%------------------------------------------------------------------------------
% 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_00743_022944__5861688_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1348 ( 512 unt;  69 typ;   0 def)
%            Number of atoms       : 3720 (1103 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 10106 ( 345   ~;  89   |; 174   &;7926   @)
%                                         (   0 <=>;1572  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :  269 ( 269   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   66 (  63 usr;  11 con; 0-3 aty)
%            Number of variables   : 3515 ( 252   ^;3216   !;  47   ?;3515   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 15:57:07.410
%------------------------------------------------------------------------------
% Could-be-implicit typings (6)
thf(ty_n_t__Risk____Free____Lending__Oaccount,type,
    risk_Free_account: $tType ).

thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
    set_real: $tType ).

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

thf(ty_n_t__Num__Onum,type,
    num: $tType ).

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

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

% Explicit typings (63)
thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal,type,
    archim7802044766580827645g_real: real > int ).

thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
    inverse_inverse_real: real > real ).

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__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__Num__Onum,type,
    plus_plus_num: num > num > num ).

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__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__Int__Oint,type,
    uminus_uminus_int: int > int ).

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__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_If_001t__Int__Oint,type,
    if_int: $o > int > int > int ).

thf(sy_c_If_001t__Nat__Onat,type,
    if_nat: $o > nat > nat > nat ).

thf(sy_c_If_001t__Num__Onum,type,
    if_num: $o > num > num > num ).

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

thf(sy_c_If_001t__Risk____Free____Lending__Oaccount,type,
    if_Risk_Free_account: $o > risk_Free_account > risk_Free_account > risk_Free_account ).

thf(sy_c_Int_Onat,type,
    nat2: int > nat ).

thf(sy_c_Int_Opower__int_001t__Real__Oreal,type,
    power_int_real: real > int > real ).

thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
    ring_1_of_int_real: int > real ).

thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
    semiri1314217659103216013at_int: nat > int ).

thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
    semiri5074537144036343181t_real: nat > real ).

thf(sy_c_Num_Onum_OBit0,type,
    bit0: num > num ).

thf(sy_c_Num_Onum__of__nat,type,
    num_of_nat: nat > num ).

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__Num__Onum,type,
    ord_less_num: num > num > $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__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__Num__Onum,type,
    ord_less_eq_num: num > num > $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_Omax_001t__Int__Oint,type,
    ord_max_int: int > int > int ).

thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
    ord_max_nat: nat > nat > nat ).

thf(sy_c_Orderings_Oord__class_Omax_001t__Num__Onum,type,
    ord_max_num: num > num > num ).

thf(sy_c_Orderings_Oord__class_Omax_001t__Real__Oreal,type,
    ord_max_real: real > real > real ).

thf(sy_c_Orderings_Oord__class_Omax_001t__Risk____Free____Lending__Oaccount,type,
    ord_ma8558070474537249246ccount: risk_Free_account > risk_Free_account > risk_Free_account ).

thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
    power_power_int: int > nat > int ).

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_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
    divide_divide_real: real > real > real ).

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_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_Ovalid__transfer,type,
    risk_F1023690899723030139ansfer: risk_Free_account > risk_Free_account > $o ).

thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
    collect_real: ( real > $o ) > set_real ).

thf(sy_c_Transcendental_Olog,type,
    log: real > real > real ).

thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
    powr_real: real > real > real ).

thf(sy_c_member_001t__Real__Oreal,type,
    member_real: real > set_real > $o ).

thf(sy_v__092_060alpha_062,type,
    alpha: risk_Free_account ).

thf(sy_v__092_060beta_062,type,
    beta: risk_Free_account ).

% Relevant facts (1267)
thf(fact_0_False,axiom,
    ~ ! [I: nat] :
        ( ( risk_F170160801229183585ccount @ ( plus_p1863581527469039996ccount @ alpha @ beta ) @ I )
        = zero_zero_real ) ).

% False
thf(fact_1__092_060open_062_092_060forall_062i_062max_A_Ishortest__period_A_092_060alpha_062_J_A_Ishortest__period_A_092_060beta_062_J_O_A_092_060pi_062_A_I_092_060alpha_062_A_L_A_092_060beta_062_J_Ai_A_061_A0_092_060close_062,axiom,
    ! [I2: nat] :
      ( ( ord_less_nat @ ( ord_max_nat @ ( risk_F4612863212915232279period @ alpha ) @ ( risk_F4612863212915232279period @ beta ) ) @ I2 )
     => ( ( risk_F170160801229183585ccount @ ( plus_p1863581527469039996ccount @ alpha @ beta ) @ I2 )
        = zero_zero_real ) ) ).

% \<open>\<forall>i>max (shortest_period \<alpha>) (shortest_period \<beta>). \<pi> (\<alpha> + \<beta>) i = 0\<close>
thf(fact_2__092_060open_062shortest__period_A_092_060alpha_062_A_092_060le_062_Amax_A_Ishortest__period_A_092_060alpha_062_J_A_Ishortest__period_A_092_060beta_062_J_092_060close_062,axiom,
    ord_less_eq_nat @ ( risk_F4612863212915232279period @ alpha ) @ ( ord_max_nat @ ( risk_F4612863212915232279period @ alpha ) @ ( risk_F4612863212915232279period @ beta ) ) ).

% \<open>shortest_period \<alpha> \<le> max (shortest_period \<alpha>) (shortest_period \<beta>)\<close>
thf(fact_3__092_060open_062shortest__period_A_092_060beta_062_A_092_060le_062_Amax_A_Ishortest__period_A_092_060alpha_062_J_A_Ishortest__period_A_092_060beta_062_J_092_060close_062,axiom,
    ord_less_eq_nat @ ( risk_F4612863212915232279period @ beta ) @ ( ord_max_nat @ ( risk_F4612863212915232279period @ alpha ) @ ( risk_F4612863212915232279period @ beta ) ) ).

% \<open>shortest_period \<beta> \<le> max (shortest_period \<alpha>) (shortest_period \<beta>)\<close>
thf(fact_4__092_060open_062_092_060forall_062i_062shortest__period_A_092_060alpha_062_O_A_092_060pi_062_A_092_060alpha_062_Ai_A_061_A0_092_060close_062,axiom,
    ! [I2: nat] :
      ( ( ord_less_nat @ ( risk_F4612863212915232279period @ alpha ) @ I2 )
     => ( ( risk_F170160801229183585ccount @ alpha @ I2 )
        = zero_zero_real ) ) ).

% \<open>\<forall>i>shortest_period \<alpha>. \<pi> \<alpha> i = 0\<close>
thf(fact_5__092_060open_062_092_060forall_062i_062shortest__period_A_092_060beta_062_O_A_092_060pi_062_A_092_060beta_062_Ai_A_061_A0_092_060close_062,axiom,
    ! [I2: nat] :
      ( ( ord_less_nat @ ( risk_F4612863212915232279period @ beta ) @ I2 )
     => ( ( risk_F170160801229183585ccount @ beta @ I2 )
        = zero_zero_real ) ) ).

% \<open>\<forall>i>shortest_period \<beta>. \<pi> \<beta> i = 0\<close>
thf(fact_6__092_060open_062_092_060forall_062i_062max_A_Ishortest__period_A_092_060alpha_062_J_A_Ishortest__period_A_092_060beta_062_J_O_A_092_060pi_062_A_092_060alpha_062_Ai_A_061_A0_092_060close_062,axiom,
    ! [I2: nat] :
      ( ( ord_less_nat @ ( ord_max_nat @ ( risk_F4612863212915232279period @ alpha ) @ ( risk_F4612863212915232279period @ beta ) ) @ I2 )
     => ( ( risk_F170160801229183585ccount @ alpha @ I2 )
        = zero_zero_real ) ) ).

% \<open>\<forall>i>max (shortest_period \<alpha>) (shortest_period \<beta>). \<pi> \<alpha> i = 0\<close>
thf(fact_7__092_060open_062_092_060forall_062i_062max_A_Ishortest__period_A_092_060alpha_062_J_A_Ishortest__period_A_092_060beta_062_J_O_A_092_060pi_062_A_092_060beta_062_Ai_A_061_A0_092_060close_062,axiom,
    ! [I2: nat] :
      ( ( ord_less_nat @ ( ord_max_nat @ ( risk_F4612863212915232279period @ alpha ) @ ( risk_F4612863212915232279period @ beta ) ) @ I2 )
     => ( ( risk_F170160801229183585ccount @ beta @ I2 )
        = zero_zero_real ) ) ).

% \<open>\<forall>i>max (shortest_period \<alpha>) (shortest_period \<beta>). \<pi> \<beta> i = 0\<close>
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_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_10_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_11_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_12_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_13_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_14_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_15_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_16_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_17_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_18_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_19_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_20_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_21_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_22_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_23_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_24_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_25_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_26_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_27_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_28_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_29_max_Oabsorb1,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( ord_max_nat @ A @ B )
        = A ) ) ).

% max.absorb1
thf(fact_30_max_Oabsorb1,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ( ord_max_real @ A @ B )
        = A ) ) ).

% max.absorb1
thf(fact_31_max_Oabsorb1,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ( ord_max_int @ A @ B )
        = A ) ) ).

% max.absorb1
thf(fact_32_max_Oabsorb1,axiom,
    ! [B: num,A: num] :
      ( ( ord_less_eq_num @ B @ A )
     => ( ( ord_max_num @ A @ B )
        = A ) ) ).

% max.absorb1
thf(fact_33_max_Oabsorb2,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_max_nat @ A @ B )
        = B ) ) ).

% max.absorb2
thf(fact_34_max_Oabsorb2,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_max_real @ A @ B )
        = B ) ) ).

% max.absorb2
thf(fact_35_max_Oabsorb2,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_max_int @ A @ B )
        = B ) ) ).

% max.absorb2
thf(fact_36_max_Oabsorb2,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_max_num @ A @ B )
        = B ) ) ).

% max.absorb2
thf(fact_37_max_Obounded__iff,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
      = ( ( ord_less_eq_nat @ B @ A )
        & ( ord_less_eq_nat @ C @ A ) ) ) ).

% max.bounded_iff
thf(fact_38_max_Obounded__iff,axiom,
    ! [B: real,C: real,A: real] :
      ( ( ord_less_eq_real @ ( ord_max_real @ B @ C ) @ A )
      = ( ( ord_less_eq_real @ B @ A )
        & ( ord_less_eq_real @ C @ A ) ) ) ).

% max.bounded_iff
thf(fact_39_max_Obounded__iff,axiom,
    ! [B: int,C: int,A: int] :
      ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
      = ( ( ord_less_eq_int @ B @ A )
        & ( ord_less_eq_int @ C @ A ) ) ) ).

% max.bounded_iff
thf(fact_40_max_Obounded__iff,axiom,
    ! [B: num,C: num,A: num] :
      ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
      = ( ( ord_less_eq_num @ B @ A )
        & ( ord_less_eq_num @ C @ A ) ) ) ).

% max.bounded_iff
thf(fact_41_add_Oright__neutral,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ) ).

% add.right_neutral
thf(fact_42_add_Oright__neutral,axiom,
    ! [A: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ A @ zero_z1425366712893667068ccount )
      = A ) ).

% add.right_neutral
thf(fact_43_add_Oright__neutral,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ A @ zero_zero_nat )
      = A ) ).

% add.right_neutral
thf(fact_44_add_Oright__neutral,axiom,
    ! [A: int] :
      ( ( plus_plus_int @ A @ zero_zero_int )
      = A ) ).

% add.right_neutral
thf(fact_45_double__zero__sym,axiom,
    ! [A: real] :
      ( ( zero_zero_real
        = ( plus_plus_real @ A @ A ) )
      = ( A = zero_zero_real ) ) ).

% double_zero_sym
thf(fact_46_double__zero__sym,axiom,
    ! [A: int] :
      ( ( zero_zero_int
        = ( plus_plus_int @ A @ A ) )
      = ( A = zero_zero_int ) ) ).

% double_zero_sym
thf(fact_47_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_48_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_49_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_50_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_51_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_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: nat,A: nat,C: nat] :
      ( ( ( plus_plus_nat @ B @ A )
        = ( plus_plus_nat @ C @ A ) )
      = ( B = C ) ) ).

% add_right_cancel
thf(fact_54_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_55_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_56_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_57_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_58_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_59_max_Oright__idem,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_max_nat @ ( ord_max_nat @ A @ B ) @ B )
      = ( ord_max_nat @ A @ B ) ) ).

% max.right_idem
thf(fact_60_max_Oleft__idem,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_max_nat @ A @ ( ord_max_nat @ A @ B ) )
      = ( ord_max_nat @ A @ B ) ) ).

% max.left_idem
thf(fact_61_max_Oidem,axiom,
    ! [A: nat] :
      ( ( ord_max_nat @ A @ A )
      = A ) ).

% max.idem
thf(fact_62_le__zero__eq,axiom,
    ! [N: nat] :
      ( ( ord_less_eq_nat @ N @ zero_zero_nat )
      = ( N = zero_zero_nat ) ) ).

% le_zero_eq
thf(fact_63_not__gr__zero,axiom,
    ! [N: nat] :
      ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
      = ( N = zero_zero_nat ) ) ).

% not_gr_zero
thf(fact_64_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_65_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_66_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_67_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_68_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_69_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_70_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_71_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_72_add__0,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ zero_zero_real @ A )
      = A ) ).

% add_0
thf(fact_73_add__0,axiom,
    ! [A: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ zero_z1425366712893667068ccount @ A )
      = A ) ).

% add_0
thf(fact_74_add__0,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ zero_zero_nat @ A )
      = A ) ).

% add_0
thf(fact_75_add__0,axiom,
    ! [A: int] :
      ( ( plus_plus_int @ zero_zero_int @ A )
      = A ) ).

% add_0
thf(fact_76_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_77_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_78_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_79_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_80_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_81_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_82_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_83_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_84_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_85_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_86_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_87_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_88_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_89_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_90_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_91_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_92_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_93_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_94_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_95_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_96_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_97_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_98_max__less__iff__conj,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
      = ( ( ord_less_nat @ X @ Z )
        & ( ord_less_nat @ Y @ Z ) ) ) ).

% max_less_iff_conj
thf(fact_99_max__less__iff__conj,axiom,
    ! [X: real,Y: real,Z: real] :
      ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z )
      = ( ( ord_less_real @ X @ Z )
        & ( ord_less_real @ Y @ Z ) ) ) ).

% max_less_iff_conj
thf(fact_100_max__less__iff__conj,axiom,
    ! [X: int,Y: int,Z: int] :
      ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
      = ( ( ord_less_int @ X @ Z )
        & ( ord_less_int @ Y @ Z ) ) ) ).

% max_less_iff_conj
thf(fact_101_max__less__iff__conj,axiom,
    ! [X: num,Y: num,Z: num] :
      ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z )
      = ( ( ord_less_num @ X @ Z )
        & ( ord_less_num @ Y @ Z ) ) ) ).

% max_less_iff_conj
thf(fact_102_max_Oabsorb4,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_max_nat @ A @ B )
        = B ) ) ).

% max.absorb4
thf(fact_103_max_Oabsorb4,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_max_real @ A @ B )
        = B ) ) ).

% max.absorb4
thf(fact_104_max_Oabsorb4,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_max_int @ A @ B )
        = B ) ) ).

% max.absorb4
thf(fact_105_max_Oabsorb4,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_num @ A @ B )
     => ( ( ord_max_num @ A @ B )
        = B ) ) ).

% max.absorb4
thf(fact_106_max_Oabsorb3,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_nat @ B @ A )
     => ( ( ord_max_nat @ A @ B )
        = A ) ) ).

% max.absorb3
thf(fact_107_max_Oabsorb3,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_real @ B @ A )
     => ( ( ord_max_real @ A @ B )
        = A ) ) ).

% max.absorb3
thf(fact_108_max_Oabsorb3,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_int @ B @ A )
     => ( ( ord_max_int @ A @ B )
        = A ) ) ).

% max.absorb3
thf(fact_109_max_Oabsorb3,axiom,
    ! [B: num,A: num] :
      ( ( ord_less_num @ B @ A )
     => ( ( ord_max_num @ A @ B )
        = A ) ) ).

% max.absorb3
thf(fact_110_Rep__account__zero,axiom,
    ( ( risk_F170160801229183585ccount @ zero_z1425366712893667068ccount )
    = ( ^ [Uu: nat] : zero_zero_real ) ) ).

% Rep_account_zero
thf(fact_111_Rep__account__plus,axiom,
    ! [Alpha_1: risk_Free_account,Alpha_2: risk_Free_account] :
      ( ( risk_F170160801229183585ccount @ ( plus_p1863581527469039996ccount @ Alpha_1 @ Alpha_2 ) )
      = ( ^ [N2: nat] : ( plus_plus_real @ ( risk_F170160801229183585ccount @ Alpha_1 @ N2 ) @ ( risk_F170160801229183585ccount @ Alpha_2 @ N2 ) ) ) ) ).

% Rep_account_plus
thf(fact_112_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_113_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_114_mem__Collect__eq,axiom,
    ! [A: real,P: real > $o] :
      ( ( member_real @ A @ ( collect_real @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_115_Collect__mem__eq,axiom,
    ! [A2: set_real] :
      ( ( collect_real
        @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_116_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_117_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_118_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_119_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_120_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_121_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_122_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_123_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_124_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_125_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_126_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_127_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_128_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_129_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_130_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_131_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_132_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_133_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_134_zero__less__iff__neq__zero,axiom,
    ! [N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
      = ( N != zero_zero_nat ) ) ).

% zero_less_iff_neq_zero
thf(fact_135_gr__implies__not__zero,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
     => ( N != zero_zero_nat ) ) ).

% gr_implies_not_zero
thf(fact_136_not__less__zero,axiom,
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ zero_zero_nat ) ).

% not_less_zero
thf(fact_137_gr__zeroI,axiom,
    ! [N: nat] :
      ( ( N != zero_zero_nat )
     => ( ord_less_nat @ zero_zero_nat @ N ) ) ).

% gr_zeroI
thf(fact_138_add__less__imp__less__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_imp_less_right
thf(fact_139_add__less__imp__less__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_imp_less_right
thf(fact_140_add__less__imp__less__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_imp_less_right
thf(fact_141_add__less__imp__less__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_imp_less_right
thf(fact_142_add__less__imp__less__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_imp_less_left
thf(fact_143_add__less__imp__less__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_imp_less_left
thf(fact_144_add__less__imp__less__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_imp_less_left
thf(fact_145_add__less__imp__less__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_imp_less_left
thf(fact_146_add__strict__right__mono,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).

% add_strict_right_mono
thf(fact_147_add__strict__right__mono,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ ( plus_p1863581527469039996ccount @ B @ C ) ) ) ).

% add_strict_right_mono
thf(fact_148_add__strict__right__mono,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).

% add_strict_right_mono
thf(fact_149_add__strict__right__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).

% add_strict_right_mono
thf(fact_150_add__strict__left__mono,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).

% add_strict_left_mono
thf(fact_151_add__strict__left__mono,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ C @ A ) @ ( plus_p1863581527469039996ccount @ C @ B ) ) ) ).

% add_strict_left_mono
thf(fact_152_add__strict__left__mono,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).

% add_strict_left_mono
thf(fact_153_add__strict__left__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).

% add_strict_left_mono
thf(fact_154_add__strict__mono,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).

% add_strict_mono
thf(fact_155_add__strict__mono,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account,D: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ord_le2131251472502387783ccount @ C @ D )
       => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ ( plus_p1863581527469039996ccount @ B @ D ) ) ) ) ).

% add_strict_mono
thf(fact_156_add__strict__mono,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_real @ C @ D )
       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).

% add_strict_mono
thf(fact_157_add__strict__mono,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ C @ D )
       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).

% add_strict_mono
thf(fact_158_add__mono__thms__linordered__field_I1_J,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ( ord_less_nat @ I3 @ J )
        & ( K = L ) )
     => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(1)
thf(fact_159_add__mono__thms__linordered__field_I1_J,axiom,
    ! [I3: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( ord_le2131251472502387783ccount @ I3 @ J )
        & ( K = L ) )
     => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ I3 @ K ) @ ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(1)
thf(fact_160_add__mono__thms__linordered__field_I1_J,axiom,
    ! [I3: real,J: real,K: real,L: real] :
      ( ( ( ord_less_real @ I3 @ J )
        & ( K = L ) )
     => ( ord_less_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(1)
thf(fact_161_add__mono__thms__linordered__field_I1_J,axiom,
    ! [I3: int,J: int,K: int,L: int] :
      ( ( ( ord_less_int @ I3 @ J )
        & ( K = L ) )
     => ( ord_less_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(1)
thf(fact_162_add__mono__thms__linordered__field_I2_J,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ( I3 = J )
        & ( ord_less_nat @ K @ L ) )
     => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(2)
thf(fact_163_add__mono__thms__linordered__field_I2_J,axiom,
    ! [I3: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( I3 = J )
        & ( ord_le2131251472502387783ccount @ K @ L ) )
     => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ I3 @ K ) @ ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(2)
thf(fact_164_add__mono__thms__linordered__field_I2_J,axiom,
    ! [I3: real,J: real,K: real,L: real] :
      ( ( ( I3 = J )
        & ( ord_less_real @ K @ L ) )
     => ( ord_less_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(2)
thf(fact_165_add__mono__thms__linordered__field_I2_J,axiom,
    ! [I3: int,J: int,K: int,L: int] :
      ( ( ( I3 = J )
        & ( ord_less_int @ K @ L ) )
     => ( ord_less_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(2)
thf(fact_166_add__mono__thms__linordered__field_I5_J,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ( ord_less_nat @ I3 @ J )
        & ( ord_less_nat @ K @ L ) )
     => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(5)
thf(fact_167_add__mono__thms__linordered__field_I5_J,axiom,
    ! [I3: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( ord_le2131251472502387783ccount @ I3 @ J )
        & ( ord_le2131251472502387783ccount @ K @ L ) )
     => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ I3 @ K ) @ ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(5)
thf(fact_168_add__mono__thms__linordered__field_I5_J,axiom,
    ! [I3: real,J: real,K: real,L: real] :
      ( ( ( ord_less_real @ I3 @ J )
        & ( ord_less_real @ K @ L ) )
     => ( ord_less_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(5)
thf(fact_169_add__mono__thms__linordered__field_I5_J,axiom,
    ! [I3: int,J: int,K: int,L: int] :
      ( ( ( ord_less_int @ I3 @ J )
        & ( ord_less_int @ K @ L ) )
     => ( ord_less_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(5)
thf(fact_170_max_Ostrict__coboundedI2,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( ord_less_nat @ C @ B )
     => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).

% max.strict_coboundedI2
thf(fact_171_max_Ostrict__coboundedI2,axiom,
    ! [C: real,B: real,A: real] :
      ( ( ord_less_real @ C @ B )
     => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).

% max.strict_coboundedI2
thf(fact_172_max_Ostrict__coboundedI2,axiom,
    ! [C: int,B: int,A: int] :
      ( ( ord_less_int @ C @ B )
     => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).

% max.strict_coboundedI2
thf(fact_173_max_Ostrict__coboundedI2,axiom,
    ! [C: num,B: num,A: num] :
      ( ( ord_less_num @ C @ B )
     => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).

% max.strict_coboundedI2
thf(fact_174_max_Ostrict__coboundedI1,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_nat @ C @ A )
     => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).

% max.strict_coboundedI1
thf(fact_175_max_Ostrict__coboundedI1,axiom,
    ! [C: real,A: real,B: real] :
      ( ( ord_less_real @ C @ A )
     => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).

% max.strict_coboundedI1
thf(fact_176_max_Ostrict__coboundedI1,axiom,
    ! [C: int,A: int,B: int] :
      ( ( ord_less_int @ C @ A )
     => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).

% max.strict_coboundedI1
thf(fact_177_max_Ostrict__coboundedI1,axiom,
    ! [C: num,A: num,B: num] :
      ( ( ord_less_num @ C @ A )
     => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).

% max.strict_coboundedI1
thf(fact_178_max_Ostrict__order__iff,axiom,
    ( ord_less_nat
    = ( ^ [B2: nat,A3: nat] :
          ( ( A3
            = ( ord_max_nat @ A3 @ B2 ) )
          & ( A3 != B2 ) ) ) ) ).

% max.strict_order_iff
thf(fact_179_max_Ostrict__order__iff,axiom,
    ( ord_less_real
    = ( ^ [B2: real,A3: real] :
          ( ( A3
            = ( ord_max_real @ A3 @ B2 ) )
          & ( A3 != B2 ) ) ) ) ).

% max.strict_order_iff
thf(fact_180_max_Ostrict__order__iff,axiom,
    ( ord_less_int
    = ( ^ [B2: int,A3: int] :
          ( ( A3
            = ( ord_max_int @ A3 @ B2 ) )
          & ( A3 != B2 ) ) ) ) ).

% max.strict_order_iff
thf(fact_181_max_Ostrict__order__iff,axiom,
    ( ord_less_num
    = ( ^ [B2: num,A3: num] :
          ( ( A3
            = ( ord_max_num @ A3 @ B2 ) )
          & ( A3 != B2 ) ) ) ) ).

% max.strict_order_iff
thf(fact_182_max_Ostrict__boundedE,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
     => ~ ( ( ord_less_nat @ B @ A )
         => ~ ( ord_less_nat @ C @ A ) ) ) ).

% max.strict_boundedE
thf(fact_183_max_Ostrict__boundedE,axiom,
    ! [B: real,C: real,A: real] :
      ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
     => ~ ( ( ord_less_real @ B @ A )
         => ~ ( ord_less_real @ C @ A ) ) ) ).

% max.strict_boundedE
thf(fact_184_max_Ostrict__boundedE,axiom,
    ! [B: int,C: int,A: int] :
      ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
     => ~ ( ( ord_less_int @ B @ A )
         => ~ ( ord_less_int @ C @ A ) ) ) ).

% max.strict_boundedE
thf(fact_185_max_Ostrict__boundedE,axiom,
    ! [B: num,C: num,A: num] :
      ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
     => ~ ( ( ord_less_num @ B @ A )
         => ~ ( ord_less_num @ C @ A ) ) ) ).

% max.strict_boundedE
thf(fact_186_less__max__iff__disj,axiom,
    ! [Z: nat,X: nat,Y: nat] :
      ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
      = ( ( ord_less_nat @ Z @ X )
        | ( ord_less_nat @ Z @ Y ) ) ) ).

% less_max_iff_disj
thf(fact_187_less__max__iff__disj,axiom,
    ! [Z: real,X: real,Y: real] :
      ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y ) )
      = ( ( ord_less_real @ Z @ X )
        | ( ord_less_real @ Z @ Y ) ) ) ).

% less_max_iff_disj
thf(fact_188_less__max__iff__disj,axiom,
    ! [Z: int,X: int,Y: int] :
      ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
      = ( ( ord_less_int @ Z @ X )
        | ( ord_less_int @ Z @ Y ) ) ) ).

% less_max_iff_disj
thf(fact_189_less__max__iff__disj,axiom,
    ! [Z: num,X: num,Y: num] :
      ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y ) )
      = ( ( ord_less_num @ Z @ X )
        | ( ord_less_num @ Z @ Y ) ) ) ).

% less_max_iff_disj
thf(fact_190_zero__reorient,axiom,
    ! [X: real] :
      ( ( zero_zero_real = X )
      = ( X = zero_zero_real ) ) ).

% zero_reorient
thf(fact_191_zero__reorient,axiom,
    ! [X: risk_Free_account] :
      ( ( zero_z1425366712893667068ccount = X )
      = ( X = zero_z1425366712893667068ccount ) ) ).

% zero_reorient
thf(fact_192_zero__reorient,axiom,
    ! [X: nat] :
      ( ( zero_zero_nat = X )
      = ( X = zero_zero_nat ) ) ).

% zero_reorient
thf(fact_193_zero__reorient,axiom,
    ! [X: int] :
      ( ( zero_zero_int = X )
      = ( X = zero_zero_int ) ) ).

% zero_reorient
thf(fact_194_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_195_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_196_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_197_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_198_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_199_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_200_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_201_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_202_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_203_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_204_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_205_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_206_add_Ocommute,axiom,
    ( plus_p1863581527469039996ccount
    = ( ^ [A3: risk_Free_account,B2: risk_Free_account] : ( plus_p1863581527469039996ccount @ B2 @ A3 ) ) ) ).

% add.commute
thf(fact_207_add_Ocommute,axiom,
    ( plus_plus_real
    = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).

% add.commute
thf(fact_208_add_Ocommute,axiom,
    ( plus_plus_nat
    = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).

% add.commute
thf(fact_209_add_Ocommute,axiom,
    ( plus_plus_int
    = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).

% add.commute
thf(fact_210_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_211_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_212_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_213_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_214_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_215_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_216_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_217_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_218_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_219_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_220_group__cancel_Oadd2,axiom,
    ! [B3: risk_Free_account,K: risk_Free_account,B: risk_Free_account,A: risk_Free_account] :
      ( ( B3
        = ( plus_p1863581527469039996ccount @ K @ B ) )
     => ( ( plus_p1863581527469039996ccount @ A @ B3 )
        = ( plus_p1863581527469039996ccount @ K @ ( plus_p1863581527469039996ccount @ A @ B ) ) ) ) ).

% group_cancel.add2
thf(fact_221_group__cancel_Oadd2,axiom,
    ! [B3: real,K: real,B: real,A: real] :
      ( ( B3
        = ( plus_plus_real @ K @ B ) )
     => ( ( plus_plus_real @ A @ B3 )
        = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).

% group_cancel.add2
thf(fact_222_group__cancel_Oadd2,axiom,
    ! [B3: nat,K: nat,B: nat,A: nat] :
      ( ( B3
        = ( plus_plus_nat @ K @ B ) )
     => ( ( plus_plus_nat @ A @ B3 )
        = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).

% group_cancel.add2
thf(fact_223_group__cancel_Oadd2,axiom,
    ! [B3: int,K: int,B: int,A: int] :
      ( ( B3
        = ( plus_plus_int @ K @ B ) )
     => ( ( plus_plus_int @ A @ B3 )
        = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).

% group_cancel.add2
thf(fact_224_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_225_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_226_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_227_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_228_add__mono__thms__linordered__semiring_I4_J,axiom,
    ! [I3: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( I3 = J )
        & ( K = L ) )
     => ( ( plus_p1863581527469039996ccount @ I3 @ K )
        = ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(4)
thf(fact_229_add__mono__thms__linordered__semiring_I4_J,axiom,
    ! [I3: real,J: real,K: real,L: real] :
      ( ( ( I3 = J )
        & ( K = L ) )
     => ( ( plus_plus_real @ I3 @ K )
        = ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(4)
thf(fact_230_add__mono__thms__linordered__semiring_I4_J,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ( I3 = J )
        & ( K = L ) )
     => ( ( plus_plus_nat @ I3 @ K )
        = ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(4)
thf(fact_231_add__mono__thms__linordered__semiring_I4_J,axiom,
    ! [I3: int,J: int,K: int,L: int] :
      ( ( ( I3 = J )
        & ( K = L ) )
     => ( ( plus_plus_int @ I3 @ K )
        = ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(4)
thf(fact_232_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_233_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_234_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_235_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_236_add__less__le__mono,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).

% add_less_le_mono
thf(fact_237_add__less__le__mono,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).

% add_less_le_mono
thf(fact_238_add__less__le__mono,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account,D: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ord_le4245800335709223507ccount @ C @ D )
       => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ ( plus_p1863581527469039996ccount @ B @ D ) ) ) ) ).

% add_less_le_mono
thf(fact_239_add__less__le__mono,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_eq_int @ C @ D )
       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).

% add_less_le_mono
thf(fact_240_add__le__less__mono,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).

% add_le_less_mono
thf(fact_241_add__le__less__mono,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_real @ C @ D )
       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).

% add_le_less_mono
thf(fact_242_add__le__less__mono,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account,D: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ord_le2131251472502387783ccount @ C @ D )
       => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ A @ C ) @ ( plus_p1863581527469039996ccount @ B @ D ) ) ) ) ).

% add_le_less_mono
thf(fact_243_add__le__less__mono,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_int @ C @ D )
       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).

% add_le_less_mono
thf(fact_244_add__mono__thms__linordered__field_I3_J,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ( ord_less_nat @ I3 @ J )
        & ( ord_less_eq_nat @ K @ L ) )
     => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(3)
thf(fact_245_add__mono__thms__linordered__field_I3_J,axiom,
    ! [I3: real,J: real,K: real,L: real] :
      ( ( ( ord_less_real @ I3 @ J )
        & ( ord_less_eq_real @ K @ L ) )
     => ( ord_less_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(3)
thf(fact_246_add__mono__thms__linordered__field_I3_J,axiom,
    ! [I3: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( ord_le2131251472502387783ccount @ I3 @ J )
        & ( ord_le4245800335709223507ccount @ K @ L ) )
     => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ I3 @ K ) @ ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(3)
thf(fact_247_add__mono__thms__linordered__field_I3_J,axiom,
    ! [I3: int,J: int,K: int,L: int] :
      ( ( ( ord_less_int @ I3 @ J )
        & ( ord_less_eq_int @ K @ L ) )
     => ( ord_less_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(3)
thf(fact_248_add__mono__thms__linordered__field_I4_J,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ( ord_less_eq_nat @ I3 @ J )
        & ( ord_less_nat @ K @ L ) )
     => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(4)
thf(fact_249_add__mono__thms__linordered__field_I4_J,axiom,
    ! [I3: real,J: real,K: real,L: real] :
      ( ( ( ord_less_eq_real @ I3 @ J )
        & ( ord_less_real @ K @ L ) )
     => ( ord_less_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(4)
thf(fact_250_add__mono__thms__linordered__field_I4_J,axiom,
    ! [I3: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( ord_le4245800335709223507ccount @ I3 @ J )
        & ( ord_le2131251472502387783ccount @ K @ L ) )
     => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ I3 @ K ) @ ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(4)
thf(fact_251_add__mono__thms__linordered__field_I4_J,axiom,
    ! [I3: int,J: int,K: int,L: int] :
      ( ( ( ord_less_eq_int @ I3 @ J )
        & ( ord_less_int @ K @ L ) )
     => ( ord_less_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_field(4)
thf(fact_252_pos__add__strict,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ A )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).

% pos_add_strict
thf(fact_253_pos__add__strict,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ A )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ord_le2131251472502387783ccount @ B @ ( plus_p1863581527469039996ccount @ A @ C ) ) ) ) ).

% pos_add_strict
thf(fact_254_pos__add__strict,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ( ( ord_less_real @ B @ C )
       => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).

% pos_add_strict
thf(fact_255_pos__add__strict,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ zero_zero_int @ A )
     => ( ( ord_less_int @ B @ C )
       => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).

% pos_add_strict
thf(fact_256_canonically__ordered__monoid__add__class_OlessE,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ! [C2: nat] :
            ( ( B
              = ( plus_plus_nat @ A @ C2 ) )
           => ( C2 = zero_zero_nat ) ) ) ).

% canonically_ordered_monoid_add_class.lessE
thf(fact_257_add__pos__pos,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ A )
     => ( ( ord_less_nat @ zero_zero_nat @ B )
       => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).

% add_pos_pos
thf(fact_258_add__pos__pos,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ A )
     => ( ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ B )
       => ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ ( plus_p1863581527469039996ccount @ A @ B ) ) ) ) ).

% add_pos_pos
thf(fact_259_add__pos__pos,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ( ( ord_less_real @ zero_zero_real @ B )
       => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).

% add_pos_pos
thf(fact_260_add__pos__pos,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ zero_zero_int @ A )
     => ( ( ord_less_int @ zero_zero_int @ B )
       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).

% add_pos_pos
thf(fact_261_add__neg__neg,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ zero_zero_nat )
     => ( ( ord_less_nat @ B @ zero_zero_nat )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).

% add_neg_neg
thf(fact_262_add__neg__neg,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ zero_z1425366712893667068ccount )
     => ( ( ord_le2131251472502387783ccount @ B @ zero_z1425366712893667068ccount )
       => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ zero_z1425366712893667068ccount ) ) ) ).

% add_neg_neg
thf(fact_263_add__neg__neg,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ zero_zero_real )
     => ( ( ord_less_real @ B @ zero_zero_real )
       => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).

% add_neg_neg
thf(fact_264_add__neg__neg,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ zero_zero_int )
     => ( ( ord_less_int @ B @ zero_zero_int )
       => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).

% add_neg_neg
thf(fact_265_max_Oleft__commute,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ord_max_nat @ B @ ( ord_max_nat @ A @ C ) )
      = ( ord_max_nat @ A @ ( ord_max_nat @ B @ C ) ) ) ).

% max.left_commute
thf(fact_266_max_Ocommute,axiom,
    ( ord_max_nat
    = ( ^ [A3: nat,B2: nat] : ( ord_max_nat @ B2 @ A3 ) ) ) ).

% max.commute
thf(fact_267_max_Oassoc,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_max_nat @ ( ord_max_nat @ A @ B ) @ C )
      = ( ord_max_nat @ A @ ( ord_max_nat @ B @ C ) ) ) ).

% max.assoc
thf(fact_268_add__strict__increasing2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ zero_zero_nat @ A )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).

% add_strict_increasing2
thf(fact_269_add__strict__increasing2,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ A )
     => ( ( ord_less_real @ B @ C )
       => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).

% add_strict_increasing2
thf(fact_270_add__strict__increasing2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ A )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ord_le2131251472502387783ccount @ B @ ( plus_p1863581527469039996ccount @ A @ C ) ) ) ) ).

% add_strict_increasing2
thf(fact_271_add__strict__increasing2,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ A )
     => ( ( ord_less_int @ B @ C )
       => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).

% add_strict_increasing2
thf(fact_272_add__strict__increasing,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ A )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).

% add_strict_increasing
thf(fact_273_add__strict__increasing,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).

% add_strict_increasing
thf(fact_274_add__strict__increasing,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ A )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ord_le2131251472502387783ccount @ B @ ( plus_p1863581527469039996ccount @ A @ C ) ) ) ) ).

% add_strict_increasing
thf(fact_275_add__strict__increasing,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ zero_zero_int @ A )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).

% add_strict_increasing
thf(fact_276_add__pos__nonneg,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ A )
     => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
       => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).

% add_pos_nonneg
thf(fact_277_add__pos__nonneg,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ zero_zero_real @ B )
       => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).

% add_pos_nonneg
thf(fact_278_add__pos__nonneg,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ A )
     => ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ B )
       => ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ ( plus_p1863581527469039996ccount @ A @ B ) ) ) ) ).

% add_pos_nonneg
thf(fact_279_add__pos__nonneg,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ zero_zero_int @ A )
     => ( ( ord_less_eq_int @ zero_zero_int @ B )
       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).

% add_pos_nonneg
thf(fact_280_add__nonpos__neg,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ zero_zero_nat )
     => ( ( ord_less_nat @ B @ zero_zero_nat )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).

% add_nonpos_neg
thf(fact_281_add__nonpos__neg,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ zero_zero_real )
     => ( ( ord_less_real @ B @ zero_zero_real )
       => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).

% add_nonpos_neg
thf(fact_282_add__nonpos__neg,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ zero_z1425366712893667068ccount )
     => ( ( ord_le2131251472502387783ccount @ B @ zero_z1425366712893667068ccount )
       => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ zero_z1425366712893667068ccount ) ) ) ).

% add_nonpos_neg
thf(fact_283_add__nonpos__neg,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ zero_zero_int )
     => ( ( ord_less_int @ B @ zero_zero_int )
       => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).

% add_nonpos_neg
thf(fact_284_add__nonneg__pos,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ zero_zero_nat @ A )
     => ( ( ord_less_nat @ zero_zero_nat @ B )
       => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).

% add_nonneg_pos
thf(fact_285_add__nonneg__pos,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ A )
     => ( ( ord_less_real @ zero_zero_real @ B )
       => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).

% add_nonneg_pos
thf(fact_286_add__nonneg__pos,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ A )
     => ( ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ B )
       => ( ord_le2131251472502387783ccount @ zero_z1425366712893667068ccount @ ( plus_p1863581527469039996ccount @ A @ B ) ) ) ) ).

% add_nonneg_pos
thf(fact_287_add__nonneg__pos,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ A )
     => ( ( ord_less_int @ zero_zero_int @ B )
       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).

% add_nonneg_pos
thf(fact_288_add__neg__nonpos,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ zero_zero_nat )
     => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).

% add_neg_nonpos
thf(fact_289_add__neg__nonpos,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ zero_zero_real )
     => ( ( ord_less_eq_real @ B @ zero_zero_real )
       => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).

% add_neg_nonpos
thf(fact_290_add__neg__nonpos,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ zero_z1425366712893667068ccount )
     => ( ( ord_le4245800335709223507ccount @ B @ zero_z1425366712893667068ccount )
       => ( ord_le2131251472502387783ccount @ ( plus_p1863581527469039996ccount @ A @ B ) @ zero_z1425366712893667068ccount ) ) ) ).

% add_neg_nonpos
thf(fact_291_add__neg__nonpos,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ zero_zero_int )
     => ( ( ord_less_eq_int @ B @ zero_zero_int )
       => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).

% add_neg_nonpos
thf(fact_292_zero__le,axiom,
    ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).

% zero_le
thf(fact_293_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_294_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_295_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_296_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_297_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_298_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_299_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_300_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_301_le__iff__add,axiom,
    ( ord_less_eq_nat
    = ( ^ [A3: nat,B2: nat] :
        ? [C3: nat] :
          ( B2
          = ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).

% le_iff_add
thf(fact_302_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_303_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_304_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_305_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_306_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_307_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_308_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_309_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_310_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_311_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_312_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_313_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_314_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_315_add__mono__thms__linordered__semiring_I1_J,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ( ord_less_eq_nat @ I3 @ J )
        & ( ord_less_eq_nat @ K @ L ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(1)
thf(fact_316_add__mono__thms__linordered__semiring_I1_J,axiom,
    ! [I3: real,J: real,K: real,L: real] :
      ( ( ( ord_less_eq_real @ I3 @ J )
        & ( ord_less_eq_real @ K @ L ) )
     => ( ord_less_eq_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(1)
thf(fact_317_add__mono__thms__linordered__semiring_I1_J,axiom,
    ! [I3: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( ord_le4245800335709223507ccount @ I3 @ J )
        & ( ord_le4245800335709223507ccount @ K @ L ) )
     => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ I3 @ K ) @ ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(1)
thf(fact_318_add__mono__thms__linordered__semiring_I1_J,axiom,
    ! [I3: int,J: int,K: int,L: int] :
      ( ( ( ord_less_eq_int @ I3 @ J )
        & ( ord_less_eq_int @ K @ L ) )
     => ( ord_less_eq_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(1)
thf(fact_319_add__mono__thms__linordered__semiring_I2_J,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ( I3 = J )
        & ( ord_less_eq_nat @ K @ L ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(2)
thf(fact_320_add__mono__thms__linordered__semiring_I2_J,axiom,
    ! [I3: real,J: real,K: real,L: real] :
      ( ( ( I3 = J )
        & ( ord_less_eq_real @ K @ L ) )
     => ( ord_less_eq_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(2)
thf(fact_321_add__mono__thms__linordered__semiring_I2_J,axiom,
    ! [I3: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( I3 = J )
        & ( ord_le4245800335709223507ccount @ K @ L ) )
     => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ I3 @ K ) @ ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(2)
thf(fact_322_add__mono__thms__linordered__semiring_I2_J,axiom,
    ! [I3: int,J: int,K: int,L: int] :
      ( ( ( I3 = J )
        & ( ord_less_eq_int @ K @ L ) )
     => ( ord_less_eq_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(2)
thf(fact_323_add__mono__thms__linordered__semiring_I3_J,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ( ord_less_eq_nat @ I3 @ J )
        & ( K = L ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(3)
thf(fact_324_add__mono__thms__linordered__semiring_I3_J,axiom,
    ! [I3: real,J: real,K: real,L: real] :
      ( ( ( ord_less_eq_real @ I3 @ J )
        & ( K = L ) )
     => ( ord_less_eq_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(3)
thf(fact_325_add__mono__thms__linordered__semiring_I3_J,axiom,
    ! [I3: risk_Free_account,J: risk_Free_account,K: risk_Free_account,L: risk_Free_account] :
      ( ( ( ord_le4245800335709223507ccount @ I3 @ J )
        & ( K = L ) )
     => ( ord_le4245800335709223507ccount @ ( plus_p1863581527469039996ccount @ I3 @ K ) @ ( plus_p1863581527469039996ccount @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(3)
thf(fact_326_add__mono__thms__linordered__semiring_I3_J,axiom,
    ! [I3: int,J: int,K: int,L: int] :
      ( ( ( ord_less_eq_int @ I3 @ J )
        & ( K = L ) )
     => ( ord_less_eq_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).

% add_mono_thms_linordered_semiring(3)
thf(fact_327_add_Ogroup__left__neutral,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ zero_zero_real @ A )
      = A ) ).

% add.group_left_neutral
thf(fact_328_add_Ogroup__left__neutral,axiom,
    ! [A: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ zero_z1425366712893667068ccount @ A )
      = A ) ).

% add.group_left_neutral
thf(fact_329_add_Ogroup__left__neutral,axiom,
    ! [A: int] :
      ( ( plus_plus_int @ zero_zero_int @ A )
      = A ) ).

% add.group_left_neutral
thf(fact_330_add_Ocomm__neutral,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ) ).

% add.comm_neutral
thf(fact_331_add_Ocomm__neutral,axiom,
    ! [A: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ A @ zero_z1425366712893667068ccount )
      = A ) ).

% add.comm_neutral
thf(fact_332_add_Ocomm__neutral,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ A @ zero_zero_nat )
      = A ) ).

% add.comm_neutral
thf(fact_333_add_Ocomm__neutral,axiom,
    ! [A: int] :
      ( ( plus_plus_int @ A @ zero_zero_int )
      = A ) ).

% add.comm_neutral
thf(fact_334_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_335_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_336_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_337_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_338_max_OcoboundedI2,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( ord_less_eq_nat @ C @ B )
     => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).

% max.coboundedI2
thf(fact_339_max_OcoboundedI2,axiom,
    ! [C: real,B: real,A: real] :
      ( ( ord_less_eq_real @ C @ B )
     => ( ord_less_eq_real @ C @ ( ord_max_real @ A @ B ) ) ) ).

% max.coboundedI2
thf(fact_340_max_OcoboundedI2,axiom,
    ! [C: int,B: int,A: int] :
      ( ( ord_less_eq_int @ C @ B )
     => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).

% max.coboundedI2
thf(fact_341_max_OcoboundedI2,axiom,
    ! [C: num,B: num,A: num] :
      ( ( ord_less_eq_num @ C @ B )
     => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).

% max.coboundedI2
thf(fact_342_max_OcoboundedI1,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_eq_nat @ C @ A )
     => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).

% max.coboundedI1
thf(fact_343_max_OcoboundedI1,axiom,
    ! [C: real,A: real,B: real] :
      ( ( ord_less_eq_real @ C @ A )
     => ( ord_less_eq_real @ C @ ( ord_max_real @ A @ B ) ) ) ).

% max.coboundedI1
thf(fact_344_max_OcoboundedI1,axiom,
    ! [C: int,A: int,B: int] :
      ( ( ord_less_eq_int @ C @ A )
     => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).

% max.coboundedI1
thf(fact_345_max_OcoboundedI1,axiom,
    ! [C: num,A: num,B: num] :
      ( ( ord_less_eq_num @ C @ A )
     => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).

% max.coboundedI1
thf(fact_346_max_Oabsorb__iff2,axiom,
    ( ord_less_eq_nat
    = ( ^ [A3: nat,B2: nat] :
          ( ( ord_max_nat @ A3 @ B2 )
          = B2 ) ) ) ).

% max.absorb_iff2
thf(fact_347_max_Oabsorb__iff2,axiom,
    ( ord_less_eq_real
    = ( ^ [A3: real,B2: real] :
          ( ( ord_max_real @ A3 @ B2 )
          = B2 ) ) ) ).

% max.absorb_iff2
thf(fact_348_max_Oabsorb__iff2,axiom,
    ( ord_less_eq_int
    = ( ^ [A3: int,B2: int] :
          ( ( ord_max_int @ A3 @ B2 )
          = B2 ) ) ) ).

% max.absorb_iff2
thf(fact_349_max_Oabsorb__iff2,axiom,
    ( ord_less_eq_num
    = ( ^ [A3: num,B2: num] :
          ( ( ord_max_num @ A3 @ B2 )
          = B2 ) ) ) ).

% max.absorb_iff2
thf(fact_350_max_Oabsorb__iff1,axiom,
    ( ord_less_eq_nat
    = ( ^ [B2: nat,A3: nat] :
          ( ( ord_max_nat @ A3 @ B2 )
          = A3 ) ) ) ).

% max.absorb_iff1
thf(fact_351_max_Oabsorb__iff1,axiom,
    ( ord_less_eq_real
    = ( ^ [B2: real,A3: real] :
          ( ( ord_max_real @ A3 @ B2 )
          = A3 ) ) ) ).

% max.absorb_iff1
thf(fact_352_max_Oabsorb__iff1,axiom,
    ( ord_less_eq_int
    = ( ^ [B2: int,A3: int] :
          ( ( ord_max_int @ A3 @ B2 )
          = A3 ) ) ) ).

% max.absorb_iff1
thf(fact_353_max_Oabsorb__iff1,axiom,
    ( ord_less_eq_num
    = ( ^ [B2: num,A3: num] :
          ( ( ord_max_num @ A3 @ B2 )
          = A3 ) ) ) ).

% max.absorb_iff1
thf(fact_354_le__max__iff__disj,axiom,
    ! [Z: nat,X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y ) )
      = ( ( ord_less_eq_nat @ Z @ X )
        | ( ord_less_eq_nat @ Z @ Y ) ) ) ).

% le_max_iff_disj
thf(fact_355_le__max__iff__disj,axiom,
    ! [Z: real,X: real,Y: real] :
      ( ( ord_less_eq_real @ Z @ ( ord_max_real @ X @ Y ) )
      = ( ( ord_less_eq_real @ Z @ X )
        | ( ord_less_eq_real @ Z @ Y ) ) ) ).

% le_max_iff_disj
thf(fact_356_le__max__iff__disj,axiom,
    ! [Z: int,X: int,Y: int] :
      ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y ) )
      = ( ( ord_less_eq_int @ Z @ X )
        | ( ord_less_eq_int @ Z @ Y ) ) ) ).

% le_max_iff_disj
thf(fact_357_le__max__iff__disj,axiom,
    ! [Z: num,X: num,Y: num] :
      ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y ) )
      = ( ( ord_less_eq_num @ Z @ X )
        | ( ord_less_eq_num @ Z @ Y ) ) ) ).

% le_max_iff_disj
thf(fact_358_max_Ocobounded2,axiom,
    ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).

% max.cobounded2
thf(fact_359_max_Ocobounded2,axiom,
    ! [B: real,A: real] : ( ord_less_eq_real @ B @ ( ord_max_real @ A @ B ) ) ).

% max.cobounded2
thf(fact_360_max_Ocobounded2,axiom,
    ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).

% max.cobounded2
thf(fact_361_max_Ocobounded2,axiom,
    ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).

% max.cobounded2
thf(fact_362_max_Ocobounded1,axiom,
    ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).

% max.cobounded1
thf(fact_363_max_Ocobounded1,axiom,
    ! [A: real,B: real] : ( ord_less_eq_real @ A @ ( ord_max_real @ A @ B ) ) ).

% max.cobounded1
thf(fact_364_max_Ocobounded1,axiom,
    ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).

% max.cobounded1
thf(fact_365_max_Ocobounded1,axiom,
    ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).

% max.cobounded1
thf(fact_366_max_Oorder__iff,axiom,
    ( ord_less_eq_nat
    = ( ^ [B2: nat,A3: nat] :
          ( A3
          = ( ord_max_nat @ A3 @ B2 ) ) ) ) ).

% max.order_iff
thf(fact_367_max_Oorder__iff,axiom,
    ( ord_less_eq_real
    = ( ^ [B2: real,A3: real] :
          ( A3
          = ( ord_max_real @ A3 @ B2 ) ) ) ) ).

% max.order_iff
thf(fact_368_max_Oorder__iff,axiom,
    ( ord_less_eq_int
    = ( ^ [B2: int,A3: int] :
          ( A3
          = ( ord_max_int @ A3 @ B2 ) ) ) ) ).

% max.order_iff
thf(fact_369_max_Oorder__iff,axiom,
    ( ord_less_eq_num
    = ( ^ [B2: num,A3: num] :
          ( A3
          = ( ord_max_num @ A3 @ B2 ) ) ) ) ).

% max.order_iff
thf(fact_370_max_OboundedI,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( ord_less_eq_nat @ C @ A )
       => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).

% max.boundedI
thf(fact_371_max_OboundedI,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ( ord_less_eq_real @ C @ A )
       => ( ord_less_eq_real @ ( ord_max_real @ B @ C ) @ A ) ) ) ).

% max.boundedI
thf(fact_372_max_OboundedI,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ( ord_less_eq_int @ C @ A )
       => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).

% max.boundedI
thf(fact_373_max_OboundedI,axiom,
    ! [B: num,A: num,C: num] :
      ( ( ord_less_eq_num @ B @ A )
     => ( ( ord_less_eq_num @ C @ A )
       => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).

% max.boundedI
thf(fact_374_max_OboundedE,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
     => ~ ( ( ord_less_eq_nat @ B @ A )
         => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).

% max.boundedE
thf(fact_375_max_OboundedE,axiom,
    ! [B: real,C: real,A: real] :
      ( ( ord_less_eq_real @ ( ord_max_real @ B @ C ) @ A )
     => ~ ( ( ord_less_eq_real @ B @ A )
         => ~ ( ord_less_eq_real @ C @ A ) ) ) ).

% max.boundedE
thf(fact_376_max_OboundedE,axiom,
    ! [B: int,C: int,A: int] :
      ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
     => ~ ( ( ord_less_eq_int @ B @ A )
         => ~ ( ord_less_eq_int @ C @ A ) ) ) ).

% max.boundedE
thf(fact_377_max_OboundedE,axiom,
    ! [B: num,C: num,A: num] :
      ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
     => ~ ( ( ord_less_eq_num @ B @ A )
         => ~ ( ord_less_eq_num @ C @ A ) ) ) ).

% max.boundedE
thf(fact_378_max_OorderI,axiom,
    ! [A: nat,B: nat] :
      ( ( A
        = ( ord_max_nat @ A @ B ) )
     => ( ord_less_eq_nat @ B @ A ) ) ).

% max.orderI
thf(fact_379_max_OorderI,axiom,
    ! [A: real,B: real] :
      ( ( A
        = ( ord_max_real @ A @ B ) )
     => ( ord_less_eq_real @ B @ A ) ) ).

% max.orderI
thf(fact_380_max_OorderI,axiom,
    ! [A: int,B: int] :
      ( ( A
        = ( ord_max_int @ A @ B ) )
     => ( ord_less_eq_int @ B @ A ) ) ).

% max.orderI
thf(fact_381_max_OorderI,axiom,
    ! [A: num,B: num] :
      ( ( A
        = ( ord_max_num @ A @ B ) )
     => ( ord_less_eq_num @ B @ A ) ) ).

% max.orderI
thf(fact_382_max_OorderE,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( A
        = ( ord_max_nat @ A @ B ) ) ) ).

% max.orderE
thf(fact_383_max_OorderE,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( A
        = ( ord_max_real @ A @ B ) ) ) ).

% max.orderE
thf(fact_384_max_OorderE,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( A
        = ( ord_max_int @ A @ B ) ) ) ).

% max.orderE
thf(fact_385_max_OorderE,axiom,
    ! [B: num,A: num] :
      ( ( ord_less_eq_num @ B @ A )
     => ( A
        = ( ord_max_num @ A @ B ) ) ) ).

% max.orderE
thf(fact_386_max_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 @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).

% max.mono
thf(fact_387_max_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 @ ( ord_max_real @ C @ D ) @ ( ord_max_real @ A @ B ) ) ) ) ).

% max.mono
thf(fact_388_max_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 @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).

% max.mono
thf(fact_389_max_Omono,axiom,
    ! [C: num,A: num,D: num,B: num] :
      ( ( ord_less_eq_num @ C @ A )
     => ( ( ord_less_eq_num @ D @ B )
       => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).

% max.mono
thf(fact_390_max__add__distrib__right,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account,Z: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ X @ ( ord_ma8558070474537249246ccount @ Y @ Z ) )
      = ( ord_ma8558070474537249246ccount @ ( plus_p1863581527469039996ccount @ X @ Y ) @ ( plus_p1863581527469039996ccount @ X @ Z ) ) ) ).

% max_add_distrib_right
thf(fact_391_max__add__distrib__right,axiom,
    ! [X: real,Y: real,Z: real] :
      ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z ) )
      = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z ) ) ) ).

% max_add_distrib_right
thf(fact_392_max__add__distrib__right,axiom,
    ! [X: int,Y: int,Z: int] :
      ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
      = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).

% max_add_distrib_right
thf(fact_393_max__add__distrib__right,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
      = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).

% max_add_distrib_right
thf(fact_394_max__add__distrib__left,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account,Z: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ ( ord_ma8558070474537249246ccount @ X @ Y ) @ Z )
      = ( ord_ma8558070474537249246ccount @ ( plus_p1863581527469039996ccount @ X @ Z ) @ ( plus_p1863581527469039996ccount @ Y @ Z ) ) ) ).

% max_add_distrib_left
thf(fact_395_max__add__distrib__left,axiom,
    ! [X: real,Y: real,Z: real] :
      ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z )
      = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).

% max_add_distrib_left
thf(fact_396_max__add__distrib__left,axiom,
    ! [X: int,Y: int,Z: int] :
      ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
      = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).

% max_add_distrib_left
thf(fact_397_max__add__distrib__left,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
      = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).

% max_add_distrib_left
thf(fact_398_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_399_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_400_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_401_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_402_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_403_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_404_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_405_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_406_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_407_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_408_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_409_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_410_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_411_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_412_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_413_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_414_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_415_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_416_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_417_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_418_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_419_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_420_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_421_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_422_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_423_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_424_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_425_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_426_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_427_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_428_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_429_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_430_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_431_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_432_field__le__epsilon,axiom,
    ! [X: real,Y: real] :
      ( ! [E: real] :
          ( ( ord_less_real @ zero_zero_real @ E )
         => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E ) ) )
     => ( ord_less_eq_real @ X @ Y ) ) ).

% field_le_epsilon
thf(fact_433_max__0R,axiom,
    ! [N: nat] :
      ( ( ord_max_nat @ N @ zero_zero_nat )
      = N ) ).

% max_0R
thf(fact_434_max__0L,axiom,
    ! [N: nat] :
      ( ( ord_max_nat @ zero_zero_nat @ N )
      = N ) ).

% max_0L
thf(fact_435_max__nat_Oright__neutral,axiom,
    ! [A: nat] :
      ( ( ord_max_nat @ A @ zero_zero_nat )
      = A ) ).

% max_nat.right_neutral
thf(fact_436_max__nat_Oneutr__eq__iff,axiom,
    ! [A: nat,B: nat] :
      ( ( zero_zero_nat
        = ( ord_max_nat @ A @ B ) )
      = ( ( A = zero_zero_nat )
        & ( B = zero_zero_nat ) ) ) ).

% max_nat.neutr_eq_iff
thf(fact_437_max__nat_Oleft__neutral,axiom,
    ! [A: nat] :
      ( ( ord_max_nat @ zero_zero_nat @ A )
      = A ) ).

% max_nat.left_neutral
thf(fact_438_max__nat_Oeq__neutr__iff,axiom,
    ! [A: nat,B: nat] :
      ( ( ( ord_max_nat @ A @ B )
        = zero_zero_nat )
      = ( ( A = zero_zero_nat )
        & ( B = zero_zero_nat ) ) ) ).

% max_nat.eq_neutr_iff
thf(fact_439_add__less__zeroD,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
     => ( ( ord_less_real @ X @ zero_zero_real )
        | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).

% add_less_zeroD
thf(fact_440_add__less__zeroD,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
     => ( ( ord_less_int @ X @ zero_zero_int )
        | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).

% add_less_zeroD
thf(fact_441_nat__add__left__cancel__le,axiom,
    ! [K: nat,M: nat,N: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
      = ( ord_less_eq_nat @ M @ N ) ) ).

% nat_add_left_cancel_le
thf(fact_442_le0,axiom,
    ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).

% le0
thf(fact_443_less__nat__zero__code,axiom,
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ zero_zero_nat ) ).

% less_nat_zero_code
thf(fact_444_neq0__conv,axiom,
    ! [N: nat] :
      ( ( N != zero_zero_nat )
      = ( ord_less_nat @ zero_zero_nat @ N ) ) ).

% neq0_conv
thf(fact_445_bot__nat__0_Onot__eq__extremum,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
      = ( ord_less_nat @ zero_zero_nat @ A ) ) ).

% bot_nat_0.not_eq_extremum
thf(fact_446_bot__nat__0_Oextremum,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).

% bot_nat_0.extremum
thf(fact_447_add__is__0,axiom,
    ! [M: nat,N: nat] :
      ( ( ( plus_plus_nat @ M @ N )
        = zero_zero_nat )
      = ( ( M = zero_zero_nat )
        & ( N = zero_zero_nat ) ) ) ).

% add_is_0
thf(fact_448_Nat_Oadd__0__right,axiom,
    ! [M: nat] :
      ( ( plus_plus_nat @ M @ zero_zero_nat )
      = M ) ).

% Nat.add_0_right
thf(fact_449_nat__add__left__cancel__less,axiom,
    ! [K: nat,M: nat,N: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
      = ( ord_less_nat @ M @ N ) ) ).

% nat_add_left_cancel_less
thf(fact_450_add__gr__0,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
      = ( ( ord_less_nat @ zero_zero_nat @ M )
        | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).

% add_gr_0
thf(fact_451_plus__nat_Oadd__0,axiom,
    ! [N: nat] :
      ( ( plus_plus_nat @ zero_zero_nat @ N )
      = N ) ).

% plus_nat.add_0
thf(fact_452_add__eq__self__zero,axiom,
    ! [M: nat,N: nat] :
      ( ( ( plus_plus_nat @ M @ N )
        = M )
     => ( N = zero_zero_nat ) ) ).

% add_eq_self_zero
thf(fact_453_linorder__neqE__linordered__idom,axiom,
    ! [X: real,Y: real] :
      ( ( X != Y )
     => ( ~ ( ord_less_real @ X @ Y )
       => ( ord_less_real @ Y @ X ) ) ) ).

% linorder_neqE_linordered_idom
thf(fact_454_linorder__neqE__linordered__idom,axiom,
    ! [X: int,Y: int] :
      ( ( X != Y )
     => ( ~ ( ord_less_int @ X @ Y )
       => ( ord_less_int @ Y @ X ) ) ) ).

% linorder_neqE_linordered_idom
thf(fact_455_linordered__field__no__ub,axiom,
    ! [X3: real] :
    ? [X_1: real] : ( ord_less_real @ X3 @ X_1 ) ).

% linordered_field_no_ub
thf(fact_456_linordered__field__no__lb,axiom,
    ! [X3: real] :
    ? [Y2: real] : ( ord_less_real @ Y2 @ X3 ) ).

% linordered_field_no_lb
thf(fact_457_less__imp__add__positive,axiom,
    ! [I3: nat,J: nat] :
      ( ( ord_less_nat @ I3 @ J )
     => ? [K2: nat] :
          ( ( ord_less_nat @ zero_zero_nat @ K2 )
          & ( ( plus_plus_nat @ I3 @ K2 )
            = J ) ) ) ).

% less_imp_add_positive
thf(fact_458_linorder__neqE__nat,axiom,
    ! [X: nat,Y: nat] :
      ( ( X != Y )
     => ( ~ ( ord_less_nat @ X @ Y )
       => ( ord_less_nat @ Y @ X ) ) ) ).

% linorder_neqE_nat
thf(fact_459_infinite__descent0,axiom,
    ! [P: nat > $o,N: nat] :
      ( ( P @ zero_zero_nat )
     => ( ! [N3: nat] :
            ( ( ord_less_nat @ zero_zero_nat @ N3 )
           => ( ~ ( P @ N3 )
             => ? [M2: nat] :
                  ( ( ord_less_nat @ M2 @ N3 )
                  & ~ ( P @ M2 ) ) ) )
       => ( P @ N ) ) ) ).

% infinite_descent0
thf(fact_460_less__add__eq__less,axiom,
    ! [K: nat,L: nat,M: nat,N: nat] :
      ( ( ord_less_nat @ K @ L )
     => ( ( ( plus_plus_nat @ M @ L )
          = ( plus_plus_nat @ K @ N ) )
       => ( ord_less_nat @ M @ N ) ) ) ).

% less_add_eq_less
thf(fact_461_infinite__descent,axiom,
    ! [P: nat > $o,N: nat] :
      ( ! [N3: nat] :
          ( ~ ( P @ N3 )
         => ? [M2: nat] :
              ( ( ord_less_nat @ M2 @ N3 )
              & ~ ( P @ M2 ) ) )
     => ( P @ N ) ) ).

% infinite_descent
thf(fact_462_trans__less__add2,axiom,
    ! [I3: nat,J: nat,M: nat] :
      ( ( ord_less_nat @ I3 @ J )
     => ( ord_less_nat @ I3 @ ( plus_plus_nat @ M @ J ) ) ) ).

% trans_less_add2
thf(fact_463_trans__less__add1,axiom,
    ! [I3: nat,J: nat,M: nat] :
      ( ( ord_less_nat @ I3 @ J )
     => ( ord_less_nat @ I3 @ ( plus_plus_nat @ J @ M ) ) ) ).

% trans_less_add1
thf(fact_464_nat__less__induct,axiom,
    ! [P: nat > $o,N: nat] :
      ( ! [N3: nat] :
          ( ! [M2: nat] :
              ( ( ord_less_nat @ M2 @ N3 )
             => ( P @ M2 ) )
         => ( P @ N3 ) )
     => ( P @ N ) ) ).

% nat_less_induct
thf(fact_465_less__irrefl__nat,axiom,
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ N ) ).

% less_irrefl_nat
thf(fact_466_gr__implies__not0,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
     => ( N != zero_zero_nat ) ) ).

% gr_implies_not0
thf(fact_467_less__not__refl3,axiom,
    ! [S: nat,T: nat] :
      ( ( ord_less_nat @ S @ T )
     => ( S != T ) ) ).

% less_not_refl3
thf(fact_468_less__not__refl2,axiom,
    ! [N: nat,M: nat] :
      ( ( ord_less_nat @ N @ M )
     => ( M != N ) ) ).

% less_not_refl2
thf(fact_469_add__less__mono1,axiom,
    ! [I3: nat,J: nat,K: nat] :
      ( ( ord_less_nat @ I3 @ J )
     => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).

% add_less_mono1
thf(fact_470_not__add__less2,axiom,
    ! [J: nat,I3: nat] :
      ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I3 ) @ I3 ) ).

% not_add_less2
thf(fact_471_not__add__less1,axiom,
    ! [I3: nat,J: nat] :
      ~ ( ord_less_nat @ ( plus_plus_nat @ I3 @ J ) @ I3 ) ).

% not_add_less1
thf(fact_472_less__not__refl,axiom,
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ N ) ).

% less_not_refl
thf(fact_473_add__less__mono,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ord_less_nat @ I3 @ J )
     => ( ( ord_less_nat @ K @ L )
       => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).

% add_less_mono
thf(fact_474_nat__neq__iff,axiom,
    ! [M: nat,N: nat] :
      ( ( M != N )
      = ( ( ord_less_nat @ M @ N )
        | ( ord_less_nat @ N @ M ) ) ) ).

% nat_neq_iff
thf(fact_475_less__zeroE,axiom,
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ zero_zero_nat ) ).

% less_zeroE
thf(fact_476_add__lessD1,axiom,
    ! [I3: nat,J: nat,K: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ I3 @ J ) @ K )
     => ( ord_less_nat @ I3 @ K ) ) ).

% add_lessD1
thf(fact_477_not__less0,axiom,
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ zero_zero_nat ) ).

% not_less0
thf(fact_478_not__gr0,axiom,
    ! [N: nat] :
      ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
      = ( N = zero_zero_nat ) ) ).

% not_gr0
thf(fact_479_gr0I,axiom,
    ! [N: nat] :
      ( ( N != zero_zero_nat )
     => ( ord_less_nat @ zero_zero_nat @ N ) ) ).

% gr0I
thf(fact_480_bot__nat__0_Oextremum__strict,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ zero_zero_nat ) ).

% bot_nat_0.extremum_strict
thf(fact_481_le__refl,axiom,
    ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).

% le_refl
thf(fact_482_le__trans,axiom,
    ! [I3: nat,J: nat,K: nat] :
      ( ( ord_less_eq_nat @ I3 @ J )
     => ( ( ord_less_eq_nat @ J @ K )
       => ( ord_less_eq_nat @ I3 @ K ) ) ) ).

% le_trans
thf(fact_483_eq__imp__le,axiom,
    ! [M: nat,N: nat] :
      ( ( M = N )
     => ( ord_less_eq_nat @ M @ N ) ) ).

% eq_imp_le
thf(fact_484_le__antisym,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ N )
     => ( ( ord_less_eq_nat @ N @ M )
       => ( M = N ) ) ) ).

% le_antisym
thf(fact_485_nat__le__linear,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ N )
      | ( ord_less_eq_nat @ N @ M ) ) ).

% nat_le_linear
thf(fact_486_Nat_Oex__has__greatest__nat,axiom,
    ! [P: nat > $o,K: nat,B: nat] :
      ( ( P @ K )
     => ( ! [Y2: nat] :
            ( ( P @ Y2 )
           => ( ord_less_eq_nat @ Y2 @ B ) )
       => ? [X4: nat] :
            ( ( P @ X4 )
            & ! [Y3: nat] :
                ( ( P @ Y3 )
               => ( ord_less_eq_nat @ Y3 @ X4 ) ) ) ) ) ).

% Nat.ex_has_greatest_nat
thf(fact_487_less__eq__nat_Osimps_I1_J,axiom,
    ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).

% less_eq_nat.simps(1)
thf(fact_488_bot__nat__0_Oextremum__unique,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ zero_zero_nat )
      = ( A = zero_zero_nat ) ) ).

% bot_nat_0.extremum_unique
thf(fact_489_bot__nat__0_Oextremum__uniqueI,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ zero_zero_nat )
     => ( A = zero_zero_nat ) ) ).

% bot_nat_0.extremum_uniqueI
thf(fact_490_le__0__eq,axiom,
    ! [N: nat] :
      ( ( ord_less_eq_nat @ N @ zero_zero_nat )
      = ( N = zero_zero_nat ) ) ).

% le_0_eq
thf(fact_491_add__leE,axiom,
    ! [M: nat,K: nat,N: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
     => ~ ( ( ord_less_eq_nat @ M @ N )
         => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).

% add_leE
thf(fact_492_le__add1,axiom,
    ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).

% le_add1
thf(fact_493_le__add2,axiom,
    ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).

% le_add2
thf(fact_494_add__leD1,axiom,
    ! [M: nat,K: nat,N: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
     => ( ord_less_eq_nat @ M @ N ) ) ).

% add_leD1
thf(fact_495_add__leD2,axiom,
    ! [M: nat,K: nat,N: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
     => ( ord_less_eq_nat @ K @ N ) ) ).

% add_leD2
thf(fact_496_le__Suc__ex,axiom,
    ! [K: nat,L: nat] :
      ( ( ord_less_eq_nat @ K @ L )
     => ? [N3: nat] :
          ( L
          = ( plus_plus_nat @ K @ N3 ) ) ) ).

% le_Suc_ex
thf(fact_497_add__le__mono,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ord_less_eq_nat @ I3 @ J )
     => ( ( ord_less_eq_nat @ K @ L )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).

% add_le_mono
thf(fact_498_add__le__mono1,axiom,
    ! [I3: nat,J: nat,K: nat] :
      ( ( ord_less_eq_nat @ I3 @ J )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).

% add_le_mono1
thf(fact_499_trans__le__add1,axiom,
    ! [I3: nat,J: nat,M: nat] :
      ( ( ord_less_eq_nat @ I3 @ J )
     => ( ord_less_eq_nat @ I3 @ ( plus_plus_nat @ J @ M ) ) ) ).

% trans_le_add1
thf(fact_500_trans__le__add2,axiom,
    ! [I3: nat,J: nat,M: nat] :
      ( ( ord_less_eq_nat @ I3 @ J )
     => ( ord_less_eq_nat @ I3 @ ( plus_plus_nat @ M @ J ) ) ) ).

% trans_le_add2
thf(fact_501_nat__le__iff__add,axiom,
    ( ord_less_eq_nat
    = ( ^ [M3: nat,N2: nat] :
        ? [K3: nat] :
          ( N2
          = ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).

% nat_le_iff_add
thf(fact_502_nat__add__max__left,axiom,
    ! [M: nat,N: nat,Q: nat] :
      ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q )
      = ( ord_max_nat @ ( plus_plus_nat @ M @ Q ) @ ( plus_plus_nat @ N @ Q ) ) ) ).

% nat_add_max_left
thf(fact_503_nat__add__max__right,axiom,
    ! [M: nat,N: nat,Q: nat] :
      ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q ) )
      = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q ) ) ) ).

% nat_add_max_right
thf(fact_504_nat__less__le,axiom,
    ( ord_less_nat
    = ( ^ [M3: nat,N2: nat] :
          ( ( ord_less_eq_nat @ M3 @ N2 )
          & ( M3 != N2 ) ) ) ) ).

% nat_less_le
thf(fact_505_less__imp__le__nat,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
     => ( ord_less_eq_nat @ M @ N ) ) ).

% less_imp_le_nat
thf(fact_506_le__eq__less__or__eq,axiom,
    ( ord_less_eq_nat
    = ( ^ [M3: nat,N2: nat] :
          ( ( ord_less_nat @ M3 @ N2 )
          | ( M3 = N2 ) ) ) ) ).

% le_eq_less_or_eq
thf(fact_507_less__or__eq__imp__le,axiom,
    ! [M: nat,N: nat] :
      ( ( ( ord_less_nat @ M @ N )
        | ( M = N ) )
     => ( ord_less_eq_nat @ M @ N ) ) ).

% less_or_eq_imp_le
thf(fact_508_le__neq__implies__less,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ N )
     => ( ( M != N )
       => ( ord_less_nat @ M @ N ) ) ) ).

% le_neq_implies_less
thf(fact_509_less__mono__imp__le__mono,axiom,
    ! [F: nat > nat,I3: nat,J: nat] :
      ( ! [I: nat,J2: nat] :
          ( ( ord_less_nat @ I @ J2 )
         => ( ord_less_nat @ ( F @ I ) @ ( F @ J2 ) ) )
     => ( ( ord_less_eq_nat @ I3 @ J )
       => ( ord_less_eq_nat @ ( F @ I3 ) @ ( F @ J ) ) ) ) ).

% less_mono_imp_le_mono
thf(fact_510_ex__least__nat__le,axiom,
    ! [P: nat > $o,N: nat] :
      ( ( P @ N )
     => ( ~ ( P @ zero_zero_nat )
       => ? [K2: nat] :
            ( ( ord_less_eq_nat @ K2 @ N )
            & ! [I2: nat] :
                ( ( ord_less_nat @ I2 @ K2 )
               => ~ ( P @ I2 ) )
            & ( P @ K2 ) ) ) ) ).

% ex_least_nat_le
thf(fact_511_mono__nat__linear__lb,axiom,
    ! [F: nat > nat,M: nat,K: nat] :
      ( ! [M4: nat,N3: nat] :
          ( ( ord_less_nat @ M4 @ N3 )
         => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).

% mono_nat_linear_lb
thf(fact_512_order__refl,axiom,
    ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).

% order_refl
thf(fact_513_order__refl,axiom,
    ! [X: real] : ( ord_less_eq_real @ X @ X ) ).

% order_refl
thf(fact_514_order__refl,axiom,
    ! [X: risk_Free_account] : ( ord_le4245800335709223507ccount @ X @ X ) ).

% order_refl
thf(fact_515_order__refl,axiom,
    ! [X: int] : ( ord_less_eq_int @ X @ X ) ).

% order_refl
thf(fact_516_order__refl,axiom,
    ! [X: num] : ( ord_less_eq_num @ X @ X ) ).

% order_refl
thf(fact_517_dual__order_Orefl,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).

% dual_order.refl
thf(fact_518_dual__order_Orefl,axiom,
    ! [A: real] : ( ord_less_eq_real @ A @ A ) ).

% dual_order.refl
thf(fact_519_dual__order_Orefl,axiom,
    ! [A: risk_Free_account] : ( ord_le4245800335709223507ccount @ A @ A ) ).

% dual_order.refl
thf(fact_520_dual__order_Orefl,axiom,
    ! [A: int] : ( ord_less_eq_int @ A @ A ) ).

% dual_order.refl
thf(fact_521_dual__order_Orefl,axiom,
    ! [A: num] : ( ord_less_eq_num @ A @ A ) ).

% dual_order.refl
thf(fact_522_cash__reserve__def,axiom,
    ( risk_F1914734008469130493eserve
    = ( ^ [Alpha: risk_Free_account] : ( risk_F170160801229183585ccount @ Alpha @ zero_zero_nat ) ) ) ).

% cash_reserve_def
thf(fact_523_max__def,axiom,
    ( ord_max_nat
    = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).

% max_def
thf(fact_524_max__def,axiom,
    ( ord_max_real
    = ( ^ [A3: real,B2: real] : ( if_real @ ( ord_less_eq_real @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).

% max_def
thf(fact_525_max__def,axiom,
    ( ord_ma8558070474537249246ccount
    = ( ^ [A3: risk_Free_account,B2: risk_Free_account] : ( if_Risk_Free_account @ ( ord_le4245800335709223507ccount @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).

% max_def
thf(fact_526_max__def,axiom,
    ( ord_max_int
    = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).

% max_def
thf(fact_527_max__def,axiom,
    ( ord_max_num
    = ( ^ [A3: num,B2: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).

% max_def
thf(fact_528_max__absorb1,axiom,
    ! [Y: nat,X: nat] :
      ( ( ord_less_eq_nat @ Y @ X )
     => ( ( ord_max_nat @ X @ Y )
        = X ) ) ).

% max_absorb1
thf(fact_529_max__absorb1,axiom,
    ! [Y: real,X: real] :
      ( ( ord_less_eq_real @ Y @ X )
     => ( ( ord_max_real @ X @ Y )
        = X ) ) ).

% max_absorb1
thf(fact_530_max__absorb1,axiom,
    ! [Y: risk_Free_account,X: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ Y @ X )
     => ( ( ord_ma8558070474537249246ccount @ X @ Y )
        = X ) ) ).

% max_absorb1
thf(fact_531_max__absorb1,axiom,
    ! [Y: int,X: int] :
      ( ( ord_less_eq_int @ Y @ X )
     => ( ( ord_max_int @ X @ Y )
        = X ) ) ).

% max_absorb1
thf(fact_532_max__absorb1,axiom,
    ! [Y: num,X: num] :
      ( ( ord_less_eq_num @ Y @ X )
     => ( ( ord_max_num @ X @ Y )
        = X ) ) ).

% max_absorb1
thf(fact_533_max__absorb2,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( ord_max_nat @ X @ Y )
        = Y ) ) ).

% max_absorb2
thf(fact_534_max__absorb2,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ X @ Y )
     => ( ( ord_max_real @ X @ Y )
        = Y ) ) ).

% max_absorb2
thf(fact_535_max__absorb2,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ X @ Y )
     => ( ( ord_ma8558070474537249246ccount @ X @ Y )
        = Y ) ) ).

% max_absorb2
thf(fact_536_max__absorb2,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ X @ Y )
     => ( ( ord_max_int @ X @ Y )
        = Y ) ) ).

% max_absorb2
thf(fact_537_max__absorb2,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_eq_num @ X @ Y )
     => ( ( ord_max_num @ X @ Y )
        = Y ) ) ).

% max_absorb2
thf(fact_538_Euclid__induct,axiom,
    ! [P: nat > nat > $o,A: nat,B: nat] :
      ( ! [A4: nat,B4: nat] :
          ( ( P @ A4 @ B4 )
          = ( P @ B4 @ A4 ) )
     => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
       => ( ! [A4: nat,B4: nat] :
              ( ( P @ A4 @ B4 )
             => ( P @ A4 @ ( plus_plus_nat @ A4 @ B4 ) ) )
         => ( P @ A @ B ) ) ) ) ).

% Euclid_induct
thf(fact_539_nat__descend__induct,axiom,
    ! [N: nat,P: nat > $o,M: nat] :
      ( ! [K2: nat] :
          ( ( ord_less_nat @ N @ K2 )
         => ( P @ K2 ) )
     => ( ! [K2: nat] :
            ( ( ord_less_eq_nat @ K2 @ N )
           => ( ! [I2: nat] :
                  ( ( ord_less_nat @ K2 @ I2 )
                 => ( P @ I2 ) )
             => ( P @ K2 ) ) )
       => ( P @ M ) ) ) ).

% nat_descend_induct
thf(fact_540_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_541_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_542_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_543_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_544_order__antisym__conv,axiom,
    ! [Y: num,X: num] :
      ( ( ord_less_eq_num @ Y @ X )
     => ( ( ord_less_eq_num @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_545_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_546_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_547_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_548_linorder__le__cases,axiom,
    ! [X: num,Y: num] :
      ( ~ ( ord_less_eq_num @ X @ Y )
     => ( ord_less_eq_num @ Y @ X ) ) ).

% linorder_le_cases
thf(fact_549_ord__le__eq__subst,axiom,
    ! [A: nat,B: nat,F: nat > nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_550_ord__le__eq__subst,axiom,
    ! [A: nat,B: nat,F: nat > real,C: real] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_551_ord__le__eq__subst,axiom,
    ! [A: nat,B: nat,F: nat > risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_le4245800335709223507ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le4245800335709223507ccount @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_552_ord__le__eq__subst,axiom,
    ! [A: nat,B: nat,F: nat > int,C: int] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_553_ord__le__eq__subst,axiom,
    ! [A: nat,B: nat,F: nat > num,C: num] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_554_ord__le__eq__subst,axiom,
    ! [A: real,B: real,F: real > nat,C: nat] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_555_ord__le__eq__subst,axiom,
    ! [A: real,B: real,F: real > real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_556_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 )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_le4245800335709223507ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le4245800335709223507ccount @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_557_ord__le__eq__subst,axiom,
    ! [A: real,B: real,F: real > int,C: int] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_558_ord__le__eq__subst,axiom,
    ! [A: real,B: real,F: real > num,C: num] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_559_ord__eq__le__subst,axiom,
    ! [A: nat,F: nat > nat,B: nat,C: nat] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_560_ord__eq__le__subst,axiom,
    ! [A: real,F: nat > real,B: nat,C: nat] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_561_ord__eq__le__subst,axiom,
    ! [A: risk_Free_account,F: nat > risk_Free_account,B: nat,C: nat] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_le4245800335709223507ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le4245800335709223507ccount @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_562_ord__eq__le__subst,axiom,
    ! [A: int,F: nat > int,B: nat,C: nat] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_563_ord__eq__le__subst,axiom,
    ! [A: num,F: nat > num,B: nat,C: nat] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_564_ord__eq__le__subst,axiom,
    ! [A: nat,F: real > nat,B: real,C: real] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_565_ord__eq__le__subst,axiom,
    ! [A: real,F: real > real,B: real,C: real] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_566_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 )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_le4245800335709223507ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le4245800335709223507ccount @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_567_ord__eq__le__subst,axiom,
    ! [A: int,F: real > int,B: real,C: real] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_568_ord__eq__le__subst,axiom,
    ! [A: num,F: real > num,B: real,C: real] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_569_linorder__linear,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
      | ( ord_less_eq_nat @ Y @ X ) ) ).

% linorder_linear
thf(fact_570_linorder__linear,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ X @ Y )
      | ( ord_less_eq_real @ Y @ X ) ) ).

% linorder_linear
thf(fact_571_linorder__linear,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ X @ Y )
      | ( ord_less_eq_int @ Y @ X ) ) ).

% linorder_linear
thf(fact_572_linorder__linear,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_eq_num @ X @ Y )
      | ( ord_less_eq_num @ Y @ X ) ) ).

% linorder_linear
thf(fact_573_order__eq__refl,axiom,
    ! [X: nat,Y: nat] :
      ( ( X = Y )
     => ( ord_less_eq_nat @ X @ Y ) ) ).

% order_eq_refl
thf(fact_574_order__eq__refl,axiom,
    ! [X: real,Y: real] :
      ( ( X = Y )
     => ( ord_less_eq_real @ X @ Y ) ) ).

% order_eq_refl
thf(fact_575_order__eq__refl,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( X = Y )
     => ( ord_le4245800335709223507ccount @ X @ Y ) ) ).

% order_eq_refl
thf(fact_576_order__eq__refl,axiom,
    ! [X: int,Y: int] :
      ( ( X = Y )
     => ( ord_less_eq_int @ X @ Y ) ) ).

% order_eq_refl
thf(fact_577_order__eq__refl,axiom,
    ! [X: num,Y: num] :
      ( ( X = Y )
     => ( ord_less_eq_num @ X @ Y ) ) ).

% order_eq_refl
thf(fact_578_order__subst2,axiom,
    ! [A: nat,B: nat,F: nat > nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_579_order__subst2,axiom,
    ! [A: nat,B: nat,F: nat > real,C: real] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_real @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_580_order__subst2,axiom,
    ! [A: nat,B: nat,F: nat > risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_le4245800335709223507ccount @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_le4245800335709223507ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le4245800335709223507ccount @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_581_order__subst2,axiom,
    ! [A: nat,B: nat,F: nat > int,C: int] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_int @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_582_order__subst2,axiom,
    ! [A: nat,B: nat,F: nat > num,C: num] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_num @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_583_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 )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_584_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 )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_585_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 )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_le4245800335709223507ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le4245800335709223507ccount @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_586_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 )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_587_order__subst2,axiom,
    ! [A: real,B: real,F: real > num,C: num] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_num @ ( F @ B ) @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_588_order__subst1,axiom,
    ! [A: nat,F: nat > nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_589_order__subst1,axiom,
    ! [A: nat,F: real > nat,B: real,C: real] :
      ( ( ord_less_eq_nat @ A @ ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_590_order__subst1,axiom,
    ! [A: nat,F: risk_Free_account > nat,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_nat @ A @ ( F @ B ) )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_591_order__subst1,axiom,
    ! [A: nat,F: int > nat,B: int,C: int] :
      ( ( ord_less_eq_nat @ A @ ( F @ B ) )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ! [X4: int,Y2: int] :
              ( ( ord_less_eq_int @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_592_order__subst1,axiom,
    ! [A: nat,F: num > nat,B: num,C: num] :
      ( ( ord_less_eq_nat @ A @ ( F @ B ) )
     => ( ( ord_less_eq_num @ B @ C )
       => ( ! [X4: num,Y2: num] :
              ( ( ord_less_eq_num @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_593_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 )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_594_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 )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_595_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 )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le4245800335709223507ccount @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_596_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 )
       => ( ! [X4: int,Y2: int] :
              ( ( ord_less_eq_int @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_597_order__subst1,axiom,
    ! [A: real,F: num > real,B: num,C: num] :
      ( ( ord_less_eq_real @ A @ ( F @ B ) )
     => ( ( ord_less_eq_num @ B @ C )
       => ( ! [X4: num,Y2: num] :
              ( ( ord_less_eq_num @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_598_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
    = ( ^ [A3: nat,B2: nat] :
          ( ( ord_less_eq_nat @ A3 @ B2 )
          & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_599_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
    = ( ^ [A3: real,B2: real] :
          ( ( ord_less_eq_real @ A3 @ B2 )
          & ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_600_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: risk_Free_account,Z2: risk_Free_account] : ( Y4 = Z2 ) )
    = ( ^ [A3: risk_Free_account,B2: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ A3 @ B2 )
          & ( ord_le4245800335709223507ccount @ B2 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_601_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
    = ( ^ [A3: int,B2: int] :
          ( ( ord_less_eq_int @ A3 @ B2 )
          & ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_602_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
    = ( ^ [A3: num,B2: num] :
          ( ( ord_less_eq_num @ A3 @ B2 )
          & ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_603_antisym,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_604_antisym,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_605_antisym,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ord_le4245800335709223507ccount @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_606_antisym,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_607_antisym,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_num @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_608_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_609_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_610_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_611_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_612_dual__order_Otrans,axiom,
    ! [B: num,A: num,C: num] :
      ( ( ord_less_eq_num @ B @ A )
     => ( ( ord_less_eq_num @ C @ B )
       => ( ord_less_eq_num @ C @ A ) ) ) ).

% dual_order.trans
thf(fact_613_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_614_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_615_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_616_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_617_dual__order_Oantisym,axiom,
    ! [B: num,A: num] :
      ( ( ord_less_eq_num @ B @ A )
     => ( ( ord_less_eq_num @ A @ B )
       => ( A = B ) ) ) ).

% dual_order.antisym
thf(fact_618_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
    = ( ^ [A3: nat,B2: nat] :
          ( ( ord_less_eq_nat @ B2 @ A3 )
          & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_619_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
    = ( ^ [A3: real,B2: real] :
          ( ( ord_less_eq_real @ B2 @ A3 )
          & ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_620_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y4: risk_Free_account,Z2: risk_Free_account] : ( Y4 = Z2 ) )
    = ( ^ [A3: risk_Free_account,B2: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ B2 @ A3 )
          & ( ord_le4245800335709223507ccount @ A3 @ B2 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_621_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
    = ( ^ [A3: int,B2: int] :
          ( ( ord_less_eq_int @ B2 @ A3 )
          & ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_622_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
    = ( ^ [A3: num,B2: num] :
          ( ( ord_less_eq_num @ B2 @ A3 )
          & ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_623_linorder__wlog,axiom,
    ! [P: nat > nat > $o,A: nat,B: nat] :
      ( ! [A4: nat,B4: nat] :
          ( ( ord_less_eq_nat @ A4 @ B4 )
         => ( P @ A4 @ B4 ) )
     => ( ! [A4: nat,B4: nat] :
            ( ( P @ B4 @ A4 )
           => ( P @ A4 @ B4 ) )
       => ( P @ A @ B ) ) ) ).

% linorder_wlog
thf(fact_624_linorder__wlog,axiom,
    ! [P: real > real > $o,A: real,B: real] :
      ( ! [A4: real,B4: real] :
          ( ( ord_less_eq_real @ A4 @ B4 )
         => ( P @ A4 @ B4 ) )
     => ( ! [A4: real,B4: real] :
            ( ( P @ B4 @ A4 )
           => ( P @ A4 @ B4 ) )
       => ( P @ A @ B ) ) ) ).

% linorder_wlog
thf(fact_625_linorder__wlog,axiom,
    ! [P: int > int > $o,A: int,B: int] :
      ( ! [A4: int,B4: int] :
          ( ( ord_less_eq_int @ A4 @ B4 )
         => ( P @ A4 @ B4 ) )
     => ( ! [A4: int,B4: int] :
            ( ( P @ B4 @ A4 )
           => ( P @ A4 @ B4 ) )
       => ( P @ A @ B ) ) ) ).

% linorder_wlog
thf(fact_626_linorder__wlog,axiom,
    ! [P: num > num > $o,A: num,B: num] :
      ( ! [A4: num,B4: num] :
          ( ( ord_less_eq_num @ A4 @ B4 )
         => ( P @ A4 @ B4 ) )
     => ( ! [A4: num,B4: num] :
            ( ( P @ B4 @ A4 )
           => ( P @ A4 @ B4 ) )
       => ( P @ A @ B ) ) ) ).

% linorder_wlog
thf(fact_627_order__trans,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( ord_less_eq_nat @ Y @ Z )
       => ( ord_less_eq_nat @ X @ Z ) ) ) ).

% order_trans
thf(fact_628_order__trans,axiom,
    ! [X: real,Y: real,Z: real] :
      ( ( ord_less_eq_real @ X @ Y )
     => ( ( ord_less_eq_real @ Y @ Z )
       => ( ord_less_eq_real @ X @ Z ) ) ) ).

% order_trans
thf(fact_629_order__trans,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account,Z: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ X @ Y )
     => ( ( ord_le4245800335709223507ccount @ Y @ Z )
       => ( ord_le4245800335709223507ccount @ X @ Z ) ) ) ).

% order_trans
thf(fact_630_order__trans,axiom,
    ! [X: int,Y: int,Z: int] :
      ( ( ord_less_eq_int @ X @ Y )
     => ( ( ord_less_eq_int @ Y @ Z )
       => ( ord_less_eq_int @ X @ Z ) ) ) ).

% order_trans
thf(fact_631_order__trans,axiom,
    ! [X: num,Y: num,Z: num] :
      ( ( ord_less_eq_num @ X @ Y )
     => ( ( ord_less_eq_num @ Y @ Z )
       => ( ord_less_eq_num @ X @ Z ) ) ) ).

% order_trans
thf(fact_632_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_633_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_634_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_635_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_636_order_Otrans,axiom,
    ! [A: num,B: num,C: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_num @ B @ C )
       => ( ord_less_eq_num @ A @ C ) ) ) ).

% order.trans
thf(fact_637_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_638_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_639_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_640_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_641_order__antisym,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_eq_num @ X @ Y )
     => ( ( ord_less_eq_num @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_642_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_643_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_644_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_645_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_646_ord__le__eq__trans,axiom,
    ! [A: num,B: num,C: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_num @ A @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_647_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_648_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_649_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_650_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_651_ord__eq__le__trans,axiom,
    ! [A: num,B: num,C: num] :
      ( ( A = B )
     => ( ( ord_less_eq_num @ B @ C )
       => ( ord_less_eq_num @ A @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_652_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
    = ( ^ [X2: nat,Y5: nat] :
          ( ( ord_less_eq_nat @ X2 @ Y5 )
          & ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_653_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
    = ( ^ [X2: real,Y5: real] :
          ( ( ord_less_eq_real @ X2 @ Y5 )
          & ( ord_less_eq_real @ Y5 @ X2 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_654_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: risk_Free_account,Z2: risk_Free_account] : ( Y4 = Z2 ) )
    = ( ^ [X2: risk_Free_account,Y5: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ X2 @ Y5 )
          & ( ord_le4245800335709223507ccount @ Y5 @ X2 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_655_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
    = ( ^ [X2: int,Y5: int] :
          ( ( ord_less_eq_int @ X2 @ Y5 )
          & ( ord_less_eq_int @ Y5 @ X2 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_656_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
    = ( ^ [X2: num,Y5: num] :
          ( ( ord_less_eq_num @ X2 @ Y5 )
          & ( ord_less_eq_num @ Y5 @ X2 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_657_le__cases3,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( ( ord_less_eq_nat @ X @ Y )
       => ~ ( ord_less_eq_nat @ Y @ Z ) )
     => ( ( ( ord_less_eq_nat @ Y @ X )
         => ~ ( ord_less_eq_nat @ X @ Z ) )
       => ( ( ( ord_less_eq_nat @ X @ Z )
           => ~ ( ord_less_eq_nat @ Z @ Y ) )
         => ( ( ( ord_less_eq_nat @ Z @ Y )
             => ~ ( ord_less_eq_nat @ Y @ X ) )
           => ( ( ( ord_less_eq_nat @ Y @ Z )
               => ~ ( ord_less_eq_nat @ Z @ X ) )
             => ~ ( ( ord_less_eq_nat @ Z @ X )
                 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).

% le_cases3
thf(fact_658_le__cases3,axiom,
    ! [X: real,Y: real,Z: real] :
      ( ( ( ord_less_eq_real @ X @ Y )
       => ~ ( ord_less_eq_real @ Y @ Z ) )
     => ( ( ( ord_less_eq_real @ Y @ X )
         => ~ ( ord_less_eq_real @ X @ Z ) )
       => ( ( ( ord_less_eq_real @ X @ Z )
           => ~ ( ord_less_eq_real @ Z @ Y ) )
         => ( ( ( ord_less_eq_real @ Z @ Y )
             => ~ ( ord_less_eq_real @ Y @ X ) )
           => ( ( ( ord_less_eq_real @ Y @ Z )
               => ~ ( ord_less_eq_real @ Z @ X ) )
             => ~ ( ( ord_less_eq_real @ Z @ X )
                 => ~ ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ) ).

% le_cases3
thf(fact_659_le__cases3,axiom,
    ! [X: int,Y: int,Z: int] :
      ( ( ( ord_less_eq_int @ X @ Y )
       => ~ ( ord_less_eq_int @ Y @ Z ) )
     => ( ( ( ord_less_eq_int @ Y @ X )
         => ~ ( ord_less_eq_int @ X @ Z ) )
       => ( ( ( ord_less_eq_int @ X @ Z )
           => ~ ( ord_less_eq_int @ Z @ Y ) )
         => ( ( ( ord_less_eq_int @ Z @ Y )
             => ~ ( ord_less_eq_int @ Y @ X ) )
           => ( ( ( ord_less_eq_int @ Y @ Z )
               => ~ ( ord_less_eq_int @ Z @ X ) )
             => ~ ( ( ord_less_eq_int @ Z @ X )
                 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).

% le_cases3
thf(fact_660_le__cases3,axiom,
    ! [X: num,Y: num,Z: num] :
      ( ( ( ord_less_eq_num @ X @ Y )
       => ~ ( ord_less_eq_num @ Y @ Z ) )
     => ( ( ( ord_less_eq_num @ Y @ X )
         => ~ ( ord_less_eq_num @ X @ Z ) )
       => ( ( ( ord_less_eq_num @ X @ Z )
           => ~ ( ord_less_eq_num @ Z @ Y ) )
         => ( ( ( ord_less_eq_num @ Z @ Y )
             => ~ ( ord_less_eq_num @ Y @ X ) )
           => ( ( ( ord_less_eq_num @ Y @ Z )
               => ~ ( ord_less_eq_num @ Z @ X ) )
             => ~ ( ( ord_less_eq_num @ Z @ X )
                 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).

% le_cases3
thf(fact_661_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_662_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_663_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_664_nle__le,axiom,
    ! [A: num,B: num] :
      ( ( ~ ( ord_less_eq_num @ A @ B ) )
      = ( ( ord_less_eq_num @ B @ A )
        & ( B != A ) ) ) ).

% nle_le
thf(fact_665_lt__ex,axiom,
    ! [X: real] :
    ? [Y2: real] : ( ord_less_real @ Y2 @ X ) ).

% lt_ex
thf(fact_666_lt__ex,axiom,
    ! [X: int] :
    ? [Y2: int] : ( ord_less_int @ Y2 @ X ) ).

% lt_ex
thf(fact_667_gt__ex,axiom,
    ! [X: nat] :
    ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).

% gt_ex
thf(fact_668_gt__ex,axiom,
    ! [X: real] :
    ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).

% gt_ex
thf(fact_669_gt__ex,axiom,
    ! [X: int] :
    ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).

% gt_ex
thf(fact_670_dense,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ X @ Y )
     => ? [Z3: real] :
          ( ( ord_less_real @ X @ Z3 )
          & ( ord_less_real @ Z3 @ Y ) ) ) ).

% dense
thf(fact_671_less__imp__neq,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_nat @ X @ Y )
     => ( X != Y ) ) ).

% less_imp_neq
thf(fact_672_less__imp__neq,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ X @ Y )
     => ( X != Y ) ) ).

% less_imp_neq
thf(fact_673_less__imp__neq,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ X @ Y )
     => ( X != Y ) ) ).

% less_imp_neq
thf(fact_674_less__imp__neq,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_int @ X @ Y )
     => ( X != Y ) ) ).

% less_imp_neq
thf(fact_675_less__imp__neq,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_num @ X @ Y )
     => ( X != Y ) ) ).

% less_imp_neq
thf(fact_676_order_Oasym,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ) ).

% order.asym
thf(fact_677_order_Oasym,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ~ ( ord_le2131251472502387783ccount @ B @ A ) ) ).

% order.asym
thf(fact_678_order_Oasym,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ B )
     => ~ ( ord_less_real @ B @ A ) ) ).

% order.asym
thf(fact_679_order_Oasym,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ) ).

% order.asym
thf(fact_680_order_Oasym,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_num @ A @ B )
     => ~ ( ord_less_num @ B @ A ) ) ).

% order.asym
thf(fact_681_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_682_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_683_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_684_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_685_ord__eq__less__trans,axiom,
    ! [A: num,B: num,C: num] :
      ( ( A = B )
     => ( ( ord_less_num @ B @ C )
       => ( ord_less_num @ A @ C ) ) ) ).

% ord_eq_less_trans
thf(fact_686_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_687_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_688_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_689_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_690_ord__less__eq__trans,axiom,
    ! [A: num,B: num,C: num] :
      ( ( ord_less_num @ A @ B )
     => ( ( B = C )
       => ( ord_less_num @ A @ C ) ) ) ).

% ord_less_eq_trans
thf(fact_691_less__induct,axiom,
    ! [P: nat > $o,A: nat] :
      ( ! [X4: nat] :
          ( ! [Y3: nat] :
              ( ( ord_less_nat @ Y3 @ X4 )
             => ( P @ Y3 ) )
         => ( P @ X4 ) )
     => ( P @ A ) ) ).

% less_induct
thf(fact_692_antisym__conv3,axiom,
    ! [Y: nat,X: nat] :
      ( ~ ( ord_less_nat @ Y @ X )
     => ( ( ~ ( ord_less_nat @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv3
thf(fact_693_antisym__conv3,axiom,
    ! [Y: real,X: real] :
      ( ~ ( ord_less_real @ Y @ X )
     => ( ( ~ ( ord_less_real @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv3
thf(fact_694_antisym__conv3,axiom,
    ! [Y: int,X: int] :
      ( ~ ( ord_less_int @ Y @ X )
     => ( ( ~ ( ord_less_int @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv3
thf(fact_695_antisym__conv3,axiom,
    ! [Y: num,X: num] :
      ( ~ ( ord_less_num @ Y @ X )
     => ( ( ~ ( ord_less_num @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv3
thf(fact_696_linorder__cases,axiom,
    ! [X: nat,Y: nat] :
      ( ~ ( ord_less_nat @ X @ Y )
     => ( ( X != Y )
       => ( ord_less_nat @ Y @ X ) ) ) ).

% linorder_cases
thf(fact_697_linorder__cases,axiom,
    ! [X: real,Y: real] :
      ( ~ ( ord_less_real @ X @ Y )
     => ( ( X != Y )
       => ( ord_less_real @ Y @ X ) ) ) ).

% linorder_cases
thf(fact_698_linorder__cases,axiom,
    ! [X: int,Y: int] :
      ( ~ ( ord_less_int @ X @ Y )
     => ( ( X != Y )
       => ( ord_less_int @ Y @ X ) ) ) ).

% linorder_cases
thf(fact_699_linorder__cases,axiom,
    ! [X: num,Y: num] :
      ( ~ ( ord_less_num @ X @ Y )
     => ( ( X != Y )
       => ( ord_less_num @ Y @ X ) ) ) ).

% linorder_cases
thf(fact_700_dual__order_Oasym,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_nat @ B @ A )
     => ~ ( ord_less_nat @ A @ B ) ) ).

% dual_order.asym
thf(fact_701_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_702_dual__order_Oasym,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_real @ B @ A )
     => ~ ( ord_less_real @ A @ B ) ) ).

% dual_order.asym
thf(fact_703_dual__order_Oasym,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_int @ B @ A )
     => ~ ( ord_less_int @ A @ B ) ) ).

% dual_order.asym
thf(fact_704_dual__order_Oasym,axiom,
    ! [B: num,A: num] :
      ( ( ord_less_num @ B @ A )
     => ~ ( ord_less_num @ A @ B ) ) ).

% dual_order.asym
thf(fact_705_dual__order_Oirrefl,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ) ).

% dual_order.irrefl
thf(fact_706_dual__order_Oirrefl,axiom,
    ! [A: risk_Free_account] :
      ~ ( ord_le2131251472502387783ccount @ A @ A ) ).

% dual_order.irrefl
thf(fact_707_dual__order_Oirrefl,axiom,
    ! [A: real] :
      ~ ( ord_less_real @ A @ A ) ).

% dual_order.irrefl
thf(fact_708_dual__order_Oirrefl,axiom,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ) ).

% dual_order.irrefl
thf(fact_709_dual__order_Oirrefl,axiom,
    ! [A: num] :
      ~ ( ord_less_num @ A @ A ) ).

% dual_order.irrefl
thf(fact_710_exists__least__iff,axiom,
    ( ( ^ [P2: nat > $o] :
        ? [X5: nat] : ( P2 @ X5 ) )
    = ( ^ [P3: nat > $o] :
        ? [N2: nat] :
          ( ( P3 @ N2 )
          & ! [M3: nat] :
              ( ( ord_less_nat @ M3 @ N2 )
             => ~ ( P3 @ M3 ) ) ) ) ) ).

% exists_least_iff
thf(fact_711_linorder__less__wlog,axiom,
    ! [P: nat > nat > $o,A: nat,B: nat] :
      ( ! [A4: nat,B4: nat] :
          ( ( ord_less_nat @ A4 @ B4 )
         => ( P @ A4 @ B4 ) )
     => ( ! [A4: nat] : ( P @ A4 @ A4 )
       => ( ! [A4: nat,B4: nat] :
              ( ( P @ B4 @ A4 )
             => ( P @ A4 @ B4 ) )
         => ( P @ A @ B ) ) ) ) ).

% linorder_less_wlog
thf(fact_712_linorder__less__wlog,axiom,
    ! [P: real > real > $o,A: real,B: real] :
      ( ! [A4: real,B4: real] :
          ( ( ord_less_real @ A4 @ B4 )
         => ( P @ A4 @ B4 ) )
     => ( ! [A4: real] : ( P @ A4 @ A4 )
       => ( ! [A4: real,B4: real] :
              ( ( P @ B4 @ A4 )
             => ( P @ A4 @ B4 ) )
         => ( P @ A @ B ) ) ) ) ).

% linorder_less_wlog
thf(fact_713_linorder__less__wlog,axiom,
    ! [P: int > int > $o,A: int,B: int] :
      ( ! [A4: int,B4: int] :
          ( ( ord_less_int @ A4 @ B4 )
         => ( P @ A4 @ B4 ) )
     => ( ! [A4: int] : ( P @ A4 @ A4 )
       => ( ! [A4: int,B4: int] :
              ( ( P @ B4 @ A4 )
             => ( P @ A4 @ B4 ) )
         => ( P @ A @ B ) ) ) ) ).

% linorder_less_wlog
thf(fact_714_linorder__less__wlog,axiom,
    ! [P: num > num > $o,A: num,B: num] :
      ( ! [A4: num,B4: num] :
          ( ( ord_less_num @ A4 @ B4 )
         => ( P @ A4 @ B4 ) )
     => ( ! [A4: num] : ( P @ A4 @ A4 )
       => ( ! [A4: num,B4: num] :
              ( ( P @ B4 @ A4 )
             => ( P @ A4 @ B4 ) )
         => ( P @ A @ B ) ) ) ) ).

% linorder_less_wlog
thf(fact_715_order_Ostrict__trans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ) ).

% order.strict_trans
thf(fact_716_order_Ostrict__trans,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ord_le2131251472502387783ccount @ A @ C ) ) ) ).

% order.strict_trans
thf(fact_717_order_Ostrict__trans,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_real @ B @ C )
       => ( ord_less_real @ A @ C ) ) ) ).

% order.strict_trans
thf(fact_718_order_Ostrict__trans,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ B @ C )
       => ( ord_less_int @ A @ C ) ) ) ).

% order.strict_trans
thf(fact_719_order_Ostrict__trans,axiom,
    ! [A: num,B: num,C: num] :
      ( ( ord_less_num @ A @ B )
     => ( ( ord_less_num @ B @ C )
       => ( ord_less_num @ A @ C ) ) ) ).

% order.strict_trans
thf(fact_720_not__less__iff__gr__or__eq,axiom,
    ! [X: nat,Y: nat] :
      ( ( ~ ( ord_less_nat @ X @ Y ) )
      = ( ( ord_less_nat @ Y @ X )
        | ( X = Y ) ) ) ).

% not_less_iff_gr_or_eq
thf(fact_721_not__less__iff__gr__or__eq,axiom,
    ! [X: real,Y: real] :
      ( ( ~ ( ord_less_real @ X @ Y ) )
      = ( ( ord_less_real @ Y @ X )
        | ( X = Y ) ) ) ).

% not_less_iff_gr_or_eq
thf(fact_722_not__less__iff__gr__or__eq,axiom,
    ! [X: int,Y: int] :
      ( ( ~ ( ord_less_int @ X @ Y ) )
      = ( ( ord_less_int @ Y @ X )
        | ( X = Y ) ) ) ).

% not_less_iff_gr_or_eq
thf(fact_723_not__less__iff__gr__or__eq,axiom,
    ! [X: num,Y: num] :
      ( ( ~ ( ord_less_num @ X @ Y ) )
      = ( ( ord_less_num @ Y @ X )
        | ( X = Y ) ) ) ).

% not_less_iff_gr_or_eq
thf(fact_724_dual__order_Ostrict__trans,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ord_less_nat @ B @ A )
     => ( ( ord_less_nat @ C @ B )
       => ( ord_less_nat @ C @ A ) ) ) ).

% dual_order.strict_trans
thf(fact_725_dual__order_Ostrict__trans,axiom,
    ! [B: risk_Free_account,A: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ B @ A )
     => ( ( ord_le2131251472502387783ccount @ C @ B )
       => ( ord_le2131251472502387783ccount @ C @ A ) ) ) ).

% dual_order.strict_trans
thf(fact_726_dual__order_Ostrict__trans,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ord_less_real @ B @ A )
     => ( ( ord_less_real @ C @ B )
       => ( ord_less_real @ C @ A ) ) ) ).

% dual_order.strict_trans
thf(fact_727_dual__order_Ostrict__trans,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ord_less_int @ B @ A )
     => ( ( ord_less_int @ C @ B )
       => ( ord_less_int @ C @ A ) ) ) ).

% dual_order.strict_trans
thf(fact_728_dual__order_Ostrict__trans,axiom,
    ! [B: num,A: num,C: num] :
      ( ( ord_less_num @ B @ A )
     => ( ( ord_less_num @ C @ B )
       => ( ord_less_num @ C @ A ) ) ) ).

% dual_order.strict_trans
thf(fact_729_order_Ostrict__implies__not__eq,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( A != B ) ) ).

% order.strict_implies_not_eq
thf(fact_730_order_Ostrict__implies__not__eq,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( A != B ) ) ).

% order.strict_implies_not_eq
thf(fact_731_order_Ostrict__implies__not__eq,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ B )
     => ( A != B ) ) ).

% order.strict_implies_not_eq
thf(fact_732_order_Ostrict__implies__not__eq,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( A != B ) ) ).

% order.strict_implies_not_eq
thf(fact_733_order_Ostrict__implies__not__eq,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_num @ A @ B )
     => ( A != B ) ) ).

% order.strict_implies_not_eq
thf(fact_734_dual__order_Ostrict__implies__not__eq,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_nat @ B @ A )
     => ( A != B ) ) ).

% dual_order.strict_implies_not_eq
thf(fact_735_dual__order_Ostrict__implies__not__eq,axiom,
    ! [B: risk_Free_account,A: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ B @ A )
     => ( A != B ) ) ).

% dual_order.strict_implies_not_eq
thf(fact_736_dual__order_Ostrict__implies__not__eq,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_real @ B @ A )
     => ( A != B ) ) ).

% dual_order.strict_implies_not_eq
thf(fact_737_dual__order_Ostrict__implies__not__eq,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_int @ B @ A )
     => ( A != B ) ) ).

% dual_order.strict_implies_not_eq
thf(fact_738_dual__order_Ostrict__implies__not__eq,axiom,
    ! [B: num,A: num] :
      ( ( ord_less_num @ B @ A )
     => ( A != B ) ) ).

% dual_order.strict_implies_not_eq
thf(fact_739_linorder__neqE,axiom,
    ! [X: nat,Y: nat] :
      ( ( X != Y )
     => ( ~ ( ord_less_nat @ X @ Y )
       => ( ord_less_nat @ Y @ X ) ) ) ).

% linorder_neqE
thf(fact_740_linorder__neqE,axiom,
    ! [X: real,Y: real] :
      ( ( X != Y )
     => ( ~ ( ord_less_real @ X @ Y )
       => ( ord_less_real @ Y @ X ) ) ) ).

% linorder_neqE
thf(fact_741_linorder__neqE,axiom,
    ! [X: int,Y: int] :
      ( ( X != Y )
     => ( ~ ( ord_less_int @ X @ Y )
       => ( ord_less_int @ Y @ X ) ) ) ).

% linorder_neqE
thf(fact_742_linorder__neqE,axiom,
    ! [X: num,Y: num] :
      ( ( X != Y )
     => ( ~ ( ord_less_num @ X @ Y )
       => ( ord_less_num @ Y @ X ) ) ) ).

% linorder_neqE
thf(fact_743_order__less__asym,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_nat @ X @ Y )
     => ~ ( ord_less_nat @ Y @ X ) ) ).

% order_less_asym
thf(fact_744_order__less__asym,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ X @ Y )
     => ~ ( ord_le2131251472502387783ccount @ Y @ X ) ) ).

% order_less_asym
thf(fact_745_order__less__asym,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ X @ Y )
     => ~ ( ord_less_real @ Y @ X ) ) ).

% order_less_asym
thf(fact_746_order__less__asym,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_int @ X @ Y )
     => ~ ( ord_less_int @ Y @ X ) ) ).

% order_less_asym
thf(fact_747_order__less__asym,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_num @ X @ Y )
     => ~ ( ord_less_num @ Y @ X ) ) ).

% order_less_asym
thf(fact_748_linorder__neq__iff,axiom,
    ! [X: nat,Y: nat] :
      ( ( X != Y )
      = ( ( ord_less_nat @ X @ Y )
        | ( ord_less_nat @ Y @ X ) ) ) ).

% linorder_neq_iff
thf(fact_749_linorder__neq__iff,axiom,
    ! [X: real,Y: real] :
      ( ( X != Y )
      = ( ( ord_less_real @ X @ Y )
        | ( ord_less_real @ Y @ X ) ) ) ).

% linorder_neq_iff
thf(fact_750_linorder__neq__iff,axiom,
    ! [X: int,Y: int] :
      ( ( X != Y )
      = ( ( ord_less_int @ X @ Y )
        | ( ord_less_int @ Y @ X ) ) ) ).

% linorder_neq_iff
thf(fact_751_linorder__neq__iff,axiom,
    ! [X: num,Y: num] :
      ( ( X != Y )
      = ( ( ord_less_num @ X @ Y )
        | ( ord_less_num @ Y @ X ) ) ) ).

% linorder_neq_iff
thf(fact_752_order__less__asym_H,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ) ).

% order_less_asym'
thf(fact_753_order__less__asym_H,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ~ ( ord_le2131251472502387783ccount @ B @ A ) ) ).

% order_less_asym'
thf(fact_754_order__less__asym_H,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ B )
     => ~ ( ord_less_real @ B @ A ) ) ).

% order_less_asym'
thf(fact_755_order__less__asym_H,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ) ).

% order_less_asym'
thf(fact_756_order__less__asym_H,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_num @ A @ B )
     => ~ ( ord_less_num @ B @ A ) ) ).

% order_less_asym'
thf(fact_757_order__less__trans,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( ord_less_nat @ X @ Y )
     => ( ( ord_less_nat @ Y @ Z )
       => ( ord_less_nat @ X @ Z ) ) ) ).

% order_less_trans
thf(fact_758_order__less__trans,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account,Z: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ X @ Y )
     => ( ( ord_le2131251472502387783ccount @ Y @ Z )
       => ( ord_le2131251472502387783ccount @ X @ Z ) ) ) ).

% order_less_trans
thf(fact_759_order__less__trans,axiom,
    ! [X: real,Y: real,Z: real] :
      ( ( ord_less_real @ X @ Y )
     => ( ( ord_less_real @ Y @ Z )
       => ( ord_less_real @ X @ Z ) ) ) ).

% order_less_trans
thf(fact_760_order__less__trans,axiom,
    ! [X: int,Y: int,Z: int] :
      ( ( ord_less_int @ X @ Y )
     => ( ( ord_less_int @ Y @ Z )
       => ( ord_less_int @ X @ Z ) ) ) ).

% order_less_trans
thf(fact_761_order__less__trans,axiom,
    ! [X: num,Y: num,Z: num] :
      ( ( ord_less_num @ X @ Y )
     => ( ( ord_less_num @ Y @ Z )
       => ( ord_less_num @ X @ Z ) ) ) ).

% order_less_trans
thf(fact_762_ord__eq__less__subst,axiom,
    ! [A: nat,F: nat > nat,B: nat,C: nat] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_763_ord__eq__less__subst,axiom,
    ! [A: risk_Free_account,F: nat > risk_Free_account,B: nat,C: nat] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_le2131251472502387783ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_764_ord__eq__less__subst,axiom,
    ! [A: real,F: nat > real,B: nat,C: nat] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_765_ord__eq__less__subst,axiom,
    ! [A: int,F: nat > int,B: nat,C: nat] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_766_ord__eq__less__subst,axiom,
    ! [A: num,F: nat > num,B: nat,C: nat] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_767_ord__eq__less__subst,axiom,
    ! [A: nat,F: risk_Free_account > nat,B: risk_Free_account,C: risk_Free_account] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_768_ord__eq__less__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_le2131251472502387783ccount @ B @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_le2131251472502387783ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_769_ord__eq__less__subst,axiom,
    ! [A: real,F: risk_Free_account > real,B: risk_Free_account,C: risk_Free_account] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_770_ord__eq__less__subst,axiom,
    ! [A: int,F: risk_Free_account > int,B: risk_Free_account,C: risk_Free_account] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_771_ord__eq__less__subst,axiom,
    ! [A: num,F: risk_Free_account > num,B: risk_Free_account,C: risk_Free_account] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_772_ord__less__eq__subst,axiom,
    ! [A: nat,B: nat,F: nat > nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_773_ord__less__eq__subst,axiom,
    ! [A: nat,B: nat,F: nat > risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_le2131251472502387783ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ ( F @ A ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_774_ord__less__eq__subst,axiom,
    ! [A: nat,B: nat,F: nat > real,C: real] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_775_ord__less__eq__subst,axiom,
    ! [A: nat,B: nat,F: nat > int,C: int] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_776_ord__less__eq__subst,axiom,
    ! [A: nat,B: nat,F: nat > num,C: num] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_777_ord__less__eq__subst,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > nat,C: nat] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_778_ord__less__eq__subst,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_le2131251472502387783ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ ( F @ A ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_779_ord__less__eq__subst,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > real,C: real] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_780_ord__less__eq__subst,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > int,C: int] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_781_ord__less__eq__subst,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > num,C: num] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_782_order__less__irrefl,axiom,
    ! [X: nat] :
      ~ ( ord_less_nat @ X @ X ) ).

% order_less_irrefl
thf(fact_783_order__less__irrefl,axiom,
    ! [X: risk_Free_account] :
      ~ ( ord_le2131251472502387783ccount @ X @ X ) ).

% order_less_irrefl
thf(fact_784_order__less__irrefl,axiom,
    ! [X: real] :
      ~ ( ord_less_real @ X @ X ) ).

% order_less_irrefl
thf(fact_785_order__less__irrefl,axiom,
    ! [X: int] :
      ~ ( ord_less_int @ X @ X ) ).

% order_less_irrefl
thf(fact_786_order__less__irrefl,axiom,
    ! [X: num] :
      ~ ( ord_less_num @ X @ X ) ).

% order_less_irrefl
thf(fact_787_order__less__subst1,axiom,
    ! [A: nat,F: nat > nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ ( F @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_788_order__less__subst1,axiom,
    ! [A: nat,F: risk_Free_account > nat,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_nat @ A @ ( F @ B ) )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_789_order__less__subst1,axiom,
    ! [A: nat,F: real > nat,B: real,C: real] :
      ( ( ord_less_nat @ A @ ( F @ B ) )
     => ( ( ord_less_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_real @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_790_order__less__subst1,axiom,
    ! [A: nat,F: int > nat,B: int,C: int] :
      ( ( ord_less_nat @ A @ ( F @ B ) )
     => ( ( ord_less_int @ B @ C )
       => ( ! [X4: int,Y2: int] :
              ( ( ord_less_int @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_791_order__less__subst1,axiom,
    ! [A: nat,F: num > nat,B: num,C: num] :
      ( ( ord_less_nat @ A @ ( F @ B ) )
     => ( ( ord_less_num @ B @ C )
       => ( ! [X4: num,Y2: num] :
              ( ( ord_less_num @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_792_order__less__subst1,axiom,
    ! [A: risk_Free_account,F: nat > risk_Free_account,B: nat,C: nat] :
      ( ( ord_le2131251472502387783ccount @ A @ ( F @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_le2131251472502387783ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ A @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_793_order__less__subst1,axiom,
    ! [A: risk_Free_account,F: risk_Free_account > risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ ( F @ B ) )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_le2131251472502387783ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ A @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_794_order__less__subst1,axiom,
    ! [A: risk_Free_account,F: real > risk_Free_account,B: real,C: real] :
      ( ( ord_le2131251472502387783ccount @ A @ ( F @ B ) )
     => ( ( ord_less_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_real @ X4 @ Y2 )
             => ( ord_le2131251472502387783ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ A @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_795_order__less__subst1,axiom,
    ! [A: risk_Free_account,F: int > risk_Free_account,B: int,C: int] :
      ( ( ord_le2131251472502387783ccount @ A @ ( F @ B ) )
     => ( ( ord_less_int @ B @ C )
       => ( ! [X4: int,Y2: int] :
              ( ( ord_less_int @ X4 @ Y2 )
             => ( ord_le2131251472502387783ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ A @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_796_order__less__subst1,axiom,
    ! [A: risk_Free_account,F: num > risk_Free_account,B: num,C: num] :
      ( ( ord_le2131251472502387783ccount @ A @ ( F @ B ) )
     => ( ( ord_less_num @ B @ C )
       => ( ! [X4: num,Y2: num] :
              ( ( ord_less_num @ X4 @ Y2 )
             => ( ord_le2131251472502387783ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ A @ ( F @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_797_order__less__subst2,axiom,
    ! [A: nat,B: nat,F: nat > nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_798_order__less__subst2,axiom,
    ! [A: nat,B: nat,F: nat > risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_le2131251472502387783ccount @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_le2131251472502387783ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ ( F @ A ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_799_order__less__subst2,axiom,
    ! [A: nat,B: nat,F: nat > real,C: real] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_real @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_800_order__less__subst2,axiom,
    ! [A: nat,B: nat,F: nat > int,C: int] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_int @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_801_order__less__subst2,axiom,
    ! [A: nat,B: nat,F: nat > num,C: num] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_num @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_802_order__less__subst2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > nat,C: nat] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ord_less_nat @ ( F @ B ) @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_803_order__less__subst2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ord_le2131251472502387783ccount @ ( F @ B ) @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_le2131251472502387783ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ ( F @ A ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_804_order__less__subst2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > real,C: real] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ord_less_real @ ( F @ B ) @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_805_order__less__subst2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > int,C: int] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ord_less_int @ ( F @ B ) @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_806_order__less__subst2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > num,C: num] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ord_less_num @ ( F @ B ) @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_807_order__less__not__sym,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_nat @ X @ Y )
     => ~ ( ord_less_nat @ Y @ X ) ) ).

% order_less_not_sym
thf(fact_808_order__less__not__sym,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ X @ Y )
     => ~ ( ord_le2131251472502387783ccount @ Y @ X ) ) ).

% order_less_not_sym
thf(fact_809_order__less__not__sym,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ X @ Y )
     => ~ ( ord_less_real @ Y @ X ) ) ).

% order_less_not_sym
thf(fact_810_order__less__not__sym,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_int @ X @ Y )
     => ~ ( ord_less_int @ Y @ X ) ) ).

% order_less_not_sym
thf(fact_811_order__less__not__sym,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_num @ X @ Y )
     => ~ ( ord_less_num @ Y @ X ) ) ).

% order_less_not_sym
thf(fact_812_order__less__imp__triv,axiom,
    ! [X: nat,Y: nat,P: $o] :
      ( ( ord_less_nat @ X @ Y )
     => ( ( ord_less_nat @ Y @ X )
       => P ) ) ).

% order_less_imp_triv
thf(fact_813_order__less__imp__triv,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account,P: $o] :
      ( ( ord_le2131251472502387783ccount @ X @ Y )
     => ( ( ord_le2131251472502387783ccount @ Y @ X )
       => P ) ) ).

% order_less_imp_triv
thf(fact_814_order__less__imp__triv,axiom,
    ! [X: real,Y: real,P: $o] :
      ( ( ord_less_real @ X @ Y )
     => ( ( ord_less_real @ Y @ X )
       => P ) ) ).

% order_less_imp_triv
thf(fact_815_order__less__imp__triv,axiom,
    ! [X: int,Y: int,P: $o] :
      ( ( ord_less_int @ X @ Y )
     => ( ( ord_less_int @ Y @ X )
       => P ) ) ).

% order_less_imp_triv
thf(fact_816_order__less__imp__triv,axiom,
    ! [X: num,Y: num,P: $o] :
      ( ( ord_less_num @ X @ Y )
     => ( ( ord_less_num @ Y @ X )
       => P ) ) ).

% order_less_imp_triv
thf(fact_817_linorder__less__linear,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_nat @ X @ Y )
      | ( X = Y )
      | ( ord_less_nat @ Y @ X ) ) ).

% linorder_less_linear
thf(fact_818_linorder__less__linear,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ X @ Y )
      | ( X = Y )
      | ( ord_less_real @ Y @ X ) ) ).

% linorder_less_linear
thf(fact_819_linorder__less__linear,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_int @ X @ Y )
      | ( X = Y )
      | ( ord_less_int @ Y @ X ) ) ).

% linorder_less_linear
thf(fact_820_linorder__less__linear,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_num @ X @ Y )
      | ( X = Y )
      | ( ord_less_num @ Y @ X ) ) ).

% linorder_less_linear
thf(fact_821_order__less__imp__not__eq,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_nat @ X @ Y )
     => ( X != Y ) ) ).

% order_less_imp_not_eq
thf(fact_822_order__less__imp__not__eq,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ X @ Y )
     => ( X != Y ) ) ).

% order_less_imp_not_eq
thf(fact_823_order__less__imp__not__eq,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ X @ Y )
     => ( X != Y ) ) ).

% order_less_imp_not_eq
thf(fact_824_order__less__imp__not__eq,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_int @ X @ Y )
     => ( X != Y ) ) ).

% order_less_imp_not_eq
thf(fact_825_order__less__imp__not__eq,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_num @ X @ Y )
     => ( X != Y ) ) ).

% order_less_imp_not_eq
thf(fact_826_order__less__imp__not__eq2,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_nat @ X @ Y )
     => ( Y != X ) ) ).

% order_less_imp_not_eq2
thf(fact_827_order__less__imp__not__eq2,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ X @ Y )
     => ( Y != X ) ) ).

% order_less_imp_not_eq2
thf(fact_828_order__less__imp__not__eq2,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ X @ Y )
     => ( Y != X ) ) ).

% order_less_imp_not_eq2
thf(fact_829_order__less__imp__not__eq2,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_int @ X @ Y )
     => ( Y != X ) ) ).

% order_less_imp_not_eq2
thf(fact_830_order__less__imp__not__eq2,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_num @ X @ Y )
     => ( Y != X ) ) ).

% order_less_imp_not_eq2
thf(fact_831_order__less__imp__not__less,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_nat @ X @ Y )
     => ~ ( ord_less_nat @ Y @ X ) ) ).

% order_less_imp_not_less
thf(fact_832_order__less__imp__not__less,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ X @ Y )
     => ~ ( ord_le2131251472502387783ccount @ Y @ X ) ) ).

% order_less_imp_not_less
thf(fact_833_order__less__imp__not__less,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ X @ Y )
     => ~ ( ord_less_real @ Y @ X ) ) ).

% order_less_imp_not_less
thf(fact_834_order__less__imp__not__less,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_int @ X @ Y )
     => ~ ( ord_less_int @ Y @ X ) ) ).

% order_less_imp_not_less
thf(fact_835_order__less__imp__not__less,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_num @ X @ Y )
     => ~ ( ord_less_num @ Y @ X ) ) ).

% order_less_imp_not_less
thf(fact_836_order__le__imp__less__or__eq,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( ord_less_nat @ X @ Y )
        | ( X = Y ) ) ) ).

% order_le_imp_less_or_eq
thf(fact_837_order__le__imp__less__or__eq,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ X @ Y )
     => ( ( ord_less_real @ X @ Y )
        | ( X = Y ) ) ) ).

% order_le_imp_less_or_eq
thf(fact_838_order__le__imp__less__or__eq,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ X @ Y )
     => ( ( ord_le2131251472502387783ccount @ X @ Y )
        | ( X = Y ) ) ) ).

% order_le_imp_less_or_eq
thf(fact_839_order__le__imp__less__or__eq,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ X @ Y )
     => ( ( ord_less_int @ X @ Y )
        | ( X = Y ) ) ) ).

% order_le_imp_less_or_eq
thf(fact_840_order__le__imp__less__or__eq,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_eq_num @ X @ Y )
     => ( ( ord_less_num @ X @ Y )
        | ( X = Y ) ) ) ).

% order_le_imp_less_or_eq
thf(fact_841_linorder__le__less__linear,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
      | ( ord_less_nat @ Y @ X ) ) ).

% linorder_le_less_linear
thf(fact_842_linorder__le__less__linear,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ X @ Y )
      | ( ord_less_real @ Y @ X ) ) ).

% linorder_le_less_linear
thf(fact_843_linorder__le__less__linear,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ X @ Y )
      | ( ord_less_int @ Y @ X ) ) ).

% linorder_le_less_linear
thf(fact_844_linorder__le__less__linear,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_eq_num @ X @ Y )
      | ( ord_less_num @ Y @ X ) ) ).

% linorder_le_less_linear
thf(fact_845_order__less__le__subst2,axiom,
    ! [A: nat,B: nat,F: nat > nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_846_order__less__le__subst2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > nat,C: nat] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_847_order__less__le__subst2,axiom,
    ! [A: real,B: real,F: real > nat,C: nat] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_real @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_848_order__less__le__subst2,axiom,
    ! [A: int,B: int,F: int > nat,C: nat] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
       => ( ! [X4: int,Y2: int] :
              ( ( ord_less_int @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_849_order__less__le__subst2,axiom,
    ! [A: num,B: num,F: num > nat,C: nat] :
      ( ( ord_less_num @ A @ B )
     => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
       => ( ! [X4: num,Y2: num] :
              ( ( ord_less_num @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_850_order__less__le__subst2,axiom,
    ! [A: nat,B: nat,F: nat > real,C: real] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_real @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_851_order__less__le__subst2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,F: risk_Free_account > real,C: real] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ord_less_eq_real @ ( F @ B ) @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_852_order__less__le__subst2,axiom,
    ! [A: real,B: real,F: real > real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_eq_real @ ( F @ B ) @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_real @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_853_order__less__le__subst2,axiom,
    ! [A: int,B: int,F: int > real,C: real] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_eq_real @ ( F @ B ) @ C )
       => ( ! [X4: int,Y2: int] :
              ( ( ord_less_int @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_854_order__less__le__subst2,axiom,
    ! [A: num,B: num,F: num > real,C: real] :
      ( ( ord_less_num @ A @ B )
     => ( ( ord_less_eq_real @ ( F @ B ) @ C )
       => ( ! [X4: num,Y2: num] :
              ( ( ord_less_num @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_855_order__less__le__subst1,axiom,
    ! [A: nat,F: nat > nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_856_order__less__le__subst1,axiom,
    ! [A: real,F: nat > real,B: nat,C: nat] :
      ( ( ord_less_real @ A @ ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_857_order__less__le__subst1,axiom,
    ! [A: risk_Free_account,F: nat > risk_Free_account,B: nat,C: nat] :
      ( ( ord_le2131251472502387783ccount @ A @ ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_le4245800335709223507ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ A @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_858_order__less__le__subst1,axiom,
    ! [A: int,F: nat > int,B: nat,C: nat] :
      ( ( ord_less_int @ A @ ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_859_order__less__le__subst1,axiom,
    ! [A: num,F: nat > num,B: nat,C: nat] :
      ( ( ord_less_num @ A @ ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_860_order__less__le__subst1,axiom,
    ! [A: nat,F: real > nat,B: real,C: real] :
      ( ( ord_less_nat @ A @ ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_861_order__less__le__subst1,axiom,
    ! [A: real,F: real > real,B: real,C: real] :
      ( ( ord_less_real @ A @ ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_862_order__less__le__subst1,axiom,
    ! [A: risk_Free_account,F: real > risk_Free_account,B: real,C: real] :
      ( ( ord_le2131251472502387783ccount @ A @ ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_le4245800335709223507ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ A @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_863_order__less__le__subst1,axiom,
    ! [A: int,F: real > int,B: real,C: real] :
      ( ( ord_less_int @ A @ ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_864_order__less__le__subst1,axiom,
    ! [A: num,F: real > num,B: real,C: real] :
      ( ( ord_less_num @ A @ ( F @ B ) )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_865_order__le__less__subst2,axiom,
    ! [A: nat,B: nat,F: nat > nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_866_order__le__less__subst2,axiom,
    ! [A: nat,B: nat,F: nat > real,C: real] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_real @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_867_order__le__less__subst2,axiom,
    ! [A: nat,B: nat,F: nat > risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_le2131251472502387783ccount @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_le4245800335709223507ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ ( F @ A ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_868_order__le__less__subst2,axiom,
    ! [A: nat,B: nat,F: nat > int,C: int] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_int @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_869_order__le__less__subst2,axiom,
    ! [A: nat,B: nat,F: nat > num,C: num] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_num @ ( F @ B ) @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_eq_nat @ X4 @ Y2 )
             => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_870_order__le__less__subst2,axiom,
    ! [A: real,B: real,F: real > nat,C: nat] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_nat @ ( F @ B ) @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_871_order__le__less__subst2,axiom,
    ! [A: real,B: real,F: real > real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_real @ ( F @ B ) @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_872_order__le__less__subst2,axiom,
    ! [A: real,B: real,F: real > risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_le2131251472502387783ccount @ ( F @ B ) @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_le4245800335709223507ccount @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_le2131251472502387783ccount @ ( F @ A ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_873_order__le__less__subst2,axiom,
    ! [A: real,B: real,F: real > int,C: int] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_int @ ( F @ B ) @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_874_order__le__less__subst2,axiom,
    ! [A: real,B: real,F: real > num,C: num] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_num @ ( F @ B ) @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_eq_real @ X4 @ Y2 )
             => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_875_order__le__less__subst1,axiom,
    ! [A: nat,F: nat > nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ ( F @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_876_order__le__less__subst1,axiom,
    ! [A: nat,F: risk_Free_account > nat,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_less_eq_nat @ A @ ( F @ B ) )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_877_order__le__less__subst1,axiom,
    ! [A: nat,F: real > nat,B: real,C: real] :
      ( ( ord_less_eq_nat @ A @ ( F @ B ) )
     => ( ( ord_less_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_real @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_878_order__le__less__subst1,axiom,
    ! [A: nat,F: int > nat,B: int,C: int] :
      ( ( ord_less_eq_nat @ A @ ( F @ B ) )
     => ( ( ord_less_int @ B @ C )
       => ( ! [X4: int,Y2: int] :
              ( ( ord_less_int @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_879_order__le__less__subst1,axiom,
    ! [A: nat,F: num > nat,B: num,C: num] :
      ( ( ord_less_eq_nat @ A @ ( F @ B ) )
     => ( ( ord_less_num @ B @ C )
       => ( ! [X4: num,Y2: num] :
              ( ( ord_less_num @ X4 @ Y2 )
             => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_880_order__le__less__subst1,axiom,
    ! [A: real,F: nat > real,B: nat,C: nat] :
      ( ( ord_less_eq_real @ A @ ( F @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X4: nat,Y2: nat] :
              ( ( ord_less_nat @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_881_order__le__less__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_le2131251472502387783ccount @ B @ C )
       => ( ! [X4: risk_Free_account,Y2: risk_Free_account] :
              ( ( ord_le2131251472502387783ccount @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_882_order__le__less__subst1,axiom,
    ! [A: real,F: real > real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ ( F @ B ) )
     => ( ( ord_less_real @ B @ C )
       => ( ! [X4: real,Y2: real] :
              ( ( ord_less_real @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_883_order__le__less__subst1,axiom,
    ! [A: real,F: int > real,B: int,C: int] :
      ( ( ord_less_eq_real @ A @ ( F @ B ) )
     => ( ( ord_less_int @ B @ C )
       => ( ! [X4: int,Y2: int] :
              ( ( ord_less_int @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_884_order__le__less__subst1,axiom,
    ! [A: real,F: num > real,B: num,C: num] :
      ( ( ord_less_eq_real @ A @ ( F @ B ) )
     => ( ( ord_less_num @ B @ C )
       => ( ! [X4: num,Y2: num] :
              ( ( ord_less_num @ X4 @ Y2 )
             => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y2 ) ) )
         => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_885_order__less__le__trans,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( ord_less_nat @ X @ Y )
     => ( ( ord_less_eq_nat @ Y @ Z )
       => ( ord_less_nat @ X @ Z ) ) ) ).

% order_less_le_trans
thf(fact_886_order__less__le__trans,axiom,
    ! [X: real,Y: real,Z: real] :
      ( ( ord_less_real @ X @ Y )
     => ( ( ord_less_eq_real @ Y @ Z )
       => ( ord_less_real @ X @ Z ) ) ) ).

% order_less_le_trans
thf(fact_887_order__less__le__trans,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account,Z: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ X @ Y )
     => ( ( ord_le4245800335709223507ccount @ Y @ Z )
       => ( ord_le2131251472502387783ccount @ X @ Z ) ) ) ).

% order_less_le_trans
thf(fact_888_order__less__le__trans,axiom,
    ! [X: int,Y: int,Z: int] :
      ( ( ord_less_int @ X @ Y )
     => ( ( ord_less_eq_int @ Y @ Z )
       => ( ord_less_int @ X @ Z ) ) ) ).

% order_less_le_trans
thf(fact_889_order__less__le__trans,axiom,
    ! [X: num,Y: num,Z: num] :
      ( ( ord_less_num @ X @ Y )
     => ( ( ord_less_eq_num @ Y @ Z )
       => ( ord_less_num @ X @ Z ) ) ) ).

% order_less_le_trans
thf(fact_890_order__le__less__trans,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( ord_less_nat @ Y @ Z )
       => ( ord_less_nat @ X @ Z ) ) ) ).

% order_le_less_trans
thf(fact_891_order__le__less__trans,axiom,
    ! [X: real,Y: real,Z: real] :
      ( ( ord_less_eq_real @ X @ Y )
     => ( ( ord_less_real @ Y @ Z )
       => ( ord_less_real @ X @ Z ) ) ) ).

% order_le_less_trans
thf(fact_892_order__le__less__trans,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account,Z: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ X @ Y )
     => ( ( ord_le2131251472502387783ccount @ Y @ Z )
       => ( ord_le2131251472502387783ccount @ X @ Z ) ) ) ).

% order_le_less_trans
thf(fact_893_order__le__less__trans,axiom,
    ! [X: int,Y: int,Z: int] :
      ( ( ord_less_eq_int @ X @ Y )
     => ( ( ord_less_int @ Y @ Z )
       => ( ord_less_int @ X @ Z ) ) ) ).

% order_le_less_trans
thf(fact_894_order__le__less__trans,axiom,
    ! [X: num,Y: num,Z: num] :
      ( ( ord_less_eq_num @ X @ Y )
     => ( ( ord_less_num @ Y @ Z )
       => ( ord_less_num @ X @ Z ) ) ) ).

% order_le_less_trans
thf(fact_895_order__neq__le__trans,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( ord_less_eq_nat @ A @ B )
       => ( ord_less_nat @ A @ B ) ) ) ).

% order_neq_le_trans
thf(fact_896_order__neq__le__trans,axiom,
    ! [A: real,B: real] :
      ( ( A != B )
     => ( ( ord_less_eq_real @ A @ B )
       => ( ord_less_real @ A @ B ) ) ) ).

% order_neq_le_trans
thf(fact_897_order__neq__le__trans,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( A != B )
     => ( ( ord_le4245800335709223507ccount @ A @ B )
       => ( ord_le2131251472502387783ccount @ A @ B ) ) ) ).

% order_neq_le_trans
thf(fact_898_order__neq__le__trans,axiom,
    ! [A: int,B: int] :
      ( ( A != B )
     => ( ( ord_less_eq_int @ A @ B )
       => ( ord_less_int @ A @ B ) ) ) ).

% order_neq_le_trans
thf(fact_899_order__neq__le__trans,axiom,
    ! [A: num,B: num] :
      ( ( A != B )
     => ( ( ord_less_eq_num @ A @ B )
       => ( ord_less_num @ A @ B ) ) ) ).

% order_neq_le_trans
thf(fact_900_order__le__neq__trans,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( A != B )
       => ( ord_less_nat @ A @ B ) ) ) ).

% order_le_neq_trans
thf(fact_901_order__le__neq__trans,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( A != B )
       => ( ord_less_real @ A @ B ) ) ) ).

% order_le_neq_trans
thf(fact_902_order__le__neq__trans,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( A != B )
       => ( ord_le2131251472502387783ccount @ A @ B ) ) ) ).

% order_le_neq_trans
thf(fact_903_order__le__neq__trans,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( A != B )
       => ( ord_less_int @ A @ B ) ) ) ).

% order_le_neq_trans
thf(fact_904_order__le__neq__trans,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( A != B )
       => ( ord_less_num @ A @ B ) ) ) ).

% order_le_neq_trans
thf(fact_905_order__less__imp__le,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_nat @ X @ Y )
     => ( ord_less_eq_nat @ X @ Y ) ) ).

% order_less_imp_le
thf(fact_906_order__less__imp__le,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ X @ Y )
     => ( ord_less_eq_real @ X @ Y ) ) ).

% order_less_imp_le
thf(fact_907_order__less__imp__le,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ X @ Y )
     => ( ord_le4245800335709223507ccount @ X @ Y ) ) ).

% order_less_imp_le
thf(fact_908_order__less__imp__le,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_int @ X @ Y )
     => ( ord_less_eq_int @ X @ Y ) ) ).

% order_less_imp_le
thf(fact_909_order__less__imp__le,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_num @ X @ Y )
     => ( ord_less_eq_num @ X @ Y ) ) ).

% order_less_imp_le
thf(fact_910_linorder__not__less,axiom,
    ! [X: nat,Y: nat] :
      ( ( ~ ( ord_less_nat @ X @ Y ) )
      = ( ord_less_eq_nat @ Y @ X ) ) ).

% linorder_not_less
thf(fact_911_linorder__not__less,axiom,
    ! [X: real,Y: real] :
      ( ( ~ ( ord_less_real @ X @ Y ) )
      = ( ord_less_eq_real @ Y @ X ) ) ).

% linorder_not_less
thf(fact_912_linorder__not__less,axiom,
    ! [X: int,Y: int] :
      ( ( ~ ( ord_less_int @ X @ Y ) )
      = ( ord_less_eq_int @ Y @ X ) ) ).

% linorder_not_less
thf(fact_913_linorder__not__less,axiom,
    ! [X: num,Y: num] :
      ( ( ~ ( ord_less_num @ X @ Y ) )
      = ( ord_less_eq_num @ Y @ X ) ) ).

% linorder_not_less
thf(fact_914_linorder__not__le,axiom,
    ! [X: nat,Y: nat] :
      ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
      = ( ord_less_nat @ Y @ X ) ) ).

% linorder_not_le
thf(fact_915_linorder__not__le,axiom,
    ! [X: real,Y: real] :
      ( ( ~ ( ord_less_eq_real @ X @ Y ) )
      = ( ord_less_real @ Y @ X ) ) ).

% linorder_not_le
thf(fact_916_linorder__not__le,axiom,
    ! [X: int,Y: int] :
      ( ( ~ ( ord_less_eq_int @ X @ Y ) )
      = ( ord_less_int @ Y @ X ) ) ).

% linorder_not_le
thf(fact_917_linorder__not__le,axiom,
    ! [X: num,Y: num] :
      ( ( ~ ( ord_less_eq_num @ X @ Y ) )
      = ( ord_less_num @ Y @ X ) ) ).

% linorder_not_le
thf(fact_918_order__less__le,axiom,
    ( ord_less_nat
    = ( ^ [X2: nat,Y5: nat] :
          ( ( ord_less_eq_nat @ X2 @ Y5 )
          & ( X2 != Y5 ) ) ) ) ).

% order_less_le
thf(fact_919_order__less__le,axiom,
    ( ord_less_real
    = ( ^ [X2: real,Y5: real] :
          ( ( ord_less_eq_real @ X2 @ Y5 )
          & ( X2 != Y5 ) ) ) ) ).

% order_less_le
thf(fact_920_order__less__le,axiom,
    ( ord_le2131251472502387783ccount
    = ( ^ [X2: risk_Free_account,Y5: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ X2 @ Y5 )
          & ( X2 != Y5 ) ) ) ) ).

% order_less_le
thf(fact_921_order__less__le,axiom,
    ( ord_less_int
    = ( ^ [X2: int,Y5: int] :
          ( ( ord_less_eq_int @ X2 @ Y5 )
          & ( X2 != Y5 ) ) ) ) ).

% order_less_le
thf(fact_922_order__less__le,axiom,
    ( ord_less_num
    = ( ^ [X2: num,Y5: num] :
          ( ( ord_less_eq_num @ X2 @ Y5 )
          & ( X2 != Y5 ) ) ) ) ).

% order_less_le
thf(fact_923_order__le__less,axiom,
    ( ord_less_eq_nat
    = ( ^ [X2: nat,Y5: nat] :
          ( ( ord_less_nat @ X2 @ Y5 )
          | ( X2 = Y5 ) ) ) ) ).

% order_le_less
thf(fact_924_order__le__less,axiom,
    ( ord_less_eq_real
    = ( ^ [X2: real,Y5: real] :
          ( ( ord_less_real @ X2 @ Y5 )
          | ( X2 = Y5 ) ) ) ) ).

% order_le_less
thf(fact_925_order__le__less,axiom,
    ( ord_le4245800335709223507ccount
    = ( ^ [X2: risk_Free_account,Y5: risk_Free_account] :
          ( ( ord_le2131251472502387783ccount @ X2 @ Y5 )
          | ( X2 = Y5 ) ) ) ) ).

% order_le_less
thf(fact_926_order__le__less,axiom,
    ( ord_less_eq_int
    = ( ^ [X2: int,Y5: int] :
          ( ( ord_less_int @ X2 @ Y5 )
          | ( X2 = Y5 ) ) ) ) ).

% order_le_less
thf(fact_927_order__le__less,axiom,
    ( ord_less_eq_num
    = ( ^ [X2: num,Y5: num] :
          ( ( ord_less_num @ X2 @ Y5 )
          | ( X2 = Y5 ) ) ) ) ).

% order_le_less
thf(fact_928_dual__order_Ostrict__implies__order,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_nat @ B @ A )
     => ( ord_less_eq_nat @ B @ A ) ) ).

% dual_order.strict_implies_order
thf(fact_929_dual__order_Ostrict__implies__order,axiom,
    ! [B: real,A: real] :
      ( ( ord_less_real @ B @ A )
     => ( ord_less_eq_real @ B @ A ) ) ).

% dual_order.strict_implies_order
thf(fact_930_dual__order_Ostrict__implies__order,axiom,
    ! [B: risk_Free_account,A: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ B @ A )
     => ( ord_le4245800335709223507ccount @ B @ A ) ) ).

% dual_order.strict_implies_order
thf(fact_931_dual__order_Ostrict__implies__order,axiom,
    ! [B: int,A: int] :
      ( ( ord_less_int @ B @ A )
     => ( ord_less_eq_int @ B @ A ) ) ).

% dual_order.strict_implies_order
thf(fact_932_dual__order_Ostrict__implies__order,axiom,
    ! [B: num,A: num] :
      ( ( ord_less_num @ B @ A )
     => ( ord_less_eq_num @ B @ A ) ) ).

% dual_order.strict_implies_order
thf(fact_933_order_Ostrict__implies__order,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ B ) ) ).

% order.strict_implies_order
thf(fact_934_order_Ostrict__implies__order,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_eq_real @ A @ B ) ) ).

% order.strict_implies_order
thf(fact_935_order_Ostrict__implies__order,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ord_le4245800335709223507ccount @ A @ B ) ) ).

% order.strict_implies_order
thf(fact_936_order_Ostrict__implies__order,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( ord_less_eq_int @ A @ B ) ) ).

% order.strict_implies_order
thf(fact_937_order_Ostrict__implies__order,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_num @ A @ B )
     => ( ord_less_eq_num @ A @ B ) ) ).

% order.strict_implies_order
thf(fact_938_dual__order_Ostrict__iff__not,axiom,
    ( ord_less_nat
    = ( ^ [B2: nat,A3: nat] :
          ( ( ord_less_eq_nat @ B2 @ A3 )
          & ~ ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).

% dual_order.strict_iff_not
thf(fact_939_dual__order_Ostrict__iff__not,axiom,
    ( ord_less_real
    = ( ^ [B2: real,A3: real] :
          ( ( ord_less_eq_real @ B2 @ A3 )
          & ~ ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).

% dual_order.strict_iff_not
thf(fact_940_dual__order_Ostrict__iff__not,axiom,
    ( ord_le2131251472502387783ccount
    = ( ^ [B2: risk_Free_account,A3: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ B2 @ A3 )
          & ~ ( ord_le4245800335709223507ccount @ A3 @ B2 ) ) ) ) ).

% dual_order.strict_iff_not
thf(fact_941_dual__order_Ostrict__iff__not,axiom,
    ( ord_less_int
    = ( ^ [B2: int,A3: int] :
          ( ( ord_less_eq_int @ B2 @ A3 )
          & ~ ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).

% dual_order.strict_iff_not
thf(fact_942_dual__order_Ostrict__iff__not,axiom,
    ( ord_less_num
    = ( ^ [B2: num,A3: num] :
          ( ( ord_less_eq_num @ B2 @ A3 )
          & ~ ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).

% dual_order.strict_iff_not
thf(fact_943_dual__order_Ostrict__trans2,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ord_less_nat @ B @ A )
     => ( ( ord_less_eq_nat @ C @ B )
       => ( ord_less_nat @ C @ A ) ) ) ).

% dual_order.strict_trans2
thf(fact_944_dual__order_Ostrict__trans2,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ord_less_real @ B @ A )
     => ( ( ord_less_eq_real @ C @ B )
       => ( ord_less_real @ C @ A ) ) ) ).

% dual_order.strict_trans2
thf(fact_945_dual__order_Ostrict__trans2,axiom,
    ! [B: risk_Free_account,A: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ B @ A )
     => ( ( ord_le4245800335709223507ccount @ C @ B )
       => ( ord_le2131251472502387783ccount @ C @ A ) ) ) ).

% dual_order.strict_trans2
thf(fact_946_dual__order_Ostrict__trans2,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ord_less_int @ B @ A )
     => ( ( ord_less_eq_int @ C @ B )
       => ( ord_less_int @ C @ A ) ) ) ).

% dual_order.strict_trans2
thf(fact_947_dual__order_Ostrict__trans2,axiom,
    ! [B: num,A: num,C: num] :
      ( ( ord_less_num @ B @ A )
     => ( ( ord_less_eq_num @ C @ B )
       => ( ord_less_num @ C @ A ) ) ) ).

% dual_order.strict_trans2
thf(fact_948_dual__order_Ostrict__trans1,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( ord_less_nat @ C @ B )
       => ( ord_less_nat @ C @ A ) ) ) ).

% dual_order.strict_trans1
thf(fact_949_dual__order_Ostrict__trans1,axiom,
    ! [B: real,A: real,C: real] :
      ( ( ord_less_eq_real @ B @ A )
     => ( ( ord_less_real @ C @ B )
       => ( ord_less_real @ C @ A ) ) ) ).

% dual_order.strict_trans1
thf(fact_950_dual__order_Ostrict__trans1,axiom,
    ! [B: risk_Free_account,A: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ B @ A )
     => ( ( ord_le2131251472502387783ccount @ C @ B )
       => ( ord_le2131251472502387783ccount @ C @ A ) ) ) ).

% dual_order.strict_trans1
thf(fact_951_dual__order_Ostrict__trans1,axiom,
    ! [B: int,A: int,C: int] :
      ( ( ord_less_eq_int @ B @ A )
     => ( ( ord_less_int @ C @ B )
       => ( ord_less_int @ C @ A ) ) ) ).

% dual_order.strict_trans1
thf(fact_952_dual__order_Ostrict__trans1,axiom,
    ! [B: num,A: num,C: num] :
      ( ( ord_less_eq_num @ B @ A )
     => ( ( ord_less_num @ C @ B )
       => ( ord_less_num @ C @ A ) ) ) ).

% dual_order.strict_trans1
thf(fact_953_dual__order_Ostrict__iff__order,axiom,
    ( ord_less_nat
    = ( ^ [B2: nat,A3: nat] :
          ( ( ord_less_eq_nat @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% dual_order.strict_iff_order
thf(fact_954_dual__order_Ostrict__iff__order,axiom,
    ( ord_less_real
    = ( ^ [B2: real,A3: real] :
          ( ( ord_less_eq_real @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% dual_order.strict_iff_order
thf(fact_955_dual__order_Ostrict__iff__order,axiom,
    ( ord_le2131251472502387783ccount
    = ( ^ [B2: risk_Free_account,A3: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% dual_order.strict_iff_order
thf(fact_956_dual__order_Ostrict__iff__order,axiom,
    ( ord_less_int
    = ( ^ [B2: int,A3: int] :
          ( ( ord_less_eq_int @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% dual_order.strict_iff_order
thf(fact_957_dual__order_Ostrict__iff__order,axiom,
    ( ord_less_num
    = ( ^ [B2: num,A3: num] :
          ( ( ord_less_eq_num @ B2 @ A3 )
          & ( A3 != B2 ) ) ) ) ).

% dual_order.strict_iff_order
thf(fact_958_dual__order_Oorder__iff__strict,axiom,
    ( ord_less_eq_nat
    = ( ^ [B2: nat,A3: nat] :
          ( ( ord_less_nat @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% dual_order.order_iff_strict
thf(fact_959_dual__order_Oorder__iff__strict,axiom,
    ( ord_less_eq_real
    = ( ^ [B2: real,A3: real] :
          ( ( ord_less_real @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% dual_order.order_iff_strict
thf(fact_960_dual__order_Oorder__iff__strict,axiom,
    ( ord_le4245800335709223507ccount
    = ( ^ [B2: risk_Free_account,A3: risk_Free_account] :
          ( ( ord_le2131251472502387783ccount @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% dual_order.order_iff_strict
thf(fact_961_dual__order_Oorder__iff__strict,axiom,
    ( ord_less_eq_int
    = ( ^ [B2: int,A3: int] :
          ( ( ord_less_int @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% dual_order.order_iff_strict
thf(fact_962_dual__order_Oorder__iff__strict,axiom,
    ( ord_less_eq_num
    = ( ^ [B2: num,A3: num] :
          ( ( ord_less_num @ B2 @ A3 )
          | ( A3 = B2 ) ) ) ) ).

% dual_order.order_iff_strict
thf(fact_963_dense__le__bounded,axiom,
    ! [X: real,Y: real,Z: real] :
      ( ( ord_less_real @ X @ Y )
     => ( ! [W: real] :
            ( ( ord_less_real @ X @ W )
           => ( ( ord_less_real @ W @ Y )
             => ( ord_less_eq_real @ W @ Z ) ) )
       => ( ord_less_eq_real @ Y @ Z ) ) ) ).

% dense_le_bounded
thf(fact_964_dense__ge__bounded,axiom,
    ! [Z: real,X: real,Y: real] :
      ( ( ord_less_real @ Z @ X )
     => ( ! [W: real] :
            ( ( ord_less_real @ Z @ W )
           => ( ( ord_less_real @ W @ X )
             => ( ord_less_eq_real @ Y @ W ) ) )
       => ( ord_less_eq_real @ Y @ Z ) ) ) ).

% dense_ge_bounded
thf(fact_965_order_Ostrict__iff__not,axiom,
    ( ord_less_nat
    = ( ^ [A3: nat,B2: nat] :
          ( ( ord_less_eq_nat @ A3 @ B2 )
          & ~ ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).

% order.strict_iff_not
thf(fact_966_order_Ostrict__iff__not,axiom,
    ( ord_less_real
    = ( ^ [A3: real,B2: real] :
          ( ( ord_less_eq_real @ A3 @ B2 )
          & ~ ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).

% order.strict_iff_not
thf(fact_967_order_Ostrict__iff__not,axiom,
    ( ord_le2131251472502387783ccount
    = ( ^ [A3: risk_Free_account,B2: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ A3 @ B2 )
          & ~ ( ord_le4245800335709223507ccount @ B2 @ A3 ) ) ) ) ).

% order.strict_iff_not
thf(fact_968_order_Ostrict__iff__not,axiom,
    ( ord_less_int
    = ( ^ [A3: int,B2: int] :
          ( ( ord_less_eq_int @ A3 @ B2 )
          & ~ ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).

% order.strict_iff_not
thf(fact_969_order_Ostrict__iff__not,axiom,
    ( ord_less_num
    = ( ^ [A3: num,B2: num] :
          ( ( ord_less_eq_num @ A3 @ B2 )
          & ~ ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).

% order.strict_iff_not
thf(fact_970_order_Ostrict__trans2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ) ).

% order.strict_trans2
thf(fact_971_order_Ostrict__trans2,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ord_less_real @ A @ C ) ) ) ).

% order.strict_trans2
thf(fact_972_order_Ostrict__trans2,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le2131251472502387783ccount @ A @ B )
     => ( ( ord_le4245800335709223507ccount @ B @ C )
       => ( ord_le2131251472502387783ccount @ A @ C ) ) ) ).

% order.strict_trans2
thf(fact_973_order_Ostrict__trans2,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ord_less_int @ A @ C ) ) ) ).

% order.strict_trans2
thf(fact_974_order_Ostrict__trans2,axiom,
    ! [A: num,B: num,C: num] :
      ( ( ord_less_num @ A @ B )
     => ( ( ord_less_eq_num @ B @ C )
       => ( ord_less_num @ A @ C ) ) ) ).

% order.strict_trans2
thf(fact_975_order_Ostrict__trans1,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ) ).

% order.strict_trans1
thf(fact_976_order_Ostrict__trans1,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_real @ B @ C )
       => ( ord_less_real @ A @ C ) ) ) ).

% order.strict_trans1
thf(fact_977_order_Ostrict__trans1,axiom,
    ! [A: risk_Free_account,B: risk_Free_account,C: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ A @ B )
     => ( ( ord_le2131251472502387783ccount @ B @ C )
       => ( ord_le2131251472502387783ccount @ A @ C ) ) ) ).

% order.strict_trans1
thf(fact_978_order_Ostrict__trans1,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_int @ B @ C )
       => ( ord_less_int @ A @ C ) ) ) ).

% order.strict_trans1
thf(fact_979_order_Ostrict__trans1,axiom,
    ! [A: num,B: num,C: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_num @ B @ C )
       => ( ord_less_num @ A @ C ) ) ) ).

% order.strict_trans1
thf(fact_980_order_Ostrict__iff__order,axiom,
    ( ord_less_nat
    = ( ^ [A3: nat,B2: nat] :
          ( ( ord_less_eq_nat @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% order.strict_iff_order
thf(fact_981_order_Ostrict__iff__order,axiom,
    ( ord_less_real
    = ( ^ [A3: real,B2: real] :
          ( ( ord_less_eq_real @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% order.strict_iff_order
thf(fact_982_order_Ostrict__iff__order,axiom,
    ( ord_le2131251472502387783ccount
    = ( ^ [A3: risk_Free_account,B2: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% order.strict_iff_order
thf(fact_983_order_Ostrict__iff__order,axiom,
    ( ord_less_int
    = ( ^ [A3: int,B2: int] :
          ( ( ord_less_eq_int @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% order.strict_iff_order
thf(fact_984_order_Ostrict__iff__order,axiom,
    ( ord_less_num
    = ( ^ [A3: num,B2: num] :
          ( ( ord_less_eq_num @ A3 @ B2 )
          & ( A3 != B2 ) ) ) ) ).

% order.strict_iff_order
thf(fact_985_order_Oorder__iff__strict,axiom,
    ( ord_less_eq_nat
    = ( ^ [A3: nat,B2: nat] :
          ( ( ord_less_nat @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% order.order_iff_strict
thf(fact_986_order_Oorder__iff__strict,axiom,
    ( ord_less_eq_real
    = ( ^ [A3: real,B2: real] :
          ( ( ord_less_real @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% order.order_iff_strict
thf(fact_987_order_Oorder__iff__strict,axiom,
    ( ord_le4245800335709223507ccount
    = ( ^ [A3: risk_Free_account,B2: risk_Free_account] :
          ( ( ord_le2131251472502387783ccount @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% order.order_iff_strict
thf(fact_988_order_Oorder__iff__strict,axiom,
    ( ord_less_eq_int
    = ( ^ [A3: int,B2: int] :
          ( ( ord_less_int @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% order.order_iff_strict
thf(fact_989_order_Oorder__iff__strict,axiom,
    ( ord_less_eq_num
    = ( ^ [A3: num,B2: num] :
          ( ( ord_less_num @ A3 @ B2 )
          | ( A3 = B2 ) ) ) ) ).

% order.order_iff_strict
thf(fact_990_not__le__imp__less,axiom,
    ! [Y: nat,X: nat] :
      ( ~ ( ord_less_eq_nat @ Y @ X )
     => ( ord_less_nat @ X @ Y ) ) ).

% not_le_imp_less
thf(fact_991_not__le__imp__less,axiom,
    ! [Y: real,X: real] :
      ( ~ ( ord_less_eq_real @ Y @ X )
     => ( ord_less_real @ X @ Y ) ) ).

% not_le_imp_less
thf(fact_992_not__le__imp__less,axiom,
    ! [Y: int,X: int] :
      ( ~ ( ord_less_eq_int @ Y @ X )
     => ( ord_less_int @ X @ Y ) ) ).

% not_le_imp_less
thf(fact_993_not__le__imp__less,axiom,
    ! [Y: num,X: num] :
      ( ~ ( ord_less_eq_num @ Y @ X )
     => ( ord_less_num @ X @ Y ) ) ).

% not_le_imp_less
thf(fact_994_less__le__not__le,axiom,
    ( ord_less_nat
    = ( ^ [X2: nat,Y5: nat] :
          ( ( ord_less_eq_nat @ X2 @ Y5 )
          & ~ ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ).

% less_le_not_le
thf(fact_995_less__le__not__le,axiom,
    ( ord_less_real
    = ( ^ [X2: real,Y5: real] :
          ( ( ord_less_eq_real @ X2 @ Y5 )
          & ~ ( ord_less_eq_real @ Y5 @ X2 ) ) ) ) ).

% less_le_not_le
thf(fact_996_less__le__not__le,axiom,
    ( ord_le2131251472502387783ccount
    = ( ^ [X2: risk_Free_account,Y5: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ X2 @ Y5 )
          & ~ ( ord_le4245800335709223507ccount @ Y5 @ X2 ) ) ) ) ).

% less_le_not_le
thf(fact_997_less__le__not__le,axiom,
    ( ord_less_int
    = ( ^ [X2: int,Y5: int] :
          ( ( ord_less_eq_int @ X2 @ Y5 )
          & ~ ( ord_less_eq_int @ Y5 @ X2 ) ) ) ) ).

% less_le_not_le
thf(fact_998_less__le__not__le,axiom,
    ( ord_less_num
    = ( ^ [X2: num,Y5: num] :
          ( ( ord_less_eq_num @ X2 @ Y5 )
          & ~ ( ord_less_eq_num @ Y5 @ X2 ) ) ) ) ).

% less_le_not_le
thf(fact_999_dense__le,axiom,
    ! [Y: real,Z: real] :
      ( ! [X4: real] :
          ( ( ord_less_real @ X4 @ Y )
         => ( ord_less_eq_real @ X4 @ Z ) )
     => ( ord_less_eq_real @ Y @ Z ) ) ).

% dense_le
thf(fact_1000_dense__ge,axiom,
    ! [Z: real,Y: real] :
      ( ! [X4: real] :
          ( ( ord_less_real @ Z @ X4 )
         => ( ord_less_eq_real @ Y @ X4 ) )
     => ( ord_less_eq_real @ Y @ Z ) ) ).

% dense_ge
thf(fact_1001_antisym__conv2,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( ~ ( ord_less_nat @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv2
thf(fact_1002_antisym__conv2,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ X @ Y )
     => ( ( ~ ( ord_less_real @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv2
thf(fact_1003_antisym__conv2,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ X @ Y )
     => ( ( ~ ( ord_le2131251472502387783ccount @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv2
thf(fact_1004_antisym__conv2,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ X @ Y )
     => ( ( ~ ( ord_less_int @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv2
thf(fact_1005_antisym__conv2,axiom,
    ! [X: num,Y: num] :
      ( ( ord_less_eq_num @ X @ Y )
     => ( ( ~ ( ord_less_num @ X @ Y ) )
        = ( X = Y ) ) ) ).

% antisym_conv2
thf(fact_1006_antisym__conv1,axiom,
    ! [X: nat,Y: nat] :
      ( ~ ( ord_less_nat @ X @ Y )
     => ( ( ord_less_eq_nat @ X @ Y )
        = ( X = Y ) ) ) ).

% antisym_conv1
thf(fact_1007_antisym__conv1,axiom,
    ! [X: real,Y: real] :
      ( ~ ( ord_less_real @ X @ Y )
     => ( ( ord_less_eq_real @ X @ Y )
        = ( X = Y ) ) ) ).

% antisym_conv1
thf(fact_1008_antisym__conv1,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ~ ( ord_le2131251472502387783ccount @ X @ Y )
     => ( ( ord_le4245800335709223507ccount @ X @ Y )
        = ( X = Y ) ) ) ).

% antisym_conv1
thf(fact_1009_antisym__conv1,axiom,
    ! [X: int,Y: int] :
      ( ~ ( ord_less_int @ X @ Y )
     => ( ( ord_less_eq_int @ X @ Y )
        = ( X = Y ) ) ) ).

% antisym_conv1
thf(fact_1010_antisym__conv1,axiom,
    ! [X: num,Y: num] :
      ( ~ ( ord_less_num @ X @ Y )
     => ( ( ord_less_eq_num @ X @ Y )
        = ( X = Y ) ) ) ).

% antisym_conv1
thf(fact_1011_nless__le,axiom,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_nat @ A @ B ) )
      = ( ~ ( ord_less_eq_nat @ A @ B )
        | ( A = B ) ) ) ).

% nless_le
thf(fact_1012_nless__le,axiom,
    ! [A: real,B: real] :
      ( ( ~ ( ord_less_real @ A @ B ) )
      = ( ~ ( ord_less_eq_real @ A @ B )
        | ( A = B ) ) ) ).

% nless_le
thf(fact_1013_nless__le,axiom,
    ! [A: risk_Free_account,B: risk_Free_account] :
      ( ( ~ ( ord_le2131251472502387783ccount @ A @ B ) )
      = ( ~ ( ord_le4245800335709223507ccount @ A @ B )
        | ( A = B ) ) ) ).

% nless_le
thf(fact_1014_nless__le,axiom,
    ! [A: int,B: int] :
      ( ( ~ ( ord_less_int @ A @ B ) )
      = ( ~ ( ord_less_eq_int @ A @ B )
        | ( A = B ) ) ) ).

% nless_le
thf(fact_1015_nless__le,axiom,
    ! [A: num,B: num] :
      ( ( ~ ( ord_less_num @ A @ B ) )
      = ( ~ ( ord_less_eq_num @ A @ B )
        | ( A = B ) ) ) ).

% nless_le
thf(fact_1016_leI,axiom,
    ! [X: nat,Y: nat] :
      ( ~ ( ord_less_nat @ X @ Y )
     => ( ord_less_eq_nat @ Y @ X ) ) ).

% leI
thf(fact_1017_leI,axiom,
    ! [X: real,Y: real] :
      ( ~ ( ord_less_real @ X @ Y )
     => ( ord_less_eq_real @ Y @ X ) ) ).

% leI
thf(fact_1018_leI,axiom,
    ! [X: int,Y: int] :
      ( ~ ( ord_less_int @ X @ Y )
     => ( ord_less_eq_int @ Y @ X ) ) ).

% leI
thf(fact_1019_leI,axiom,
    ! [X: num,Y: num] :
      ( ~ ( ord_less_num @ X @ Y )
     => ( ord_less_eq_num @ Y @ X ) ) ).

% leI
thf(fact_1020_leD,axiom,
    ! [Y: nat,X: nat] :
      ( ( ord_less_eq_nat @ Y @ X )
     => ~ ( ord_less_nat @ X @ Y ) ) ).

% leD
thf(fact_1021_leD,axiom,
    ! [Y: real,X: real] :
      ( ( ord_less_eq_real @ Y @ X )
     => ~ ( ord_less_real @ X @ Y ) ) ).

% leD
thf(fact_1022_leD,axiom,
    ! [Y: risk_Free_account,X: risk_Free_account] :
      ( ( ord_le4245800335709223507ccount @ Y @ X )
     => ~ ( ord_le2131251472502387783ccount @ X @ Y ) ) ).

% leD
thf(fact_1023_leD,axiom,
    ! [Y: int,X: int] :
      ( ( ord_less_eq_int @ Y @ X )
     => ~ ( ord_less_int @ X @ Y ) ) ).

% leD
thf(fact_1024_leD,axiom,
    ! [Y: num,X: num] :
      ( ( ord_less_eq_num @ Y @ X )
     => ~ ( ord_less_num @ X @ Y ) ) ).

% leD
thf(fact_1025_verit__sum__simplify,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ) ).

% verit_sum_simplify
thf(fact_1026_verit__sum__simplify,axiom,
    ! [A: risk_Free_account] :
      ( ( plus_p1863581527469039996ccount @ A @ zero_z1425366712893667068ccount )
      = A ) ).

% verit_sum_simplify
thf(fact_1027_verit__sum__simplify,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ A @ zero_zero_nat )
      = A ) ).

% verit_sum_simplify
thf(fact_1028_verit__sum__simplify,axiom,
    ! [A: int] :
      ( ( plus_plus_int @ A @ zero_zero_int )
      = A ) ).

% verit_sum_simplify
thf(fact_1029_add__0__iff,axiom,
    ! [B: real,A: real] :
      ( ( B
        = ( plus_plus_real @ B @ A ) )
      = ( A = zero_zero_real ) ) ).

% add_0_iff
thf(fact_1030_add__0__iff,axiom,
    ! [B: nat,A: nat] :
      ( ( B
        = ( plus_plus_nat @ B @ A ) )
      = ( A = zero_zero_nat ) ) ).

% add_0_iff
thf(fact_1031_add__0__iff,axiom,
    ! [B: int,A: int] :
      ( ( B
        = ( plus_plus_int @ B @ A ) )
      = ( A = zero_zero_int ) ) ).

% add_0_iff
thf(fact_1032_field__lbound__gt__zero,axiom,
    ! [D1: real,D2: real] :
      ( ( ord_less_real @ zero_zero_real @ D1 )
     => ( ( ord_less_real @ zero_zero_real @ D2 )
       => ? [E: real] :
            ( ( ord_less_real @ zero_zero_real @ E )
            & ( ord_less_real @ E @ D1 )
            & ( ord_less_real @ E @ D2 ) ) ) ) ).

% field_lbound_gt_zero
thf(fact_1033_less__numeral__extra_I3_J,axiom,
    ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).

% less_numeral_extra(3)
thf(fact_1034_less__numeral__extra_I3_J,axiom,
    ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).

% less_numeral_extra(3)
thf(fact_1035_less__numeral__extra_I3_J,axiom,
    ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).

% less_numeral_extra(3)
thf(fact_1036_complete__interval,axiom,
    ! [A: nat,B: nat,P: nat > $o] :
      ( ( ord_less_nat @ A @ B )
     => ( ( P @ A )
       => ( ~ ( P @ B )
         => ? [C2: nat] :
              ( ( ord_less_eq_nat @ A @ C2 )
              & ( ord_less_eq_nat @ C2 @ B )
              & ! [X3: nat] :
                  ( ( ( ord_less_eq_nat @ A @ X3 )
                    & ( ord_less_nat @ X3 @ C2 ) )
                 => ( P @ X3 ) )
              & ! [D3: nat] :
                  ( ! [X4: nat] :
                      ( ( ( ord_less_eq_nat @ A @ X4 )
                        & ( ord_less_nat @ X4 @ D3 ) )
                     => ( P @ X4 ) )
                 => ( ord_less_eq_nat @ D3 @ C2 ) ) ) ) ) ) ).

% complete_interval
thf(fact_1037_complete__interval,axiom,
    ! [A: real,B: real,P: real > $o] :
      ( ( ord_less_real @ A @ B )
     => ( ( P @ A )
       => ( ~ ( P @ B )
         => ? [C2: real] :
              ( ( ord_less_eq_real @ A @ C2 )
              & ( ord_less_eq_real @ C2 @ B )
              & ! [X3: real] :
                  ( ( ( ord_less_eq_real @ A @ X3 )
                    & ( ord_less_real @ X3 @ C2 ) )
                 => ( P @ X3 ) )
              & ! [D3: real] :
                  ( ! [X4: real] :
                      ( ( ( ord_less_eq_real @ A @ X4 )
                        & ( ord_less_real @ X4 @ D3 ) )
                     => ( P @ X4 ) )
                 => ( ord_less_eq_real @ D3 @ C2 ) ) ) ) ) ) ).

% complete_interval
thf(fact_1038_complete__interval,axiom,
    ! [A: int,B: int,P: int > $o] :
      ( ( ord_less_int @ A @ B )
     => ( ( P @ A )
       => ( ~ ( P @ B )
         => ? [C2: int] :
              ( ( ord_less_eq_int @ A @ C2 )
              & ( ord_less_eq_int @ C2 @ B )
              & ! [X3: int] :
                  ( ( ( ord_less_eq_int @ A @ X3 )
                    & ( ord_less_int @ X3 @ C2 ) )
                 => ( P @ X3 ) )
              & ! [D3: int] :
                  ( ! [X4: int] :
                      ( ( ( ord_less_eq_int @ A @ X4 )
                        & ( ord_less_int @ X4 @ D3 ) )
                     => ( P @ X4 ) )
                 => ( ord_less_eq_int @ D3 @ C2 ) ) ) ) ) ) ).

% complete_interval
thf(fact_1039_verit__comp__simplify1_I3_J,axiom,
    ! [B5: nat,A5: nat] :
      ( ( ~ ( ord_less_eq_nat @ B5 @ A5 ) )
      = ( ord_less_nat @ A5 @ B5 ) ) ).

% verit_comp_simplify1(3)
thf(fact_1040_verit__comp__simplify1_I3_J,axiom,
    ! [B5: real,A5: real] :
      ( ( ~ ( ord_less_eq_real @ B5 @ A5 ) )
      = ( ord_less_real @ A5 @ B5 ) ) ).

% verit_comp_simplify1(3)
thf(fact_1041_verit__comp__simplify1_I3_J,axiom,
    ! [B5: int,A5: int] :
      ( ( ~ ( ord_less_eq_int @ B5 @ A5 ) )
      = ( ord_less_int @ A5 @ B5 ) ) ).

% verit_comp_simplify1(3)
thf(fact_1042_verit__comp__simplify1_I3_J,axiom,
    ! [B5: num,A5: num] :
      ( ( ~ ( ord_less_eq_num @ B5 @ A5 ) )
      = ( ord_less_num @ A5 @ B5 ) ) ).

% verit_comp_simplify1(3)
thf(fact_1043_pinf_I6_J,axiom,
    ! [T: nat] :
    ? [Z3: nat] :
    ! [X3: nat] :
      ( ( ord_less_nat @ Z3 @ X3 )
     => ~ ( ord_less_eq_nat @ X3 @ T ) ) ).

% pinf(6)
thf(fact_1044_pinf_I6_J,axiom,
    ! [T: real] :
    ? [Z3: real] :
    ! [X3: real] :
      ( ( ord_less_real @ Z3 @ X3 )
     => ~ ( ord_less_eq_real @ X3 @ T ) ) ).

% pinf(6)
thf(fact_1045_pinf_I6_J,axiom,
    ! [T: int] :
    ? [Z3: int] :
    ! [X3: int] :
      ( ( ord_less_int @ Z3 @ X3 )
     => ~ ( ord_less_eq_int @ X3 @ T ) ) ).

% pinf(6)
thf(fact_1046_pinf_I6_J,axiom,
    ! [T: num] :
    ? [Z3: num] :
    ! [X3: num] :
      ( ( ord_less_num @ Z3 @ X3 )
     => ~ ( ord_less_eq_num @ X3 @ T ) ) ).

% pinf(6)
thf(fact_1047_verit__comp__simplify1_I2_J,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).

% verit_comp_simplify1(2)
thf(fact_1048_verit__comp__simplify1_I2_J,axiom,
    ! [A: real] : ( ord_less_eq_real @ A @ A ) ).

% verit_comp_simplify1(2)
thf(fact_1049_verit__comp__simplify1_I2_J,axiom,
    ! [A: risk_Free_account] : ( ord_le4245800335709223507ccount @ A @ A ) ).

% verit_comp_simplify1(2)
thf(fact_1050_verit__comp__simplify1_I2_J,axiom,
    ! [A: int] : ( ord_less_eq_int @ A @ A ) ).

% verit_comp_simplify1(2)
thf(fact_1051_verit__comp__simplify1_I2_J,axiom,
    ! [A: num] : ( ord_less_eq_num @ A @ A ) ).

% verit_comp_simplify1(2)
thf(fact_1052_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_1053_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_1054_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_1055_verit__la__disequality,axiom,
    ! [A: num,B: num] :
      ( ( A = B )
      | ~ ( ord_less_eq_num @ A @ B )
      | ~ ( ord_less_eq_num @ B @ A ) ) ).

% verit_la_disequality
thf(fact_1056_ex__gt__or__lt,axiom,
    ! [A: real] :
    ? [B4: real] :
      ( ( ord_less_real @ A @ B4 )
      | ( ord_less_real @ B4 @ A ) ) ).

% ex_gt_or_lt
thf(fact_1057_verit__comp__simplify1_I1_J,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ) ).

% verit_comp_simplify1(1)
thf(fact_1058_verit__comp__simplify1_I1_J,axiom,
    ! [A: risk_Free_account] :
      ~ ( ord_le2131251472502387783ccount @ A @ A ) ).

% verit_comp_simplify1(1)
thf(fact_1059_verit__comp__simplify1_I1_J,axiom,
    ! [A: real] :
      ~ ( ord_less_real @ A @ A ) ).

% verit_comp_simplify1(1)
thf(fact_1060_verit__comp__simplify1_I1_J,axiom,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ) ).

% verit_comp_simplify1(1)
thf(fact_1061_verit__comp__simplify1_I1_J,axiom,
    ! [A: num] :
      ~ ( ord_less_num @ A @ A ) ).

% verit_comp_simplify1(1)
thf(fact_1062_pinf_I1_J,axiom,
    ! [P: int > $o,P4: int > $o,Q2: int > $o,Q3: int > $o] :
      ( ? [Z4: int] :
        ! [X4: int] :
          ( ( ord_less_int @ Z4 @ X4 )
         => ( ( P @ X4 )
            = ( P4 @ X4 ) ) )
     => ( ? [Z4: int] :
          ! [X4: int] :
            ( ( ord_less_int @ Z4 @ X4 )
           => ( ( Q2 @ X4 )
              = ( Q3 @ X4 ) ) )
       => ? [Z3: int] :
          ! [X3: int] :
            ( ( ord_less_int @ Z3 @ X3 )
           => ( ( ( P @ X3 )
                & ( Q2 @ X3 ) )
              = ( ( P4 @ X3 )
                & ( Q3 @ X3 ) ) ) ) ) ) ).

% pinf(1)
thf(fact_1063_pinf_I1_J,axiom,
    ! [P: num > $o,P4: num > $o,Q2: num > $o,Q3: num > $o] :
      ( ? [Z4: num] :
        ! [X4: num] :
          ( ( ord_less_num @ Z4 @ X4 )
         => ( ( P @ X4 )
            = ( P4 @ X4 ) ) )
     => ( ? [Z4: num] :
          ! [X4: num] :
            ( ( ord_less_num @ Z4 @ X4 )
           => ( ( Q2 @ X4 )
              = ( Q3 @ X4 ) ) )
       => ? [Z3: num] :
          ! [X3: num] :
            ( ( ord_less_num @ Z3 @ X3 )
           => ( ( ( P @ X3 )
                & ( Q2 @ X3 ) )
              = ( ( P4 @ X3 )
                & ( Q3 @ X3 ) ) ) ) ) ) ).

% pinf(1)
thf(fact_1064_Rep__account__just__cash,axiom,
    ! [C: real] :
      ( ( risk_F170160801229183585ccount @ ( risk_Free_just_cash @ C ) )
      = ( ^ [N2: nat] : ( if_real @ ( N2 = zero_zero_nat ) @ C @ zero_zero_real ) ) ) ).

% Rep_account_just_cash
thf(fact_1065_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_1066_strictly__solvent__non__negative__cash,axiom,
    ! [Alpha2: risk_Free_account] :
      ( ( risk_F1636578016437888323olvent @ Alpha2 )
     => ( ord_less_eq_real @ zero_zero_real @ ( risk_F1914734008469130493eserve @ Alpha2 ) ) ) ).

% strictly_solvent_non_negative_cash
thf(fact_1067_num__of__nat__plus__distrib,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ M )
     => ( ( ord_less_nat @ zero_zero_nat @ N )
       => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
          = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).

% num_of_nat_plus_distrib
thf(fact_1068_valid__transfer__alt__def,axiom,
    ( risk_F1023690899723030139ansfer
    = ( ^ [Alpha: risk_Free_account,Tau: risk_Free_account] :
          ( ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount @ Tau )
          & ( ord_le4245800335709223507ccount @ Tau @ Alpha ) ) ) ) ).

% valid_transfer_alt_def
thf(fact_1069_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_1070_complete__real,axiom,
    ! [S2: set_real] :
      ( ? [X3: real] : ( member_real @ X3 @ S2 )
     => ( ? [Z4: real] :
          ! [X4: real] :
            ( ( member_real @ X4 @ S2 )
           => ( ord_less_eq_real @ X4 @ Z4 ) )
       => ? [Y2: real] :
            ( ! [X3: real] :
                ( ( member_real @ X3 @ S2 )
               => ( ord_less_eq_real @ X3 @ Y2 ) )
            & ! [Z4: real] :
                ( ! [X4: real] :
                    ( ( member_real @ X4 @ S2 )
                   => ( ord_less_eq_real @ X4 @ Z4 ) )
               => ( ord_less_eq_real @ Y2 @ Z4 ) ) ) ) ) ).

% complete_real
thf(fact_1071_just__cash__order__embed,axiom,
    ( ord_less_eq_real
    = ( ^ [A3: real,B2: real] : ( ord_le4245800335709223507ccount @ ( risk_Free_just_cash @ A3 ) @ ( risk_Free_just_cash @ B2 ) ) ) ) ).

% just_cash_order_embed
thf(fact_1072_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_1073_less__eq__real__def,axiom,
    ( ord_less_eq_real
    = ( ^ [X2: real,Y5: real] :
          ( ( ord_less_real @ X2 @ Y5 )
          | ( X2 = Y5 ) ) ) ) ).

% less_eq_real_def
thf(fact_1074_just__cash__valid__transfer,axiom,
    ! [C: real,T: real] :
      ( ( risk_F1023690899723030139ansfer @ ( risk_Free_just_cash @ C ) @ ( risk_Free_just_cash @ T ) )
      = ( ( ord_less_eq_real @ zero_zero_real @ T )
        & ( ord_less_eq_real @ T @ C ) ) ) ).

% just_cash_valid_transfer
thf(fact_1075_just__cash__embed,axiom,
    ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
    = ( ^ [A3: real,B2: real] :
          ( ( risk_Free_just_cash @ A3 )
          = ( risk_Free_just_cash @ B2 ) ) ) ) ).

% just_cash_embed
thf(fact_1076_only__strictly__solvent__accounts__can__transfer,axiom,
    ! [Alpha2: risk_Free_account,Tau2: risk_Free_account] :
      ( ( risk_F1023690899723030139ansfer @ Alpha2 @ Tau2 )
     => ( risk_F1636578016437888323olvent @ Alpha2 ) ) ).

% only_strictly_solvent_accounts_can_transfer
thf(fact_1077_int__ops_I1_J,axiom,
    ( ( semiri1314217659103216013at_int @ zero_zero_nat )
    = zero_zero_int ) ).

% int_ops(1)
thf(fact_1078_nat__int__comparison_I2_J,axiom,
    ( ord_less_nat
    = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).

% nat_int_comparison(2)
thf(fact_1079_zle__int,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
      = ( ord_less_eq_nat @ M @ N ) ) ).

% zle_int
thf(fact_1080_nat__int__comparison_I3_J,axiom,
    ( ord_less_eq_nat
    = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).

% nat_int_comparison(3)
thf(fact_1081_zadd__int__left,axiom,
    ! [M: nat,N: nat,Z: int] :
      ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
      = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).

% zadd_int_left
thf(fact_1082_int__ops_I5_J,axiom,
    ! [A: nat,B: nat] :
      ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
      = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).

% int_ops(5)
thf(fact_1083_int__plus,axiom,
    ! [N: nat,M: nat] :
      ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
      = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).

% int_plus
thf(fact_1084_zero__less__imp__eq__int,axiom,
    ! [K: int] :
      ( ( ord_less_int @ zero_zero_int @ K )
     => ? [N3: nat] :
          ( ( ord_less_nat @ zero_zero_nat @ N3 )
          & ( K
            = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).

% zero_less_imp_eq_int
thf(fact_1085_pos__int__cases,axiom,
    ! [K: int] :
      ( ( ord_less_int @ zero_zero_int @ K )
     => ~ ! [N3: nat] :
            ( ( K
              = ( semiri1314217659103216013at_int @ N3 ) )
           => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).

% pos_int_cases
thf(fact_1086_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_1087_strictly__solvent__alt__def,axiom,
    ( risk_F1636578016437888323olvent
    = ( ord_le4245800335709223507ccount @ zero_z1425366712893667068ccount ) ) ).

% strictly_solvent_alt_def
thf(fact_1088_zero__account__alt__def,axiom,
    ( ( risk_Free_just_cash @ zero_zero_real )
    = zero_z1425366712893667068ccount ) ).

% zero_account_alt_def
thf(fact_1089_num__of__nat__double,axiom,
    ! [N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
        = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).

% num_of_nat_double
thf(fact_1090_verit__eq__simplify_I8_J,axiom,
    ! [X22: num,Y22: num] :
      ( ( ( bit0 @ X22 )
        = ( bit0 @ Y22 ) )
      = ( X22 = Y22 ) ) ).

% verit_eq_simplify(8)
thf(fact_1091_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_1092_int__if,axiom,
    ! [P: $o,A: nat,B: nat] :
      ( ( P
       => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
          = ( semiri1314217659103216013at_int @ A ) ) )
      & ( ~ P
       => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
          = ( semiri1314217659103216013at_int @ B ) ) ) ) ).

% int_if
thf(fact_1093_nat__int__comparison_I1_J,axiom,
    ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
    = ( ^ [A3: nat,B2: nat] :
          ( ( semiri1314217659103216013at_int @ A3 )
          = ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).

% nat_int_comparison(1)
thf(fact_1094_conj__le__cong,axiom,
    ! [X: int,X6: int,P: $o,P4: $o] :
      ( ( X = X6 )
     => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
         => ( P = P4 ) )
       => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
            & P )
          = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
            & P4 ) ) ) ) ).

% conj_le_cong
thf(fact_1095_imp__le__cong,axiom,
    ! [X: int,X6: int,P: $o,P4: $o] :
      ( ( X = X6 )
     => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
         => ( P = P4 ) )
       => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
           => P )
          = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
           => P4 ) ) ) ) ).

% imp_le_cong
thf(fact_1096_zero__le__imp__eq__int,axiom,
    ! [K: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ K )
     => ? [N3: nat] :
          ( K
          = ( semiri1314217659103216013at_int @ N3 ) ) ) ).

% zero_le_imp_eq_int
thf(fact_1097_nonneg__int__cases,axiom,
    ! [K: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ K )
     => ~ ! [N3: nat] :
            ( K
           != ( semiri1314217659103216013at_int @ N3 ) ) ) ).

% nonneg_int_cases
thf(fact_1098_zle__iff__zadd,axiom,
    ( ord_less_eq_int
    = ( ^ [W2: int,Z5: int] :
        ? [N2: nat] :
          ( Z5
          = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).

% zle_iff_zadd
thf(fact_1099_less__eq__int__code_I1_J,axiom,
    ord_less_eq_int @ zero_zero_int @ zero_zero_int ).

% less_eq_int_code(1)
thf(fact_1100_less__int__code_I1_J,axiom,
    ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).

% less_int_code(1)
thf(fact_1101_plus__int__code_I2_J,axiom,
    ! [L: int] :
      ( ( plus_plus_int @ zero_zero_int @ L )
      = L ) ).

% plus_int_code(2)
thf(fact_1102_plus__int__code_I1_J,axiom,
    ! [K: int] :
      ( ( plus_plus_int @ K @ zero_zero_int )
      = K ) ).

% plus_int_code(1)
thf(fact_1103_int__int__eq,axiom,
    ! [M: nat,N: nat] :
      ( ( ( semiri1314217659103216013at_int @ M )
        = ( semiri1314217659103216013at_int @ N ) )
      = ( M = N ) ) ).

% int_int_eq
thf(fact_1104_semiring__norm_I6_J,axiom,
    ! [M: num,N: num] :
      ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
      = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).

% semiring_norm(6)
thf(fact_1105_semiring__norm_I71_J,axiom,
    ! [M: num,N: num] :
      ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
      = ( ord_less_eq_num @ M @ N ) ) ).

% semiring_norm(71)
thf(fact_1106_semiring__norm_I78_J,axiom,
    ! [M: num,N: num] :
      ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
      = ( ord_less_num @ M @ N ) ) ).

% semiring_norm(78)
thf(fact_1107_neg__int__cases,axiom,
    ! [K: int] :
      ( ( ord_less_int @ K @ zero_zero_int )
     => ~ ! [N3: nat] :
            ( ( K
              = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
           => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).

% neg_int_cases
thf(fact_1108_nat__less__iff,axiom,
    ! [W3: int,M: nat] :
      ( ( ord_less_eq_int @ zero_zero_int @ W3 )
     => ( ( ord_less_nat @ ( nat2 @ W3 ) @ M )
        = ( ord_less_int @ W3 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).

% nat_less_iff
thf(fact_1109_nat__int,axiom,
    ! [N: nat] :
      ( ( nat2 @ ( semiri1314217659103216013at_int @ N ) )
      = N ) ).

% nat_int
thf(fact_1110_negative__eq__positive,axiom,
    ! [N: nat,M: nat] :
      ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
        = ( semiri1314217659103216013at_int @ M ) )
      = ( ( N = zero_zero_nat )
        & ( M = zero_zero_nat ) ) ) ).

% negative_eq_positive
thf(fact_1111_negative__zle,axiom,
    ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).

% negative_zle
thf(fact_1112_nat__0__iff,axiom,
    ! [I3: int] :
      ( ( ( nat2 @ I3 )
        = zero_zero_nat )
      = ( ord_less_eq_int @ I3 @ zero_zero_int ) ) ).

% nat_0_iff
thf(fact_1113_nat__le__0,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ Z @ zero_zero_int )
     => ( ( nat2 @ Z )
        = zero_zero_nat ) ) ).

% nat_le_0
thf(fact_1114_zless__nat__conj,axiom,
    ! [W3: int,Z: int] :
      ( ( ord_less_nat @ ( nat2 @ W3 ) @ ( nat2 @ Z ) )
      = ( ( ord_less_int @ zero_zero_int @ Z )
        & ( ord_less_int @ W3 @ Z ) ) ) ).

% zless_nat_conj
thf(fact_1115_nat__zminus__int,axiom,
    ! [N: nat] :
      ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
      = zero_zero_nat ) ).

% nat_zminus_int
thf(fact_1116_int__nat__eq,axiom,
    ! [Z: int] :
      ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
          = Z ) )
      & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
          = zero_zero_int ) ) ) ).

% int_nat_eq
thf(fact_1117_zero__less__nat__eq,axiom,
    ! [Z: int] :
      ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
      = ( ord_less_int @ zero_zero_int @ Z ) ) ).

% zero_less_nat_eq
thf(fact_1118_uminus__int__code_I1_J,axiom,
    ( ( uminus_uminus_int @ zero_zero_int )
    = zero_zero_int ) ).

% uminus_int_code(1)
thf(fact_1119_int__cases2,axiom,
    ! [Z: int] :
      ( ! [N3: nat] :
          ( Z
         != ( semiri1314217659103216013at_int @ N3 ) )
     => ~ ! [N3: nat] :
            ( Z
           != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).

% int_cases2
thf(fact_1120_nat__zero__as__int,axiom,
    ( zero_zero_nat
    = ( nat2 @ zero_zero_int ) ) ).

% nat_zero_as_int
thf(fact_1121_nat__mono,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ X @ Y )
     => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).

% nat_mono
thf(fact_1122_ex__nat,axiom,
    ( ( ^ [P2: nat > $o] :
        ? [X5: nat] : ( P2 @ X5 ) )
    = ( ^ [P3: nat > $o] :
        ? [X2: int] :
          ( ( ord_less_eq_int @ zero_zero_int @ X2 )
          & ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).

% ex_nat
thf(fact_1123_all__nat,axiom,
    ( ( ^ [P2: nat > $o] :
        ! [X5: nat] : ( P2 @ X5 ) )
    = ( ^ [P3: nat > $o] :
        ! [X2: int] :
          ( ( ord_less_eq_int @ zero_zero_int @ X2 )
         => ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).

% all_nat
thf(fact_1124_eq__nat__nat__iff,axiom,
    ! [Z: int,Z6: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
       => ( ( ( nat2 @ Z )
            = ( nat2 @ Z6 ) )
          = ( Z = Z6 ) ) ) ) ).

% eq_nat_nat_iff
thf(fact_1125_not__int__zless__negative,axiom,
    ! [N: nat,M: nat] :
      ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).

% not_int_zless_negative
thf(fact_1126_nat__mono__iff,axiom,
    ! [Z: int,W3: int] :
      ( ( ord_less_int @ zero_zero_int @ Z )
     => ( ( ord_less_nat @ ( nat2 @ W3 ) @ ( nat2 @ Z ) )
        = ( ord_less_int @ W3 @ Z ) ) ) ).

% nat_mono_iff
thf(fact_1127_zless__nat__eq__int__zless,axiom,
    ! [M: nat,Z: int] :
      ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
      = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).

% zless_nat_eq_int_zless
thf(fact_1128_nat__le__iff,axiom,
    ! [X: int,N: nat] :
      ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
      = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).

% nat_le_iff
thf(fact_1129_nat__0__le,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
        = Z ) ) ).

% nat_0_le
thf(fact_1130_int__eq__iff,axiom,
    ! [M: nat,Z: int] :
      ( ( ( semiri1314217659103216013at_int @ M )
        = Z )
      = ( ( M
          = ( nat2 @ Z ) )
        & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).

% int_eq_iff
thf(fact_1131_nat__int__add,axiom,
    ! [A: nat,B: nat] :
      ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
      = ( plus_plus_nat @ A @ B ) ) ).

% nat_int_add
thf(fact_1132_int__cases4,axiom,
    ! [M: int] :
      ( ! [N3: nat] :
          ( M
         != ( semiri1314217659103216013at_int @ N3 ) )
     => ~ ! [N3: nat] :
            ( ( ord_less_nat @ zero_zero_nat @ N3 )
           => ( M
             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).

% int_cases4
thf(fact_1133_int__zle__neg,axiom,
    ! [N: nat,M: nat] :
      ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
      = ( ( N = zero_zero_nat )
        & ( M = zero_zero_nat ) ) ) ).

% int_zle_neg
thf(fact_1134_negative__zle__0,axiom,
    ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).

% negative_zle_0
thf(fact_1135_nonpos__int__cases,axiom,
    ! [K: int] :
      ( ( ord_less_eq_int @ K @ zero_zero_int )
     => ~ ! [N3: nat] :
            ( K
           != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).

% nonpos_int_cases
thf(fact_1136_nat__less__eq__zless,axiom,
    ! [W3: int,Z: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ W3 )
     => ( ( ord_less_nat @ ( nat2 @ W3 ) @ ( nat2 @ Z ) )
        = ( ord_less_int @ W3 @ Z ) ) ) ).

% nat_less_eq_zless
thf(fact_1137_nat__le__eq__zle,axiom,
    ! [W3: int,Z: int] :
      ( ( ( ord_less_int @ zero_zero_int @ W3 )
        | ( ord_less_eq_int @ zero_zero_int @ Z ) )
     => ( ( ord_less_eq_nat @ ( nat2 @ W3 ) @ ( nat2 @ Z ) )
        = ( ord_less_eq_int @ W3 @ Z ) ) ) ).

% nat_le_eq_zle
thf(fact_1138_nat__eq__iff,axiom,
    ! [W3: int,M: nat] :
      ( ( ( nat2 @ W3 )
        = M )
      = ( ( ( ord_less_eq_int @ zero_zero_int @ W3 )
         => ( W3
            = ( semiri1314217659103216013at_int @ M ) ) )
        & ( ~ ( ord_less_eq_int @ zero_zero_int @ W3 )
         => ( M = zero_zero_nat ) ) ) ) ).

% nat_eq_iff
thf(fact_1139_nat__eq__iff2,axiom,
    ! [M: nat,W3: int] :
      ( ( M
        = ( nat2 @ W3 ) )
      = ( ( ( ord_less_eq_int @ zero_zero_int @ W3 )
         => ( W3
            = ( semiri1314217659103216013at_int @ M ) ) )
        & ( ~ ( ord_less_eq_int @ zero_zero_int @ W3 )
         => ( M = zero_zero_nat ) ) ) ) ).

% nat_eq_iff2
thf(fact_1140_split__nat,axiom,
    ! [P: nat > $o,I3: int] :
      ( ( P @ ( nat2 @ I3 ) )
      = ( ! [N2: nat] :
            ( ( I3
              = ( semiri1314217659103216013at_int @ N2 ) )
           => ( P @ N2 ) )
        & ( ( ord_less_int @ I3 @ zero_zero_int )
         => ( P @ zero_zero_nat ) ) ) ) ).

% split_nat
thf(fact_1141_le__nat__iff,axiom,
    ! [K: int,N: nat] :
      ( ( ord_less_eq_int @ zero_zero_int @ K )
     => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
        = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).

% le_nat_iff
thf(fact_1142_nat__add__distrib,axiom,
    ! [Z: int,Z6: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
       => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
          = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).

% nat_add_distrib
thf(fact_1143_int__cases3,axiom,
    ! [K: int] :
      ( ( K != zero_zero_int )
     => ( ! [N3: nat] :
            ( ( K
              = ( semiri1314217659103216013at_int @ N3 ) )
           => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
       => ~ ! [N3: nat] :
              ( ( K
                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).

% int_cases3
thf(fact_1144_Rep__account__uminus,axiom,
    ! [Alpha2: risk_Free_account] :
      ( ( risk_F170160801229183585ccount @ ( uminus3377898441596595772ccount @ Alpha2 ) )
      = ( ^ [N2: nat] : ( uminus_uminus_real @ ( risk_F170160801229183585ccount @ Alpha2 @ N2 ) ) ) ) ).

% Rep_account_uminus
thf(fact_1145_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_1146_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_1147_shortest__period__uminus,axiom,
    ! [Alpha2: risk_Free_account] :
      ( ( risk_F4612863212915232279period @ ( uminus3377898441596595772ccount @ Alpha2 ) )
      = ( risk_F4612863212915232279period @ Alpha2 ) ) ).

% shortest_period_uminus
thf(fact_1148_real__0__less__add__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
      = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).

% real_0_less_add_iff
thf(fact_1149_real__add__less__0__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
      = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).

% real_add_less_0_iff
thf(fact_1150_real__add__le__0__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
      = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).

% real_add_le_0_iff
thf(fact_1151_real__0__le__add__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
      = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).

% real_0_le_add_iff
thf(fact_1152_real__arch__inverse,axiom,
    ! [E2: real] :
      ( ( ord_less_real @ zero_zero_real @ E2 )
      = ( ? [N2: nat] :
            ( ( N2 != zero_zero_nat )
            & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
            & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E2 ) ) ) ) ).

% real_arch_inverse
thf(fact_1153_forall__pos__mono,axiom,
    ! [P: real > $o,E2: real] :
      ( ! [D4: real,E: real] :
          ( ( ord_less_real @ D4 @ E )
         => ( ( P @ D4 )
           => ( P @ E ) ) )
     => ( ! [N3: nat] :
            ( ( N3 != zero_zero_nat )
           => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
       => ( ( ord_less_real @ zero_zero_real @ E2 )
         => ( P @ E2 ) ) ) ) ).

% forall_pos_mono
thf(fact_1154_nat__ceiling__le__eq,axiom,
    ! [X: real,A: nat] :
      ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
      = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).

% nat_ceiling_le_eq
thf(fact_1155_real__nat__ceiling__ge,axiom,
    ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).

% real_nat_ceiling_ge
thf(fact_1156_less__one,axiom,
    ! [N: nat] :
      ( ( ord_less_nat @ N @ one_one_nat )
      = ( N = zero_zero_nat ) ) ).

% less_one
thf(fact_1157_zle__add1__eq__le,axiom,
    ! [W3: int,Z: int] :
      ( ( ord_less_int @ W3 @ ( plus_plus_int @ Z @ one_one_int ) )
      = ( ord_less_eq_int @ W3 @ Z ) ) ).

% zle_add1_eq_le
thf(fact_1158_int__ops_I2_J,axiom,
    ( ( semiri1314217659103216013at_int @ one_one_nat )
    = one_one_int ) ).

% int_ops(2)
thf(fact_1159_nat__power__eq,axiom,
    ! [Z: int,N: nat] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ( nat2 @ ( power_power_int @ Z @ N ) )
        = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).

% nat_power_eq
thf(fact_1160_nat__one__as__int,axiom,
    ( one_one_nat
    = ( nat2 @ one_one_int ) ) ).

% nat_one_as_int
thf(fact_1161_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_1162_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_1163_odd__nonzero,axiom,
    ! [Z: int] :
      ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
     != zero_zero_int ) ).

% odd_nonzero
thf(fact_1164_int__ge__induct,axiom,
    ! [K: int,I3: int,P: int > $o] :
      ( ( ord_less_eq_int @ K @ I3 )
     => ( ( P @ K )
       => ( ! [I: int] :
              ( ( ord_less_eq_int @ K @ I )
             => ( ( P @ I )
               => ( P @ ( plus_plus_int @ I @ one_one_int ) ) ) )
         => ( P @ I3 ) ) ) ) ).

% int_ge_induct
thf(fact_1165_zless__add1__eq,axiom,
    ! [W3: int,Z: int] :
      ( ( ord_less_int @ W3 @ ( plus_plus_int @ Z @ one_one_int ) )
      = ( ( ord_less_int @ W3 @ Z )
        | ( W3 = Z ) ) ) ).

% zless_add1_eq
thf(fact_1166_int__gr__induct,axiom,
    ! [K: int,I3: int,P: int > $o] :
      ( ( ord_less_int @ K @ I3 )
     => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
       => ( ! [I: int] :
              ( ( ord_less_int @ K @ I )
             => ( ( P @ I )
               => ( P @ ( plus_plus_int @ I @ one_one_int ) ) ) )
         => ( P @ I3 ) ) ) ) ).

% int_gr_induct
thf(fact_1167_int__one__le__iff__zero__less,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ one_one_int @ Z )
      = ( ord_less_int @ zero_zero_int @ Z ) ) ).

% int_one_le_iff_zero_less
thf(fact_1168_int__le__real__less,axiom,
    ( ord_less_eq_int
    = ( ^ [N2: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).

% int_le_real_less
thf(fact_1169_odd__less__0__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
      = ( ord_less_int @ Z @ zero_zero_int ) ) ).

% odd_less_0_iff
thf(fact_1170_int__less__real__le,axiom,
    ( ord_less_int
    = ( ^ [N2: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).

% int_less_real_le
thf(fact_1171_add1__zle__eq,axiom,
    ! [W3: int,Z: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ W3 @ one_one_int ) @ Z )
      = ( ord_less_int @ W3 @ Z ) ) ).

% add1_zle_eq
thf(fact_1172_zless__imp__add1__zle,axiom,
    ! [W3: int,Z: int] :
      ( ( ord_less_int @ W3 @ Z )
     => ( ord_less_eq_int @ ( plus_plus_int @ W3 @ one_one_int ) @ Z ) ) ).

% zless_imp_add1_zle
thf(fact_1173_nat__less__real__le,axiom,
    ( ord_less_nat
    = ( ^ [N2: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).

% nat_less_real_le
thf(fact_1174_le__imp__0__less,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).

% le_imp_0_less
thf(fact_1175_nat__le__real__less,axiom,
    ( ord_less_eq_nat
    = ( ^ [N2: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).

% nat_le_real_less
thf(fact_1176_nat__zero__less__power__iff,axiom,
    ! [X: nat,N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
      = ( ( ord_less_nat @ zero_zero_nat @ X )
        | ( N = zero_zero_nat ) ) ) ).

% nat_zero_less_power_iff
thf(fact_1177_nat__power__less__imp__less,axiom,
    ! [I3: nat,M: nat,N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ I3 )
     => ( ( ord_less_nat @ ( power_power_nat @ I3 @ M ) @ ( power_power_nat @ I3 @ N ) )
       => ( ord_less_nat @ M @ N ) ) ) ).

% nat_power_less_imp_less
thf(fact_1178_realpow__pos__nth__unique,axiom,
    ! [N: nat,A: real] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ( ord_less_real @ zero_zero_real @ A )
       => ? [X4: real] :
            ( ( ord_less_real @ zero_zero_real @ X4 )
            & ( ( power_power_real @ X4 @ N )
              = A )
            & ! [Y3: real] :
                ( ( ( ord_less_real @ zero_zero_real @ Y3 )
                  & ( ( power_power_real @ Y3 @ N )
                    = A ) )
               => ( Y3 = X4 ) ) ) ) ) ).

% realpow_pos_nth_unique
thf(fact_1179_realpow__pos__nth,axiom,
    ! [N: nat,A: real] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ( ord_less_real @ zero_zero_real @ A )
       => ? [R: real] :
            ( ( ord_less_real @ zero_zero_real @ R )
            & ( ( power_power_real @ R @ N )
              = A ) ) ) ) ).

% realpow_pos_nth
thf(fact_1180_bounded__Max__nat,axiom,
    ! [P: nat > $o,X: nat,M5: nat] :
      ( ( P @ X )
     => ( ! [X4: nat] :
            ( ( P @ X4 )
           => ( ord_less_eq_nat @ X4 @ M5 ) )
       => ~ ! [M4: nat] :
              ( ( P @ M4 )
             => ~ ! [X3: nat] :
                    ( ( P @ X3 )
                   => ( ord_less_eq_nat @ X3 @ M4 ) ) ) ) ) ).

% bounded_Max_nat
thf(fact_1181_powr__real__of__int,axiom,
    ! [X: real,N: int] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
         => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
            = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
        & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
         => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
            = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).

% powr_real_of_int
thf(fact_1182_Bernoulli__inequality,axiom,
    ! [X: real,N: nat] :
      ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
     => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).

% Bernoulli_inequality
thf(fact_1183_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_1184_powr__gt__zero,axiom,
    ! [X: real,A: real] :
      ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
      = ( X != zero_zero_real ) ) ).

% powr_gt_zero
thf(fact_1185_powr__nonneg__iff,axiom,
    ! [A: real,X: real] :
      ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
      = ( A = zero_zero_real ) ) ).

% powr_nonneg_iff
thf(fact_1186_powr__less__cancel__iff,axiom,
    ! [X: real,A: real,B: real] :
      ( ( ord_less_real @ one_one_real @ X )
     => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
        = ( ord_less_real @ A @ B ) ) ) ).

% powr_less_cancel_iff
thf(fact_1187_powr__eq__one__iff,axiom,
    ! [A: real,X: real] :
      ( ( ord_less_real @ one_one_real @ A )
     => ( ( ( powr_real @ A @ X )
          = one_one_real )
        = ( X = zero_zero_real ) ) ) ).

% powr_eq_one_iff
thf(fact_1188_powr__one__gt__zero__iff,axiom,
    ! [X: real] :
      ( ( ( powr_real @ X @ one_one_real )
        = X )
      = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).

% powr_one_gt_zero_iff
thf(fact_1189_powr__one,axiom,
    ! [X: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ( powr_real @ X @ one_one_real )
        = X ) ) ).

% powr_one
thf(fact_1190_powr__le__cancel__iff,axiom,
    ! [X: real,A: real,B: real] :
      ( ( ord_less_real @ one_one_real @ X )
     => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
        = ( ord_less_eq_real @ A @ B ) ) ) ).

% powr_le_cancel_iff
thf(fact_1191_powr__less__cancel,axiom,
    ! [X: real,A: real,B: real] :
      ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
     => ( ( ord_less_real @ one_one_real @ X )
       => ( ord_less_real @ A @ B ) ) ) ).

% powr_less_cancel
thf(fact_1192_powr__less__mono,axiom,
    ! [A: real,B: real,X: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_real @ one_one_real @ X )
       => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).

% powr_less_mono
thf(fact_1193_gr__one__powr,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ one_one_real @ X )
     => ( ( ord_less_real @ zero_zero_real @ Y )
       => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y ) ) ) ) ).

% gr_one_powr
thf(fact_1194_powr__inj,axiom,
    ! [A: real,X: real,Y: real] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ( ( A != one_one_real )
       => ( ( ( powr_real @ A @ X )
            = ( powr_real @ A @ Y ) )
          = ( X = Y ) ) ) ) ).

% powr_inj
thf(fact_1195_powr__le1,axiom,
    ! [A: real,X: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ zero_zero_real @ X )
       => ( ( ord_less_eq_real @ X @ one_one_real )
         => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).

% powr_le1
thf(fact_1196_powr__mono__both,axiom,
    ! [A: real,B: real,X: real,Y: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ A @ B )
       => ( ( ord_less_eq_real @ one_one_real @ X )
         => ( ( ord_less_eq_real @ X @ Y )
           => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).

% powr_mono_both
thf(fact_1197_powr__mult__base,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
        = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).

% powr_mult_base
thf(fact_1198_ge__one__powr__ge__zero,axiom,
    ! [X: real,A: real] :
      ( ( ord_less_eq_real @ one_one_real @ X )
     => ( ( ord_less_eq_real @ zero_zero_real @ A )
       => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).

% ge_one_powr_ge_zero
thf(fact_1199_powr__mono,axiom,
    ! [A: real,B: real,X: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ one_one_real @ X )
       => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).

% powr_mono
thf(fact_1200_powr__mono2_H,axiom,
    ! [A: real,X: real,Y: real] :
      ( ( ord_less_eq_real @ A @ zero_zero_real )
     => ( ( ord_less_real @ zero_zero_real @ X )
       => ( ( ord_less_eq_real @ X @ Y )
         => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).

% powr_mono2'
thf(fact_1201_powr__less__mono2,axiom,
    ! [A: real,X: real,Y: real] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ zero_zero_real @ X )
       => ( ( ord_less_real @ X @ Y )
         => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).

% powr_less_mono2
thf(fact_1202_inverse__powr,axiom,
    ! [Y: real,A: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ Y )
     => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
        = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).

% inverse_powr
thf(fact_1203_powr__non__neg,axiom,
    ! [A: real,X: real] :
      ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).

% powr_non_neg
thf(fact_1204_powr__less__mono2__neg,axiom,
    ! [A: real,X: real,Y: real] :
      ( ( ord_less_real @ A @ zero_zero_real )
     => ( ( ord_less_real @ zero_zero_real @ X )
       => ( ( ord_less_real @ X @ Y )
         => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).

% powr_less_mono2_neg
thf(fact_1205_powr__ge__pzero,axiom,
    ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).

% powr_ge_pzero
thf(fact_1206_powr__mono2,axiom,
    ! [A: real,X: real,Y: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ zero_zero_real @ X )
       => ( ( ord_less_eq_real @ X @ Y )
         => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).

% powr_mono2
thf(fact_1207_powr__mult,axiom,
    ! [X: real,Y: real,A: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ( ord_less_eq_real @ zero_zero_real @ Y )
       => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
          = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).

% powr_mult
thf(fact_1208_real__minus__mult__self__le,axiom,
    ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).

% real_minus_mult_self_le
thf(fact_1209_powr__realpow,axiom,
    ! [X: real,N: nat] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
        = ( power_power_real @ X @ N ) ) ) ).

% powr_realpow
thf(fact_1210_reals__Archimedean3,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ! [Y3: real] :
        ? [N3: nat] : ( ord_less_real @ Y3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).

% reals_Archimedean3
thf(fact_1211_powr__real__of__int_H,axiom,
    ! [X: real,N: int] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ( ( X != zero_zero_real )
          | ( ord_less_int @ zero_zero_int @ N ) )
       => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
          = ( power_int_real @ X @ N ) ) ) ) ).

% powr_real_of_int'
thf(fact_1212_real__archimedian__rdiv__eq__0,axiom,
    ! [X: real,C: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ( ord_less_eq_real @ zero_zero_real @ C )
       => ( ! [M4: nat] :
              ( ( ord_less_nat @ zero_zero_nat @ M4 )
             => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X ) @ C ) )
         => ( X = zero_zero_real ) ) ) ) ).

% real_archimedian_rdiv_eq_0
thf(fact_1213_linear__plus__1__le__power,axiom,
    ! [X: real,N: nat] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).

% linear_plus_1_le_power
thf(fact_1214_mult__is__0,axiom,
    ! [M: nat,N: nat] :
      ( ( ( times_times_nat @ M @ N )
        = zero_zero_nat )
      = ( ( M = zero_zero_nat )
        | ( N = zero_zero_nat ) ) ) ).

% mult_is_0
thf(fact_1215_mult__0__right,axiom,
    ! [M: nat] :
      ( ( times_times_nat @ M @ zero_zero_nat )
      = zero_zero_nat ) ).

% mult_0_right
thf(fact_1216_mult__cancel1,axiom,
    ! [K: nat,M: nat,N: nat] :
      ( ( ( times_times_nat @ K @ M )
        = ( times_times_nat @ K @ N ) )
      = ( ( M = N )
        | ( K = zero_zero_nat ) ) ) ).

% mult_cancel1
thf(fact_1217_mult__cancel2,axiom,
    ! [M: nat,K: nat,N: nat] :
      ( ( ( times_times_nat @ M @ K )
        = ( times_times_nat @ N @ K ) )
      = ( ( M = N )
        | ( K = zero_zero_nat ) ) ) ).

% mult_cancel2
thf(fact_1218_nat__mult__eq__1__iff,axiom,
    ! [M: nat,N: nat] :
      ( ( ( times_times_nat @ M @ N )
        = one_one_nat )
      = ( ( M = one_one_nat )
        & ( N = one_one_nat ) ) ) ).

% nat_mult_eq_1_iff
thf(fact_1219_nat__1__eq__mult__iff,axiom,
    ! [M: nat,N: nat] :
      ( ( one_one_nat
        = ( times_times_nat @ M @ N ) )
      = ( ( M = one_one_nat )
        & ( N = one_one_nat ) ) ) ).

% nat_1_eq_mult_iff
thf(fact_1220_nat__0__less__mult__iff,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
      = ( ( ord_less_nat @ zero_zero_nat @ M )
        & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).

% nat_0_less_mult_iff
thf(fact_1221_mult__less__cancel2,axiom,
    ! [M: nat,K: nat,N: nat] :
      ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
      = ( ( ord_less_nat @ zero_zero_nat @ K )
        & ( ord_less_nat @ M @ N ) ) ) ).

% mult_less_cancel2
thf(fact_1222_nat__mult__less__cancel__disj,axiom,
    ! [K: nat,M: nat,N: nat] :
      ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
      = ( ( ord_less_nat @ zero_zero_nat @ K )
        & ( ord_less_nat @ M @ N ) ) ) ).

% nat_mult_less_cancel_disj
thf(fact_1223_mult__le__cancel2,axiom,
    ! [M: nat,K: nat,N: nat] :
      ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
      = ( ( ord_less_nat @ zero_zero_nat @ K )
       => ( ord_less_eq_nat @ M @ N ) ) ) ).

% mult_le_cancel2
thf(fact_1224_nat__mult__le__cancel__disj,axiom,
    ! [K: nat,M: nat,N: nat] :
      ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
      = ( ( ord_less_nat @ zero_zero_nat @ K )
       => ( ord_less_eq_nat @ M @ N ) ) ) ).

% nat_mult_le_cancel_disj
thf(fact_1225_nat__mult__1__right,axiom,
    ! [N: nat] :
      ( ( times_times_nat @ N @ one_one_nat )
      = N ) ).

% nat_mult_1_right
thf(fact_1226_nat__mult__1,axiom,
    ! [N: nat] :
      ( ( times_times_nat @ one_one_nat @ N )
      = N ) ).

% nat_mult_1
thf(fact_1227_nat__mult__distrib__neg,axiom,
    ! [Z: int,Z6: int] :
      ( ( ord_less_eq_int @ Z @ zero_zero_int )
     => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
        = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).

% nat_mult_distrib_neg
thf(fact_1228_int__ops_I7_J,axiom,
    ! [A: nat,B: nat] :
      ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
      = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).

% int_ops(7)
thf(fact_1229_nat__mult__max__right,axiom,
    ! [M: nat,N: nat,Q: nat] :
      ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q ) )
      = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q ) ) ) ).

% nat_mult_max_right
thf(fact_1230_nat__mult__max__left,axiom,
    ! [M: nat,N: nat,Q: nat] :
      ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q )
      = ( ord_max_nat @ ( times_times_nat @ M @ Q ) @ ( times_times_nat @ N @ Q ) ) ) ).

% nat_mult_max_left
thf(fact_1231_nat__mult__distrib,axiom,
    ! [Z: int,Z6: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
        = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).

% nat_mult_distrib
thf(fact_1232_int__distrib_I2_J,axiom,
    ! [W3: int,Z1: int,Z22: int] :
      ( ( times_times_int @ W3 @ ( plus_plus_int @ Z1 @ Z22 ) )
      = ( plus_plus_int @ ( times_times_int @ W3 @ Z1 ) @ ( times_times_int @ W3 @ Z22 ) ) ) ).

% int_distrib(2)
thf(fact_1233_int__distrib_I1_J,axiom,
    ! [Z1: int,Z22: int,W3: int] :
      ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W3 )
      = ( plus_plus_int @ ( times_times_int @ Z1 @ W3 ) @ ( times_times_int @ Z22 @ W3 ) ) ) ).

% int_distrib(1)
thf(fact_1234_add__mult__distrib,axiom,
    ! [M: nat,N: nat,K: nat] :
      ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
      = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).

% add_mult_distrib
thf(fact_1235_add__mult__distrib2,axiom,
    ! [K: nat,M: nat,N: nat] :
      ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
      = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).

% add_mult_distrib2
thf(fact_1236_times__int__code_I1_J,axiom,
    ! [K: int] :
      ( ( times_times_int @ K @ zero_zero_int )
      = zero_zero_int ) ).

% times_int_code(1)
thf(fact_1237_times__int__code_I2_J,axiom,
    ! [L: int] :
      ( ( times_times_int @ zero_zero_int @ L )
      = zero_zero_int ) ).

% times_int_code(2)
thf(fact_1238_le__cube,axiom,
    ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).

% le_cube
thf(fact_1239_le__square,axiom,
    ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).

% le_square
thf(fact_1240_mult__le__mono,axiom,
    ! [I3: nat,J: nat,K: nat,L: nat] :
      ( ( ord_less_eq_nat @ I3 @ J )
     => ( ( ord_less_eq_nat @ K @ L )
       => ( ord_less_eq_nat @ ( times_times_nat @ I3 @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).

% mult_le_mono
thf(fact_1241_mult__le__mono1,axiom,
    ! [I3: nat,J: nat,K: nat] :
      ( ( ord_less_eq_nat @ I3 @ J )
     => ( ord_less_eq_nat @ ( times_times_nat @ I3 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).

% mult_le_mono1
thf(fact_1242_mult__le__mono2,axiom,
    ! [I3: nat,J: nat,K: nat] :
      ( ( ord_less_eq_nat @ I3 @ J )
     => ( ord_less_eq_nat @ ( times_times_nat @ K @ I3 ) @ ( times_times_nat @ K @ J ) ) ) ).

% mult_le_mono2
thf(fact_1243_mult__0,axiom,
    ! [N: nat] :
      ( ( times_times_nat @ zero_zero_nat @ N )
      = zero_zero_nat ) ).

% mult_0
thf(fact_1244_nat__mult__eq__cancel__disj,axiom,
    ! [K: nat,M: nat,N: nat] :
      ( ( ( times_times_nat @ K @ M )
        = ( times_times_nat @ K @ N ) )
      = ( ( K = zero_zero_nat )
        | ( M = N ) ) ) ).

% nat_mult_eq_cancel_disj
thf(fact_1245_left__add__mult__distrib,axiom,
    ! [I3: nat,U: nat,J: nat,K: nat] :
      ( ( plus_plus_nat @ ( times_times_nat @ I3 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I3 @ J ) @ U ) @ K ) ) ).

% left_add_mult_distrib
thf(fact_1246_zmult__zless__mono2,axiom,
    ! [I3: int,J: int,K: int] :
      ( ( ord_less_int @ I3 @ J )
     => ( ( ord_less_int @ zero_zero_int @ K )
       => ( ord_less_int @ ( times_times_int @ K @ I3 ) @ ( times_times_int @ K @ J ) ) ) ) ).

% zmult_zless_mono2
thf(fact_1247_mult__eq__self__implies__10,axiom,
    ! [M: nat,N: nat] :
      ( ( M
        = ( times_times_nat @ M @ N ) )
     => ( ( N = one_one_nat )
        | ( M = zero_zero_nat ) ) ) ).

% mult_eq_self_implies_10
thf(fact_1248_mult__less__mono2,axiom,
    ! [I3: nat,J: nat,K: nat] :
      ( ( ord_less_nat @ I3 @ J )
     => ( ( ord_less_nat @ zero_zero_nat @ K )
       => ( ord_less_nat @ ( times_times_nat @ K @ I3 ) @ ( times_times_nat @ K @ J ) ) ) ) ).

% mult_less_mono2
thf(fact_1249_mult__less__mono1,axiom,
    ! [I3: nat,J: nat,K: nat] :
      ( ( ord_less_nat @ I3 @ J )
     => ( ( ord_less_nat @ zero_zero_nat @ K )
       => ( ord_less_nat @ ( times_times_nat @ I3 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).

% mult_less_mono1
thf(fact_1250_nat__mult__less__cancel1,axiom,
    ! [K: nat,M: nat,N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ K )
     => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
        = ( ord_less_nat @ M @ N ) ) ) ).

% nat_mult_less_cancel1
thf(fact_1251_nat__mult__eq__cancel1,axiom,
    ! [K: nat,M: nat,N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ K )
     => ( ( ( times_times_nat @ K @ M )
          = ( times_times_nat @ K @ N ) )
        = ( M = N ) ) ) ).

% nat_mult_eq_cancel1
thf(fact_1252_pos__zmult__eq__1__iff__lemma,axiom,
    ! [M: int,N: int] :
      ( ( ( times_times_int @ M @ N )
        = one_one_int )
     => ( ( M = one_one_int )
        | ( M
          = ( uminus_uminus_int @ one_one_int ) ) ) ) ).

% pos_zmult_eq_1_iff_lemma
thf(fact_1253_zmult__eq__1__iff,axiom,
    ! [M: int,N: int] :
      ( ( ( times_times_int @ M @ N )
        = one_one_int )
      = ( ( ( M = one_one_int )
          & ( N = one_one_int ) )
        | ( ( M
            = ( uminus_uminus_int @ one_one_int ) )
          & ( N
            = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).

% zmult_eq_1_iff
thf(fact_1254_nat__mult__le__cancel1,axiom,
    ! [K: nat,M: nat,N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ K )
     => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
        = ( ord_less_eq_nat @ M @ N ) ) ) ).

% nat_mult_le_cancel1
thf(fact_1255_pos__zmult__eq__1__iff,axiom,
    ! [M: int,N: int] :
      ( ( ord_less_int @ zero_zero_int @ M )
     => ( ( ( times_times_int @ M @ N )
          = one_one_int )
        = ( ( M = one_one_int )
          & ( N = one_one_int ) ) ) ) ).

% pos_zmult_eq_1_iff
thf(fact_1256_zmult__zless__mono2__lemma,axiom,
    ! [I3: int,J: int,K: nat] :
      ( ( ord_less_int @ I3 @ J )
     => ( ( ord_less_nat @ zero_zero_nat @ K )
       => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I3 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).

% zmult_zless_mono2_lemma
thf(fact_1257_incr__mult__lemma,axiom,
    ! [D: int,P: int > $o,K: int] :
      ( ( ord_less_int @ zero_zero_int @ D )
     => ( ! [X4: int] :
            ( ( P @ X4 )
           => ( P @ ( plus_plus_int @ X4 @ D ) ) )
       => ( ( ord_less_eq_int @ zero_zero_int @ K )
         => ! [X3: int] :
              ( ( P @ X3 )
             => ( P @ ( plus_plus_int @ X3 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).

% incr_mult_lemma
thf(fact_1258_ceiling__log__eq__powr__iff,axiom,
    ! [X: real,B: real,K: nat] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ one_one_real @ B )
       => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
            = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
          = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
            & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).

% ceiling_log_eq_powr_iff
thf(fact_1259_powr__int,axiom,
    ! [X: real,I3: int] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ( ord_less_eq_int @ zero_zero_int @ I3 )
         => ( ( powr_real @ X @ ( ring_1_of_int_real @ I3 ) )
            = ( power_power_real @ X @ ( nat2 @ I3 ) ) ) )
        & ( ~ ( ord_less_eq_int @ zero_zero_int @ I3 )
         => ( ( powr_real @ X @ ( ring_1_of_int_real @ I3 ) )
            = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I3 ) ) ) ) ) ) ) ) ).

% powr_int
thf(fact_1260_log__one,axiom,
    ! [A: real] :
      ( ( log @ A @ one_one_real )
      = zero_zero_real ) ).

% log_one
thf(fact_1261_log__eq__one,axiom,
    ! [A: real] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ( ( A != one_one_real )
       => ( ( log @ A @ A )
          = one_one_real ) ) ) ).

% log_eq_one
thf(fact_1262_log__less__cancel__iff,axiom,
    ! [A: real,X: real,Y: real] :
      ( ( ord_less_real @ one_one_real @ A )
     => ( ( ord_less_real @ zero_zero_real @ X )
       => ( ( ord_less_real @ zero_zero_real @ Y )
         => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
            = ( ord_less_real @ X @ Y ) ) ) ) ) ).

% log_less_cancel_iff
thf(fact_1263_log__less__one__cancel__iff,axiom,
    ! [A: real,X: real] :
      ( ( ord_less_real @ one_one_real @ A )
     => ( ( ord_less_real @ zero_zero_real @ X )
       => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
          = ( ord_less_real @ X @ A ) ) ) ) ).

% log_less_one_cancel_iff
thf(fact_1264_one__less__log__cancel__iff,axiom,
    ! [A: real,X: real] :
      ( ( ord_less_real @ one_one_real @ A )
     => ( ( ord_less_real @ zero_zero_real @ X )
       => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
          = ( ord_less_real @ A @ X ) ) ) ) ).

% one_less_log_cancel_iff
thf(fact_1265_log__less__zero__cancel__iff,axiom,
    ! [A: real,X: real] :
      ( ( ord_less_real @ one_one_real @ A )
     => ( ( ord_less_real @ zero_zero_real @ X )
       => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
          = ( ord_less_real @ X @ one_one_real ) ) ) ) ).

% log_less_zero_cancel_iff
thf(fact_1266_zero__less__log__cancel__iff,axiom,
    ! [A: real,X: real] :
      ( ( ord_less_real @ one_one_real @ A )
     => ( ( ord_less_real @ zero_zero_real @ X )
       => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
          = ( ord_less_real @ one_one_real @ X ) ) ) ) ).

% zero_less_log_cancel_iff

% Helper facts (11)
thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
    ! [X: int,Y: int] :
      ( ( if_int @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
    ! [X: int,Y: int] :
      ( ( if_int @ $true @ X @ Y )
      = X ) ).

thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ( if_nat @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ( if_nat @ $true @ X @ Y )
      = X ) ).

thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
    ! [X: num,Y: num] :
      ( ( if_num @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
    ! [X: num,Y: num] :
      ( ( if_num @ $true @ X @ Y )
      = X ) ).

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 ) ).

thf(help_If_3_1_If_001t__Risk____Free____Lending__Oaccount_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__Risk____Free____Lending__Oaccount_T,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( if_Risk_Free_account @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Risk____Free____Lending__Oaccount_T,axiom,
    ! [X: risk_Free_account,Y: risk_Free_account] :
      ( ( if_Risk_Free_account @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ! [I: nat] :
      ( ( ( risk_F170160801229183585ccount @ ( plus_p1863581527469039996ccount @ alpha @ beta ) @ I )
        = zero_zero_real )
      | ( ord_less_eq_nat @ I @ ( ord_max_nat @ ( risk_F4612863212915232279period @ alpha ) @ ( risk_F4612863212915232279period @ beta ) ) ) ) ).

%------------------------------------------------------------------------------