709223507ccount @ A @ zero_z1425366712893667068ccount ) ) ).

% add_le_same_cancel1
thf(fact_182_add__le__same__cancel1,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
      = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).

% add_le_same_cancel1
thf(fact_183_add__le__same__cancel1,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
      = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).

% add_le_same_cancel1
thf(fact_184_add__le__same__cancel1,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
      = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).

% add_le_same_cancel1
thf(fact_185_diff__ge__0__iff__ge,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ ( minus_4846202936726426316ccount @ A @ B ) )
      = ( ord_le4245800335709223507ccount @ B @ A ) ) ).

% diff_ge_0_iff_ge
thf(fact_186_diff__ge__0__iff__ge,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
      = ( ord_less_eq_real @ B @ A ) ) ).

% diff_ge_0_iff_ge
thf(fact_187_diff__ge__0__iff__ge,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
      = ( ord_less_eq_int @ B @ A ) ) ).

% diff_ge_0_iff_ge
thf(fact_188_le__add__diff__inverse2,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
        = A ) ) ).

% le_add_diff_inverse2
thf(fact_189_le__add__diff__inverse2,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
        = A ) ) ).

% le_add_diff_inverse2
thf(fact_190_le__add__diff__inverse2,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
        = A ) ) ).

% le_add_diff_inverse2
thf(fact_191_le__add__diff__inverse,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
        = A ) ) ).

% le_add_diff_inverse
thf(fact_192_le__add__diff__inverse,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
        = A ) ) ).

% le_add_diff_inverse
thf(fact_193_le__add__diff__inverse,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
        = A ) ) ).

% le_add_diff_inverse
thf(fact_194_diff__add__zero,axiom,
    ! [A: nat,B: nat] :
      ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
      = zero_zero_nat ) ).

% diff_add_zero
thf(fact_195_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).

% ab_semigroup_add_class.add_ac(1)
thf(fact_196_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ C )
      = ( plus_p1863581527469039996ccount @ A @ ( plus_p1863581527469039996ccount @ B @ C ) ) ) ).

% ab_semigroup_add_class.add_ac(1)
thf(fact_197_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).

% ab_semigroup_add_class.add_ac(1)
thf(fact_198_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [A: int,B: int,C: int] :
      ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
      = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).

% ab_semigroup_add_class.add_ac(1)
thf(fact_199_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
      = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).

% ab_semigroup_add_class.add_ac(1)
thf(fact_200_is__num__normalize_I1_J,axiom,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).

% is_num_normalize(1)
thf(fact_201_is__num__normalize_I1_J,axiom,
    ! [A: int,B: int,C: int] :
      ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
      = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).

% is_num_normalize(1)
thf(fact_202_is__num__normalize_I1_J,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
      = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).

% is_num_normalize(1)
thf(fact_203_add__mono__thms__linordered__semiring_I4_J,axiom,
    ! [I: real,J: real,K: real,L: real] :
      ( ( ( I = J )
        & ( K = L ) )
     => ( ( plus_plus_real @ I @ K )
        = ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(4)
thf(fact_204_add__mono__thms__linordered__semiring_I4_J,axiom,
    ! [I: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( I = J )
        & ( K = L ) )
     => ( ( plus_p1863581527469039996ccount @ I @ K )
        = ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(4)
thf(fact_205_add__mono__thms__linordered__semiring_I4_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( ( I = J )
        & ( K = L ) )
     => ( ( plus_plus_nat @ I @ K )
        = ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(4)
thf(fact_206_add__mono__thms__linordered__semiring_I4_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( ( I = J )
        & ( K = L ) )
     => ( ( plus_plus_int @ I @ K )
        = ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(4)
thf(fact_207_add__mono__thms__linordered__semiring_I3_J,axiom,
    ! [I: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( ord_le4245800335709223507ccount @ I @ J )
        & ( K = L ) )
     => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ I @ K ) @ ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(3)
thf(fact_208_add__mono__thms__linordered__semiring_I3_J,axiom,
    ! [I: real,J: real,K: real,L: real] :
      ( ( ( ord_less_eq_real @ I @ J )
        & ( K = L ) )
     => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(3)
thf(fact_209_add__mono__thms__linordered__semiring_I3_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( ( ord_less_eq_int @ I @ J )
        & ( K = L ) )
     => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(3)
thf(fact_210_add__mono__thms__linordered__semiring_I3_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( ( ord_less_eq_nat @ I @ J )
        & ( K = L ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(3)
thf(fact_211_add__mono__thms__linordered__semiring_I2_J,axiom,
    ! [I: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( I = J )
        & ( ord_le4245800335709223507ccount @ K @ L ) )
     => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ I @ K ) @ ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(2)
thf(fact_212_add__mono__thms__linordered__semiring_I2_J,axiom,
    ! [I: real,J: real,K: real,L: real] :
      ( ( ( I = J )
        & ( ord_less_eq_real @ K @ L ) )
     => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(2)
thf(fact_213_add__mono__thms__linordered__semiring_I2_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( ( I = J )
        & ( ord_less_eq_int @ K @ L ) )
     => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(2)
thf(fact_214_add__mono__thms__linordered__semiring_I2_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( ( I = J )
        & ( ord_less_eq_nat @ K @ L ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(2)
thf(fact_215_add__mono__thms__linordered__semiring_I1_J,axiom,
    ! [I: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( ord_le4245800335709223507ccount @ I @ J )
        & ( ord_le4245800335709223507ccount @ K @ L ) )
     => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ I @ K ) @ ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(1)
thf(fact_216_add__mono__thms__linordered__semiring_I1_J,axiom,
    ! [I: real,J: real,K: real,L: real] :
      ( ( ( ord_less_eq_real @ I @ J )
        & ( ord_less_eq_real @ K @ L ) )
     => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(1)
thf(fact_217_add__mono__thms__linordered__semiring_I1_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( ( ord_less_eq_int @ I @ J )
        & ( ord_less_eq_int @ K @ L ) )
     => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(1)
thf(fact_218_add__mono__thms__linordered__semiring_I1_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( ( ord_less_eq_nat @ I @ J )
        & ( ord_less_eq_nat @ K @ L ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(1)
thf(fact_219_group__cancel_Oadd1,axiom,
    ! [A2: real,K: real,A: real,B: real] :
      ( ( A2
        = ( plus_plus_real @ K @ A ) )
     => ( ( plus_plus_real @ A2 @ B )
        = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).

% group_cancel.add1
thf(fact_220_group__cancel_Oadd1,axiom,
    ! [A2: risk_Free_account,K: risk_Free_account,A: risk_Free_account,B: risk_Free_account] :
      ( ( A2
        = ( plus_p1863581527469039996ccount @ K @ A ) )
     => ( ( plus_p1863581527469039996ccount @ A2 @ B )
        = ( plus_p1863581527469039996ccount @ K @ ( plus_p1863581527469039996ccount @ A @ B ) ) ) ) ).

% group_cancel.add1
thf(fact_221_group__cancel_Oadd1,axiom,
    ! [A2: nat,K: nat,A: nat,B: nat] :
      ( ( A2
        = ( plus_plus_nat @ K @ A ) )
     => ( ( plus_plus_nat @ A2 @ B )
        = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).

% group_cancel.add1
thf(fact_222_group__cancel_Oadd1,axiom,
    ! [A2: int,K: int,A: int,B: int] :
      ( ( A2
        = ( plus_plus_int @ K @ A ) )
     => ( ( plus_plus_int @ A2 @ B )
        = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).

% group_cancel.add1
thf(fact_223_group__cancel_Oadd1,axiom,
    ! [A2: complex,K: complex,A: complex,B: complex] :
      ( ( A2
        = ( plus_plus_complex @ K @ A ) )
     => ( ( plus_plus_complex @ A2 @ B )
        = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).

% group_cancel.add1
thf(fact_224_group__cancel_Oadd2,axiom,
    ! [B2: real,K: real,B: real,A: real] :
      ( ( B2
        = ( plus_plus_real @ K @ B ) )
     => ( ( plus_plus_real @ A @ B2 )
        = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).

% group_cancel.add2
thf(fact_225_group__cancel_Oadd2,axiom,
    ! [B2: risk_Free_account,K: risk_Free_account,B: risk_Free_account,A: risk_Free_account] :
      ( ( B2
        = ( plus_p1863581527469039996ccount @ K @ B ) )
     => ( ( plus_p1863581527469039996ccount @ A @ B2 )
        = ( plus_p1863581527469039996ccount @ K @ ( plus_p1863581527469039996ccount @ A @ B ) ) ) ) ).

% group_cancel.add2
thf(fact_226_group__cancel_Oadd2,axiom,
    ! [B2: nat,K: nat,B: nat,A: nat] :
      ( ( B2
        = ( plus_plus_nat @ K @ B ) )
     => ( ( plus_plus_nat @ A @ B2 )
        = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).

% group_cancel.add2
thf(fact_227_group__cancel_Oadd2,axiom,
    ! [B2: int,K: int,B: int,A: int] :
      ( ( B2
        = ( plus_plus_int @ K @ B ) )
     => ( ( plus_plus_int @ A @ B2 )
        = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).

% group_cancel.add2
thf(fact_228_group__cancel_Oadd2,axiom,
    ! [B2: complex,K: complex,B: complex,A: complex] :
      ( ( B2
        = ( plus_plus_complex @ K @ B ) )
     => ( ( plus_plus_complex @ A @ B2 )
        = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).

% group_cancel.add2
thf(fact_229_add_Oassoc,axiom,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).

% add.assoc
thf(fact_230_add_Oassoc,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ C )
      = ( plus_p1863581527469039996ccount @ A @ ( plus_p1863581527469039996ccount @ B @ C ) ) ) ).

% add.assoc
thf(fact_231_add_Oassoc,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).

% add.assoc
thf(fact_232_add_Oassoc,axiom,
    ! [A: int,B: int,C: int] :
      ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
      = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).

% add.assoc
thf(fact_233_add_Oassoc,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
      = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).

% add.assoc
thf(fact_234_add_Oleft__cancel,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
      = ( B = C ) ) ).

% add.left_cancel
thf(fact_235_add_Oleft__cancel,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ( plus_p1863581527469039996ccount @ A @ B )
        = ( plus_p1863581527469039996ccount @ A @ C ) )
      = ( B = C ) ) ).

% add.left_cancel
thf(fact_236_add_Oleft__cancel,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ( plus_plus_int @ A @ B )
        = ( plus_plus_int @ A @ C ) )
      = ( B = C ) ) ).

% add.left_cancel
thf(fact_237_add_Oleft__cancel,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( ( plus_plus_complex @ A @ B )
        = ( plus_plus_complex @ A @ C ) )
      = ( B = C ) ) ).

% add.left_cancel
thf(fact_238_add_Oright__cancel,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ( plus_plus_real @ B @ A )
        = ( plus_plus_real @ C @ A ) )
      = ( B = C ) ) ).

% add.right_cancel
thf(fact_239_add_Oright__cancel,axiom,
    ! [B: risk_Free_account,A: risk_Free_account,C: risk_Free_account] :
      ( ( ( plus_p1863581527469039996ccount @ B @ A )
        = ( plus_p1863581527469039996ccount @ C @ A ) )
      = ( B = C ) ) ).

% add.right_cancel
thf(fact_240_add_Oright__cancel,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ( plus_plus_int @ B @ A )
        = ( plus_plus_int @ C @ A ) )
      = ( B = C ) ) ).

% add.right_cancel
thf(fact_241_add_Oright__cancel,axiom,
    ! [B: complex,A: complex,C: complex] :
      ( ( ( plus_plus_complex @ B @ A )
        = ( plus_plus_complex @ C @ A ) )
      = ( B = C ) ) ).

% add.right_cancel
thf(fact_242_add_Ocommute,axiom,
    ( plus_plus_real
    = ( ^ [A3: real,B3: real] : ( plus_plus_real @ B3 @ A3 ) ) ) ).

% add.commute
thf(fact_243_add_Ocommute,axiom,
    ( plus_p1863581527469039996ccount
    = ( ^ [A3: risk_Free_account,B3: risk_Free_account] : ( plus_p1863581527469039996ccount @ B3 @ A3 ) ) ) ).

% add.commute
thf(fact_244_add_Ocommute,axiom,
    ( plus_plus_nat
    = ( ^ [A3: nat,B3: nat] : ( plus_plus_nat @ B3 @ A3 ) ) ) ).

% add.commute
thf(fact_245_add_Ocommute,axiom,
    ( plus_plus_int
    = ( ^ [A3: int,B3: int] : ( plus_plus_int @ B3 @ A3 ) ) ) ).

% add.commute
thf(fact_246_add_Ocommute,axiom,
    ( plus_plus_complex
    = ( ^ [A3: complex,B3: complex] : ( plus_plus_complex @ B3 @ A3 ) ) ) ).

% add.commute
thf(fact_247_add_Oleft__commute,axiom,
    ! [B: real,A: real,C: real] :
      ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
      = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).

% add.left_commute
thf(fact_248_add_Oleft__commute,axiom,
    ! [B: risk_Free_account,A: risk_Free_account,C: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ B @ ( plus_p1863581527469039996ccount @ A @ C ) )
      = ( plus_p1863581527469039996ccount @ A @ ( plus_p1863581527469039996ccount @ B @ C ) ) ) ).

% add.left_commute
thf(fact_249_add_Oleft__commute,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).

% add.left_commute
thf(fact_250_add_Oleft__commute,axiom,
    ! [B: int,A: int,C: int] :
      ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
      = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).

% add.left_commute
thf(fact_251_add_Oleft__commute,axiom,
    ! [B: complex,A: complex,C: complex] :
      ( ( plus_plus_complex @ B @ ( plus_plus_complex @ A @ C ) )
      = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).

% add.left_commute
thf(fact_252_add__mono,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account,D: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ord_le4245800335709223507ccount @ C @ D )
       => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ ( plus_p1863581527469039996ccount @ B @ D ) ) ) ) ).

% add_mono
thf(fact_253_add__mono,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).

% add_mono
thf(fact_254_add__mono,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ C @ D )
       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).

% add_mono
thf(fact_255_add__mono,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).

% add_mono
thf(fact_256_add__left__imp__eq,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
     => ( B = C ) ) ).

% add_left_imp_eq
thf(fact_257_add__left__imp__eq,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ( plus_p1863581527469039996ccount @ A @ B )
        = ( plus_p1863581527469039996ccount @ A @ C ) )
     => ( B = C ) ) ).

% add_left_imp_eq
thf(fact_258_add__left__imp__eq,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
     => ( B = C ) ) ).

% add_left_imp_eq
thf(fact_259_add__left__imp__eq,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ( plus_plus_int @ A @ B )
        = ( plus_plus_int @ A @ C ) )
     => ( B = C ) ) ).

% add_left_imp_eq
thf(fact_260_add__left__imp__eq,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( ( plus_plus_complex @ A @ B )
        = ( plus_plus_complex @ A @ C ) )
     => ( B = C ) ) ).

% add_left_imp_eq
thf(fact_261_add__right__imp__eq,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ( plus_plus_real @ B @ A )
        = ( plus_plus_real @ C @ A ) )
     => ( B = C ) ) ).

% add_right_imp_eq
thf(fact_262_add__right__imp__eq,axiom,
    ! [B: risk_Free_account,A: risk_Free_account,C: risk_Free_account] :
      ( ( ( plus_p1863581527469039996ccount @ B @ A )
        = ( plus_p1863581527469039996ccount @ C @ A ) )
     => ( B = C ) ) ).

% add_right_imp_eq
thf(fact_263_add__right__imp__eq,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ( plus_plus_nat @ B @ A )
        = ( plus_plus_nat @ C @ A ) )
     => ( B = C ) ) ).

% add_right_imp_eq
thf(fact_264_add__right__imp__eq,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ( plus_plus_int @ B @ A )
        = ( plus_plus_int @ C @ A ) )
     => ( B = C ) ) ).

% add_right_imp_eq
thf(fact_265_add__right__imp__eq,axiom,
    ! [B: complex,A: complex,C: complex] :
      ( ( ( plus_plus_complex @ B @ A )
        = ( plus_plus_complex @ C @ A ) )
     => ( B = C ) ) ).

% add_right_imp_eq
thf(fact_266_add__left__mono,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ C @ A ) @ ( plus_p1863581527469039996ccount @ C @ B ) ) ) ).

% add_left_mono
thf(fact_267_add__left__mono,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).

% add_left_mono
thf(fact_268_add__left__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).

% add_left_mono
thf(fact_269_add__left__mono,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).

% add_left_mono
thf(fact_270_less__eqE,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ~ ! [C2: nat] :
            ( B
           != ( plus_plus_nat @ A @ C2 ) ) ) ).

% less_eqE
thf(fact_271_add__right__mono,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ ( plus_p1863581527469039996ccount @ B @ C ) ) ) ).

% add_right_mono
thf(fact_272_add__right__mono,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).

% add_right_mono
thf(fact_273_add__right__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).

% add_right_mono
thf(fact_274_add__right__mono,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).

% add_right_mono
thf(fact_275_le__iff__add,axiom,
    ( ord_less_eq_nat
    = ( ^ [A3: nat,B3: nat] :
        ? [C3: nat] :
          ( B3
          = ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).

% le_iff_add
thf(fact_276_add__le__imp__le__left,axiom,
    ! [C: risk_Free_account,A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ C @ A ) @ ( plus_p1863581527469039996ccount @ C @ B ) )
     => ( ord_le4245800335709223507ccount @ A @ B ) ) ).

% add_le_imp_le_left
thf(fact_277_add__le__imp__le__left,axiom,
    ! [C: real,A: real,B: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
     => ( ord_less_eq_real @ A @ B ) ) ).

% add_le_imp_le_left
thf(fact_278_add__le__imp__le__left,axiom,
    ! [C: int,A: int,B: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
     => ( ord_less_eq_int @ A @ B ) ) ).

% add_le_imp_le_left
thf(fact_279_add__le__imp__le__left,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
     => ( ord_less_eq_nat @ A @ B ) ) ).

% add_le_imp_le_left
thf(fact_280_add__le__imp__le__right,axiom,
    ! [A: risk_Free_account,C: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ ( plus_p1863581527469039996ccount @ B @ C ) )
     => ( ord_le4245800335709223507ccount @ A @ B ) ) ).

% add_le_imp_le_right
thf(fact_281_add__le__imp__le__right,axiom,
    ! [A: real,C: real,B: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
     => ( ord_less_eq_real @ A @ B ) ) ).

% add_le_imp_le_right
thf(fact_282_add__le__imp__le__right,axiom,
    ! [A: int,C: int,B: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
     => ( ord_less_eq_int @ A @ B ) ) ).

% add_le_imp_le_right
thf(fact_283_add__le__imp__le__right,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
     => ( ord_less_eq_nat @ A @ B ) ) ).

% add_le_imp_le_right
thf(fact_284_add__nonpos__eq__0__iff,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ X @ zero_z1425366712893667068ccount )
     => ( ( ord_le4245800335709223507ccount @ Y @ zero_z1425366712893667068ccount )
       => ( ( ( plus_p1863581527469039996ccount @ X @ Y )
            = zero_z1425366712893667068ccount )
          = ( ( X = zero_z1425366712893667068ccount )
            & ( Y = zero_z1425366712893667068ccount ) ) ) ) ) ).

% add_nonpos_eq_0_iff
thf(fact_285_add__nonpos__eq__0__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ X @ zero_zero_real )
     => ( ( ord_less_eq_real @ Y @ zero_zero_real )
       => ( ( ( plus_plus_real @ X @ Y )
            = zero_zero_real )
          = ( ( X = zero_zero_real )
            & ( Y = zero_zero_real ) ) ) ) ) ).

% add_nonpos_eq_0_iff
thf(fact_286_add__nonpos__eq__0__iff,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ X @ zero_zero_int )
     => ( ( ord_less_eq_int @ Y @ zero_zero_int )
       => ( ( ( plus_plus_int @ X @ Y )
            = zero_zero_int )
          = ( ( X = zero_zero_int )
            & ( Y = zero_zero_int ) ) ) ) ) ).

% add_nonpos_eq_0_iff
thf(fact_287_add__nonpos__eq__0__iff,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ zero_zero_nat )
     => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
       => ( ( ( plus_plus_nat @ X @ Y )
            = zero_zero_nat )
          = ( ( X = zero_zero_nat )
            & ( Y = zero_zero_nat ) ) ) ) ) ).

% add_nonpos_eq_0_iff
thf(fact_288_add__nonneg__eq__0__iff,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ X )
     => ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ Y )
       => ( ( ( plus_p1863581527469039996ccount @ X @ Y )
            = zero_z1425366712893667068ccount )
          = ( ( X = zero_z1425366712893667068ccount )
            & ( Y = zero_z1425366712893667068ccount ) ) ) ) ) ).

% add_nonneg_eq_0_iff
thf(fact_289_add__nonneg__eq__0__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ( ord_less_eq_real @ zero_zero_real @ Y )
       => ( ( ( plus_plus_real @ X @ Y )
            = zero_zero_real )
          = ( ( X = zero_zero_real )
            & ( Y = zero_zero_real ) ) ) ) ) ).

% add_nonneg_eq_0_iff
thf(fact_290_add__nonneg__eq__0__iff,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ X )
     => ( ( ord_less_eq_int @ zero_zero_int @ Y )
       => ( ( ( plus_plus_int @ X @ Y )
            = zero_zero_int )
          = ( ( X = zero_zero_int )
            & ( Y = zero_zero_int ) ) ) ) ) ).

% add_nonneg_eq_0_iff
thf(fact_291_add__nonneg__eq__0__iff,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ zero_zero_nat @ X )
     => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
       => ( ( ( plus_plus_nat @ X @ Y )
            = zero_zero_nat )
          = ( ( X = zero_zero_nat )
            & ( Y = zero_zero_nat ) ) ) ) ) ).

% add_nonneg_eq_0_iff
thf(fact_292_add__nonpos__nonpos,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ zero_z1425366712893667068ccount )
     => ( ( ord_le4245800335709223507ccount @ B @ zero_z1425366712893667068ccount )
       => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ zero_z1425366712893667068ccount ) ) ) ).

% add_nonpos_nonpos
thf(fact_293_add__nonpos__nonpos,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ zero_zero_real )
     => ( ( ord_less_eq_real @ B @ zero_zero_real )
       => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).

% add_nonpos_nonpos
thf(fact_294_add__nonpos__nonpos,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ zero_zero_int )
     => ( ( ord_less_eq_int @ B @ zero_zero_int )
       => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).

% add_nonpos_nonpos
thf(fact_295_add__nonpos__nonpos,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ zero_zero_nat )
     => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).

% add_nonpos_nonpos
thf(fact_296_add__nonneg__nonneg,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ A )
     => ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ B )
       => ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ ( plus_p1863581527469039996ccount @ A @ B ) ) ) ) ).

% add_nonneg_nonneg
thf(fact_297_add__nonneg__nonneg,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ zero_zero_real @ B )
       => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).

% add_nonneg_nonneg
thf(fact_298_add__nonneg__nonneg,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ A )
     => ( ( ord_less_eq_int @ zero_zero_int @ B )
       => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).

% add_nonneg_nonneg
thf(fact_299_add__nonneg__nonneg,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ zero_zero_nat @ A )
     => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
       => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).

% add_nonneg_nonneg
thf(fact_300_add__increasing2,axiom,
    ! [C: risk_Free_account,B: risk_Free_account,A: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ C )
     => ( ( ord_le4245800335709223507ccount @ B @ A )
       => ( ord_le4245800335709223507ccount @ B @ ( plus_p1863581527469039996ccount @ A @ C ) ) ) ) ).

% add_increasing2
thf(fact_301_add__increasing2,axiom,
    ! [C: real,B: real,A: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ C )
     => ( ( ord_less_eq_real @ B @ A )
       => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).

% add_increasing2
thf(fact_302_add__increasing2,axiom,
    ! [C: int,B: int,A: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ C )
     => ( ( ord_less_eq_int @ B @ A )
       => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).

% add_increasing2
thf(fact_303_add__increasing2,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( ord_less_eq_nat @ zero_zero_nat @ C )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).

% add_increasing2
thf(fact_304_add__decreasing2,axiom,
    ! [C: risk_Free_account,A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ C @ zero_z1425366712893667068ccount )
     => ( ( ord_le4245800335709223507ccount @ A @ B )
       => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ B ) ) ) ).

% add_decreasing2
thf(fact_305_add__decreasing2,axiom,
    ! [C: real,A: real,B: real] :
      ( ( ord_less_eq_real @ C @ zero_zero_real )
     => ( ( ord_less_eq_real @ A @ B )
       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).

% add_decreasing2
thf(fact_306_add__decreasing2,axiom,
    ! [C: int,A: int,B: int] :
      ( ( ord_less_eq_int @ C @ zero_zero_int )
     => ( ( ord_less_eq_int @ A @ B )
       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).

% add_decreasing2
thf(fact_307_add__decreasing2,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_eq_nat @ C @ zero_zero_nat )
     => ( ( ord_less_eq_nat @ A @ B )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).

% add_decreasing2
thf(fact_308_add__increasing,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ A )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ord_le4245800335709223507ccount @ B @ ( plus_p1863581527469039996ccount @ A @ C ) ) ) ) ).

% add_increasing
thf(fact_309_add__increasing,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).

% add_increasing
thf(fact_310_add__increasing,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ A )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).

% add_increasing
thf(fact_311_add__increasing,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ zero_zero_nat @ A )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).

% add_increasing
thf(fact_312_add__decreasing,axiom,
    ! [A: risk_Free_account,C: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ zero_z1425366712893667068ccount )
     => ( ( ord_le4245800335709223507ccount @ C @ B )
       => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ B ) ) ) ).

% add_decreasing
thf(fact_313_add__decreasing,axiom,
    ! [A: real,C: real,B: real] :
      ( ( ord_less_eq_real @ A @ zero_zero_real )
     => ( ( ord_less_eq_real @ C @ B )
       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).

% add_decreasing
thf(fact_314_add__decreasing,axiom,
    ! [A: int,C: int,B: int] :
      ( ( ord_less_eq_int @ A @ zero_zero_int )
     => ( ( ord_less_eq_int @ C @ B )
       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).

% add_decreasing
thf(fact_315_add__decreasing,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ zero_zero_nat )
     => ( ( ord_less_eq_nat @ C @ B )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).

% add_decreasing
thf(fact_316_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ A @ B )
       => ( ( ( minus_minus_nat @ B @ A )
            = C )
          = ( B
            = ( plus_plus_nat @ C @ A ) ) ) ) ) ).

% ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
thf(fact_317_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
        = B ) ) ).

% ordered_cancel_comm_monoid_diff_class.add_diff_inverse
thf(fact_318_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).

% ordered_cancel_comm_monoid_diff_class.diff_diff_right
thf(fact_319_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
        = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).

% ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
thf(fact_320_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
        = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).

% ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
thf(fact_321_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
        = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).

% ordered_cancel_comm_monoid_diff_class.diff_add_assoc
thf(fact_322_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).

% ordered_cancel_comm_monoid_diff_class.add_diff_assoc
thf(fact_323_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).

% ordered_cancel_comm_monoid_diff_class.le_diff_conv2
thf(fact_324_le__add__diff,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).

% le_add_diff
thf(fact_325_add__le__add__imp__diff__le,axiom,
    ! [I: real,K: real,N2: real,J: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
     => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
       => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
         => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
           => ( ord_less_eq_real @ ( minus_minus_real @ N2 @ K ) @ J ) ) ) ) ) ).

% add_le_add_imp_diff_le
thf(fact_326_add__le__add__imp__diff__le,axiom,
    ! [I: int,K: int,N2: int,J: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
     => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
       => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
         => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
           => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).

% add_le_add_imp_diff_le
thf(fact_327_add__le__add__imp__diff__le,axiom,
    ! [I: nat,K: nat,N2: nat,J: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
     => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
         => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
           => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).

% add_le_add_imp_diff_le
thf(fact_328_diff__add,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
        = B ) ) ).

% diff_add
thf(fact_329_add__le__imp__le__diff,axiom,
    ! [I: real,K: real,N2: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
     => ( ord_less_eq_real @ I @ ( minus_minus_real @ N2 @ K ) ) ) ).

% add_le_imp_le_diff
thf(fact_330_add__le__imp__le__diff,axiom,
    ! [I: int,K: int,N2: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
     => ( ord_less_eq_int @ I @ ( minus_minus_int @ N2 @ K ) ) ) ).

% add_le_imp_le_diff
thf(fact_331_add__le__imp__le__diff,axiom,
    ! [I: nat,K: nat,N2: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
     => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N2 @ K ) ) ) ).

% add_le_imp_le_diff
thf(fact_332_le__diff__eq,axiom,
    ! [A: risk_Free_account,C: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ ( minus_4846202936726426316ccount @ C @ B ) )
      = ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ C ) ) ).

% le_diff_eq
thf(fact_333_le__diff__eq,axiom,
    ! [A: real,C: real,B: real] :
      ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
      = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).

% le_diff_eq
thf(fact_334_le__diff__eq,axiom,
    ! [A: int,C: int,B: int] :
      ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
      = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).

% le_diff_eq
thf(fact_335_diff__le__eq,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ ( minus_4846202936726426316ccount @ A @ B ) @ C )
      = ( ord_le4245800335709223507ccount @ A @ ( plus_p1863581527469039996ccount @ C @ B ) ) ) ).

% diff_le_eq
thf(fact_336_diff__le__eq,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).

% diff_le_eq
thf(fact_337_diff__le__eq,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
      = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).

% diff_le_eq
thf(fact_338_add_Ogroup__left__neutral,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ zero_zero_real @ A )
      = A ) ).

% add.group_left_neutral
thf(fact_339_add_Ogroup__left__neutral,axiom,
    ! [A: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ zero_z1425366712893667068ccount @ A )
      = A ) ).

% add.group_left_neutral
thf(fact_340_add_Ogroup__left__neutral,axiom,
    ! [A: int] :
      ( ( plus_plus_int @ zero_zero_int @ A )
      = A ) ).

% add.group_left_neutral
thf(fact_341_add_Ogroup__left__neutral,axiom,
    ! [A: complex] :
      ( ( plus_plus_complex @ zero_zero_complex @ A )
      = A ) ).

% add.group_left_neutral
thf(fact_342_add_Ocomm__neutral,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ) ).

% add.comm_neutral
thf(fact_343_add_Ocomm__neutral,axiom,
    ! [A: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ A @ zero_z1425366712893667068ccount )
      = A ) ).

% add.comm_neutral
thf(fact_344_add_Ocomm__neutral,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ A @ zero_zero_nat )
      = A ) ).

% add.comm_neutral
thf(fact_345_add_Ocomm__neutral,axiom,
    ! [A: int] :
      ( ( plus_plus_int @ A @ zero_zero_int )
      = A ) ).

% add.comm_neutral
thf(fact_346_add_Ocomm__neutral,axiom,
    ! [A: complex] :
      ( ( plus_plus_complex @ A @ zero_zero_complex )
      = A ) ).

% add.comm_neutral
thf(fact_347_comm__monoid__add__class_Oadd__0,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ zero_zero_real @ A )
      = A ) ).

% comm_monoid_add_class.add_0
thf(fact_348_comm__monoid__add__class_Oadd__0,axiom,
    ! [A: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ zero_z1425366712893667068ccount @ A )
      = A ) ).

% comm_monoid_add_class.add_0
thf(fact_349_comm__monoid__add__class_Oadd__0,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ zero_zero_nat @ A )
      = A ) ).

% comm_monoid_add_class.add_0
thf(fact_350_comm__monoid__add__class_Oadd__0,axiom,
    ! [A: int] :
      ( ( plus_plus_int @ zero_zero_int @ A )
      = A ) ).

% comm_monoid_add_class.add_0
thf(fact_351_comm__monoid__add__class_Oadd__0,axiom,
    ! [A: complex] :
      ( ( plus_plus_complex @ zero_zero_complex @ A )
      = A ) ).

% comm_monoid_add_class.add_0
thf(fact_352_zero__le,axiom,
    ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).

% zero_le
thf(fact_353_le__numeral__extra_I3_J,axiom,
    ord_less_eq_real @ zero_zero_real @ zero_zero_real ).

% le_numeral_extra(3)
thf(fact_354_le__numeral__extra_I3_J,axiom,
    ord_less_eq_int @ zero_zero_int @ zero_zero_int ).

% le_numeral_extra(3)
thf(fact_355_le__numeral__extra_I3_J,axiom,
    ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).

% le_numeral_extra(3)
thf(fact_356_combine__common__factor,axiom,
    ! [A: complex,E: complex,B: complex,C: complex] :
      ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ C ) )
      = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ E ) @ C ) ) ).

% combine_common_factor
thf(fact_357_combine__common__factor,axiom,
    ! [A: real,E: real,B: real,C: real] :
      ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
      = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).

% combine_common_factor
thf(fact_358_combine__common__factor,axiom,
    ! [A: int,E: int,B: int,C: int] :
      ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
      = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).

% combine_common_factor
thf(fact_359_combine__common__factor,axiom,
    ! [A: nat,E: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).

% combine_common_factor
thf(fact_360_distrib__right,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
      = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).

% distrib_right
thf(fact_361_distrib__right,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).

% distrib_right
thf(fact_362_distrib__right,axiom,
    ! [A: int,B: int,C: int] :
      ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
      = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).

% distrib_right
thf(fact_363_distrib__right,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).

% distrib_right
thf(fact_364_distrib__left,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
      = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).

% distrib_left
thf(fact_365_distrib__left,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
      = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).

% distrib_left
thf(fact_366_distrib__left,axiom,
    ! [A: int,B: int,C: int] :
      ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
      = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).

% distrib_left
thf(fact_367_distrib__left,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
      = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).

% distrib_left
thf(fact_368_comm__semiring__class_Odistrib,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
      = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).

% comm_semiring_class.distrib
thf(fact_369_comm__semiring__class_Odistrib,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).

% comm_semiring_class.distrib
thf(fact_370_comm__semiring__class_Odistrib,axiom,
    ! [A: int,B: int,C: int] :
      ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
      = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).

% comm_semiring_class.distrib
thf(fact_371_comm__semiring__class_Odistrib,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).

% comm_semiring_class.distrib
thf(fact_372_ring__class_Oring__distribs_I1_J,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
      = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).

% ring_class.ring_distribs(1)
thf(fact_373_ring__class_Oring__distribs_I1_J,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
      = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).

% ring_class.ring_distribs(1)
thf(fact_374_ring__class_Oring__distribs_I1_J,axiom,
    ! [A: int,B: int,C: int] :
      ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
      = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).

% ring_class.ring_distribs(1)
thf(fact_375_ring__class_Oring__distribs_I2_J,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
      = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).

% ring_class.ring_distribs(2)
thf(fact_376_ring__class_Oring__distribs_I2_J,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).

% ring_class.ring_distribs(2)
thf(fact_377_ring__class_Oring__distribs_I2_J,axiom,
    ! [A: int,B: int,C: int] :
      ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
      = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).

% ring_class.ring_distribs(2)
thf(fact_378_diff__diff__eq,axiom,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).

% diff_diff_eq
thf(fact_379_diff__diff__eq,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ ( minus_4846202936726426316ccount @ A @ B ) @ C )
      = ( minus_4846202936726426316ccount @ A @ ( plus_p1863581527469039996ccount @ B @ C ) ) ) ).

% diff_diff_eq
thf(fact_380_diff__diff__eq,axiom,
    ! [A: int,B: int,C: int] :
      ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
      = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).

% diff_diff_eq
thf(fact_381_diff__diff__eq,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).

% diff_diff_eq
thf(fact_382_diff__diff__eq,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C )
      = ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).

% diff_diff_eq
thf(fact_383_add__implies__diff,axiom,
    ! [C: real,B: real,A: real] :
      ( ( ( plus_plus_real @ C @ B )
        = A )
     => ( C
        = ( minus_minus_real @ A @ B ) ) ) ).

% add_implies_diff
thf(fact_384_add__implies__diff,axiom,
    ! [C: risk_Free_account,B: risk_Free_account,A: risk_Free_account] :
      ( ( ( plus_p1863581527469039996ccount @ C @ B )
        = A )
     => ( C
        = ( minus_4846202936726426316ccount @ A @ B ) ) ) ).

% add_implies_diff
thf(fact_385_add__implies__diff,axiom,
    ! [C: int,B: int,A: int] :
      ( ( ( plus_plus_int @ C @ B )
        = A )
     => ( C
        = ( minus_minus_int @ A @ B ) ) ) ).

% add_implies_diff
thf(fact_386_add__implies__diff,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( plus_plus_nat @ C @ B )
        = A )
     => ( C
        = ( minus_minus_nat @ A @ B ) ) ) ).

% add_implies_diff
thf(fact_387_add__implies__diff,axiom,
    ! [C: complex,B: complex,A: complex] :
      ( ( ( plus_plus_complex @ C @ B )
        = A )
     => ( C
        = ( minus_minus_complex @ A @ B ) ) ) ).

% add_implies_diff
thf(fact_388_diff__add__eq__diff__diff__swap,axiom,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
      = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).

% diff_add_eq_diff_diff_swap
thf(fact_389_diff__add__eq__diff__diff__swap,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ A @ ( plus_p1863581527469039996ccount @ B @ C ) )
      = ( minus_4846202936726426316ccount @ ( minus_4846202936726426316ccount @ A @ C ) @ B ) ) ).

% diff_add_eq_diff_diff_swap
thf(fact_390_diff__add__eq__diff__diff__swap,axiom,
    ! [A: int,B: int,C: int] :
      ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
      = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).

% diff_add_eq_diff_diff_swap
thf(fact_391_diff__add__eq__diff__diff__swap,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) )
      = ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B ) ) ).

% diff_add_eq_diff_diff_swap
thf(fact_392_diff__add__eq,axiom,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).

% diff_add_eq
thf(fact_393_diff__add__eq,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ ( minus_4846202936726426316ccount @ A @ B ) @ C )
      = ( minus_4846202936726426316ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ B ) ) ).

% diff_add_eq
thf(fact_394_diff__add__eq,axiom,
    ! [A: int,B: int,C: int] :
      ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
      = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).

% diff_add_eq
thf(fact_395_diff__add__eq,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ C )
      = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).

% diff_add_eq
thf(fact_396_diff__diff__eq2,axiom,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).

% diff_diff_eq2
thf(fact_397_diff__diff__eq2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ A @ ( minus_4846202936726426316ccount @ B @ C ) )
      = ( minus_4846202936726426316ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ B ) ) ).

% diff_diff_eq2
thf(fact_398_diff__diff__eq2,axiom,
    ! [A: int,B: int,C: int] :
      ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
      = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).

% diff_diff_eq2
thf(fact_399_diff__diff__eq2,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( minus_minus_complex @ A @ ( minus_minus_complex @ B @ C ) )
      = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).

% diff_diff_eq2
thf(fact_400_add__diff__eq,axiom,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).

% add_diff_eq
thf(fact_401_add__diff__eq,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ A @ ( minus_4846202936726426316ccount @ B @ C ) )
      = ( minus_4846202936726426316ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ C ) ) ).

% add_diff_eq
thf(fact_402_add__diff__eq,axiom,
    ! [A: int,B: int,C: int] :
      ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
      = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).

% add_diff_eq
thf(fact_403_add__diff__eq,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( plus_plus_complex @ A @ ( minus_minus_complex @ B @ C ) )
      = ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ C ) ) ).

% add_diff_eq
thf(fact_404_eq__diff__eq,axiom,
    ! [A: real,C: real,B: real] :
      ( ( A
        = ( minus_minus_real @ C @ B ) )
      = ( ( plus_plus_real @ A @ B )
        = C ) ) ).

% eq_diff_eq
thf(fact_405_eq__diff__eq,axiom,
    ! [A: risk_Free_account,C: risk_Free_account,B: risk_Free_account] :
      ( ( A
        = ( minus_4846202936726426316ccount @ C @ B ) )
      = ( ( plus_p1863581527469039996ccount @ A @ B )
        = C ) ) ).

% eq_diff_eq
thf(fact_406_eq__diff__eq,axiom,
    ! [A: int,C: int,B: int] :
      ( ( A
        = ( minus_minus_int @ C @ B ) )
      = ( ( plus_plus_int @ A @ B )
        = C ) ) ).

% eq_diff_eq
thf(fact_407_eq__diff__eq,axiom,
    ! [A: complex,C: complex,B: complex] :
      ( ( A
        = ( minus_minus_complex @ C @ B ) )
      = ( ( plus_plus_complex @ A @ B )
        = C ) ) ).

% eq_diff_eq
thf(fact_408_diff__eq__eq,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( minus_minus_real @ A @ B )
        = C )
      = ( A
        = ( plus_plus_real @ C @ B ) ) ) ).

% diff_eq_eq
thf(fact_409_diff__eq__eq,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ( minus_4846202936726426316ccount @ A @ B )
        = C )
      = ( A
        = ( plus_p1863581527469039996ccount @ C @ B ) ) ) ).

% diff_eq_eq
thf(fact_410_diff__eq__eq,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ( minus_minus_int @ A @ B )
        = C )
      = ( A
        = ( plus_plus_int @ C @ B ) ) ) ).

% diff_eq_eq
thf(fact_411_diff__eq__eq,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( ( minus_minus_complex @ A @ B )
        = C )
      = ( A
        = ( plus_plus_complex @ C @ B ) ) ) ).

% diff_eq_eq
thf(fact_412_group__cancel_Osub1,axiom,
    ! [A2: real,K: real,A: real,B: real] :
      ( ( A2
        = ( plus_plus_real @ K @ A ) )
     => ( ( minus_minus_real @ A2 @ B )
        = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).

% group_cancel.sub1
thf(fact_413_group__cancel_Osub1,axiom,
    ! [A2: risk_Free_account,K: risk_Free_account,A: risk_Free_account,B: risk_Free_account] :
      ( ( A2
        = ( plus_p1863581527469039996ccount @ K @ A ) )
     => ( ( minus_4846202936726426316ccount @ A2 @ B )
        = ( plus_p1863581527469039996ccount @ K @ ( minus_4846202936726426316ccount @ A @ B ) ) ) ) ).

% group_cancel.sub1
thf(fact_414_group__cancel_Osub1,axiom,
    ! [A2: int,K: int,A: int,B: int] :
      ( ( A2
        = ( plus_plus_int @ K @ A ) )
     => ( ( minus_minus_int @ A2 @ B )
        = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).

% group_cancel.sub1
thf(fact_415_group__cancel_Osub1,axiom,
    ! [A2: complex,K: complex,A: complex,B: complex] :
      ( ( A2
        = ( plus_plus_complex @ K @ A ) )
     => ( ( minus_minus_complex @ A2 @ B )
        = ( plus_plus_complex @ K @ ( minus_minus_complex @ A @ B ) ) ) ) ).

% group_cancel.sub1
thf(fact_416_le__numeral__extra_I4_J,axiom,
    ord_less_eq_real @ one_one_real @ one_one_real ).

% le_numeral_extra(4)
thf(fact_417_le__numeral__extra_I4_J,axiom,
    ord_less_eq_int @ one_one_int @ one_one_int ).

% le_numeral_extra(4)
thf(fact_418_le__numeral__extra_I4_J,axiom,
    ord_less_eq_nat @ one_one_nat @ one_one_nat ).

% le_numeral_extra(4)
thf(fact_419_diff__eq__diff__less__eq,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account,D: risk_Free_account] :
      ( ( ( minus_4846202936726426316ccount @ A @ B )
        = ( minus_4846202936726426316ccount @ C @ D ) )
     => ( ( ord_le4245800335709223507ccount @ A @ B )
        = ( ord_le4245800335709223507ccount @ C @ D ) ) ) ).

% diff_eq_diff_less_eq
thf(fact_420_diff__eq__diff__less__eq,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( minus_minus_real @ A @ B )
        = ( minus_minus_real @ C @ D ) )
     => ( ( ord_less_eq_real @ A @ B )
        = ( ord_less_eq_real @ C @ D ) ) ) ).

% diff_eq_diff_less_eq
thf(fact_421_diff__eq__diff__less__eq,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ( minus_minus_int @ A @ B )
        = ( minus_minus_int @ C @ D ) )
     => ( ( ord_less_eq_int @ A @ B )
        = ( ord_less_eq_int @ C @ D ) ) ) ).

% diff_eq_diff_less_eq
thf(fact_422_diff__right__mono,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ord_le4245800335709223507ccount @ ( minus_4846202936726426316ccount @ A @ C ) @ ( minus_4846202936726426316ccount @ B @ C ) ) ) ).

% diff_right_mono
thf(fact_423_diff__right__mono,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).

% diff_right_mono
thf(fact_424_diff__right__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).

% diff_right_mono
thf(fact_425_diff__left__mono,axiom,
    ! [B: risk_Free_account,A: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ B @ A )
     => ( ord_le4245800335709223507ccount @ ( minus_4846202936726426316ccount @ C @ A ) @ ( minus_4846202936726426316ccount @ C @ B ) ) ) ).

% diff_left_mono
thf(fact_426_diff__left__mono,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).

% diff_left_mono
thf(fact_427_diff__left__mono,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).

% diff_left_mono
thf(fact_428_diff__mono,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,D: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ord_le4245800335709223507ccount @ D @ C )
       => ( ord_le4245800335709223507ccount @ ( minus_4846202936726426316ccount @ A @ C ) @ ( minus_4846202936726426316ccount @ B @ D ) ) ) ) ).

% diff_mono
thf(fact_429_diff__mono,axiom,
    ! [A: real,B: real,D: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ D @ C )
       => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).

% diff_mono
thf(fact_430_diff__mono,axiom,
    ! [A: int,B: int,D: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ D @ C )
       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).

% diff_mono
thf(fact_431_sum__squares__ge__zero,axiom,
    ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).

% sum_squares_ge_zero
thf(fact_432_sum__squares__ge__zero,axiom,
    ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).

% sum_squares_ge_zero
thf(fact_433_ordered__ring__class_Ole__add__iff2,axiom,
    ! [A: real,E: real,C: real,B: real,D: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
      = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).

% ordered_ring_class.le_add_iff2
thf(fact_434_ordered__ring__class_Ole__add__iff2,axiom,
    ! [A: int,E: int,C: int,B: int,D: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
      = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).

% ordered_ring_class.le_add_iff2
thf(fact_435_ordered__ring__class_Ole__add__iff1,axiom,
    ! [A: real,E: real,C: real,B: real,D: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
      = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).

% ordered_ring_class.le_add_iff1
thf(fact_436_ordered__ring__class_Ole__add__iff1,axiom,
    ! [A: int,E: int,C: int,B: int,D: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
      = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).

% ordered_ring_class.le_add_iff1
thf(fact_437_zero__reorient,axiom,
    ! [X: real] :
      ( ( zero_zero_real = X )
      = ( X = zero_zero_real ) ) ).

% zero_reorient
thf(fact_438_zero__reorient,axiom,
    ! [X: risk_Free_account] :
      ( ( zero_z1425366712893667068ccount = X )
      = ( X = zero_z1425366712893667068ccount ) ) ).

% zero_reorient
thf(fact_439_zero__reorient,axiom,
    ! [X: nat] :
      ( ( zero_zero_nat = X )
      = ( X = zero_zero_nat ) ) ).

% zero_reorient
thf(fact_440_zero__reorient,axiom,
    ! [X: int] :
      ( ( zero_zero_int = X )
      = ( X = zero_zero_int ) ) ).

% zero_reorient
thf(fact_441_zero__reorient,axiom,
    ! [X: complex] :
      ( ( zero_zero_complex = X )
      = ( X = zero_zero_complex ) ) ).

% zero_reorient
thf(fact_442_mult_Oleft__commute,axiom,
    ! [B: real,A: real,C: real] :
      ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
      = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).

% mult.left_commute
thf(fact_443_mult_Oleft__commute,axiom,
    ! [B: int,A: int,C: int] :
      ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
      = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).

% mult.left_commute
thf(fact_444_mult_Oleft__commute,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
      = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).

% mult.left_commute
thf(fact_445_mult_Ocommute,axiom,
    ( times_times_real
    = ( ^ [A3: real,B3: real] : ( times_times_real @ B3 @ A3 ) ) ) ).

% mult.commute
thf(fact_446_mult_Ocommute,axiom,
    ( times_times_int
    = ( ^ [A3: int,B3: int] : ( times_times_int @ B3 @ A3 ) ) ) ).

% mult.commute
thf(fact_447_mult_Ocommute,axiom,
    ( times_times_nat
    = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).

% mult.commute
thf(fact_448_mult_Oassoc,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
      = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).

% mult.assoc
thf(fact_449_mult_Oassoc,axiom,
    ! [A: int,B: int,C: int] :
      ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
      = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).

% mult.assoc
thf(fact_450_mult_Oassoc,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
      = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).

% mult.assoc
thf(fact_451_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
      = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).

% ab_semigroup_mult_class.mult_ac(1)
thf(fact_452_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [A: int,B: int,C: int] :
      ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
      = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).

% ab_semigroup_mult_class.mult_ac(1)
thf(fact_453_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
      = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).

% ab_semigroup_mult_class.mult_ac(1)
thf(fact_454_one__reorient,axiom,
    ! [X: real] :
      ( ( one_one_real = X )
      = ( X = one_one_real ) ) ).

% one_reorient
thf(fact_455_one__reorient,axiom,
    ! [X: nat] :
      ( ( one_one_nat = X )
      = ( X = one_one_nat ) ) ).

% one_reorient
thf(fact_456_one__reorient,axiom,
    ! [X: int] :
      ( ( one_one_int = X )
      = ( X = one_one_int ) ) ).

% one_reorient
thf(fact_457_one__reorient,axiom,
    ! [X: complex] :
      ( ( one_one_complex = X )
      = ( X = one_one_complex ) ) ).

% one_reorient
thf(fact_458_diff__right__commute,axiom,
    ! [A: real,C: real,B: real] :
      ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
      = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).

% diff_right_commute
thf(fact_459_diff__right__commute,axiom,
    ! [A: risk_Free_account,C: risk_Free_account,B: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ ( minus_4846202936726426316ccount @ A @ C ) @ B )
      = ( minus_4846202936726426316ccount @ ( minus_4846202936726426316ccount @ A @ B ) @ C ) ) ).

% diff_right_commute
thf(fact_460_diff__right__commute,axiom,
    ! [A: int,C: int,B: int] :
      ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
      = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).

% diff_right_commute
thf(fact_461_diff__right__commute,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
      = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).

% diff_right_commute
thf(fact_462_diff__right__commute,axiom,
    ! [A: complex,C: complex,B: complex] :
      ( ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B )
      = ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C ) ) ).

% diff_right_commute
thf(fact_463_diff__eq__diff__eq,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( minus_minus_real @ A @ B )
        = ( minus_minus_real @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ) ).

% diff_eq_diff_eq
thf(fact_464_diff__eq__diff__eq,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account,D: risk_Free_account] :
      ( ( ( minus_4846202936726426316ccount @ A @ B )
        = ( minus_4846202936726426316ccount @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ) ).

% diff_eq_diff_eq
thf(fact_465_diff__eq__diff__eq,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ( minus_minus_int @ A @ B )
        = ( minus_minus_int @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ) ).

% diff_eq_diff_eq
thf(fact_466_diff__eq__diff__eq,axiom,
    ! [A: complex,B: complex,C: complex,D: complex] :
      ( ( ( minus_minus_complex @ A @ B )
        = ( minus_minus_complex @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ) ).

% diff_eq_diff_eq
thf(fact_467_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ zero_zero_real @ C )
       => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).

% ordered_comm_semiring_class.comm_mult_left_mono
thf(fact_468_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ zero_zero_int @ C )
       => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).

% ordered_comm_semiring_class.comm_mult_left_mono
thf(fact_469_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
       => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).

% ordered_comm_semiring_class.comm_mult_left_mono
thf(fact_470_zero__le__mult__iff,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
      = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
          & ( ord_less_eq_real @ zero_zero_real @ B ) )
        | ( ( ord_less_eq_real @ A @ zero_zero_real )
          & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).

% zero_le_mult_iff
thf(fact_471_zero__le__mult__iff,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
      = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
          & ( ord_less_eq_int @ zero_zero_int @ B ) )
        | ( ( ord_less_eq_int @ A @ zero_zero_int )
          & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).

% zero_le_mult_iff
thf(fact_472_mult__nonneg__nonpos2,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ B @ zero_zero_real )
       => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).

% mult_nonneg_nonpos2
thf(fact_473_mult__nonneg__nonpos2,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ A )
     => ( ( ord_less_eq_int @ B @ zero_zero_int )
       => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).

% mult_nonneg_nonpos2
thf(fact_474_mult__nonneg__nonpos2,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ zero_zero_nat @ A )
     => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
       => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).

% mult_nonneg_nonpos2
thf(fact_475_mult__nonpos__nonneg,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ zero_zero_real )
     => ( ( ord_less_eq_real @ zero_zero_real @ B )
       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).

% mult_nonpos_nonneg
thf(fact_476_mult__nonpos__nonneg,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ zero_zero_int )
     => ( ( ord_less_eq_int @ zero_zero_int @ B )
       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).

% mult_nonpos_nonneg
thf(fact_477_mult__nonpos__nonneg,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ zero_zero_nat )
     => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).

% mult_nonpos_nonneg
thf(fact_478_mult__nonneg__nonpos,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ B @ zero_zero_real )
       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).

% mult_nonneg_nonpos
thf(fact_479_mult__nonneg__nonpos,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ A )
     => ( ( ord_less_eq_int @ B @ zero_zero_int )
       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).

% mult_nonneg_nonpos
thf(fact_480_mult__nonneg__nonpos,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ zero_zero_nat @ A )
     => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).

% mult_nonneg_nonpos
thf(fact_481_mult__nonneg__nonneg,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ zero_zero_real @ B )
       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).

% mult_nonneg_nonneg
thf(fact_482_mult__nonneg__nonneg,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ A )
     => ( ( ord_less_eq_int @ zero_zero_int @ B )
       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).

% mult_nonneg_nonneg
thf(fact_483_mult__nonneg__nonneg,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ zero_zero_nat @ A )
     => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
       => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).

% mult_nonneg_nonneg
thf(fact_484_split__mult__neg__le,axiom,
    ! [A: real,B: real] :
      ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
          & ( ord_less_eq_real @ B @ zero_zero_real ) )
        | ( ( ord_less_eq_real @ A @ zero_zero_real )
          & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
     => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).

% split_mult_neg_le
thf(fact_485_split__mult__neg__le,axiom,
    ! [A: int,B: int] :
      ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
          & ( ord_less_eq_int @ B @ zero_zero_int ) )
        | ( ( ord_less_eq_int @ A @ zero_zero_int )
          & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
     => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).

% split_mult_neg_le
thf(fact_486_split__mult__neg__le,axiom,
    ! [A: nat,B: nat] :
      ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
          & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
        | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
          & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
     => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).

% split_mult_neg_le
thf(fact_487_mult__le__0__iff,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
      = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
          & ( ord_less_eq_real @ B @ zero_zero_real ) )
        | ( ( ord_less_eq_real @ A @ zero_zero_real )
          & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).

% mult_le_0_iff
thf(fact_488_mult__le__0__iff,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
      = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
          & ( ord_less_eq_int @ B @ zero_zero_int ) )
        | ( ( ord_less_eq_int @ A @ zero_zero_int )
          & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).

% mult_le_0_iff
thf(fact_489_mult__right__mono,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ zero_zero_real @ C )
       => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).

% mult_right_mono
thf(fact_490_mult__right__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ zero_zero_int @ C )
       => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).

% mult_right_mono
thf(fact_491_mult__right__mono,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
       => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).

% mult_right_mono
thf(fact_492_mult__right__mono__neg,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ( ord_less_eq_real @ C @ zero_zero_real )
       => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).

% mult_right_mono_neg
thf(fact_493_mult__right__mono__neg,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ( ord_less_eq_int @ C @ zero_zero_int )
       => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).

% mult_right_mono_neg
thf(fact_494_mult__left__mono,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ zero_zero_real @ C )
       => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).

% mult_left_mono
thf(fact_495_mult__left__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ zero_zero_int @ C )
       => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).

% mult_left_mono
thf(fact_496_mult__left__mono,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
       => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).

% mult_left_mono
thf(fact_497_mult__nonpos__nonpos,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ zero_zero_real )
     => ( ( ord_less_eq_real @ B @ zero_zero_real )
       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).

% mult_nonpos_nonpos
thf(fact_498_mult__nonpos__nonpos,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ zero_zero_int )
     => ( ( ord_less_eq_int @ B @ zero_zero_int )
       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).

% mult_nonpos_nonpos
thf(fact_499_mult__left__mono__neg,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ( ord_less_eq_real @ C @ zero_zero_real )
       => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).

% mult_left_mono_neg
thf(fact_500_mult__left__mono__neg,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ( ord_less_eq_int @ C @ zero_zero_int )
       => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).

% mult_left_mono_neg
thf(fact_501_split__mult__pos__le,axiom,
    ! [A: real,B: real] :
      ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
          & ( ord_less_eq_real @ zero_zero_real @ B ) )
        | ( ( ord_less_eq_real @ A @ zero_zero_real )
          & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
     => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).

% split_mult_pos_le
thf(fact_502_split__mult__pos__le,axiom,
    ! [A: int,B: int] :
      ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
          & ( ord_less_eq_int @ zero_zero_int @ B ) )
        | ( ( ord_less_eq_int @ A @ zero_zero_int )
          & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
     => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).

% split_mult_pos_le
thf(fact_503_zero__le__square,axiom,
    ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).

% zero_le_square
thf(fact_504_zero__le__square,axiom,
    ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).

% zero_le_square
thf(fact_505_mult__mono_H,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ( ord_less_eq_real @ zero_zero_real @ A )
         => ( ( ord_less_eq_real @ zero_zero_real @ C )
           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).

% mult_mono'
thf(fact_506_mult__mono_H,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ C @ D )
       => ( ( ord_less_eq_int @ zero_zero_int @ A )
         => ( ( ord_less_eq_int @ zero_zero_int @ C )
           => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).

% mult_mono'
thf(fact_507_mult__mono_H,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
         => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
           => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).

% mult_mono'
thf(fact_508_mult__mono,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ( ord_less_eq_real @ zero_zero_real @ B )
         => ( ( ord_less_eq_real @ zero_zero_real @ C )
           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).

% mult_mono
thf(fact_509_mult__mono,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ C @ D )
       => ( ( ord_less_eq_int @ zero_zero_int @ B )
         => ( ( ord_less_eq_int @ zero_zero_int @ C )
           => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).

% mult_mono
thf(fact_510_mult__mono,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
         => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
           => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).

% mult_mono
thf(fact_511_not__one__le__zero,axiom,
    ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).

% not_one_le_zero
thf(fact_512_not__one__le__zero,axiom,
    ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).

% not_one_le_zero
thf(fact_513_not__one__le__zero,axiom,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).

% not_one_le_zero
thf(fact_514_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
    ord_less_eq_real @ zero_zero_real @ one_one_real ).

% linordered_nonzero_semiring_class.zero_le_one
thf(fact_515_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
    ord_less_eq_int @ zero_zero_int @ one_one_int ).

% linordered_nonzero_semiring_class.zero_le_one
thf(fact_516_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
    ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).

% linordered_nonzero_semiring_class.zero_le_one
thf(fact_517_zero__less__one__class_Ozero__le__one,axiom,
    ord_less_eq_real @ zero_zero_real @ one_one_real ).

% zero_less_one_class.zero_le_one
thf(fact_518_zero__less__one__class_Ozero__le__one,axiom,
    ord_less_eq_int @ zero_zero_int @ one_one_int ).

% zero_less_one_class.zero_le_one
thf(fact_519_zero__less__one__class_Ozero__le__one,axiom,
    ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).

% zero_less_one_class.zero_le_one
thf(fact_520_square__diff__square__factored,axiom,
    ! [X: complex,Y: complex] :
      ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ ( times_times_complex @ Y @ Y ) )
      = ( times_times_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_complex @ X @ Y ) ) ) ).

% square_diff_square_factored
thf(fact_521_square__diff__square__factored,axiom,
    ! [X: real,Y: real] :
      ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
      = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).

% square_diff_square_factored
thf(fact_522_square__diff__square__factored,axiom,
    ! [X: int,Y: int] :
      ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
      = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).

% square_diff_square_factored
thf(fact_523_eq__add__iff2,axiom,
    ! [A: complex,E: complex,C: complex,B: complex,D: complex] :
      ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
        = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D ) )
      = ( C
        = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B @ A ) @ E ) @ D ) ) ) ).

% eq_add_iff2
thf(fact_524_eq__add__iff2,axiom,
    ! [A: real,E: real,C: real,B: real,D: real] :
      ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
        = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
      = ( C
        = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).

% eq_add_iff2
thf(fact_525_eq__add__iff2,axiom,
    ! [A: int,E: int,C: int,B: int,D: int] :
      ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
        = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
      = ( C
        = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).

% eq_add_iff2
thf(fact_526_eq__add__iff1,axiom,
    ! [A: complex,E: complex,C: complex,B: complex,D: complex] :
      ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
        = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D ) )
      = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ E ) @ C )
        = D ) ) ).

% eq_add_iff1
thf(fact_527_eq__add__iff1,axiom,
    ! [A: real,E: real,C: real,B: real,D: real] :
      ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
        = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
      = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
        = D ) ) ).

% eq_add_iff1
thf(fact_528_eq__add__iff1,axiom,
    ! [A: int,E: int,C: int,B: int,D: int] :
      ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
        = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
      = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
        = D ) ) ).

% eq_add_iff1
thf(fact_529_le__iff__diff__le__0,axiom,
    ( ord_le4245800335709223507ccount
    = ( ^ [A3: risk_Free_account,B3: risk_Free_account] : ( ord_le4245800335709223507ccount @ ( minus_4846202936726426316ccount @ A3 @ B3 ) @ zero_z1425366712893667068ccount ) ) ) ).

% le_iff_diff_le_0
thf(fact_530_le__iff__diff__le__0,axiom,
    ( ord_less_eq_real
    = ( ^ [A3: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B3 ) @ zero_zero_real ) ) ) ).

% le_iff_diff_le_0
thf(fact_531_le__iff__diff__le__0,axiom,
    ( ord_less_eq_int
    = ( ^ [A3: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).

% le_iff_diff_le_0
thf(fact_532_convex__bound__le,axiom,
    ! [X: real,A: real,Y: real,U: real,V: real] :
      ( ( ord_less_eq_real @ X @ A )
     => ( ( ord_less_eq_real @ Y @ A )
       => ( ( ord_less_eq_real @ zero_zero_real @ U )
         => ( ( ord_less_eq_real @ zero_zero_real @ V )
           => ( ( ( plus_plus_real @ U @ V )
                = one_one_real )
             => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).

% convex_bound_le
thf(fact_533_convex__bound__le,axiom,
    ! [X: int,A: int,Y: int,U: int,V: int] :
      ( ( ord_less_eq_int @ X @ A )
     => ( ( ord_less_eq_int @ Y @ A )
       => ( ( ord_less_eq_int @ zero_zero_int @ U )
         => ( ( ord_less_eq_int @ zero_zero_int @ V )
           => ( ( ( plus_plus_int @ U @ V )
                = one_one_int )
             => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).

% convex_bound_le
thf(fact_534_square__diff__one__factored,axiom,
    ! [X: complex] :
      ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
      = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).

% square_diff_one_factored
thf(fact_535_square__diff__one__factored,axiom,
    ! [X: real] :
      ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
      = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).

% square_diff_one_factored
thf(fact_536_square__diff__one__factored,axiom,
    ! [X: int] :
      ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
      = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).

% square_diff_one_factored
thf(fact_537_mult__left__le,axiom,
    ! [C: real,A: real] :
      ( ( ord_less_eq_real @ C @ one_one_real )
     => ( ( ord_less_eq_real @ zero_zero_real @ A )
       => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).

% mult_left_le
thf(fact_538_mult__left__le,axiom,
    ! [C: int,A: int] :
      ( ( ord_less_eq_int @ C @ one_one_int )
     => ( ( ord_less_eq_int @ zero_zero_int @ A )
       => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).

% mult_left_le
thf(fact_539_mult__left__le,axiom,
    ! [C: nat,A: nat] :
      ( ( ord_less_eq_nat @ C @ one_one_nat )
     => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
       => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).

% mult_left_le
thf(fact_540_mult__le__one,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ one_one_real )
     => ( ( ord_less_eq_real @ zero_zero_real @ B )
       => ( ( ord_less_eq_real @ B @ one_one_real )
         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).

% mult_le_one
thf(fact_541_mult__le__one,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ one_one_int )
     => ( ( ord_less_eq_int @ zero_zero_int @ B )
       => ( ( ord_less_eq_int @ B @ one_one_int )
         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).

% mult_le_one
thf(fact_542_mult__le__one,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ one_one_nat )
     => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
       => ( ( ord_less_eq_nat @ B @ one_one_nat )
         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).

% mult_le_one
thf(fact_543_mult__right__le__one__le,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ( ord_less_eq_real @ zero_zero_real @ Y )
       => ( ( ord_less_eq_real @ Y @ one_one_real )
         => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).

% mult_right_le_one_le
thf(fact_544_mult__right__le__one__le,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ X )
     => ( ( ord_less_eq_int @ zero_zero_int @ Y )
       => ( ( ord_less_eq_int @ Y @ one_one_int )
         => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).

% mult_right_le_one_le
thf(fact_545_mult__left__le__one__le,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ( ord_less_eq_real @ zero_zero_real @ Y )
       => ( ( ord_less_eq_real @ Y @ one_one_real )
         => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).

% mult_left_le_one_le
thf(fact_546_mult__left__le__one__le,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ X )
     => ( ( ord_less_eq_int @ zero_zero_int @ Y )
       => ( ( ord_less_eq_int @ Y @ one_one_int )
         => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).

% mult_left_le_one_le
thf(fact_547_mult__right__cancel,axiom,
    ! [C: complex,A: complex,B: complex] :
      ( ( C != zero_zero_complex )
     => ( ( ( times_times_complex @ A @ C )
          = ( times_times_complex @ B @ C ) )
        = ( A = B ) ) ) ).

% mult_right_cancel
thf(fact_548_mult__right__cancel,axiom,
    ! [C: real,A: real,B: real] :
      ( ( C != zero_zero_real )
     => ( ( ( times_times_real @ A @ C )
          = ( times_times_real @ B @ C ) )
        = ( A = B ) ) ) ).

% mult_right_cancel
thf(fact_549_mult__right__cancel,axiom,
    ! [C: int,A: int,B: int] :
      ( ( C != zero_zero_int )
     => ( ( ( times_times_int @ A @ C )
          = ( times_times_int @ B @ C ) )
        = ( A = B ) ) ) ).

% mult_right_cancel
thf(fact_550_mult__right__cancel,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( C != zero_zero_nat )
     => ( ( ( times_times_nat @ A @ C )
          = ( times_times_nat @ B @ C ) )
        = ( A = B ) ) ) ).

% mult_right_cancel
thf(fact_551_mult__left__cancel,axiom,
    ! [C: complex,A: complex,B: complex] :
      ( ( C != zero_zero_complex )
     => ( ( ( times_times_complex @ C @ A )
          = ( times_times_complex @ C @ B ) )
        = ( A = B ) ) ) ).

% mult_left_cancel
thf(fact_552_mult__left__cancel,axiom,
    ! [C: real,A: real,B: real] :
      ( ( C != zero_zero_real )
     => ( ( ( times_times_real @ C @ A )
          = ( times_times_real @ C @ B ) )
        = ( A = B ) ) ) ).

% mult_left_cancel
thf(fact_553_mult__left__cancel,axiom,
    ! [C: int,A: int,B: int] :
      ( ( C != zero_zero_int )
     => ( ( ( times_times_int @ C @ A )
          = ( times_times_int @ C @ B ) )
        = ( A = B ) ) ) ).

% mult_left_cancel
thf(fact_554_mult__left__cancel,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( C != zero_zero_nat )
     => ( ( ( times_times_nat @ C @ A )
          = ( times_times_nat @ C @ B ) )
        = ( A = B ) ) ) ).

% mult_left_cancel
thf(fact_555_no__zero__divisors,axiom,
    ! [A: complex,B: complex] :
      ( ( A != zero_zero_complex )
     => ( ( B != zero_zero_complex )
       => ( ( times_times_complex @ A @ B )
         != zero_zero_complex ) ) ) ).

% no_zero_divisors
thf(fact_556_no__zero__divisors,axiom,
    ! [A: real,B: real] :
      ( ( A != zero_zero_real )
     => ( ( B != zero_zero_real )
       => ( ( times_times_real @ A @ B )
         != zero_zero_real ) ) ) ).

% no_zero_divisors
thf(fact_557_no__zero__divisors,axiom,
    ! [A: int,B: int] :
      ( ( A != zero_zero_int )
     => ( ( B != zero_zero_int )
       => ( ( times_times_int @ A @ B )
         != zero_zero_int ) ) ) ).

% no_zero_divisors
thf(fact_558_no__zero__divisors,axiom,
    ! [A: nat,B: nat] :
      ( ( A != zero_zero_nat )
     => ( ( B != zero_zero_nat )
       => ( ( times_times_nat @ A @ B )
         != zero_zero_nat ) ) ) ).

% no_zero_divisors
thf(fact_559_divisors__zero,axiom,
    ! [A: complex,B: complex] :
      ( ( ( times_times_complex @ A @ B )
        = zero_zero_complex )
     => ( ( A = zero_zero_complex )
        | ( B = zero_zero_complex ) ) ) ).

% divisors_zero
thf(fact_560_divisors__zero,axiom,
    ! [A: real,B: real] :
      ( ( ( times_times_real @ A @ B )
        = zero_zero_real )
     => ( ( A = zero_zero_real )
        | ( B = zero_zero_real ) ) ) ).

% divisors_zero
thf(fact_561_divisors__zero,axiom,
    ! [A: int,B: int] :
      ( ( ( times_times_int @ A @ B )
        = zero_zero_int )
     => ( ( A = zero_zero_int )
        | ( B = zero_zero_int ) ) ) ).

% divisors_zero
thf(fact_562_divisors__zero,axiom,
    ! [A: nat,B: nat] :
      ( ( ( times_times_nat @ A @ B )
        = zero_zero_nat )
     => ( ( A = zero_zero_nat )
        | ( B = zero_zero_nat ) ) ) ).

% divisors_zero
thf(fact_563_mult__not__zero,axiom,
    ! [A: complex,B: complex] :
      ( ( ( times_times_complex @ A @ B )
       != zero_zero_complex )
     => ( ( A != zero_zero_complex )
        & ( B != zero_zero_complex ) ) ) ).

% mult_not_zero
thf(fact_564_mult__not__zero,axiom,
    ! [A: real,B: real] :
      ( ( ( times_times_real @ A @ B )
       != zero_zero_real )
     => ( ( A != zero_zero_real )
        & ( B != zero_zero_real ) ) ) ).

% mult_not_zero
thf(fact_565_mult__not__zero,axiom,
    ! [A: int,B: int] :
      ( ( ( times_times_int @ A @ B )
       != zero_zero_int )
     => ( ( A != zero_zero_int )
        & ( B != zero_zero_int ) ) ) ).

% mult_not_zero
thf(fact_566_mult__not__zero,axiom,
    ! [A: nat,B: nat] :
      ( ( ( times_times_nat @ A @ B )
       != zero_zero_nat )
     => ( ( A != zero_zero_nat )
        & ( B != zero_zero_nat ) ) ) ).

% mult_not_zero
thf(fact_567_zero__neq__one,axiom,
    zero_zero_real != one_one_real ).

% zero_neq_one
thf(fact_568_zero__neq__one,axiom,
    zero_zero_nat != one_one_nat ).

% zero_neq_one
thf(fact_569_zero__neq__one,axiom,
    zero_zero_int != one_one_int ).

% zero_neq_one
thf(fact_570_zero__neq__one,axiom,
    zero_zero_complex != one_one_complex ).

% zero_neq_one
thf(fact_571_eq__iff__diff__eq__0,axiom,
    ( ( ^ [Y2: real,Z: real] : ( Y2 = Z ) )
    = ( ^ [A3: real,B3: real] :
          ( ( minus_minus_real @ A3 @ B3 )
          = zero_zero_real ) ) ) ).

% eq_iff_diff_eq_0
thf(fact_572_eq__iff__diff__eq__0,axiom,
    ( ( ^ [Y2: risk_Free_account,Z: risk_Free_account] : ( Y2 = Z ) )
    = ( ^ [A3: risk_Free_account,B3: risk_Free_account] :
          ( ( minus_4846202936726426316ccount @ A3 @ B3 )
          = zero_z1425366712893667068ccount ) ) ) ).

% eq_iff_diff_eq_0
thf(fact_573_eq__iff__diff__eq__0,axiom,
    ( ( ^ [Y2: int,Z: int] : ( Y2 = Z ) )
    = ( ^ [A3: int,B3: int] :
          ( ( minus_minus_int @ A3 @ B3 )
          = zero_zero_int ) ) ) ).

% eq_iff_diff_eq_0
thf(fact_574_eq__iff__diff__eq__0,axiom,
    ( ( ^ [Y2: complex,Z: complex] : ( Y2 = Z ) )
    = ( ^ [A3: complex,B3: complex] :
          ( ( minus_minus_complex @ A3 @ B3 )
          = zero_zero_complex ) ) ) ).

% eq_iff_diff_eq_0
thf(fact_575_mult_Ocomm__neutral,axiom,
    ! [A: complex] :
      ( ( times_times_complex @ A @ one_one_complex )
      = A ) ).

% mult.comm_neutral
thf(fact_576_mult_Ocomm__neutral,axiom,
    ! [A: real] :
      ( ( times_times_real @ A @ one_one_real )
      = A ) ).

% mult.comm_neutral
thf(fact_577_mult_Ocomm__neutral,axiom,
    ! [A: int] :
      ( ( times_times_int @ A @ one_one_int )
      = A ) ).

% mult.comm_neutral
thf(fact_578_mult_Ocomm__neutral,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ A @ one_one_nat )
      = A ) ).

% mult.comm_neutral
thf(fact_579_comm__monoid__mult__class_Omult__1,axiom,
    ! [A: complex] :
      ( ( times_times_complex @ one_one_complex @ A )
      = A ) ).

% comm_monoid_mult_class.mult_1
thf(fact_580_comm__monoid__mult__class_Omult__1,axiom,
    ! [A: real] :
      ( ( times_times_real @ one_one_real @ A )
      = A ) ).

% comm_monoid_mult_class.mult_1
thf(fact_581_comm__monoid__mult__class_Omult__1,axiom,
    ! [A: int] :
      ( ( times_times_int @ one_one_int @ A )
      = A ) ).

% comm_monoid_mult_class.mult_1
thf(fact_582_comm__monoid__mult__class_Omult__1,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ one_one_nat @ A )
      = A ) ).

% comm_monoid_mult_class.mult_1
thf(fact_583_right__diff__distrib_H,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
      = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).

% right_diff_distrib'
thf(fact_584_right__diff__distrib_H,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).

% right_diff_distrib'
thf(fact_585_right__diff__distrib_H,axiom,
    ! [A: int,B: int,C: int] :
      ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
      = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).

% right_diff_distrib'
thf(fact_586_right__diff__distrib_H,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
      = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).

% right_diff_distrib'
thf(fact_587_left__diff__distrib_H,axiom,
    ! [B: complex,C: complex,A: complex] :
      ( ( times_times_complex @ ( minus_minus_complex @ B @ C ) @ A )
      = ( minus_minus_complex @ ( times_times_complex @ B @ A ) @ ( times_times_complex @ C @ A ) ) ) ).

% left_diff_distrib'
thf(fact_588_left__diff__distrib_H,axiom,
    ! [B: real,C: real,A: real] :
      ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
      = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).

% left_diff_distrib'
thf(fact_589_left__diff__distrib_H,axiom,
    ! [B: int,C: int,A: int] :
      ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
      = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).

% left_diff_distrib'
thf(fact_590_left__diff__distrib_H,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
      = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).

% left_diff_distrib'
thf(fact_591_right__diff__distrib,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
      = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).

% right_diff_distrib
thf(fact_592_right__diff__distrib,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).

% right_diff_distrib
thf(fact_593_right__diff__distrib,axiom,
    ! [A: int,B: int,C: int] :
      ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
      = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).

% right_diff_distrib
thf(fact_594_left__diff__distrib,axiom,
    ! [A: complex,B: complex,C: complex] :
      ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ C )
      = ( minus_minus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).

% left_diff_distrib
thf(fact_595_left__diff__distrib,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).

% left_diff_distrib
thf(fact_596_left__diff__distrib,axiom,
    ! [A: int,B: int,C: int] :
      ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
      = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).

% left_diff_distrib
thf(fact_597_lambda__zero,axiom,
    ( ( ^ [H: complex] : zero_zero_complex )
    = ( times_times_complex @ zero_zero_complex ) ) ).

% lambda_zero
thf(fact_598_lambda__zero,axiom,
    ( ( ^ [H: real] : zero_zero_real )
    = ( times_times_real @ zero_zero_real ) ) ).

% lambda_zero
thf(fact_599_lambda__zero,axiom,
    ( ( ^ [H: int] : zero_zero_int )
    = ( times_times_int @ zero_zero_int ) ) ).

% lambda_zero
thf(fact_600_lambda__zero,axiom,
    ( ( ^ [H: nat] : zero_zero_nat )
    = ( times_times_nat @ zero_zero_nat ) ) ).

% lambda_zero
thf(fact_601_lambda__one,axiom,
    ( ( ^ [X3: complex] : X3 )
    = ( times_times_complex @ one_one_complex ) ) ).

% lambda_one
thf(fact_602_lambda__one,axiom,
    ( ( ^ [X3: real] : X3 )
    = ( times_times_real @ one_one_real ) ) ).

% lambda_one
thf(fact_603_lambda__one,axiom,
    ( ( ^ [X3: int] : X3 )
    = ( times_times_int @ one_one_int ) ) ).

% lambda_one
thf(fact_604_lambda__one,axiom,
    ( ( ^ [X3: nat] : X3 )
    = ( times_times_nat @ one_one_nat ) ) ).

% lambda_one
thf(fact_605_fin__support__closed__under__addition,axiom,
    ! [F: nat > real,A2: set_nat,G: nat > real] :
      ( ( member_nat_real @ F @ ( ordina1579063754167848977al_nat @ zero_zero_real @ A2 ) )
     => ( ( member_nat_real @ G @ ( ordina1579063754167848977al_nat @ zero_zero_real @ A2 ) )
       => ( member_nat_real
          @ ^ [X3: nat] : ( plus_plus_real @ ( F @ X3 ) @ ( G @ X3 ) )
          @ ( ordina1579063754167848977al_nat @ zero_zero_real @ A2 ) ) ) ) ).

% fin_support_closed_under_addition
thf(fact_606_sum__squares__eq__zero__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
        = zero_zero_real )
      = ( ( X = zero_zero_real )
        & ( Y = zero_zero_real ) ) ) ).

% sum_squares_eq_zero_iff
thf(fact_607_sum__squares__eq__zero__iff,axiom,
    ! [X: int,Y: int] :
      ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
        = zero_zero_int )
      = ( ( X = zero_zero_int )
        & ( Y = zero_zero_int ) ) ) ).

% sum_squares_eq_zero_iff
thf(fact_608_support__Un,axiom,
    ! [Z2: real,A2: set_nat,B2: set_nat,F: nat > real] :
      ( ( ordina7525502726642723294al_nat @ Z2 @ ( sup_sup_set_nat @ A2 @ B2 ) @ F )
      = ( sup_sup_set_nat @ ( ordina7525502726642723294al_nat @ Z2 @ A2 @ F ) @ ( ordina7525502726642723294al_nat @ Z2 @ B2 @ F ) ) ) ).

% support_Un
thf(fact_609_Un__subset__iff,axiom,
    ! [A2: set_nat,B2: set_nat,C4: set_nat] :
      ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C4 )
      = ( ( ord_less_eq_set_nat @ A2 @ C4 )
        & ( ord_less_eq_set_nat @ B2 @ C4 ) ) ) ).

% Un_subset_iff
thf(fact_610_boolean__algebra_Odisj__one__right,axiom,
    ! [X: set_nat] :
      ( ( sup_sup_set_nat @ X @ top_top_set_nat )
      = top_top_set_nat ) ).

% boolean_algebra.disj_one_right
thf(fact_611_boolean__algebra_Odisj__one__right,axiom,
    ! [X: set_int] :
      ( ( sup_sup_set_int @ X @ top_top_set_int )
      = top_top_set_int ) ).

% boolean_algebra.disj_one_right
thf(fact_612_boolean__algebra_Odisj__one__left,axiom,
    ! [X: set_nat] :
      ( ( sup_sup_set_nat @ top_top_set_nat @ X )
      = top_top_set_nat ) ).

% boolean_algebra.disj_one_left
thf(fact_613_boolean__algebra_Odisj__one__left,axiom,
    ! [X: set_int] :
      ( ( sup_sup_set_int @ top_top_set_int @ X )
      = top_top_set_int ) ).

% boolean_algebra.disj_one_left
thf(fact_614_sup__top__right,axiom,
    ! [X: set_nat] :
      ( ( sup_sup_set_nat @ X @ top_top_set_nat )
      = top_top_set_nat ) ).

% sup_top_right
thf(fact_615_sup__top__right,axiom,
    ! [X: set_int] :
      ( ( sup_sup_set_int @ X @ top_top_set_int )
      = top_top_set_int ) ).

% sup_top_right
thf(fact_616_sup__top__left,axiom,
    ! [X: set_nat] :
      ( ( sup_sup_set_nat @ top_top_set_nat @ X )
      = top_top_set_nat ) ).

% sup_top_left
thf(fact_617_sup__top__left,axiom,
    ! [X: set_int] :
      ( ( sup_sup_set_int @ top_top_set_int @ X )
      = top_top_set_int ) ).

% sup_top_left
thf(fact_618_le__sup__iff,axiom,
    ! [X: set_nat,Y: set_nat,Z2: set_nat] :
      ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z2 )
      = ( ( ord_less_eq_set_nat @ X @ Z2 )
        & ( ord_less_eq_set_nat @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_619_le__sup__iff,axiom,
    ! [X: real,Y: real,Z2: real] :
      ( ( ord_less_eq_real @ ( sup_sup_real @ X @ Y ) @ Z2 )
      = ( ( ord_less_eq_real @ X @ Z2 )
        & ( ord_less_eq_real @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_620_le__sup__iff,axiom,
    ! [X: int,Y: int,Z2: int] :
      ( ( ord_less_eq_int @ ( sup_sup_int @ X @ Y ) @ Z2 )
      = ( ( ord_less_eq_int @ X @ Z2 )
        & ( ord_less_eq_int @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_621_le__sup__iff,axiom,
    ! [X: nat,Y: nat,Z2: nat] :
      ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z2 )
      = ( ( ord_less_eq_nat @ X @ Z2 )
        & ( ord_less_eq_nat @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_622_sup_Obounded__iff,axiom,
    ! [B: set_nat,C: set_nat,A: set_nat] :
      ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
      = ( ( ord_less_eq_set_nat @ B @ A )
        & ( ord_less_eq_set_nat @ C @ A ) ) ) ).

% sup.bounded_iff
thf(fact_623_sup_Obounded__iff,axiom,
    ! [B: real,C: real,A: real] :
      ( ( ord_less_eq_real @ ( sup_sup_real @ B @ C ) @ A )
      = ( ( ord_less_eq_real @ B @ A )
        & ( ord_less_eq_real @ C @ A ) ) ) ).

% sup.bounded_iff
thf(fact_624_sup_Obounded__iff,axiom,
    ! [B: int,C: int,A: int] :
      ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A )
      = ( ( ord_less_eq_int @ B @ A )
        & ( ord_less_eq_int @ C @ A ) ) ) ).

% sup.bounded_iff
thf(fact_625_sup_Obounded__iff,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
      = ( ( ord_less_eq_nat @ B @ A )
        & ( ord_less_eq_nat @ C @ A ) ) ) ).

% sup.bounded_iff
thf(fact_626_double__eq__0__iff,axiom,
    ! [A: real] :
      ( ( ( plus_plus_real @ A @ A )
        = zero_zero_real )
      = ( A = zero_zero_real ) ) ).

% double_eq_0_iff
thf(fact_627_double__eq__0__iff,axiom,
    ! [A: int] :
      ( ( ( plus_plus_int @ A @ A )
        = zero_zero_int )
      = ( A = zero_zero_int ) ) ).

% double_eq_0_iff
thf(fact_628_sum__squares__le__zero__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
      = ( ( X = zero_zero_real )
        & ( Y = zero_zero_real ) ) ) ).

% sum_squares_le_zero_iff
thf(fact_629_sum__squares__le__zero__iff,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
      = ( ( X = zero_zero_int )
        & ( Y = zero_zero_int ) ) ) ).

% sum_squares_le_zero_iff
thf(fact_630_UNIV__I,axiom,
    ! [X: nat > real] : ( member_nat_real @ X @ top_top_set_nat_real ) ).

% UNIV_I
thf(fact_631_UNIV__I,axiom,
    ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).

% UNIV_I
thf(fact_632_UNIV__I,axiom,
    ! [X: int] : ( member_int @ X @ top_top_set_int ) ).

% UNIV_I
thf(fact_633_subset__antisym,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ B2 )
     => ( ( ord_less_eq_set_nat @ B2 @ A2 )
       => ( A2 = B2 ) ) ) ).

% subset_antisym
thf(fact_634_subsetI,axiom,
    ! [A2: set_nat_real,B2: set_nat_real] :
      ( ! [X2: nat > real] :
          ( ( member_nat_real @ X2 @ A2 )
         => ( member_nat_real @ X2 @ B2 ) )
     => ( ord_le2908806416726583473t_real @ A2 @ B2 ) ) ).

% subsetI
thf(fact_635_subsetI,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A2 )
         => ( member_nat @ X2 @ B2 ) )
     => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).

% subsetI
thf(fact_636_sup_Oright__idem,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ B )
      = ( sup_sup_set_nat @ A @ B ) ) ).

% sup.right_idem
thf(fact_637_sup__left__idem,axiom,
    ! [X: set_nat,Y: set_nat] :
      ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
      = ( sup_sup_set_nat @ X @ Y ) ) ).

% sup_left_idem
thf(fact_638_sup_Oleft__idem,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) )
      = ( sup_sup_set_nat @ A @ B ) ) ).

% sup.left_idem
thf(fact_639_sup__idem,axiom,
    ! [X: set_nat] :
      ( ( sup_sup_set_nat @ X @ X )
      = X ) ).

% sup_idem
thf(fact_640_sup_Oidem,axiom,
    ! [A: set_nat] :
      ( ( sup_sup_set_nat @ A @ A )
      = A ) ).

% sup.idem
thf(fact_641_Un__Diff__cancel2,axiom,
    ! [B2: set_nat,A2: set_nat] :
      ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ B2 @ A2 ) @ A2 )
      = ( sup_sup_set_nat @ B2 @ A2 ) ) ).

% Un_Diff_cancel2
thf(fact_642_Un__Diff__cancel,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( sup_sup_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ A2 ) )
      = ( sup_sup_set_nat @ A2 @ B2 ) ) ).

% Un_Diff_cancel
thf(fact_643_Un__iff,axiom,
    ! [C: nat > real,A2: set_nat_real,B2: set_nat_real] :
      ( ( member_nat_real @ C @ ( sup_sup_set_nat_real @ A2 @ B2 ) )
      = ( ( member_nat_real @ C @ A2 )
        | ( member_nat_real @ C @ B2 ) ) ) ).

% Un_iff
thf(fact_644_Un__iff,axiom,
    ! [C: nat,A2: set_nat,B2: set_nat] :
      ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) )
      = ( ( member_nat @ C @ A2 )
        | ( member_nat @ C @ B2 ) ) ) ).

% Un_iff
thf(fact_645_UnCI,axiom,
    ! [C: nat > real,B2: set_nat_real,A2: set_nat_real] :
      ( ( ~ ( member_nat_real @ C @ B2 )
       => ( member_nat_real @ C @ A2 ) )
     => ( member_nat_real @ C @ ( sup_sup_set_nat_real @ A2 @ B2 ) ) ) ).

% UnCI
thf(fact_646_UnCI,axiom,
    ! [C: nat,B2: set_nat,A2: set_nat] :
      ( ( ~ ( member_nat @ C @ B2 )
       => ( member_nat @ C @ A2 ) )
     => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).

% UnCI
thf(fact_647_Rep__account__plus,axiom,
    ! [Alpha_1: risk_Free_account,Alpha_2: risk_Free_account] :
      ( ( risk_F170160801229183585ccount @ ( plus_p1863581527469039996ccount @ Alpha_1 @ Alpha_2 ) )
      = ( ^ [N: nat] : ( plus_plus_real @ ( risk_F170160801229183585ccount @ Alpha_1 @ N ) @ ( risk_F170160801229183585ccount @ Alpha_2 @ N ) ) ) ) ).

% Rep_account_plus
thf(fact_648_top__set__def,axiom,
    ( top_top_set_complex
    = ( collect_complex @ top_top_complex_o ) ) ).

% top_set_def
thf(fact_649_top__set__def,axiom,
    ( top_top_set_nat
    = ( collect_nat @ top_top_nat_o ) ) ).

% top_set_def
thf(fact_650_top__set__def,axiom,
    ( top_top_set_int
    = ( collect_int @ top_top_int_o ) ) ).

% top_set_def
thf(fact_651_sup__set__def,axiom,
    ( sup_sup_set_nat_real
    = ( ^ [A4: set_nat_real,B4: set_nat_real] :
          ( collect_nat_real
          @ ( sup_sup_nat_real_o
            @ ^ [X3: nat > real] : ( member_nat_real @ X3 @ A4 )
            @ ^ [X3: nat > real] : ( member_nat_real @ X3 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_652_sup__set__def,axiom,
    ( sup_sup_set_int
    = ( ^ [A4: set_int,B4: set_int] :
          ( collect_int
          @ ( sup_sup_int_o
            @ ^ [X3: int] : ( member_int @ X3 @ A4 )
            @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_653_sup__set__def,axiom,
    ( sup_sup_set_complex
    = ( ^ [A4: set_complex,B4: set_complex] :
          ( collect_complex
          @ ( sup_sup_complex_o
            @ ^ [X3: complex] : ( member_complex @ X3 @ A4 )
            @ ^ [X3: complex] : ( member_complex @ X3 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_654_sup__set__def,axiom,
    ( sup_sup_set_nat
    = ( ^ [A4: set_nat,B4: set_nat] :
          ( collect_nat
          @ ( sup_sup_nat_o
            @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
            @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_655_less__eq__set__def,axiom,
    ( ord_le2908806416726583473t_real
    = ( ^ [A4: set_nat_real,B4: set_nat_real] :
          ( ord_le7676461544873280788real_o
          @ ^ [X3: nat > real] : ( member_nat_real @ X3 @ A4 )
          @ ^ [X3: nat > real] : ( member_nat_real @ X3 @ B4 ) ) ) ) ).

% less_eq_set_def
thf(fact_656_less__eq__set__def,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [A4: set_nat,B4: set_nat] :
          ( ord_less_eq_nat_o
          @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
          @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ).

% less_eq_set_def
thf(fact_657_UNIV__eq__I,axiom,
    ! [A2: set_nat_real] :
      ( ! [X2: nat > real] : ( member_nat_real @ X2 @ A2 )
     => ( top_top_set_nat_real = A2 ) ) ).

% UNIV_eq_I
thf(fact_658_UNIV__eq__I,axiom,
    ! [A2: set_nat] :
      ( ! [X2: nat] : ( member_nat @ X2 @ A2 )
     => ( top_top_set_nat = A2 ) ) ).

% UNIV_eq_I
thf(fact_659_UNIV__eq__I,axiom,
    ! [A2: set_int] :
      ( ! [X2: int] : ( member_int @ X2 @ A2 )
     => ( top_top_set_int = A2 ) ) ).

% UNIV_eq_I
thf(fact_660_UNIV__witness,axiom,
    ? [X2: nat > real] : ( member_nat_real @ X2 @ top_top_set_nat_real ) ).

% UNIV_witness
thf(fact_661_UNIV__witness,axiom,
    ? [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ).

% UNIV_witness
thf(fact_662_UNIV__witness,axiom,
    ? [X2: int] : ( member_int @ X2 @ top_top_set_int ) ).

% UNIV_witness
thf(fact_663_Collect__mono__iff,axiom,
    ! [P: int > $o,Q: int > $o] :
      ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
      = ( ! [X3: int] :
            ( ( P @ X3 )
           => ( Q @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_664_Collect__mono__iff,axiom,
    ! [P: complex > $o,Q: complex > $o] :
      ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
      = ( ! [X3: complex] :
            ( ( P @ X3 )
           => ( Q @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_665_Collect__mono__iff,axiom,
    ! [P: nat > $o,Q: nat > $o] :
      ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
      = ( ! [X3: nat] :
            ( ( P @ X3 )
           => ( Q @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_666_set__eq__subset,axiom,
    ( ( ^ [Y2: set_nat,Z: set_nat] : ( Y2 = Z ) )
    = ( ^ [A4: set_nat,B4: set_nat] :
          ( ( ord_less_eq_set_nat @ A4 @ B4 )
          & ( ord_less_eq_set_nat @ B4 @ A4 ) ) ) ) ).

% set_eq_subset
thf(fact_667_subset__trans,axiom,
    ! [A2: set_nat,B2: set_nat,C4: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ B2 )
     => ( ( ord_less_eq_set_nat @ B2 @ C4 )
       => ( ord_less_eq_set_nat @ A2 @ C4 ) ) ) ).

% subset_trans
thf(fact_668_Collect__mono,axiom,
    ! [P: int > $o,Q: int > $o] :
      ( ! [X2: int] :
          ( ( P @ X2 )
         => ( Q @ X2 ) )
     => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).

% Collect_mono
thf(fact_669_Collect__mono,axiom,
    ! [P: complex > $o,Q: complex > $o] :
      ( ! [X2: complex] :
          ( ( P @ X2 )
         => ( Q @ X2 ) )
     => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).

% Collect_mono
thf(fact_670_Collect__mono,axiom,
    ! [P: nat > $o,Q: nat > $o] :
      ( ! [X2: nat] :
          ( ( P @ X2 )
         => ( Q @ X2 ) )
     => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).

% Collect_mono
thf(fact_671_subset__refl,axiom,
    ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ A2 ) ).

% subset_refl
thf(fact_672_double__diff,axiom,
    ! [A2: set_nat,B2: set_nat,C4: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ B2 )
     => ( ( ord_less_eq_set_nat @ B2 @ C4 )
       => ( ( minus_minus_set_nat @ B2 @ ( minus_minus_set_nat @ C4 @ A2 ) )
          = A2 ) ) ) ).

% double_diff
thf(fact_673_Diff__subset,axiom,
    ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ A2 ) ).

% Diff_subset
thf(fact_674_subset__iff,axiom,
    ( ord_le2908806416726583473t_real
    = ( ^ [A4: set_nat_real,B4: set_nat_real] :
        ! [T: nat > real] :
          ( ( member_nat_real @ T @ A4 )
         => ( member_nat_real @ T @ B4 ) ) ) ) ).

% subset_iff
thf(fact_675_subset__iff,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [A4: set_nat,B4: set_nat] :
        ! [T: nat] :
          ( ( member_nat @ T @ A4 )
         => ( member_nat @ T @ B4 ) ) ) ) ).

% subset_iff
thf(fact_676_equalityD2,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( A2 = B2 )
     => ( ord_less_eq_set_nat @ B2 @ A2 ) ) ).

% equalityD2
thf(fact_677_equalityD1,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( A2 = B2 )
     => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).

% equalityD1
thf(fact_678_subset__eq,axiom,
    ( ord_le2908806416726583473t_real
    = ( ^ [A4: set_nat_real,B4: set_nat_real] :
        ! [X3: nat > real] :
          ( ( member_nat_real @ X3 @ A4 )
         => ( member_nat_real @ X3 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_679_subset__eq,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [A4: set_nat,B4: set_nat] :
        ! [X3: nat] :
          ( ( member_nat @ X3 @ A4 )
         => ( member_nat @ X3 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_680_equalityE,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( A2 = B2 )
     => ~ ( ( ord_less_eq_set_nat @ A2 @ B2 )
         => ~ ( ord_less_eq_set_nat @ B2 @ A2 ) ) ) ).

% equalityE
thf(fact_681_Diff__mono,axiom,
    ! [A2: set_nat,C4: set_nat,D2: set_nat,B2: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ C4 )
     => ( ( ord_less_eq_set_nat @ D2 @ B2 )
       => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ C4 @ D2 ) ) ) ) ).

% Diff_mono
thf(fact_682_subsetD,axiom,
    ! [A2: set_nat_real,B2: set_nat_real,C: nat > real] :
      ( ( ord_le2908806416726583473t_real @ A2 @ B2 )
     => ( ( member_nat_real @ C @ A2 )
       => ( member_nat_real @ C @ B2 ) ) ) ).

% subsetD
thf(fact_683_subsetD,axiom,
    ! [A2: set_nat,B2: set_nat,C: nat] :
      ( ( ord_less_eq_set_nat @ A2 @ B2 )
     => ( ( member_nat @ C @ A2 )
       => ( member_nat @ C @ B2 ) ) ) ).

% subsetD
thf(fact_684_in__mono,axiom,
    ! [A2: set_nat_real,B2: set_nat_real,X: nat > real] :
      ( ( ord_le2908806416726583473t_real @ A2 @ B2 )
     => ( ( member_nat_real @ X @ A2 )
       => ( member_nat_real @ X @ B2 ) ) ) ).

% in_mono
thf(fact_685_in__mono,axiom,
    ! [A2: set_nat,B2: set_nat,X: nat] :
      ( ( ord_less_eq_set_nat @ A2 @ B2 )
     => ( ( member_nat @ X @ A2 )
       => ( member_nat @ X @ B2 ) ) ) ).

% in_mono
thf(fact_686_sup__left__commute,axiom,
    ! [X: set_nat,Y: set_nat,Z2: set_nat] :
      ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z2 ) )
      = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z2 ) ) ) ).

% sup_left_commute
thf(fact_687_sup_Oleft__commute,axiom,
    ! [B: set_nat,A: set_nat,C: set_nat] :
      ( ( sup_sup_set_nat @ B @ ( sup_sup_set_nat @ A @ C ) )
      = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C ) ) ) ).

% sup.left_commute
thf(fact_688_boolean__algebra__cancel_Osup2,axiom,
    ! [B2: set_nat,K: set_nat,B: set_nat,A: set_nat] :
      ( ( B2
        = ( sup_sup_set_nat @ K @ B ) )
     => ( ( sup_sup_set_nat @ A @ B2 )
        = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.sup2
thf(fact_689_boolean__algebra__cancel_Osup1,axiom,
    ! [A2: set_nat,K: set_nat,A: set_nat,B: set_nat] :
      ( ( A2
        = ( sup_sup_set_nat @ K @ A ) )
     => ( ( sup_sup_set_nat @ A2 @ B )
        = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.sup1
thf(fact_690_sup__commute,axiom,
    ( sup_sup_set_nat
    = ( ^ [X3: set_nat,Y3: set_nat] : ( sup_sup_set_nat @ Y3 @ X3 ) ) ) ).

% sup_commute
thf(fact_691_sup_Ocommute,axiom,
    ( sup_sup_set_nat
    = ( ^ [A3: set_nat,B3: set_nat] : ( sup_sup_set_nat @ B3 @ A3 ) ) ) ).

% sup.commute
thf(fact_692_sup__assoc,axiom,
    ! [X: set_nat,Y: set_nat,Z2: set_nat] :
      ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z2 )
      = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z2 ) ) ) ).

% sup_assoc
thf(fact_693_sup_Oassoc,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ C )
      = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C ) ) ) ).

% sup.assoc
thf(fact_694_inf__sup__aci_I5_J,axiom,
    ( sup_sup_set_nat
    = ( ^ [X3: set_nat,Y3: set_nat] : ( sup_sup_set_nat @ Y3 @ X3 ) ) ) ).

% inf_sup_aci(5)
thf(fact_695_inf__sup__aci_I6_J,axiom,
    ! [X: set_nat,Y: set_nat,Z2: set_nat] :
      ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z2 )
      = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z2 ) ) ) ).

% inf_sup_aci(6)
thf(fact_696_inf__sup__aci_I7_J,axiom,
    ! [X: set_nat,Y: set_nat,Z2: set_nat] :
      ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z2 ) )
      = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z2 ) ) ) ).

% inf_sup_aci(7)
thf(fact_697_inf__sup__aci_I8_J,axiom,
    ! [X: set_nat,Y: set_nat] :
      ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
      = ( sup_sup_set_nat @ X @ Y ) ) ).

% inf_sup_aci(8)
thf(fact_698_Un__left__commute,axiom,
    ! [A2: set_nat,B2: set_nat,C4: set_nat] :
      ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C4 ) )
      = ( sup_sup_set_nat @ B2 @ ( sup_sup_set_nat @ A2 @ C4 ) ) ) ).

% Un_left_commute
thf(fact_699_Un__left__absorb,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
      = ( sup_sup_set_nat @ A2 @ B2 ) ) ).

% Un_left_absorb
thf(fact_700_Un__commute,axiom,
    ( sup_sup_set_nat
    = ( ^ [A4: set_nat,B4: set_nat] : ( sup_sup_set_nat @ B4 @ A4 ) ) ) ).

% Un_commute
thf(fact_701_Un__absorb,axiom,
    ! [A2: set_nat] :
      ( ( sup_sup_set_nat @ A2 @ A2 )
      = A2 ) ).

% Un_absorb
thf(fact_702_Un__assoc,axiom,
    ! [A2: set_nat,B2: set_nat,C4: set_nat] :
      ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C4 )
      = ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C4 ) ) ) ).

% Un_assoc
thf(fact_703_ball__Un,axiom,
    ! [A2: set_nat,B2: set_nat,P: nat > $o] :
      ( ( ! [X3: nat] :
            ( ( member_nat @ X3 @ ( sup_sup_set_nat @ A2 @ B2 ) )
           => ( P @ X3 ) ) )
      = ( ! [X3: nat] :
            ( ( member_nat @ X3 @ A2 )
           => ( P @ X3 ) )
        & ! [X3: nat] :
            ( ( member_nat @ X3 @ B2 )
           => ( P @ X3 ) ) ) ) ).

% ball_Un
thf(fact_704_Un__Diff,axiom,
    ! [A2: set_nat,B2: set_nat,C4: set_nat] :
      ( ( minus_minus_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C4 )
      = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A2 @ C4 ) @ ( minus_minus_set_nat @ B2 @ C4 ) ) ) ).

% Un_Diff
thf(fact_705_bex__Un,axiom,
    ! [A2: set_nat,B2: set_nat,P: nat > $o] :
      ( ( ? [X3: nat] :
            ( ( member_nat @ X3 @ ( sup_sup_set_nat @ A2 @ B2 ) )
            & ( P @ X3 ) ) )
      = ( ? [X3: nat] :
            ( ( member_nat @ X3 @ A2 )
            & ( P @ X3 ) )
        | ? [X3: nat] :
            ( ( member_nat @ X3 @ B2 )
            & ( P @ X3 ) ) ) ) ).

% bex_Un
thf(fact_706_UnI2,axiom,
    ! [C: nat > real,B2: set_nat_real,A2: set_nat_real] :
      ( ( member_nat_real @ C @ B2 )
     => ( member_nat_real @ C @ ( sup_sup_set_nat_real @ A2 @ B2 ) ) ) ).

% UnI2
thf(fact_707_UnI2,axiom,
    ! [C: nat,B2: set_nat,A2: set_nat] :
      ( ( member_nat @ C @ B2 )
     => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).

% UnI2
thf(fact_708_UnI1,axiom,
    ! [C: nat > real,A2: set_nat_real,B2: set_nat_real] :
      ( ( member_nat_real @ C @ A2 )
     => ( member_nat_real @ C @ ( sup_sup_set_nat_real @ A2 @ B2 ) ) ) ).

% UnI1
thf(fact_709_UnI1,axiom,
    ! [C: nat,A2: set_nat,B2: set_nat] :
      ( ( member_nat @ C @ A2 )
     => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).

% UnI1
thf(fact_710_UnE,axiom,
    ! [C: nat > real,A2: set_nat_real,B2: set_nat_real] :
      ( ( member_nat_real @ C @ ( sup_sup_set_nat_real @ A2 @ B2 ) )
     => ( ~ ( member_nat_real @ C @ A2 )
       => ( member_nat_real @ C @ B2 ) ) ) ).

% UnE
thf(fact_711_UnE,axiom,
    ! [C: nat,A2: set_nat,B2: set_nat] :
      ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) )
     => ( ~ ( member_nat @ C @ A2 )
       => ( member_nat @ C @ B2 ) ) ) ).

% UnE
thf(fact_712_UNIV__def,axiom,
    ( top_top_set_complex
    = ( collect_complex
      @ ^ [X3: complex] : $true ) ) ).

% UNIV_def
thf(fact_713_UNIV__def,axiom,
    ( top_top_set_nat
    = ( collect_nat
      @ ^ [X3: nat] : $true ) ) ).

% UNIV_def
thf(fact_714_UNIV__def,axiom,
    ( top_top_set_int
    = ( collect_int
      @ ^ [X3: int] : $true ) ) ).

% UNIV_def
thf(fact_715_Collect__subset,axiom,
    ! [A2: set_nat_real,P: ( nat > real ) > $o] :
      ( ord_le2908806416726583473t_real
      @ ( collect_nat_real
        @ ^ [X3: nat > real] :
            ( ( member_nat_real @ X3 @ A2 )
            & ( P @ X3 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_716_Collect__subset,axiom,
    ! [A2: set_int,P: int > $o] :
      ( ord_less_eq_set_int
      @ ( collect_int
        @ ^ [X3: int] :
            ( ( member_int @ X3 @ A2 )
            & ( P @ X3 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_717_Collect__subset,axiom,
    ! [A2: set_complex,P: complex > $o] :
      ( ord_le211207098394363844omplex
      @ ( collect_complex
        @ ^ [X3: complex] :
            ( ( member_complex @ X3 @ A2 )
            & ( P @ X3 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_718_Collect__subset,axiom,
    ! [A2: set_nat,P: nat > $o] :
      ( ord_less_eq_set_nat
      @ ( collect_nat
        @ ^ [X3: nat] :
            ( ( member_nat @ X3 @ A2 )
            & ( P @ X3 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_719_Un__def,axiom,
    ( sup_sup_set_nat_real
    = ( ^ [A4: set_nat_real,B4: set_nat_real] :
          ( collect_nat_real
          @ ^ [X3: nat > real] :
              ( ( member_nat_real @ X3 @ A4 )
              | ( member_nat_real @ X3 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_720_Un__def,axiom,
    ( sup_sup_set_int
    = ( ^ [A4: set_int,B4: set_int] :
          ( collect_int
          @ ^ [X3: int] :
              ( ( member_int @ X3 @ A4 )
              | ( member_int @ X3 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_721_Un__def,axiom,
    ( sup_sup_set_complex
    = ( ^ [A4: set_complex,B4: set_complex] :
          ( collect_complex
          @ ^ [X3: complex] :
              ( ( member_complex @ X3 @ A4 )
              | ( member_complex @ X3 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_722_Un__def,axiom,
    ( sup_sup_set_nat
    = ( ^ [A4: set_nat,B4: set_nat] :
          ( collect_nat
          @ ^ [X3: nat] :
              ( ( member_nat @ X3 @ A4 )
              | ( member_nat @ X3 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_723_Collect__disj__eq,axiom,
    ! [P: int > $o,Q: int > $o] :
      ( ( collect_int
        @ ^ [X3: int] :
            ( ( P @ X3 )
            | ( Q @ X3 ) ) )
      = ( sup_sup_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_724_Collect__disj__eq,axiom,
    ! [P: complex > $o,Q: complex > $o] :
      ( ( collect_complex
        @ ^ [X3: complex] :
            ( ( P @ X3 )
            | ( Q @ X3 ) ) )
      = ( sup_sup_set_complex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_725_Collect__disj__eq,axiom,
    ! [P: nat > $o,Q: nat > $o] :
      ( ( collect_nat
        @ ^ [X3: nat] :
            ( ( P @ X3 )
            | ( Q @ X3 ) ) )
      = ( sup_sup_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_726_support__def,axiom,
    ( ordina7525502726642723294al_nat
    = ( ^ [Z3: real,A4: set_nat,F2: nat > real] :
          ( collect_nat
          @ ^ [X3: nat] :
              ( ( member_nat @ X3 @ A4 )
              & ( ( F2 @ X3 )
               != Z3 ) ) ) ) ) ).

% support_def
thf(fact_727_sup_OcoboundedI2,axiom,
    ! [C: set_nat,B: set_nat,A: set_nat] :
      ( ( ord_less_eq_set_nat @ C @ B )
     => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_728_sup_OcoboundedI2,axiom,
    ! [C: real,B: real,A: real] :
      ( ( ord_less_eq_real @ C @ B )
     => ( ord_less_eq_real @ C @ ( sup_sup_real @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_729_sup_OcoboundedI2,axiom,
    ! [C: int,B: int,A: int] :
      ( ( ord_less_eq_int @ C @ B )
     => ( ord_less_eq_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_730_sup_OcoboundedI2,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( ord_less_eq_nat @ C @ B )
     => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_731_sup_OcoboundedI1,axiom,
    ! [C: set_nat,A: set_nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ C @ A )
     => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_732_sup_OcoboundedI1,axiom,
    ! [C: real,A: real,B: real] :
      ( ( ord_less_eq_real @ C @ A )
     => ( ord_less_eq_real @ C @ ( sup_sup_real @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_733_sup_OcoboundedI1,axiom,
    ! [C: int,A: int,B: int] :
      ( ( ord_less_eq_int @ C @ A )
     => ( ord_less_eq_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_734_sup_OcoboundedI1,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_eq_nat @ C @ A )
     => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_735_sup_Oabsorb__iff2,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [A3: set_nat,B3: set_nat] :
          ( ( sup_sup_set_nat @ A3 @ B3 )
          = B3 ) ) ) ).

% sup.absorb_iff2
thf(fact_736_sup_Oabsorb__iff2,axiom,
    ( ord_less_eq_real
    = ( ^ [A3: real,B3: real] :
          ( ( sup_sup_real @ A3 @ B3 )
          = B3 ) ) ) ).

% sup.absorb_iff2
thf(fact_737_sup_Oabsorb__iff2,axiom,
    ( ord_less_eq_int
    = ( ^ [A3: int,B3: int] :
          ( ( sup_sup_int @ A3 @ B3 )
          = B3 ) ) ) ).

% sup.absorb_iff2
thf(fact_738_sup_Oabsorb__iff2,axiom,
    ( ord_less_eq_nat
    = ( ^ [A3: nat,B3: nat] :
          ( ( sup_sup_nat @ A3 @ B3 )
          = B3 ) ) ) ).

% sup.absorb_iff2
thf(fact_739_sup_Oabsorb__iff1,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [B3: set_nat,A3: set_nat] :
          ( ( sup_sup_set_nat @ A3 @ B3 )
          = A3 ) ) ) ).

% sup.absorb_iff1
thf(fact_740_sup_Oabsorb__iff1,axiom,
    ( ord_less_eq_real
    = ( ^ [B3: real,A3: real] :
          ( ( sup_sup_real @ A3 @ B3 )
          = A3 ) ) ) ).

% sup.absorb_iff1
thf(fact_741_sup_Oabsorb__iff1,axiom,
    ( ord_less_eq_int
    = ( ^ [B3: int,A3: int] :
          ( ( sup_sup_int @ A3 @ B3 )
          = A3 ) ) ) ).

% sup.absorb_iff1
thf(fact_742_sup_Oabsorb__iff1,axiom,
    ( ord_less_eq_nat
    = ( ^ [B3: nat,A3: nat] :
          ( ( sup_sup_nat @ A3 @ B3 )
          = A3 ) ) ) ).

% sup.absorb_iff1
thf(fact_743_sup_Ocobounded2,axiom,
    ! [B: set_nat,A: set_nat] : ( ord_less_eq_set_nat @ B @ ( sup_sup_set_nat @ A @ B ) ) ).

% sup.cobounded2
thf(fact_744_sup_Ocobounded2,axiom,
    ! [B: real,A: real] : ( ord_less_eq_real @ B @ ( sup_sup_real @ A @ B ) ) ).

% sup.cobounded2
thf(fact_745_sup_Ocobounded2,axiom,
    ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( sup_sup_int @ A @ B ) ) ).

% sup.cobounded2
thf(fact_746_sup_Ocobounded2,axiom,
    ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( sup_sup_nat @ A @ B ) ) ).

% sup.cobounded2
thf(fact_747_sup_Ocobounded1,axiom,
    ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) ) ).

% sup.cobounded1
thf(fact_748_sup_Ocobounded1,axiom,
    ! [A: real,B: real] : ( ord_less_eq_real @ A @ ( sup_sup_real @ A @ B ) ) ).

% sup.cobounded1
thf(fact_749_sup_Ocobounded1,axiom,
    ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ) ).

% sup.cobounded1
thf(fact_750_sup_Ocobounded1,axiom,
    ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B ) ) ).

% sup.cobounded1
thf(fact_751_sup_Oorder__iff,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [B3: set_nat,A3: set_nat] :
          ( A3
          = ( sup_sup_set_nat @ A3 @ B3 ) ) ) ) ).

% sup.order_iff
thf(fact_752_sup_Oorder__iff,axiom,
    ( ord_less_eq_real
    = ( ^ [B3: real,A3: real] :
          ( A3
          = ( sup_sup_real @ A3 @ B3 ) ) ) ) ).

% sup.order_iff
thf(fact_753_sup_Oorder__iff,axiom,
    ( ord_less_eq_int
    = ( ^ [B3: int,A3: int] :
          ( A3
          = ( sup_sup_int @ A3 @ B3 ) ) ) ) ).

% sup.order_iff
thf(fact_754_sup_Oorder__iff,axiom,
    ( ord_less_eq_nat
    = ( ^ [B3: nat,A3: nat] :
          ( A3
          = ( sup_sup_nat @ A3 @ B3 ) ) ) ) ).

% sup.order_iff
thf(fact_755_sup_OboundedI,axiom,
    ! [B: set_nat,A: set_nat,C: set_nat] :
      ( ( ord_less_eq_set_nat @ B @ A )
     => ( ( ord_less_eq_set_nat @ C @ A )
       => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A ) ) ) ).

% sup.boundedI
thf(fact_756_sup_OboundedI,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ( ord_less_eq_real @ C @ A )
       => ( ord_less_eq_real @ ( sup_sup_real @ B @ C ) @ A ) ) ) ).

% sup.boundedI
thf(fact_757_sup_OboundedI,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ( ord_less_eq_int @ C @ A )
       => ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A ) ) ) ).

% sup.boundedI
thf(fact_758_sup_OboundedI,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( ord_less_eq_nat @ C @ A )
       => ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A ) ) ) ).

% sup.boundedI
thf(fact_759_sup_OboundedE,axiom,
    ! [B: set_nat,C: set_nat,A: set_nat] :
      ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
     => ~ ( ( ord_less_eq_set_nat @ B @ A )
         => ~ ( ord_less_eq_set_nat @ C @ A ) ) ) ).

% sup.boundedE
thf(fact_760_sup_OboundedE,axiom,
    ! [B: real,C: real,A: real] :
      ( ( ord_less_eq_real @ ( sup_sup_real @ B @ C ) @ A )
     => ~ ( ( ord_less_eq_real @ B @ A )
         => ~ ( ord_less_eq_real @ C @ A ) ) ) ).

% sup.boundedE
thf(fact_761_sup_OboundedE,axiom,
    ! [B: int,C: int,A: int] :
      ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A )
     => ~ ( ( ord_less_eq_int @ B @ A )
         => ~ ( ord_less_eq_int @ C @ A ) ) ) ).

% sup.boundedE
thf(fact_762_sup_OboundedE,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
     => ~ ( ( ord_less_eq_nat @ B @ A )
         => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).

% sup.boundedE
thf(fact_763_sup__absorb2,axiom,
    ! [X: set_nat,Y: set_nat] :
      ( ( ord_less_eq_set_nat @ X @ Y )
     => ( ( sup_sup_set_nat @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_764_sup__absorb2,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ X @ Y )
     => ( ( sup_sup_real @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_765_sup__absorb2,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ X @ Y )
     => ( ( sup_sup_int @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_766_sup__absorb2,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( sup_sup_nat @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_767_sup__absorb1,axiom,
    ! [Y: set_nat,X: set_nat] :
      ( ( ord_less_eq_set_nat @ Y @ X )
     => ( ( sup_sup_set_nat @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_768_sup__absorb1,axiom,
    ! [Y: real,X: real] :
      ( ( ord_less_eq_real @ Y @ X )
     => ( ( sup_sup_real @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_769_sup__absorb1,axiom,
    ! [Y: int,X: int] :
      ( ( ord_less_eq_int @ Y @ X )
     => ( ( sup_sup_int @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_770_sup__absorb1,axiom,
    ! [Y: nat,X: nat] :
      ( ( ord_less_eq_nat @ Y @ X )
     => ( ( sup_sup_nat @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_771_sup_Oabsorb2,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ A @ B )
     => ( ( sup_sup_set_nat @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_772_sup_Oabsorb2,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( sup_sup_real @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_773_sup_Oabsorb2,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( sup_sup_int @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_774_sup_Oabsorb2,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( sup_sup_nat @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_775_sup_Oabsorb1,axiom,
    ! [B: set_nat,A: set_nat] :
      ( ( ord_less_eq_set_nat @ B @ A )
     => ( ( sup_sup_set_nat @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_776_sup_Oabsorb1,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ( sup_sup_real @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_777_sup_Oabsorb1,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ( sup_sup_int @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_778_sup_Oabsorb1,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( sup_sup_nat @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_779_sup__unique,axiom,
    ! [F: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
      ( ! [X2: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ X2 @ ( F @ X2 @ Y4 ) )
     => ( ! [X2: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ Y4 @ ( F @ X2 @ Y4 ) )
       => ( ! [X2: set_nat,Y4: set_nat,Z4: set_nat] :
              ( ( ord_less_eq_set_nat @ Y4 @ X2 )
             => ( ( ord_less_eq_set_nat @ Z4 @ X2 )
               => ( ord_less_eq_set_nat @ ( F @ Y4 @ Z4 ) @ X2 ) ) )
         => ( ( sup_sup_set_nat @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_780_sup__unique,axiom,
    ! [F: real > real > real,X: real,Y: real] :
      ( ! [X2: real,Y4: real] : ( ord_less_eq_real @ X2 @ ( F @ X2 @ Y4 ) )
     => ( ! [X2: real,Y4: real] : ( ord_less_eq_real @ Y4 @ ( F @ X2 @ Y4 ) )
       => ( ! [X2: real,Y4: real,Z4: real] :
              ( ( ord_less_eq_real @ Y4 @ X2 )
             => ( ( ord_less_eq_real @ Z4 @ X2 )
               => ( ord_less_eq_real @ ( F @ Y4 @ Z4 ) @ X2 ) ) )
         => ( ( sup_sup_real @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_781_sup__unique,axiom,
    ! [F: int > int > int,X: int,Y: int] :
      ( ! [X2: int,Y4: int] : ( ord_less_eq_int @ X2 @ ( F @ X2 @ Y4 ) )
     => ( ! [X2: int,Y4: int] : ( ord_less_eq_int @ Y4 @ ( F @ X2 @ Y4 ) )
       => ( ! [X2: int,Y4: int,Z4: int] :
              ( ( ord_less_eq_int @ Y4 @ X2 )
             => ( ( ord_less_eq_int @ Z4 @ X2 )
               => ( ord_less_eq_int @ ( F @ Y4 @ Z4 ) @ X2 ) ) )
         => ( ( sup_sup_int @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_782_sup__unique,axiom,
    ! [F: nat > nat > nat,X: nat,Y: nat] :
      ( ! [X2: nat,Y4: nat] : ( ord_less_eq_nat @ X2 @ ( F @ X2 @ Y4 ) )
     => ( ! [X2: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ ( F @ X2 @ Y4 ) )
       => ( ! [X2: nat,Y4: nat,Z4: nat] :
              ( ( ord_less_eq_nat @ Y4 @ X2 )
             => ( ( ord_less_eq_nat @ Z4 @ X2 )
               => ( ord_less_eq_nat @ ( F @ Y4 @ Z4 ) @ X2 ) ) )
         => ( ( sup_sup_nat @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_783_sup_OorderI,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( A
        = ( sup_sup_set_nat @ A @ B ) )
     => ( ord_less_eq_set_nat @ B @ A ) ) ).

% sup.orderI
thf(fact_784_sup_OorderI,axiom,
    ! [A: real,B: real] :
      ( ( A
        = ( sup_sup_real @ A @ B ) )
     => ( ord_less_eq_real @ B @ A ) ) ).

% sup.orderI
thf(fact_785_sup_OorderI,axiom,
    ! [A: int,B: int] :
      ( ( A
        = ( sup_sup_int @ A @ B ) )
     => ( ord_less_eq_int @ B @ A ) ) ).

% sup.orderI
thf(fact_786_sup_OorderI,axiom,
    ! [A: nat,B: nat] :
      ( ( A
        = ( sup_sup_nat @ A @ B ) )
     => ( ord_less_eq_nat @ B @ A ) ) ).

% sup.orderI
thf(fact_787_sup_OorderE,axiom,
    ! [B: set_nat,A: set_nat] :
      ( ( ord_less_eq_set_nat @ B @ A )
     => ( A
        = ( sup_sup_set_nat @ A @ B ) ) ) ).

% sup.orderE
thf(fact_788_sup_OorderE,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( A
        = ( sup_sup_real @ A @ B ) ) ) ).

% sup.orderE
thf(fact_789_sup_OorderE,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( A
        = ( sup_sup_int @ A @ B ) ) ) ).

% sup.orderE
thf(fact_790_sup_OorderE,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( A
        = ( sup_sup_nat @ A @ B ) ) ) ).

% sup.orderE
thf(fact_791_le__iff__sup,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [X3: set_nat,Y3: set_nat] :
          ( ( sup_sup_set_nat @ X3 @ Y3 )
          = Y3 ) ) ) ).

% le_iff_sup
thf(fact_792_le__iff__sup,axiom,
    ( ord_less_eq_real
    = ( ^ [X3: real,Y3: real] :
          ( ( sup_sup_real @ X3 @ Y3 )
          = Y3 ) ) ) ).

% le_iff_sup
thf(fact_793_le__iff__sup,axiom,
    ( ord_less_eq_int
    = ( ^ [X3: int,Y3: int] :
          ( ( sup_sup_int @ X3 @ Y3 )
          = Y3 ) ) ) ).

% le_iff_sup
thf(fact_794_le__iff__sup,axiom,
    ( ord_less_eq_nat
    = ( ^ [X3: nat,Y3: nat] :
          ( ( sup_sup_nat @ X3 @ Y3 )
          = Y3 ) ) ) ).

% le_iff_sup
thf(fact_795_sup__least,axiom,
    ! [Y: set_nat,X: set_nat,Z2: set_nat] :
      ( ( ord_less_eq_set_nat @ Y @ X )
     => ( ( ord_less_eq_set_nat @ Z2 @ X )
       => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ Y @ Z2 ) @ X ) ) ) ).

% sup_least
thf(fact_796_sup__least,axiom,
    ! [Y: real,X: real,Z2: real] :
      ( ( ord_less_eq_real @ Y @ X )
     => ( ( ord_less_eq_real @ Z2 @ X )
       => ( ord_less_eq_real @ ( sup_sup_real @ Y @ Z2 ) @ X ) ) ) ).

% sup_least
thf(fact_797_sup__least,axiom,
    ! [Y: int,X: int,Z2: int] :
      ( ( ord_less_eq_int @ Y @ X )
     => ( ( ord_less_eq_int @ Z2 @ X )
       => ( ord_less_eq_int @ ( sup_sup_int @ Y @ Z2 ) @ X ) ) ) ).

% sup_least
thf(fact_798_sup__least,axiom,
    ! [Y: nat,X: nat,Z2: nat] :
      ( ( ord_less_eq_nat @ Y @ X )
     => ( ( ord_less_eq_nat @ Z2 @ X )
       => ( ord_less_eq_nat @ ( sup_sup_nat @ Y @ Z2 ) @ X ) ) ) ).

% sup_least
thf(fact_799_sup__mono,axiom,
    ! [A: set_nat,C: set_nat,B: set_nat,D: set_nat] :
      ( ( ord_less_eq_set_nat @ A @ C )
     => ( ( ord_less_eq_set_nat @ B @ D )
       => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ C @ D ) ) ) ) ).

% sup_mono
thf(fact_800_sup__mono,axiom,
    ! [A: real,C: real,B: real,D: real] :
      ( ( ord_less_eq_real @ A @ C )
     => ( ( ord_less_eq_real @ B @ D )
       => ( ord_less_eq_real @ ( sup_sup_real @ A @ B ) @ ( sup_sup_real @ C @ D ) ) ) ) ).

% sup_mono
thf(fact_801_sup__mono,axiom,
    ! [A: int,C: int,B: int,D: int] :
      ( ( ord_less_eq_int @ A @ C )
     => ( ( ord_less_eq_int @ B @ D )
       => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ ( sup_sup_int @ C @ D ) ) ) ) ).

% sup_mono
thf(fact_802_sup__mono,axiom,
    ! [A: nat,C: nat,B: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ C )
     => ( ( ord_less_eq_nat @ B @ D )
       => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ ( sup_sup_nat @ C @ D ) ) ) ) ).

% sup_mono
thf(fact_803_sup_Omono,axiom,
    ! [C: set_nat,A: set_nat,D: set_nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ C @ A )
     => ( ( ord_less_eq_set_nat @ D @ B )
       => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ C @ D ) @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_804_sup_Omono,axiom,
    ! [C: real,A: real,D: real,B: real] :
      ( ( ord_less_eq_real @ C @ A )
     => ( ( ord_less_eq_real @ D @ B )
       => ( ord_less_eq_real @ ( sup_sup_real @ C @ D ) @ ( sup_sup_real @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_805_sup_Omono,axiom,
    ! [C: int,A: int,D: int,B: int] :
      ( ( ord_less_eq_int @ C @ A )
     => ( ( ord_less_eq_int @ D @ B )
       => ( ord_less_eq_int @ ( sup_sup_int @ C @ D ) @ ( sup_sup_int @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_806_sup_Omono,axiom,
    ! [C: nat,A: nat,D: nat,B: nat] :
      ( ( ord_less_eq_nat @ C @ A )
     => ( ( ord_less_eq_nat @ D @ B )
       => ( ord_less_eq_nat @ ( sup_sup_nat @ C @ D ) @ ( sup_sup_nat @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_807_le__supI2,axiom,
    ! [X: set_nat,B: set_nat,A: set_nat] :
      ( ( ord_less_eq_set_nat @ X @ B )
     => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).

% le_supI2
thf(fact_808_le__supI2,axiom,
    ! [X: real,B: real,A: real] :
      ( ( ord_less_eq_real @ X @ B )
     => ( ord_less_eq_real @ X @ ( sup_sup_real @ A @ B ) ) ) ).

% le_supI2
thf(fact_809_le__supI2,axiom,
    ! [X: int,B: int,A: int] :
      ( ( ord_less_eq_int @ X @ B )
     => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).

% le_supI2
thf(fact_810_le__supI2,axiom,
    ! [X: nat,B: nat,A: nat] :
      ( ( ord_less_eq_nat @ X @ B )
     => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).

% le_supI2
thf(fact_811_le__supI1,axiom,
    ! [X: set_nat,A: set_nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ X @ A )
     => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).

% le_supI1
thf(fact_812_le__supI1,axiom,
    ! [X: real,A: real,B: real] :
      ( ( ord_less_eq_real @ X @ A )
     => ( ord_less_eq_real @ X @ ( sup_sup_real @ A @ B ) ) ) ).

% le_supI1
thf(fact_813_le__supI1,axiom,
    ! [X: int,A: int,B: int] :
      ( ( ord_less_eq_int @ X @ A )
     => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).

% le_supI1
thf(fact_814_le__supI1,axiom,
    ! [X: nat,A: nat,B: nat] :
      ( ( ord_less_eq_nat @ X @ A )
     => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).

% le_supI1
thf(fact_815_sup__ge2,axiom,
    ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).

% sup_ge2
thf(fact_816_sup__ge2,axiom,
    ! [Y: real,X: real] : ( ord_less_eq_real @ Y @ ( sup_sup_real @ X @ Y ) ) ).

% sup_ge2
thf(fact_817_sup__ge2,axiom,
    ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).

% sup_ge2
thf(fact_818_sup__ge2,axiom,
    ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).

% sup_ge2
thf(fact_819_sup__ge1,axiom,
    ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).

% sup_ge1
thf(fact_820_sup__ge1,axiom,
    ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sup_sup_real @ X @ Y ) ) ).

% sup_ge1
thf(fact_821_sup__ge1,axiom,
    ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).

% sup_ge1
thf(fact_822_sup__ge1,axiom,
    ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).

% sup_ge1
thf(fact_823_le__supI,axiom,
    ! [A: set_nat,X: set_nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ A @ X )
     => ( ( ord_less_eq_set_nat @ B @ X )
       => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X ) ) ) ).

% le_supI
thf(fact_824_le__supI,axiom,
    ! [A: real,X: real,B: real] :
      ( ( ord_less_eq_real @ A @ X )
     => ( ( ord_less_eq_real @ B @ X )
       => ( ord_less_eq_real @ ( sup_sup_real @ A @ B ) @ X ) ) ) ).

% le_supI
thf(fact_825_le__supI,axiom,
    ! [A: int,X: int,B: int] :
      ( ( ord_less_eq_int @ A @ X )
     => ( ( ord_less_eq_int @ B @ X )
       => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X ) ) ) ).

% le_supI
thf(fact_826_le__supI,axiom,
    ! [A: nat,X: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ X )
     => ( ( ord_less_eq_nat @ B @ X )
       => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X ) ) ) ).

% le_supI
thf(fact_827_le__supE,axiom,
    ! [A: set_nat,B: set_nat,X: set_nat] :
      ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X )
     => ~ ( ( ord_less_eq_set_nat @ A @ X )
         => ~ ( ord_less_eq_set_nat @ B @ X ) ) ) ).

% le_supE
thf(fact_828_le__supE,axiom,
    ! [A: real,B: real,X: real] :
      ( ( ord_less_eq_real @ ( sup_sup_real @ A @ B ) @ X )
     => ~ ( ( ord_less_eq_real @ A @ X )
         => ~ ( ord_less_eq_real @ B @ X ) ) ) ).

% le_supE
thf(fact_829_le__supE,axiom,
    ! [A: int,B: int,X: int] :
      ( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X )
     => ~ ( ( ord_less_eq_int @ A @ X )
         => ~ ( ord_less_eq_int @ B @ X ) ) ) ).

% le_supE
thf(fact_830_le__supE,axiom,
    ! [A: nat,B: nat,X: nat] :
      ( ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X )
     => ~ ( ( ord_less_eq_nat @ A @ X )
         => ~ ( ord_less_eq_nat @ B @ X ) ) ) ).

% le_supE
thf(fact_831_inf__sup__ord_I3_J,axiom,
    ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_832_inf__sup__ord_I3_J,axiom,
    ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sup_sup_real @ X @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_833_inf__sup__ord_I3_J,axiom,
    ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_834_inf__sup__ord_I3_J,axiom,
    ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_835_inf__sup__ord_I4_J,axiom,
    ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_836_inf__sup__ord_I4_J,axiom,
    ! [Y: real,X: real] : ( ord_less_eq_real @ Y @ ( sup_sup_real @ X @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_837_inf__sup__ord_I4_J,axiom,
    ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_838_inf__sup__ord_I4_J,axiom,
    ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_839_subset__UNIV,axiom,
    ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ top_top_set_int ) ).

% subset_UNIV
thf(fact_840_subset__UNIV,axiom,
    ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ top_top_set_nat ) ).

% subset_UNIV
thf(fact_841_Un__UNIV__left,axiom,
    ! [B2: set_nat] :
      ( ( sup_sup_set_nat @ top_top_set_nat @ B2 )
      = top_top_set_nat ) ).

% Un_UNIV_left
thf(fact_842_Un__UNIV__left,axiom,
    ! [B2: set_int] :
      ( ( sup_sup_set_int @ top_top_set_int @ B2 )
      = top_top_set_int ) ).

% Un_UNIV_left
thf(fact_843_Un__UNIV__right,axiom,
    ! [A2: set_nat] :
      ( ( sup_sup_set_nat @ A2 @ top_top_set_nat )
      = top_top_set_nat ) ).

% Un_UNIV_right
thf(fact_844_Un__UNIV__right,axiom,
    ! [A2: set_int] :
      ( ( sup_sup_set_int @ A2 @ top_top_set_int )
      = top_top_set_int ) ).

% Un_UNIV_right
thf(fact_845_Diff__subset__conv,axiom,
    ! [A2: set_nat,B2: set_nat,C4: set_nat] :
      ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ C4 )
      = ( ord_less_eq_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C4 ) ) ) ).

% Diff_subset_conv
thf(fact_846_Diff__partition,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ B2 )
     => ( ( sup_sup_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ A2 ) )
        = B2 ) ) ).

% Diff_partition
thf(fact_847_subset__Un__eq,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [A4: set_nat,B4: set_nat] :
          ( ( sup_sup_set_nat @ A4 @ B4 )
          = B4 ) ) ) ).

% subset_Un_eq
thf(fact_848_subset__UnE,axiom,
    ! [C4: set_nat,A2: set_nat,B2: set_nat] :
      ( ( ord_less_eq_set_nat @ C4 @ ( sup_sup_set_nat @ A2 @ B2 ) )
     => ~ ! [A5: set_nat] :
            ( ( ord_less_eq_set_nat @ A5 @ A2 )
           => ! [B5: set_nat] :
                ( ( ord_less_eq_set_nat @ B5 @ B2 )
               => ( C4
                 != ( sup_sup_set_nat @ A5 @ B5 ) ) ) ) ) ).

% subset_UnE
thf(fact_849_Un__absorb2,axiom,
    ! [B2: set_nat,A2: set_nat] :
      ( ( ord_less_eq_set_nat @ B2 @ A2 )
     => ( ( sup_sup_set_nat @ A2 @ B2 )
        = A2 ) ) ).

% Un_absorb2
thf(fact_850_Un__absorb1,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ B2 )
     => ( ( sup_sup_set_nat @ A2 @ B2 )
        = B2 ) ) ).

% Un_absorb1
thf(fact_851_Un__upper2,axiom,
    ! [B2: set_nat,A2: set_nat] : ( ord_less_eq_set_nat @ B2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) ).

% Un_upper2
thf(fact_852_Un__upper1,axiom,
    ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) ).

% Un_upper1
thf(fact_853_Un__least,axiom,
    ! [A2: set_nat,C4: set_nat,B2: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ C4 )
     => ( ( ord_less_eq_set_nat @ B2 @ C4 )
       => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C4 ) ) ) ).

% Un_least
thf(fact_854_Un__mono,axiom,
    ! [A2: set_nat,C4: set_nat,B2: set_nat,D2: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ C4 )
     => ( ( ord_less_eq_set_nat @ B2 @ D2 )
       => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ ( sup_sup_set_nat @ C4 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_855_return__loans__def,axiom,
    ( risk_F2121631595377017831_loans
    = ( ^ [Rho2: nat > real,Alpha2: risk_Free_account] :
          ( risk_F5458100604530014700ccount
          @ ^ [N: nat] : ( times_times_real @ ( minus_minus_real @ one_one_real @ ( Rho2 @ N ) ) @ ( risk_F170160801229183585ccount @ Alpha2 @ N ) ) ) ) ) ).

% return_loans_def
thf(fact_856_mult__diff__mult,axiom,
    ! [X: complex,Y: complex,A: complex,B: complex] :
      ( ( minus_minus_complex @ ( times_times_complex @ X @ Y ) @ ( times_times_complex @ A @ B ) )
      = ( plus_plus_complex @ ( times_times_complex @ X @ ( minus_minus_complex @ Y @ B ) ) @ ( times_times_complex @ ( minus_minus_complex @ X @ A ) @ B ) ) ) ).

% mult_diff_mult
thf(fact_857_mult__diff__mult,axiom,
    ! [X: real,Y: real,A: real,B: real] :
      ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
      = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).

% mult_diff_mult
thf(fact_858_mult__diff__mult,axiom,
    ! [X: int,Y: int,A: int,B: int] :
      ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
      = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).

% mult_diff_mult
thf(fact_859_add__scale__eq__noteq,axiom,
    ! [R: complex,A: complex,B: complex,C: complex,D: complex] :
      ( ( R != zero_zero_complex )
     => ( ( ( A = B )
          & ( C != D ) )
       => ( ( plus_plus_complex @ A @ ( times_times_complex @ R @ C ) )
         != ( plus_plus_complex @ B @ ( times_times_complex @ R @ D ) ) ) ) ) ).

% add_scale_eq_noteq
thf(fact_860_add__scale__eq__noteq,axiom,
    ! [R: real,A: real,B: real,C: real,D: real] :
      ( ( R != zero_zero_real )
     => ( ( ( A = B )
          & ( C != D ) )
       => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C ) )
         != ( plus_plus_real @ B @ ( times_times_real @ R @ D ) ) ) ) ) ).

% add_scale_eq_noteq
thf(fact_861_add__scale__eq__noteq,axiom,
    ! [R: int,A: int,B: int,C: int,D: int] :
      ( ( R != zero_zero_int )
     => ( ( ( A = B )
          & ( C != D ) )
       => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
         != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).

% add_scale_eq_noteq
thf(fact_862_add__scale__eq__noteq,axiom,
    ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
      ( ( R != zero_zero_nat )
     => ( ( ( A = B )
          & ( C != D ) )
       => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
         != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).

% add_scale_eq_noteq
thf(fact_863_iso__tuple__UNIV__I,axiom,
    ! [X: nat > real] : ( member_nat_real @ X @ top_top_set_nat_real ) ).

% iso_tuple_UNIV_I
thf(fact_864_iso__tuple__UNIV__I,axiom,
    ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).

% iso_tuple_UNIV_I
thf(fact_865_iso__tuple__UNIV__I,axiom,
    ! [X: int] : ( member_int @ X @ top_top_set_int ) ).

% iso_tuple_UNIV_I
thf(fact_866_dual__order_Orefl,axiom,
    ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).

% dual_order.refl
thf(fact_867_dual__order_Orefl,axiom,
    ! [A: risk_Free_account] : ( ord_le4245800335709223507ccount @ A @ A ) ).

% dual_order.refl
thf(fact_868_dual__order_Orefl,axiom,
    ! [A: real] : ( ord_less_eq_real @ A @ A ) ).

% dual_order.refl
thf(fact_869_dual__order_Orefl,axiom,
    ! [A: int] : ( ord_less_eq_int @ A @ A ) ).

% dual_order.refl
thf(fact_870_dual__order_Orefl,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).

% dual_order.refl
thf(fact_871_order__refl,axiom,
    ! [X: set_nat] : ( ord_less_eq_set_nat @ X @ X ) ).

% order_refl
thf(fact_872_order__refl,axiom,
    ! [X: risk_Free_account] : ( ord_le4245800335709223507ccount @ X @ X ) ).

% order_refl
thf(fact_873_order__refl,axiom,
    ! [X: real] : ( ord_less_eq_real @ X @ X ) ).

% order_refl
thf(fact_874_order__refl,axiom,
    ! [X: int] : ( ord_less_eq_int @ X @ X ) ).

% order_refl
thf(fact_875_order__refl,axiom,
    ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).

% order_refl
thf(fact_876_Abs__account__inverse,axiom,
    ! [Y: nat > real] :
      ( ( member_nat_real @ Y @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) )
     => ( ( risk_F170160801229183585ccount @ ( risk_F5458100604530014700ccount @ Y ) )
        = Y ) ) ).

% Abs_account_inverse
thf(fact_877_DiffI,axiom,
    ! [C: nat > real,A2: set_nat_real,B2: set_nat_real] :
      ( ( member_nat_real @ C @ A2 )
     => ( ~ ( member_nat_real @ C @ B2 )
       => ( member_nat_real @ C @ ( minus_3492551254948764970t_real @ A2 @ B2 ) ) ) ) ).

% DiffI
thf(fact_878_Diff__iff,axiom,
    ! [C: nat > real,A2: set_nat_real,B2: set_nat_real] :
      ( ( member_nat_real @ C @ ( minus_3492551254948764970t_real @ A2 @ B2 ) )
      = ( ( member_nat_real @ C @ A2 )
        & ~ ( member_nat_real @ C @ B2 ) ) ) ).

% Diff_iff
thf(fact_879_DiffE,axiom,
    ! [C: nat > real,A2: set_nat_real,B2: set_nat_real] :
      ( ( member_nat_real @ C @ ( minus_3492551254948764970t_real @ A2 @ B2 ) )
     => ~ ( ( member_nat_real @ C @ A2 )
         => ( member_nat_real @ C @ B2 ) ) ) ).

% DiffE
thf(fact_880_DiffD1,axiom,
    ! [C: nat > real,A2: set_nat_real,B2: set_nat_real] :
      ( ( member_nat_real @ C @ ( minus_3492551254948764970t_real @ A2 @ B2 ) )
     => ( member_nat_real @ C @ A2 ) ) ).

% DiffD1
thf(fact_881_DiffD2,axiom,
    ! [C: nat > real,A2: set_nat_real,B2: set_nat_real] :
      ( ( member_nat_real @ C @ ( minus_3492551254948764970t_real @ A2 @ B2 ) )
     => ~ ( member_nat_real @ C @ B2 ) ) ).

% DiffD2
thf(fact_882_set__diff__eq,axiom,
    ( minus_3492551254948764970t_real
    = ( ^ [A4: set_nat_real,B4: set_nat_real] :
          ( collect_nat_real
          @ ^ [X3: nat > real] :
              ( ( member_nat_real @ X3 @ A4 )
              & ~ ( member_nat_real @ X3 @ B4 ) ) ) ) ) ).

% set_diff_eq
thf(fact_883_set__diff__eq,axiom,
    ( minus_minus_set_nat
    = ( ^ [A4: set_nat,B4: set_nat] :
          ( collect_nat
          @ ^ [X3: nat] :
              ( ( member_nat @ X3 @ A4 )
              & ~ ( member_nat @ X3 @ B4 ) ) ) ) ) ).

% set_diff_eq
thf(fact_884_set__diff__eq,axiom,
    ( minus_minus_set_int
    = ( ^ [A4: set_int,B4: set_int] :
          ( collect_int
          @ ^ [X3: int] :
              ( ( member_int @ X3 @ A4 )
              & ~ ( member_int @ X3 @ B4 ) ) ) ) ) ).

% set_diff_eq
thf(fact_885_set__diff__eq,axiom,
    ( minus_811609699411566653omplex
    = ( ^ [A4: set_complex,B4: set_complex] :
          ( collect_complex
          @ ^ [X3: complex] :
              ( ( member_complex @ X3 @ A4 )
              & ~ ( member_complex @ X3 @ B4 ) ) ) ) ) ).

% set_diff_eq
thf(fact_886_minus__set__def,axiom,
    ( minus_3492551254948764970t_real
    = ( ^ [A4: set_nat_real,B4: set_nat_real] :
          ( collect_nat_real
          @ ( minus_930488207635846619real_o
            @ ^ [X3: nat > real] : ( member_nat_real @ X3 @ A4 )
            @ ^ [X3: nat > real] : ( member_nat_real @ X3 @ B4 ) ) ) ) ) ).

% minus_set_def
thf(fact_887_minus__set__def,axiom,
    ( minus_minus_set_nat
    = ( ^ [A4: set_nat,B4: set_nat] :
          ( collect_nat
          @ ( minus_minus_nat_o
            @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
            @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ) ).

% minus_set_def
thf(fact_888_minus__set__def,axiom,
    ( minus_minus_set_int
    = ( ^ [A4: set_int,B4: set_int] :
          ( collect_int
          @ ( minus_minus_int_o
            @ ^ [X3: int] : ( member_int @ X3 @ A4 )
            @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ) ).

% minus_set_def
thf(fact_889_minus__set__def,axiom,
    ( minus_811609699411566653omplex
    = ( ^ [A4: set_complex,B4: set_complex] :
          ( collect_complex
          @ ( minus_8727706125548526216plex_o
            @ ^ [X3: complex] : ( member_complex @ X3 @ A4 )
            @ ^ [X3: complex] : ( member_complex @ X3 @ B4 ) ) ) ) ) ).

% minus_set_def
thf(fact_890_Rep__account__inverse,axiom,
    ! [X: risk_Free_account] :
      ( ( risk_F5458100604530014700ccount @ ( risk_F170160801229183585ccount @ X ) )
      = X ) ).

% Rep_account_inverse
thf(fact_891_nle__le,axiom,
    ! [A: real,B: real] :
      ( ( ~ ( ord_less_eq_real @ A @ B ) )
      = ( ( ord_less_eq_real @ B @ A )
        & ( B != A ) ) ) ).

% nle_le
thf(fact_892_nle__le,axiom,
    ! [A: int,B: int] :
      ( ( ~ ( ord_less_eq_int @ A @ B ) )
      = ( ( ord_less_eq_int @ B @ A )
        & ( B != A ) ) ) ).

% nle_le
thf(fact_893_nle__le,axiom,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_eq_nat @ A @ B ) )
      = ( ( ord_less_eq_nat @ B @ A )
        & ( B != A ) ) ) ).

% nle_le
thf(fact_894_le__cases3,axiom,
    ! [X: real,Y: real,Z2: real] :
      ( ( ( ord_less_eq_real @ X @ Y )
       => ~ ( ord_less_eq_real @ Y @ Z2 ) )
     => ( ( ( ord_less_eq_real @ Y @ X )
         => ~ ( ord_less_eq_real @ X @ Z2 ) )
       => ( ( ( ord_less_eq_real @ X @ Z2 )
           => ~ ( ord_less_eq_real @ Z2 @ Y ) )
         => ( ( ( ord_less_eq_real @ Z2 @ Y )
             => ~ ( ord_less_eq_real @ Y @ X ) )
           => ( ( ( ord_less_eq_real @ Y @ Z2 )
               => ~ ( ord_less_eq_real @ Z2 @ X ) )
             => ~ ( ( ord_less_eq_real @ Z2 @ X )
                 => ~ ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ) ).

% le_cases3
thf(fact_895_le__cases3,axiom,
    ! [X: int,Y: int,Z2: int] :
      ( ( ( ord_less_eq_int @ X @ Y )
       => ~ ( ord_less_eq_int @ Y @ Z2 ) )
     => ( ( ( ord_less_eq_int @ Y @ X )
         => ~ ( ord_less_eq_int @ X @ Z2 ) )
       => ( ( ( ord_less_eq_int @ X @ Z2 )
           => ~ ( ord_less_eq_int @ Z2 @ Y ) )
         => ( ( ( ord_less_eq_int @ Z2 @ Y )
             => ~ ( ord_less_eq_int @ Y @ X ) )
           => ( ( ( ord_less_eq_int @ Y @ Z2 )
               => ~ ( ord_less_eq_int @ Z2 @ X ) )
             => ~ ( ( ord_less_eq_int @ Z2 @ X )
                 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).

% le_cases3
thf(fact_896_le__cases3,axiom,
    ! [X: nat,Y: nat,Z2: nat] :
      ( ( ( ord_less_eq_nat @ X @ Y )
       => ~ ( ord_less_eq_nat @ Y @ Z2 ) )
     => ( ( ( ord_less_eq_nat @ Y @ X )
         => ~ ( ord_less_eq_nat @ X @ Z2 ) )
       => ( ( ( ord_less_eq_nat @ X @ Z2 )
           => ~ ( ord_less_eq_nat @ Z2 @ Y ) )
         => ( ( ( ord_less_eq_nat @ Z2 @ Y )
             => ~ ( ord_less_eq_nat @ Y @ X ) )
           => ( ( ( ord_less_eq_nat @ Y @ Z2 )
               => ~ ( ord_less_eq_nat @ Z2 @ X ) )
             => ~ ( ( ord_less_eq_nat @ Z2 @ X )
                 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).

% le_cases3
thf(fact_897_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: set_nat,Z: set_nat] : ( Y2 = Z ) )
    = ( ^ [X3: set_nat,Y3: set_nat] :
          ( ( ord_less_eq_set_nat @ X3 @ Y3 )
          & ( ord_less_eq_set_nat @ Y3 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_898_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: risk_Free_account,Z: risk_Free_account] : ( Y2 = Z ) )
    = ( ^ [X3: risk_Free_account,Y3: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ X3 @ Y3 )
          & ( ord_le4245800335709223507ccount @ Y3 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_899_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: real,Z: real] : ( Y2 = Z ) )
    = ( ^ [X3: real,Y3: real] :
          ( ( ord_less_eq_real @ X3 @ Y3 )
          & ( ord_less_eq_real @ Y3 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_900_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: int,Z: int] : ( Y2 = Z ) )
    = ( ^ [X3: int,Y3: int] :
          ( ( ord_less_eq_int @ X3 @ Y3 )
          & ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_901_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
    = ( ^ [X3: nat,Y3: nat] :
          ( ( ord_less_eq_nat @ X3 @ Y3 )
          & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_902_ord__eq__le__trans,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( A = B )
     => ( ( ord_less_eq_set_nat @ B @ C )
       => ( ord_less_eq_set_nat @ A @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_903_ord__eq__le__trans,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( A = B )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ord_le4245800335709223507ccount @ A @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_904_ord__eq__le__trans,axiom,
    ! [A: real,B: real,C: real] :
      ( ( A = B )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ord_less_eq_real @ A @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_905_ord__eq__le__trans,axiom,
    ! [A: int,B: int,C: int] :
      ( ( A = B )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ord_less_eq_int @ A @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_906_ord__eq__le__trans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( A = B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_907_ord__le__eq__trans,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ord_less_eq_set_nat @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_set_nat @ A @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_908_ord__le__eq__trans,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( B = C )
       => ( ord_le4245800335709223507ccount @ A @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_909_ord__le__eq__trans,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_real @ A @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_910_ord__le__eq__trans,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_int @ A @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_911_ord__le__eq__trans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_nat @ A @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_912_order__antisym,axiom,
    ! [X: set_nat,Y: set_nat] :
      ( ( ord_less_eq_set_nat @ X @ Y )
     => ( ( ord_less_eq_set_nat @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_913_order__antisym,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ X @ Y )
     => ( ( ord_le4245800335709223507ccount @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_914_order__antisym,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ X @ Y )
     => ( ( ord_less_eq_real @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_915_order__antisym,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ X @ Y )
     => ( ( ord_less_eq_int @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_916_order__antisym,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( ord_less_eq_nat @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_917_order_Otrans,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ord_less_eq_set_nat @ A @ B )
     => ( ( ord_less_eq_set_nat @ B @ C )
       => ( ord_less_eq_set_nat @ A @ C ) ) ) ).

% order.trans
thf(fact_918_order_Otrans,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ord_le4245800335709223507ccount @ A @ C ) ) ) ).

% order.trans
thf(fact_919_order_Otrans,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ord_less_eq_real @ A @ C ) ) ) ).

% order.trans
thf(fact_920_order_Otrans,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ord_less_eq_int @ A @ C ) ) ) ).

% order.trans
thf(fact_921_order_Otrans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ) ).

% order.trans
thf(fact_922_order__trans,axiom,
    ! [X: set_nat,Y: set_nat,Z2: set_nat] :
      ( ( ord_less_eq_set_nat @ X @ Y )
     => ( ( ord_less_eq_set_nat @ Y @ Z2 )
       => ( ord_less_eq_set_nat @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_923_order__trans,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account,Z2: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ X @ Y )
     => ( ( ord_le4245800335709223507ccount @ Y @ Z2 )
       => ( ord_le4245800335709223507ccount @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_924_order__trans,axiom,
    ! [X: real,Y: real,Z2: real] :
      ( ( ord_less_eq_real @ X @ Y )
     => ( ( ord_less_eq_real @ Y @ Z2 )
       => ( ord_less_eq_real @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_925_order__trans,axiom,
    ! [X: int,Y: int,Z2: int] :
      ( ( ord_less_eq_int @ X @ Y )
     => ( ( ord_less_eq_int @ Y @ Z2 )
       => ( ord_less_eq_int @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_926_order__trans,axiom,
    ! [X: nat,Y: nat,Z2: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( ord_less_eq_nat @ Y @ Z2 )
       => ( ord_less_eq_nat @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_927_linorder__wlog,axiom,
    ! [P: real > real > $o,A: real,B: real] :
      ( ! [A6: real,B6: real] :
          ( ( ord_less_eq_real @ A6 @ B6 )
         => ( P @ A6 @ B6 ) )
     => ( ! [A6: real,B6: real] :
            ( ( P @ B6 @ A6 )
           => ( P @ A6 @ B6 ) )
       => ( P @ A @ B ) ) ) ).

% linorder_wlog
thf(fact_928_linorder__wlog,axiom,
    ! [P: int > int > $o,A: int,B: int] :
      ( ! [A6: int,B6: int] :
          ( ( ord_less_eq_int @ A6 @ B6 )
         => ( P @ A6 @ B6 ) )
     => ( ! [A6: int,B6: int] :
            ( ( P @ B6 @ A6 )
           => ( P @ A6 @ B6 ) )
       => ( P @ A @ B ) ) ) ).

% linorder_wlog
thf(fact_929_linorder__wlog,axiom,
    ! [P: nat > nat > $o,A: nat,B: nat] :
      ( ! [A6: nat,B6: nat] :
          ( ( ord_less_eq_nat @ A6 @ B6 )
         => ( P @ A6 @ B6 ) )
     => ( ! [A6: nat,B6: nat] :
            ( ( P @ B6 @ A6 )
           => ( P @ A6 @ B6 ) )
       => ( P @ A @ B ) ) ) ).

% linorder_wlog
thf(fact_930_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y2: set_nat,Z: set_nat] : ( Y2 = Z ) )
    = ( ^ [A3: set_nat,B3: set_nat] :
          ( ( ord_less_eq_set_nat @ B3 @ A3 )
          & ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_931_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y2: risk_Free_account,Z: risk_Free_account] : ( Y2 = Z ) )
    = ( ^ [A3: risk_Free_account,B3: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ B3 @ A3 )
          & ( ord_le4245800335709223507ccount @ A3 @ B3 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_932_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y2: real,Z: real] : ( Y2 = Z ) )
    = ( ^ [A3: real,B3: real] :
          ( ( ord_less_eq_real @ B3 @ A3 )
          & ( ord_less_eq_real @ A3 @ B3 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_933_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y2: int,Z: int] : ( Y2 = Z ) )
    = ( ^ [A3: int,B3: int] :
          ( ( ord_less_eq_int @ B3 @ A3 )
          & ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_934_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
    = ( ^ [A3: nat,B3: nat] :
          ( ( ord_less_eq_nat @ B3 @ A3 )
          & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_935_dual__order_Oantisym,axiom,
    ! [B: set_nat,A: set_nat] :
      ( ( ord_less_eq_set_nat @ B @ A )
     => ( ( ord_less_eq_set_nat @ A @ B )
       => ( A = B ) ) ) ).

% dual_order.antisym
thf(fact_936_dual__order_Oantisym,axiom,
    ! [B: risk_Free_account,A: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ B @ A )
     => ( ( ord_le4245800335709223507ccount @ A @ B )
       => ( A = B ) ) ) ).

% dual_order.antisym
thf(fact_937_dual__order_Oantisym,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ( ord_less_eq_real @ A @ B )
       => ( A = B ) ) ) ).

% dual_order.antisym
thf(fact_938_dual__order_Oantisym,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ( ord_less_eq_int @ A @ B )
       => ( A = B ) ) ) ).

% dual_order.antisym
thf(fact_939_dual__order_Oantisym,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( ord_less_eq_nat @ A @ B )
       => ( A = B ) ) ) ).

% dual_order.antisym
thf(fact_940_dual__order_Otrans,axiom,
    ! [B: set_nat,A: set_nat,C: set_nat] :
      ( ( ord_less_eq_set_nat @ B @ A )
     => ( ( ord_less_eq_set_nat @ C @ B )
       => ( ord_less_eq_set_nat @ C @ A ) ) ) ).

% dual_order.trans
thf(fact_941_dual__order_Otrans,axiom,
    ! [B: risk_Free_account,A: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ B @ A )
     => ( ( ord_le4245800335709223507ccount @ C @ B )
       => ( ord_le4245800335709223507ccount @ C @ A ) ) ) ).

% dual_order.trans
thf(fact_942_dual__order_Otrans,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ( ord_less_eq_real @ C @ B )
       => ( ord_less_eq_real @ C @ A ) ) ) ).

% dual_order.trans
thf(fact_943_dual__order_Otrans,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ( ord_less_eq_int @ C @ B )
       => ( ord_less_eq_int @ C @ A ) ) ) ).

% dual_order.trans
thf(fact_944_dual__order_Otrans,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( ord_less_eq_nat @ C @ B )
       => ( ord_less_eq_nat @ C @ A ) ) ) ).

% dual_order.trans
thf(fact_945_antisym,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ A @ B )
     => ( ( ord_less_eq_set_nat @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_946_antisym,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ord_le4245800335709223507ccount @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_947_antisym,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_948_antisym,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_949_antisym,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_950_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: set_nat,Z: set_nat] : ( Y2 = Z ) )
    = ( ^ [A3: set_nat,B3: set_nat] :
          ( ( ord_less_eq_set_nat @ A3 @ B3 )
          & ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_951_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: risk_Free_account,Z: risk_Free_account] : ( Y2 = Z ) )
    = ( ^ [A3: risk_Free_account,B3: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ A3 @ B3 )
          & ( ord_le4245800335709223507ccount @ B3 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_952_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: real,Z: real] : ( Y2 = Z ) )
    = ( ^ [A3: real,B3: real] :
          ( ( ord_less_eq_real @ A3 @ B3 )
          & ( ord_less_eq_real @ B3 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_953_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: int,Z: int] : ( Y2 = Z ) )
    = ( ^ [A3: int,B3: int] :
          ( ( ord_less_eq_int @ A3 @ B3 )
          & ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_954_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
    = ( ^ [A3: nat,B3: nat] :
          ( ( ord_less_eq_nat @ A3 @ B3 )
          & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_955_order__subst1,axiom,
    ! [A: risk_Free_account,F: risk_Free_account > risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ ( F @ B ) )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_956_order__subst1,axiom,
    ! [A: risk_Free_account,F: real > risk_Free_account,B: real,C: real] :
      ( ( ord_le4245800335709223507ccount @ A @ ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_957_order__subst1,axiom,
    ! [A: risk_Free_account,F: int > risk_Free_account,B: int,C: int] :
      ( ( ord_le4245800335709223507ccount @ A @ ( F @ B ) )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ! [X2: int,Y4: int] :
              ( ( ord_less_eq_int @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_958_order__subst1,axiom,
    ! [A: risk_Free_account,F: nat > risk_Free_account,B: nat,C: nat] :
      ( ( ord_le4245800335709223507ccount @ A @ ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X2: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_959_order__subst1,axiom,
    ! [A: real,F: risk_Free_account > real,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_real @ A @ ( F @ B ) )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_960_order__subst1,axiom,
    ! [A: real,F: real > real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_961_order__subst1,axiom,
    ! [A: real,F: int > real,B: int,C: int] :
      ( ( ord_less_eq_real @ A @ ( F @ B ) )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ! [X2: int,Y4: int] :
              ( ( ord_less_eq_int @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_962_order__subst1,axiom,
    ! [A: real,F: nat > real,B: nat,C: nat] :
      ( ( ord_less_eq_real @ A @ ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X2: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_963_order__subst1,axiom,
    ! [A: int,F: risk_Free_account > int,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_int @ A @ ( F @ B ) )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_less_eq_int @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_964_order__subst1,axiom,
    ! [A: int,F: real > int,B: real,C: real] :
      ( ( ord_less_eq_int @ A @ ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_less_eq_int @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_965_order__subst2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ord_le4245800335709223507ccount @ ( F @ B ) @ C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_966_order__subst2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > real,C: real] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ord_less_eq_real @ ( F @ B ) @ C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_967_order__subst2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > int,C: int] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ord_less_eq_int @ ( F @ B ) @ C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_less_eq_int @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_968_order__subst2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > nat,C: nat] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_969_order__subst2,axiom,
    ! [A: real,B: real,F: real > risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_le4245800335709223507ccount @ ( F @ B ) @ C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_970_order__subst2,axiom,
    ! [A: real,B: real,F: real > real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ ( F @ B ) @ C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_971_order__subst2,axiom,
    ! [A: real,B: real,F: real > int,C: int] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_int @ ( F @ B ) @ C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_less_eq_int @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_972_order__subst2,axiom,
    ! [A: real,B: real,F: real > nat,C: nat] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_973_order__subst2,axiom,
    ! [A: int,B: int,F: int > risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_le4245800335709223507ccount @ ( F @ B ) @ C )
       => ( ! [X2: int,Y4: int] :
              ( ( ord_less_eq_int @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_974_order__subst2,axiom,
    ! [A: int,B: int,F: int > real,C: real] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_real @ ( F @ B ) @ C )
       => ( ! [X2: int,Y4: int] :
              ( ( ord_less_eq_int @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_975_order__eq__refl,axiom,
    ! [X: set_nat,Y: set_nat] :
      ( ( X = Y )
     => ( ord_less_eq_set_nat @ X @ Y ) ) ).

% order_eq_refl
thf(fact_976_order__eq__refl,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( X = Y )
     => ( ord_le4245800335709223507ccount @ X @ Y ) ) ).

% order_eq_refl
thf(fact_977_order__eq__refl,axiom,
    ! [X: real,Y: real] :
      ( ( X = Y )
     => ( ord_less_eq_real @ X @ Y ) ) ).

% order_eq_refl
thf(fact_978_order__eq__refl,axiom,
    ! [X: int,Y: int] :
      ( ( X = Y )
     => ( ord_less_eq_int @ X @ Y ) ) ).

% order_eq_refl
thf(fact_979_order__eq__refl,axiom,
    ! [X: nat,Y: nat] :
      ( ( X = Y )
     => ( ord_less_eq_nat @ X @ Y ) ) ).

% order_eq_refl
thf(fact_980_linorder__linear,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ X @ Y )
      | ( ord_less_eq_real @ Y @ X ) ) ).

% linorder_linear
thf(fact_981_linorder__linear,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ X @ Y )
      | ( ord_less_eq_int @ Y @ X ) ) ).

% linorder_linear
thf(fact_982_linorder__linear,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
      | ( ord_less_eq_nat @ Y @ X ) ) ).

% linorder_linear
thf(fact_983_ord__eq__le__subst,axiom,
    ! [A: risk_Free_account,F: risk_Free_account > risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_984_ord__eq__le__subst,axiom,
    ! [A: real,F: risk_Free_account > real,B: risk_Free_account,C: risk_Free_account] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_985_ord__eq__le__subst,axiom,
    ! [A: int,F: risk_Free_account > int,B: risk_Free_account,C: risk_Free_account] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_less_eq_int @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_986_ord__eq__le__subst,axiom,
    ! [A: nat,F: risk_Free_account > nat,B: risk_Free_account,C: risk_Free_account] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_987_ord__eq__le__subst,axiom,
    ! [A: risk_Free_account,F: real > risk_Free_account,B: real,C: real] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_988_ord__eq__le__subst,axiom,
    ! [A: real,F: real > real,B: real,C: real] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_989_ord__eq__le__subst,axiom,
    ! [A: int,F: real > int,B: real,C: real] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_less_eq_int @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_990_ord__eq__le__subst,axiom,
    ! [A: nat,F: real > nat,B: real,C: real] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_991_ord__eq__le__subst,axiom,
    ! [A: risk_Free_account,F: int > risk_Free_account,B: int,C: int] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ! [X2: int,Y4: int] :
              ( ( ord_less_eq_int @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_992_ord__eq__le__subst,axiom,
    ! [A: real,F: int > real,B: int,C: int] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ! [X2: int,Y4: int] :
              ( ( ord_less_eq_int @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_993_ord__le__eq__subst,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_994_ord__le__eq__subst,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > real,C: real] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_995_ord__le__eq__subst,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > int,C: int] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_less_eq_int @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_996_ord__le__eq__subst,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > nat,C: nat] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: risk_Free_account,Y4: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X2 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_997_ord__le__eq__subst,axiom,
    ! [A: real,B: real,F: real > risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_998_ord__le__eq__subst,axiom,
    ! [A: real,B: real,F: real > real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_999_ord__le__eq__subst,axiom,
    ! [A: real,B: real,F: real > int,C: int] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_less_eq_int @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_1000_ord__le__eq__subst,axiom,
    ! [A: real,B: real,F: real > nat,C: nat] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: real,Y4: real] :
              ( ( ord_less_eq_real @ X2 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_1001_ord__le__eq__subst,axiom,
    ! [A: int,B: int,F: int > risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: int,Y4: int] :
              ( ( ord_less_eq_int @ X2 @ Y4 )
             => ( ord_le4245800335709223507ccount @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_le4245800335709223507ccount @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_1002_ord__le__eq__subst,axiom,
    ! [A: int,B: int,F: int > real,C: real] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: int,Y4: int] :
              ( ( ord_less_eq_int @ X2 @ Y4 )
             => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_1003_linorder__le__cases,axiom,
    ! [X: real,Y: real] :
      ( ~ ( ord_less_eq_real @ X @ Y )
     => ( ord_less_eq_real @ Y @ X ) ) ).

% linorder_le_cases
thf(fact_1004_linorder__le__cases,axiom,
    ! [X: int,Y: int] :
      ( ~ ( ord_less_eq_int @ X @ Y )
     => ( ord_less_eq_int @ Y @ X ) ) ).

% linorder_le_cases
thf(fact_1005_linorder__le__cases,axiom,
    ! [X: nat,Y: nat] :
      ( ~ ( ord_less_eq_nat @ X @ Y )
     => ( ord_less_eq_nat @ Y @ X ) ) ).

% linorder_le_cases
thf(fact_1006_order__antisym__conv,axiom,
    ! [Y: set_nat,X: set_nat] :
      ( ( ord_less_eq_set_nat @ Y @ X )
     => ( ( ord_less_eq_set_nat @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_1007_order__antisym__conv,axiom,
    ! [Y: risk_Free_account,X: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ Y @ X )
     => ( ( ord_le4245800335709223507ccount @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_1008_order__antisym__conv,axiom,
    ! [Y: real,X: real] :
      ( ( ord_less_eq_real @ Y @ X )
     => ( ( ord_less_eq_real @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_1009_order__antisym__conv,axiom,
    ! [Y: int,X: int] :
      ( ( ord_less_eq_int @ Y @ X )
     => ( ( ord_less_eq_int @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_1010_order__antisym__conv,axiom,
    ! [Y: nat,X: nat] :
      ( ( ord_less_eq_nat @ Y @ X )
     => ( ( ord_less_eq_nat @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_1011_plus__account__def,axiom,
    ( plus_p1863581527469039996ccount
    = ( ^ [Alpha_12: risk_Free_account,Alpha_22: risk_Free_account] :
          ( risk_F5458100604530014700ccount
          @ ^ [N: nat] : ( plus_plus_real @ ( risk_F170160801229183585ccount @ Alpha_12 @ N ) @ ( risk_F170160801229183585ccount @ Alpha_22 @ N ) ) ) ) ) ).

% plus_account_def
thf(fact_1012_zero__account__def,axiom,
    ( zero_z1425366712893667068ccount
    = ( risk_F5458100604530014700ccount
      @ ^ [Uu: nat] : zero_zero_real ) ) ).

% zero_account_def
thf(fact_1013_Abs__account__inject,axiom,
    ! [X: nat > real,Y: nat > real] :
      ( ( member_nat_real @ X @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) )
     => ( ( member_nat_real @ Y @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) )
       => ( ( ( risk_F5458100604530014700ccount @ X )
            = ( risk_F5458100604530014700ccount @ Y ) )
          = ( X = Y ) ) ) ) ).

% Abs_account_inject
thf(fact_1014_Abs__account__induct,axiom,
    ! [P: risk_Free_account > $o,X: risk_Free_account] :
      ( ! [Y4: nat > real] :
          ( ( member_nat_real @ Y4 @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) )
         => ( P @ ( risk_F5458100604530014700ccount @ Y4 ) ) )
     => ( P @ X ) ) ).

% Abs_account_induct
thf(fact_1015_Abs__account__cases,axiom,
    ! [X: risk_Free_account] :
      ~ ! [Y4: nat > real] :
          ( ( X
            = ( risk_F5458100604530014700ccount @ Y4 ) )
         => ~ ( member_nat_real @ Y4 @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) ) ) ).

% Abs_account_cases
thf(fact_1016_top_Oextremum__uniqueI,axiom,
    ! [A: set_int] :
      ( ( ord_less_eq_set_int @ top_top_set_int @ A )
     => ( A = top_top_set_int ) ) ).

% top.extremum_uniqueI
thf(fact_1017_top_Oextremum__uniqueI,axiom,
    ! [A: set_nat] :
      ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
     => ( A = top_top_set_nat ) ) ).

% top.extremum_uniqueI
thf(fact_1018_top_Oextremum__unique,axiom,
    ! [A: set_int] :
      ( ( ord_less_eq_set_int @ top_top_set_int @ A )
      = ( A = top_top_set_int ) ) ).

% top.extremum_unique
thf(fact_1019_top_Oextremum__unique,axiom,
    ! [A: set_nat] :
      ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
      = ( A = top_top_set_nat ) ) ).

% top.extremum_unique
thf(fact_1020_top__greatest,axiom,
    ! [A: set_int] : ( ord_less_eq_set_int @ A @ top_top_set_int ) ).

% top_greatest
thf(fact_1021_top__greatest,axiom,
    ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).

% top_greatest
thf(fact_1022_add__0__iff,axiom,
    ! [B: real,A: real] :
      ( ( B
        = ( plus_plus_real @ B @ A ) )
      = ( A = zero_zero_real ) ) ).

% add_0_iff
thf(fact_1023_add__0__iff,axiom,
    ! [B: nat,A: nat] :
      ( ( B
        = ( plus_plus_nat @ B @ A ) )
      = ( A = zero_zero_nat ) ) ).

% add_0_iff
thf(fact_1024_add__0__iff,axiom,
    ! [B: int,A: int] :
      ( ( B
        = ( plus_plus_int @ B @ A ) )
      = ( A = zero_zero_int ) ) ).

% add_0_iff
thf(fact_1025_add__0__iff,axiom,
    ! [B: complex,A: complex] :
      ( ( B
        = ( plus_plus_complex @ B @ A ) )
      = ( A = zero_zero_complex ) ) ).

% add_0_iff
thf(fact_1026_crossproduct__noteq,axiom,
    ! [A: complex,B: complex,C: complex,D: complex] :
      ( ( ( A != B )
        & ( C != D ) )
      = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) )
       != ( plus_plus_complex @ ( times_times_complex @ A @ D ) @ ( times_times_complex @ B @ C ) ) ) ) ).

% crossproduct_noteq
thf(fact_1027_crossproduct__noteq,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( A != B )
        & ( C != D ) )
      = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
       != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).

% crossproduct_noteq
thf(fact_1028_crossproduct__noteq,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ( A != B )
        & ( C != D ) )
      = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
       != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).

% crossproduct_noteq
thf(fact_1029_crossproduct__noteq,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A != B )
        & ( C != D ) )
      = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
       != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).

% crossproduct_noteq
thf(fact_1030_crossproduct__eq,axiom,
    ! [W: complex,Y: complex,X: complex,Z2: complex] :
      ( ( ( plus_plus_complex @ ( times_times_complex @ W @ Y ) @ ( times_times_complex @ X @ Z2 ) )
        = ( plus_plus_complex @ ( times_times_complex @ W @ Z2 ) @ ( times_times_complex @ X @ Y ) ) )
      = ( ( W = X )
        | ( Y = Z2 ) ) ) ).

% crossproduct_eq
thf(fact_1031_crossproduct__eq,axiom,
    ! [W: real,Y: real,X: real,Z2: real] :
      ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X @ Z2 ) )
        = ( plus_plus_real @ ( times_times_real @ W @ Z2 ) @ ( times_times_real @ X @ Y ) ) )
      = ( ( W = X )
        | ( Y = Z2 ) ) ) ).

% crossproduct_eq
thf(fact_1032_crossproduct__eq,axiom,
    ! [W: int,Y: int,X: int,Z2: int] :
      ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z2 ) )
        = ( plus_plus_int @ ( times_times_int @ W @ Z2 ) @ ( times_times_int @ X @ Y ) ) )
      = ( ( W = X )
        | ( Y = Z2 ) ) ) ).

% crossproduct_eq
thf(fact_1033_crossproduct__eq,axiom,
    ! [W: nat,Y: nat,X: nat,Z2: nat] :
      ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z2 ) )
        = ( plus_plus_nat @ ( times_times_nat @ W @ Z2 ) @ ( times_times_nat @ X @ Y ) ) )
      = ( ( W = X )
        | ( Y = Z2 ) ) ) ).

% crossproduct_eq
thf(fact_1034_add__diff__add,axiom,
    ! [A: real,C: real,B: real,D: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
      = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).

% add_diff_add
thf(fact_1035_add__diff__add,axiom,
    ! [A: risk_Free_account,C: risk_Free_account,B: risk_Free_account,D: risk_Free_account] :
      ( ( minus_4846202936726426316ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ ( plus_p1863581527469039996ccount @ B @ D ) )
      = ( plus_p1863581527469039996ccount @ ( minus_4846202936726426316ccount @ A @ B ) @ ( minus_4846202936726426316ccount @ C @ D ) ) ) ).

% add_diff_add
thf(fact_1036_add__diff__add,axiom,
    ! [A: int,C: int,B: int,D: int] :
      ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
      = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).

% add_diff_add
thf(fact_1037_add__diff__add,axiom,
    ! [A: complex,C: complex,B: complex,D: complex] :
      ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ D ) )
      = ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ ( minus_minus_complex @ C @ D ) ) ) ).

% add_diff_add
thf(fact_1038_sup__Un__eq,axiom,
    ! [R2: set_nat_real,S: set_nat_real] :
      ( ( sup_sup_nat_real_o
        @ ^ [X3: nat > real] : ( member_nat_real @ X3 @ R2 )
        @ ^ [X3: nat > real] : ( member_nat_real @ X3 @ S ) )
      = ( ^ [X3: nat > real] : ( member_nat_real @ X3 @ ( sup_sup_set_nat_real @ R2 @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_1039_sup__Un__eq,axiom,
    ! [R2: set_nat,S: set_nat] :
      ( ( sup_sup_nat_o
        @ ^ [X3: nat] : ( member_nat @ X3 @ R2 )
        @ ^ [X3: nat] : ( member_nat @ X3 @ S ) )
      = ( ^ [X3: nat] : ( member_nat @ X3 @ ( sup_sup_set_nat @ R2 @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_1040_pred__subset__eq,axiom,
    ! [R2: set_nat_real,S: set_nat_real] :
      ( ( ord_le7676461544873280788real_o
        @ ^ [X3: nat > real] : ( member_nat_real @ X3 @ R2 )
        @ ^ [X3: nat > real] : ( member_nat_real @ X3 @ S ) )
      = ( ord_le2908806416726583473t_real @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_1041_pred__subset__eq,axiom,
    ! [R2: set_nat,S: set_nat] :
      ( ( ord_less_eq_nat_o
        @ ^ [X3: nat] : ( member_nat @ X3 @ R2 )
        @ ^ [X3: nat] : ( member_nat @ X3 @ S ) )
      = ( ord_less_eq_set_nat @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_1042_top__empty__eq,axiom,
    ( top_top_nat_real_o
    = ( ^ [X3: nat > real] : ( member_nat_real @ X3 @ top_top_set_nat_real ) ) ) ).

% top_empty_eq
thf(fact_1043_top__empty__eq,axiom,
    ( top_top_nat_o
    = ( ^ [X3: nat] : ( member_nat @ X3 @ top_top_set_nat ) ) ) ).

% top_empty_eq
thf(fact_1044_top__empty__eq,axiom,
    ( top_top_int_o
    = ( ^ [X3: int] : ( member_int @ X3 @ top_top_set_int ) ) ) ).

% top_empty_eq
thf(fact_1045_eq__diff__eq_H,axiom,
    ! [X: real,Y: real,Z2: real] :
      ( ( X
        = ( minus_minus_real @ Y @ Z2 ) )
      = ( Y
        = ( plus_plus_real @ X @ Z2 ) ) ) ).

% eq_diff_eq'
thf(fact_1046_inf__period_I1_J,axiom,
    ! [P: complex > $o,D2: complex,Q: complex > $o] :
      ( ! [X2: complex,K2: complex] :
          ( ( P @ X2 )
          = ( P @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K2 @ D2 ) ) ) )
     => ( ! [X2: complex,K2: complex] :
            ( ( Q @ X2 )
            = ( Q @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K2 @ D2 ) ) ) )
       => ! [X4: complex,K3: complex] :
            ( ( ( P @ X4 )
              & ( Q @ X4 ) )
            = ( ( P @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D2 ) ) )
              & ( Q @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D2 ) ) ) ) ) ) ) ).

% inf_period(1)
thf(fact_1047_inf__period_I1_J,axiom,
    ! [P: real > $o,D2: real,Q: real > $o] :
      ( ! [X2: real,K2: real] :
          ( ( P @ X2 )
          = ( P @ ( minus_minus_real @ X2 @ ( times_times_real @ K2 @ D2 ) ) ) )
     => ( ! [X2: real,K2: real] :
            ( ( Q @ X2 )
            = ( Q @ ( minus_minus_real @ X2 @ ( times_times_real @ K2 @ D2 ) ) ) )
       => ! [X4: real,K3: real] :
            ( ( ( P @ X4 )
              & ( Q @ X4 ) )
            = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D2 ) ) )
              & ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D2 ) ) ) ) ) ) ) ).

% inf_period(1)
thf(fact_1048_inf__period_I1_J,axiom,
    ! [P: int > $o,D2: int,Q: int > $o] :
      ( ! [X2: int,K2: int] :
          ( ( P @ X2 )
          = ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D2 ) ) ) )
     => ( ! [X2: int,K2: int] :
            ( ( Q @ X2 )
            = ( Q @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D2 ) ) ) )
       => ! [X4: int,K3: int] :
            ( ( ( P @ X4 )
              & ( Q @ X4 ) )
            = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D2 ) ) )
              & ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D2 ) ) ) ) ) ) ) ).

% inf_period(1)
thf(fact_1049_inf__period_I2_J,axiom,
    ! [P: complex > $o,D2: complex,Q: complex > $o] :
      ( ! [X2: complex,K2: complex] :
          ( ( P @ X2 )
          = ( P @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K2 @ D2 ) ) ) )
     => ( ! [X2: complex,K2: complex] :
            ( ( Q @ X2 )
            = ( Q @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K2 @ D2 ) ) ) )
       => ! [X4: complex,K3: complex] :
            ( ( ( P @ X4 )
              | ( Q @ X4 ) )
            = ( ( P @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D2 ) ) )
              | ( Q @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D2 ) ) ) ) ) ) ) ).

% inf_period(2)
thf(fact_1050_inf__period_I2_J,axiom,
    ! [P: real > $o,D2: real,Q: real > $o] :
      ( ! [X2: real,K2: real] :
          ( ( P @ X2 )
          = ( P @ ( minus_minus_real @ X2 @ ( times_times_real @ K2 @ D2 ) ) ) )
     => ( ! [X2: real,K2: real] :
            ( ( Q @ X2 )
            = ( Q @ ( minus_minus_real @ X2 @ ( times_times_real @ K2 @ D2 ) ) ) )
       => ! [X4: real,K3: real] :
            ( ( ( P @ X4 )
              | ( Q @ X4 ) )
            = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D2 ) ) )
              | ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D2 ) ) ) ) ) ) ) ).

% inf_period(2)
thf(fact_1051_inf__period_I2_J,axiom,
    ! [P: int > $o,D2: int,Q: int > $o] :
      ( ! [X2: int,K2: int] :
          ( ( P @ X2 )
          = ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D2 ) ) ) )
     => ( ! [X2: int,K2: int] :
            ( ( Q @ X2 )
            = ( Q @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D2 ) ) ) )
       => ! [X4: int,K3: int] :
            ( ( ( P @ X4 )
              | ( Q @ X4 ) )
            = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D2 ) ) )
              | ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D2 ) ) ) ) ) ) ) ).

% inf_period(2)
thf(fact_1052_verit__sum__simplify,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ) ).

% verit_sum_simplify
thf(fact_1053_verit__sum__simplify,axiom,
    ! [A: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ A @ zero_z1425366712893667068ccount )
      = A ) ).

% verit_sum_simplify
thf(fact_1054_verit__sum__simplify,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ A @ zero_zero_nat )
      = A ) ).

% verit_sum_simplify
thf(fact_1055_verit__sum__simplify,axiom,
    ! [A: int] :
      ( ( plus_plus_int @ A @ zero_zero_int )
      = A ) ).

% verit_sum_simplify
thf(fact_1056_verit__sum__simplify,axiom,
    ! [A: complex] :
      ( ( plus_plus_complex @ A @ zero_zero_complex )
      = A ) ).

% verit_sum_simplify
thf(fact_1057_dbl__inc__simps_I2_J,axiom,
    ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
    = one_one_real ) ).

% dbl_inc_simps(2)
thf(fact_1058_dbl__inc__simps_I2_J,axiom,
    ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
    = one_one_int ) ).

% dbl_inc_simps(2)
thf(fact_1059_dbl__inc__simps_I2_J,axiom,
    ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
    = one_one_complex ) ).

% dbl_inc_simps(2)
thf(fact_1060_type__definition__account,axiom,
    type_d8982087200295354172t_real @ risk_F170160801229183585ccount @ risk_F5458100604530014700ccount @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) ).

% type_definition_account
thf(fact_1061_dbl__dec__def,axiom,
    ( neg_nu6075765906172075777c_real
    = ( ^ [X3: real] : ( minus_minus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).

% dbl_dec_def
thf(fact_1062_dbl__dec__def,axiom,
    ( neg_nu3811975205180677377ec_int
    = ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).

% dbl_dec_def
thf(fact_1063_dbl__dec__def,axiom,
    ( neg_nu6511756317524482435omplex
    = ( ^ [X3: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).

% dbl_dec_def
thf(fact_1064_net__asset__value__zero,axiom,
    ( ( risk_F2906766666041932210_value @ zero_z1425366712893667068ccount )
    = zero_zero_real ) ).

% net_asset_value_zero
thf(fact_1065_dbl__dec__simps_I3_J,axiom,
    ( ( neg_nu6075765906172075777c_real @ one_one_real )
    = one_one_real ) ).

% dbl_dec_simps(3)
thf(fact_1066_dbl__dec__simps_I3_J,axiom,
    ( ( neg_nu3811975205180677377ec_int @ one_one_int )
    = one_one_int ) ).

% dbl_dec_simps(3)
thf(fact_1067_dbl__dec__simps_I3_J,axiom,
    ( ( neg_nu6511756317524482435omplex @ one_one_complex )
    = one_one_complex ) ).

% dbl_dec_simps(3)
thf(fact_1068_net__asset__value__mono,axiom,
    ! [Alpha: risk_Free_account,Beta: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ Alpha @ Beta )
     => ( ord_less_eq_real @ ( risk_F2906766666041932210_value @ Alpha ) @ ( risk_F2906766666041932210_value @ Beta ) ) ) ).

% net_asset_value_mono
thf(fact_1069_net__asset__value__minus,axiom,
    ! [Alpha: risk_Free_account,Beta: risk_Free_account] :
      ( ( risk_F2906766666041932210_value @ ( minus_4846202936726426316ccount @ Alpha @ Beta ) )
      = ( minus_minus_real @ ( risk_F2906766666041932210_value @ Alpha ) @ ( risk_F2906766666041932210_value @ Beta ) ) ) ).

% net_asset_value_minus
thf(fact_1070_verit__comp__simplify1_I2_J,axiom,
    ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).

% verit_comp_simplify1(2)
thf(fact_1071_verit__comp__simplify1_I2_J,axiom,
    ! [A: risk_Free_account] : ( ord_le4245800335709223507ccount @ A @ A ) ).

% verit_comp_simplify1(2)
thf(fact_1072_verit__comp__simplify1_I2_J,axiom,
    ! [A: real] : ( ord_less_eq_real @ A @ A ) ).

% verit_comp_simplify1(2)
thf(fact_1073_verit__comp__simplify1_I2_J,axiom,
    ! [A: int] : ( ord_less_eq_int @ A @ A ) ).

% verit_comp_simplify1(2)
thf(fact_1074_verit__comp__simplify1_I2_J,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).

% verit_comp_simplify1(2)
thf(fact_1075_verit__la__disequality,axiom,
    ! [A: real,B: real] :
      ( ( A = B )
      | ~ ( ord_less_eq_real @ A @ B )
      | ~ ( ord_less_eq_real @ B @ A ) ) ).

% verit_la_disequality
thf(fact_1076_verit__la__disequality,axiom,
    ! [A: int,B: int] :
      ( ( A = B )
      | ~ ( ord_less_eq_int @ A @ B )
      | ~ ( ord_less_eq_int @ B @ A ) ) ).

% verit_la_disequality
thf(fact_1077_verit__la__disequality,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
      | ~ ( ord_less_eq_nat @ A @ B )
      | ~ ( ord_less_eq_nat @ B @ A ) ) ).

% verit_la_disequality
thf(fact_1078_net__asset__value__plus,axiom,
    ! [Alpha: risk_Free_account,Beta: risk_Free_account] :
      ( ( risk_F2906766666041932210_value @ ( plus_p1863581527469039996ccount @ Alpha @ Beta ) )
      = ( plus_plus_real @ ( risk_F2906766666041932210_value @ Alpha ) @ ( risk_F2906766666041932210_value @ Beta ) ) ) ).

% net_asset_value_plus
thf(fact_1079_dbl__inc__def,axiom,
    ( neg_nu8295874005876285629c_real
    = ( ^ [X3: real] : ( plus_plus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).

% dbl_inc_def
thf(fact_1080_dbl__inc__def,axiom,
    ( neg_nu5851722552734809277nc_int
    = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).

% dbl_inc_def
thf(fact_1081_dbl__inc__def,axiom,
    ( neg_nu8557863876264182079omplex
    = ( ^ [X3: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).

% dbl_inc_def
thf(fact_1082_type__copy__obj__one__point__absE,axiom,
    ! [Rep: risk_Free_account > nat > real,Abs: ( nat > real ) > risk_Free_account,S2: risk_Free_account] :
      ( ( type_d8982087200295354172t_real @ Rep @ Abs @ top_top_set_nat_real )
     => ~ ! [X2: nat > real] :
            ( S2
           != ( Abs @ X2 ) ) ) ).

% type_copy_obj_one_point_absE
thf(fact_1083_type__copy__ex__RepI,axiom,
    ! [Rep: risk_Free_account > nat > real,Abs: ( nat > real ) > risk_Free_account,F3: ( nat > real ) > $o] :
      ( ( type_d8982087200295354172t_real @ Rep @ Abs @ top_top_set_nat_real )
     => ( ( ? [X5: nat > real] : ( F3 @ X5 ) )
        = ( ? [B3: risk_Free_account] : ( F3 @ ( Rep @ B3 ) ) ) ) ) ).

% type_copy_ex_RepI
thf(fact_1084_update__account__def,axiom,
    ( risk_F444380041991734328ccount
    = ( ^ [Rho2: nat > real,I2: real,Alpha2: risk_Free_account] : ( plus_p1863581527469039996ccount @ ( risk_Free_just_cash @ ( times_times_real @ I2 @ ( risk_F2906766666041932210_value @ Alpha2 ) ) ) @ ( risk_F2121631595377017831_loans @ Rho2 @ Alpha2 ) ) ) ) ).

% update_account_def
thf(fact_1085_convex__bound__lt,axiom,
    ! [X: real,A: real,Y: real,U: real,V: real] :
      ( ( ord_less_real @ X @ A )
     => ( ( ord_less_real @ Y @ A )
       => ( ( ord_less_eq_real @ zero_zero_real @ U )
         => ( ( ord_less_eq_real @ zero_zero_real @ V )
           => ( ( ( plus_plus_real @ U @ V )
                = one_one_real )
             => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).

% convex_bound_lt
thf(fact_1086_convex__bound__lt,axiom,
    ! [X: int,A: int,Y: int,U: int,V: int] :
      ( ( ord_less_int @ X @ A )
     => ( ( ord_less_int @ Y @ A )
       => ( ( ord_less_eq_int @ zero_zero_int @ U )
         => ( ( ord_less_eq_int @ zero_zero_int @ V )
           => ( ( ( plus_plus_int @ U @ V )
                = one_one_int )
             => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).

% convex_bound_lt
thf(fact_1087_psubsetI,axiom,
    ! [A2: set_nat,B2: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ B2 )
     => ( ( A2 != B2 )
       => ( ord_less_set_nat @ A2 @ B2 ) ) ) ).

% psubsetI
thf(fact_1088_not__gr__zero,axiom,
    ! [N2: nat] :
      ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
      = ( N2 = zero_zero_nat ) ) ).

% not_gr_zero
thf(fact_1089_add__less__cancel__right,axiom,
    ! [A: risk_Free_account,C: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ ( plus_p1863581527469039996ccount @ B @ C ) )
      = ( ord_le2131251472502387783ccount @ A @ B ) ) ).

% add_less_cancel_right
thf(fact_1090_add__less__cancel__right,axiom,
    ! [A: real,C: real,B: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
      = ( ord_less_real @ A @ B ) ) ).

% add_less_cancel_right
thf(fact_1091_add__less__cancel__right,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
      = ( ord_less_nat @ A @ B ) ) ).

% add_less_cancel_right
thf(fact_1092_add__less__cancel__right,axiom,
    ! [A: int,C: int,B: int] :
      ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
      = ( ord_less_int @ A @ B ) ) ).

% add_less_cancel_right
thf(fact_1093_add__less__cancel__left,axiom,
    ! [C: risk_Free_account,A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ C @ A ) @ ( plus_p1863581527469039996ccount @ C @ B ) )
      = ( ord_le2131251472502387783ccount @ A @ B ) ) ).

% add_less_cancel_left
thf(fact_1094_add__less__cancel__left,axiom,
    ! [C: real,A: real,B: real] :
      ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
      = ( ord_less_real @ A @ B ) ) ).

% add_less_cancel_left
thf(fact_1095_add__less__cancel__left,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
      = ( ord_less_nat @ A @ B ) ) ).

% add_less_cancel_left
thf(fact_1096_add__less__cancel__left,axiom,
    ! [C: int,A: int,B: int] :
      ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
      = ( ord_less_int @ A @ B ) ) ).

% add_less_cancel_left
thf(fact_1097_add__less__same__cancel1,axiom,
    ! [B: risk_Free_account,A: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ B @ A ) @ B )
      = ( ord_le2131251472502387783ccount @ A @ zero_z1425366712893667068ccount ) ) ).

% add_less_same_cancel1
thf(fact_1098_add__less__same__cancel1,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
      = ( ord_less_real @ A @ zero_zero_real ) ) ).

% add_less_same_cancel1
thf(fact_1099_add__less__same__cancel1,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
      = ( ord_less_nat @ A @ zero_zero_nat ) ) ).

% add_less_same_cancel1
thf(fact_1100_add__less__same__cancel1,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
      = ( ord_less_int @ A @ zero_zero_int ) ) ).

% add_less_same_cancel1
thf(fact_1101_add__less__same__cancel2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ B )
      = ( ord_le2131251472502387783ccount @ A @ zero_z1425366712893667068ccount ) ) ).

% add_less_same_cancel2
thf(fact_1102_add__less__same__cancel2,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
      = ( ord_less_real @ A @ zero_zero_real ) ) ).

% add_less_same_cancel2
thf(fact_1103_add__less__same__cancel2,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
      = ( ord_less_nat @ A @ zero_zero_nat ) ) ).

% add_less_same_cancel2
thf(fact_1104_add__less__same__cancel2,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
      = ( ord_less_int @ A @ zero_zero_int ) ) ).

% add_less_same_cancel2
thf(fact_1105_less__add__same__cancel1,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ ( plus_p1863581527469039996ccount @ A @ B ) )
      = ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ B ) ) ).

% less_add_same_cancel1
thf(fact_1106_less__add__same__cancel1,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
      = ( ord_less_real @ zero_zero_real @ B ) ) ).

% less_add_same_cancel1
thf(fact_1107_less__add__same__cancel1,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
      = ( ord_less_nat @ zero_zero_nat @ B ) ) ).

% less_add_same_cancel1
thf(fact_1108_less__add__same__cancel1,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
      = ( ord_less_int @ zero_zero_int @ B ) ) ).

% less_add_same_cancel1
thf(fact_1109_less__add__same__cancel2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ ( plus_p1863581527469039996ccount @ B @ A ) )
      = ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ B ) ) ).

% less_add_same_cancel2
thf(fact_1110_less__add__same__cancel2,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
      = ( ord_less_real @ zero_zero_real @ B ) ) ).

% less_add_same_cancel2
thf(fact_1111_less__add__same__cancel2,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
      = ( ord_less_nat @ zero_zero_nat @ B ) ) ).

% less_add_same_cancel2
thf(fact_1112_less__add__same__cancel2,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
      = ( ord_less_int @ zero_zero_int @ B ) ) ).

% less_add_same_cancel2
thf(fact_1113_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [A: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
      = ( ord_less_real @ A @ zero_zero_real ) ) ).

% double_add_less_zero_iff_single_add_less_zero
thf(fact_1114_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [A: int] :
      ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
      = ( ord_less_int @ A @ zero_zero_int ) ) ).

% double_add_less_zero_iff_single_add_less_zero
thf(fact_1115_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [A: real] :
      ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
      = ( ord_less_real @ zero_zero_real @ A ) ) ).

% zero_less_double_add_iff_zero_less_single_add
thf(fact_1116_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [A: int] :
      ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
      = ( ord_less_int @ zero_zero_int @ A ) ) ).

% zero_less_double_add_iff_zero_less_single_add
thf(fact_1117_diff__gt__0__iff__gt,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ ( minus_4846202936726426316ccount @ A @ B ) )
      = ( ord_le2131251472502387783ccount @ B @ A ) ) ).

% diff_gt_0_iff_gt
thf(fact_1118_diff__gt__0__iff__gt,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
      = ( ord_less_real @ B @ A ) ) ).

% diff_gt_0_iff_gt
thf(fact_1119_diff__gt__0__iff__gt,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
      = ( ord_less_int @ B @ A ) ) ).

% diff_gt_0_iff_gt
thf(fact_1120_Rep__account__just__cash,axiom,
    ! [C: real] :
      ( ( risk_F170160801229183585ccount @ ( risk_Free_just_cash @ C ) )
      = ( ^ [N: nat] : ( if_real @ ( N = zero_zero_nat ) @ C @ zero_zero_real ) ) ) ).

% Rep_account_just_cash
thf(fact_1121_just__cash__plus,axiom,
    ! [A: real,B: real] :
      ( ( plus_p1863581527469039996ccount @ ( risk_Free_just_cash @ A ) @ ( risk_Free_just_cash @ B ) )
      = ( risk_Free_just_cash @ ( plus_plus_real @ A @ B ) ) ) ).

% just_cash_plus
thf(fact_1122_just__cash__subtract,axiom,
    ! [A: real,B: real] :
      ( ( minus_4846202936726426316ccount @ ( risk_Free_just_cash @ A ) @ ( risk_Free_just_cash @ B ) )
      = ( risk_Free_just_cash @ ( minus_minus_real @ A @ B ) ) ) ).

% just_cash_subtract
thf(fact_1123_verit__comp__simplify1_I1_J,axiom,
    ! [A: risk_Free_account] :
      ~ ( ord_le2131251472502387783ccount @ A @ A ) ).

% verit_comp_simplify1(1)
thf(fact_1124_verit__comp__simplify1_I1_J,axiom,
    ! [A: real] :
      ~ ( ord_less_real @ A @ A ) ).

% verit_comp_simplify1(1)
thf(fact_1125_verit__comp__simplify1_I1_J,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ) ).

% verit_comp_simplify1(1)
thf(fact_1126_verit__comp__simplify1_I1_J,axiom,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ) ).

% verit_comp_simplify1(1)
thf(fact_1127_lt__ex,axiom,
    ! [X: real] :
    ? [Y4: real] : ( ord_less_real @ Y4 @ X ) ).

% lt_ex
thf(fact_1128_lt__ex,axiom,
    ! [X: int] :
    ? [Y4: int] : ( ord_less_int @ Y4 @ X ) ).

% lt_ex
thf(fact_1129_gt__ex,axiom,
    ! [X: real] :
    ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).

% gt_ex
thf(fact_1130_gt__ex,axiom,
    ! [X: nat] :
    ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).

% gt_ex
thf(fact_1131_gt__ex,axiom,
    ! [X: int] :
    ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).

% gt_ex
thf(fact_1132_dense,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ X @ Y )
     => ? [Z4: real] :
          ( ( ord_less_real @ X @ Z4 )
          & ( ord_less_real @ Z4 @ Y ) ) ) ).

% dense
thf(fact_1133_less__imp__neq,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ X @ Y )
     => ( X != Y ) ) ).

% less_imp_neq
thf(fact_1134_less__imp__neq,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ X @ Y )
     => ( X != Y ) ) ).

% less_imp_neq
thf(fact_1135_less__imp__neq,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_nat @ X @ Y )
     => ( X != Y ) ) ).

% less_imp_neq
thf(fact_1136_less__imp__neq,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_int @ X @ Y )
     => ( X != Y ) ) ).

% less_imp_neq
thf(fact_1137_order_Oasym,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ~ ( ord_le2131251472502387783ccount @ B @ A ) ) ).

% order.asym
thf(fact_1138_order_Oasym,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ B )
     => ~ ( ord_less_real @ B @ A ) ) ).

% order.asym
thf(fact_1139_order_Oasym,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ) ).

% order.asym
thf(fact_1140_order_Oasym,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ) ).

% order.asym
thf(fact_1141_ord__eq__less__trans,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( A = B )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ord_le2131251472502387783ccount @ A @ C ) ) ) ).

% ord_eq_less_trans
thf(fact_1142_ord__eq__less__trans,axiom,
    ! [A: real,B: real,C: real] :
      ( ( A = B )
     => ( ( ord_less_real @ B @ C )
       => ( ord_less_real @ A @ C ) ) ) ).

% ord_eq_less_trans
thf(fact_1143_ord__eq__less__trans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( A = B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ) ).

% ord_eq_less_trans
thf(fact_1144_ord__eq__less__trans,axiom,
    ! [A: int,B: int,C: int] :
      ( ( A = B )
     => ( ( ord_less_int @ B @ C )
       => ( ord_less_int @ A @ C ) ) ) ).

% ord_eq_less_trans
thf(fact_1145_ord__less__eq__trans,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( B = C )
       => ( ord_le2131251472502387783ccount @ A @ C ) ) ) ).

% ord_less_eq_trans
thf(fact_1146_ord__less__eq__trans,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( B = C )
       => ( ord_less_real @ A @ C ) ) ) ).

% ord_less_eq_trans
thf(fact_1147_ord__less__eq__trans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( B = C )
       => ( ord_less_nat @ A @ C ) ) ) ).

% ord_less_eq_trans
thf(fact_1148_ord__less__eq__trans,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( B = C )
       => ( ord_less_int @ A @ C ) ) ) ).

% ord_less_eq_trans
thf(fact_1149_less__induct,axiom,
    ! [P: nat > $o,A: nat] :
      ( ! [X2: nat] :
          ( ! [Y5: nat] :
              ( ( ord_less_nat @ Y5 @ X2 )
             => ( P @ Y5 ) )
         => ( P @ X2 ) )
     => ( P @ A ) ) ).

% less_induct
thf(fact_1150_antisym__conv3,axiom,
    ! [Y: real,X: real] :
      ( ~ ( ord_less_real @ Y @ X )
     => ( ( ~ ( ord_less_real @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv3
thf(fact_1151_antisym__conv3,axiom,
    ! [Y: nat,X: nat] :
      ( ~ ( ord_less_nat @ Y @ X )
     => ( ( ~ ( ord_less_nat @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv3
thf(fact_1152_antisym__conv3,axiom,
    ! [Y: int,X: int] :
      ( ~ ( ord_less_int @ Y @ X )
     => ( ( ~ ( ord_less_int @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv3
thf(fact_1153_linorder__cases,axiom,
    ! [X: real,Y: real] :
      ( ~ ( ord_less_real @ X @ Y )
     => ( ( X != Y )
       => ( ord_less_real @ Y @ X ) ) ) ).

% linorder_cases
thf(fact_1154_linorder__cases,axiom,
    ! [X: nat,Y: nat] :
      ( ~ ( ord_less_nat @ X @ Y )
     => ( ( X != Y )
       => ( ord_less_nat @ Y @ X ) ) ) ).

% linorder_cases
thf(fact_1155_linorder__cases,axiom,
    ! [X: int,Y: int] :
      ( ~ ( ord_less_int @ X @ Y )
     => ( ( X != Y )
       => ( ord_less_int @ Y @ X ) ) ) ).

% linorder_cases
thf(fact_1156_dual__order_Oasym,axiom,
    ! [B: risk_Free_account,A: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ B @ A )
     => ~ ( ord_le2131251472502387783ccount @ A @ B ) ) ).

% dual_order.asym
thf(fact_1157_dual__order_Oasym,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_real @ B @ A )
     => ~ ( ord_less_real @ A @ B ) ) ).

% dual_order.asym
thf(fact_1158_dual__order_Oasym,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_nat @ B @ A )
     => ~ ( ord_less_nat @ A @ B ) ) ).

% dual_order.asym
thf(fact_1159_dual__order_Oasym,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_int @ B @ A )
     => ~ ( ord_less_int @ A @ B ) ) ).

% dual_order.asym
thf(fact_1160_dual__order_Oirrefl,axiom,
    ! [A: risk_Free_account] :
      ~ ( ord_le2131251472502387783ccount @ A @ A ) ).

% dual_order.irrefl
thf(fact_1161_dual__order_Oirrefl,axiom,
    ! [A: real] :
      ~ ( ord_less_real @ A @ A ) ).

% dual_order.irrefl
thf(fact_1162_dual__order_Oirrefl,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ) ).

% dual_order.irrefl
thf(fact_1163_dual__order_Oirrefl,axiom,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ) ).

% dual_order.irrefl
thf(fact_1164_exists__least__iff,axiom,
    ( ( ^ [P2: nat > $o] :
        ? [X6: nat] : ( P2 @ X6 ) )
    = ( ^ [P3: nat > $o] :
        ? [N: nat] :
          ( ( P3 @ N )
          & ! [M: nat] :
              ( ( ord_less_nat @ M @ N )
             => ~ ( P3 @ M ) ) ) ) ) ).

% exists_least_iff
thf(fact_1165_linorder__less__wlog,axiom,
    ! [P: real > real > $o,A: real,B: real] :
      ( ! [A6: real,B6: real] :
          ( ( ord_less_real @ A6 @ B6 )
         => ( P @ A6 @ B6 ) )
     => ( ! [A6: real] : ( P @ A6 @ A6 )
       => ( ! [A6: real,B6: real] :
              ( ( P @ B6 @ A6 )
             => ( P @ A6 @ B6 ) )
         => ( P @ A @ B ) ) ) ) ).

% linorder_less_wlog
thf(fact_1166_linorder__less__wlog,axiom,
    ! [P: nat > nat > $o,A: nat,B: nat] :
      ( ! [A6: nat,B6: nat] :
          ( ( ord_less_nat @ A6 @ B6 )
         => ( P @ A6 @ B6 ) )
     => ( ! [A6: nat] : ( P @ A6 @ A6 )
       => ( ! [A6: nat,B6: nat] :
              ( ( P @ B6 @ A6 )
             => ( P @ A6 @ B6 ) )
         => ( P @ A @ B ) ) ) ) ).

% linorder_less_wlog
thf(fact_1167_linorder__less__wlog,axiom,
    ! [P: int > int > $o,A: int,B: int] :
      ( ! [A6: int,B6: int] :
          ( ( ord_less_int @ A6 @ B6 )
         => ( P @ A6 @ B6 ) )
     => ( ! [A6: int] : ( P @ A6 @ A6 )
       => ( ! [A6: int,B6: int] :
              ( ( P @ B6 @ A6 )
             => ( P @ A6 @ B6 ) )
         => ( P @ A @ B ) ) ) ) ).

% linorder_less_wlog
thf(fact_1168_just__cash__embed,axiom,
    ( ( ^ [Y2: real,Z: real] : ( Y2 = Z ) )
    = ( ^ [A3: real,B3: real] :
          ( ( risk_Free_just_cash @ A3 )
          = ( risk_Free_just_cash @ B3 ) ) ) ) ).

% just_cash_embed
thf(fact_1169_just__cash__order__embed,axiom,
    ( ord_less_eq_real
    = ( ^ [A3: real,B3: real] : ( ord_le4245800335709223507ccount @ ( risk_Free_just_cash @ A3 ) @ ( risk_Free_just_cash @ B3 ) ) ) ) ).

% just_cash_order_embed
thf(fact_1170_less__account__def,axiom,
    ( ord_le2131251472502387783ccount
    = ( ^ [Alpha_12: risk_Free_account,Alpha_22: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ Alpha_12 @ Alpha_22 )
          & ~ ( ord_le4245800335709223507ccount @ Alpha_22 @ Alpha_12 ) ) ) ) ).

% less_account_def
thf(fact_1171_less__eq__real__def,axiom,
    ( ord_less_eq_real
    = ( ^ [X3: real,Y3: real] :
          ( ( ord_less_real @ X3 @ Y3 )
          | ( X3 = Y3 ) ) ) ) ).

% less_eq_real_def
thf(fact_1172_net__asset__value__just__cash__left__inverse,axiom,
    ! [C: real] :
      ( ( risk_F2906766666041932210_value @ ( risk_Free_just_cash @ C ) )
      = C ) ).

% net_asset_value_just_cash_left_inverse
thf(fact_1173_zero__account__alt__def,axiom,
    ( ( risk_Free_just_cash @ zero_zero_real )
    = zero_z1425366712893667068ccount ) ).

% zero_account_alt_def
thf(fact_1174_just__cash__def,axiom,
    ( risk_Free_just_cash
    = ( ^ [C3: real] :
          ( risk_F5458100604530014700ccount
          @ ^ [N: nat] : ( if_real @ ( N = zero_zero_nat ) @ C3 @ zero_zero_real ) ) ) ) ).

% just_cash_def
thf(fact_1175_not__real__square__gt__zero,axiom,
    ! [X: real] :
      ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
      = ( X = zero_zero_real ) ) ).

% not_real_square_gt_zero
thf(fact_1176_Bolzano,axiom,
    ! [A: real,B: real,P: real > real > $o] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ! [A6: real,B6: real,C2: real] :
            ( ( P @ A6 @ B6 )
           => ( ( P @ B6 @ C2 )
             => ( ( ord_less_eq_real @ A6 @ B6 )
               => ( ( ord_less_eq_real @ B6 @ C2 )
                 => ( P @ A6 @ C2 ) ) ) ) )
       => ( ! [X2: real] :
              ( ( ord_less_eq_real @ A @ X2 )
             => ( ( ord_less_eq_real @ X2 @ B )
               => ? [D3: real] :
                    ( ( ord_less_real @ zero_zero_real @ D3 )
                    & ! [A6: real,B6: real] :
                        ( ( ( ord_less_eq_real @ A6 @ X2 )
                          & ( ord_less_eq_real @ X2 @ B6 )
                          & ( ord_less_real @ ( minus_minus_real @ B6 @ A6 ) @ D3 ) )
                       => ( P @ A6 @ B6 ) ) ) ) )
         => ( P @ A @ B ) ) ) ) ).

% Bolzano
thf(fact_1177_just__cash__valid__transfer,axiom,
    ! [C: real,T2: real] :
      ( ( risk_F1023690899723030139ansfer @ ( risk_Free_just_cash @ C ) @ ( risk_Free_just_cash @ T2 ) )
      = ( ( ord_less_eq_real @ zero_zero_real @ T2 )
        & ( ord_less_eq_real @ T2 @ C ) ) ) ).

% just_cash_valid_transfer
thf(fact_1178_cash__reserve__def,axiom,
    ( risk_F1914734008469130493eserve
    = ( ^ [Alpha2: risk_Free_account] : ( risk_F170160801229183585ccount @ Alpha2 @ zero_zero_nat ) ) ) ).

% cash_reserve_def
thf(fact_1179_valid__transfer__alt__def,axiom,
    ( risk_F1023690899723030139ansfer
    = ( ^ [Alpha2: risk_Free_account,Tau: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ Tau )
          & ( ord_le4245800335709223507ccount @ Tau @ Alpha2 ) ) ) ) ).

% valid_transfer_alt_def
thf(fact_1180_net__asset__value__def,axiom,
    ( risk_F2906766666041932210_value
    = ( ^ [Alpha2: risk_Free_account] :
          ( groups6591440286371151544t_real @ ( risk_F170160801229183585ccount @ Alpha2 )
          @ ( collect_nat
            @ ^ [I2: nat] :
                ( ( risk_F170160801229183585ccount @ Alpha2 @ I2 )
               != zero_zero_real ) ) ) ) ) ).

% net_asset_value_def
thf(fact_1181_nat0__intermed__int__val,axiom,
    ! [N2: nat,F: nat > int,K: int] :
      ( ! [I3: nat] :
          ( ( ord_less_nat @ I3 @ N2 )
         => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
     => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
       => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
         => ? [I3: nat] :
              ( ( ord_less_eq_nat @ I3 @ N2 )
              & ( ( F @ I3 )
                = K ) ) ) ) ) ).

% nat0_intermed_int_val
thf(fact_1182_additive__strictly__solvent,axiom,
    ! [Alpha_1: risk_Free_account,Alpha_2: risk_Free_account] :
      ( ( risk_F1636578016437888323olvent @ Alpha_1 )
     => ( ( risk_F1636578016437888323olvent @ Alpha_2 )
       => ( risk_F1636578016437888323olvent @ ( plus_p1863581527469039996ccount @ Alpha_1 @ Alpha_2 ) ) ) ) ).

% additive_strictly_solvent
thf(fact_1183_only__strictly__solvent__accounts__can__transfer,axiom,
    ! [Alpha: risk_Free_account,Tau2: risk_Free_account] :
      ( ( risk_F1023690899723030139ansfer @ Alpha @ Tau2 )
     => ( risk_F1636578016437888323olvent @ Alpha ) ) ).

% only_strictly_solvent_accounts_can_transfer
thf(fact_1184_finite__account__support,axiom,
    ! [Alpha: risk_Free_account] :
      ( finite_finite_nat
      @ ( collect_nat
        @ ^ [I2: nat] :
            ( ( risk_F170160801229183585ccount @ Alpha @ I2 )
           != zero_zero_real ) ) ) ).

% finite_account_support
thf(fact_1185_sin__bound__lemma,axiom,
    ! [X: real,Y: real,U: real,V: real] :
      ( ( X = Y )
     => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y ) ) @ V ) ) ) ).

% sin_bound_lemma
thf(fact_1186_strictly__solvent__alt__def,axiom,
    ( risk_F1636578016437888323olvent
    = ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount ) ) ).

% strictly_solvent_alt_def
thf(fact_1187_valid__transfer__def,axiom,
    ( risk_F1023690899723030139ansfer
    = ( ^ [Alpha2: risk_Free_account,Tau: risk_Free_account] :
          ( ( risk_F1636578016437888323olvent @ Tau )
          & ( risk_F1636578016437888323olvent @ ( minus_4846202936726426316ccount @ Alpha2 @ Tau ) ) ) ) ) ).

% valid_transfer_def
thf(fact_1188_strictly__solvent__just__cash__equiv,axiom,
    ! [C: real] :
      ( ( risk_F1636578016437888323olvent @ ( risk_Free_just_cash @ C ) )
      = ( ord_less_eq_real @ zero_zero_real @ C ) ) ).

% strictly_solvent_just_cash_equiv
thf(fact_1189_strictly__solvent__net__asset__value,axiom,
    ! [Alpha: risk_Free_account] :
      ( ( risk_F1636578016437888323olvent @ Alpha )
     => ( ord_less_eq_real @ zero_zero_real @ ( risk_F2906766666041932210_value @ Alpha ) ) ) ).

% strictly_solvent_net_asset_value
thf(fact_1190_strictly__solvent__non__negative__cash,axiom,
    ! [Alpha: risk_Free_account] :
      ( ( risk_F1636578016437888323olvent @ Alpha )
     => ( ord_less_eq_real @ zero_zero_real @ ( risk_F1914734008469130493eserve @ Alpha ) ) ) ).

% strictly_solvent_non_negative_cash
thf(fact_1191_finite__interval__int1,axiom,
    ! [A: int,B: int] :
      ( finite_finite_int
      @ ( collect_int
        @ ^ [I2: int] :
            ( ( ord_less_eq_int @ A @ I2 )
            & ( ord_less_eq_int @ I2 @ B ) ) ) ) ).

% finite_interval_int1
thf(fact_1192_finite__interval__int3,axiom,
    ! [A: int,B: int] :
      ( finite_finite_int
      @ ( collect_int
        @ ^ [I2: int] :
            ( ( ord_less_int @ A @ I2 )
            & ( ord_less_eq_int @ I2 @ B ) ) ) ) ).

% finite_interval_int3
thf(fact_1193_finite__interval__int2,axiom,
    ! [A: int,B: int] :
      ( finite_finite_int
      @ ( collect_int
        @ ^ [I2: int] :
            ( ( ord_less_eq_int @ A @ I2 )
            & ( ord_less_int @ I2 @ B ) ) ) ) ).

% finite_interval_int2
thf(fact_1194_zle__add1__eq__le,axiom,
    ! [W: int,Z2: int] :
      ( ( ord_less_int @ W @ ( plus_plus_int @ Z2 @ one_one_int ) )
      = ( ord_less_eq_int @ W @ Z2 ) ) ).

% zle_add1_eq_le
thf(fact_1195_zabs__less__one__iff,axiom,
    ! [Z2: int] :
      ( ( ord_less_int @ ( abs_abs_int @ Z2 ) @ one_one_int )
      = ( Z2 = zero_zero_int ) ) ).

% zabs_less_one_iff
thf(fact_1196_finite__Collect__less__nat,axiom,
    ! [K: nat] :
      ( finite_finite_nat
      @ ( collect_nat
        @ ^ [N: nat] : ( ord_less_nat @ N @ K ) ) ) ).

% finite_Collect_less_nat
thf(fact_1197_finite__Collect__le__nat,axiom,
    ! [K: nat] :
      ( finite_finite_nat
      @ ( collect_nat
        @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).

% finite_Collect_le_nat
thf(fact_1198_zle__diff1__eq,axiom,
    ! [W: int,Z2: int] :
      ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z2 @ one_one_int ) )
      = ( ord_less_int @ W @ Z2 ) ) ).

% zle_diff1_eq
thf(fact_1199_abs__zmult__eq__1,axiom,
    ! [M2: int,N2: int] :
      ( ( ( abs_abs_int @ ( times_times_int @ M2 @ N2 ) )
        = one_one_int )
     => ( ( abs_abs_int @ M2 )
        = one_one_int ) ) ).

% abs_zmult_eq_1
thf(fact_1200_incr__lemma,axiom,
    ! [D: int,Z2: int,X: int] :
      ( ( ord_less_int @ zero_zero_int @ D )
     => ( ord_less_int @ Z2 @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z2 ) ) @ one_one_int ) @ D ) ) ) ) ).

% incr_lemma
thf(fact_1201_decr__lemma,axiom,
    ! [D: int,X: int,Z2: int] :
      ( ( ord_less_int @ zero_zero_int @ D )
     => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z2 ) ) @ one_one_int ) @ D ) ) @ Z2 ) ) ).

% decr_lemma
thf(fact_1202_add1__zle__eq,axiom,
    ! [W: int,Z2: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z2 )
      = ( ord_less_int @ W @ Z2 ) ) ).

% add1_zle_eq
thf(fact_1203_le__imp__0__less,axiom,
    ! [Z2: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
     => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ).

% le_imp_0_less
thf(fact_1204_int__less__induct,axiom,
    ! [I: int,K: int,P: int > $o] :
      ( ( ord_less_int @ I @ K )
     => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
       => ( ! [I3: int] :
              ( ( ord_less_int @ I3 @ K )
             => ( ( P @ I3 )
               => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
         => ( P @ I ) ) ) ) ).

% int_less_induct
thf(fact_1205_zless__imp__add1__zle,axiom,
    ! [W: int,Z2: int] :
      ( ( ord_less_int @ W @ Z2 )
     => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z2 ) ) ).

% zless_imp_add1_zle
thf(fact_1206_plusinfinity,axiom,
    ! [D: int,P4: int > $o,P: int > $o] :
      ( ( ord_less_int @ zero_zero_int @ D )
     => ( ! [X2: int,K2: int] :
            ( ( P4 @ X2 )
            = ( P4 @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D ) ) ) )
       => ( ? [Z5: int] :
            ! [X2: int] :
              ( ( ord_less_int @ Z5 @ X2 )
             => ( ( P @ X2 )
                = ( P4 @ X2 ) ) )
         => ( ? [X_12: int] : ( P4 @ X_12 )
           => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).

% plusinfinity
thf(fact_1207_minusinfinity,axiom,
    ! [D: int,P1: int > $o,P: int > $o] :
      ( ( ord_less_int @ zero_zero_int @ D )
     => ( ! [X2: int,K2: int] :
            ( ( P1 @ X2 )
            = ( P1 @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D ) ) ) )
       => ( ? [Z5: int] :
            ! [X2: int] :
              ( ( ord_less_int @ X2 @ Z5 )
             => ( ( P @ X2 )
                = ( P1 @ X2 ) ) )
         => ( ? [X_12: int] : ( P1 @ X_12 )
           => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).

% minusinfinity
thf(fact_1208_decr__mult__lemma,axiom,
    ! [D: int,P: int > $o,K: int] :
      ( ( ord_less_int @ zero_zero_int @ D )
     => ( ! [X2: int] :
            ( ( P @ X2 )
           => ( P @ ( minus_minus_int @ X2 @ D ) ) )
       => ( ( ord_less_eq_int @ zero_zero_int @ K )
         => ! [X4: int] :
              ( ( P @ X4 )
             => ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).

% decr_mult_lemma
thf(fact_1209_incr__mult__lemma,axiom,
    ! [D: int,P: int > $o,K: int] :
      ( ( ord_less_int @ zero_zero_int @ D )
     => ( ! [X2: int] :
            ( ( P @ X2 )
           => ( P @ ( plus_plus_int @ X2 @ D ) ) )
       => ( ( ord_less_eq_int @ zero_zero_int @ K )
         => ! [X4: int] :
              ( ( P @ X4 )
             => ( P @ ( plus_plus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).

% incr_mult_lemma
thf(fact_1210_int__one__le__iff__zero__less,axiom,
    ! [Z2: int] :
      ( ( ord_less_eq_int @ one_one_int @ Z2 )
      = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).

% int_one_le_iff_zero_less
thf(fact_1211_pos__zmult__eq__1__iff,axiom,
    ! [M2: int,N2: int] :
      ( ( ord_less_int @ zero_zero_int @ M2 )
     => ( ( ( times_times_int @ M2 @ N2 )
          = one_one_int )
        = ( ( M2 = one_one_int )
          & ( N2 = one_one_int ) ) ) ) ).

% pos_zmult_eq_1_iff
thf(fact_1212_odd__less__0__iff,axiom,
    ! [Z2: int] :
      ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 ) @ zero_zero_int )
      = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).

% odd_less_0_iff
thf(fact_1213_zless__add1__eq,axiom,
    ! [W: int,Z2: int] :
      ( ( ord_less_int @ W @ ( plus_plus_int @ Z2 @ one_one_int ) )
      = ( ( ord_less_int @ W @ Z2 )
        | ( W = Z2 ) ) ) ).

% zless_add1_eq
thf(fact_1214_int__gr__induct,axiom,
    ! [K: int,I: int,P: int > $o] :
      ( ( ord_less_int @ K @ I )
     => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
       => ( ! [I3: int] :
              ( ( ord_less_int @ K @ I3 )
             => ( ( P @ I3 )
               => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
         => ( P @ I ) ) ) ) ).

% int_gr_induct
thf(fact_1215_verit__la__generic,axiom,
    ! [A: int,X: int] :
      ( ( ord_less_eq_int @ A @ X )
      | ( A = X )
      | ( ord_less_eq_int @ X @ A ) ) ).

% verit_la_generic
thf(fact_1216_infinite__UNIV__nat,axiom,
    ~ ( finite_finite_nat @ top_top_set_nat ) ).

% infinite_UNIV_nat
thf(fact_1217_lemma__interval,axiom,
    ! [A: real,X: real,B: real] :
      ( ( ord_less_real @ A @ X )
     => ( ( ord_less_real @ X @ B )
       => ? [D4: real] :
            ( ( ord_less_real @ zero_zero_real @ D4 )
            & ! [Y5: real] :
                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D4 )
               => ( ( ord_less_eq_real @ A @ Y5 )
                  & ( ord_less_eq_real @ Y5 @ B ) ) ) ) ) ) ).

% lemma_interval
thf(fact_1218_lemma__interval__lt,axiom,
    ! [A: real,X: real,B: real] :
      ( ( ord_less_real @ A @ X )
     => ( ( ord_less_real @ X @ B )
       => ? [D4: real] :
            ( ( ord_less_real @ zero_zero_real @ D4 )
            & ! [Y5: real] :
                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D4 )
               => ( ( ord_less_real @ A @ Y5 )
                  & ( ord_less_real @ Y5 @ B ) ) ) ) ) ) ).

% lemma_interval_lt
thf(fact_1219_finite__interval__int4,axiom,
    ! [A: int,B: int] :
      ( finite_finite_int
      @ ( collect_int
        @ ^ [I2: int] :
            ( ( ord_less_int @ A @ I2 )
            & ( ord_less_int @ I2 @ B ) ) ) ) ).

% finite_interval_int4
thf(fact_1220_infinite__UNIV__int,axiom,
    ~ ( finite_finite_int @ top_top_set_int ) ).

% infinite_UNIV_int
thf(fact_1221_zmult__zless__mono2,axiom,
    ! [I: int,J: int,K: int] :
      ( ( ord_less_int @ I @ J )
     => ( ( ord_less_int @ zero_zero_int @ K )
       => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).

% zmult_zless_mono2
thf(fact_1222_less__int__code_I1_J,axiom,
    ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).

% less_int_code(1)
thf(fact_1223_finite__less__ub,axiom,
    ! [F: nat > nat,U: nat] :
      ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
     => ( finite_finite_nat
        @ ( collect_nat
          @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).

% finite_less_ub
thf(fact_1224_finite__M__bounded__by__nat,axiom,
    ! [P: nat > $o,I: nat] :
      ( finite_finite_nat
      @ ( collect_nat
        @ ^ [K4: nat] :
            ( ( P @ K4 )
            & ( ord_less_nat @ K4 @ I ) ) ) ) ).

% finite_M_bounded_by_nat
thf(fact_1225_nat__ivt__aux,axiom,
    ! [N2: nat,F: nat > int,K: int] :
      ( ! [I3: nat] :
          ( ( ord_less_nat @ I3 @ N2 )
         => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
     => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
       => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
         => ? [I3: nat] :
              ( ( ord_less_eq_nat @ I3 @ N2 )
              & ( ( F @ I3 )
                = K ) ) ) ) ) ).

% nat_ivt_aux
thf(fact_1226_nat__power__eq__Suc__0__iff,axiom,
    ! [X: nat,M2: nat] :
      ( ( ( power_power_nat @ X @ M2 )
        = ( suc @ zero_zero_nat ) )
      = ( ( M2 = zero_zero_nat )
        | ( X
          = ( suc @ zero_zero_nat ) ) ) ) ).

% nat_power_eq_Suc_0_iff
thf(fact_1227_power__Suc__0,axiom,
    ! [N2: nat] :
      ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N2 )
      = ( suc @ zero_zero_nat ) ) ).

% power_Suc_0
thf(fact_1228_nat__zero__less__power__iff,axiom,
    ! [X: nat,N2: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N2 ) )
      = ( ( ord_less_nat @ zero_zero_nat @ X )
        | ( N2 = zero_zero_nat ) ) ) ).

% nat_zero_less_power_iff
thf(fact_1229_power__gt__expt,axiom,
    ! [N2: nat,K: nat] :
      ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
     => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).

% power_gt_expt
thf(fact_1230_realpow__pos__nth2,axiom,
    ! [A: real,N2: nat] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ? [R3: real] :
          ( ( ord_less_real @ zero_zero_real @ R3 )
          & ( ( power_power_real @ R3 @ ( suc @ N2 ) )
            = A ) ) ) ).

% realpow_pos_nth2
thf(fact_1231_real__arch__pow,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ one_one_real @ X )
     => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N3 ) ) ) ).

% real_arch_pow
thf(fact_1232_nat__power__less__imp__less,axiom,
    ! [I: nat,M2: nat,N2: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ I )
     => ( ( ord_less_nat @ ( power_power_nat @ I @ M2 ) @ ( power_power_nat @ I @ N2 ) )
       => ( ord_less_nat @ M2 @ N2 ) ) ) ).

% nat_power_less_imp_less
thf(fact_1233_nat__one__le__power,axiom,
    ! [I: nat,N2: nat] :
      ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
     => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N2 ) ) ) ).

% nat_one_le_power
thf(fact_1234_real__arch__pow__inv,axiom,
    ! [Y: real,X: real] :
      ( ( ord_less_real @ zero_zero_real @ Y )
     => ( ( ord_less_real @ X @ one_one_real )
       => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X @ N3 ) @ Y ) ) ) ).

% real_arch_pow_inv
thf(fact_1235_realpow__pos__nth,axiom,
    ! [N2: nat,A: real] :
      ( ( ord_less_nat @ zero_zero_nat @ N2 )
     => ( ( ord_less_real @ zero_zero_real @ A )
       => ? [R3: real] :
            ( ( ord_less_real @ zero_zero_real @ R3 )
            & ( ( power_power_real @ R3 @ N2 )
              = A ) ) ) ) ).

% realpow_pos_nth
thf(fact_1236_realpow__pos__nth__unique,axiom,
    ! [N2: nat,A: real] :
      ( ( ord_less_nat @ zero_zero_nat @ N2 )
     => ( ( ord_less_real @ zero_zero_real @ A )
       => ? [X2: real] :
            ( ( ord_less_real @ zero_zero_real @ X2 )
            & ( ( power_power_real @ X2 @ N2 )
              = A )
            & ! [Y5: real] :
                ( ( ( ord_less_real @ zero_zero_real @ Y5 )
                  & ( ( power_power_real @ Y5 @ N2 )
                    = A ) )
               => ( Y5 = X2 ) ) ) ) ) ).

% realpow_pos_nth_unique
thf(fact_1237_nat__intermed__int__val,axiom,
    ! [M2: nat,N2: nat,F: nat > int,K: int] :
      ( ! [I3: nat] :
          ( ( ( ord_less_eq_nat @ M2 @ I3 )
            & ( ord_less_nat @ I3 @ N2 ) )
         => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
     => ( ( ord_less_eq_nat @ M2 @ N2 )
       => ( ( ord_less_eq_int @ ( F @ M2 ) @ K )
         => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
           => ? [I3: nat] :
                ( ( ord_less_eq_nat @ M2 @ I3 )
                & ( ord_less_eq_nat @ I3 @ N2 )
                & ( ( F @ I3 )
                  = K ) ) ) ) ) ) ).

% nat_intermed_int_val
thf(fact_1238_finite__nth__roots,axiom,
    ! [N2: nat,C: complex] :
      ( ( ord_less_nat @ zero_zero_nat @ N2 )
     => ( finite3207457112153483333omplex
        @ ( collect_complex
          @ ^ [Z3: complex] :
              ( ( power_power_complex @ Z3 @ N2 )
              = C ) ) ) ) ).

% finite_nth_roots
thf(fact_1239_sum__nth__roots,axiom,
    ! [N2: nat,C: complex] :
      ( ( ord_less_nat @ one_one_nat @ N2 )
     => ( ( groups7754918857620584856omplex
          @ ^ [X3: complex] : X3
          @ ( collect_complex
            @ ^ [Z3: complex] :
                ( ( power_power_complex @ Z3 @ N2 )
                = C ) ) )
        = zero_zero_complex ) ) ).

% sum_nth_roots
thf(fact_1240_sum__roots__unity,axiom,
    ! [N2: nat] :
      ( ( ord_less_nat @ one_one_nat @ N2 )
     => ( ( groups7754918857620584856omplex
          @ ^ [X3: complex] : X3
          @ ( collect_complex
            @ ^ [Z3: complex] :
                ( ( power_power_complex @ Z3 @ N2 )
                = one_one_complex ) ) )
        = zero_zero_complex ) ) ).

% sum_roots_unity
thf(fact_1241_ln__inj__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ zero_zero_real @ Y )
       => ( ( ( ln_ln_real @ X )
            = ( ln_ln_real @ Y ) )
          = ( X = Y ) ) ) ) ).

% ln_inj_iff
thf(fact_1242_ln__less__cancel__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ zero_zero_real @ Y )
       => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
          = ( ord_less_real @ X @ Y ) ) ) ) ).

% ln_less_cancel_iff
thf(fact_1243_ln__le__cancel__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ zero_zero_real @ Y )
       => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
          = ( ord_less_eq_real @ X @ Y ) ) ) ) ).

% ln_le_cancel_iff
thf(fact_1244_ln__less__zero__iff,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
        = ( ord_less_real @ X @ one_one_real ) ) ) ).

% ln_less_zero_iff
thf(fact_1245_ln__gt__zero__iff,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
        = ( ord_less_real @ one_one_real @ X ) ) ) ).

% ln_gt_zero_iff
thf(fact_1246_ln__eq__zero__iff,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ( ln_ln_real @ X )
          = zero_zero_real )
        = ( X = one_one_real ) ) ) ).

% ln_eq_zero_iff
thf(fact_1247_ln__le__zero__iff,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
        = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).

% ln_le_zero_iff
thf(fact_1248_ln__ge__zero__iff,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
        = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).

% ln_ge_zero_iff
thf(fact_1249_partial__nav__just__cash,axiom,
    ! [A: real,N2: nat] :
      ( ( groups6591440286371151544t_real @ ( risk_F170160801229183585ccount @ ( risk_Free_just_cash @ A ) ) @ ( set_ord_atMost_nat @ N2 ) )
      = A ) ).

% partial_nav_just_cash
thf(fact_1250_ln__ge__zero,axiom,
    ! [X: real] :
      ( ( ord_less_eq_real @ one_one_real @ X )
     => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).

% ln_ge_zero
thf(fact_1251_ln__gt__zero__imp__gt__one,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
     => ( ( ord_less_real @ zero_zero_real @ X )
       => ( ord_less_real @ one_one_real @ X ) ) ) ).

% ln_gt_zero_imp_gt_one
thf(fact_1252_ln__less__zero,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ X @ one_one_real )
       => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).

% ln_less_zero
thf(fact_1253_ln__gt__zero,axiom,
    ! [X: real] :
      ( ( ord_less_real @ one_one_real @ X )
     => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).

% ln_gt_zero
thf(fact_1254_ln__less__self,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).

% ln_less_self
thf(fact_1255_ln__bound,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).

% ln_bound
thf(fact_1256_ln__ge__zero__imp__ge__one,axiom,
    ! [X: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
     => ( ( ord_less_real @ zero_zero_real @ X )
       => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).

% ln_ge_zero_imp_ge_one
thf(fact_1257_ln__add__one__self__le__self,axiom,
    ! [X: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).

% ln_add_one_self_le_self
thf(fact_1258_ln__mult,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ zero_zero_real @ Y )
       => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
          = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).

% ln_mult
thf(fact_1259_ln__eq__minus__one,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ( ln_ln_real @ X )
          = ( minus_minus_real @ X @ one_one_real ) )
       => ( X = one_one_real ) ) ) ).

% ln_eq_minus_one
thf(fact_1260_ln__le__minus__one,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).

% ln_le_minus_one
thf(fact_1261_less__eq__account__def,axiom,
    ( ord_le4245800335709223507ccount
    = ( ^ [Alpha_12: risk_Free_account,Alpha_22: risk_Free_account] :
        ! [N: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ ( risk_F170160801229183585ccount @ Alpha_12 ) @ ( set_ord_atMost_nat @ N ) ) @ ( groups6591440286371151544t_real @ ( risk_F170160801229183585ccount @ Alpha_22 ) @ ( set_ord_atMost_nat @ N ) ) ) ) ) ).

% less_eq_account_def
thf(fact_1262_strictly__solvent__def,axiom,
    ( risk_F1636578016437888323olvent
    = ( ^ [Alpha2: risk_Free_account] :
        ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( groups6591440286371151544t_real @ ( risk_F170160801229183585ccount @ Alpha2 ) @ ( set_ord_atMost_nat @ N ) ) ) ) ) ).

% strictly_solvent_def
thf(fact_1263_polynomial__product__nat,axiom,
    ! [M2: nat,A: nat > nat,N2: nat,B: nat > nat,X: nat] :
      ( ! [I3: nat] :
          ( ( ord_less_nat @ M2 @ I3 )
         => ( ( A @ I3 )
            = zero_zero_nat ) )
     => ( ! [J2: nat] :
            ( ( ord_less_nat @ N2 @ J2 )
           => ( ( B @ J2 )
              = zero_zero_nat ) )
       => ( ( times_times_nat
            @ ( groups3542108847815614940at_nat
              @ ^ [I2: nat] : ( times_times_nat @ ( A @ I2 ) @ ( power_power_nat @ X @ I2 ) )
              @ ( set_ord_atMost_nat @ M2 ) )
            @ ( groups3542108847815614940at_nat
              @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
              @ ( set_ord_atMost_nat @ N2 ) ) )
          = ( groups3542108847815614940at_nat
            @ ^ [R4: nat] :
                ( times_times_nat
                @ ( groups3542108847815614940at_nat
                  @ ^ [K4: nat] : ( times_times_nat @ ( A @ K4 ) @ ( B @ ( minus_minus_nat @ R4 @ K4 ) ) )
                  @ ( set_ord_atMost_nat @ R4 ) )
                @ ( power_power_nat @ X @ R4 ) )
            @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ) ) ).

% polynomial_product_nat
thf(fact_1264_net__asset__value__shortest__period__ge,axiom,
    ! [Alpha: risk_Free_account,N2: nat] :
      ( ( ord_less_eq_nat @ ( risk_F4612863212915232279period @ Alpha ) @ N2 )
     => ( ( risk_F2906766666041932210_value @ Alpha )
        = ( groups6591440286371151544t_real @ ( risk_F170160801229183585ccount @ Alpha ) @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).

% net_asset_value_shortest_period_ge
thf(fact_1265_complex__mod__triangle__ineq2,axiom,
    ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).

% complex_mod_triangle_ineq2
thf(fact_1266_shortest__period___092_060pi_062,axiom,
    ! [Alpha: risk_Free_account,I: nat] :
      ( ( ( risk_F170160801229183585ccount @ Alpha @ I )
       != zero_zero_real )
     => ( ( risk_F170160801229183585ccount @ Alpha @ ( risk_F4612863212915232279period @ Alpha ) )
       != zero_zero_real ) ) ).

% shortest_period_\<pi>
thf(fact_1267_greater__than__shortest__period__zero,axiom,
    ! [Alpha: risk_Free_account,M2: nat] :
      ( ( ord_less_nat @ ( risk_F4612863212915232279period @ Alpha ) @ M2 )
     => ( ( risk_F170160801229183585ccount @ Alpha @ M2 )
        = zero_zero_real ) ) ).

% greater_than_shortest_period_zero
thf(fact_1268_shortest__period__bound,axiom,
    ! [Alpha: risk_Free_account,I: nat] :
      ( ( ( risk_F170160801229183585ccount @ Alpha @ I )
       != zero_zero_real )
     => ( ord_less_eq_nat @ I @ ( risk_F4612863212915232279period @ Alpha ) ) ) ).

% shortest_period_bound
thf(fact_1269_net__asset__value__alt__def,axiom,
    ( risk_F2906766666041932210_value
    = ( ^ [Alpha2: risk_Free_account] : ( groups6591440286371151544t_real @ ( risk_F170160801229183585ccount @ Alpha2 ) @ ( set_ord_atMost_nat @ ( risk_F4612863212915232279period @ Alpha2 ) ) ) ) ) ).

% net_asset_value_alt_def
thf(fact_1270_Rep__account__uminus,axiom,
    ! [Alpha: risk_Free_account] :
      ( ( risk_F170160801229183585ccount @ ( uminus3377898441596595772ccount @ Alpha ) )
      = ( ^ [N: nat] : ( uminus_uminus_real @ ( risk_F170160801229183585ccount @ Alpha @ N ) ) ) ) ).

% Rep_account_uminus
thf(fact_1271_just__cash__uminus,axiom,
    ! [A: real] :
      ( ( uminus3377898441596595772ccount @ ( risk_Free_just_cash @ A ) )
      = ( risk_Free_just_cash @ ( uminus_uminus_real @ A ) ) ) ).

% just_cash_uminus
thf(fact_1272_real__add__minus__iff,axiom,
    ! [X: real,A: real] :
      ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
        = zero_zero_real )
      = ( X = A ) ) ).

% real_add_minus_iff
thf(fact_1273_artanh__minus__real,axiom,
    ! [X: real] :
      ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
     => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
        = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).

% artanh_minus_real

% Helper facts (3)
thf(help_If_3_1_If_001t__Real__Oreal_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
    ! [X: real,Y: real] :
      ( ( if_real @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
    ! [X: real,Y: real] :
      ( ( if_real @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ( member_nat_real
    @ ^ [N: nat] : ( times_times_real @ ( minus_minus_real @ one_one_real @ ( rho @ N ) ) @ ( risk_F170160801229183585ccount @ alpha @ N ) )
    @ ( ordina1579063754167848977al_nat @ zero_zero_real @ top_top_set_nat ) ) ).

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