% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Fundamental_Theorem_Algebra/prob_437__5371834_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:30:08.828

% Could-be-implicit typings (3)
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__Nat__Onat, type,
    nat : $tType).

% Explicit typings (19)
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__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > real > real).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal, type,
    uminus_uminus_real : real > real).
thf(sy_c_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat, type,
    semiri1382578993at_nat : nat > nat).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal, type,
    semiri2110766477t_real : nat > real).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat, type,
    order_769474267at_nat : (nat > nat) > $o).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat, type,
    divide_divide_nat : nat > nat > nat).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_c_Set_OCollect_001t__Real__Oreal, type,
    collect_real : (real > $o) > set_real).
thf(sy_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_N1____, type,
    n1 : nat).
thf(sy_v_N2____, type,
    n2 : nat).
thf(sy_v_f____, type,
    f : nat > nat).
thf(sy_v_s____, type,
    s : real).

% Relevant facts (194)
thf(fact_0_th000_I2_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % th000(2)
thf(fact_1__092_060open_0621_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_A_092_060le_062_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_092_060close_062, axiom,
    ((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (semiri2110766477t_real @ (suc @ (f @ (plus_plus_nat @ n1 @ n2))))) @ (divide_divide_real @ one_one_real @ (semiri2110766477t_real @ (suc @ (plus_plus_nat @ n1 @ n2))))))). % \<open>1 / real (Suc (f (N1 + N2))) \<le> 1 / real (Suc (N1 + N2))\<close>
thf(fact_2_fz_I1_J, axiom,
    ((order_769474267at_nat @ f))). % fz(1)
thf(fact_3_th00, axiom,
    ((ord_less_eq_real @ (semiri2110766477t_real @ (suc @ (plus_plus_nat @ n1 @ n2))) @ (semiri2110766477t_real @ (suc @ (f @ (plus_plus_nat @ n1 @ n2))))))). % th00
thf(fact_4_of__nat__Suc, axiom,
    ((![M : nat]: ((semiri1382578993at_nat @ (suc @ M)) = (plus_plus_nat @ one_one_nat @ (semiri1382578993at_nat @ M)))))). % of_nat_Suc
thf(fact_5_of__nat__Suc, axiom,
    ((![M : nat]: ((semiri2110766477t_real @ (suc @ M)) = (plus_plus_real @ one_one_real @ (semiri2110766477t_real @ M)))))). % of_nat_Suc
thf(fact_6_of__nat__add, axiom,
    ((![M : nat, N : nat]: ((semiri1382578993at_nat @ (plus_plus_nat @ M @ N)) = (plus_plus_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)))))). % of_nat_add
thf(fact_7_of__nat__add, axiom,
    ((![M : nat, N : nat]: ((semiri2110766477t_real @ (plus_plus_nat @ M @ N)) = (plus_plus_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)))))). % of_nat_add
thf(fact_8_divide__minus1, axiom,
    ((![X : real]: ((divide_divide_real @ X @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ X))))). % divide_minus1
thf(fact_9__092_060open_062N1_A_L_AN2_A_092_060le_062_Af_A_IN1_A_L_AN2_J_092_060close_062, axiom,
    ((ord_less_eq_nat @ (plus_plus_nat @ n1 @ n2) @ (f @ (plus_plus_nat @ n1 @ n2))))). % \<open>N1 + N2 \<le> f (N1 + N2)\<close>
thf(fact_10_add__Suc__right, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ M @ (suc @ N)) = (suc @ (plus_plus_nat @ M @ N)))))). % add_Suc_right
thf(fact_11_of__nat__1, axiom,
    (((semiri2110766477t_real @ one_one_nat) = one_one_real))). % of_nat_1
thf(fact_12_of__nat__1, axiom,
    (((semiri1382578993at_nat @ one_one_nat) = one_one_nat))). % of_nat_1
thf(fact_13_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_real = (semiri2110766477t_real @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_14_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_nat = (semiri1382578993at_nat @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_15_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri2110766477t_real @ N) = one_one_real) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_16_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri1382578993at_nat @ N) = one_one_nat) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_17_of__nat__le__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N)) = (ord_less_eq_nat @ M @ N))))). % of_nat_le_iff
thf(fact_18_of__nat__le__iff, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)) = (ord_less_eq_nat @ M @ N))))). % of_nat_le_iff
thf(fact_19_div__by__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ one_one_real) = A)))). % div_by_1
thf(fact_20_div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % div_by_1
thf(fact_21_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_22_nat_Oinject, axiom,
    ((![X2 : nat, Y2 : nat]: (((suc @ X2) = (suc @ Y2)) = (X2 = Y2))))). % nat.inject
thf(fact_23_of__nat__eq__iff, axiom,
    ((![M : nat, N : nat]: (((semiri2110766477t_real @ M) = (semiri2110766477t_real @ N)) = (M = N))))). % of_nat_eq_iff
thf(fact_24_of__nat__eq__iff, axiom,
    ((![M : nat, N : nat]: (((semiri1382578993at_nat @ M) = (semiri1382578993at_nat @ N)) = (M = N))))). % of_nat_eq_iff
thf(fact_25_Suc__le__mono, axiom,
    ((![N : nat, M : nat]: ((ord_less_eq_nat @ (suc @ N) @ (suc @ M)) = (ord_less_eq_nat @ N @ M))))). % Suc_le_mono
thf(fact_26_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_27_le__refl, axiom,
    ((![N : nat]: (ord_less_eq_nat @ N @ N)))). % le_refl
thf(fact_28_le__trans, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ J @ K) => (ord_less_eq_nat @ I @ K)))))). % le_trans
thf(fact_29_eq__imp__le, axiom,
    ((![M : nat, N : nat]: ((M = N) => (ord_less_eq_nat @ M @ N))))). % eq_imp_le
thf(fact_30_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_31_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_32_Nat_Oex__has__greatest__nat, axiom,
    ((![P : nat > $o, K : nat, B : nat]: ((P @ K) => ((![Y : nat]: ((P @ Y) => (ord_less_eq_nat @ Y @ B))) => (?[X3 : nat]: ((P @ X3) & (![Y3 : nat]: ((P @ Y3) => (ord_less_eq_nat @ Y3 @ X3)))))))))). % Nat.ex_has_greatest_nat
thf(fact_33_div__le__mono, axiom,
    ((![M : nat, N : nat, K : nat]: ((ord_less_eq_nat @ M @ N) => (ord_less_eq_nat @ (divide_divide_nat @ M @ K) @ (divide_divide_nat @ N @ K)))))). % div_le_mono
thf(fact_34_strict__mono__imp__increasing, axiom,
    ((![F : nat > nat, N : nat]: ((order_769474267at_nat @ F) => (ord_less_eq_nat @ N @ (F @ N)))))). % strict_mono_imp_increasing
thf(fact_35_Suc__div__le__mono, axiom,
    ((![M : nat, N : nat]: (ord_less_eq_nat @ (divide_divide_nat @ M @ N) @ (divide_divide_nat @ (suc @ M) @ N))))). % Suc_div_le_mono
thf(fact_36_div__le__dividend, axiom,
    ((![M : nat, N : nat]: (ord_less_eq_nat @ (divide_divide_nat @ M @ N) @ M)))). % div_le_dividend
thf(fact_37_transitive__stepwise__le, axiom,
    ((![M : nat, N : nat, R : nat > nat > $o]: ((ord_less_eq_nat @ M @ N) => ((![X3 : nat]: (R @ X3 @ X3)) => ((![X3 : nat, Y : nat, Z : nat]: ((R @ X3 @ Y) => ((R @ Y @ Z) => (R @ X3 @ Z)))) => ((![N2 : nat]: (R @ N2 @ (suc @ N2))) => (R @ M @ N)))))))). % transitive_stepwise_le
thf(fact_38_nat__induct__at__least, axiom,
    ((![M : nat, N : nat, P : nat > $o]: ((ord_less_eq_nat @ M @ N) => ((P @ M) => ((![N2 : nat]: ((ord_less_eq_nat @ M @ N2) => ((P @ N2) => (P @ (suc @ N2))))) => (P @ N))))))). % nat_induct_at_least
thf(fact_39_full__nat__induct, axiom,
    ((![P : nat > $o, N : nat]: ((![N2 : nat]: ((![M2 : nat]: ((ord_less_eq_nat @ (suc @ M2) @ N2) => (P @ M2))) => (P @ N2))) => (P @ N))))). % full_nat_induct
thf(fact_40_not__less__eq__eq, axiom,
    ((![M : nat, N : nat]: ((~ ((ord_less_eq_nat @ M @ N))) = (ord_less_eq_nat @ (suc @ N) @ M))))). % not_less_eq_eq
thf(fact_41_Suc__n__not__le__n, axiom,
    ((![N : nat]: (~ ((ord_less_eq_nat @ (suc @ N) @ N)))))). % Suc_n_not_le_n
thf(fact_42_le__Suc__eq, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ (suc @ N)) = (((ord_less_eq_nat @ M @ N)) | ((M = (suc @ N)))))))). % le_Suc_eq
thf(fact_43_Suc__le__D, axiom,
    ((![N : nat, M3 : nat]: ((ord_less_eq_nat @ (suc @ N) @ M3) => (?[M4 : nat]: (M3 = (suc @ M4))))))). % Suc_le_D
thf(fact_44_le__SucI, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => (ord_less_eq_nat @ M @ (suc @ N)))))). % le_SucI
thf(fact_45_le__SucE, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ (suc @ N)) => ((~ ((ord_less_eq_nat @ M @ N))) => (M = (suc @ N))))))). % le_SucE
thf(fact_46_Suc__leD, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ (suc @ M) @ N) => (ord_less_eq_nat @ M @ N))))). % Suc_leD
thf(fact_47_nat__le__iff__add, axiom,
    ((ord_less_eq_nat = (^[M5 : nat]: (^[N3 : nat]: (?[K2 : nat]: (N3 = (plus_plus_nat @ M5 @ K2)))))))). % nat_le_iff_add
thf(fact_48_trans__le__add2, axiom,
    ((![I : nat, J : nat, M : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ I @ (plus_plus_nat @ M @ J)))))). % trans_le_add2
thf(fact_49_trans__le__add1, axiom,
    ((![I : nat, J : nat, M : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ I @ (plus_plus_nat @ J @ M)))))). % trans_le_add1
thf(fact_50_mem__Collect__eq, axiom,
    ((![A : real, P : real > $o]: ((member_real @ A @ (collect_real @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_51_Collect__mem__eq, axiom,
    ((![A2 : set_real]: ((collect_real @ (^[X4 : real]: (member_real @ X4 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_52_add__le__mono1, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ K)))))). % add_le_mono1
thf(fact_53_add__le__mono, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ K @ L) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L))))))). % add_le_mono
thf(fact_54_le__Suc__ex, axiom,
    ((![K : nat, L : nat]: ((ord_less_eq_nat @ K @ L) => (?[N2 : nat]: (L = (plus_plus_nat @ K @ N2))))))). % le_Suc_ex
thf(fact_55_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_56_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_57_le__add2, axiom,
    ((![N : nat, M : nat]: (ord_less_eq_nat @ N @ (plus_plus_nat @ M @ N))))). % le_add2
thf(fact_58_le__add1, axiom,
    ((![N : nat, M : nat]: (ord_less_eq_nat @ N @ (plus_plus_nat @ N @ M))))). % le_add1
thf(fact_59_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_60_Suc__eq__plus1__left, axiom,
    ((suc = (plus_plus_nat @ one_one_nat)))). % Suc_eq_plus1_left
thf(fact_61_plus__1__eq__Suc, axiom,
    (((plus_plus_nat @ one_one_nat) = suc))). % plus_1_eq_Suc
thf(fact_62_Suc__eq__plus1, axiom,
    ((suc = (^[N3 : nat]: (plus_plus_nat @ N3 @ one_one_nat))))). % Suc_eq_plus1
thf(fact_63_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_64_Suc__inject, axiom,
    ((![X : nat, Y4 : nat]: (((suc @ X) = (suc @ Y4)) => (X = Y4))))). % Suc_inject
thf(fact_65_lift__Suc__antimono__le, axiom,
    ((![F : nat > real, N : nat, N4 : nat]: ((![N2 : nat]: (ord_less_eq_real @ (F @ (suc @ N2)) @ (F @ N2))) => ((ord_less_eq_nat @ N @ N4) => (ord_less_eq_real @ (F @ N4) @ (F @ N))))))). % lift_Suc_antimono_le
thf(fact_66_lift__Suc__antimono__le, axiom,
    ((![F : nat > nat, N : nat, N4 : nat]: ((![N2 : nat]: (ord_less_eq_nat @ (F @ (suc @ N2)) @ (F @ N2))) => ((ord_less_eq_nat @ N @ N4) => (ord_less_eq_nat @ (F @ N4) @ (F @ N))))))). % lift_Suc_antimono_le
thf(fact_67_lift__Suc__mono__le, axiom,
    ((![F : nat > real, N : nat, N4 : nat]: ((![N2 : nat]: (ord_less_eq_real @ (F @ N2) @ (F @ (suc @ N2)))) => ((ord_less_eq_nat @ N @ N4) => (ord_less_eq_real @ (F @ N) @ (F @ N4))))))). % lift_Suc_mono_le
thf(fact_68_lift__Suc__mono__le, axiom,
    ((![F : nat > nat, N : nat, N4 : nat]: ((![N2 : nat]: (ord_less_eq_nat @ (F @ N2) @ (F @ (suc @ N2)))) => ((ord_less_eq_nat @ N @ N4) => (ord_less_eq_nat @ (F @ N) @ (F @ N4))))))). % lift_Suc_mono_le
thf(fact_69_add__divide__distrib, axiom,
    ((![A : real, B : real, C : real]: ((divide_divide_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)))))). % add_divide_distrib
thf(fact_70_of__nat__mono, axiom,
    ((![I : nat, J : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_real @ (semiri2110766477t_real @ I) @ (semiri2110766477t_real @ J)))))). % of_nat_mono
thf(fact_71_of__nat__mono, axiom,
    ((![I : nat, J : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (semiri1382578993at_nat @ I) @ (semiri1382578993at_nat @ J)))))). % of_nat_mono
thf(fact_72_minus__divide__left, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (uminus_uminus_real @ A) @ B))))). % minus_divide_left
thf(fact_73_minus__divide__divide, axiom,
    ((![A : real, B : real]: ((divide_divide_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (divide_divide_real @ A @ B))))). % minus_divide_divide
thf(fact_74_minus__divide__right, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ A @ (uminus_uminus_real @ B)))))). % minus_divide_right
thf(fact_75_unique__euclidean__semiring__with__nat__class_Oof__nat__div, axiom,
    ((![M : nat, N : nat]: ((semiri1382578993at_nat @ (divide_divide_nat @ M @ N)) = (divide_divide_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)))))). % unique_euclidean_semiring_with_nat_class.of_nat_div
thf(fact_76_add__Suc, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ (suc @ M) @ N) = (suc @ (plus_plus_nat @ M @ N)))))). % add_Suc
thf(fact_77_nat__arith_Osuc1, axiom,
    ((![A2 : nat, K : nat, A : nat]: ((A2 = (plus_plus_nat @ K @ A)) => ((suc @ A2) = (plus_plus_nat @ K @ (suc @ A))))))). % nat_arith.suc1
thf(fact_78_add__Suc__shift, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ (suc @ M) @ N) = (plus_plus_nat @ M @ (suc @ N)))))). % add_Suc_shift
thf(fact_79_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_80_minus__add__distrib, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)))))). % minus_add_distrib
thf(fact_81_minus__add__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ (plus_plus_real @ A @ B)) = B)))). % minus_add_cancel
thf(fact_82_add__minus__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ A @ (plus_plus_real @ (uminus_uminus_real @ A) @ B)) = B)))). % add_minus_cancel
thf(fact_83_neg__le__iff__le, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ B))))). % neg_le_iff_le
thf(fact_84_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_85_add__le__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_right
thf(fact_86_add__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_87_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_88_real__of__nat__div4, axiom,
    ((![N : nat, X : nat]: (ord_less_eq_real @ (semiri2110766477t_real @ (divide_divide_nat @ N @ X)) @ (divide_divide_real @ (semiri2110766477t_real @ N) @ (semiri2110766477t_real @ X)))))). % real_of_nat_div4
thf(fact_89_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_90_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_91_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_92_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_93_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_94_neg__equal__iff__equal, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_95_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_96_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_97_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (K = L)) => ((plus_plus_real @ I @ K) = (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_98_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (K = L)) => ((plus_plus_nat @ I @ K) = (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_99_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_100_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_101_group__cancel_Oadd2, axiom,
    ((![B2 : real, K : real, B : real, A : real]: ((B2 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B2) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_102_group__cancel_Oadd2, axiom,
    ((![B2 : nat, K : nat, B : nat, A : nat]: ((B2 = (plus_plus_nat @ K @ B)) => ((plus_plus_nat @ A @ B2) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add2
thf(fact_103_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_104_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_105_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_106_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_107_add_Ocommute, axiom,
    ((plus_plus_real = (^[A3 : real]: (^[B3 : real]: (plus_plus_real @ B3 @ A3)))))). % add.commute
thf(fact_108_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A3 : nat]: (^[B3 : nat]: (plus_plus_nat @ B3 @ A3)))))). % add.commute
thf(fact_109_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_110_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_111_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_112_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_113_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_114_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_115_one__reorient, axiom,
    ((![X : real]: ((one_one_real = X) = (X = one_one_real))))). % one_reorient
thf(fact_116_one__reorient, axiom,
    ((![X : nat]: ((one_one_nat = X) = (X = one_one_nat))))). % one_reorient
thf(fact_117_equation__minus__iff, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A)))))). % equation_minus_iff
thf(fact_118_minus__equation__iff, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A))))). % minus_equation_iff
thf(fact_119_complete__real, axiom,
    ((![S : set_real]: ((?[X5 : real]: (member_real @ X5 @ S)) => ((?[Z2 : real]: (![X3 : real]: ((member_real @ X3 @ S) => (ord_less_eq_real @ X3 @ Z2)))) => (?[Y : real]: ((![X5 : real]: ((member_real @ X5 @ S) => (ord_less_eq_real @ X5 @ Y))) & (![Z2 : real]: ((![X3 : real]: ((member_real @ X3 @ S) => (ord_less_eq_real @ X3 @ Z2))) => (ord_less_eq_real @ Y @ Z2)))))))))). % complete_real
thf(fact_120_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (K = L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_121_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (K = L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_122_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_123_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (ord_less_eq_nat @ K @ L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_124_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_125_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (ord_less_eq_nat @ K @ L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_126_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_127_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_128_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_129_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_130_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_131_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_132_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_133_le__iff__add, axiom,
    ((ord_less_eq_nat = (^[A3 : nat]: (^[B3 : nat]: (?[C3 : nat]: (B3 = (plus_plus_nat @ A3 @ C3)))))))). % le_iff_add
thf(fact_134_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_135_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_136_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_137_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_138_le__minus__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ B)) = (ord_less_eq_real @ B @ (uminus_uminus_real @ A)))))). % le_minus_iff
thf(fact_139_minus__le__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ A))))). % minus_le_iff
thf(fact_140_le__imp__neg__le, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % le_imp_neg_le
thf(fact_141_group__cancel_Oneg1, axiom,
    ((![A2 : real, K : real, A : real]: ((A2 = (plus_plus_real @ K @ A)) => ((uminus_uminus_real @ A2) = (plus_plus_real @ (uminus_uminus_real @ K) @ (uminus_uminus_real @ A))))))). % group_cancel.neg1
thf(fact_142_add_Oinverse__distrib__swap, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % add.inverse_distrib_swap
thf(fact_143_le__minus__one__simps_I4_J, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))))). % le_minus_one_simps(4)
thf(fact_144_le__minus__one__simps_I2_J, axiom,
    ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ one_one_real))). % le_minus_one_simps(2)
thf(fact_145_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_146_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_147_order__refl, axiom,
    ((![X : nat]: (ord_less_eq_nat @ X @ X)))). % order_refl
thf(fact_148_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_149_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_150_dual__order_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z3 : real]: (Y5 = Z3))) = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ B3 @ A3)) & ((ord_less_eq_real @ A3 @ B3)))))))). % dual_order.eq_iff
thf(fact_151_dual__order_Oeq__iff, axiom,
    (((^[Y5 : nat]: (^[Z3 : nat]: (Y5 = Z3))) = (^[A3 : nat]: (^[B3 : nat]: (((ord_less_eq_nat @ B3 @ A3)) & ((ord_less_eq_nat @ A3 @ B3)))))))). % dual_order.eq_iff
thf(fact_152_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_153_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_154_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_155_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_156_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_157_dual__order_Orefl, axiom,
    ((![A : nat]: (ord_less_eq_nat @ A @ A)))). % dual_order.refl
thf(fact_158_order__trans, axiom,
    ((![X : real, Y4 : real, Z4 : real]: ((ord_less_eq_real @ X @ Y4) => ((ord_less_eq_real @ Y4 @ Z4) => (ord_less_eq_real @ X @ Z4)))))). % order_trans
thf(fact_159_order__trans, axiom,
    ((![X : nat, Y4 : nat, Z4 : nat]: ((ord_less_eq_nat @ X @ Y4) => ((ord_less_eq_nat @ Y4 @ Z4) => (ord_less_eq_nat @ X @ Z4)))))). % order_trans
thf(fact_160_order__class_Oorder_Oantisym, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_161_order__class_Oorder_Oantisym, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_162_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_163_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_164_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_165_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_166_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : real]: (^[Z3 : real]: (Y5 = Z3))) = (^[A3 : real]: (^[B3 : real]: (((ord_less_eq_real @ A3 @ B3)) & ((ord_less_eq_real @ B3 @ A3)))))))). % order_class.order.eq_iff
thf(fact_167_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : nat]: (^[Z3 : nat]: (Y5 = Z3))) = (^[A3 : nat]: (^[B3 : nat]: (((ord_less_eq_nat @ A3 @ B3)) & ((ord_less_eq_nat @ B3 @ A3)))))))). % order_class.order.eq_iff
thf(fact_168_antisym__conv, axiom,
    ((![Y4 : real, X : real]: ((ord_less_eq_real @ Y4 @ X) => ((ord_less_eq_real @ X @ Y4) = (X = Y4)))))). % antisym_conv
thf(fact_169_antisym__conv, axiom,
    ((![Y4 : nat, X : nat]: ((ord_less_eq_nat @ Y4 @ X) => ((ord_less_eq_nat @ X @ Y4) = (X = Y4)))))). % antisym_conv
thf(fact_170_le__cases3, axiom,
    ((![X : real, Y4 : real, Z4 : real]: (((ord_less_eq_real @ X @ Y4) => (~ ((ord_less_eq_real @ Y4 @ Z4)))) => (((ord_less_eq_real @ Y4 @ X) => (~ ((ord_less_eq_real @ X @ Z4)))) => (((ord_less_eq_real @ X @ Z4) => (~ ((ord_less_eq_real @ Z4 @ Y4)))) => (((ord_less_eq_real @ Z4 @ Y4) => (~ ((ord_less_eq_real @ Y4 @ X)))) => (((ord_less_eq_real @ Y4 @ Z4) => (~ ((ord_less_eq_real @ Z4 @ X)))) => (~ (((ord_less_eq_real @ Z4 @ X) => (~ ((ord_less_eq_real @ X @ Y4)))))))))))))). % le_cases3
thf(fact_171_le__cases3, axiom,
    ((![X : nat, Y4 : nat, Z4 : nat]: (((ord_less_eq_nat @ X @ Y4) => (~ ((ord_less_eq_nat @ Y4 @ Z4)))) => (((ord_less_eq_nat @ Y4 @ X) => (~ ((ord_less_eq_nat @ X @ Z4)))) => (((ord_less_eq_nat @ X @ Z4) => (~ ((ord_less_eq_nat @ Z4 @ Y4)))) => (((ord_less_eq_nat @ Z4 @ Y4) => (~ ((ord_less_eq_nat @ Y4 @ X)))) => (((ord_less_eq_nat @ Y4 @ Z4) => (~ ((ord_less_eq_nat @ Z4 @ X)))) => (~ (((ord_less_eq_nat @ Z4 @ X) => (~ ((ord_less_eq_nat @ X @ Y4)))))))))))))). % le_cases3
thf(fact_172_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_173_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_174_le__cases, axiom,
    ((![X : real, Y4 : real]: ((~ ((ord_less_eq_real @ X @ Y4))) => (ord_less_eq_real @ Y4 @ X))))). % le_cases
thf(fact_175_le__cases, axiom,
    ((![X : nat, Y4 : nat]: ((~ ((ord_less_eq_nat @ X @ Y4))) => (ord_less_eq_nat @ Y4 @ X))))). % le_cases
thf(fact_176_eq__refl, axiom,
    ((![X : real, Y4 : real]: ((X = Y4) => (ord_less_eq_real @ X @ Y4))))). % eq_refl
thf(fact_177_eq__refl, axiom,
    ((![X : nat, Y4 : nat]: ((X = Y4) => (ord_less_eq_nat @ X @ Y4))))). % eq_refl
thf(fact_178_linear, axiom,
    ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) | (ord_less_eq_real @ Y4 @ X))))). % linear
thf(fact_179_linear, axiom,
    ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) | (ord_less_eq_nat @ Y4 @ X))))). % linear
thf(fact_180_antisym, axiom,
    ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => ((ord_less_eq_real @ Y4 @ X) => (X = Y4)))))). % antisym
thf(fact_181_antisym, axiom,
    ((![X : nat, Y4 : nat]: ((ord_less_eq_nat @ X @ Y4) => ((ord_less_eq_nat @ Y4 @ X) => (X = Y4)))))). % antisym
thf(fact_182_eq__iff, axiom,
    (((^[Y5 : real]: (^[Z3 : real]: (Y5 = Z3))) = (^[X4 : real]: (^[Y6 : real]: (((ord_less_eq_real @ X4 @ Y6)) & ((ord_less_eq_real @ Y6 @ X4)))))))). % eq_iff
thf(fact_183_eq__iff, axiom,
    (((^[Y5 : nat]: (^[Z3 : nat]: (Y5 = Z3))) = (^[X4 : nat]: (^[Y6 : nat]: (((ord_less_eq_nat @ X4 @ Y6)) & ((ord_less_eq_nat @ Y6 @ X4)))))))). % eq_iff
thf(fact_184_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_185_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > nat, C : nat]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_186_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F : nat > real, C : real]: ((ord_less_eq_nat @ A @ B) => (((F @ B) = C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_187_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (((F @ B) = C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_188_ord__eq__le__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_189_ord__eq__le__subst, axiom,
    ((![A : nat, F : real > nat, B : real, C : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_190_ord__eq__le__subst, axiom,
    ((![A : real, F : nat > real, B : nat, C : nat]: ((A = (F @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_191_ord__eq__le__subst, axiom,
    ((![A : nat, F : nat > nat, B : nat, C : nat]: ((A = (F @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ Y) => (ord_less_eq_nat @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_nat @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_192_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_193_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

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_eq_real @ (plus_plus_real @ (uminus_uminus_real @ s) @ (divide_divide_real @ one_one_real @ (semiri2110766477t_real @ (suc @ (f @ (plus_plus_nat @ n1 @ n2)))))) @ (plus_plus_real @ (uminus_uminus_real @ s) @ (divide_divide_real @ one_one_real @ (semiri2110766477t_real @ (suc @ (plus_plus_nat @ n1 @ n2)))))))).
