% 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_453__5372382_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:30:16.132

% Could-be-implicit typings (9)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    poly_poly_real : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    poly_poly_nat : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_real : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (43)
thf(sy_c_Groups_Oabs__class_Oabs_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    abs_abs_poly_real : poly_real > poly_real).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_real : real > real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex, type,
    minus_minus_complex : complex > complex > complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat, type,
    minus_minus_nat : nat > nat > nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    minus_174331535omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    minus_minus_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    minus_1169194391omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    minus_181436949y_real : poly_poly_real > poly_poly_real > poly_poly_real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    minus_240770701y_real : poly_real > poly_real > poly_real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex, type,
    plus_plus_complex : complex > complex > complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    plus_p1547158847omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    plus_plus_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    plus_p138939463omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    plus_p1835221865ly_nat : poly_poly_nat > poly_poly_nat > poly_poly_nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    plus_p639965381y_real : poly_poly_real > poly_poly_real > poly_poly_real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    plus_plus_poly_real : poly_real > poly_real > poly_real).
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_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $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__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_le1180086932y_real : poly_real > poly_real > $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_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_poly_nat2 : poly_poly_nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_poly_real2 : poly_poly_real > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_v_N1____, type,
    n1 : nat).
thf(sy_v_N2____, type,
    n2 : nat).
thf(sy_v_d____, type,
    d : real).
thf(sy_v_f____, type,
    f : nat > nat).
thf(sy_v_g____, type,
    g : nat > complex).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_r, type,
    r : real).
thf(sy_v_w____, type,
    w : complex).
thf(sy_v_z____, type,
    z : complex).

% Relevant facts (248)
thf(fact_0_fz_I1_J, axiom,
    ((order_769474267at_nat @ f))). % fz(1)
thf(fact_1_g_I1_J, axiom,
    ((![N : nat]: (ord_less_eq_real @ (real_V638595069omplex @ (g @ N)) @ r)))). % g(1)
thf(fact_2_wr, axiom,
    ((ord_less_eq_real @ (real_V638595069omplex @ w) @ r))). % wr
thf(fact_3_le__add__diff__inverse, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ B @ A) => ((plus_plus_poly_real @ B @ (minus_240770701y_real @ A @ B)) = A))))). % le_add_diff_inverse
thf(fact_4_le__add__diff__inverse, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((plus_plus_real @ B @ (minus_minus_real @ A @ B)) = A))))). % le_add_diff_inverse
thf(fact_5_le__add__diff__inverse, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ B @ A) => ((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A))))). % le_add_diff_inverse
thf(fact_6_le__add__diff__inverse2, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ B @ A) => ((plus_plus_poly_real @ (minus_240770701y_real @ A @ B) @ B) = A))))). % le_add_diff_inverse2
thf(fact_7_le__add__diff__inverse2, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))))). % le_add_diff_inverse2
thf(fact_8_le__add__diff__inverse2, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ B @ A) => ((plus_plus_nat @ (minus_minus_nat @ A @ B) @ B) = A))))). % le_add_diff_inverse2
thf(fact_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_abs__norm__cancel, axiom,
    ((![A : complex]: ((abs_abs_real @ (real_V638595069omplex @ A)) = (real_V638595069omplex @ A))))). % abs_norm_cancel
thf(fact_11_abs__norm__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (real_V646646907m_real @ A)) = (real_V646646907m_real @ A))))). % abs_norm_cancel
thf(fact_12_poly__diff, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex, X : poly_complex]: ((poly_poly_complex2 @ (minus_1169194391omplex @ P @ Q) @ X) = (minus_174331535omplex @ (poly_poly_complex2 @ P @ X) @ (poly_poly_complex2 @ Q @ X)))))). % poly_diff
thf(fact_13_poly__diff, axiom,
    ((![P : poly_poly_real, Q : poly_poly_real, X : poly_real]: ((poly_poly_real2 @ (minus_181436949y_real @ P @ Q) @ X) = (minus_240770701y_real @ (poly_poly_real2 @ P @ X) @ (poly_poly_real2 @ Q @ X)))))). % poly_diff
thf(fact_14_poly__diff, axiom,
    ((![P : poly_real, Q : poly_real, X : real]: ((poly_real2 @ (minus_240770701y_real @ P @ Q) @ X) = (minus_minus_real @ (poly_real2 @ P @ X) @ (poly_real2 @ Q @ X)))))). % poly_diff
thf(fact_15_poly__diff, axiom,
    ((![P : poly_complex, Q : poly_complex, X : complex]: ((poly_complex2 @ (minus_174331535omplex @ P @ Q) @ X) = (minus_minus_complex @ (poly_complex2 @ P @ X) @ (poly_complex2 @ Q @ X)))))). % poly_diff
thf(fact_16_poly__add, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex, X : poly_complex]: ((poly_poly_complex2 @ (plus_p138939463omplex @ P @ Q) @ X) = (plus_p1547158847omplex @ (poly_poly_complex2 @ P @ X) @ (poly_poly_complex2 @ Q @ X)))))). % poly_add
thf(fact_17_poly__add, axiom,
    ((![P : poly_poly_real, Q : poly_poly_real, X : poly_real]: ((poly_poly_real2 @ (plus_p639965381y_real @ P @ Q) @ X) = (plus_plus_poly_real @ (poly_poly_real2 @ P @ X) @ (poly_poly_real2 @ Q @ X)))))). % poly_add
thf(fact_18_poly__add, axiom,
    ((![P : poly_poly_nat, Q : poly_poly_nat, X : poly_nat]: ((poly_poly_nat2 @ (plus_p1835221865ly_nat @ P @ Q) @ X) = (plus_plus_poly_nat @ (poly_poly_nat2 @ P @ X) @ (poly_poly_nat2 @ Q @ X)))))). % poly_add
thf(fact_19_poly__add, axiom,
    ((![P : poly_nat, Q : poly_nat, X : nat]: ((poly_nat2 @ (plus_plus_poly_nat @ P @ Q) @ X) = (plus_plus_nat @ (poly_nat2 @ P @ X) @ (poly_nat2 @ Q @ X)))))). % poly_add
thf(fact_20_poly__add, axiom,
    ((![P : poly_real, Q : poly_real, X : real]: ((poly_real2 @ (plus_plus_poly_real @ P @ Q) @ X) = (plus_plus_real @ (poly_real2 @ P @ X) @ (poly_real2 @ Q @ X)))))). % poly_add
thf(fact_21_poly__add, axiom,
    ((![P : poly_complex, Q : poly_complex, X : complex]: ((poly_complex2 @ (plus_p1547158847omplex @ P @ Q) @ X) = (plus_plus_complex @ (poly_complex2 @ P @ X) @ (poly_complex2 @ Q @ X)))))). % poly_add
thf(fact_22_norm__triangle__ineq3, axiom,
    ((![A : complex, B : complex]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B))) @ (real_V638595069omplex @ (minus_minus_complex @ A @ B)))))). % norm_triangle_ineq3
thf(fact_23_norm__triangle__ineq3, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B))) @ (real_V646646907m_real @ (minus_minus_real @ A @ B)))))). % norm_triangle_ineq3
thf(fact_24_abs__add__abs, axiom,
    ((![A : real, B : real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_add_abs
thf(fact_25_abs__add__abs, axiom,
    ((![A : poly_real, B : poly_real]: ((abs_abs_poly_real @ (plus_plus_poly_real @ (abs_abs_poly_real @ A) @ (abs_abs_poly_real @ B))) = (plus_plus_poly_real @ (abs_abs_poly_real @ A) @ (abs_abs_poly_real @ B)))))). % abs_add_abs
thf(fact_26_add__diff__cancel, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_27_add__diff__cancel, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_28_add__diff__cancel, axiom,
    ((![A : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (plus_p1547158847omplex @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_29_add__diff__cancel, axiom,
    ((![A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_30_diff__add__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_31_diff__add__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_32_diff__add__cancel, axiom,
    ((![A : poly_complex, B : poly_complex]: ((plus_p1547158847omplex @ (minus_174331535omplex @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_33_diff__add__cancel, axiom,
    ((![A : poly_real, B : poly_real]: ((plus_plus_poly_real @ (minus_240770701y_real @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_34_add__diff__cancel__left, axiom,
    ((![C : poly_nat, A : poly_nat, B : poly_nat]: ((minus_minus_poly_nat @ (plus_plus_poly_nat @ C @ A) @ (plus_plus_poly_nat @ C @ B)) = (minus_minus_poly_nat @ A @ B))))). % add_diff_cancel_left
thf(fact_35_add__diff__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_left
thf(fact_36_add__diff__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ C @ A) @ (plus_plus_complex @ C @ B)) = (minus_minus_complex @ A @ B))))). % add_diff_cancel_left
thf(fact_37_add__diff__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ B))))). % add_diff_cancel_left
thf(fact_38_add__diff__cancel__left, axiom,
    ((![C : poly_complex, A : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (plus_p1547158847omplex @ C @ A) @ (plus_p1547158847omplex @ C @ B)) = (minus_174331535omplex @ A @ B))))). % add_diff_cancel_left
thf(fact_39_add__diff__cancel__left, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ C @ A) @ (plus_plus_poly_real @ C @ B)) = (minus_240770701y_real @ A @ B))))). % add_diff_cancel_left
thf(fact_40_ath2, axiom,
    ((![A : real, B : real, C : real, M : real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ B @ M)) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ A @ M)) @ C)))))). % ath2
thf(fact_41_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_42_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_43_add__right__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_44_add__right__cancel, axiom,
    ((![B : poly_complex, A : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ B @ A) = (plus_p1547158847omplex @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_45_add__right__cancel, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: (((plus_plus_poly_real @ B @ A) = (plus_plus_poly_real @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_46_add__right__cancel, axiom,
    ((![B : poly_nat, A : poly_nat, C : poly_nat]: (((plus_plus_poly_nat @ B @ A) = (plus_plus_poly_nat @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_47_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_48_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_49_add__left__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_50_add__left__cancel, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ A @ B) = (plus_p1547158847omplex @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_51_add__left__cancel, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: (((plus_plus_poly_real @ A @ B) = (plus_plus_poly_real @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_52_add__left__cancel, axiom,
    ((![A : poly_nat, B : poly_nat, C : poly_nat]: (((plus_plus_poly_nat @ A @ B) = (plus_plus_poly_nat @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_53_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_54_abs__abs, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_abs
thf(fact_55_True, axiom,
    ((ord_less_eq_real @ zero_zero_real @ r))). % True
thf(fact_56_add__le__cancel__right, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ C)) = (ord_le1180086932y_real @ A @ B))))). % add_le_cancel_right
thf(fact_57_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_58_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_59_add__le__cancel__left, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ C @ A) @ (plus_plus_poly_real @ C @ B)) = (ord_le1180086932y_real @ A @ B))))). % add_le_cancel_left
thf(fact_60_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_61_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_62_add__diff__cancel__right_H, axiom,
    ((![A : poly_nat, B : poly_nat]: ((minus_minus_poly_nat @ (plus_plus_poly_nat @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_63_add__diff__cancel__right_H, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_64_add__diff__cancel__right_H, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_65_add__diff__cancel__right_H, axiom,
    ((![A : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_66_add__diff__cancel__right_H, axiom,
    ((![A : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (plus_p1547158847omplex @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_67_add__diff__cancel__right_H, axiom,
    ((![A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_68_add__diff__cancel__right, axiom,
    ((![A : poly_nat, C : poly_nat, B : poly_nat]: ((minus_minus_poly_nat @ (plus_plus_poly_nat @ A @ C) @ (plus_plus_poly_nat @ B @ C)) = (minus_minus_poly_nat @ A @ B))))). % add_diff_cancel_right
thf(fact_69_add__diff__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (minus_minus_real @ A @ B))))). % add_diff_cancel_right
thf(fact_70_add__diff__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ C) @ (plus_plus_complex @ B @ C)) = (minus_minus_complex @ A @ B))))). % add_diff_cancel_right
thf(fact_71_add__diff__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (minus_minus_nat @ A @ B))))). % add_diff_cancel_right
thf(fact_72_add__diff__cancel__right, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (plus_p1547158847omplex @ A @ C) @ (plus_p1547158847omplex @ B @ C)) = (minus_174331535omplex @ A @ B))))). % add_diff_cancel_right
thf(fact_73_add__diff__cancel__right, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ C)) = (minus_240770701y_real @ A @ B))))). % add_diff_cancel_right
thf(fact_74_add__diff__cancel__left_H, axiom,
    ((![A : poly_nat, B : poly_nat]: ((minus_minus_poly_nat @ (plus_plus_poly_nat @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_75_add__diff__cancel__left_H, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_76_add__diff__cancel__left_H, axiom,
    ((![A : complex, B : complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_77_add__diff__cancel__left_H, axiom,
    ((![A : nat, B : nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_78_add__diff__cancel__left_H, axiom,
    ((![A : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (plus_p1547158847omplex @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_79_add__diff__cancel__left_H, axiom,
    ((![A : poly_real, B : poly_real]: ((minus_240770701y_real @ (plus_plus_poly_real @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_80_real__norm__def, axiom,
    ((real_V646646907m_real = abs_abs_real))). % real_norm_def
thf(fact_81_complex__mod__triangle__sub, axiom,
    ((![W : complex, Z : complex]: (ord_less_eq_real @ (real_V638595069omplex @ W) @ (plus_plus_real @ (real_V638595069omplex @ (plus_plus_complex @ W @ Z)) @ (real_V638595069omplex @ Z)))))). % complex_mod_triangle_sub
thf(fact_82_norm__triangle__le__diff, axiom,
    ((![X : complex, Y : complex, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y)) @ E) => (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ X @ Y)) @ E))))). % norm_triangle_le_diff
thf(fact_83_norm__triangle__le__diff, axiom,
    ((![X : real, Y : real, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)) @ E) => (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ X @ Y)) @ E))))). % norm_triangle_le_diff
thf(fact_84_norm__diff__triangle__le, axiom,
    ((![X : complex, Y : complex, E1 : real, Z : complex, E2 : real]: ((ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ X @ Y)) @ E1) => ((ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ Y @ Z)) @ E2) => (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ X @ Z)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_le
thf(fact_85_norm__diff__triangle__le, axiom,
    ((![X : real, Y : real, E1 : real, Z : real, E2 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ X @ Y)) @ E1) => ((ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ Y @ Z)) @ E2) => (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ X @ Z)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_le
thf(fact_86_norm__triangle__ineq4, axiom,
    ((![A : complex, B : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ A @ B)) @ (plus_plus_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)))))). % norm_triangle_ineq4
thf(fact_87_norm__triangle__ineq4, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)))))). % norm_triangle_ineq4
thf(fact_88_norm__triangle__sub, axiom,
    ((![X : complex, Y : complex]: (ord_less_eq_real @ (real_V638595069omplex @ X) @ (plus_plus_real @ (real_V638595069omplex @ Y) @ (real_V638595069omplex @ (minus_minus_complex @ X @ Y))))))). % norm_triangle_sub
thf(fact_89_norm__triangle__sub, axiom,
    ((![X : real, Y : real]: (ord_less_eq_real @ (real_V646646907m_real @ X) @ (plus_plus_real @ (real_V646646907m_real @ Y) @ (real_V646646907m_real @ (minus_minus_real @ X @ Y))))))). % norm_triangle_sub
thf(fact_90_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_91_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_92_add__right__imp__eq, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_93_add__right__imp__eq, axiom,
    ((![B : poly_complex, A : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ B @ A) = (plus_p1547158847omplex @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_94_add__right__imp__eq, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: (((plus_plus_poly_real @ B @ A) = (plus_plus_poly_real @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_95_add__right__imp__eq, axiom,
    ((![B : poly_nat, A : poly_nat, C : poly_nat]: (((plus_plus_poly_nat @ B @ A) = (plus_plus_poly_nat @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_96_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_97_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_98_add__left__imp__eq, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_99_add__left__imp__eq, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ A @ B) = (plus_p1547158847omplex @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_100_add__left__imp__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: (((plus_plus_poly_real @ A @ B) = (plus_plus_poly_real @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_101_add__left__imp__eq, axiom,
    ((![A : poly_nat, B : poly_nat, C : poly_nat]: (((plus_plus_poly_nat @ A @ B) = (plus_plus_poly_nat @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_102_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_103_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_104_add_Oleft__commute, axiom,
    ((![B : complex, A : complex, C : complex]: ((plus_plus_complex @ B @ (plus_plus_complex @ A @ C)) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.left_commute
thf(fact_105_add_Oleft__commute, axiom,
    ((![B : poly_complex, A : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ B @ (plus_p1547158847omplex @ A @ C)) = (plus_p1547158847omplex @ A @ (plus_p1547158847omplex @ B @ C)))))). % add.left_commute
thf(fact_106_add_Oleft__commute, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: ((plus_plus_poly_real @ B @ (plus_plus_poly_real @ A @ C)) = (plus_plus_poly_real @ A @ (plus_plus_poly_real @ B @ C)))))). % add.left_commute
thf(fact_107_add_Oleft__commute, axiom,
    ((![B : poly_nat, A : poly_nat, C : poly_nat]: ((plus_plus_poly_nat @ B @ (plus_plus_poly_nat @ A @ C)) = (plus_plus_poly_nat @ A @ (plus_plus_poly_nat @ B @ C)))))). % add.left_commute
thf(fact_108_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A2 : nat]: (^[B2 : nat]: (plus_plus_nat @ B2 @ A2)))))). % add.commute
thf(fact_109_add_Ocommute, axiom,
    ((plus_plus_real = (^[A2 : real]: (^[B2 : real]: (plus_plus_real @ B2 @ A2)))))). % add.commute
thf(fact_110_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A2 : complex]: (^[B2 : complex]: (plus_plus_complex @ B2 @ A2)))))). % add.commute
thf(fact_111_add_Ocommute, axiom,
    ((plus_p1547158847omplex = (^[A2 : poly_complex]: (^[B2 : poly_complex]: (plus_p1547158847omplex @ B2 @ A2)))))). % add.commute
thf(fact_112_add_Ocommute, axiom,
    ((plus_plus_poly_real = (^[A2 : poly_real]: (^[B2 : poly_real]: (plus_plus_poly_real @ B2 @ A2)))))). % add.commute
thf(fact_113_add_Ocommute, axiom,
    ((plus_plus_poly_nat = (^[A2 : poly_nat]: (^[B2 : poly_nat]: (plus_plus_poly_nat @ B2 @ A2)))))). % add.commute
thf(fact_114_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_115_add_Oright__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_116_add_Oright__cancel, axiom,
    ((![B : poly_complex, A : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ B @ A) = (plus_p1547158847omplex @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_117_add_Oright__cancel, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: (((plus_plus_poly_real @ B @ A) = (plus_plus_poly_real @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_118_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_119_add_Oleft__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_120_add_Oleft__cancel, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ A @ B) = (plus_p1547158847omplex @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_121_add_Oleft__cancel, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: (((plus_plus_poly_real @ A @ B) = (plus_plus_poly_real @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_122_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_123_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_124_add_Oassoc, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.assoc
thf(fact_125_add_Oassoc, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ (plus_p1547158847omplex @ A @ B) @ C) = (plus_p1547158847omplex @ A @ (plus_p1547158847omplex @ B @ C)))))). % add.assoc
thf(fact_126_add_Oassoc, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((plus_plus_poly_real @ (plus_plus_poly_real @ A @ B) @ C) = (plus_plus_poly_real @ A @ (plus_plus_poly_real @ B @ C)))))). % add.assoc
thf(fact_127_add_Oassoc, axiom,
    ((![A : poly_nat, B : poly_nat, C : poly_nat]: ((plus_plus_poly_nat @ (plus_plus_poly_nat @ A @ B) @ C) = (plus_plus_poly_nat @ A @ (plus_plus_poly_nat @ B @ C)))))). % add.assoc
thf(fact_128_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_129_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_130_group__cancel_Oadd2, axiom,
    ((![B3 : complex, K : complex, B : complex, A : complex]: ((B3 = (plus_plus_complex @ K @ B)) => ((plus_plus_complex @ A @ B3) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add2
thf(fact_131_group__cancel_Oadd2, axiom,
    ((![B3 : poly_complex, K : poly_complex, B : poly_complex, A : poly_complex]: ((B3 = (plus_p1547158847omplex @ K @ B)) => ((plus_p1547158847omplex @ A @ B3) = (plus_p1547158847omplex @ K @ (plus_p1547158847omplex @ A @ B))))))). % group_cancel.add2
thf(fact_132_group__cancel_Oadd2, axiom,
    ((![B3 : poly_real, K : poly_real, B : poly_real, A : poly_real]: ((B3 = (plus_plus_poly_real @ K @ B)) => ((plus_plus_poly_real @ A @ B3) = (plus_plus_poly_real @ K @ (plus_plus_poly_real @ A @ B))))))). % group_cancel.add2
thf(fact_133_group__cancel_Oadd2, axiom,
    ((![B3 : poly_nat, K : poly_nat, B : poly_nat, A : poly_nat]: ((B3 = (plus_plus_poly_nat @ K @ B)) => ((plus_plus_poly_nat @ A @ B3) = (plus_plus_poly_nat @ K @ (plus_plus_poly_nat @ A @ B))))))). % group_cancel.add2
thf(fact_134_group__cancel_Oadd1, axiom,
    ((![A3 : nat, K : nat, A : nat, B : nat]: ((A3 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A3 @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add1
thf(fact_135_group__cancel_Oadd1, axiom,
    ((![A3 : real, K : real, A : real, B : real]: ((A3 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A3 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1
thf(fact_136_group__cancel_Oadd1, axiom,
    ((![A3 : complex, K : complex, A : complex, B : complex]: ((A3 = (plus_plus_complex @ K @ A)) => ((plus_plus_complex @ A3 @ B) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add1
thf(fact_137_group__cancel_Oadd1, axiom,
    ((![A3 : poly_complex, K : poly_complex, A : poly_complex, B : poly_complex]: ((A3 = (plus_p1547158847omplex @ K @ A)) => ((plus_p1547158847omplex @ A3 @ B) = (plus_p1547158847omplex @ K @ (plus_p1547158847omplex @ A @ B))))))). % group_cancel.add1
thf(fact_138_group__cancel_Oadd1, axiom,
    ((![A3 : poly_real, K : poly_real, A : poly_real, B : poly_real]: ((A3 = (plus_plus_poly_real @ K @ A)) => ((plus_plus_poly_real @ A3 @ B) = (plus_plus_poly_real @ K @ (plus_plus_poly_real @ A @ B))))))). % group_cancel.add1
thf(fact_139_group__cancel_Oadd1, axiom,
    ((![A3 : poly_nat, K : poly_nat, A : poly_nat, B : poly_nat]: ((A3 = (plus_plus_poly_nat @ K @ A)) => ((plus_plus_poly_nat @ A3 @ B) = (plus_plus_poly_nat @ K @ (plus_plus_poly_nat @ A @ B))))))). % group_cancel.add1
thf(fact_140_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_141_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_142_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : poly_real, J : poly_real, K : poly_real, L : poly_real]: (((I = J) & (K = L)) => ((plus_plus_poly_real @ I @ K) = (plus_plus_poly_real @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_143_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_144_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_145_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_146_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ (plus_p1547158847omplex @ A @ B) @ C) = (plus_p1547158847omplex @ A @ (plus_p1547158847omplex @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_147_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((plus_plus_poly_real @ (plus_plus_poly_real @ A @ B) @ C) = (plus_plus_poly_real @ A @ (plus_plus_poly_real @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_148_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : poly_nat, B : poly_nat, C : poly_nat]: ((plus_plus_poly_nat @ (plus_plus_poly_nat @ A @ B) @ C) = (plus_plus_poly_nat @ A @ (plus_plus_poly_nat @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_149_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (minus_minus_real @ A @ C) @ B) = (minus_minus_real @ (minus_minus_real @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_150_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : complex, C : complex, B : complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ C) @ B) = (minus_minus_complex @ (minus_minus_complex @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_151_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : nat, C : nat, B : nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ C) @ B) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_152_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: ((minus_174331535omplex @ (minus_174331535omplex @ A @ C) @ B) = (minus_174331535omplex @ (minus_174331535omplex @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_153_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((minus_240770701y_real @ (minus_240770701y_real @ A @ C) @ B) = (minus_240770701y_real @ (minus_240770701y_real @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_154_diff__eq__diff__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_155_diff__eq__diff__eq, axiom,
    ((![A : complex, B : complex, C : complex, D : complex]: (((minus_minus_complex @ A @ B) = (minus_minus_complex @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_156_diff__eq__diff__eq, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex, D : poly_complex]: (((minus_174331535omplex @ A @ B) = (minus_174331535omplex @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_157_diff__eq__diff__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: (((minus_240770701y_real @ A @ B) = (minus_240770701y_real @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_158_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_complex, Q : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_159_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_real, Q : poly_real]: (((poly_real2 @ P) = (poly_real2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_160_add__le__imp__le__right, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ C)) => (ord_le1180086932y_real @ A @ B))))). % add_le_imp_le_right
thf(fact_161_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_162_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_163_add__le__imp__le__left, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ C @ A) @ (plus_plus_poly_real @ C @ B)) => (ord_le1180086932y_real @ A @ B))))). % add_le_imp_le_left
thf(fact_164_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_165_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_166_le__iff__add, axiom,
    ((ord_less_eq_nat = (^[A2 : nat]: (^[B2 : nat]: (?[C2 : nat]: (B2 = (plus_plus_nat @ A2 @ C2)))))))). % le_iff_add
thf(fact_167_add__right__mono, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ A @ B) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ C)))))). % add_right_mono
thf(fact_168_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_169_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_170_less__eqE, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => (~ ((![C3 : nat]: (~ ((B = (plus_plus_nat @ A @ C3))))))))))). % less_eqE
thf(fact_171_add__left__mono, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ A @ B) => (ord_le1180086932y_real @ (plus_plus_poly_real @ C @ A) @ (plus_plus_poly_real @ C @ B)))))). % add_left_mono
thf(fact_172_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_173_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_174_add__mono, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: ((ord_le1180086932y_real @ A @ B) => ((ord_le1180086932y_real @ C @ D) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ (plus_plus_poly_real @ B @ D))))))). % add_mono
thf(fact_175_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_176_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_177_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : poly_real, J : poly_real, K : poly_real, L : poly_real]: (((ord_le1180086932y_real @ I @ J) & (ord_le1180086932y_real @ K @ L)) => (ord_le1180086932y_real @ (plus_plus_poly_real @ I @ K) @ (plus_plus_poly_real @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_178_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_179_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_180_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : poly_real, J : poly_real, K : poly_real, L : poly_real]: (((I = J) & (ord_le1180086932y_real @ K @ L)) => (ord_le1180086932y_real @ (plus_plus_poly_real @ I @ K) @ (plus_plus_poly_real @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_181_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_182_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_183_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : poly_real, J : poly_real, K : poly_real, L : poly_real]: (((ord_le1180086932y_real @ I @ J) & (K = L)) => (ord_le1180086932y_real @ (plus_plus_poly_real @ I @ K) @ (plus_plus_poly_real @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_184_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_185_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_186_diff__eq__diff__less__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: (((minus_240770701y_real @ A @ B) = (minus_240770701y_real @ C @ D)) => ((ord_le1180086932y_real @ A @ B) = (ord_le1180086932y_real @ C @ D)))))). % diff_eq_diff_less_eq
thf(fact_187_diff__eq__diff__less__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D)))))). % diff_eq_diff_less_eq
thf(fact_188_diff__right__mono, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ A @ B) => (ord_le1180086932y_real @ (minus_240770701y_real @ A @ C) @ (minus_240770701y_real @ B @ C)))))). % diff_right_mono
thf(fact_189_diff__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)))))). % diff_right_mono
thf(fact_190_diff__left__mono, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: ((ord_le1180086932y_real @ B @ A) => (ord_le1180086932y_real @ (minus_240770701y_real @ C @ A) @ (minus_240770701y_real @ C @ B)))))). % diff_left_mono
thf(fact_191_diff__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B)))))). % diff_left_mono
thf(fact_192_diff__mono, axiom,
    ((![A : poly_real, B : poly_real, D : poly_real, C : poly_real]: ((ord_le1180086932y_real @ A @ B) => ((ord_le1180086932y_real @ D @ C) => (ord_le1180086932y_real @ (minus_240770701y_real @ A @ C) @ (minus_240770701y_real @ B @ D))))))). % diff_mono
thf(fact_193_diff__mono, axiom,
    ((![A : real, B : real, D : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ D @ C) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))))). % diff_mono
thf(fact_194_add__implies__diff, axiom,
    ((![C : poly_nat, B : poly_nat, A : poly_nat]: (((plus_plus_poly_nat @ C @ B) = A) => (C = (minus_minus_poly_nat @ A @ B)))))). % add_implies_diff
thf(fact_195_add__implies__diff, axiom,
    ((![C : real, B : real, A : real]: (((plus_plus_real @ C @ B) = A) => (C = (minus_minus_real @ A @ B)))))). % add_implies_diff
thf(fact_196_add__implies__diff, axiom,
    ((![C : complex, B : complex, A : complex]: (((plus_plus_complex @ C @ B) = A) => (C = (minus_minus_complex @ A @ B)))))). % add_implies_diff
thf(fact_197_add__implies__diff, axiom,
    ((![C : nat, B : nat, A : nat]: (((plus_plus_nat @ C @ B) = A) => (C = (minus_minus_nat @ A @ B)))))). % add_implies_diff
thf(fact_198_add__implies__diff, axiom,
    ((![C : poly_complex, B : poly_complex, A : poly_complex]: (((plus_p1547158847omplex @ C @ B) = A) => (C = (minus_174331535omplex @ A @ B)))))). % add_implies_diff
thf(fact_199_add__implies__diff, axiom,
    ((![C : poly_real, B : poly_real, A : poly_real]: (((plus_plus_poly_real @ C @ B) = A) => (C = (minus_240770701y_real @ A @ B)))))). % add_implies_diff
thf(fact_200_diff__diff__add, axiom,
    ((![A : poly_nat, B : poly_nat, C : poly_nat]: ((minus_minus_poly_nat @ (minus_minus_poly_nat @ A @ B) @ C) = (minus_minus_poly_nat @ A @ (plus_plus_poly_nat @ B @ C)))))). % diff_diff_add
thf(fact_201_diff__diff__add, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ A @ (plus_plus_real @ B @ C)))))). % diff_diff_add
thf(fact_202_diff__diff__add, axiom,
    ((![A : complex, B : complex, C : complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ A @ (plus_plus_complex @ B @ C)))))). % diff_diff_add
thf(fact_203_diff__diff__add, axiom,
    ((![A : nat, B : nat, C : nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C)))))). % diff_diff_add
thf(fact_204_diff__diff__add, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((minus_174331535omplex @ (minus_174331535omplex @ A @ B) @ C) = (minus_174331535omplex @ A @ (plus_p1547158847omplex @ B @ C)))))). % diff_diff_add
thf(fact_205_diff__diff__add, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((minus_240770701y_real @ (minus_240770701y_real @ A @ B) @ C) = (minus_240770701y_real @ A @ (plus_plus_poly_real @ B @ C)))))). % diff_diff_add
thf(fact_206_diff__add__eq__diff__diff__swap, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ A @ (plus_plus_real @ B @ C)) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_207_diff__add__eq__diff__diff__swap, axiom,
    ((![A : complex, B : complex, C : complex]: ((minus_minus_complex @ A @ (plus_plus_complex @ B @ C)) = (minus_minus_complex @ (minus_minus_complex @ A @ C) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_208_diff__add__eq__diff__diff__swap, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((minus_174331535omplex @ A @ (plus_p1547158847omplex @ B @ C)) = (minus_174331535omplex @ (minus_174331535omplex @ A @ C) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_209_diff__add__eq__diff__diff__swap, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((minus_240770701y_real @ A @ (plus_plus_poly_real @ B @ C)) = (minus_240770701y_real @ (minus_240770701y_real @ A @ C) @ B))))). % diff_add_eq_diff_diff_swap
thf(fact_210_diff__add__eq, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B))))). % diff_add_eq
thf(fact_211_diff__add__eq, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (plus_plus_complex @ A @ C) @ B))))). % diff_add_eq
thf(fact_212_diff__add__eq, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ (minus_174331535omplex @ A @ B) @ C) = (minus_174331535omplex @ (plus_p1547158847omplex @ A @ C) @ B))))). % diff_add_eq
thf(fact_213_diff__add__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((plus_plus_poly_real @ (minus_240770701y_real @ A @ B) @ C) = (minus_240770701y_real @ (plus_plus_poly_real @ A @ C) @ B))))). % diff_add_eq
thf(fact_214_diff__diff__eq2, axiom,
    ((![A : real, B : real, C : real]: ((minus_minus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B))))). % diff_diff_eq2
thf(fact_215_diff__diff__eq2, axiom,
    ((![A : complex, B : complex, C : complex]: ((minus_minus_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (plus_plus_complex @ A @ C) @ B))))). % diff_diff_eq2
thf(fact_216_diff__diff__eq2, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((minus_174331535omplex @ A @ (minus_174331535omplex @ B @ C)) = (minus_174331535omplex @ (plus_p1547158847omplex @ A @ C) @ B))))). % diff_diff_eq2
thf(fact_217_diff__diff__eq2, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((minus_240770701y_real @ A @ (minus_240770701y_real @ B @ C)) = (minus_240770701y_real @ (plus_plus_poly_real @ A @ C) @ B))))). % diff_diff_eq2
thf(fact_218_add__diff__eq, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ B) @ C))))). % add_diff_eq
thf(fact_219_add__diff__eq, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (plus_plus_complex @ A @ B) @ C))))). % add_diff_eq
thf(fact_220_add__diff__eq, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ A @ (minus_174331535omplex @ B @ C)) = (minus_174331535omplex @ (plus_p1547158847omplex @ A @ B) @ C))))). % add_diff_eq
thf(fact_221_add__diff__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((plus_plus_poly_real @ A @ (minus_240770701y_real @ B @ C)) = (minus_240770701y_real @ (plus_plus_poly_real @ A @ B) @ C))))). % add_diff_eq
thf(fact_222_eq__diff__eq, axiom,
    ((![A : real, C : real, B : real]: ((A = (minus_minus_real @ C @ B)) = ((plus_plus_real @ A @ B) = C))))). % eq_diff_eq
thf(fact_223_eq__diff__eq, axiom,
    ((![A : complex, C : complex, B : complex]: ((A = (minus_minus_complex @ C @ B)) = ((plus_plus_complex @ A @ B) = C))))). % eq_diff_eq
thf(fact_224_eq__diff__eq, axiom,
    ((![A : poly_complex, C : poly_complex, B : poly_complex]: ((A = (minus_174331535omplex @ C @ B)) = ((plus_p1547158847omplex @ A @ B) = C))))). % eq_diff_eq
thf(fact_225_eq__diff__eq, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((A = (minus_240770701y_real @ C @ B)) = ((plus_plus_poly_real @ A @ B) = C))))). % eq_diff_eq
thf(fact_226_diff__eq__eq, axiom,
    ((![A : real, B : real, C : real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B)))))). % diff_eq_eq
thf(fact_227_diff__eq__eq, axiom,
    ((![A : complex, B : complex, C : complex]: (((minus_minus_complex @ A @ B) = C) = (A = (plus_plus_complex @ C @ B)))))). % diff_eq_eq
thf(fact_228_diff__eq__eq, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: (((minus_174331535omplex @ A @ B) = C) = (A = (plus_p1547158847omplex @ C @ B)))))). % diff_eq_eq
thf(fact_229_diff__eq__eq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: (((minus_240770701y_real @ A @ B) = C) = (A = (plus_plus_poly_real @ C @ B)))))). % diff_eq_eq
thf(fact_230_group__cancel_Osub1, axiom,
    ((![A3 : real, K : real, A : real, B : real]: ((A3 = (plus_plus_real @ K @ A)) => ((minus_minus_real @ A3 @ B) = (plus_plus_real @ K @ (minus_minus_real @ A @ B))))))). % group_cancel.sub1
thf(fact_231_group__cancel_Osub1, axiom,
    ((![A3 : complex, K : complex, A : complex, B : complex]: ((A3 = (plus_plus_complex @ K @ A)) => ((minus_minus_complex @ A3 @ B) = (plus_plus_complex @ K @ (minus_minus_complex @ A @ B))))))). % group_cancel.sub1
thf(fact_232_group__cancel_Osub1, axiom,
    ((![A3 : poly_complex, K : poly_complex, A : poly_complex, B : poly_complex]: ((A3 = (plus_p1547158847omplex @ K @ A)) => ((minus_174331535omplex @ A3 @ B) = (plus_p1547158847omplex @ K @ (minus_174331535omplex @ A @ B))))))). % group_cancel.sub1
thf(fact_233_group__cancel_Osub1, axiom,
    ((![A3 : poly_real, K : poly_real, A : poly_real, B : poly_real]: ((A3 = (plus_plus_poly_real @ K @ A)) => ((minus_240770701y_real @ A3 @ B) = (plus_plus_poly_real @ K @ (minus_240770701y_real @ A @ B))))))). % group_cancel.sub1
thf(fact_234_abs__ge__self, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ (abs_abs_real @ A))))). % abs_ge_self
thf(fact_235_abs__le__D1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ A @ B))))). % abs_le_D1
thf(fact_236_N1, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ n1 @ N) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ N)) @ z)) @ d))))). % N1
thf(fact_237_mth1, axiom,
    ((?[X2 : real, Z2 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z2) @ r) & ((real_V638595069omplex @ (poly_complex2 @ p @ Z2)) = (uminus_uminus_real @ X2)))))). % mth1
thf(fact_238_Nat_Oadd__diff__assoc, axiom,
    ((![K : nat, J : nat, I : nat]: ((ord_less_eq_nat @ K @ J) => ((plus_plus_nat @ I @ (minus_minus_nat @ J @ K)) = (minus_minus_nat @ (plus_plus_nat @ I @ J) @ K)))))). % Nat.add_diff_assoc
thf(fact_239_Nat_Oadd__diff__assoc2, axiom,
    ((![K : nat, J : nat, I : nat]: ((ord_less_eq_nat @ K @ J) => ((plus_plus_nat @ (minus_minus_nat @ J @ K) @ I) = (minus_minus_nat @ (plus_plus_nat @ J @ I) @ K)))))). % Nat.add_diff_assoc2
thf(fact_240_Nat_Odiff__diff__right, axiom,
    ((![K : nat, J : nat, I : nat]: ((ord_less_eq_nat @ K @ J) => ((minus_minus_nat @ I @ (minus_minus_nat @ J @ K)) = (minus_minus_nat @ (plus_plus_nat @ I @ K) @ J)))))). % Nat.diff_diff_right
thf(fact_241_nat__add__left__cancel__le, axiom,
    ((![K : nat, M : nat, N2 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ K @ M) @ (plus_plus_nat @ K @ N2)) = (ord_less_eq_nat @ M @ N2))))). % nat_add_left_cancel_le
thf(fact_242_fz_I2_J, axiom,
    ((![E3 : real]: ((ord_less_real @ zero_zero_real @ E3) => (?[N3 : nat]: (![N : nat]: ((ord_less_eq_nat @ N3 @ N) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ N)) @ z)) @ E3)))))))). % fz(2)
thf(fact_243_complex__mod__triangle__ineq2, axiom,
    ((![B : complex, A : complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V638595069omplex @ (plus_plus_complex @ B @ A)) @ (real_V638595069omplex @ B)) @ (real_V638595069omplex @ A))))). % complex_mod_triangle_ineq2
thf(fact_244_sin__bound__lemma, axiom,
    ((![X : real, Y : real, U : real, V : real]: ((X = Y) => ((ord_less_eq_real @ (abs_abs_real @ U) @ V) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ X @ U) @ Y)) @ V)))))). % sin_bound_lemma
thf(fact_245__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062N1_O_A_092_060forall_062n_092_060ge_062N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![N1 : nat]: (~ ((![N : nat]: ((ord_less_eq_nat @ N1 @ N) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ N)) @ z)) @ d)))))))))). % \<open>\<And>thesis. (\<And>N1. \<forall>n\<ge>N1. cmod (g (f n) - z) < d \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_246_d_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ d))). % d(1)
thf(fact_247_ath, axiom,
    ((![M : real, X : real, E : real]: ((ord_less_eq_real @ M @ X) => ((ord_less_real @ X @ (plus_plus_real @ M @ E)) => (ord_less_real @ (abs_abs_real @ (minus_minus_real @ X @ M)) @ E)))))). % ath

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2))))) @ (real_V638595069omplex @ (poly_complex2 @ p @ z)))) @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2)))) @ (poly_complex2 @ p @ z)))))).
