% 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_457__5372398_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:30:17.593

% Could-be-implicit typings (5)
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Num__Onum, type,
    num : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (46)
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_real : real > real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex, type,
    minus_minus_complex : complex > complex > complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex, type,
    plus_plus_complex : complex > complex > complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum, type,
    plus_plus_num : num > num > num).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > 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__Nat__Onat, type,
    times_times_nat : nat > nat > nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum, type,
    times_times_num : num > num > num).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal, type,
    times_times_real : real > real > real).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Complex__Ocomplex, type,
    uminus1204672759omplex : complex > complex).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal, type,
    uminus_uminus_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__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex, type,
    semiri356525583omplex : nat > complex).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal, type,
    semiri2110766477t_real : nat > real).
thf(sy_c_Num_Onum_OBit0, type,
    bit0 : num > num).
thf(sy_c_Num_Onum_OOne, type,
    one : num).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex, type,
    numera632737353omplex : num > complex).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat, type,
    numeral_numeral_nat : num > nat).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal, type,
    numeral_numeral_real : num > real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum, type,
    ord_less_num : num > num > $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__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum, type,
    ord_less_eq_num : num > num > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat, type,
    order_769474267at_nat : (nat > nat) > $o).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_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_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex, type,
    divide1210191872omplex : complex > complex > complex).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_v_N1____, type,
    n1 : nat).
thf(sy_v_N2____, type,
    n2 : nat).
thf(sy_v_d____, type,
    d : real).
thf(sy_v_f____, type,
    f : nat > nat).
thf(sy_v_g____, type,
    g : nat > complex).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_r, type,
    r : real).
thf(sy_v_s____, type,
    s : real).
thf(sy_v_w____, type,
    w : complex).
thf(sy_v_z____, type,
    z : complex).

% Relevant facts (198)
thf(fact_0_ath2, axiom,
    ((![A : real, B : real, C : real, M : real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ B @ M)) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ A @ M)) @ C)))))). % ath2
thf(fact_1_fz_I1_J, axiom,
    ((order_769474267at_nat @ f))). % fz(1)
thf(fact_2__092_060open_062_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_A_092_060le_062_A_092_060bar_062cmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_092_060bar_062_A_L_Acmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_A_N_Apoly_Ap_Az_J_092_060close_062, axiom,
    ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2))))) @ (uminus_uminus_real @ s))) @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2)))) @ (poly_complex2 @ p @ z))))))). % \<open>\<bar>cmod (poly p z) - - s\<bar> \<le> \<bar>cmod (poly p (g (f (N1 + N2)))) - - s\<bar> + cmod (poly p (g (f (N1 + N2))) - poly p z)\<close>
thf(fact_3__092_060open_062_092_060And_062n_O_A_N_As_A_092_060le_062_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_092_060close_062, axiom,
    ((![N : nat]: (ord_less_eq_real @ (uminus_uminus_real @ s) @ (real_V638595069omplex @ (poly_complex2 @ p @ (g @ N))))))). % \<open>\<And>n. - s \<le> cmod (poly p (g n))\<close>
thf(fact_4_g_I1_J, axiom,
    ((![N2 : nat]: (ord_less_eq_real @ (real_V638595069omplex @ (g @ N2)) @ r)))). % g(1)
thf(fact_5_th31, axiom,
    ((ord_less_eq_real @ (uminus_uminus_real @ s) @ (real_V638595069omplex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2)))))))). % th31
thf(fact_6_th22, axiom,
    ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2))))) @ (real_V638595069omplex @ (poly_complex2 @ p @ z)))) @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2)))) @ (poly_complex2 @ p @ z)))))). % th22
thf(fact_7_th2, axiom,
    ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2)))) @ (poly_complex2 @ p @ z))) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))). % th2
thf(fact_8_thc1, axiom,
    ((ord_less_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2))))) @ (uminus_uminus_real @ s))) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))). % thc1
thf(fact_9_real__average__minus__first, axiom,
    ((![A : real, B : real]: ((minus_minus_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))) @ A) = (divide_divide_real @ (minus_minus_real @ B @ A) @ (numeral_numeral_real @ (bit0 @ one))))))). % real_average_minus_first
thf(fact_10_real__average__minus__second, axiom,
    ((![B : real, A : real]: ((minus_minus_real @ (divide_divide_real @ (plus_plus_real @ B @ A) @ (numeral_numeral_real @ (bit0 @ one))) @ A) = (divide_divide_real @ (minus_minus_real @ B @ A) @ (numeral_numeral_real @ (bit0 @ one))))))). % real_average_minus_second
thf(fact_11_norm__divide__numeral, axiom,
    ((![A : complex, W : num]: ((real_V638595069omplex @ (divide1210191872omplex @ A @ (numera632737353omplex @ W))) = (divide_divide_real @ (real_V638595069omplex @ A) @ (numeral_numeral_real @ W)))))). % norm_divide_numeral
thf(fact_12_norm__divide__numeral, axiom,
    ((![A : real, W : num]: ((real_V646646907m_real @ (divide_divide_real @ A @ (numeral_numeral_real @ W))) = (divide_divide_real @ (real_V646646907m_real @ A) @ (numeral_numeral_real @ W)))))). % norm_divide_numeral
thf(fact_13_norm__mult__numeral1, axiom,
    ((![W : num, A : complex]: ((real_V638595069omplex @ (times_times_complex @ (numera632737353omplex @ W) @ A)) = (times_times_real @ (numeral_numeral_real @ W) @ (real_V638595069omplex @ A)))))). % norm_mult_numeral1
thf(fact_14_norm__mult__numeral1, axiom,
    ((![W : num, A : real]: ((real_V646646907m_real @ (times_times_real @ (numeral_numeral_real @ W) @ A)) = (times_times_real @ (numeral_numeral_real @ W) @ (real_V646646907m_real @ A)))))). % norm_mult_numeral1
thf(fact_15_norm__mult__numeral2, axiom,
    ((![A : complex, W : num]: ((real_V638595069omplex @ (times_times_complex @ A @ (numera632737353omplex @ W))) = (times_times_real @ (real_V638595069omplex @ A) @ (numeral_numeral_real @ W)))))). % norm_mult_numeral2
thf(fact_16_norm__mult__numeral2, axiom,
    ((![A : real, W : num]: ((real_V646646907m_real @ (times_times_real @ A @ (numeral_numeral_real @ W))) = (times_times_real @ (real_V646646907m_real @ A) @ (numeral_numeral_real @ W)))))). % norm_mult_numeral2
thf(fact_17_divide__le__eq__numeral1_I2_J, axiom,
    ((![B : real, W : num, A : real]: ((ord_less_eq_real @ (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ W))) @ A) = (ord_less_eq_real @ (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ W))) @ B))))). % divide_le_eq_numeral1(2)
thf(fact_18_le__divide__eq__numeral1_I2_J, axiom,
    ((![A : real, B : real, W : num]: ((ord_less_eq_real @ A @ (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ W)))) = (ord_less_eq_real @ B @ (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ W)))))))). % le_divide_eq_numeral1(2)
thf(fact_19_norm__neg__numeral, axiom,
    ((![W : num]: ((real_V638595069omplex @ (uminus1204672759omplex @ (numera632737353omplex @ W))) = (numeral_numeral_real @ W))))). % norm_neg_numeral
thf(fact_20_norm__neg__numeral, axiom,
    ((![W : num]: ((real_V646646907m_real @ (uminus_uminus_real @ (numeral_numeral_real @ W))) = (numeral_numeral_real @ W))))). % norm_neg_numeral
thf(fact_21_wr, axiom,
    ((ord_less_eq_real @ (real_V638595069omplex @ w) @ r))). % wr
thf(fact_22_divide__le__eq__numeral1_I1_J, axiom,
    ((![B : real, W : num, A : real]: ((ord_less_eq_real @ (divide_divide_real @ B @ (numeral_numeral_real @ W)) @ A) = (ord_less_eq_real @ B @ (times_times_real @ A @ (numeral_numeral_real @ W))))))). % divide_le_eq_numeral1(1)
thf(fact_23_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_real @ M) = (numeral_numeral_real @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_24_ath, axiom,
    ((![M : real, X : real, E : real]: ((ord_less_eq_real @ M @ X) => ((ord_less_real @ X @ (plus_plus_real @ M @ E)) => (ord_less_real @ (abs_abs_real @ (minus_minus_real @ X @ M)) @ E)))))). % ath
thf(fact_25_s, axiom,
    ((![Y : real]: ((?[X2 : real]: (((?[Z : complex]: (((ord_less_eq_real @ (real_V638595069omplex @ Z) @ r)) & (((real_V638595069omplex @ (poly_complex2 @ p @ Z)) = (uminus_uminus_real @ X2)))))) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ s))))). % s
thf(fact_26__092_060open_062N1_A_L_AN2_A_092_060le_062_Af_A_IN1_A_L_AN2_J_092_060close_062, axiom,
    ((ord_less_eq_nat @ (plus_plus_nat @ n1 @ n2) @ (f @ (plus_plus_nat @ n1 @ n2))))). % \<open>N1 + N2 \<le> f (N1 + N2)\<close>
thf(fact_27_True, axiom,
    ((ord_less_eq_real @ zero_zero_real @ r))). % True
thf(fact_28_mth1, axiom,
    ((?[X3 : real, Z2 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z2) @ r) & ((real_V638595069omplex @ (poly_complex2 @ p @ Z2)) = (uminus_uminus_real @ X3)))))). % mth1
thf(fact_29_numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (ord_less_eq_num @ M @ N))))). % numeral_le_iff
thf(fact_30_numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (ord_less_eq_num @ M @ N))))). % numeral_le_iff
thf(fact_31_numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (ord_less_num @ M @ N))))). % numeral_less_iff
thf(fact_32_numeral__times__numeral, axiom,
    ((![M : num, N : num]: ((times_times_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (numeral_numeral_real @ (times_times_num @ M @ N)))))). % numeral_times_numeral
thf(fact_33_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z3 : real]: ((times_times_real @ (numeral_numeral_real @ V) @ (times_times_real @ (numeral_numeral_real @ W) @ Z3)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ V @ W)) @ Z3))))). % mult_numeral_left_semiring_numeral
thf(fact_34_numeral__plus__numeral, axiom,
    ((![M : num, N : num]: ((plus_plus_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (plus_plus_num @ M @ N)))))). % numeral_plus_numeral
thf(fact_35_numeral__plus__numeral, axiom,
    ((![M : num, N : num]: ((plus_plus_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (numeral_numeral_real @ (plus_plus_num @ M @ N)))))). % numeral_plus_numeral
thf(fact_36_add__numeral__left, axiom,
    ((![V : num, W : num, Z3 : nat]: ((plus_plus_nat @ (numeral_numeral_nat @ V) @ (plus_plus_nat @ (numeral_numeral_nat @ W) @ Z3)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ V @ W)) @ Z3))))). % add_numeral_left
thf(fact_37_add__numeral__left, axiom,
    ((![V : num, W : num, Z3 : real]: ((plus_plus_real @ (numeral_numeral_real @ V) @ (plus_plus_real @ (numeral_numeral_real @ W) @ Z3)) = (plus_plus_real @ (numeral_numeral_real @ (plus_plus_num @ V @ W)) @ Z3))))). % add_numeral_left
thf(fact_38_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (uminus_uminus_real @ (numeral_numeral_real @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_39_num__double, axiom,
    ((![N : num]: ((times_times_num @ (bit0 @ one) @ N) = (bit0 @ N))))). % num_double
thf(fact_40_abs__numeral, axiom,
    ((![N : num]: ((abs_abs_real @ (numeral_numeral_real @ N)) = (numeral_numeral_real @ N))))). % abs_numeral
thf(fact_41_norm__minus__cancel, axiom,
    ((![X : complex]: ((real_V638595069omplex @ (uminus1204672759omplex @ X)) = (real_V638595069omplex @ X))))). % norm_minus_cancel
thf(fact_42_norm__minus__cancel, axiom,
    ((![X : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X)) = (real_V646646907m_real @ X))))). % norm_minus_cancel
thf(fact_43_abs__norm__cancel, axiom,
    ((![A : complex]: ((abs_abs_real @ (real_V638595069omplex @ A)) = (real_V638595069omplex @ A))))). % abs_norm_cancel
thf(fact_44_abs__norm__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (real_V646646907m_real @ A)) = (real_V646646907m_real @ A))))). % abs_norm_cancel
thf(fact_45_mth2, axiom,
    ((?[Z2 : real]: (![X4 : real]: ((?[Za : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Za) @ r) & ((real_V638595069omplex @ (poly_complex2 @ p @ Za)) = (uminus_uminus_real @ X4)))) => (ord_less_real @ X4 @ Z2)))))). % mth2
thf(fact_46__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_O_A_092_060forall_062y_O_A_I_092_060exists_062x_O_A_I_092_060exists_062z_O_Acmod_Az_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_092_060and_062_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![S : real]: (~ ((![Y : real]: ((?[X2 : real]: (((?[Z : complex]: (((ord_less_eq_real @ (real_V638595069omplex @ Z) @ r)) & (((real_V638595069omplex @ (poly_complex2 @ p @ Z)) = (uminus_uminus_real @ X2)))))) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S)))))))))). % \<open>\<And>thesis. (\<And>s. \<forall>y. (\<exists>x. (\<exists>z. cmod z \<le> r \<and> cmod (poly p z) = - x) \<and> y < x) = (y < s) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_47__092_060open_062_092_060exists_062s_O_A_092_060forall_062y_O_A_I_092_060exists_062x_O_A_I_092_060exists_062z_O_Acmod_Az_A_092_060le_062_Ar_A_092_060and_062_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_092_060and_062_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_092_060close_062, axiom,
    ((?[S : real]: (![Y : real]: ((?[X2 : real]: (((?[Z : complex]: (((ord_less_eq_real @ (real_V638595069omplex @ Z) @ r)) & (((real_V638595069omplex @ (poly_complex2 @ p @ Z)) = (uminus_uminus_real @ X2)))))) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S)))))). % \<open>\<exists>s. \<forall>y. (\<exists>x. (\<exists>z. cmod z \<le> r \<and> cmod (poly p z) = - x) \<and> y < x) = (y < s)\<close>
thf(fact_48_th0, axiom,
    ((![A : real, E2 : real, B : real, M : real]: ((ord_less_real @ A @ E2) => ((ord_less_real @ (abs_abs_real @ (minus_minus_real @ B @ M)) @ E2) => (~ ((ord_less_eq_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ E2) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ B @ M)) @ A))))))))). % th0
thf(fact_49_s1m, axiom,
    ((![Z3 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z3) @ r) => (ord_less_eq_real @ (uminus_uminus_real @ s) @ (real_V638595069omplex @ (poly_complex2 @ p @ Z3))))))). % s1m
thf(fact_50_distrib__right__numeral, axiom,
    ((![A : nat, B : nat, V : num]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ (numeral_numeral_nat @ V)) = (plus_plus_nat @ (times_times_nat @ A @ (numeral_numeral_nat @ V)) @ (times_times_nat @ B @ (numeral_numeral_nat @ V))))))). % distrib_right_numeral
thf(fact_51_distrib__right__numeral, axiom,
    ((![A : real, B : real, V : num]: ((times_times_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ V)) = (plus_plus_real @ (times_times_real @ A @ (numeral_numeral_real @ V)) @ (times_times_real @ B @ (numeral_numeral_real @ V))))))). % distrib_right_numeral
thf(fact_52_distrib__left__numeral, axiom,
    ((![V : num, B : nat, C : nat]: ((times_times_nat @ (numeral_numeral_nat @ V) @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ V) @ B) @ (times_times_nat @ (numeral_numeral_nat @ V) @ C)))))). % distrib_left_numeral
thf(fact_53_distrib__left__numeral, axiom,
    ((![V : num, B : real, C : real]: ((times_times_real @ (numeral_numeral_real @ V) @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ V) @ B) @ (times_times_real @ (numeral_numeral_real @ V) @ C)))))). % distrib_left_numeral
thf(fact_54_neg__numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (ord_less_eq_num @ N @ M))))). % neg_numeral_le_iff
thf(fact_55_right__diff__distrib__numeral, axiom,
    ((![V : num, B : complex, C : complex]: ((times_times_complex @ (numera632737353omplex @ V) @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (times_times_complex @ (numera632737353omplex @ V) @ B) @ (times_times_complex @ (numera632737353omplex @ V) @ C)))))). % right_diff_distrib_numeral
thf(fact_56_right__diff__distrib__numeral, axiom,
    ((![V : num, B : real, C : real]: ((times_times_real @ (numeral_numeral_real @ V) @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ V) @ B) @ (times_times_real @ (numeral_numeral_real @ V) @ C)))))). % right_diff_distrib_numeral
thf(fact_57_left__diff__distrib__numeral, axiom,
    ((![A : complex, B : complex, V : num]: ((times_times_complex @ (minus_minus_complex @ A @ B) @ (numera632737353omplex @ V)) = (minus_minus_complex @ (times_times_complex @ A @ (numera632737353omplex @ V)) @ (times_times_complex @ B @ (numera632737353omplex @ V))))))). % left_diff_distrib_numeral
thf(fact_58_left__diff__distrib__numeral, axiom,
    ((![A : real, B : real, V : num]: ((times_times_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ V)) = (minus_minus_real @ (times_times_real @ A @ (numeral_numeral_real @ V)) @ (times_times_real @ B @ (numeral_numeral_real @ V))))))). % left_diff_distrib_numeral
thf(fact_59_neg__numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (ord_less_num @ N @ M))))). % neg_numeral_less_iff
thf(fact_60_mult__neg__numeral__simps_I1_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (numeral_numeral_real @ (times_times_num @ M @ N)))))). % mult_neg_numeral_simps(1)
thf(fact_61_mult__neg__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N)) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(2)
thf(fact_62_mult__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(3)
thf(fact_63_add__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (uminus_uminus_real @ (plus_plus_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N))))))). % add_neg_numeral_simps(3)
thf(fact_64_abs__neg__numeral, axiom,
    ((![N : num]: ((abs_abs_real @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (numeral_numeral_real @ N))))). % abs_neg_numeral
thf(fact_65_norm__numeral, axiom,
    ((![W : num]: ((real_V638595069omplex @ (numera632737353omplex @ W)) = (numeral_numeral_real @ W))))). % norm_numeral
thf(fact_66_norm__numeral, axiom,
    ((![W : num]: ((real_V646646907m_real @ (numeral_numeral_real @ W)) = (numeral_numeral_real @ W))))). % norm_numeral
thf(fact_67_N1, axiom,
    ((![N2 : nat]: ((ord_less_eq_nat @ n1 @ N2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ N2)) @ z)) @ d))))). % N1
thf(fact_68_le__divide__eq__numeral1_I1_J, axiom,
    ((![A : real, B : real, W : num]: ((ord_less_eq_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ W))) = (ord_less_eq_real @ (times_times_real @ A @ (numeral_numeral_real @ W)) @ B))))). % le_divide_eq_numeral1(1)
thf(fact_69_less__divide__eq__numeral1_I1_J, axiom,
    ((![A : real, B : real, W : num]: ((ord_less_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ W))) = (ord_less_real @ (times_times_real @ A @ (numeral_numeral_real @ W)) @ B))))). % less_divide_eq_numeral1(1)
thf(fact_70_divide__less__eq__numeral1_I1_J, axiom,
    ((![B : real, W : num, A : real]: ((ord_less_real @ (divide_divide_real @ B @ (numeral_numeral_real @ W)) @ A) = (ord_less_real @ B @ (times_times_real @ A @ (numeral_numeral_real @ W))))))). % divide_less_eq_numeral1(1)
thf(fact_71_less__divide__eq__numeral1_I2_J, axiom,
    ((![A : real, B : real, W : num]: ((ord_less_real @ A @ (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ W)))) = (ord_less_real @ B @ (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ W)))))))). % less_divide_eq_numeral1(2)
thf(fact_72_divide__less__eq__numeral1_I2_J, axiom,
    ((![B : real, W : num, A : real]: ((ord_less_real @ (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ W))) @ A) = (ord_less_real @ (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ W))) @ B))))). % divide_less_eq_numeral1(2)
thf(fact_73_fz_I2_J, axiom,
    ((![E3 : real]: ((ord_less_real @ zero_zero_real @ E3) => (?[N3 : nat]: (![N2 : nat]: ((ord_less_eq_nat @ N3 @ N2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ N2)) @ z)) @ E3)))))))). % fz(2)
thf(fact_74_e, axiom,
    ((ord_less_real @ zero_zero_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s)))))). % e
thf(fact_75_N2, axiom,
    ((ord_less_real @ (divide_divide_real @ (numeral_numeral_real @ (bit0 @ one)) @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s)))) @ (semiri2110766477t_real @ n2)))). % N2
thf(fact_76_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z4 : real]: (![X3 : real]: ((P @ X3) => (ord_less_real @ X3 @ Z4)))) => (?[S : real]: (![Y : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_77_le__num__One__iff, axiom,
    ((![X : num]: ((ord_less_eq_num @ X @ one) = (X = one))))). % le_num_One_iff
thf(fact_78_real__norm__def, axiom,
    ((real_V646646907m_real = abs_abs_real))). % real_norm_def
thf(fact_79_not__numeral__less__neg__numeral, axiom,
    ((![M : num, N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % not_numeral_less_neg_numeral
thf(fact_80_neg__numeral__less__numeral, axiom,
    ((![M : num, N : num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N))))). % neg_numeral_less_numeral
thf(fact_81_norm__mult__less, axiom,
    ((![X : complex, R : real, Y2 : complex, S2 : real]: ((ord_less_real @ (real_V638595069omplex @ X) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y2) @ S2) => (ord_less_real @ (real_V638595069omplex @ (times_times_complex @ X @ Y2)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_82_norm__mult__less, axiom,
    ((![X : real, R : real, Y2 : real, S2 : real]: ((ord_less_real @ (real_V646646907m_real @ X) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y2) @ S2) => (ord_less_real @ (real_V646646907m_real @ (times_times_real @ X @ Y2)) @ (times_times_real @ R @ S2))))))). % norm_mult_less
thf(fact_83_norm__triangle__lt, axiom,
    ((![X : complex, Y2 : complex, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y2)) @ E) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_84_norm__triangle__lt, axiom,
    ((![X : real, Y2 : real, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y2)) @ E) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_85_norm__add__less, axiom,
    ((![X : complex, R : real, Y2 : complex, S2 : real]: ((ord_less_real @ (real_V638595069omplex @ X) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y2) @ S2) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X @ Y2)) @ (plus_plus_real @ R @ S2))))))). % norm_add_less
thf(fact_86_norm__add__less, axiom,
    ((![X : real, R : real, Y2 : real, S2 : real]: ((ord_less_real @ (real_V646646907m_real @ X) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y2) @ S2) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X @ Y2)) @ (plus_plus_real @ R @ S2))))))). % norm_add_less
thf(fact_87_norm__diff__triangle__less, axiom,
    ((![X : complex, Y2 : complex, E1 : real, Z3 : complex, E2 : real]: ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ X @ Y2)) @ E1) => ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ Y2 @ Z3)) @ E2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ X @ Z3)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_less
thf(fact_88_norm__diff__triangle__less, axiom,
    ((![X : real, Y2 : real, E1 : real, Z3 : real, E2 : real]: ((ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ X @ Y2)) @ E1) => ((ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ Y2 @ Z3)) @ E2) => (ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ X @ Z3)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_less
thf(fact_89_is__num__normalize_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % is_num_normalize(1)
thf(fact_90_is__num__normalize_I8_J, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % is_num_normalize(8)
thf(fact_91_numeral__neq__neg__numeral, axiom,
    ((![M : num, N : num]: (~ (((numeral_numeral_real @ M) = (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % numeral_neq_neg_numeral
thf(fact_92_neg__numeral__neq__numeral, axiom,
    ((![M : num, N : num]: (~ (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (numeral_numeral_real @ N))))))). % neg_numeral_neq_numeral
thf(fact_93_norm__minus__commute, axiom,
    ((![A : complex, B : complex]: ((real_V638595069omplex @ (minus_minus_complex @ A @ B)) = (real_V638595069omplex @ (minus_minus_complex @ B @ A)))))). % norm_minus_commute
thf(fact_94_norm__minus__commute, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (minus_minus_real @ A @ B)) = (real_V646646907m_real @ (minus_minus_real @ B @ A)))))). % norm_minus_commute
thf(fact_95_not__numeral__le__neg__numeral, axiom,
    ((![M : num, N : num]: (~ ((ord_less_eq_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N)))))))). % not_numeral_le_neg_numeral
thf(fact_96_neg__numeral__le__numeral, axiom,
    ((![M : num, N : num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N))))). % neg_numeral_le_numeral
thf(fact_97_numeral__Bit0, axiom,
    ((![N : num]: ((numeral_numeral_nat @ (bit0 @ N)) = (plus_plus_nat @ (numeral_numeral_nat @ N) @ (numeral_numeral_nat @ N)))))). % numeral_Bit0
thf(fact_98_numeral__Bit0, axiom,
    ((![N : num]: ((numeral_numeral_real @ (bit0 @ N)) = (plus_plus_real @ (numeral_numeral_real @ N) @ (numeral_numeral_real @ N)))))). % numeral_Bit0
thf(fact_99_mult__numeral__1__right, axiom,
    ((![A : real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A)))). % mult_numeral_1_right
thf(fact_100_mult__numeral__1, axiom,
    ((![A : real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A)))). % mult_numeral_1
thf(fact_101_divide__numeral__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ (numeral_numeral_real @ one)) = A)))). % divide_numeral_1
thf(fact_102_norm__mult, axiom,
    ((![X : complex, Y2 : complex]: ((real_V638595069omplex @ (times_times_complex @ X @ Y2)) = (times_times_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y2)))))). % norm_mult
thf(fact_103_norm__mult, axiom,
    ((![X : real, Y2 : real]: ((real_V646646907m_real @ (times_times_real @ X @ Y2)) = (times_times_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y2)))))). % norm_mult
thf(fact_104_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_105_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_106_mult__1s__ring__1_I1_J, axiom,
    ((![B : real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ one)) @ B) = (uminus_uminus_real @ B))))). % mult_1s_ring_1(1)
thf(fact_107_mult__1s__ring__1_I2_J, axiom,
    ((![B : real]: ((times_times_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ one))) = (uminus_uminus_real @ B))))). % mult_1s_ring_1(2)
thf(fact_108_norm__uminus__minus, axiom,
    ((![X : complex, Y2 : complex]: ((real_V638595069omplex @ (minus_minus_complex @ (uminus1204672759omplex @ X) @ Y2)) = (real_V638595069omplex @ (plus_plus_complex @ X @ Y2)))))). % norm_uminus_minus
thf(fact_109_norm__uminus__minus, axiom,
    ((![X : real, Y2 : real]: ((real_V646646907m_real @ (minus_minus_real @ (uminus_uminus_real @ X) @ Y2)) = (real_V646646907m_real @ (plus_plus_real @ X @ Y2)))))). % norm_uminus_minus
thf(fact_110_norm__mult__ineq, axiom,
    ((![X : complex, Y2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (times_times_complex @ X @ Y2)) @ (times_times_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y2)))))). % norm_mult_ineq
thf(fact_111_norm__mult__ineq, axiom,
    ((![X : real, Y2 : real]: (ord_less_eq_real @ (real_V646646907m_real @ (times_times_real @ X @ Y2)) @ (times_times_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y2)))))). % norm_mult_ineq
thf(fact_112_norm__triangle__mono, axiom,
    ((![A : complex, R : real, B : complex, S2 : real]: ((ord_less_eq_real @ (real_V638595069omplex @ A) @ R) => ((ord_less_eq_real @ (real_V638595069omplex @ B) @ S2) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ (plus_plus_real @ R @ S2))))))). % norm_triangle_mono
thf(fact_113_norm__triangle__mono, axiom,
    ((![A : real, R : real, B : real, S2 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ A) @ R) => ((ord_less_eq_real @ (real_V646646907m_real @ B) @ S2) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ R @ S2))))))). % norm_triangle_mono
thf(fact_114_norm__triangle__ineq, axiom,
    ((![X : complex, Y2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X @ Y2)) @ (plus_plus_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y2)))))). % norm_triangle_ineq
thf(fact_115_norm__triangle__ineq, axiom,
    ((![X : real, Y2 : real]: (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X @ Y2)) @ (plus_plus_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y2)))))). % norm_triangle_ineq
thf(fact_116_norm__triangle__le, axiom,
    ((![X : complex, Y2 : complex, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y2)) @ E) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X @ Y2)) @ E))))). % norm_triangle_le
thf(fact_117_norm__triangle__le, axiom,
    ((![X : real, Y2 : real, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y2)) @ E) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X @ Y2)) @ E))))). % norm_triangle_le
thf(fact_118_norm__add__leD, axiom,
    ((![A : complex, B : complex, C : real]: ((ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ C) => (ord_less_eq_real @ (real_V638595069omplex @ B) @ (plus_plus_real @ (real_V638595069omplex @ A) @ C)))))). % norm_add_leD
thf(fact_119_norm__add__leD, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ C) => (ord_less_eq_real @ (real_V646646907m_real @ B) @ (plus_plus_real @ (real_V646646907m_real @ A) @ C)))))). % norm_add_leD
thf(fact_120_norm__triangle__le__diff, axiom,
    ((![X : complex, Y2 : complex, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V638595069omplex @ X) @ (real_V638595069omplex @ Y2)) @ E) => (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ X @ Y2)) @ E))))). % norm_triangle_le_diff
thf(fact_121_norm__triangle__le__diff, axiom,
    ((![X : real, Y2 : real, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y2)) @ E) => (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ X @ Y2)) @ E))))). % norm_triangle_le_diff
thf(fact_122_norm__diff__triangle__le, axiom,
    ((![X : complex, Y2 : complex, E1 : real, Z3 : complex, E2 : real]: ((ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ X @ Y2)) @ E1) => ((ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ Y2 @ Z3)) @ E2) => (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ X @ Z3)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_le
thf(fact_123_norm__diff__triangle__le, axiom,
    ((![X : real, Y2 : real, E1 : real, Z3 : real, E2 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ X @ Y2)) @ E1) => ((ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ Y2 @ Z3)) @ E2) => (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ X @ Z3)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_le
thf(fact_124_norm__triangle__ineq4, axiom,
    ((![A : complex, B : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ A @ B)) @ (plus_plus_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)))))). % norm_triangle_ineq4
thf(fact_125_norm__triangle__ineq4, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)))))). % norm_triangle_ineq4
thf(fact_126_norm__triangle__sub, axiom,
    ((![X : complex, Y2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ X) @ (plus_plus_real @ (real_V638595069omplex @ Y2) @ (real_V638595069omplex @ (minus_minus_complex @ X @ Y2))))))). % norm_triangle_sub
thf(fact_127_norm__triangle__sub, axiom,
    ((![X : real, Y2 : real]: (ord_less_eq_real @ (real_V646646907m_real @ X) @ (plus_plus_real @ (real_V646646907m_real @ Y2) @ (real_V646646907m_real @ (minus_minus_real @ X @ Y2))))))). % norm_triangle_sub
thf(fact_128_norm__diff__ineq, axiom,
    ((![A : complex, B : complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)) @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)))))). % norm_diff_ineq
thf(fact_129_norm__diff__ineq, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)) @ (real_V646646907m_real @ (plus_plus_real @ A @ B)))))). % norm_diff_ineq
thf(fact_130_norm__triangle__ineq2, axiom,
    ((![A : complex, B : complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B)) @ (real_V638595069omplex @ (minus_minus_complex @ A @ B)))))). % norm_triangle_ineq2
thf(fact_131_norm__triangle__ineq2, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)) @ (real_V646646907m_real @ (minus_minus_real @ A @ B)))))). % norm_triangle_ineq2
thf(fact_132_left__add__twice, axiom,
    ((![A : nat, B : nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B))))). % left_add_twice
thf(fact_133_left__add__twice, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ A @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B))))). % left_add_twice
thf(fact_134_mult__2__right, axiom,
    ((![Z3 : nat]: ((times_times_nat @ Z3 @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ Z3 @ Z3))))). % mult_2_right
thf(fact_135_mult__2__right, axiom,
    ((![Z3 : real]: ((times_times_real @ Z3 @ (numeral_numeral_real @ (bit0 @ one))) = (plus_plus_real @ Z3 @ Z3))))). % mult_2_right
thf(fact_136_mult__2, axiom,
    ((![Z3 : nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ Z3) = (plus_plus_nat @ Z3 @ Z3))))). % mult_2
thf(fact_137_mult__2, axiom,
    ((![Z3 : real]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ Z3) = (plus_plus_real @ Z3 @ Z3))))). % mult_2
thf(fact_138_norm__diff__triangle__ineq, axiom,
    ((![A : complex, B : complex, C : complex, D : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (minus_minus_complex @ (plus_plus_complex @ A @ B) @ (plus_plus_complex @ C @ D))) @ (plus_plus_real @ (real_V638595069omplex @ (minus_minus_complex @ A @ C)) @ (real_V638595069omplex @ (minus_minus_complex @ B @ D))))))). % norm_diff_triangle_ineq
thf(fact_139_norm__diff__triangle__ineq, axiom,
    ((![A : real, B : real, C : real, D : real]: (ord_less_eq_real @ (real_V646646907m_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (real_V646646907m_real @ (minus_minus_real @ A @ C)) @ (real_V646646907m_real @ (minus_minus_real @ B @ D))))))). % norm_diff_triangle_ineq
thf(fact_140_norm__triangle__ineq3, axiom,
    ((![A : complex, B : complex]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ A) @ (real_V638595069omplex @ B))) @ (real_V638595069omplex @ (minus_minus_complex @ A @ B)))))). % norm_triangle_ineq3
thf(fact_141_norm__triangle__ineq3, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B))) @ (real_V646646907m_real @ (minus_minus_real @ A @ B)))))). % norm_triangle_ineq3
thf(fact_142_th1, axiom,
    ((![W : complex]: ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ W @ z)) @ d) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ W) @ (poly_complex2 @ p @ z))) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))))). % th1
thf(fact_143__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062N1_O_A_092_060forall_062n_092_060ge_062N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![N1 : nat]: (~ ((![N2 : nat]: ((ord_less_eq_nat @ N1 @ N2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (f @ N2)) @ z)) @ d)))))))))). % \<open>\<And>thesis. (\<And>N1. \<forall>n\<ge>N1. cmod (g (f n) - z) < d \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_144__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_A_092_060lbrakk_0620_A_060_Ad_059_A_092_060forall_062w_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_092_060and_062_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_092_060longrightarrow_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_A_P_A2_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![D2 : real]: ((ord_less_real @ zero_zero_real @ D2) => (~ ((![W2 : complex]: (((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z))) & (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z)) @ D2)) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ W2) @ (poly_complex2 @ p @ z))) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))))))))))). % \<open>\<And>thesis. (\<And>d. \<lbrakk>0 < d; \<forall>w. 0 < cmod (w - z) \<and> cmod (w - z) < d \<longrightarrow> cmod (poly p w - poly p z) < \<bar>cmod (poly p z) - - s\<bar> / 2\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_145__092_060open_062_092_060exists_062d_0620_O_A_092_060forall_062w_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_092_060and_062_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_092_060longrightarrow_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_A_P_A2_092_060close_062, axiom,
    ((?[D2 : real]: ((ord_less_real @ zero_zero_real @ D2) & (![W2 : complex]: (((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z))) & (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z)) @ D2)) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ W2) @ (poly_complex2 @ p @ z))) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))))))). % \<open>\<exists>d>0. \<forall>w. 0 < cmod (w - z) \<and> cmod (w - z) < d \<longrightarrow> cmod (poly p w - poly p z) < \<bar>cmod (poly p z) - - s\<bar> / 2\<close>
thf(fact_146_e2, axiom,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))). % e2
thf(fact_147_d_I2_J, axiom,
    ((![W2 : complex]: (((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z))) & (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ W2 @ z)) @ d)) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ W2) @ (poly_complex2 @ p @ z))) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))))). % d(2)
thf(fact_148__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062N2_O_A2_A_P_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_A_060_Areal_AN2_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![N22 : nat]: (~ ((ord_less_real @ (divide_divide_real @ (numeral_numeral_real @ (bit0 @ one)) @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s)))) @ (semiri2110766477t_real @ N22))))))))). % \<open>\<And>thesis. (\<And>N2. 2 / \<bar>cmod (poly p z) - - s\<bar> < real N2 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_149__092_060open_062_092_060exists_062n_O_A2_A_P_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_A_060_Areal_An_092_060close_062, axiom,
    ((?[N4 : nat]: (ord_less_real @ (divide_divide_real @ (numeral_numeral_real @ (bit0 @ one)) @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s)))) @ (semiri2110766477t_real @ N4))))). % \<open>\<exists>n. 2 / \<bar>cmod (poly p z) - - s\<bar> < real n\<close>
thf(fact_150__092_060open_062_092_060And_062z_Ax_O_A_092_060lbrakk_062cmod_Az_A_092_060le_062_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_092_060not_062_Ax_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
    ((![Z3 : complex, X : real]: ((ord_less_eq_real @ (real_V638595069omplex @ Z3) @ r) => (((real_V638595069omplex @ (poly_complex2 @ p @ Z3)) = (uminus_uminus_real @ X)) => (ord_less_real @ X @ one_one_real)))))). % \<open>\<And>z x. \<lbrakk>cmod z \<le> r; cmod (poly p z) = - x; \<not> x < 1\<rbrakk> \<Longrightarrow> False\<close>
thf(fact_151_th000_I2_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % th000(2)
thf(fact_152_d_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ d))). % d(1)
thf(fact_153_th000_I1_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % th000(1)
thf(fact_154_of__nat__numeral, axiom,
    ((![N : num]: ((semiri2110766477t_real @ (numeral_numeral_nat @ N)) = (numeral_numeral_real @ N))))). % of_nat_numeral
thf(fact_155__092_060open_062_092_060exists_062f_Az_O_Astrict__mono_Af_A_092_060and_062_A_I_092_060forall_062e_0620_O_A_092_060exists_062N_O_A_092_060forall_062n_092_060ge_062N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ae_J_092_060close_062, axiom,
    ((?[F : nat > nat, Z2 : complex]: ((order_769474267at_nat @ F) & (![E3 : real]: ((ord_less_real @ zero_zero_real @ E3) => (?[N3 : nat]: (![N2 : nat]: ((ord_less_eq_nat @ N3 @ N2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (F @ N2)) @ Z2)) @ E3)))))))))). % \<open>\<exists>f z. strict_mono f \<and> (\<forall>e>0. \<exists>N. \<forall>n\<ge>N. cmod (g (f n) - z) < e)\<close>
thf(fact_156__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062f_Az_O_A_092_060lbrakk_062strict__mono_Af_059_A_092_060forall_062e_0620_O_A_092_060exists_062N_O_A_092_060forall_062n_092_060ge_062N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ae_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![F : nat > nat]: ((order_769474267at_nat @ F) => (![Z2 : complex]: (~ ((![E3 : real]: ((ord_less_real @ zero_zero_real @ E3) => (?[N3 : nat]: (![N2 : nat]: ((ord_less_eq_nat @ N3 @ N2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ (g @ (F @ N2)) @ Z2)) @ E3))))))))))))))). % \<open>\<And>thesis. (\<And>f z. \<lbrakk>strict_mono f; \<forall>e>0. \<exists>N. \<forall>n\<ge>N. cmod (g (f n) - z) < e\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_157_diff__numeral__special_I9_J, axiom,
    (((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real))). % diff_numeral_special(9)
thf(fact_158_diff__numeral__special_I9_J, axiom,
    (((minus_minus_complex @ one_one_complex @ one_one_complex) = zero_zero_complex))). % diff_numeral_special(9)
thf(fact_159_mult__minus1, axiom,
    ((![Z3 : real]: ((times_times_real @ (uminus_uminus_real @ one_one_real) @ Z3) = (uminus_uminus_real @ Z3))))). % mult_minus1
thf(fact_160_mult__minus1__right, axiom,
    ((![Z3 : real]: ((times_times_real @ Z3 @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ Z3))))). % mult_minus1_right
thf(fact_161_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_real @ N) = one_one_real) = (N = one))))). % numeral_eq_one_iff
thf(fact_162_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_real = (numeral_numeral_real @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_163_norm__eq__zero, axiom,
    ((![X : complex]: (((real_V638595069omplex @ X) = zero_zero_real) = (X = zero_zero_complex))))). % norm_eq_zero
thf(fact_164_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_165_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_166_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_167_abs__neg__one, axiom,
    (((abs_abs_real @ (uminus_uminus_real @ one_one_real)) = one_one_real))). % abs_neg_one
thf(fact_168_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_169_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_170_norm__of__nat, axiom,
    ((![N : nat]: ((real_V638595069omplex @ (semiri356525583omplex @ N)) = (semiri2110766477t_real @ N))))). % norm_of_nat
thf(fact_171_norm__of__nat, axiom,
    ((![N : nat]: ((real_V646646907m_real @ (semiri2110766477t_real @ N)) = (semiri2110766477t_real @ N))))). % norm_of_nat
thf(fact_172_divide__eq__eq__numeral1_I1_J, axiom,
    ((![B : real, W : num, A : real]: (((divide_divide_real @ B @ (numeral_numeral_real @ W)) = A) = (((((~ (((numeral_numeral_real @ W) = zero_zero_real)))) => ((B = (times_times_real @ A @ (numeral_numeral_real @ W)))))) & (((((numeral_numeral_real @ W) = zero_zero_real)) => ((A = zero_zero_real))))))))). % divide_eq_eq_numeral1(1)
thf(fact_173_eq__divide__eq__numeral1_I1_J, axiom,
    ((![A : real, B : real, W : num]: ((A = (divide_divide_real @ B @ (numeral_numeral_real @ W))) = (((((~ (((numeral_numeral_real @ W) = zero_zero_real)))) => (((times_times_real @ A @ (numeral_numeral_real @ W)) = B)))) & (((((numeral_numeral_real @ W) = zero_zero_real)) => ((A = zero_zero_real))))))))). % eq_divide_eq_numeral1(1)
thf(fact_174_add__neg__numeral__special_I8_J, axiom,
    (((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = zero_zero_real))). % add_neg_numeral_special(8)
thf(fact_175_add__neg__numeral__special_I7_J, axiom,
    (((plus_plus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = zero_zero_real))). % add_neg_numeral_special(7)
thf(fact_176_diff__numeral__special_I12_J, axiom,
    (((minus_minus_complex @ (uminus1204672759omplex @ one_one_complex) @ (uminus1204672759omplex @ one_one_complex)) = zero_zero_complex))). % diff_numeral_special(12)
thf(fact_177_diff__numeral__special_I12_J, axiom,
    (((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ one_one_real)) = zero_zero_real))). % diff_numeral_special(12)
thf(fact_178_neg__one__eq__numeral__iff, axiom,
    ((![N : num]: (((uminus_uminus_real @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ N))) = (N = one))))). % neg_one_eq_numeral_iff
thf(fact_179_numeral__eq__neg__one__iff, axiom,
    ((![N : num]: (((uminus_uminus_real @ (numeral_numeral_real @ N)) = (uminus_uminus_real @ one_one_real)) = (N = one))))). % numeral_eq_neg_one_iff
thf(fact_180_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_181_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_182_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_183_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_184_diff__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((minus_minus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ (numera632737353omplex @ N)) = (uminus1204672759omplex @ (numera632737353omplex @ (plus_plus_num @ M @ N))))))). % diff_numeral_simps(3)
thf(fact_185_diff__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N)) = (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ M @ N))))))). % diff_numeral_simps(3)
thf(fact_186_diff__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((minus_minus_complex @ (numera632737353omplex @ M) @ (uminus1204672759omplex @ (numera632737353omplex @ N))) = (numera632737353omplex @ (plus_plus_num @ M @ N)))))). % diff_numeral_simps(2)
thf(fact_187_diff__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((minus_minus_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (numeral_numeral_real @ (plus_plus_num @ M @ N)))))). % diff_numeral_simps(2)
thf(fact_188_divide__eq__eq__numeral1_I2_J, axiom,
    ((![B : real, W : num, A : real]: (((divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ W))) = A) = (((((~ (((uminus_uminus_real @ (numeral_numeral_real @ W)) = zero_zero_real)))) => ((B = (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ W))))))) & (((((uminus_uminus_real @ (numeral_numeral_real @ W)) = zero_zero_real)) => ((A = zero_zero_real))))))))). % divide_eq_eq_numeral1(2)
thf(fact_189_eq__divide__eq__numeral1_I2_J, axiom,
    ((![A : real, B : real, W : num]: ((A = (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ W)))) = (((((~ (((uminus_uminus_real @ (numeral_numeral_real @ W)) = zero_zero_real)))) => (((times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ W))) = B)))) & (((((uminus_uminus_real @ (numeral_numeral_real @ W)) = zero_zero_real)) => ((A = zero_zero_real))))))))). % eq_divide_eq_numeral1(2)
thf(fact_190_not__neg__one__le__neg__numeral__iff, axiom,
    ((![M : num]: ((~ ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (numeral_numeral_real @ M))))) = (~ ((M = one))))))). % not_neg_one_le_neg_numeral_iff
thf(fact_191_neg__numeral__less__neg__one__iff, axiom,
    ((![M : num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ one_one_real)) = (~ ((M = one))))))). % neg_numeral_less_neg_one_iff
thf(fact_192_one__add__one, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % one_add_one
thf(fact_193_one__add__one, axiom,
    (((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one))))). % one_add_one
thf(fact_194_numeral__plus__one, axiom,
    ((![N : num]: ((plus_plus_nat @ (numeral_numeral_nat @ N) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ N @ one)))))). % numeral_plus_one
thf(fact_195_numeral__plus__one, axiom,
    ((![N : num]: ((plus_plus_real @ (numeral_numeral_real @ N) @ one_one_real) = (numeral_numeral_real @ (plus_plus_num @ N @ one)))))). % numeral_plus_one
thf(fact_196_one__plus__numeral, axiom,
    ((![N : num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (plus_plus_num @ one @ N)))))). % one_plus_numeral
thf(fact_197_one__plus__numeral, axiom,
    ((![N : num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ N)) = (numeral_numeral_real @ (plus_plus_num @ one @ N)))))). % one_plus_numeral

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_eq_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2))))) @ (uminus_uminus_real @ s))) @ (real_V638595069omplex @ (minus_minus_complex @ (poly_complex2 @ p @ (g @ (f @ (plus_plus_nat @ n1 @ n2)))) @ (poly_complex2 @ p @ z))))))).
