% 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_41__5367034_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:26:31.965

% 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_Itf__a_J_J, type,
    poly_poly_a : $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_Itf__a_J, type,
    poly_a : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (50)
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__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__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__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__Polynomial__Opoly_Itf__a_J_J, type,
    plus_p1976640465poly_a : poly_poly_a > poly_poly_a > poly_poly_a).
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__Polynomial__Opoly_Itf__a_J, type,
    plus_plus_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > real > real).
thf(sy_c_Groups_Oplus__class_Oplus_001tf__a, type,
    plus_plus_a : a > a > a).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex, type,
    times_times_complex : complex > complex > complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    times_1246143675omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    times_614468161y_real : poly_poly_real > poly_poly_real > poly_poly_real).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    times_545135445poly_a : poly_poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    times_775122617y_real : poly_real > poly_real > poly_real).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_Itf__a_J, type,
    times_times_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal, type,
    times_times_real : real > real > real).
thf(sy_c_Groups_Otimes__class_Otimes_001tf__a, type,
    times_times_a : a > a > a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    zero_z1746442943omplex : poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    zero_zero_poly_real : poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_Itf__a_J, type,
    zero_zero_poly_a : poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Groups_Ozero__class_Ozero_001tf__a, type,
    zero_zero_a : a).
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__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_Polynomial_OpCons_001t__Complex__Ocomplex, type,
    pCons_complex : complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    pCons_poly_complex : poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    pCons_poly_real : poly_real > poly_poly_real > poly_poly_real).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_Itf__a_J, type,
    pCons_poly_a : poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_OpCons_001t__Real__Oreal, type,
    pCons_real : real > poly_real > poly_real).
thf(sy_c_Polynomial_OpCons_001tf__a, type,
    pCons_a : a > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
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__Real__Oreal_J, type,
    poly_poly_real2 : poly_poly_real > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_Itf__a_J, type,
    poly_poly_a2 : poly_poly_a > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Polynomial_Opoly_001tf__a, type,
    poly_a2 : poly_a > a > a).
thf(sy_c_Real__Vector__Spaces_Obounded__linear__axioms_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    real_V479504201omplex : (complex > complex) > $o).
thf(sy_c_Real__Vector__Spaces_Obounded__linear__axioms_001t__Complex__Ocomplex_001tf__a, type,
    real_V301987619plex_a : (complex > a) > $o).
thf(sy_c_Real__Vector__Spaces_Obounded__linear__axioms_001tf__a_001t__Complex__Ocomplex, type,
    real_V451440129omplex : (a > complex) > $o).
thf(sy_c_Real__Vector__Spaces_Obounded__linear__axioms_001tf__a_001tf__a, type,
    real_V2136407659ms_a_a : (a > a) > $o).
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_c_Real__Vector__Spaces_Onorm__class_Onorm_001tf__a, type,
    real_V1022479215norm_a : a > real).
thf(sy_v_c____, type,
    c : a).
thf(sy_v_cs____, type,
    cs : poly_a).
thf(sy_v_m____, type,
    m : real).
thf(sy_v_r, type,
    r : real).
thf(sy_v_z____, type,
    z : a).

% Relevant facts (248)
thf(fact_0_that, axiom,
    ((ord_less_eq_real @ (real_V1022479215norm_a @ z) @ r))). % that
thf(fact_1__092_060open_062norm_A_Ic_A_L_Az_A_K_Apoly_Acs_Az_J_A_092_060le_062_Anorm_Ac_A_L_Anorm_A_Iz_A_K_Apoly_Acs_Az_J_092_060close_062, axiom,
    ((ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ c @ (times_times_a @ z @ (poly_a2 @ cs @ z)))) @ (plus_plus_real @ (real_V1022479215norm_a @ c) @ (real_V1022479215norm_a @ (times_times_a @ z @ (poly_a2 @ cs @ z))))))). % \<open>norm (c + z * poly cs z) \<le> norm c + norm (z * poly cs z)\<close>
thf(fact_2_th, axiom,
    ((ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ z)) @ m))). % th
thf(fact_3_m, axiom,
    ((![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ r) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z)) @ m))))). % m
thf(fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_092_060forall_062z_O_Anorm_Az_A_092_060le_062_Ar_A_092_060longrightarrow_062_Anorm_A_Ipoly_Acs_Az_J_A_092_060le_062_Am_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![M : real]: (~ ((![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ r) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z)) @ M)))))))))). % \<open>\<And>thesis. (\<And>m. \<forall>z. norm z \<le> r \<longrightarrow> norm (poly cs z) \<le> m \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_5_poly__pCons, axiom,
    ((![A : poly_complex, P : poly_poly_complex, X : poly_complex]: ((poly_poly_complex2 @ (pCons_poly_complex @ A @ P) @ X) = (plus_p1547158847omplex @ A @ (times_1246143675omplex @ X @ (poly_poly_complex2 @ P @ X))))))). % poly_pCons
thf(fact_6_poly__pCons, axiom,
    ((![A : poly_real, P : poly_poly_real, X : poly_real]: ((poly_poly_real2 @ (pCons_poly_real @ A @ P) @ X) = (plus_plus_poly_real @ A @ (times_775122617y_real @ X @ (poly_poly_real2 @ P @ X))))))). % poly_pCons
thf(fact_7_poly__pCons, axiom,
    ((![A : poly_a, P : poly_poly_a, X : poly_a]: ((poly_poly_a2 @ (pCons_poly_a @ A @ P) @ X) = (plus_plus_poly_a @ A @ (times_times_poly_a @ X @ (poly_poly_a2 @ P @ X))))))). % poly_pCons
thf(fact_8_poly__pCons, axiom,
    ((![A : complex, P : poly_complex, X : complex]: ((poly_complex2 @ (pCons_complex @ A @ P) @ X) = (plus_plus_complex @ A @ (times_times_complex @ X @ (poly_complex2 @ P @ X))))))). % poly_pCons
thf(fact_9_poly__pCons, axiom,
    ((![A : a, P : poly_a, X : a]: ((poly_a2 @ (pCons_a @ A @ P) @ X) = (plus_plus_a @ A @ (times_times_a @ X @ (poly_a2 @ P @ X))))))). % poly_pCons
thf(fact_10_poly__pCons, axiom,
    ((![A : real, P : poly_real, X : real]: ((poly_real2 @ (pCons_real @ A @ P) @ X) = (plus_plus_real @ A @ (times_times_real @ X @ (poly_real2 @ P @ X))))))). % poly_pCons
thf(fact_11_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_12_poly__add, axiom,
    ((![P : poly_poly_a, Q : poly_poly_a, X : poly_a]: ((poly_poly_a2 @ (plus_p1976640465poly_a @ P @ Q) @ X) = (plus_plus_poly_a @ (poly_poly_a2 @ P @ X) @ (poly_poly_a2 @ Q @ X)))))). % poly_add
thf(fact_13_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_14_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_15_poly__add, axiom,
    ((![P : poly_a, Q : poly_a, X : a]: ((poly_a2 @ (plus_plus_poly_a @ P @ Q) @ X) = (plus_plus_a @ (poly_a2 @ P @ X) @ (poly_a2 @ Q @ X)))))). % poly_add
thf(fact_16_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_17_poly__mult, axiom,
    ((![P : poly_complex, Q : poly_complex, X : complex]: ((poly_complex2 @ (times_1246143675omplex @ P @ Q) @ X) = (times_times_complex @ (poly_complex2 @ P @ X) @ (poly_complex2 @ Q @ X)))))). % poly_mult
thf(fact_18_poly__mult, axiom,
    ((![P : poly_poly_real, Q : poly_poly_real, X : poly_real]: ((poly_poly_real2 @ (times_614468161y_real @ P @ Q) @ X) = (times_775122617y_real @ (poly_poly_real2 @ P @ X) @ (poly_poly_real2 @ Q @ X)))))). % poly_mult
thf(fact_19_poly__mult, axiom,
    ((![P : poly_poly_a, Q : poly_poly_a, X : poly_a]: ((poly_poly_a2 @ (times_545135445poly_a @ P @ Q) @ X) = (times_times_poly_a @ (poly_poly_a2 @ P @ X) @ (poly_poly_a2 @ Q @ X)))))). % poly_mult
thf(fact_20_poly__mult, axiom,
    ((![P : poly_a, Q : poly_a, X : a]: ((poly_a2 @ (times_times_poly_a @ P @ Q) @ X) = (times_times_a @ (poly_a2 @ P @ X) @ (poly_a2 @ Q @ X)))))). % poly_mult
thf(fact_21_poly__mult, axiom,
    ((![P : poly_real, Q : poly_real, X : real]: ((poly_real2 @ (times_775122617y_real @ P @ Q) @ X) = (times_times_real @ (poly_real2 @ P @ X) @ (poly_real2 @ Q @ X)))))). % poly_mult
thf(fact_22_add__pCons, axiom,
    ((![A : poly_complex, P : poly_poly_complex, B : poly_complex, Q : poly_poly_complex]: ((plus_p138939463omplex @ (pCons_poly_complex @ A @ P) @ (pCons_poly_complex @ B @ Q)) = (pCons_poly_complex @ (plus_p1547158847omplex @ A @ B) @ (plus_p138939463omplex @ P @ Q)))))). % add_pCons
thf(fact_23_add__pCons, axiom,
    ((![A : poly_a, P : poly_poly_a, B : poly_a, Q : poly_poly_a]: ((plus_p1976640465poly_a @ (pCons_poly_a @ A @ P) @ (pCons_poly_a @ B @ Q)) = (pCons_poly_a @ (plus_plus_poly_a @ A @ B) @ (plus_p1976640465poly_a @ P @ Q)))))). % add_pCons
thf(fact_24_add__pCons, axiom,
    ((![A : poly_real, P : poly_poly_real, B : poly_real, Q : poly_poly_real]: ((plus_p639965381y_real @ (pCons_poly_real @ A @ P) @ (pCons_poly_real @ B @ Q)) = (pCons_poly_real @ (plus_plus_poly_real @ A @ B) @ (plus_p639965381y_real @ P @ Q)))))). % add_pCons
thf(fact_25_add__pCons, axiom,
    ((![A : real, P : poly_real, B : real, Q : poly_real]: ((plus_plus_poly_real @ (pCons_real @ A @ P) @ (pCons_real @ B @ Q)) = (pCons_real @ (plus_plus_real @ A @ B) @ (plus_plus_poly_real @ P @ Q)))))). % add_pCons
thf(fact_26_add__pCons, axiom,
    ((![A : a, P : poly_a, B : a, Q : poly_a]: ((plus_plus_poly_a @ (pCons_a @ A @ P) @ (pCons_a @ B @ Q)) = (pCons_a @ (plus_plus_a @ A @ B) @ (plus_plus_poly_a @ P @ Q)))))). % add_pCons
thf(fact_27_add__pCons, axiom,
    ((![A : complex, P : poly_complex, B : complex, Q : poly_complex]: ((plus_p1547158847omplex @ (pCons_complex @ A @ P) @ (pCons_complex @ B @ Q)) = (pCons_complex @ (plus_plus_complex @ A @ B) @ (plus_p1547158847omplex @ P @ Q)))))). % add_pCons
thf(fact_28_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_29_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_30_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_31_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_32_norm__add__leD, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ C) => (ord_less_eq_real @ (real_V646646907m_real @ B) @ (plus_plus_real @ (real_V646646907m_real @ A) @ C)))))). % norm_add_leD
thf(fact_33_norm__add__leD, axiom,
    ((![A : a, B : a, C : real]: ((ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ A @ B)) @ C) => (ord_less_eq_real @ (real_V1022479215norm_a @ B) @ (plus_plus_real @ (real_V1022479215norm_a @ A) @ C)))))). % norm_add_leD
thf(fact_34_norm__add__leD, axiom,
    ((![A : complex, B : complex, C : real]: ((ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ C) => (ord_less_eq_real @ (real_V638595069omplex @ B) @ (plus_plus_real @ (real_V638595069omplex @ A) @ C)))))). % norm_add_leD
thf(fact_35_norm__triangle__le, 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 @ (plus_plus_real @ X @ Y)) @ E))))). % norm_triangle_le
thf(fact_36_norm__triangle__le, axiom,
    ((![X : a, Y : a, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V1022479215norm_a @ X) @ (real_V1022479215norm_a @ Y)) @ E) => (ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ X @ Y)) @ E))))). % norm_triangle_le
thf(fact_37_norm__triangle__le, 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 @ (plus_plus_complex @ X @ Y)) @ E))))). % norm_triangle_le
thf(fact_38_norm__triangle__ineq, axiom,
    ((![X : real, Y : real]: (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X @ Y)) @ (plus_plus_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)))))). % norm_triangle_ineq
thf(fact_39_norm__triangle__ineq, axiom,
    ((![X : a, Y : a]: (ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ X @ Y)) @ (plus_plus_real @ (real_V1022479215norm_a @ X) @ (real_V1022479215norm_a @ Y)))))). % norm_triangle_ineq
thf(fact_40_norm__triangle__ineq, axiom,
    ((![X : complex, Y : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X @ Y)) @ (plus_plus_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y)))))). % norm_triangle_ineq
thf(fact_41_norm__triangle__mono, axiom,
    ((![A : real, R : real, B : real, S : real]: ((ord_less_eq_real @ (real_V646646907m_real @ A) @ R) => ((ord_less_eq_real @ (real_V646646907m_real @ B) @ S) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ R @ S))))))). % norm_triangle_mono
thf(fact_42_norm__triangle__mono, axiom,
    ((![A : a, R : real, B : a, S : real]: ((ord_less_eq_real @ (real_V1022479215norm_a @ A) @ R) => ((ord_less_eq_real @ (real_V1022479215norm_a @ B) @ S) => (ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ A @ B)) @ (plus_plus_real @ R @ S))))))). % norm_triangle_mono
thf(fact_43_norm__triangle__mono, axiom,
    ((![A : complex, R : real, B : complex, S : real]: ((ord_less_eq_real @ (real_V638595069omplex @ A) @ R) => ((ord_less_eq_real @ (real_V638595069omplex @ B) @ S) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ (plus_plus_real @ R @ S))))))). % norm_triangle_mono
thf(fact_44_norm__mult__ineq, axiom,
    ((![X : real, Y : real]: (ord_less_eq_real @ (real_V646646907m_real @ (times_times_real @ X @ Y)) @ (times_times_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)))))). % norm_mult_ineq
thf(fact_45_norm__mult__ineq, axiom,
    ((![X : a, Y : a]: (ord_less_eq_real @ (real_V1022479215norm_a @ (times_times_a @ X @ Y)) @ (times_times_real @ (real_V1022479215norm_a @ X) @ (real_V1022479215norm_a @ Y)))))). % norm_mult_ineq
thf(fact_46_norm__mult__ineq, axiom,
    ((![X : complex, Y : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (times_times_complex @ X @ Y)) @ (times_times_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y)))))). % norm_mult_ineq
thf(fact_47_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_48_add__right__cancel, axiom,
    ((![B : a, A : a, C : a]: (((plus_plus_a @ B @ A) = (plus_plus_a @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_49_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_50_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_51_add__right__cancel, axiom,
    ((![B : poly_a, A : poly_a, C : poly_a]: (((plus_plus_poly_a @ B @ A) = (plus_plus_poly_a @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_52_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_53_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_54_add__left__cancel, axiom,
    ((![A : a, B : a, C : a]: (((plus_plus_a @ A @ B) = (plus_plus_a @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_55_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_56_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_57_add__left__cancel, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: (((plus_plus_poly_a @ A @ B) = (plus_plus_poly_a @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_58_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_59_pCons__eq__iff, axiom,
    ((![A : a, P : poly_a, B : a, Q : poly_a]: (((pCons_a @ A @ P) = (pCons_a @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_60_pCons__eq__iff, axiom,
    ((![A : real, P : poly_real, B : real, Q : poly_real]: (((pCons_real @ A @ P) = (pCons_real @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_61_pCons__eq__iff, axiom,
    ((![A : complex, P : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A @ P) = (pCons_complex @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_62_mult__poly__add__left, axiom,
    ((![P : poly_complex, Q : poly_complex, R : poly_complex]: ((times_1246143675omplex @ (plus_p1547158847omplex @ P @ Q) @ R) = (plus_p1547158847omplex @ (times_1246143675omplex @ P @ R) @ (times_1246143675omplex @ Q @ R)))))). % mult_poly_add_left
thf(fact_63_mult__poly__add__left, axiom,
    ((![P : poly_real, Q : poly_real, R : poly_real]: ((times_775122617y_real @ (plus_plus_poly_real @ P @ Q) @ R) = (plus_plus_poly_real @ (times_775122617y_real @ P @ R) @ (times_775122617y_real @ Q @ R)))))). % mult_poly_add_left
thf(fact_64_mult__poly__add__left, axiom,
    ((![P : poly_a, Q : poly_a, R : poly_a]: ((times_times_poly_a @ (plus_plus_poly_a @ P @ Q) @ R) = (plus_plus_poly_a @ (times_times_poly_a @ P @ R) @ (times_times_poly_a @ Q @ R)))))). % mult_poly_add_left
thf(fact_65_complex__mod__triangle__sub, axiom,
    ((![W : complex, Z2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ W) @ (plus_plus_real @ (real_V638595069omplex @ (plus_plus_complex @ W @ Z2)) @ (real_V638595069omplex @ Z2)))))). % complex_mod_triangle_sub
thf(fact_66_mult_Oleft__commute, axiom,
    ((![B : a, A : a, C : a]: ((times_times_a @ B @ (times_times_a @ A @ C)) = (times_times_a @ A @ (times_times_a @ B @ C)))))). % mult.left_commute
thf(fact_67_mult_Oleft__commute, axiom,
    ((![B : real, A : real, C : real]: ((times_times_real @ B @ (times_times_real @ A @ C)) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.left_commute
thf(fact_68_mult_Oleft__commute, axiom,
    ((![B : complex, A : complex, C : complex]: ((times_times_complex @ B @ (times_times_complex @ A @ C)) = (times_times_complex @ A @ (times_times_complex @ B @ C)))))). % mult.left_commute
thf(fact_69_mult_Oleft__commute, axiom,
    ((![B : poly_real, A : poly_real, C : poly_real]: ((times_775122617y_real @ B @ (times_775122617y_real @ A @ C)) = (times_775122617y_real @ A @ (times_775122617y_real @ B @ C)))))). % mult.left_commute
thf(fact_70_mult_Oleft__commute, axiom,
    ((![B : poly_a, A : poly_a, C : poly_a]: ((times_times_poly_a @ B @ (times_times_poly_a @ A @ C)) = (times_times_poly_a @ A @ (times_times_poly_a @ B @ C)))))). % mult.left_commute
thf(fact_71_mult_Ocommute, axiom,
    ((times_times_a = (^[A2 : a]: (^[B2 : a]: (times_times_a @ B2 @ A2)))))). % mult.commute
thf(fact_72_mult_Ocommute, axiom,
    ((times_times_real = (^[A2 : real]: (^[B2 : real]: (times_times_real @ B2 @ A2)))))). % mult.commute
thf(fact_73_mult_Ocommute, axiom,
    ((times_times_complex = (^[A2 : complex]: (^[B2 : complex]: (times_times_complex @ B2 @ A2)))))). % mult.commute
thf(fact_74_mult_Ocommute, axiom,
    ((times_775122617y_real = (^[A2 : poly_real]: (^[B2 : poly_real]: (times_775122617y_real @ B2 @ A2)))))). % mult.commute
thf(fact_75_mult_Ocommute, axiom,
    ((times_times_poly_a = (^[A2 : poly_a]: (^[B2 : poly_a]: (times_times_poly_a @ B2 @ A2)))))). % mult.commute
thf(fact_76_mult_Oassoc, axiom,
    ((![A : a, B : a, C : a]: ((times_times_a @ (times_times_a @ A @ B) @ C) = (times_times_a @ A @ (times_times_a @ B @ C)))))). % mult.assoc
thf(fact_77_mult_Oassoc, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.assoc
thf(fact_78_mult_Oassoc, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C)))))). % mult.assoc
thf(fact_79_mult_Oassoc, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((times_775122617y_real @ (times_775122617y_real @ A @ B) @ C) = (times_775122617y_real @ A @ (times_775122617y_real @ B @ C)))))). % mult.assoc
thf(fact_80_mult_Oassoc, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: ((times_times_poly_a @ (times_times_poly_a @ A @ B) @ C) = (times_times_poly_a @ A @ (times_times_poly_a @ B @ C)))))). % mult.assoc
thf(fact_81_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : a, B : a, C : a]: ((times_times_a @ (times_times_a @ A @ B) @ C) = (times_times_a @ A @ (times_times_a @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_82_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_83_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_84_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((times_775122617y_real @ (times_775122617y_real @ A @ B) @ C) = (times_775122617y_real @ A @ (times_775122617y_real @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_85_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: ((times_times_poly_a @ (times_times_poly_a @ A @ B) @ C) = (times_times_poly_a @ A @ (times_times_poly_a @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_86_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_87_add__right__imp__eq, axiom,
    ((![B : a, A : a, C : a]: (((plus_plus_a @ B @ A) = (plus_plus_a @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_88_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_89_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_90_add__right__imp__eq, axiom,
    ((![B : poly_a, A : poly_a, C : poly_a]: (((plus_plus_poly_a @ B @ A) = (plus_plus_poly_a @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_91_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_92_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_93_add__left__imp__eq, axiom,
    ((![A : a, B : a, C : a]: (((plus_plus_a @ A @ B) = (plus_plus_a @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_94_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_95_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_96_add__left__imp__eq, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: (((plus_plus_poly_a @ A @ B) = (plus_plus_poly_a @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_97_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_98_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_99_add_Oleft__commute, axiom,
    ((![B : a, A : a, C : a]: ((plus_plus_a @ B @ (plus_plus_a @ A @ C)) = (plus_plus_a @ A @ (plus_plus_a @ B @ C)))))). % add.left_commute
thf(fact_100_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_101_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_102_add_Oleft__commute, axiom,
    ((![B : poly_a, A : poly_a, C : poly_a]: ((plus_plus_poly_a @ B @ (plus_plus_poly_a @ A @ C)) = (plus_plus_poly_a @ A @ (plus_plus_poly_a @ B @ C)))))). % add.left_commute
thf(fact_103_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_104_add_Ocommute, axiom,
    ((plus_plus_real = (^[A2 : real]: (^[B2 : real]: (plus_plus_real @ B2 @ A2)))))). % add.commute
thf(fact_105_add_Ocommute, axiom,
    ((plus_plus_a = (^[A2 : a]: (^[B2 : a]: (plus_plus_a @ B2 @ A2)))))). % add.commute
thf(fact_106_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A2 : complex]: (^[B2 : complex]: (plus_plus_complex @ B2 @ A2)))))). % add.commute
thf(fact_107_add_Ocommute, axiom,
    ((plus_p1547158847omplex = (^[A2 : poly_complex]: (^[B2 : poly_complex]: (plus_p1547158847omplex @ B2 @ A2)))))). % add.commute
thf(fact_108_add_Ocommute, axiom,
    ((plus_plus_poly_a = (^[A2 : poly_a]: (^[B2 : poly_a]: (plus_plus_poly_a @ B2 @ A2)))))). % add.commute
thf(fact_109_add_Ocommute, axiom,
    ((plus_plus_poly_real = (^[A2 : poly_real]: (^[B2 : poly_real]: (plus_plus_poly_real @ B2 @ A2)))))). % add.commute
thf(fact_110_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_111_add_Oright__cancel, axiom,
    ((![B : a, A : a, C : a]: (((plus_plus_a @ B @ A) = (plus_plus_a @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_112_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_113_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_114_add_Oright__cancel, axiom,
    ((![B : poly_a, A : poly_a, C : poly_a]: (((plus_plus_poly_a @ B @ A) = (plus_plus_poly_a @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_115_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_116_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_117_add_Oleft__cancel, axiom,
    ((![A : a, B : a, C : a]: (((plus_plus_a @ A @ B) = (plus_plus_a @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_118_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_119_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_120_add_Oleft__cancel, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: (((plus_plus_poly_a @ A @ B) = (plus_plus_poly_a @ 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 : 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_123_add_Oassoc, axiom,
    ((![A : a, B : a, C : a]: ((plus_plus_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ A @ (plus_plus_a @ 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_a, B : poly_a, C : poly_a]: ((plus_plus_poly_a @ (plus_plus_poly_a @ A @ B) @ C) = (plus_plus_poly_a @ A @ (plus_plus_poly_a @ B @ C)))))). % add.assoc
thf(fact_127_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_128_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_129_group__cancel_Oadd2, axiom,
    ((![B3 : a, K : a, B : a, A : a]: ((B3 = (plus_plus_a @ K @ B)) => ((plus_plus_a @ A @ B3) = (plus_plus_a @ K @ (plus_plus_a @ 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_a, K : poly_a, B : poly_a, A : poly_a]: ((B3 = (plus_plus_poly_a @ K @ B)) => ((plus_plus_poly_a @ A @ B3) = (plus_plus_poly_a @ K @ (plus_plus_poly_a @ A @ B))))))). % group_cancel.add2
thf(fact_133_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_134_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_135_group__cancel_Oadd1, axiom,
    ((![A3 : a, K : a, A : a, B : a]: ((A3 = (plus_plus_a @ K @ A)) => ((plus_plus_a @ A3 @ B) = (plus_plus_a @ K @ (plus_plus_a @ 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_a, K : poly_a, A : poly_a, B : poly_a]: ((A3 = (plus_plus_poly_a @ K @ A)) => ((plus_plus_poly_a @ A3 @ B) = (plus_plus_poly_a @ K @ (plus_plus_poly_a @ A @ B))))))). % group_cancel.add1
thf(fact_139_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_140_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_141_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_142_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_143_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : a, B : a, C : a]: ((plus_plus_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ A @ (plus_plus_a @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_144_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_145_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_146_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: ((plus_plus_poly_a @ (plus_plus_poly_a @ A @ B) @ C) = (plus_plus_poly_a @ A @ (plus_plus_poly_a @ 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_pderiv_Ocases, axiom,
    ((![X : poly_real]: (~ ((![A4 : real, P2 : poly_real]: (~ ((X = (pCons_real @ A4 @ P2)))))))))). % pderiv.cases
thf(fact_149_pderiv_Ocases, axiom,
    ((![X : poly_complex]: (~ ((![A4 : complex, P2 : poly_complex]: (~ ((X = (pCons_complex @ A4 @ P2)))))))))). % pderiv.cases
thf(fact_150_pCons__cases, axiom,
    ((![P : poly_a]: (~ ((![A4 : a, Q2 : poly_a]: (~ ((P = (pCons_a @ A4 @ Q2)))))))))). % pCons_cases
thf(fact_151_pCons__cases, axiom,
    ((![P : poly_real]: (~ ((![A4 : real, Q2 : poly_real]: (~ ((P = (pCons_real @ A4 @ Q2)))))))))). % pCons_cases
thf(fact_152_pCons__cases, axiom,
    ((![P : poly_complex]: (~ ((![A4 : complex, Q2 : poly_complex]: (~ ((P = (pCons_complex @ A4 @ Q2)))))))))). % pCons_cases
thf(fact_153_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_154_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_155_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_156_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_157_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_158_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_159_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_160_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_161_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_162_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_163_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_164_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_165_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_166_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_167_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_168_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_169_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_170_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_171_norm__mult, axiom,
    ((![X : real, Y : real]: ((real_V646646907m_real @ (times_times_real @ X @ Y)) = (times_times_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)))))). % norm_mult
thf(fact_172_norm__mult, axiom,
    ((![X : a, Y : a]: ((real_V1022479215norm_a @ (times_times_a @ X @ Y)) = (times_times_real @ (real_V1022479215norm_a @ X) @ (real_V1022479215norm_a @ Y)))))). % norm_mult
thf(fact_173_norm__mult, axiom,
    ((![X : complex, Y : complex]: ((real_V638595069omplex @ (times_times_complex @ X @ Y)) = (times_times_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y)))))). % norm_mult
thf(fact_174_pCons_Ohyps_I2_J, axiom,
    ((?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ r) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z)) @ M))))))). % pCons.hyps(2)
thf(fact_175_rp, axiom,
    ((ord_less_eq_real @ zero_zero_real @ r))). % rp
thf(fact_176_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_177_pCons_Ohyps_I1_J, axiom,
    (((~ ((c = zero_zero_a))) | (~ ((cs = zero_zero_poly_a)))))). % pCons.hyps(1)
thf(fact_178_bounded__linear__axioms_Ointro, axiom,
    ((![F : a > a]: ((?[K2 : real]: (![X2 : a]: (ord_less_eq_real @ (real_V1022479215norm_a @ (F @ X2)) @ (times_times_real @ (real_V1022479215norm_a @ X2) @ K2)))) => (real_V2136407659ms_a_a @ F))))). % bounded_linear_axioms.intro
thf(fact_179_bounded__linear__axioms_Ointro, axiom,
    ((![F : complex > a]: ((?[K2 : real]: (![X2 : complex]: (ord_less_eq_real @ (real_V1022479215norm_a @ (F @ X2)) @ (times_times_real @ (real_V638595069omplex @ X2) @ K2)))) => (real_V301987619plex_a @ F))))). % bounded_linear_axioms.intro
thf(fact_180_bounded__linear__axioms_Ointro, axiom,
    ((![F : a > complex]: ((?[K2 : real]: (![X2 : a]: (ord_less_eq_real @ (real_V638595069omplex @ (F @ X2)) @ (times_times_real @ (real_V1022479215norm_a @ X2) @ K2)))) => (real_V451440129omplex @ F))))). % bounded_linear_axioms.intro
thf(fact_181_bounded__linear__axioms_Ointro, axiom,
    ((![F : complex > complex]: ((?[K2 : real]: (![X2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (F @ X2)) @ (times_times_real @ (real_V638595069omplex @ X2) @ K2)))) => (real_V479504201omplex @ F))))). % bounded_linear_axioms.intro
thf(fact_182_bounded__linear__axioms__def, axiom,
    ((real_V2136407659ms_a_a = (^[F2 : a > a]: (?[K3 : real]: (![X3 : a]: (ord_less_eq_real @ (real_V1022479215norm_a @ (F2 @ X3)) @ (times_times_real @ (real_V1022479215norm_a @ X3) @ K3)))))))). % bounded_linear_axioms_def
thf(fact_183_bounded__linear__axioms__def, axiom,
    ((real_V301987619plex_a = (^[F2 : complex > a]: (?[K3 : real]: (![X3 : complex]: (ord_less_eq_real @ (real_V1022479215norm_a @ (F2 @ X3)) @ (times_times_real @ (real_V638595069omplex @ X3) @ K3)))))))). % bounded_linear_axioms_def
thf(fact_184_bounded__linear__axioms__def, axiom,
    ((real_V451440129omplex = (^[F2 : a > complex]: (?[K3 : real]: (![X3 : a]: (ord_less_eq_real @ (real_V638595069omplex @ (F2 @ X3)) @ (times_times_real @ (real_V1022479215norm_a @ X3) @ K3)))))))). % bounded_linear_axioms_def
thf(fact_185_bounded__linear__axioms__def, axiom,
    ((real_V479504201omplex = (^[F2 : complex > complex]: (?[K3 : real]: (![X3 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (F2 @ X3)) @ (times_times_real @ (real_V638595069omplex @ X3) @ K3)))))))). % bounded_linear_axioms_def
thf(fact_186_crossproduct__noteq, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex, D : poly_complex]: ((((~ ((A = B)))) & ((~ ((C = D))))) = (~ (((plus_p1547158847omplex @ (times_1246143675omplex @ A @ C) @ (times_1246143675omplex @ B @ D)) = (plus_p1547158847omplex @ (times_1246143675omplex @ A @ D) @ (times_1246143675omplex @ B @ C))))))))). % crossproduct_noteq
thf(fact_187_crossproduct__noteq, axiom,
    ((![A : real, B : real, C : real, D : real]: ((((~ ((A = B)))) & ((~ ((C = D))))) = (~ (((plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) = (plus_plus_real @ (times_times_real @ A @ D) @ (times_times_real @ B @ C))))))))). % crossproduct_noteq
thf(fact_188_crossproduct__noteq, axiom,
    ((![A : complex, B : complex, C : complex, D : complex]: ((((~ ((A = B)))) & ((~ ((C = D))))) = (~ (((plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ D)) = (plus_plus_complex @ (times_times_complex @ A @ D) @ (times_times_complex @ B @ C))))))))). % crossproduct_noteq
thf(fact_189_crossproduct__noteq, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real, D : poly_real]: ((((~ ((A = B)))) & ((~ ((C = D))))) = (~ (((plus_plus_poly_real @ (times_775122617y_real @ A @ C) @ (times_775122617y_real @ B @ D)) = (plus_plus_poly_real @ (times_775122617y_real @ A @ D) @ (times_775122617y_real @ B @ C))))))))). % crossproduct_noteq
thf(fact_190_crossproduct__eq, axiom,
    ((![W : poly_complex, Y : poly_complex, X : poly_complex, Z2 : poly_complex]: (((plus_p1547158847omplex @ (times_1246143675omplex @ W @ Y) @ (times_1246143675omplex @ X @ Z2)) = (plus_p1547158847omplex @ (times_1246143675omplex @ W @ Z2) @ (times_1246143675omplex @ X @ Y))) = (((W = X)) | ((Y = Z2))))))). % crossproduct_eq
thf(fact_191_crossproduct__eq, axiom,
    ((![W : real, Y : real, X : real, Z2 : real]: (((plus_plus_real @ (times_times_real @ W @ Y) @ (times_times_real @ X @ Z2)) = (plus_plus_real @ (times_times_real @ W @ Z2) @ (times_times_real @ X @ Y))) = (((W = X)) | ((Y = Z2))))))). % crossproduct_eq
thf(fact_192_crossproduct__eq, axiom,
    ((![W : complex, Y : complex, X : complex, Z2 : complex]: (((plus_plus_complex @ (times_times_complex @ W @ Y) @ (times_times_complex @ X @ Z2)) = (plus_plus_complex @ (times_times_complex @ W @ Z2) @ (times_times_complex @ X @ Y))) = (((W = X)) | ((Y = Z2))))))). % crossproduct_eq
thf(fact_193_crossproduct__eq, axiom,
    ((![W : poly_real, Y : poly_real, X : poly_real, Z2 : poly_real]: (((plus_plus_poly_real @ (times_775122617y_real @ W @ Y) @ (times_775122617y_real @ X @ Z2)) = (plus_plus_poly_real @ (times_775122617y_real @ W @ Z2) @ (times_775122617y_real @ X @ Y))) = (((W = X)) | ((Y = Z2))))))). % crossproduct_eq
thf(fact_194_combine__common__factor, axiom,
    ((![A : poly_complex, E : poly_complex, B : poly_complex, C : poly_complex]: ((plus_p1547158847omplex @ (times_1246143675omplex @ A @ E) @ (plus_p1547158847omplex @ (times_1246143675omplex @ B @ E) @ C)) = (plus_p1547158847omplex @ (times_1246143675omplex @ (plus_p1547158847omplex @ A @ B) @ E) @ C))))). % combine_common_factor
thf(fact_195_combine__common__factor, axiom,
    ((![A : a, E : a, B : a, C : a]: ((plus_plus_a @ (times_times_a @ A @ E) @ (plus_plus_a @ (times_times_a @ B @ E) @ C)) = (plus_plus_a @ (times_times_a @ (plus_plus_a @ A @ B) @ E) @ C))))). % combine_common_factor
thf(fact_196_combine__common__factor, axiom,
    ((![A : real, E : real, B : real, C : real]: ((plus_plus_real @ (times_times_real @ A @ E) @ (plus_plus_real @ (times_times_real @ B @ E) @ C)) = (plus_plus_real @ (times_times_real @ (plus_plus_real @ A @ B) @ E) @ C))))). % combine_common_factor
thf(fact_197_combine__common__factor, axiom,
    ((![A : complex, E : complex, B : complex, C : complex]: ((plus_plus_complex @ (times_times_complex @ A @ E) @ (plus_plus_complex @ (times_times_complex @ B @ E) @ C)) = (plus_plus_complex @ (times_times_complex @ (plus_plus_complex @ A @ B) @ E) @ C))))). % combine_common_factor
thf(fact_198_combine__common__factor, axiom,
    ((![A : poly_real, E : poly_real, B : poly_real, C : poly_real]: ((plus_plus_poly_real @ (times_775122617y_real @ A @ E) @ (plus_plus_poly_real @ (times_775122617y_real @ B @ E) @ C)) = (plus_plus_poly_real @ (times_775122617y_real @ (plus_plus_poly_real @ A @ B) @ E) @ C))))). % combine_common_factor
thf(fact_199_combine__common__factor, axiom,
    ((![A : poly_a, E : poly_a, B : poly_a, C : poly_a]: ((plus_plus_poly_a @ (times_times_poly_a @ A @ E) @ (plus_plus_poly_a @ (times_times_poly_a @ B @ E) @ C)) = (plus_plus_poly_a @ (times_times_poly_a @ (plus_plus_poly_a @ A @ B) @ E) @ C))))). % combine_common_factor
thf(fact_200_mult__zero__left, axiom,
    ((![A : a]: ((times_times_a @ zero_zero_a @ A) = zero_zero_a)))). % mult_zero_left
thf(fact_201_mult__zero__left, axiom,
    ((![A : real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real)))). % mult_zero_left
thf(fact_202_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_203_mult__zero__left, axiom,
    ((![A : poly_real]: ((times_775122617y_real @ zero_zero_poly_real @ A) = zero_zero_poly_real)))). % mult_zero_left
thf(fact_204_mult__zero__left, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ zero_zero_poly_a @ A) = zero_zero_poly_a)))). % mult_zero_left
thf(fact_205_mult__zero__right, axiom,
    ((![A : a]: ((times_times_a @ A @ zero_zero_a) = zero_zero_a)))). % mult_zero_right
thf(fact_206_mult__zero__right, axiom,
    ((![A : real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real)))). % mult_zero_right
thf(fact_207_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_208_mult__zero__right, axiom,
    ((![A : poly_real]: ((times_775122617y_real @ A @ zero_zero_poly_real) = zero_zero_poly_real)))). % mult_zero_right
thf(fact_209_mult__zero__right, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ A @ zero_zero_poly_a) = zero_zero_poly_a)))). % mult_zero_right
thf(fact_210_mult__eq__0__iff, axiom,
    ((![A : a, B : a]: (((times_times_a @ A @ B) = zero_zero_a) = (((A = zero_zero_a)) | ((B = zero_zero_a))))))). % mult_eq_0_iff
thf(fact_211_mult__eq__0__iff, axiom,
    ((![A : real, B : real]: (((times_times_real @ A @ B) = zero_zero_real) = (((A = zero_zero_real)) | ((B = zero_zero_real))))))). % mult_eq_0_iff
thf(fact_212_mult__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % mult_eq_0_iff
thf(fact_213_mult__eq__0__iff, axiom,
    ((![A : poly_real, B : poly_real]: (((times_775122617y_real @ A @ B) = zero_zero_poly_real) = (((A = zero_zero_poly_real)) | ((B = zero_zero_poly_real))))))). % mult_eq_0_iff
thf(fact_214_mult__eq__0__iff, axiom,
    ((![A : poly_a, B : poly_a]: (((times_times_poly_a @ A @ B) = zero_zero_poly_a) = (((A = zero_zero_poly_a)) | ((B = zero_zero_poly_a))))))). % mult_eq_0_iff
thf(fact_215_mult__cancel__left, axiom,
    ((![C : a, A : a, B : a]: (((times_times_a @ C @ A) = (times_times_a @ C @ B)) = (((C = zero_zero_a)) | ((A = B))))))). % mult_cancel_left
thf(fact_216_mult__cancel__left, axiom,
    ((![C : real, A : real, B : real]: (((times_times_real @ C @ A) = (times_times_real @ C @ B)) = (((C = zero_zero_real)) | ((A = B))))))). % mult_cancel_left
thf(fact_217_mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_left
thf(fact_218_mult__cancel__left, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: (((times_775122617y_real @ C @ A) = (times_775122617y_real @ C @ B)) = (((C = zero_zero_poly_real)) | ((A = B))))))). % mult_cancel_left
thf(fact_219_mult__cancel__right, axiom,
    ((![A : a, C : a, B : a]: (((times_times_a @ A @ C) = (times_times_a @ B @ C)) = (((C = zero_zero_a)) | ((A = B))))))). % mult_cancel_right
thf(fact_220_mult__cancel__right, axiom,
    ((![A : real, C : real, B : real]: (((times_times_real @ A @ C) = (times_times_real @ B @ C)) = (((C = zero_zero_real)) | ((A = B))))))). % mult_cancel_right
thf(fact_221_mult__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_right
thf(fact_222_mult__cancel__right, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: (((times_775122617y_real @ A @ C) = (times_775122617y_real @ B @ C)) = (((C = zero_zero_poly_real)) | ((A = B))))))). % mult_cancel_right
thf(fact_223_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_224_add_Oleft__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ zero_z1746442943omplex @ A) = A)))). % add.left_neutral
thf(fact_225_add_Oleft__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ zero_zero_poly_real @ A) = A)))). % add.left_neutral
thf(fact_226_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_227_add_Oleft__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ zero_zero_a @ A) = A)))). % add.left_neutral
thf(fact_228_add_Oleft__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ zero_zero_poly_a @ A) = A)))). % add.left_neutral
thf(fact_229_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_230_add_Oright__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ A @ zero_z1746442943omplex) = A)))). % add.right_neutral
thf(fact_231_add_Oright__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ A @ zero_zero_poly_real) = A)))). % add.right_neutral
thf(fact_232_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_233_add_Oright__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ A @ zero_zero_a) = A)))). % add.right_neutral
thf(fact_234_add_Oright__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ A @ zero_zero_poly_a) = A)))). % add.right_neutral
thf(fact_235_double__zero, axiom,
    ((![A : poly_real]: (((plus_plus_poly_real @ A @ A) = zero_zero_poly_real) = (A = zero_zero_poly_real))))). % double_zero
thf(fact_236_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_237_double__zero__sym, axiom,
    ((![A : poly_real]: ((zero_zero_poly_real = (plus_plus_poly_real @ A @ A)) = (A = zero_zero_poly_real))))). % double_zero_sym
thf(fact_238_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_239_add__cancel__left__left, axiom,
    ((![B : complex, A : complex]: (((plus_plus_complex @ B @ A) = A) = (B = zero_zero_complex))))). % add_cancel_left_left
thf(fact_240_add__cancel__left__left, axiom,
    ((![B : poly_complex, A : poly_complex]: (((plus_p1547158847omplex @ B @ A) = A) = (B = zero_z1746442943omplex))))). % add_cancel_left_left
thf(fact_241_add__cancel__left__left, axiom,
    ((![B : poly_real, A : poly_real]: (((plus_plus_poly_real @ B @ A) = A) = (B = zero_zero_poly_real))))). % add_cancel_left_left
thf(fact_242_add__cancel__left__left, axiom,
    ((![B : real, A : real]: (((plus_plus_real @ B @ A) = A) = (B = zero_zero_real))))). % add_cancel_left_left
thf(fact_243_add__cancel__left__left, axiom,
    ((![B : a, A : a]: (((plus_plus_a @ B @ A) = A) = (B = zero_zero_a))))). % add_cancel_left_left
thf(fact_244_add__cancel__left__left, axiom,
    ((![B : poly_a, A : poly_a]: (((plus_plus_poly_a @ B @ A) = A) = (B = zero_zero_poly_a))))). % add_cancel_left_left
thf(fact_245_poly__IVT, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (times_times_real @ (poly_real2 @ P @ A) @ (poly_real2 @ P @ B)) @ zero_zero_real) => (?[X2 : real]: ((ord_less_real @ A @ X2) & ((ord_less_real @ X2 @ B) & ((poly_real2 @ P @ X2) = zero_zero_real))))))))). % poly_IVT
thf(fact_246_poly__IVT__neg, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ A)) => ((ord_less_real @ (poly_real2 @ P @ B) @ zero_zero_real) => (?[X2 : real]: ((ord_less_real @ A @ X2) & ((ord_less_real @ X2 @ B) & ((poly_real2 @ P @ X2) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_247_poly__IVT__pos, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ B)) => (?[X2 : real]: ((ord_less_real @ A @ X2) & ((ord_less_real @ X2 @ B) & ((poly_real2 @ P @ X2) = zero_zero_real)))))))))). % poly_IVT_pos

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ (pCons_a @ c @ cs) @ z)) @ (plus_plus_real @ (real_V1022479215norm_a @ c) @ (real_V1022479215norm_a @ (times_times_a @ z @ (poly_a2 @ cs @ z))))))).
