% 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_864__5376256_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:33:50.167

% Could-be-implicit typings (9)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    poly_p1267267526omplex : $tType).
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__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__Set__Oset_It__Real__Oreal_J, type,
    set_real : $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 (49)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    one_one_poly_complex : poly_complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    one_on1331105667omplex : poly_poly_complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    one_one_poly_real : poly_real).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
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__Complex__Ocomplex_J_J, type,
    times_1460995011omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
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__Real__Oreal, type,
    times_times_real : real > real > real).
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__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    zero_z1040703943omplex : poly_poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    zero_z1200043727omplex : poly_p1267267526omplex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    zero_z1423781445y_real : poly_poly_real).
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__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_less_poly_real : poly_real > poly_real > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Orderings_Oord__class_Oless__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__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    pCons_1087637536omplex : poly_poly_complex > poly_p1267267526omplex > poly_p1267267526omplex).
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__Real__Oreal, type,
    pCons_real : real > poly_real > poly_real).
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__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_p282434315omplex : poly_p1267267526omplex > poly_poly_complex > poly_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__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_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex, type,
    real_V306493662omplex : real > complex).
thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal, type,
    real_V1205483228l_real : real > real).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex, type,
    divide1210191872omplex : complex > complex > complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    divide1187762952omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    divide350004240omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    divide1727078534y_real : poly_real > poly_real > poly_real).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_c_Set_OCollect_001t__Real__Oreal, type,
    collect_real : (real > $o) > set_real).
thf(sy_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_c____, type,
    c : complex).
thf(sy_v_cs____, type,
    cs : poly_complex).
thf(sy_v_d____, type,
    d : complex).
thf(sy_v_ds____, type,
    ds : poly_complex).
thf(sy_v_m____, type,
    m : real).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_x____, type,
    x : real).

% Relevant facts (246)
thf(fact_0_False, axiom,
    ((~ ((d = zero_zero_complex))))). % False
thf(fact_1__092_060open_062cmod_A_Icomplex__of__real_Ax_A_K_Apoly_Ads_A_Icomplex__of__real_Ax_J_J_A_092_060noteq_062_Acmod_Ad_092_060close_062, axiom,
    ((~ (((real_V638595069omplex @ (times_times_complex @ (real_V306493662omplex @ x) @ (poly_complex2 @ ds @ (real_V306493662omplex @ x)))) = (real_V638595069omplex @ d)))))). % \<open>cmod (complex_of_real x * poly ds (complex_of_real x)) \<noteq> cmod d\<close>
thf(fact_2_cth, axiom,
    (((real_V638595069omplex @ (times_times_complex @ (real_V306493662omplex @ x) @ (poly_complex2 @ ds @ (real_V306493662omplex @ x)))) = (real_V638595069omplex @ d)))). % cth
thf(fact_3_pCons_Ohyps_I1_J, axiom,
    (((~ ((d = zero_zero_complex))) | (~ ((ds = zero_z1746442943omplex)))))). % pCons.hyps(1)
thf(fact_4_assms, axiom,
    ((~ ((?[A : complex, L : poly_complex]: ((~ ((A = zero_zero_complex))) & ((L = zero_z1746442943omplex) & (p = (pCons_complex @ A @ L))))))))). % assms
thf(fact_5_pCons_Oprems, axiom,
    ((![W : complex]: ((~ ((W = zero_zero_complex))) => ((poly_complex2 @ (pCons_complex @ d @ ds) @ W) = zero_zero_complex))))). % pCons.prems
thf(fact_6_pCons_Ohyps_I2_J, axiom,
    (((![W2 : complex]: ((~ ((W2 = zero_zero_complex))) => ((poly_complex2 @ ds @ W2) = zero_zero_complex))) => (ds = zero_z1746442943omplex)))). % pCons.hyps(2)
thf(fact_7_pCons__0__0, axiom,
    (((pCons_poly_real @ zero_zero_poly_real @ zero_z1423781445y_real) = zero_z1423781445y_real))). % pCons_0_0
thf(fact_8_pCons__0__0, axiom,
    (((pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) = zero_z1200043727omplex))). % pCons_0_0
thf(fact_9_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_10_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_11_pCons__0__0, axiom,
    (((pCons_real @ zero_zero_real @ zero_zero_poly_real) = zero_zero_poly_real))). % pCons_0_0
thf(fact_12_pCons__eq__0__iff, axiom,
    ((![A2 : poly_real, P : poly_poly_real]: (((pCons_poly_real @ A2 @ P) = zero_z1423781445y_real) = (((A2 = zero_zero_poly_real)) & ((P = zero_z1423781445y_real))))))). % pCons_eq_0_iff
thf(fact_13_pCons__eq__0__iff, axiom,
    ((![A2 : poly_poly_complex, P : poly_p1267267526omplex]: (((pCons_1087637536omplex @ A2 @ P) = zero_z1200043727omplex) = (((A2 = zero_z1040703943omplex)) & ((P = zero_z1200043727omplex))))))). % pCons_eq_0_iff
thf(fact_14_pCons__eq__0__iff, axiom,
    ((![A2 : poly_complex, P : poly_poly_complex]: (((pCons_poly_complex @ A2 @ P) = zero_z1040703943omplex) = (((A2 = zero_z1746442943omplex)) & ((P = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_15_pCons__eq__0__iff, axiom,
    ((![A2 : real, P : poly_real]: (((pCons_real @ A2 @ P) = zero_zero_poly_real) = (((A2 = zero_zero_real)) & ((P = zero_zero_poly_real))))))). % pCons_eq_0_iff
thf(fact_16_pCons__eq__0__iff, axiom,
    ((![A2 : complex, P : poly_complex]: (((pCons_complex @ A2 @ P) = zero_z1746442943omplex) = (((A2 = zero_zero_complex)) & ((P = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_17_pCons__induct, axiom,
    ((![P2 : poly_poly_real > $o, P : poly_poly_real]: ((P2 @ zero_z1423781445y_real) => ((![A3 : poly_real, P3 : poly_poly_real]: (((~ ((A3 = zero_zero_poly_real))) | (~ ((P3 = zero_z1423781445y_real)))) => ((P2 @ P3) => (P2 @ (pCons_poly_real @ A3 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_18_pCons__induct, axiom,
    ((![P2 : poly_p1267267526omplex > $o, P : poly_p1267267526omplex]: ((P2 @ zero_z1200043727omplex) => ((![A3 : poly_poly_complex, P3 : poly_p1267267526omplex]: (((~ ((A3 = zero_z1040703943omplex))) | (~ ((P3 = zero_z1200043727omplex)))) => ((P2 @ P3) => (P2 @ (pCons_1087637536omplex @ A3 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_19_pCons__induct, axiom,
    ((![P2 : poly_poly_complex > $o, P : poly_poly_complex]: ((P2 @ zero_z1040703943omplex) => ((![A3 : poly_complex, P3 : poly_poly_complex]: (((~ ((A3 = zero_z1746442943omplex))) | (~ ((P3 = zero_z1040703943omplex)))) => ((P2 @ P3) => (P2 @ (pCons_poly_complex @ A3 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_20_pCons__induct, axiom,
    ((![P2 : poly_real > $o, P : poly_real]: ((P2 @ zero_zero_poly_real) => ((![A3 : real, P3 : poly_real]: (((~ ((A3 = zero_zero_real))) | (~ ((P3 = zero_zero_poly_real)))) => ((P2 @ P3) => (P2 @ (pCons_real @ A3 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_21_pCons__induct, axiom,
    ((![P2 : poly_complex > $o, P : poly_complex]: ((P2 @ zero_z1746442943omplex) => ((![A3 : complex, P3 : poly_complex]: (((~ ((A3 = zero_zero_complex))) | (~ ((P3 = zero_z1746442943omplex)))) => ((P2 @ P3) => (P2 @ (pCons_complex @ A3 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_22_pCons__eq__iff, axiom,
    ((![A2 : complex, P : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A2 @ P) = (pCons_complex @ B @ Q)) = (((A2 = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_23_pCons__eq__iff, axiom,
    ((![A2 : real, P : poly_real, B : real, Q : poly_real]: (((pCons_real @ A2 @ P) = (pCons_real @ B @ Q)) = (((A2 = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_24_pCons__eq__iff, axiom,
    ((![A2 : poly_complex, P : poly_poly_complex, B : poly_complex, Q : poly_poly_complex]: (((pCons_poly_complex @ A2 @ P) = (pCons_poly_complex @ B @ Q)) = (((A2 = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_25_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_complex > $o, P : poly_complex, Q : poly_complex]: ((P2 @ zero_z1746442943omplex @ zero_z1746442943omplex) => ((![A3 : complex, P3 : poly_complex, B2 : complex, Q2 : poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_complex @ A3 @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_26_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_real > $o, P : poly_complex, Q : poly_real]: ((P2 @ zero_z1746442943omplex @ zero_zero_poly_real) => ((![A3 : complex, P3 : poly_complex, B2 : real, Q2 : poly_real]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_complex @ A3 @ P3) @ (pCons_real @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_27_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_poly_complex > $o, P : poly_complex, Q : poly_poly_complex]: ((P2 @ zero_z1746442943omplex @ zero_z1040703943omplex) => ((![A3 : complex, P3 : poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_complex @ A3 @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_28_poly__induct2, axiom,
    ((![P2 : poly_real > poly_complex > $o, P : poly_real, Q : poly_complex]: ((P2 @ zero_zero_poly_real @ zero_z1746442943omplex) => ((![A3 : real, P3 : poly_real, B2 : complex, Q2 : poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_real @ A3 @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_29_poly__induct2, axiom,
    ((![P2 : poly_real > poly_real > $o, P : poly_real, Q : poly_real]: ((P2 @ zero_zero_poly_real @ zero_zero_poly_real) => ((![A3 : real, P3 : poly_real, B2 : real, Q2 : poly_real]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_real @ A3 @ P3) @ (pCons_real @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_30_poly__induct2, axiom,
    ((![P2 : poly_real > poly_poly_complex > $o, P : poly_real, Q : poly_poly_complex]: ((P2 @ zero_zero_poly_real @ zero_z1040703943omplex) => ((![A3 : real, P3 : poly_real, B2 : poly_complex, Q2 : poly_poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_real @ A3 @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_31_poly__induct2, axiom,
    ((![P2 : poly_poly_complex > poly_complex > $o, P : poly_poly_complex, Q : poly_complex]: ((P2 @ zero_z1040703943omplex @ zero_z1746442943omplex) => ((![A3 : poly_complex, P3 : poly_poly_complex, B2 : complex, Q2 : poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_complex @ A3 @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_32_poly__induct2, axiom,
    ((![P2 : poly_poly_complex > poly_real > $o, P : poly_poly_complex, Q : poly_real]: ((P2 @ zero_z1040703943omplex @ zero_zero_poly_real) => ((![A3 : poly_complex, P3 : poly_poly_complex, B2 : real, Q2 : poly_real]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_complex @ A3 @ P3) @ (pCons_real @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_33_poly__induct2, axiom,
    ((![P2 : poly_poly_complex > poly_poly_complex > $o, P : poly_poly_complex, Q : poly_poly_complex]: ((P2 @ zero_z1040703943omplex @ zero_z1040703943omplex) => ((![A3 : poly_complex, P3 : poly_poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_complex @ A3 @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_34_pderiv_Oinduct, axiom,
    ((![P2 : poly_complex > $o, A0 : poly_complex]: ((![A3 : complex, P3 : poly_complex]: (((~ ((P3 = zero_z1746442943omplex))) => (P2 @ P3)) => (P2 @ (pCons_complex @ A3 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_35_pderiv_Oinduct, axiom,
    ((![P2 : poly_real > $o, A0 : poly_real]: ((![A3 : real, P3 : poly_real]: (((~ ((P3 = zero_zero_poly_real))) => (P2 @ P3)) => (P2 @ (pCons_real @ A3 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_36_pderiv_Oinduct, axiom,
    ((![P2 : poly_poly_complex > $o, A0 : poly_poly_complex]: ((![A3 : poly_complex, P3 : poly_poly_complex]: (((~ ((P3 = zero_z1040703943omplex))) => (P2 @ P3)) => (P2 @ (pCons_poly_complex @ A3 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_37__092_060open_062poly_A_IpCons_Ad_Ads_J_A_Icomplex__of__real_Ax_J_A_061_A0_092_060close_062, axiom,
    (((poly_complex2 @ (pCons_complex @ d @ ds) @ (real_V306493662omplex @ x)) = zero_zero_complex))). % \<open>poly (pCons d ds) (complex_of_real x) = 0\<close>
thf(fact_38_poly__0, axiom,
    ((![X : poly_real]: ((poly_poly_real2 @ zero_z1423781445y_real @ X) = zero_zero_poly_real)))). % poly_0
thf(fact_39_poly__0, axiom,
    ((![X : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X) = zero_z1040703943omplex)))). % poly_0
thf(fact_40_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_41_poly__0, axiom,
    ((![X : real]: ((poly_real2 @ zero_zero_poly_real @ X) = zero_zero_real)))). % poly_0
thf(fact_42_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_43_cx_I1_J, axiom,
    ((~ (((real_V306493662omplex @ x) = zero_zero_complex))))). % cx(1)
thf(fact_44_x_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ x))). % x(1)
thf(fact_45_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_46_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_47__092_060open_062_092_060forall_062w_O_Aw_A_092_060noteq_062_A0_A_092_060longrightarrow_062_Apoly_Acs_Aw_A_061_A0_092_060close_062, axiom,
    ((![W : complex]: ((~ ((W = zero_zero_complex))) => ((poly_complex2 @ cs @ W) = zero_zero_complex))))). % \<open>\<forall>w. w \<noteq> 0 \<longrightarrow> poly cs w = 0\<close>
thf(fact_48_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A2 : complex, B : complex, C : complex]: ((times_times_complex @ (times_times_complex @ A2 @ B) @ C) = (times_times_complex @ A2 @ (times_times_complex @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_49_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A2 : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A2 @ B) @ C) = (times_times_real @ A2 @ (times_times_real @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_50_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_51_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_52_mult_Oassoc, axiom,
    ((![A2 : complex, B : complex, C : complex]: ((times_times_complex @ (times_times_complex @ A2 @ B) @ C) = (times_times_complex @ A2 @ (times_times_complex @ B @ C)))))). % mult.assoc
thf(fact_53_mult_Oassoc, axiom,
    ((![A2 : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A2 @ B) @ C) = (times_times_real @ A2 @ (times_times_real @ B @ C)))))). % mult.assoc
thf(fact_54_mult_Ocommute, axiom,
    ((times_times_complex = (^[A4 : complex]: (^[B3 : complex]: (times_times_complex @ B3 @ A4)))))). % mult.commute
thf(fact_55_mult_Ocommute, axiom,
    ((times_times_real = (^[A4 : real]: (^[B3 : real]: (times_times_real @ B3 @ A4)))))). % mult.commute
thf(fact_56_mult_Oleft__commute, axiom,
    ((![B : complex, A2 : complex, C : complex]: ((times_times_complex @ B @ (times_times_complex @ A2 @ C)) = (times_times_complex @ A2 @ (times_times_complex @ B @ C)))))). % mult.left_commute
thf(fact_57_mult_Oleft__commute, axiom,
    ((![B : real, A2 : real, C : real]: ((times_times_real @ B @ (times_times_real @ A2 @ C)) = (times_times_real @ A2 @ (times_times_real @ B @ C)))))). % mult.left_commute
thf(fact_58_zero__reorient, axiom,
    ((![X : poly_complex]: ((zero_z1746442943omplex = X) = (X = zero_z1746442943omplex))))). % zero_reorient
thf(fact_59_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_60_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_61_zero__reorient, axiom,
    ((![X : poly_real]: ((zero_zero_poly_real = X) = (X = zero_zero_poly_real))))). % zero_reorient
thf(fact_62_zero__reorient, axiom,
    ((![X : poly_poly_complex]: ((zero_z1040703943omplex = X) = (X = zero_z1040703943omplex))))). % zero_reorient
thf(fact_63_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X2 : poly_complex]: ((poly_poly_complex2 @ P @ X2) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_64_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X2 : complex]: ((poly_complex2 @ P @ X2) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_65_poly__all__0__iff__0, axiom,
    ((![P : poly_real]: ((![X2 : real]: ((poly_real2 @ P @ X2) = zero_zero_real)) = (P = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_66_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_real]: ((![X2 : poly_real]: ((poly_poly_real2 @ P @ X2) = zero_zero_poly_real)) = (P = zero_z1423781445y_real))))). % poly_all_0_iff_0
thf(fact_67_poly__all__0__iff__0, axiom,
    ((![P : poly_p1267267526omplex]: ((![X2 : poly_poly_complex]: ((poly_p282434315omplex @ P @ X2) = zero_z1040703943omplex)) = (P = zero_z1200043727omplex))))). % poly_all_0_iff_0
thf(fact_68_pderiv_Ocases, axiom,
    ((![X : poly_complex]: (~ ((![A3 : complex, P3 : poly_complex]: (~ ((X = (pCons_complex @ A3 @ P3)))))))))). % pderiv.cases
thf(fact_69_pderiv_Ocases, axiom,
    ((![X : poly_real]: (~ ((![A3 : real, P3 : poly_real]: (~ ((X = (pCons_real @ A3 @ P3)))))))))). % pderiv.cases
thf(fact_70_pderiv_Ocases, axiom,
    ((![X : poly_poly_complex]: (~ ((![A3 : poly_complex, P3 : poly_poly_complex]: (~ ((X = (pCons_poly_complex @ A3 @ P3)))))))))). % pderiv.cases
thf(fact_71_pCons__cases, axiom,
    ((![P : poly_complex]: (~ ((![A3 : complex, Q2 : poly_complex]: (~ ((P = (pCons_complex @ A3 @ Q2)))))))))). % pCons_cases
thf(fact_72_pCons__cases, axiom,
    ((![P : poly_real]: (~ ((![A3 : real, Q2 : poly_real]: (~ ((P = (pCons_real @ A3 @ Q2)))))))))). % pCons_cases
thf(fact_73_pCons__cases, axiom,
    ((![P : poly_poly_complex]: (~ ((![A3 : poly_complex, Q2 : poly_poly_complex]: (~ ((P = (pCons_poly_complex @ A3 @ Q2)))))))))). % pCons_cases
thf(fact_74_of__real__mult, axiom,
    ((![X : real, Y : real]: ((real_V1205483228l_real @ (times_times_real @ X @ Y)) = (times_times_real @ (real_V1205483228l_real @ X) @ (real_V1205483228l_real @ Y)))))). % of_real_mult
thf(fact_75_of__real__mult, axiom,
    ((![X : real, Y : real]: ((real_V306493662omplex @ (times_times_real @ X @ Y)) = (times_times_complex @ (real_V306493662omplex @ X) @ (real_V306493662omplex @ Y)))))). % of_real_mult
thf(fact_76_of__real__eq__0__iff, axiom,
    ((![X : real]: (((real_V1205483228l_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % of_real_eq_0_iff
thf(fact_77_of__real__eq__0__iff, axiom,
    ((![X : real]: (((real_V306493662omplex @ X) = zero_zero_complex) = (X = zero_zero_real))))). % of_real_eq_0_iff
thf(fact_78_of__real__0, axiom,
    (((real_V1205483228l_real @ zero_zero_real) = zero_zero_real))). % of_real_0
thf(fact_79_of__real__0, axiom,
    (((real_V306493662omplex @ zero_zero_real) = zero_zero_complex))). % of_real_0
thf(fact_80_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_81_norm__eq__zero, axiom,
    ((![X : complex]: (((real_V638595069omplex @ X) = zero_zero_real) = (X = zero_zero_complex))))). % norm_eq_zero
thf(fact_82_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_83_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_84_mult__cancel__right, axiom,
    ((![A2 : poly_complex, C : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A2 @ C) = (times_1246143675omplex @ B @ C)) = (((C = zero_z1746442943omplex)) | ((A2 = B))))))). % mult_cancel_right
thf(fact_85_mult__cancel__right, axiom,
    ((![A2 : poly_real, C : poly_real, B : poly_real]: (((times_775122617y_real @ A2 @ C) = (times_775122617y_real @ B @ C)) = (((C = zero_zero_poly_real)) | ((A2 = B))))))). % mult_cancel_right
thf(fact_86_mult__cancel__right, axiom,
    ((![A2 : poly_poly_complex, C : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ A2 @ C) = (times_1460995011omplex @ B @ C)) = (((C = zero_z1040703943omplex)) | ((A2 = B))))))). % mult_cancel_right
thf(fact_87_mult__cancel__right, axiom,
    ((![A2 : complex, C : complex, B : complex]: (((times_times_complex @ A2 @ C) = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((A2 = B))))))). % mult_cancel_right
thf(fact_88_mult__cancel__right, axiom,
    ((![A2 : real, C : real, B : real]: (((times_times_real @ A2 @ C) = (times_times_real @ B @ C)) = (((C = zero_zero_real)) | ((A2 = B))))))). % mult_cancel_right
thf(fact_89_mult__cancel__left, axiom,
    ((![C : poly_complex, A2 : poly_complex, B : poly_complex]: (((times_1246143675omplex @ C @ A2) = (times_1246143675omplex @ C @ B)) = (((C = zero_z1746442943omplex)) | ((A2 = B))))))). % mult_cancel_left
thf(fact_90_mult__cancel__left, axiom,
    ((![C : poly_real, A2 : poly_real, B : poly_real]: (((times_775122617y_real @ C @ A2) = (times_775122617y_real @ C @ B)) = (((C = zero_zero_poly_real)) | ((A2 = B))))))). % mult_cancel_left
thf(fact_91_mult__cancel__left, axiom,
    ((![C : poly_poly_complex, A2 : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ C @ A2) = (times_1460995011omplex @ C @ B)) = (((C = zero_z1040703943omplex)) | ((A2 = B))))))). % mult_cancel_left
thf(fact_92_mult__cancel__left, axiom,
    ((![C : complex, A2 : complex, B : complex]: (((times_times_complex @ C @ A2) = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((A2 = B))))))). % mult_cancel_left
thf(fact_93_mult__cancel__left, axiom,
    ((![C : real, A2 : real, B : real]: (((times_times_real @ C @ A2) = (times_times_real @ C @ B)) = (((C = zero_zero_real)) | ((A2 = B))))))). % mult_cancel_left
thf(fact_94_mult__eq__0__iff, axiom,
    ((![A2 : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A2 @ B) = zero_z1746442943omplex) = (((A2 = zero_z1746442943omplex)) | ((B = zero_z1746442943omplex))))))). % mult_eq_0_iff
thf(fact_95_mult__eq__0__iff, axiom,
    ((![A2 : poly_real, B : poly_real]: (((times_775122617y_real @ A2 @ B) = zero_zero_poly_real) = (((A2 = zero_zero_poly_real)) | ((B = zero_zero_poly_real))))))). % mult_eq_0_iff
thf(fact_96_mult__eq__0__iff, axiom,
    ((![A2 : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ A2 @ B) = zero_z1040703943omplex) = (((A2 = zero_z1040703943omplex)) | ((B = zero_z1040703943omplex))))))). % mult_eq_0_iff
thf(fact_97_mult__eq__0__iff, axiom,
    ((![A2 : complex, B : complex]: (((times_times_complex @ A2 @ B) = zero_zero_complex) = (((A2 = zero_zero_complex)) | ((B = zero_zero_complex))))))). % mult_eq_0_iff
thf(fact_98_mult__eq__0__iff, axiom,
    ((![A2 : real, B : real]: (((times_times_real @ A2 @ B) = zero_zero_real) = (((A2 = zero_zero_real)) | ((B = zero_zero_real))))))). % mult_eq_0_iff
thf(fact_99_mult__zero__right, axiom,
    ((![A2 : poly_complex]: ((times_1246143675omplex @ A2 @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % mult_zero_right
thf(fact_100_mult__zero__right, axiom,
    ((![A2 : poly_real]: ((times_775122617y_real @ A2 @ zero_zero_poly_real) = zero_zero_poly_real)))). % mult_zero_right
thf(fact_101_mult__zero__right, axiom,
    ((![A2 : poly_poly_complex]: ((times_1460995011omplex @ A2 @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % mult_zero_right
thf(fact_102_mult__zero__right, axiom,
    ((![A2 : complex]: ((times_times_complex @ A2 @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_103_mult__zero__right, axiom,
    ((![A2 : real]: ((times_times_real @ A2 @ zero_zero_real) = zero_zero_real)))). % mult_zero_right
thf(fact_104_m_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ m))). % m(1)
thf(fact_105_of__real__eq__iff, axiom,
    ((![X : real, Y : real]: (((real_V306493662omplex @ X) = (real_V306493662omplex @ Y)) = (X = Y))))). % of_real_eq_iff
thf(fact_106_mult__zero__left, axiom,
    ((![A2 : poly_complex]: ((times_1246143675omplex @ zero_z1746442943omplex @ A2) = zero_z1746442943omplex)))). % mult_zero_left
thf(fact_107_mult__zero__left, axiom,
    ((![A2 : poly_real]: ((times_775122617y_real @ zero_zero_poly_real @ A2) = zero_zero_poly_real)))). % mult_zero_left
thf(fact_108_mult__zero__left, axiom,
    ((![A2 : poly_poly_complex]: ((times_1460995011omplex @ zero_z1040703943omplex @ A2) = zero_z1040703943omplex)))). % mult_zero_left
thf(fact_109_mult__zero__left, axiom,
    ((![A2 : complex]: ((times_times_complex @ zero_zero_complex @ A2) = zero_zero_complex)))). % mult_zero_left
thf(fact_110_mult__zero__left, axiom,
    ((![A2 : real]: ((times_times_real @ zero_zero_real @ A2) = zero_zero_real)))). % mult_zero_left
thf(fact_111_x_I3_J, axiom,
    ((ord_less_real @ x @ one_one_real))). % x(3)
thf(fact_112_nc, axiom,
    ((fundam1158420650omplex @ (poly_complex2 @ (pCons_complex @ c @ cs))))). % nc
thf(fact_113_zero__less__norm__iff, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X)) = (~ ((X = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_114_zero__less__norm__iff, axiom,
    ((![X : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X)) = (~ ((X = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_115_mem__Collect__eq, axiom,
    ((![A2 : real, P2 : real > $o]: ((member_real @ A2 @ (collect_real @ P2)) = (P2 @ A2))))). % mem_Collect_eq
thf(fact_116_Collect__mem__eq, axiom,
    ((![A5 : set_real]: ((collect_real @ (^[X2 : real]: (member_real @ X2 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_117__092_060open_062_092_060And_062y_O_Apoly_A_IpCons_Ac_Acs_J_A0_A_061_Apoly_A_IpCons_Ac_Acs_J_Ay_092_060close_062, axiom,
    ((![Y : complex]: ((poly_complex2 @ (pCons_complex @ c @ cs) @ zero_zero_complex) = (poly_complex2 @ (pCons_complex @ c @ cs) @ Y))))). % \<open>\<And>y. poly (pCons c cs) 0 = poly (pCons c cs) y\<close>
thf(fact_118_poly__IVT, axiom,
    ((![A2 : real, B : real, P : poly_real]: ((ord_less_real @ A2 @ B) => ((ord_less_real @ (times_times_real @ (poly_real2 @ P @ A2) @ (poly_real2 @ P @ B)) @ zero_zero_real) => (?[X3 : real]: ((ord_less_real @ A2 @ X3) & ((ord_less_real @ X3 @ B) & ((poly_real2 @ P @ X3) = zero_zero_real))))))))). % poly_IVT
thf(fact_119_poly__IVT__neg, axiom,
    ((![A2 : real, B : real, P : poly_real]: ((ord_less_real @ A2 @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ A2)) => ((ord_less_real @ (poly_real2 @ P @ B) @ zero_zero_real) => (?[X3 : real]: ((ord_less_real @ A2 @ X3) & ((ord_less_real @ X3 @ B) & ((poly_real2 @ P @ X3) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_120_poly__IVT__pos, axiom,
    ((![A2 : real, B : real, P : poly_real]: ((ord_less_real @ A2 @ B) => ((ord_less_real @ (poly_real2 @ P @ A2) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ B)) => (?[X3 : real]: ((ord_less_real @ A2 @ X3) & ((ord_less_real @ X3 @ B) & ((poly_real2 @ P @ X3) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_121_real__sup__exists, axiom,
    ((![P2 : real > $o]: ((?[X_1 : real]: (P2 @ X_1)) => ((?[Z : real]: (![X3 : real]: ((P2 @ X3) => (ord_less_real @ X3 @ Z)))) => (?[S : real]: (![Y2 : real]: ((?[X2 : real]: (((P2 @ X2)) & ((ord_less_real @ Y2 @ X2)))) = (ord_less_real @ Y2 @ S))))))))). % real_sup_exists
thf(fact_122_linorder__neqE__linordered__idom, axiom,
    ((![X : real, Y : real]: ((~ ((X = Y))) => ((~ ((ord_less_real @ X @ Y))) => (ord_less_real @ Y @ X)))))). % linorder_neqE_linordered_idom
thf(fact_123_norm__not__less__zero, axiom,
    ((![X : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_124_mult__poly__0__left, axiom,
    ((![Q : poly_complex]: ((times_1246143675omplex @ zero_z1746442943omplex @ Q) = zero_z1746442943omplex)))). % mult_poly_0_left
thf(fact_125_mult__poly__0__left, axiom,
    ((![Q : poly_real]: ((times_775122617y_real @ zero_zero_poly_real @ Q) = zero_zero_poly_real)))). % mult_poly_0_left
thf(fact_126_mult__poly__0__left, axiom,
    ((![Q : poly_poly_complex]: ((times_1460995011omplex @ zero_z1040703943omplex @ Q) = zero_z1040703943omplex)))). % mult_poly_0_left
thf(fact_127_mult__poly__0__right, axiom,
    ((![P : poly_complex]: ((times_1246143675omplex @ P @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % mult_poly_0_right
thf(fact_128_mult__poly__0__right, axiom,
    ((![P : poly_real]: ((times_775122617y_real @ P @ zero_zero_poly_real) = zero_zero_poly_real)))). % mult_poly_0_right
thf(fact_129_mult__poly__0__right, axiom,
    ((![P : poly_poly_complex]: ((times_1460995011omplex @ P @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % mult_poly_0_right
thf(fact_130_mult__neg__neg, axiom,
    ((![A2 : poly_real, B : poly_real]: ((ord_less_poly_real @ A2 @ zero_zero_poly_real) => ((ord_less_poly_real @ B @ zero_zero_poly_real) => (ord_less_poly_real @ zero_zero_poly_real @ (times_775122617y_real @ A2 @ B))))))). % mult_neg_neg
thf(fact_131_mult__neg__neg, axiom,
    ((![A2 : real, B : real]: ((ord_less_real @ A2 @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (times_times_real @ A2 @ B))))))). % mult_neg_neg
thf(fact_132_not__square__less__zero, axiom,
    ((![A2 : poly_real]: (~ ((ord_less_poly_real @ (times_775122617y_real @ A2 @ A2) @ zero_zero_poly_real)))))). % not_square_less_zero
thf(fact_133_not__square__less__zero, axiom,
    ((![A2 : real]: (~ ((ord_less_real @ (times_times_real @ A2 @ A2) @ zero_zero_real)))))). % not_square_less_zero
thf(fact_134_mult__less__0__iff, axiom,
    ((![A2 : poly_real, B : poly_real]: ((ord_less_poly_real @ (times_775122617y_real @ A2 @ B) @ zero_zero_poly_real) = (((((ord_less_poly_real @ zero_zero_poly_real @ A2)) & ((ord_less_poly_real @ B @ zero_zero_poly_real)))) | ((((ord_less_poly_real @ A2 @ zero_zero_poly_real)) & ((ord_less_poly_real @ zero_zero_poly_real @ B))))))))). % mult_less_0_iff
thf(fact_135_mult__less__0__iff, axiom,
    ((![A2 : real, B : real]: ((ord_less_real @ (times_times_real @ A2 @ B) @ zero_zero_real) = (((((ord_less_real @ zero_zero_real @ A2)) & ((ord_less_real @ B @ zero_zero_real)))) | ((((ord_less_real @ A2 @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B))))))))). % mult_less_0_iff
thf(fact_136_mult__neg__pos, axiom,
    ((![A2 : poly_real, B : poly_real]: ((ord_less_poly_real @ A2 @ zero_zero_poly_real) => ((ord_less_poly_real @ zero_zero_poly_real @ B) => (ord_less_poly_real @ (times_775122617y_real @ A2 @ B) @ zero_zero_poly_real)))))). % mult_neg_pos
thf(fact_137_mult__neg__pos, axiom,
    ((![A2 : real, B : real]: ((ord_less_real @ A2 @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ (times_times_real @ A2 @ B) @ zero_zero_real)))))). % mult_neg_pos
thf(fact_138_mult__pos__neg, axiom,
    ((![A2 : poly_real, B : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ A2) => ((ord_less_poly_real @ B @ zero_zero_poly_real) => (ord_less_poly_real @ (times_775122617y_real @ A2 @ B) @ zero_zero_poly_real)))))). % mult_pos_neg
thf(fact_139_mult__pos__neg, axiom,
    ((![A2 : real, B : real]: ((ord_less_real @ zero_zero_real @ A2) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ A2 @ B) @ zero_zero_real)))))). % mult_pos_neg
thf(fact_140_mult__pos__pos, axiom,
    ((![A2 : poly_real, B : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ A2) => ((ord_less_poly_real @ zero_zero_poly_real @ B) => (ord_less_poly_real @ zero_zero_poly_real @ (times_775122617y_real @ A2 @ B))))))). % mult_pos_pos
thf(fact_141_mult__pos__pos, axiom,
    ((![A2 : real, B : real]: ((ord_less_real @ zero_zero_real @ A2) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (times_times_real @ A2 @ B))))))). % mult_pos_pos
thf(fact_142_mult__pos__neg2, axiom,
    ((![A2 : poly_real, B : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ A2) => ((ord_less_poly_real @ B @ zero_zero_poly_real) => (ord_less_poly_real @ (times_775122617y_real @ B @ A2) @ zero_zero_poly_real)))))). % mult_pos_neg2
thf(fact_143_mult__pos__neg2, axiom,
    ((![A2 : real, B : real]: ((ord_less_real @ zero_zero_real @ A2) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ B @ A2) @ zero_zero_real)))))). % mult_pos_neg2
thf(fact_144_zero__less__mult__iff, axiom,
    ((![A2 : poly_real, B : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (times_775122617y_real @ A2 @ B)) = (((((ord_less_poly_real @ zero_zero_poly_real @ A2)) & ((ord_less_poly_real @ zero_zero_poly_real @ B)))) | ((((ord_less_poly_real @ A2 @ zero_zero_poly_real)) & ((ord_less_poly_real @ B @ zero_zero_poly_real))))))))). % zero_less_mult_iff
thf(fact_145_zero__less__mult__iff, axiom,
    ((![A2 : real, B : real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A2 @ B)) = (((((ord_less_real @ zero_zero_real @ A2)) & ((ord_less_real @ zero_zero_real @ B)))) | ((((ord_less_real @ A2 @ zero_zero_real)) & ((ord_less_real @ B @ zero_zero_real))))))))). % zero_less_mult_iff
thf(fact_146_zero__less__mult__pos, axiom,
    ((![A2 : poly_real, B : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (times_775122617y_real @ A2 @ B)) => ((ord_less_poly_real @ zero_zero_poly_real @ A2) => (ord_less_poly_real @ zero_zero_poly_real @ B)))))). % zero_less_mult_pos
thf(fact_147_zero__less__mult__pos, axiom,
    ((![A2 : real, B : real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A2 @ B)) => ((ord_less_real @ zero_zero_real @ A2) => (ord_less_real @ zero_zero_real @ B)))))). % zero_less_mult_pos
thf(fact_148_zero__less__mult__pos2, axiom,
    ((![B : poly_real, A2 : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (times_775122617y_real @ B @ A2)) => ((ord_less_poly_real @ zero_zero_poly_real @ A2) => (ord_less_poly_real @ zero_zero_poly_real @ B)))))). % zero_less_mult_pos2
thf(fact_149_zero__less__mult__pos2, axiom,
    ((![B : real, A2 : real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ B @ A2)) => ((ord_less_real @ zero_zero_real @ A2) => (ord_less_real @ zero_zero_real @ B)))))). % zero_less_mult_pos2
thf(fact_150_mult__less__cancel__left__neg, axiom,
    ((![C : poly_real, A2 : poly_real, B : poly_real]: ((ord_less_poly_real @ C @ zero_zero_poly_real) => ((ord_less_poly_real @ (times_775122617y_real @ C @ A2) @ (times_775122617y_real @ C @ B)) = (ord_less_poly_real @ B @ A2)))))). % mult_less_cancel_left_neg
thf(fact_151_mult__less__cancel__left__neg, axiom,
    ((![C : real, A2 : real, B : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ (times_times_real @ C @ A2) @ (times_times_real @ C @ B)) = (ord_less_real @ B @ A2)))))). % mult_less_cancel_left_neg
thf(fact_152_mult__less__cancel__left__pos, axiom,
    ((![C : poly_real, A2 : poly_real, B : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ C) => ((ord_less_poly_real @ (times_775122617y_real @ C @ A2) @ (times_775122617y_real @ C @ B)) = (ord_less_poly_real @ A2 @ B)))))). % mult_less_cancel_left_pos
thf(fact_153_mult__less__cancel__left__pos, axiom,
    ((![C : real, A2 : real, B : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ (times_times_real @ C @ A2) @ (times_times_real @ C @ B)) = (ord_less_real @ A2 @ B)))))). % mult_less_cancel_left_pos
thf(fact_154_mult__strict__left__mono__neg, axiom,
    ((![B : poly_real, A2 : poly_real, C : poly_real]: ((ord_less_poly_real @ B @ A2) => ((ord_less_poly_real @ C @ zero_zero_poly_real) => (ord_less_poly_real @ (times_775122617y_real @ C @ A2) @ (times_775122617y_real @ C @ B))))))). % mult_strict_left_mono_neg
thf(fact_155_mult__strict__left__mono__neg, axiom,
    ((![B : real, A2 : real, C : real]: ((ord_less_real @ B @ A2) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (times_times_real @ C @ A2) @ (times_times_real @ C @ B))))))). % mult_strict_left_mono_neg
thf(fact_156_mult__strict__left__mono, axiom,
    ((![A2 : poly_real, B : poly_real, C : poly_real]: ((ord_less_poly_real @ A2 @ B) => ((ord_less_poly_real @ zero_zero_poly_real @ C) => (ord_less_poly_real @ (times_775122617y_real @ C @ A2) @ (times_775122617y_real @ C @ B))))))). % mult_strict_left_mono
thf(fact_157_mult__strict__left__mono, axiom,
    ((![A2 : real, B : real, C : real]: ((ord_less_real @ A2 @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ C @ A2) @ (times_times_real @ C @ B))))))). % mult_strict_left_mono
thf(fact_158_mult__less__cancel__left__disj, axiom,
    ((![C : poly_real, A2 : poly_real, B : poly_real]: ((ord_less_poly_real @ (times_775122617y_real @ C @ A2) @ (times_775122617y_real @ C @ B)) = (((((ord_less_poly_real @ zero_zero_poly_real @ C)) & ((ord_less_poly_real @ A2 @ B)))) | ((((ord_less_poly_real @ C @ zero_zero_poly_real)) & ((ord_less_poly_real @ B @ A2))))))))). % mult_less_cancel_left_disj
thf(fact_159_mult__less__cancel__left__disj, axiom,
    ((![C : real, A2 : real, B : real]: ((ord_less_real @ (times_times_real @ C @ A2) @ (times_times_real @ C @ B)) = (((((ord_less_real @ zero_zero_real @ C)) & ((ord_less_real @ A2 @ B)))) | ((((ord_less_real @ C @ zero_zero_real)) & ((ord_less_real @ B @ A2))))))))). % mult_less_cancel_left_disj
thf(fact_160_mult__strict__right__mono__neg, axiom,
    ((![B : poly_real, A2 : poly_real, C : poly_real]: ((ord_less_poly_real @ B @ A2) => ((ord_less_poly_real @ C @ zero_zero_poly_real) => (ord_less_poly_real @ (times_775122617y_real @ A2 @ C) @ (times_775122617y_real @ B @ C))))))). % mult_strict_right_mono_neg
thf(fact_161_mult__strict__right__mono__neg, axiom,
    ((![B : real, A2 : real, C : real]: ((ord_less_real @ B @ A2) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (times_times_real @ A2 @ C) @ (times_times_real @ B @ C))))))). % mult_strict_right_mono_neg
thf(fact_162_mult__strict__right__mono, axiom,
    ((![A2 : poly_real, B : poly_real, C : poly_real]: ((ord_less_poly_real @ A2 @ B) => ((ord_less_poly_real @ zero_zero_poly_real @ C) => (ord_less_poly_real @ (times_775122617y_real @ A2 @ C) @ (times_775122617y_real @ B @ C))))))). % mult_strict_right_mono
thf(fact_163_mult__strict__right__mono, axiom,
    ((![A2 : real, B : real, C : real]: ((ord_less_real @ A2 @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A2 @ C) @ (times_times_real @ B @ C))))))). % mult_strict_right_mono
thf(fact_164_mult__less__cancel__right__disj, axiom,
    ((![A2 : poly_real, C : poly_real, B : poly_real]: ((ord_less_poly_real @ (times_775122617y_real @ A2 @ C) @ (times_775122617y_real @ B @ C)) = (((((ord_less_poly_real @ zero_zero_poly_real @ C)) & ((ord_less_poly_real @ A2 @ B)))) | ((((ord_less_poly_real @ C @ zero_zero_poly_real)) & ((ord_less_poly_real @ B @ A2))))))))). % mult_less_cancel_right_disj
thf(fact_165_mult__less__cancel__right__disj, axiom,
    ((![A2 : real, C : real, B : real]: ((ord_less_real @ (times_times_real @ A2 @ C) @ (times_times_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) & ((ord_less_real @ A2 @ B)))) | ((((ord_less_real @ C @ zero_zero_real)) & ((ord_less_real @ B @ A2))))))))). % mult_less_cancel_right_disj
thf(fact_166_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom,
    ((![A2 : poly_real, B : poly_real, C : poly_real]: ((ord_less_poly_real @ A2 @ B) => ((ord_less_poly_real @ zero_zero_poly_real @ C) => (ord_less_poly_real @ (times_775122617y_real @ C @ A2) @ (times_775122617y_real @ C @ B))))))). % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
thf(fact_167_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom,
    ((![A2 : real, B : real, C : real]: ((ord_less_real @ A2 @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ C @ A2) @ (times_times_real @ C @ B))))))). % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
thf(fact_168_norm__mult__less, axiom,
    ((![X : real, R : real, Y : real, S2 : real]: ((ord_less_real @ (real_V646646907m_real @ X) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y) @ S2) => (ord_less_real @ (real_V646646907m_real @ (times_times_real @ X @ Y)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_169_norm__mult__less, axiom,
    ((![X : complex, R : real, Y : complex, S2 : real]: ((ord_less_real @ (real_V638595069omplex @ X) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y) @ S2) => (ord_less_real @ (real_V638595069omplex @ (times_times_complex @ X @ Y)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_170_mult__not__zero, axiom,
    ((![A2 : poly_complex, B : poly_complex]: ((~ (((times_1246143675omplex @ A2 @ B) = zero_z1746442943omplex))) => ((~ ((A2 = zero_z1746442943omplex))) & (~ ((B = zero_z1746442943omplex)))))))). % mult_not_zero
thf(fact_171_mult__not__zero, axiom,
    ((![A2 : poly_real, B : poly_real]: ((~ (((times_775122617y_real @ A2 @ B) = zero_zero_poly_real))) => ((~ ((A2 = zero_zero_poly_real))) & (~ ((B = zero_zero_poly_real)))))))). % mult_not_zero
thf(fact_172_mult__not__zero, axiom,
    ((![A2 : poly_poly_complex, B : poly_poly_complex]: ((~ (((times_1460995011omplex @ A2 @ B) = zero_z1040703943omplex))) => ((~ ((A2 = zero_z1040703943omplex))) & (~ ((B = zero_z1040703943omplex)))))))). % mult_not_zero
thf(fact_173_mult__not__zero, axiom,
    ((![A2 : complex, B : complex]: ((~ (((times_times_complex @ A2 @ B) = zero_zero_complex))) => ((~ ((A2 = zero_zero_complex))) & (~ ((B = zero_zero_complex)))))))). % mult_not_zero
thf(fact_174_mult__not__zero, axiom,
    ((![A2 : real, B : real]: ((~ (((times_times_real @ A2 @ B) = zero_zero_real))) => ((~ ((A2 = zero_zero_real))) & (~ ((B = zero_zero_real)))))))). % mult_not_zero
thf(fact_175_divisors__zero, axiom,
    ((![A2 : poly_complex, B : poly_complex]: (((times_1246143675omplex @ A2 @ B) = zero_z1746442943omplex) => ((A2 = zero_z1746442943omplex) | (B = zero_z1746442943omplex)))))). % divisors_zero
thf(fact_176_divisors__zero, axiom,
    ((![A2 : poly_real, B : poly_real]: (((times_775122617y_real @ A2 @ B) = zero_zero_poly_real) => ((A2 = zero_zero_poly_real) | (B = zero_zero_poly_real)))))). % divisors_zero
thf(fact_177_divisors__zero, axiom,
    ((![A2 : poly_poly_complex, B : poly_poly_complex]: (((times_1460995011omplex @ A2 @ B) = zero_z1040703943omplex) => ((A2 = zero_z1040703943omplex) | (B = zero_z1040703943omplex)))))). % divisors_zero
thf(fact_178_divisors__zero, axiom,
    ((![A2 : complex, B : complex]: (((times_times_complex @ A2 @ B) = zero_zero_complex) => ((A2 = zero_zero_complex) | (B = zero_zero_complex)))))). % divisors_zero
thf(fact_179_divisors__zero, axiom,
    ((![A2 : real, B : real]: (((times_times_real @ A2 @ B) = zero_zero_real) => ((A2 = zero_zero_real) | (B = zero_zero_real)))))). % divisors_zero
thf(fact_180_no__zero__divisors, axiom,
    ((![A2 : poly_complex, B : poly_complex]: ((~ ((A2 = zero_z1746442943omplex))) => ((~ ((B = zero_z1746442943omplex))) => (~ (((times_1246143675omplex @ A2 @ B) = zero_z1746442943omplex)))))))). % no_zero_divisors
thf(fact_181_no__zero__divisors, axiom,
    ((![A2 : poly_real, B : poly_real]: ((~ ((A2 = zero_zero_poly_real))) => ((~ ((B = zero_zero_poly_real))) => (~ (((times_775122617y_real @ A2 @ B) = zero_zero_poly_real)))))))). % no_zero_divisors
thf(fact_182_no__zero__divisors, axiom,
    ((![A2 : poly_poly_complex, B : poly_poly_complex]: ((~ ((A2 = zero_z1040703943omplex))) => ((~ ((B = zero_z1040703943omplex))) => (~ (((times_1460995011omplex @ A2 @ B) = zero_z1040703943omplex)))))))). % no_zero_divisors
thf(fact_183_no__zero__divisors, axiom,
    ((![A2 : complex, B : complex]: ((~ ((A2 = zero_zero_complex))) => ((~ ((B = zero_zero_complex))) => (~ (((times_times_complex @ A2 @ B) = zero_zero_complex)))))))). % no_zero_divisors
thf(fact_184_no__zero__divisors, axiom,
    ((![A2 : real, B : real]: ((~ ((A2 = zero_zero_real))) => ((~ ((B = zero_zero_real))) => (~ (((times_times_real @ A2 @ B) = zero_zero_real)))))))). % no_zero_divisors
thf(fact_185_mult__left__cancel, axiom,
    ((![C : poly_complex, A2 : poly_complex, B : poly_complex]: ((~ ((C = zero_z1746442943omplex))) => (((times_1246143675omplex @ C @ A2) = (times_1246143675omplex @ C @ B)) = (A2 = B)))))). % mult_left_cancel
thf(fact_186_mult__left__cancel, axiom,
    ((![C : poly_real, A2 : poly_real, B : poly_real]: ((~ ((C = zero_zero_poly_real))) => (((times_775122617y_real @ C @ A2) = (times_775122617y_real @ C @ B)) = (A2 = B)))))). % mult_left_cancel
thf(fact_187_mult__left__cancel, axiom,
    ((![C : poly_poly_complex, A2 : poly_poly_complex, B : poly_poly_complex]: ((~ ((C = zero_z1040703943omplex))) => (((times_1460995011omplex @ C @ A2) = (times_1460995011omplex @ C @ B)) = (A2 = B)))))). % mult_left_cancel
thf(fact_188_mult__left__cancel, axiom,
    ((![C : complex, A2 : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ C @ A2) = (times_times_complex @ C @ B)) = (A2 = B)))))). % mult_left_cancel
thf(fact_189_mult__left__cancel, axiom,
    ((![C : real, A2 : real, B : real]: ((~ ((C = zero_zero_real))) => (((times_times_real @ C @ A2) = (times_times_real @ C @ B)) = (A2 = B)))))). % mult_left_cancel
thf(fact_190_mult__right__cancel, axiom,
    ((![C : poly_complex, A2 : poly_complex, B : poly_complex]: ((~ ((C = zero_z1746442943omplex))) => (((times_1246143675omplex @ A2 @ C) = (times_1246143675omplex @ B @ C)) = (A2 = B)))))). % mult_right_cancel
thf(fact_191_mult__right__cancel, axiom,
    ((![C : poly_real, A2 : poly_real, B : poly_real]: ((~ ((C = zero_zero_poly_real))) => (((times_775122617y_real @ A2 @ C) = (times_775122617y_real @ B @ C)) = (A2 = B)))))). % mult_right_cancel
thf(fact_192_mult__right__cancel, axiom,
    ((![C : poly_poly_complex, A2 : poly_poly_complex, B : poly_poly_complex]: ((~ ((C = zero_z1040703943omplex))) => (((times_1460995011omplex @ A2 @ C) = (times_1460995011omplex @ B @ C)) = (A2 = B)))))). % mult_right_cancel
thf(fact_193_mult__right__cancel, axiom,
    ((![C : complex, A2 : complex, B : complex]: ((~ ((C = zero_zero_complex))) => (((times_times_complex @ A2 @ C) = (times_times_complex @ B @ C)) = (A2 = B)))))). % mult_right_cancel
thf(fact_194_mult__right__cancel, axiom,
    ((![C : real, A2 : real, B : real]: ((~ ((C = zero_zero_real))) => (((times_times_real @ A2 @ C) = (times_times_real @ B @ C)) = (A2 = B)))))). % mult_right_cancel
thf(fact_195_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_196_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_197__092_060open_062x_A_K_Am_A_060_Acmod_Ad_092_060close_062, axiom,
    ((ord_less_real @ (times_times_real @ x @ m) @ (real_V638595069omplex @ d)))). % \<open>x * m < cmod d\<close>
thf(fact_198_not__real__square__gt__zero, axiom,
    ((![X : real]: ((~ ((ord_less_real @ zero_zero_real @ (times_times_real @ X @ X)))) = (X = zero_zero_real))))). % not_real_square_gt_zero
thf(fact_199_x_I2_J, axiom,
    ((ord_less_real @ x @ (divide_divide_real @ (real_V638595069omplex @ d) @ m)))). % x(2)
thf(fact_200_mult__less__iff1, axiom,
    ((![Z2 : poly_real, X : poly_real, Y : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ Z2) => ((ord_less_poly_real @ (times_775122617y_real @ X @ Z2) @ (times_775122617y_real @ Y @ Z2)) = (ord_less_poly_real @ X @ Y)))))). % mult_less_iff1
thf(fact_201_mult__less__iff1, axiom,
    ((![Z2 : real, X : real, Y : real]: ((ord_less_real @ zero_zero_real @ Z2) => ((ord_less_real @ (times_times_real @ X @ Z2) @ (times_times_real @ Y @ Z2)) = (ord_less_real @ X @ Y)))))). % mult_less_iff1
thf(fact_202_th0, axiom,
    ((ord_less_eq_real @ (real_V638595069omplex @ (times_times_complex @ (real_V306493662omplex @ x) @ (poly_complex2 @ ds @ (real_V306493662omplex @ x)))) @ (times_times_real @ x @ m)))). % th0
thf(fact_203__092_060open_062cmod_A_Ipoly_Ads_A_Icomplex__of__real_Ax_J_J_A_092_060le_062_Am_092_060close_062, axiom,
    ((ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ ds @ (real_V306493662omplex @ x))) @ m))). % \<open>cmod (poly ds (complex_of_real x)) \<le> m\<close>
thf(fact_204_field__lbound__gt__zero, axiom,
    ((![D1 : real, D2 : real]: ((ord_less_real @ zero_zero_real @ D1) => ((ord_less_real @ zero_zero_real @ D2) => (?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ D1) & (ord_less_real @ E @ D2))))))))). % field_lbound_gt_zero
thf(fact_205_m_I2_J, axiom,
    ((![Z : a, Za : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Za) @ one_one_real) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ ds @ Za)) @ m))))). % m(2)
thf(fact_206_cx_I2_J, axiom,
    ((ord_less_eq_real @ (real_V638595069omplex @ (real_V306493662omplex @ x)) @ one_one_real))). % cx(2)
thf(fact_207_div__by__0, axiom,
    ((![A2 : poly_complex]: ((divide1187762952omplex @ A2 @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % div_by_0
thf(fact_208_div__by__0, axiom,
    ((![A2 : complex]: ((divide1210191872omplex @ A2 @ zero_zero_complex) = zero_zero_complex)))). % div_by_0
thf(fact_209_div__by__0, axiom,
    ((![A2 : poly_real]: ((divide1727078534y_real @ A2 @ zero_zero_poly_real) = zero_zero_poly_real)))). % div_by_0
thf(fact_210_div__by__0, axiom,
    ((![A2 : poly_poly_complex]: ((divide350004240omplex @ A2 @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % div_by_0
thf(fact_211_div__by__0, axiom,
    ((![A2 : real]: ((divide_divide_real @ A2 @ zero_zero_real) = zero_zero_real)))). % div_by_0
thf(fact_212_div__0, axiom,
    ((![A2 : poly_complex]: ((divide1187762952omplex @ zero_z1746442943omplex @ A2) = zero_z1746442943omplex)))). % div_0
thf(fact_213_div__0, axiom,
    ((![A2 : complex]: ((divide1210191872omplex @ zero_zero_complex @ A2) = zero_zero_complex)))). % div_0
thf(fact_214_div__0, axiom,
    ((![A2 : poly_real]: ((divide1727078534y_real @ zero_zero_poly_real @ A2) = zero_zero_poly_real)))). % div_0
thf(fact_215_div__0, axiom,
    ((![A2 : poly_poly_complex]: ((divide350004240omplex @ zero_z1040703943omplex @ A2) = zero_z1040703943omplex)))). % div_0
thf(fact_216_div__0, axiom,
    ((![A2 : real]: ((divide_divide_real @ zero_zero_real @ A2) = zero_zero_real)))). % div_0
thf(fact_217_mult_Oleft__neutral, axiom,
    ((![A2 : complex]: ((times_times_complex @ one_one_complex @ A2) = A2)))). % mult.left_neutral
thf(fact_218_mult_Oleft__neutral, axiom,
    ((![A2 : real]: ((times_times_real @ one_one_real @ A2) = A2)))). % mult.left_neutral
thf(fact_219_mult_Oright__neutral, axiom,
    ((![A2 : complex]: ((times_times_complex @ A2 @ one_one_complex) = A2)))). % mult.right_neutral
thf(fact_220_mult_Oright__neutral, axiom,
    ((![A2 : real]: ((times_times_real @ A2 @ one_one_real) = A2)))). % mult.right_neutral
thf(fact_221_div__by__1, axiom,
    ((![A2 : real]: ((divide_divide_real @ A2 @ one_one_real) = A2)))). % div_by_1
thf(fact_222_dm, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ (real_V638595069omplex @ d) @ m)))). % dm
thf(fact_223__092_060open_062_092_060exists_062m_0620_O_A_092_060forall_062z_O_Acmod_Az_A_092_060le_062_A1_A_092_060longrightarrow_062_Acmod_A_Ipoly_Ads_Az_J_A_092_060le_062_Am_092_060close_062, axiom,
    ((?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z) @ one_one_real) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ ds @ Z)) @ M))))))). % \<open>\<exists>m>0. \<forall>z. cmod z \<le> 1 \<longrightarrow> cmod (poly ds z) \<le> m\<close>
thf(fact_224_real__divide__square__eq, axiom,
    ((![R : real, A2 : real]: ((divide_divide_real @ (times_times_real @ R @ A2) @ (times_times_real @ R @ R)) = (divide_divide_real @ A2 @ R))))). % real_divide_square_eq
thf(fact_225_poly__1, axiom,
    ((![X : complex]: ((poly_complex2 @ one_one_poly_complex @ X) = one_one_complex)))). % poly_1
thf(fact_226_poly__1, axiom,
    ((![X : real]: ((poly_real2 @ one_one_poly_real @ X) = one_one_real)))). % poly_1
thf(fact_227__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_A_092_060lbrakk_0620_A_060_Ax_059_Ax_A_060_Acmod_Ad_A_P_Am_059_Ax_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![X3 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ X3 @ (divide_divide_real @ (real_V638595069omplex @ d) @ m)) => (~ ((ord_less_real @ X3 @ one_one_real)))))))))). % \<open>\<And>thesis. (\<And>x. \<lbrakk>0 < x; x < cmod d / m; x < 1\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_228__092_060open_062_092_060exists_062e_0620_O_Ae_A_060_Acmod_Ad_A_P_Am_A_092_060and_062_Ae_A_060_A1_092_060close_062, axiom,
    ((?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ (divide_divide_real @ (real_V638595069omplex @ d) @ m)) & (ord_less_real @ E @ one_one_real)))))). % \<open>\<exists>e>0. e < cmod d / m \<and> e < 1\<close>
thf(fact_229_mult__cancel__right2, axiom,
    ((![A2 : poly_complex, C : poly_complex]: (((times_1246143675omplex @ A2 @ C) = C) = (((C = zero_z1746442943omplex)) | ((A2 = one_one_poly_complex))))))). % mult_cancel_right2
thf(fact_230_mult__cancel__right2, axiom,
    ((![A2 : poly_real, C : poly_real]: (((times_775122617y_real @ A2 @ C) = C) = (((C = zero_zero_poly_real)) | ((A2 = one_one_poly_real))))))). % mult_cancel_right2
thf(fact_231_mult__cancel__right2, axiom,
    ((![A2 : poly_poly_complex, C : poly_poly_complex]: (((times_1460995011omplex @ A2 @ C) = C) = (((C = zero_z1040703943omplex)) | ((A2 = one_on1331105667omplex))))))). % mult_cancel_right2
thf(fact_232_mult__cancel__right2, axiom,
    ((![A2 : complex, C : complex]: (((times_times_complex @ A2 @ C) = C) = (((C = zero_zero_complex)) | ((A2 = one_one_complex))))))). % mult_cancel_right2
thf(fact_233_mult__cancel__right2, axiom,
    ((![A2 : real, C : real]: (((times_times_real @ A2 @ C) = C) = (((C = zero_zero_real)) | ((A2 = one_one_real))))))). % mult_cancel_right2
thf(fact_234_mult__cancel__right1, axiom,
    ((![C : poly_complex, B : poly_complex]: ((C = (times_1246143675omplex @ B @ C)) = (((C = zero_z1746442943omplex)) | ((B = one_one_poly_complex))))))). % mult_cancel_right1
thf(fact_235_mult__cancel__right1, axiom,
    ((![C : poly_real, B : poly_real]: ((C = (times_775122617y_real @ B @ C)) = (((C = zero_zero_poly_real)) | ((B = one_one_poly_real))))))). % mult_cancel_right1
thf(fact_236_mult__cancel__right1, axiom,
    ((![C : poly_poly_complex, B : poly_poly_complex]: ((C = (times_1460995011omplex @ B @ C)) = (((C = zero_z1040703943omplex)) | ((B = one_on1331105667omplex))))))). % mult_cancel_right1
thf(fact_237_mult__cancel__right1, axiom,
    ((![C : complex, B : complex]: ((C = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((B = one_one_complex))))))). % mult_cancel_right1
thf(fact_238_mult__cancel__right1, axiom,
    ((![C : real, B : real]: ((C = (times_times_real @ B @ C)) = (((C = zero_zero_real)) | ((B = one_one_real))))))). % mult_cancel_right1
thf(fact_239_mult__cancel__left2, axiom,
    ((![C : poly_complex, A2 : poly_complex]: (((times_1246143675omplex @ C @ A2) = C) = (((C = zero_z1746442943omplex)) | ((A2 = one_one_poly_complex))))))). % mult_cancel_left2
thf(fact_240_mult__cancel__left2, axiom,
    ((![C : poly_real, A2 : poly_real]: (((times_775122617y_real @ C @ A2) = C) = (((C = zero_zero_poly_real)) | ((A2 = one_one_poly_real))))))). % mult_cancel_left2
thf(fact_241_mult__cancel__left2, axiom,
    ((![C : poly_poly_complex, A2 : poly_poly_complex]: (((times_1460995011omplex @ C @ A2) = C) = (((C = zero_z1040703943omplex)) | ((A2 = one_on1331105667omplex))))))). % mult_cancel_left2
thf(fact_242_mult__cancel__left2, axiom,
    ((![C : complex, A2 : complex]: (((times_times_complex @ C @ A2) = C) = (((C = zero_zero_complex)) | ((A2 = one_one_complex))))))). % mult_cancel_left2
thf(fact_243_mult__cancel__left2, axiom,
    ((![C : real, A2 : real]: (((times_times_real @ C @ A2) = C) = (((C = zero_zero_real)) | ((A2 = one_one_real))))))). % mult_cancel_left2
thf(fact_244_less__eq__real__def, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y3 : real]: (((ord_less_real @ X2 @ Y3)) | ((X2 = Y3)))))))). % less_eq_real_def
thf(fact_245_complete__real, axiom,
    ((![S3 : set_real]: ((?[X4 : real]: (member_real @ X4 @ S3)) => ((?[Z : real]: (![X3 : real]: ((member_real @ X3 @ S3) => (ord_less_eq_real @ X3 @ Z)))) => (?[Y4 : real]: ((![X4 : real]: ((member_real @ X4 @ S3) => (ord_less_eq_real @ X4 @ Y4))) & (![Z : real]: ((![X3 : real]: ((member_real @ X3 @ S3) => (ord_less_eq_real @ X3 @ Z))) => (ord_less_eq_real @ Y4 @ Z)))))))))). % complete_real

% Conjectures (1)
thf(conj_0, conjecture,
    (((pCons_complex @ d @ ds) = zero_z1746442943omplex))).
