% 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_852__5376158_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:33:42.826

% Could-be-implicit typings (7)
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__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 (34)
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__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_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__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__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__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__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__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 (183)
thf(fact_0_m_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ m))). % m(1)
thf(fact_1_False, axiom,
    ((~ ((d = zero_zero_complex))))). % False
thf(fact_2_x_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ x))). % x(1)
thf(fact_3_x_I3_J, axiom,
    ((ord_less_real @ x @ one_one_real))). % x(3)
thf(fact_4_x_I2_J, axiom,
    ((ord_less_real @ x @ (divide_divide_real @ (real_V638595069omplex @ d) @ m)))). % x(2)
thf(fact_5_of__real__0, axiom,
    (((real_V1205483228l_real @ zero_zero_real) = zero_zero_real))). % of_real_0
thf(fact_6_of__real__0, axiom,
    (((real_V306493662omplex @ zero_zero_real) = zero_zero_complex))). % of_real_0
thf(fact_7_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_8_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_9_of__real__eq__iff, axiom,
    ((![X : real, Y : real]: (((real_V1205483228l_real @ X) = (real_V1205483228l_real @ Y)) = (X = Y))))). % of_real_eq_iff
thf(fact_10_of__real__eq__iff, axiom,
    ((![X : real, Y : real]: (((real_V306493662omplex @ X) = (real_V306493662omplex @ Y)) = (X = Y))))). % of_real_eq_iff
thf(fact_11_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_12_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_13_zero__reorient, axiom,
    ((![X : poly_complex]: ((zero_z1746442943omplex = X) = (X = zero_z1746442943omplex))))). % zero_reorient
thf(fact_14_div__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ zero_zero_complex @ A) = zero_zero_complex)))). % div_0
thf(fact_15_div__0, axiom,
    ((![A : poly_complex]: ((divide1187762952omplex @ zero_z1746442943omplex @ A) = zero_z1746442943omplex)))). % div_0
thf(fact_16_div__0, axiom,
    ((![A : real]: ((divide_divide_real @ zero_zero_real @ A) = zero_zero_real)))). % div_0
thf(fact_17_divide__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % divide_eq_0_iff
thf(fact_18_divide__eq__0__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = zero_zero_real) = (((A = zero_zero_real)) | ((B = zero_zero_real))))))). % divide_eq_0_iff
thf(fact_19_div__by__0, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % div_by_0
thf(fact_20_div__by__0, axiom,
    ((![A : poly_complex]: ((divide1187762952omplex @ A @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % div_by_0
thf(fact_21_div__by__0, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % div_by_0
thf(fact_22_divide__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((divide1210191872omplex @ C @ A) = (divide1210191872omplex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_left
thf(fact_23_divide__cancel__left, axiom,
    ((![C : real, A : real, B : real]: (((divide_divide_real @ C @ A) = (divide_divide_real @ C @ B)) = (((C = zero_zero_real)) | ((A = B))))))). % divide_cancel_left
thf(fact_24_divide__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((divide1210191872omplex @ A @ C) = (divide1210191872omplex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % divide_cancel_right
thf(fact_25_divide__cancel__right, axiom,
    ((![A : real, C : real, B : real]: (((divide_divide_real @ A @ C) = (divide_divide_real @ B @ C)) = (((C = zero_zero_real)) | ((A = B))))))). % divide_cancel_right
thf(fact_26_pCons_Ohyps_I1_J, axiom,
    (((~ ((d = zero_zero_complex))) | (~ ((ds = zero_z1746442943omplex)))))). % pCons.hyps(1)
thf(fact_27_division__ring__divide__zero, axiom,
    ((![A : complex]: ((divide1210191872omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % division_ring_divide_zero
thf(fact_28_division__ring__divide__zero, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % division_ring_divide_zero
thf(fact_29_div__by__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ one_one_real) = A)))). % div_by_1
thf(fact_30_dm, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ (real_V638595069omplex @ d) @ m)))). % dm
thf(fact_31__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_32__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,
    ((~ ((![X2 : real]: ((ord_less_real @ zero_zero_real @ X2) => ((ord_less_real @ X2 @ (divide_divide_real @ (real_V638595069omplex @ d) @ m)) => (~ ((ord_less_real @ X2 @ 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_33_zero__eq__1__divide__iff, axiom,
    ((![A : real]: ((zero_zero_real = (divide_divide_real @ one_one_real @ A)) = (A = zero_zero_real))))). % zero_eq_1_divide_iff
thf(fact_34_one__divide__eq__0__iff, axiom,
    ((![A : real]: (((divide_divide_real @ one_one_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % one_divide_eq_0_iff
thf(fact_35_eq__divide__eq__1, axiom,
    ((![B : real, A : real]: ((one_one_real = (divide_divide_real @ B @ A)) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % eq_divide_eq_1
thf(fact_36_divide__eq__eq__1, axiom,
    ((![B : real, A : real]: (((divide_divide_real @ B @ A) = one_one_real) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % divide_eq_eq_1
thf(fact_37_divide__self__if, axiom,
    ((![A : complex]: (((A = zero_zero_complex) => ((divide1210191872omplex @ A @ A) = zero_zero_complex)) & ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex)))))). % divide_self_if
thf(fact_38_divide__self__if, axiom,
    ((![A : real]: (((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real)) & ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real)))))). % divide_self_if
thf(fact_39_divide__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % divide_self
thf(fact_40_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_41_one__eq__divide__iff, axiom,
    ((![A : complex, B : complex]: ((one_one_complex = (divide1210191872omplex @ A @ B)) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_42_one__eq__divide__iff, axiom,
    ((![A : real, B : real]: ((one_one_real = (divide_divide_real @ A @ B)) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_43_div__self, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((divide1210191872omplex @ A @ A) = one_one_complex))))). % div_self
thf(fact_44_div__self, axiom,
    ((![A : poly_complex]: ((~ ((A = zero_z1746442943omplex))) => ((divide1187762952omplex @ A @ A) = one_one_poly_complex))))). % div_self
thf(fact_45_div__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % div_self
thf(fact_46_divide__eq__1__iff, axiom,
    ((![A : complex, B : complex]: (((divide1210191872omplex @ A @ B) = one_one_complex) = (((~ ((B = zero_zero_complex)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_47_divide__eq__1__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = one_one_real) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_48_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_49_norm__eq__zero, axiom,
    ((![X : complex]: (((real_V638595069omplex @ X) = zero_zero_real) = (X = zero_zero_complex))))). % norm_eq_zero
thf(fact_50_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_51_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_52_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_53_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_54_of__real__eq__1__iff, axiom,
    ((![X : real]: (((real_V306493662omplex @ X) = one_one_complex) = (X = one_one_real))))). % of_real_eq_1_iff
thf(fact_55_of__real__eq__1__iff, axiom,
    ((![X : real]: (((real_V1205483228l_real @ X) = one_one_real) = (X = one_one_real))))). % of_real_eq_1_iff
thf(fact_56_of__real__1, axiom,
    (((real_V306493662omplex @ one_one_real) = one_one_complex))). % of_real_1
thf(fact_57_of__real__1, axiom,
    (((real_V1205483228l_real @ one_one_real) = one_one_real))). % of_real_1
thf(fact_58_of__real__divide, axiom,
    ((![X : real, Y : real]: ((real_V306493662omplex @ (divide_divide_real @ X @ Y)) = (divide1210191872omplex @ (real_V306493662omplex @ X) @ (real_V306493662omplex @ Y)))))). % of_real_divide
thf(fact_59_of__real__divide, axiom,
    ((![X : real, Y : real]: ((real_V1205483228l_real @ (divide_divide_real @ X @ Y)) = (divide_divide_real @ (real_V1205483228l_real @ X) @ (real_V1205483228l_real @ Y)))))). % of_real_divide
thf(fact_60_zero__less__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_divide_1_iff
thf(fact_61_less__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ A @ B)))))). % less_divide_eq_1_pos
thf(fact_62_less__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ B @ A)))))). % less_divide_eq_1_neg
thf(fact_63_divide__less__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ B @ A)))))). % divide_less_eq_1_pos
thf(fact_64_mem__Collect__eq, axiom,
    ((![A : real, P : real > $o]: ((member_real @ A @ (collect_real @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_65_Collect__mem__eq, axiom,
    ((![A2 : set_real]: ((collect_real @ (^[X3 : real]: (member_real @ X3 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_66_divide__less__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ A @ B)))))). % divide_less_eq_1_neg
thf(fact_67_divide__less__0__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % divide_less_0_1_iff
thf(fact_68_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_69_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_70_one__reorient, axiom,
    ((![X : real]: ((one_one_real = X) = (X = one_one_real))))). % one_reorient
thf(fact_71_norm__divide, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)))))). % norm_divide
thf(fact_72_norm__divide, axiom,
    ((![A : complex, B : complex]: ((real_V638595069omplex @ (divide1210191872omplex @ A @ B)) = (divide_divide_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)))))). % norm_divide
thf(fact_73_linordered__field__no__lb, axiom,
    ((![X4 : real]: (?[Y2 : real]: (ord_less_real @ Y2 @ X4))))). % linordered_field_no_lb
thf(fact_74_linordered__field__no__ub, axiom,
    ((![X4 : real]: (?[X_1 : real]: (ord_less_real @ X4 @ X_1))))). % linordered_field_no_ub
thf(fact_75_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_76_norm__not__less__zero, axiom,
    ((![X : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_77_nonzero__norm__divide, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => ((real_V646646907m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B))))))). % nonzero_norm_divide
thf(fact_78_nonzero__norm__divide, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => ((real_V638595069omplex @ (divide1210191872omplex @ A @ B)) = (divide_divide_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B))))))). % nonzero_norm_divide
thf(fact_79_less__divide__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ A @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ A))))))))). % less_divide_eq_1
thf(fact_80_divide__less__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B @ A)))) | ((((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ A @ B)))) | ((A = zero_zero_real))))))))). % divide_less_eq_1
thf(fact_81_nonzero__of__real__divide, axiom,
    ((![Y : real, X : real]: ((~ ((Y = zero_zero_real))) => ((real_V306493662omplex @ (divide_divide_real @ X @ Y)) = (divide1210191872omplex @ (real_V306493662omplex @ X) @ (real_V306493662omplex @ Y))))))). % nonzero_of_real_divide
thf(fact_82_nonzero__of__real__divide, axiom,
    ((![Y : real, X : real]: ((~ ((Y = zero_zero_real))) => ((real_V1205483228l_real @ (divide_divide_real @ X @ Y)) = (divide_divide_real @ (real_V1205483228l_real @ X) @ (real_V1205483228l_real @ Y))))))). % nonzero_of_real_divide
thf(fact_83_divide__strict__right__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono_neg
thf(fact_84_divide__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono
thf(fact_85_zero__less__divide__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ zero_zero_real @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ zero_zero_real))))))))). % zero_less_divide_iff
thf(fact_86_divide__less__cancel, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ B)))) & ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ A)))) & ((~ ((C = zero_zero_real))))))))))). % divide_less_cancel
thf(fact_87_divide__less__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B @ zero_zero_real)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B))))))))). % divide_less_0_iff
thf(fact_88_divide__pos__pos, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ zero_zero_real @ Y) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X @ Y))))))). % divide_pos_pos
thf(fact_89_divide__pos__neg, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ Y @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ X @ Y) @ zero_zero_real)))))). % divide_pos_neg
thf(fact_90_divide__neg__pos, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y) => (ord_less_real @ (divide_divide_real @ X @ Y) @ zero_zero_real)))))). % divide_neg_pos
thf(fact_91_divide__neg__neg, axiom,
    ((![X : real, Y : real]: ((ord_less_real @ X @ zero_zero_real) => ((ord_less_real @ Y @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X @ Y))))))). % divide_neg_neg
thf(fact_92_right__inverse__eq, axiom,
    ((![B : complex, A : complex]: ((~ ((B = zero_zero_complex))) => (((divide1210191872omplex @ A @ B) = one_one_complex) = (A = B)))))). % right_inverse_eq
thf(fact_93_right__inverse__eq, axiom,
    ((![B : real, A : real]: ((~ ((B = zero_zero_real))) => (((divide_divide_real @ A @ B) = one_one_real) = (A = B)))))). % right_inverse_eq
thf(fact_94_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_95_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_96_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_12 : real]: (P @ X_12)) => ((?[Z : real]: (![X2 : real]: ((P @ X2) => (ord_less_real @ X2 @ Z)))) => (?[S : real]: (![Y3 : real]: ((?[X3 : real]: (((P @ X3)) & ((ord_less_real @ Y3 @ X3)))) = (ord_less_real @ Y3 @ S))))))))). % real_sup_exists
thf(fact_97_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_98_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_99_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_100_assms, axiom,
    ((~ ((?[A3 : complex, L : poly_complex]: ((~ ((A3 = zero_zero_complex))) & ((L = zero_z1746442943omplex) & (p = (pCons_complex @ A3 @ L))))))))). % assms
thf(fact_101_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_102_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_103_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_104_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_105_divide__le__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ A @ B)))))). % divide_le_eq_1_neg
thf(fact_106_divide__le__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ B @ A)))))). % divide_le_eq_1_pos
thf(fact_107_le__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ B @ A)))))). % le_divide_eq_1_neg
thf(fact_108_le__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ A @ B)))))). % le_divide_eq_1_pos
thf(fact_109_norm__le__zero__iff, axiom,
    ((![X : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X) @ zero_zero_real) = (X = zero_zero_real))))). % norm_le_zero_iff
thf(fact_110_norm__le__zero__iff, axiom,
    ((![X : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X) @ zero_zero_real) = (X = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_111_divide__le__0__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % divide_le_0_1_iff
thf(fact_112_zero__le__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_divide_1_iff
thf(fact_113_pCons_Ohyps_I2_J, axiom,
    (((![W : complex]: ((~ ((W = zero_zero_complex))) => ((poly_complex2 @ ds @ W) = zero_zero_complex))) => (ds = zero_z1746442943omplex)))). % pCons.hyps(2)
thf(fact_114_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_115_pCons_Oprems, axiom,
    ((![W2 : complex]: ((~ ((W2 = zero_zero_complex))) => ((poly_complex2 @ (pCons_complex @ d @ ds) @ W2) = zero_zero_complex))))). % pCons.prems
thf(fact_116_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_117_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % le_numeral_extra(4)
thf(fact_118_less__eq__real__def, axiom,
    ((ord_less_eq_real = (^[X3 : real]: (^[Y4 : real]: (((ord_less_real @ X3 @ Y4)) | ((X3 = Y4)))))))). % less_eq_real_def
thf(fact_119_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_120_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_121_divide__le__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ zero_zero_real)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ B))))))))). % divide_le_0_iff
thf(fact_122_divide__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_right_mono
thf(fact_123_zero__le__divide__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ zero_zero_real @ B)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ B @ zero_zero_real))))))))). % zero_le_divide_iff
thf(fact_124_divide__nonneg__nonneg, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_eq_real @ zero_zero_real @ Y) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X @ Y))))))). % divide_nonneg_nonneg
thf(fact_125_divide__nonneg__nonpos, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_eq_real @ Y @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ X @ Y) @ zero_zero_real)))))). % divide_nonneg_nonpos
thf(fact_126_divide__nonpos__nonneg, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ Y) => (ord_less_eq_real @ (divide_divide_real @ X @ Y) @ zero_zero_real)))))). % divide_nonpos_nonneg
thf(fact_127_divide__nonpos__nonpos, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ zero_zero_real) => ((ord_less_eq_real @ Y @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X @ Y))))))). % divide_nonpos_nonpos
thf(fact_128_divide__right__mono__neg, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ B @ C) @ (divide_divide_real @ A @ C))))))). % divide_right_mono_neg
thf(fact_129_norm__ge__zero, axiom,
    ((![X : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X))))). % norm_ge_zero
thf(fact_130_divide__nonpos__pos, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y) => (ord_less_eq_real @ (divide_divide_real @ X @ Y) @ zero_zero_real)))))). % divide_nonpos_pos
thf(fact_131_divide__nonpos__neg, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ zero_zero_real) => ((ord_less_real @ Y @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X @ Y))))))). % divide_nonpos_neg
thf(fact_132_divide__nonneg__pos, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_real @ zero_zero_real @ Y) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X @ Y))))))). % divide_nonneg_pos
thf(fact_133_divide__nonneg__neg, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_real @ Y @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ X @ Y) @ zero_zero_real)))))). % divide_nonneg_neg
thf(fact_134_divide__le__cancel, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ A @ B)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ B @ A))))))))). % divide_le_cancel
thf(fact_135_frac__less2, axiom,
    ((![X : real, Y : real, W3 : real, Z2 : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_eq_real @ X @ Y) => ((ord_less_real @ zero_zero_real @ W3) => ((ord_less_real @ W3 @ Z2) => (ord_less_real @ (divide_divide_real @ X @ Z2) @ (divide_divide_real @ Y @ W3))))))))). % frac_less2
thf(fact_136_frac__less, axiom,
    ((![X : real, Y : real, W3 : real, Z2 : real]: ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_real @ X @ Y) => ((ord_less_real @ zero_zero_real @ W3) => ((ord_less_eq_real @ W3 @ Z2) => (ord_less_real @ (divide_divide_real @ X @ Z2) @ (divide_divide_real @ Y @ W3))))))))). % frac_less
thf(fact_137_frac__le, axiom,
    ((![Y : real, X : real, W3 : real, Z2 : real]: ((ord_less_eq_real @ zero_zero_real @ Y) => ((ord_less_eq_real @ X @ Y) => ((ord_less_real @ zero_zero_real @ W3) => ((ord_less_eq_real @ W3 @ Z2) => (ord_less_eq_real @ (divide_divide_real @ X @ Z2) @ (divide_divide_real @ Y @ W3))))))))). % frac_le
thf(fact_138_le__divide__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ A @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ B @ A))))))))). % le_divide_eq_1
thf(fact_139_divide__le__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ A)))) | ((((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ A @ B)))) | ((A = zero_zero_real))))))))). % divide_le_eq_1
thf(fact_140_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_real = (pCons_real @ one_one_real @ zero_zero_poly_real)))). % one_poly_eq_simps(1)
thf(fact_141_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_complex = (pCons_complex @ one_one_complex @ zero_z1746442943omplex)))). % one_poly_eq_simps(1)
thf(fact_142_one__poly__eq__simps_I2_J, axiom,
    (((pCons_real @ one_one_real @ zero_zero_poly_real) = one_one_poly_real))). % one_poly_eq_simps(2)
thf(fact_143_one__poly__eq__simps_I2_J, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % one_poly_eq_simps(2)
thf(fact_144_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_145_pCons__0__0, axiom,
    (((pCons_real @ zero_zero_real @ zero_zero_poly_real) = zero_zero_poly_real))). % pCons_0_0
thf(fact_146_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_147_pCons__eq__iff, axiom,
    ((![A : complex, P2 : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A @ P2) = (pCons_complex @ B @ Q)) = (((A = B)) & ((P2 = Q))))))). % pCons_eq_iff
thf(fact_148__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_149_pCons__eq__0__iff, axiom,
    ((![A : real, P2 : poly_real]: (((pCons_real @ A @ P2) = zero_zero_poly_real) = (((A = zero_zero_real)) & ((P2 = zero_zero_poly_real))))))). % pCons_eq_0_iff
thf(fact_150_pCons__eq__0__iff, axiom,
    ((![A : poly_complex, P2 : poly_poly_complex]: (((pCons_poly_complex @ A @ P2) = zero_z1040703943omplex) = (((A = zero_z1746442943omplex)) & ((P2 = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_151_pCons__eq__0__iff, axiom,
    ((![A : complex, P2 : poly_complex]: (((pCons_complex @ A @ P2) = zero_z1746442943omplex) = (((A = zero_zero_complex)) & ((P2 = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_152_poly__0, axiom,
    ((![X : real]: ((poly_real2 @ zero_zero_poly_real @ X) = zero_zero_real)))). % poly_0
thf(fact_153_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_154_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_155_poly__1, axiom,
    ((![X : complex]: ((poly_complex2 @ one_one_poly_complex @ X) = one_one_complex)))). % poly_1
thf(fact_156_poly__1, axiom,
    ((![X : real]: ((poly_real2 @ one_one_poly_real @ X) = one_one_real)))). % poly_1
thf(fact_157__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,
    ((![W2 : complex]: ((~ ((W2 = zero_zero_complex))) => ((poly_complex2 @ cs @ W2) = zero_zero_complex))))). % \<open>\<forall>w. w \<noteq> 0 \<longrightarrow> poly cs w = 0\<close>
thf(fact_158_poly__minimum__modulus, axiom,
    ((![P2 : poly_complex]: (?[Z3 : complex]: (![W2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P2 @ Z3)) @ (real_V638595069omplex @ (poly_complex2 @ P2 @ W2)))))))). % poly_minimum_modulus
thf(fact_159_poly__minimum__modulus__disc, axiom,
    ((![R : real, P2 : poly_complex]: (?[Z3 : complex]: (![W2 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ W2) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P2 @ Z3)) @ (real_V638595069omplex @ (poly_complex2 @ P2 @ W2))))))))). % poly_minimum_modulus_disc
thf(fact_160_poly__all__0__iff__0, axiom,
    ((![P2 : poly_complex]: ((![X3 : complex]: ((poly_complex2 @ P2 @ X3) = zero_zero_complex)) = (P2 = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_161_poly__all__0__iff__0, axiom,
    ((![P2 : poly_real]: ((![X3 : real]: ((poly_real2 @ P2 @ X3) = zero_zero_real)) = (P2 = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_162_poly__all__0__iff__0, axiom,
    ((![P2 : poly_poly_complex]: ((![X3 : poly_complex]: ((poly_poly_complex2 @ P2 @ X3) = zero_z1746442943omplex)) = (P2 = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_163_complete__real, axiom,
    ((![S2 : set_real]: ((?[X4 : real]: (member_real @ X4 @ S2)) => ((?[Z : real]: (![X2 : real]: ((member_real @ X2 @ S2) => (ord_less_eq_real @ X2 @ Z)))) => (?[Y2 : real]: ((![X4 : real]: ((member_real @ X4 @ S2) => (ord_less_eq_real @ X4 @ Y2))) & (![Z : real]: ((![X2 : real]: ((member_real @ X2 @ S2) => (ord_less_eq_real @ X2 @ Z))) => (ord_less_eq_real @ Y2 @ Z)))))))))). % complete_real
thf(fact_164_poly__eq__poly__eq__iff, axiom,
    ((![P2 : poly_complex, Q : poly_complex]: (((poly_complex2 @ P2) = (poly_complex2 @ Q)) = (P2 = Q))))). % poly_eq_poly_eq_iff
thf(fact_165_poly__eq__poly__eq__iff, axiom,
    ((![P2 : poly_real, Q : poly_real]: (((poly_real2 @ P2) = (poly_real2 @ Q)) = (P2 = Q))))). % poly_eq_poly_eq_iff
thf(fact_166_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_real]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : real]: ((ord_less_eq_real @ (real_V646646907m_real @ Z) @ R) => (ord_less_eq_real @ (real_V646646907m_real @ (poly_real2 @ P2 @ Z)) @ M)))))))). % poly_bound_exists
thf(fact_167_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_complex]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P2 @ Z)) @ M)))))))). % poly_bound_exists
thf(fact_168_poly__infinity, axiom,
    ((![P2 : poly_real, D : real, A : real]: ((~ ((P2 = zero_zero_poly_real))) => (?[R2 : real]: (![Z : real]: ((ord_less_eq_real @ R2 @ (real_V646646907m_real @ Z)) => (ord_less_eq_real @ D @ (real_V646646907m_real @ (poly_real2 @ (pCons_real @ A @ P2) @ Z)))))))))). % poly_infinity
thf(fact_169_poly__infinity, axiom,
    ((![P2 : poly_complex, D : real, A : complex]: ((~ ((P2 = zero_z1746442943omplex))) => (?[R2 : real]: (![Z : complex]: ((ord_less_eq_real @ R2 @ (real_V638595069omplex @ Z)) => (ord_less_eq_real @ D @ (real_V638595069omplex @ (poly_complex2 @ (pCons_complex @ A @ P2) @ Z)))))))))). % poly_infinity
thf(fact_170_divide__poly__0, axiom,
    ((![F : poly_complex]: ((divide1187762952omplex @ F @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % divide_poly_0
thf(fact_171_pCons__cases, axiom,
    ((![P2 : poly_complex]: (~ ((![A4 : complex, Q2 : poly_complex]: (~ ((P2 = (pCons_complex @ A4 @ Q2)))))))))). % pCons_cases
thf(fact_172_pderiv_Ocases, axiom,
    ((![X : poly_complex]: (~ ((![A4 : complex, P3 : poly_complex]: (~ ((X = (pCons_complex @ A4 @ P3)))))))))). % pderiv.cases
thf(fact_173_pderiv_Oinduct, axiom,
    ((![P : poly_complex > $o, A0 : poly_complex]: ((![A4 : complex, P3 : poly_complex]: (((~ ((P3 = zero_z1746442943omplex))) => (P @ P3)) => (P @ (pCons_complex @ A4 @ P3)))) => (P @ A0))))). % pderiv.induct
thf(fact_174_poly__induct2, axiom,
    ((![P : poly_complex > poly_complex > $o, P2 : poly_complex, Q : poly_complex]: ((P @ zero_z1746442943omplex @ zero_z1746442943omplex) => ((![A4 : complex, P3 : poly_complex, B2 : complex, Q2 : poly_complex]: ((P @ P3 @ Q2) => (P @ (pCons_complex @ A4 @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P @ P2 @ Q)))))). % poly_induct2
thf(fact_175_pCons__induct, axiom,
    ((![P : poly_real > $o, P2 : poly_real]: ((P @ zero_zero_poly_real) => ((![A4 : real, P3 : poly_real]: (((~ ((A4 = zero_zero_real))) | (~ ((P3 = zero_zero_poly_real)))) => ((P @ P3) => (P @ (pCons_real @ A4 @ P3))))) => (P @ P2)))))). % pCons_induct
thf(fact_176_pCons__induct, axiom,
    ((![P : poly_poly_complex > $o, P2 : poly_poly_complex]: ((P @ zero_z1040703943omplex) => ((![A4 : poly_complex, P3 : poly_poly_complex]: (((~ ((A4 = zero_z1746442943omplex))) | (~ ((P3 = zero_z1040703943omplex)))) => ((P @ P3) => (P @ (pCons_poly_complex @ A4 @ P3))))) => (P @ P2)))))). % pCons_induct
thf(fact_177_pCons__induct, axiom,
    ((![P : poly_complex > $o, P2 : poly_complex]: ((P @ zero_z1746442943omplex) => ((![A4 : complex, P3 : poly_complex]: (((~ ((A4 = zero_zero_complex))) | (~ ((P3 = zero_z1746442943omplex)))) => ((P @ P3) => (P @ (pCons_complex @ A4 @ P3))))) => (P @ P2)))))). % pCons_induct
thf(fact_178_pCons__one, axiom,
    (((pCons_real @ one_one_real @ zero_zero_poly_real) = one_one_poly_real))). % pCons_one
thf(fact_179_pCons__one, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % pCons_one
thf(fact_180_nc, axiom,
    ((fundam1158420650omplex @ (poly_complex2 @ (pCons_complex @ c @ cs))))). % nc
thf(fact_181__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_182_poly__IVT__pos, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P2 @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P2 @ B)) => (?[X2 : real]: ((ord_less_real @ A @ X2) & ((ord_less_real @ X2 @ B) & ((poly_real2 @ P2 @ X2) = zero_zero_real)))))))))). % poly_IVT_pos

% Conjectures (1)
thf(conj_0, conjecture,
    ((~ (((real_V306493662omplex @ x) = zero_zero_complex))))).
