% 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_446__5371922_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:30:11.730

% 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 (42)
thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex, type,
    invers502456322omplex : complex > complex).
thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal, type,
    inverse_inverse_real : real > real).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_real : real > real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex, type,
    minus_minus_complex : complex > complex > complex).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat, type,
    minus_minus_nat : nat > nat > nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__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__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_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__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Nat_OSuc, type,
    suc : nat > nat).
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__Nat__Onat, type,
    semiri1382578993at_nat : nat > nat).
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__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
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_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__Nat__Onat, type,
    divide_divide_nat : nat > nat > nat).
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_g____, type,
    g : nat > complex).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_s____, type,
    s : real).
thf(sy_v_z____, type,
    z : complex).

% Relevant facts (182)
thf(fact_0_d_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ d))). % d(1)
thf(fact_1_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_2_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_3__092_060open_0622_A_P_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_092_060close_062, 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 @ (suc @ (plus_plus_nat @ n1 @ n2)))))). % \<open>2 / \<bar>cmod (poly p z) - - s\<bar> < real (Suc (N1 + N2))\<close>
thf(fact_4_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_5__092_060open_062_092_060lbrakk_0622_A_P_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_A_092_060bar_062cmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_092_060bar_062_J_092_060close_062, 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 @ (suc @ (plus_plus_nat @ n1 @ n2)))) => ((ord_less_real @ zero_zero_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))))) => (ord_less_real @ (inverse_inverse_real @ (semiri2110766477t_real @ (suc @ (plus_plus_nat @ n1 @ n2)))) @ (inverse_inverse_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)))))))))). % \<open>\<lbrakk>2 / \<bar>cmod (poly p z) - - s\<bar> < real (Suc (N1 + N2)); 0 < 2 / \<bar>cmod (poly p z) - - s\<bar>\<rbrakk> \<Longrightarrow> inverse (real (Suc (N1 + N2))) < inverse (2 / \<bar>cmod (poly p z) - - s\<bar>)\<close>
thf(fact_6_th000_I3_J, axiom,
    ((ord_less_real @ zero_zero_real @ (semiri2110766477t_real @ (suc @ (plus_plus_nat @ n1 @ n2)))))). % th000(3)
thf(fact_7__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,
    ((?[N : 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 @ N))))). % \<open>\<exists>n. 2 / \<bar>cmod (poly p z) - - s\<bar> < real n\<close>
thf(fact_8__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,
    ((~ ((![N2 : 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 @ N2))))))))). % \<open>\<And>thesis. (\<And>N2. 2 / \<bar>cmod (poly p z) - - s\<bar> < real N2 \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_9_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z : real]: (![X : real]: ((P @ X) => (ord_less_real @ X @ Z)))) => (?[S : real]: (![Y : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_10_diff__numeral__special_I11_J, axiom,
    (((minus_minus_complex @ one_one_complex @ (uminus1204672759omplex @ one_one_complex)) = (numera632737353omplex @ (bit0 @ one))))). % diff_numeral_special(11)
thf(fact_11_diff__numeral__special_I11_J, axiom,
    (((minus_minus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = (numeral_numeral_real @ (bit0 @ one))))). % diff_numeral_special(11)
thf(fact_12_diff__numeral__special_I10_J, axiom,
    (((minus_minus_complex @ (uminus1204672759omplex @ one_one_complex) @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ (bit0 @ one)))))). % diff_numeral_special(10)
thf(fact_13_diff__numeral__special_I10_J, axiom,
    (((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one)))))). % diff_numeral_special(10)
thf(fact_14_add__neg__numeral__special_I9_J, axiom,
    (((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one)))))). % add_neg_numeral_special(9)
thf(fact_15_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_16_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_17_one__add__one, axiom,
    (((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one))))). % one_add_one
thf(fact_18_one__add__one, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % one_add_one
thf(fact_19_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_20_norm__neg__numeral, axiom,
    ((![W : num]: ((real_V638595069omplex @ (uminus1204672759omplex @ (numera632737353omplex @ W))) = (numeral_numeral_real @ W))))). % norm_neg_numeral
thf(fact_21_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_22_of__nat__Suc, axiom,
    ((![M : nat]: ((semiri1382578993at_nat @ (suc @ M)) = (plus_plus_nat @ one_one_nat @ (semiri1382578993at_nat @ M)))))). % of_nat_Suc
thf(fact_23_of__nat__Suc, axiom,
    ((![M : nat]: ((semiri2110766477t_real @ (suc @ M)) = (plus_plus_real @ one_one_real @ (semiri2110766477t_real @ M)))))). % of_nat_Suc
thf(fact_24_neg__one__eq__numeral__iff, axiom,
    ((![N3 : num]: (((uminus_uminus_real @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ N3))) = (N3 = one))))). % neg_one_eq_numeral_iff
thf(fact_25_numeral__eq__neg__one__iff, axiom,
    ((![N3 : num]: (((uminus_uminus_real @ (numeral_numeral_real @ N3)) = (uminus_uminus_real @ one_one_real)) = (N3 = one))))). % numeral_eq_neg_one_iff
thf(fact_26_numeral__plus__one, axiom,
    ((![N3 : num]: ((plus_plus_real @ (numeral_numeral_real @ N3) @ one_one_real) = (numeral_numeral_real @ (plus_plus_num @ N3 @ one)))))). % numeral_plus_one
thf(fact_27_numeral__plus__one, axiom,
    ((![N3 : num]: ((plus_plus_nat @ (numeral_numeral_nat @ N3) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ N3 @ one)))))). % numeral_plus_one
thf(fact_28_numeral__eq__iff, axiom,
    ((![M : num, N3 : num]: (((numeral_numeral_real @ M) = (numeral_numeral_real @ N3)) = (M = N3))))). % numeral_eq_iff
thf(fact_29_numeral__eq__iff, axiom,
    ((![M : num, N3 : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N3)) = (M = N3))))). % numeral_eq_iff
thf(fact_30_diff__Suc__1, axiom,
    ((![N3 : nat]: ((minus_minus_nat @ (suc @ N3) @ one_one_nat) = N3)))). % diff_Suc_1
thf(fact_31_Suc__diff__diff, axiom,
    ((![M : nat, N3 : nat, K : nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ M) @ N3) @ (suc @ K)) = (minus_minus_nat @ (minus_minus_nat @ M @ N3) @ K))))). % Suc_diff_diff
thf(fact_32_diff__Suc__Suc, axiom,
    ((![M : nat, N3 : nat]: ((minus_minus_nat @ (suc @ M) @ (suc @ N3)) = (minus_minus_nat @ M @ N3))))). % diff_Suc_Suc
thf(fact_33_Suc__less__eq, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_nat @ (suc @ M) @ (suc @ N3)) = (ord_less_nat @ M @ N3))))). % Suc_less_eq
thf(fact_34_Suc__mono, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_nat @ M @ N3) => (ord_less_nat @ (suc @ M) @ (suc @ N3)))))). % Suc_mono
thf(fact_35_lessI, axiom,
    ((![N3 : nat]: (ord_less_nat @ N3 @ (suc @ N3))))). % lessI
thf(fact_36_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_37_nat_Oinject, axiom,
    ((![X22 : nat, Y2 : nat]: (((suc @ X22) = (suc @ Y2)) = (X22 = Y2))))). % nat.inject
thf(fact_38_of__nat__eq__iff, axiom,
    ((![M : nat, N3 : nat]: (((semiri2110766477t_real @ M) = (semiri2110766477t_real @ N3)) = (M = N3))))). % of_nat_eq_iff
thf(fact_39_diff__diff__left, axiom,
    ((![I : nat, J : nat, K : nat]: ((minus_minus_nat @ (minus_minus_nat @ I @ J) @ K) = (minus_minus_nat @ I @ (plus_plus_nat @ J @ K)))))). % diff_diff_left
thf(fact_40_nat__add__left__cancel__less, axiom,
    ((![K : nat, M : nat, N3 : nat]: ((ord_less_nat @ (plus_plus_nat @ K @ M) @ (plus_plus_nat @ K @ N3)) = (ord_less_nat @ M @ N3))))). % nat_add_left_cancel_less
thf(fact_41_numeral__less__iff, axiom,
    ((![M : num, N3 : num]: ((ord_less_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N3)) = (ord_less_num @ M @ N3))))). % numeral_less_iff
thf(fact_42_numeral__less__iff, axiom,
    ((![M : num, N3 : num]: ((ord_less_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N3)) = (ord_less_num @ M @ N3))))). % numeral_less_iff
thf(fact_43_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri2110766477t_real @ M) = zero_zero_real) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_44_of__nat__0__eq__iff, axiom,
    ((![N3 : nat]: ((zero_zero_real = (semiri2110766477t_real @ N3)) = (zero_zero_nat = N3))))). % of_nat_0_eq_iff
thf(fact_45_of__nat__0, axiom,
    (((semiri2110766477t_real @ zero_zero_nat) = zero_zero_real))). % of_nat_0
thf(fact_46_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_47_neg__numeral__eq__iff, axiom,
    ((![M : num, N3 : num]: (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (uminus_uminus_real @ (numeral_numeral_real @ N3))) = (M = N3))))). % neg_numeral_eq_iff
thf(fact_48_of__nat__less__iff, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N3)) = (ord_less_nat @ M @ N3))))). % of_nat_less_iff
thf(fact_49_of__nat__less__iff, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N3)) = (ord_less_nat @ M @ N3))))). % of_nat_less_iff
thf(fact_50_of__nat__eq__1__iff, axiom,
    ((![N3 : nat]: (((semiri1382578993at_nat @ N3) = one_one_nat) = (N3 = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_51_of__nat__eq__1__iff, axiom,
    ((![N3 : nat]: (((semiri2110766477t_real @ N3) = one_one_real) = (N3 = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_52_of__nat__1__eq__iff, axiom,
    ((![N3 : nat]: ((one_one_nat = (semiri1382578993at_nat @ N3)) = (N3 = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_53_of__nat__1__eq__iff, axiom,
    ((![N3 : nat]: ((one_one_real = (semiri2110766477t_real @ N3)) = (N3 = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_54_of__nat__1, axiom,
    (((semiri1382578993at_nat @ one_one_nat) = one_one_nat))). % of_nat_1
thf(fact_55_of__nat__1, axiom,
    (((semiri2110766477t_real @ one_one_nat) = one_one_real))). % of_nat_1
thf(fact_56_of__nat__numeral, axiom,
    ((![N3 : num]: ((semiri1382578993at_nat @ (numeral_numeral_nat @ N3)) = (numeral_numeral_nat @ N3))))). % of_nat_numeral
thf(fact_57_of__nat__numeral, axiom,
    ((![N3 : num]: ((semiri2110766477t_real @ (numeral_numeral_nat @ N3)) = (numeral_numeral_real @ N3))))). % of_nat_numeral
thf(fact_58_abs__numeral, axiom,
    ((![N3 : num]: ((abs_abs_real @ (numeral_numeral_real @ N3)) = (numeral_numeral_real @ N3))))). % abs_numeral
thf(fact_59_add__Suc__right, axiom,
    ((![M : nat, N3 : nat]: ((plus_plus_nat @ M @ (suc @ N3)) = (suc @ (plus_plus_nat @ M @ N3)))))). % add_Suc_right
thf(fact_60_norm__minus__cancel, axiom,
    ((![X3 : complex]: ((real_V638595069omplex @ (uminus1204672759omplex @ X3)) = (real_V638595069omplex @ X3))))). % norm_minus_cancel
thf(fact_61_norm__minus__cancel, axiom,
    ((![X3 : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X3)) = (real_V646646907m_real @ X3))))). % norm_minus_cancel
thf(fact_62_abs__of__nat, axiom,
    ((![N3 : nat]: ((abs_abs_real @ (semiri2110766477t_real @ N3)) = (semiri2110766477t_real @ N3))))). % abs_of_nat
thf(fact_63_abs__norm__cancel, axiom,
    ((![A : complex]: ((abs_abs_real @ (real_V638595069omplex @ A)) = (real_V638595069omplex @ A))))). % abs_norm_cancel
thf(fact_64_abs__norm__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (real_V646646907m_real @ A)) = (real_V646646907m_real @ A))))). % abs_norm_cancel
thf(fact_65_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_66_diff__numeral__special_I9_J, axiom,
    (((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real))). % diff_numeral_special(9)
thf(fact_67_diff__numeral__special_I9_J, axiom,
    (((minus_minus_complex @ one_one_complex @ one_one_complex) = zero_zero_complex))). % diff_numeral_special(9)
thf(fact_68_of__nat__0__less__iff, axiom,
    ((![N3 : nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1382578993at_nat @ N3)) = (ord_less_nat @ zero_zero_nat @ N3))))). % of_nat_0_less_iff
thf(fact_69_of__nat__0__less__iff, axiom,
    ((![N3 : nat]: ((ord_less_real @ zero_zero_real @ (semiri2110766477t_real @ N3)) = (ord_less_nat @ zero_zero_nat @ N3))))). % of_nat_0_less_iff
thf(fact_70_neg__numeral__less__iff, axiom,
    ((![M : num, N3 : num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N3))) = (ord_less_num @ N3 @ M))))). % neg_numeral_less_iff
thf(fact_71_add__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N3 : num]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N3))) = (uminus_uminus_real @ (plus_plus_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N3))))))). % add_neg_numeral_simps(3)
thf(fact_72_one__eq__numeral__iff, axiom,
    ((![N3 : num]: ((one_one_real = (numeral_numeral_real @ N3)) = (one = N3))))). % one_eq_numeral_iff
thf(fact_73_one__eq__numeral__iff, axiom,
    ((![N3 : num]: ((one_one_nat = (numeral_numeral_nat @ N3)) = (one = N3))))). % one_eq_numeral_iff
thf(fact_74_numeral__eq__one__iff, axiom,
    ((![N3 : num]: (((numeral_numeral_real @ N3) = one_one_real) = (N3 = one))))). % numeral_eq_one_iff
thf(fact_75_numeral__eq__one__iff, axiom,
    ((![N3 : num]: (((numeral_numeral_nat @ N3) = one_one_nat) = (N3 = one))))). % numeral_eq_one_iff
thf(fact_76_Suc__1, axiom,
    (((suc @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % Suc_1
thf(fact_77_norm__eq__zero, axiom,
    ((![X3 : complex]: (((real_V638595069omplex @ X3) = zero_zero_real) = (X3 = zero_zero_complex))))). % norm_eq_zero
thf(fact_78_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_79_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_80_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_81_abs__neg__one, axiom,
    (((abs_abs_real @ (uminus_uminus_real @ one_one_real)) = one_one_real))). % abs_neg_one
thf(fact_82_abs__neg__numeral, axiom,
    ((![N3 : num]: ((abs_abs_real @ (uminus_uminus_real @ (numeral_numeral_real @ N3))) = (numeral_numeral_real @ N3))))). % abs_neg_numeral
thf(fact_83_of__nat__add, axiom,
    ((![M : nat, N3 : nat]: ((semiri1382578993at_nat @ (plus_plus_nat @ M @ N3)) = (plus_plus_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N3)))))). % of_nat_add
thf(fact_84_of__nat__add, axiom,
    ((![M : nat, N3 : nat]: ((semiri2110766477t_real @ (plus_plus_nat @ M @ N3)) = (plus_plus_real @ (semiri2110766477t_real @ M) @ (semiri2110766477t_real @ N3)))))). % of_nat_add
thf(fact_85_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_86_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_87_norm__numeral, axiom,
    ((![W : num]: ((real_V638595069omplex @ (numera632737353omplex @ W)) = (numeral_numeral_real @ W))))). % norm_numeral
thf(fact_88_norm__numeral, axiom,
    ((![W : num]: ((real_V646646907m_real @ (numeral_numeral_real @ W)) = (numeral_numeral_real @ W))))). % norm_numeral
thf(fact_89_numeral__plus__numeral, axiom,
    ((![M : num, N3 : num]: ((plus_plus_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N3)) = (numeral_numeral_real @ (plus_plus_num @ M @ N3)))))). % numeral_plus_numeral
thf(fact_90_numeral__plus__numeral, axiom,
    ((![M : num, N3 : num]: ((plus_plus_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N3)) = (numeral_numeral_nat @ (plus_plus_num @ M @ N3)))))). % numeral_plus_numeral
thf(fact_91_add__numeral__left, axiom,
    ((![V : num, W : num, Z2 : real]: ((plus_plus_real @ (numeral_numeral_real @ V) @ (plus_plus_real @ (numeral_numeral_real @ W) @ Z2)) = (plus_plus_real @ (numeral_numeral_real @ (plus_plus_num @ V @ W)) @ Z2))))). % add_numeral_left
thf(fact_92_add__numeral__left, axiom,
    ((![V : num, W : num, Z2 : nat]: ((plus_plus_nat @ (numeral_numeral_nat @ V) @ (plus_plus_nat @ (numeral_numeral_nat @ W) @ Z2)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ V @ W)) @ Z2))))). % add_numeral_left
thf(fact_93_norm__of__nat, axiom,
    ((![N3 : nat]: ((real_V638595069omplex @ (semiri356525583omplex @ N3)) = (semiri2110766477t_real @ N3))))). % norm_of_nat
thf(fact_94_norm__of__nat, axiom,
    ((![N3 : nat]: ((real_V646646907m_real @ (semiri2110766477t_real @ N3)) = (semiri2110766477t_real @ N3))))). % norm_of_nat
thf(fact_95_Suc__numeral, axiom,
    ((![N3 : num]: ((suc @ (numeral_numeral_nat @ N3)) = (numeral_numeral_nat @ (plus_plus_num @ N3 @ one)))))). % Suc_numeral
thf(fact_96_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_97_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_98_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_99_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_100_one__less__numeral__iff, axiom,
    ((![N3 : num]: ((ord_less_real @ one_one_real @ (numeral_numeral_real @ N3)) = (ord_less_num @ one @ N3))))). % one_less_numeral_iff
thf(fact_101_one__less__numeral__iff, axiom,
    ((![N3 : num]: ((ord_less_nat @ one_one_nat @ (numeral_numeral_nat @ N3)) = (ord_less_num @ one @ N3))))). % one_less_numeral_iff
thf(fact_102_zero__less__norm__iff, axiom,
    ((![X3 : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X3)) = (~ ((X3 = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_103_zero__less__norm__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X3)) = (~ ((X3 = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_104_inverse__eq__divide__numeral, axiom,
    ((![W : num]: ((inverse_inverse_real @ (numeral_numeral_real @ W)) = (divide_divide_real @ one_one_real @ (numeral_numeral_real @ W)))))). % inverse_eq_divide_numeral
thf(fact_105_add__2__eq__Suc_H, axiom,
    ((![N3 : nat]: ((plus_plus_nat @ N3 @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (suc @ N3)))))). % add_2_eq_Suc'
thf(fact_106_add__2__eq__Suc, axiom,
    ((![N3 : nat]: ((plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ N3) = (suc @ (suc @ N3)))))). % add_2_eq_Suc
thf(fact_107_diff__numeral__simps_I2_J, axiom,
    ((![M : num, N3 : num]: ((minus_minus_complex @ (numera632737353omplex @ M) @ (uminus1204672759omplex @ (numera632737353omplex @ N3))) = (numera632737353omplex @ (plus_plus_num @ M @ N3)))))). % diff_numeral_simps(2)
thf(fact_108_diff__numeral__simps_I2_J, axiom,
    ((![M : num, N3 : num]: ((minus_minus_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N3))) = (numeral_numeral_real @ (plus_plus_num @ M @ N3)))))). % diff_numeral_simps(2)
thf(fact_109_diff__numeral__simps_I3_J, axiom,
    ((![M : num, N3 : num]: ((minus_minus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ (numera632737353omplex @ N3)) = (uminus1204672759omplex @ (numera632737353omplex @ (plus_plus_num @ M @ N3))))))). % diff_numeral_simps(3)
thf(fact_110_diff__numeral__simps_I3_J, axiom,
    ((![M : num, N3 : num]: ((minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N3)) = (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ M @ N3))))))). % diff_numeral_simps(3)
thf(fact_111__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,
    ((~ ((![D : real]: ((ord_less_real @ zero_zero_real @ D) => (~ ((![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)))))))))))))). % \<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_112__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,
    ((?[D : real]: ((ord_less_real @ zero_zero_real @ D) & (![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)))))))))). % \<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_113_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_114_inverse__eq__divide__neg__numeral, axiom,
    ((![W : num]: ((inverse_inverse_real @ (uminus_uminus_real @ (numeral_numeral_real @ W))) = (divide_divide_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ W))))))). % inverse_eq_divide_neg_numeral
thf(fact_115_one__plus__numeral, axiom,
    ((![N3 : num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ N3)) = (numeral_numeral_real @ (plus_plus_num @ one @ N3)))))). % one_plus_numeral
thf(fact_116_one__plus__numeral, axiom,
    ((![N3 : num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ N3)) = (numeral_numeral_nat @ (plus_plus_num @ one @ N3)))))). % one_plus_numeral
thf(fact_117_bits__1__div__2, axiom,
    (((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))). % bits_1_div_2
thf(fact_118_diff__numeral__special_I3_J, axiom,
    ((![N3 : num]: ((minus_minus_complex @ one_one_complex @ (uminus1204672759omplex @ (numera632737353omplex @ N3))) = (numera632737353omplex @ (plus_plus_num @ one @ N3)))))). % diff_numeral_special(3)
thf(fact_119_diff__numeral__special_I3_J, axiom,
    ((![N3 : num]: ((minus_minus_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ N3))) = (numeral_numeral_real @ (plus_plus_num @ one @ N3)))))). % diff_numeral_special(3)
thf(fact_120_diff__numeral__special_I4_J, axiom,
    ((![M : num]: ((minus_minus_complex @ (uminus1204672759omplex @ (numera632737353omplex @ M)) @ one_one_complex) = (uminus1204672759omplex @ (numera632737353omplex @ (plus_plus_num @ M @ one))))))). % diff_numeral_special(4)
thf(fact_121_diff__numeral__special_I4_J, axiom,
    ((![M : num]: ((minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ M @ one))))))). % diff_numeral_special(4)
thf(fact_122_g_I2_J, axiom,
    ((![N4 : nat]: (ord_less_real @ (real_V638595069omplex @ (poly_complex2 @ p @ (g @ N4))) @ (plus_plus_real @ (uminus_uminus_real @ s) @ (divide_divide_real @ one_one_real @ (semiri2110766477t_real @ (suc @ N4)))))))). % g(2)
thf(fact_123_numerals_I1_J, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numerals(1)
thf(fact_124_Suc__diff__Suc, axiom,
    ((![N3 : nat, M : nat]: ((ord_less_nat @ N3 @ M) => ((suc @ (minus_minus_nat @ M @ (suc @ N3))) = (minus_minus_nat @ M @ N3)))))). % Suc_diff_Suc
thf(fact_125_diff__less__Suc, axiom,
    ((![M : nat, N3 : nat]: (ord_less_nat @ (minus_minus_nat @ M @ N3) @ (suc @ M))))). % diff_less_Suc
thf(fact_126_less__diff__conv, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_nat @ I @ (minus_minus_nat @ J @ K)) = (ord_less_nat @ (plus_plus_nat @ I @ K) @ J))))). % less_diff_conv
thf(fact_127_add__diff__inverse__nat, axiom,
    ((![M : nat, N3 : nat]: ((~ ((ord_less_nat @ M @ N3))) => ((plus_plus_nat @ N3 @ (minus_minus_nat @ M @ N3)) = M))))). % add_diff_inverse_nat
thf(fact_128_diff__Suc__eq__diff__pred, axiom,
    ((![M : nat, N3 : nat]: ((minus_minus_nat @ M @ (suc @ N3)) = (minus_minus_nat @ (minus_minus_nat @ M @ one_one_nat) @ N3))))). % diff_Suc_eq_diff_pred
thf(fact_129_add__One__commute, axiom,
    ((![N3 : num]: ((plus_plus_num @ one @ N3) = (plus_plus_num @ N3 @ one))))). % add_One_commute
thf(fact_130_zero__induct__lemma, axiom,
    ((![P : nat > $o, K : nat, I : nat]: ((P @ K) => ((![N : nat]: ((P @ (suc @ N)) => (P @ N))) => (P @ (minus_minus_nat @ K @ I))))))). % zero_induct_lemma
thf(fact_131_not__less__less__Suc__eq, axiom,
    ((![N3 : nat, M : nat]: ((~ ((ord_less_nat @ N3 @ M))) => ((ord_less_nat @ N3 @ (suc @ M)) = (N3 = M)))))). % not_less_less_Suc_eq
thf(fact_132_strict__inc__induct, axiom,
    ((![I : nat, J : nat, P : nat > $o]: ((ord_less_nat @ I @ J) => ((![I2 : nat]: ((J = (suc @ I2)) => (P @ I2))) => ((![I2 : nat]: ((ord_less_nat @ I2 @ J) => ((P @ (suc @ I2)) => (P @ I2)))) => (P @ I))))))). % strict_inc_induct
thf(fact_133_less__Suc__induct, axiom,
    ((![I : nat, J : nat, P : nat > nat > $o]: ((ord_less_nat @ I @ J) => ((![I2 : nat]: (P @ I2 @ (suc @ I2))) => ((![I2 : nat, J2 : nat, K2 : nat]: ((ord_less_nat @ I2 @ J2) => ((ord_less_nat @ J2 @ K2) => ((P @ I2 @ J2) => ((P @ J2 @ K2) => (P @ I2 @ K2)))))) => (P @ I @ J))))))). % less_Suc_induct
thf(fact_134_less__trans__Suc, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_nat @ I @ J) => ((ord_less_nat @ J @ K) => (ord_less_nat @ (suc @ I) @ K)))))). % less_trans_Suc
thf(fact_135_Suc__less__SucD, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_nat @ (suc @ M) @ (suc @ N3)) => (ord_less_nat @ M @ N3))))). % Suc_less_SucD
thf(fact_136_less__antisym, axiom,
    ((![N3 : nat, M : nat]: ((~ ((ord_less_nat @ N3 @ M))) => ((ord_less_nat @ N3 @ (suc @ M)) => (M = N3)))))). % less_antisym
thf(fact_137_Suc__less__eq2, axiom,
    ((![N3 : nat, M : nat]: ((ord_less_nat @ (suc @ N3) @ M) = (?[M2 : nat]: (((M = (suc @ M2))) & ((ord_less_nat @ N3 @ M2)))))))). % Suc_less_eq2
thf(fact_138_All__less__Suc, axiom,
    ((![N3 : nat, P : nat > $o]: ((![I3 : nat]: (((ord_less_nat @ I3 @ (suc @ N3))) => ((P @ I3)))) = (((P @ N3)) & ((![I3 : nat]: (((ord_less_nat @ I3 @ N3)) => ((P @ I3)))))))))). % All_less_Suc
thf(fact_139_not__less__eq, axiom,
    ((![M : nat, N3 : nat]: ((~ ((ord_less_nat @ M @ N3))) = (ord_less_nat @ N3 @ (suc @ M)))))). % not_less_eq
thf(fact_140_less__Suc__eq, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_nat @ M @ (suc @ N3)) = (((ord_less_nat @ M @ N3)) | ((M = N3))))))). % less_Suc_eq
thf(fact_141_Ex__less__Suc, axiom,
    ((![N3 : nat, P : nat > $o]: ((?[I3 : nat]: (((ord_less_nat @ I3 @ (suc @ N3))) & ((P @ I3)))) = (((P @ N3)) | ((?[I3 : nat]: (((ord_less_nat @ I3 @ N3)) & ((P @ I3)))))))))). % Ex_less_Suc
thf(fact_142_less__SucI, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_nat @ M @ N3) => (ord_less_nat @ M @ (suc @ N3)))))). % less_SucI
thf(fact_143_less__SucE, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_nat @ M @ (suc @ N3)) => ((~ ((ord_less_nat @ M @ N3))) => (M = N3)))))). % less_SucE
thf(fact_144_Suc__lessI, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_nat @ M @ N3) => ((~ (((suc @ M) = N3))) => (ord_less_nat @ (suc @ M) @ N3)))))). % Suc_lessI
thf(fact_145_Suc__lessE, axiom,
    ((![I : nat, K : nat]: ((ord_less_nat @ (suc @ I) @ K) => (~ ((![J2 : nat]: ((ord_less_nat @ I @ J2) => (~ ((K = (suc @ J2)))))))))))). % Suc_lessE
thf(fact_146_Suc__lessD, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_nat @ (suc @ M) @ N3) => (ord_less_nat @ M @ N3))))). % Suc_lessD
thf(fact_147_Nat_OlessE, axiom,
    ((![I : nat, K : nat]: ((ord_less_nat @ I @ K) => ((~ ((K = (suc @ I)))) => (~ ((![J2 : nat]: ((ord_less_nat @ I @ J2) => (~ ((K = (suc @ J2))))))))))))). % Nat.lessE
thf(fact_148_diff__add__inverse2, axiom,
    ((![M : nat, N3 : nat]: ((minus_minus_nat @ (plus_plus_nat @ M @ N3) @ N3) = M)))). % diff_add_inverse2
thf(fact_149_diff__add__inverse, axiom,
    ((![N3 : nat, M : nat]: ((minus_minus_nat @ (plus_plus_nat @ N3 @ M) @ N3) = M)))). % diff_add_inverse
thf(fact_150_diff__cancel2, axiom,
    ((![M : nat, K : nat, N3 : nat]: ((minus_minus_nat @ (plus_plus_nat @ M @ K) @ (plus_plus_nat @ N3 @ K)) = (minus_minus_nat @ M @ N3))))). % diff_cancel2
thf(fact_151_Nat_Odiff__cancel, axiom,
    ((![K : nat, M : nat, N3 : nat]: ((minus_minus_nat @ (plus_plus_nat @ K @ M) @ (plus_plus_nat @ K @ N3)) = (minus_minus_nat @ M @ N3))))). % Nat.diff_cancel
thf(fact_152_less__add__eq__less, axiom,
    ((![K : nat, L : nat, M : nat, N3 : nat]: ((ord_less_nat @ K @ L) => (((plus_plus_nat @ M @ L) = (plus_plus_nat @ K @ N3)) => (ord_less_nat @ M @ N3)))))). % less_add_eq_less
thf(fact_153_trans__less__add2, axiom,
    ((![I : nat, J : nat, M : nat]: ((ord_less_nat @ I @ J) => (ord_less_nat @ I @ (plus_plus_nat @ M @ J)))))). % trans_less_add2
thf(fact_154_trans__less__add1, axiom,
    ((![I : nat, J : nat, M : nat]: ((ord_less_nat @ I @ J) => (ord_less_nat @ I @ (plus_plus_nat @ J @ M)))))). % trans_less_add1
thf(fact_155_add__less__mono1, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_nat @ I @ J) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ K)))))). % add_less_mono1
thf(fact_156_not__add__less2, axiom,
    ((![J : nat, I : nat]: (~ ((ord_less_nat @ (plus_plus_nat @ J @ I) @ I)))))). % not_add_less2
thf(fact_157_not__add__less1, axiom,
    ((![I : nat, J : nat]: (~ ((ord_less_nat @ (plus_plus_nat @ I @ J) @ I)))))). % not_add_less1
thf(fact_158_add__less__mono, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: ((ord_less_nat @ I @ J) => ((ord_less_nat @ K @ L) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L))))))). % add_less_mono
thf(fact_159_add__lessD1, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_nat @ (plus_plus_nat @ I @ J) @ K) => (ord_less_nat @ I @ K))))). % add_lessD1
thf(fact_160_real__norm__def, axiom,
    ((real_V646646907m_real = abs_abs_real))). % real_norm_def
thf(fact_161_nonzero__norm__inverse, axiom,
    ((![A : complex]: ((~ ((A = zero_zero_complex))) => ((real_V638595069omplex @ (invers502456322omplex @ A)) = (inverse_inverse_real @ (real_V638595069omplex @ A))))))). % nonzero_norm_inverse
thf(fact_162_nonzero__norm__inverse, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((real_V646646907m_real @ (inverse_inverse_real @ A)) = (inverse_inverse_real @ (real_V646646907m_real @ A))))))). % nonzero_norm_inverse
thf(fact_163_norm__inverse, axiom,
    ((![A : complex]: ((real_V638595069omplex @ (invers502456322omplex @ A)) = (inverse_inverse_real @ (real_V638595069omplex @ A)))))). % norm_inverse
thf(fact_164_norm__inverse, axiom,
    ((![A : real]: ((real_V646646907m_real @ (inverse_inverse_real @ A)) = (inverse_inverse_real @ (real_V646646907m_real @ A)))))). % norm_inverse
thf(fact_165_Suc__nat__number__of__add, axiom,
    ((![V : num, N3 : nat]: ((suc @ (plus_plus_nat @ (numeral_numeral_nat @ V) @ N3)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ V @ one)) @ N3))))). % Suc_nat_number_of_add
thf(fact_166_nat__1__add__1, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % nat_1_add_1
thf(fact_167_less__imp__Suc__add, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_nat @ M @ N3) => (?[K2 : nat]: (N3 = (suc @ (plus_plus_nat @ M @ K2)))))))). % less_imp_Suc_add
thf(fact_168_less__iff__Suc__add, axiom,
    ((ord_less_nat = (^[M3 : nat]: (^[N5 : nat]: (?[K3 : nat]: (N5 = (suc @ (plus_plus_nat @ M3 @ K3))))))))). % less_iff_Suc_add
thf(fact_169_less__add__Suc2, axiom,
    ((![I : nat, M : nat]: (ord_less_nat @ I @ (suc @ (plus_plus_nat @ M @ I)))))). % less_add_Suc2
thf(fact_170_less__add__Suc1, axiom,
    ((![I : nat, M : nat]: (ord_less_nat @ I @ (suc @ (plus_plus_nat @ I @ M)))))). % less_add_Suc1
thf(fact_171_less__natE, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_nat @ M @ N3) => (~ ((![Q : nat]: (~ ((N3 = (suc @ (plus_plus_nat @ M @ Q)))))))))))). % less_natE
thf(fact_172_Suc__eq__plus1__left, axiom,
    ((suc = (plus_plus_nat @ one_one_nat)))). % Suc_eq_plus1_left
thf(fact_173_plus__1__eq__Suc, axiom,
    (((plus_plus_nat @ one_one_nat) = suc))). % plus_1_eq_Suc
thf(fact_174_Suc__eq__plus1, axiom,
    ((suc = (^[N5 : nat]: (plus_plus_nat @ N5 @ one_one_nat))))). % Suc_eq_plus1
thf(fact_175_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_176_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_177_zero__neq__numeral, axiom,
    ((![N3 : num]: (~ ((zero_zero_real = (numeral_numeral_real @ N3))))))). % zero_neq_numeral
thf(fact_178_zero__neq__numeral, axiom,
    ((![N3 : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N3))))))). % zero_neq_numeral
thf(fact_179_norm__diff__triangle__less, axiom,
    ((![X3 : complex, Y3 : complex, E1 : real, Z2 : complex, E2 : real]: ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ X3 @ Y3)) @ E1) => ((ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ Y3 @ Z2)) @ E2) => (ord_less_real @ (real_V638595069omplex @ (minus_minus_complex @ X3 @ Z2)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_less
thf(fact_180_norm__diff__triangle__less, axiom,
    ((![X3 : real, Y3 : real, E1 : real, Z2 : real, E2 : real]: ((ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ X3 @ Y3)) @ E1) => ((ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ Y3 @ Z2)) @ E2) => (ord_less_real @ (real_V646646907m_real @ (minus_minus_real @ X3 @ Z2)) @ (plus_plus_real @ E1 @ E2))))))). % norm_diff_triangle_less
thf(fact_181_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)

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_real @ (divide_divide_real @ one_one_real @ (semiri2110766477t_real @ (suc @ (plus_plus_nat @ n1 @ n2)))) @ (divide_divide_real @ (abs_abs_real @ (minus_minus_real @ (real_V638595069omplex @ (poly_complex2 @ p @ z)) @ (uminus_uminus_real @ s))) @ (numeral_numeral_real @ (bit0 @ one)))))).
