% 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_274__5370268_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:28:51.627

% Could-be-implicit typings (3)
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (33)
thf(sy_c_Complex_Ocomplex_OIm, type,
    im : complex > real).
thf(sy_c_Complex_Ocomplex_ORe, type,
    re : complex > real).
thf(sy_c_Complex_Ocomplex_Ocase__complex_001t__Real__Oreal, type,
    case_complex_real : (real > real > real) > complex > real).
thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Real__Oreal_001t__Nat__Onat, type,
    comp_c1631780367al_nat : (complex > real) > (nat > complex) > nat > real).
thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat, type,
    comp_nat_nat_nat : (nat > nat) > (nat > nat) > nat > nat).
thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Real__Oreal_001t__Nat__Onat, type,
    comp_nat_real_nat : (nat > real) > (nat > nat) > nat > real).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex, type,
    abs_abs_complex : complex > complex).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_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__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_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__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Real__Oreal, type,
    order_106095024t_real : (nat > 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_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Real__Oreal, type,
    order_952716343t_real : (nat > real) > $o).
thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Real__Oreal_001t__Real__Oreal, type,
    order_1818878995l_real : (real > real) > $o).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal, type,
    topolo144289241q_real : (nat > real) > $o).
thf(sy_c_Topological__Spaces_Otopological__space__class_Oconvergent_001t__Real__Oreal, type,
    topolo795669587t_real : (nat > real) > $o).
thf(sy_v_f____, type,
    f : nat > nat).
thf(sy_v_g____, type,
    g : nat > nat).
thf(sy_v_r, type,
    r : real).
thf(sy_v_s, type,
    s : nat > complex).

% Relevant facts (215)
thf(fact_0_g_I2_J, axiom,
    ((topolo144289241q_real @ (^[N : nat]: (im @ (s @ (f @ (g @ N)))))))). % g(2)
thf(fact_1_f_I1_J, axiom,
    ((order_769474267at_nat @ f))). % f(1)
thf(fact_2_g_I1_J, axiom,
    ((order_769474267at_nat @ g))). % g(1)
thf(fact_3_f_I2_J, axiom,
    ((topolo144289241q_real @ (^[N : nat]: (re @ (s @ (f @ N))))))). % f(2)
thf(fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062g_O_A_092_060lbrakk_062strict__mono_Ag_059_Amonoseq_A_I_092_060lambda_062n_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![G : nat > nat]: ((order_769474267at_nat @ G) => (~ ((topolo144289241q_real @ (^[N : nat]: (im @ (s @ (f @ (G @ N)))))))))))))). % \<open>\<And>thesis. (\<And>g. \<lbrakk>strict_mono g; monoseq (\<lambda>n. Im (s (f (g n))))\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_5_conv1, axiom,
    ((topolo795669587t_real @ (^[N : nat]: (re @ (s @ (f @ N))))))). % conv1
thf(fact_6__092_060open_062_092_060exists_062fa_O_Astrict__mono_Afa_A_092_060and_062_Amonoseq_A_I_092_060lambda_062n_O_A_IIm_A_092_060circ_062_As_A_092_060circ_062_Af_J_A_Ifa_An_J_J_092_060close_062, axiom,
    ((?[F : nat > nat]: ((order_769474267at_nat @ F) & (topolo144289241q_real @ (^[N : nat]: (comp_nat_real_nat @ (comp_c1631780367al_nat @ im @ s) @ f @ (F @ N)))))))). % \<open>\<exists>fa. strict_mono fa \<and> monoseq (\<lambda>n. (Im \<circ> s \<circ> f) (fa n))\<close>
thf(fact_7__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062f_O_A_092_060lbrakk_062strict__mono_Af_059_Amonoseq_A_I_092_060lambda_062n_O_ARe_A_Is_A_If_An_J_J_J_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) => (~ ((topolo144289241q_real @ (^[N : nat]: (re @ (s @ (F @ N))))))))))))). % \<open>\<And>thesis. (\<And>f. \<lbrakk>strict_mono f; monoseq (\<lambda>n. Re (s (f n)))\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_8_r, axiom,
    ((![N2 : nat]: (ord_less_eq_real @ (real_V638595069omplex @ (s @ N2)) @ r)))). % r
thf(fact_9__092_060open_062_092_060exists_062f_O_Astrict__mono_Af_A_092_060and_062_Amonoseq_A_I_092_060lambda_062n_O_A_IRe_A_092_060circ_062_As_J_A_If_An_J_J_092_060close_062, axiom,
    ((?[F : nat > nat]: ((order_769474267at_nat @ F) & (topolo144289241q_real @ (^[N : nat]: (comp_c1631780367al_nat @ re @ s @ (F @ N)))))))). % \<open>\<exists>f. strict_mono f \<and> monoseq (\<lambda>n. (Re \<circ> s) (f n))\<close>
thf(fact_10_Im__def, axiom,
    ((im = (case_complex_real @ (^[X1 : real]: (^[X2 : real]: X2)))))). % Im_def
thf(fact_11_seq__monosub, axiom,
    ((![S : nat > real]: (?[F : nat > nat]: ((order_769474267at_nat @ F) & (topolo144289241q_real @ (^[N : nat]: (S @ (F @ N))))))))). % seq_monosub
thf(fact_12_monoseq__minus, axiom,
    ((![A : nat > real]: ((topolo144289241q_real @ A) => (topolo144289241q_real @ (^[N : nat]: (uminus_uminus_real @ (A @ N)))))))). % monoseq_minus
thf(fact_13_decseq__imp__monoseq, axiom,
    ((![X : nat > real]: ((order_106095024t_real @ X) => (topolo144289241q_real @ X))))). % decseq_imp_monoseq
thf(fact_14_th, axiom,
    ((![N2 : nat]: (ord_less_eq_real @ (abs_abs_real @ (im @ (s @ N2))) @ (plus_plus_real @ r @ one_one_real))))). % th
thf(fact_15_uminus__complex_Osimps_I2_J, axiom,
    ((![X3 : complex]: ((im @ (uminus1204672759omplex @ X3)) = (uminus_uminus_real @ (im @ X3)))))). % uminus_complex.simps(2)
thf(fact_16_uminus__complex_Osimps_I1_J, axiom,
    ((![X3 : complex]: ((re @ (uminus1204672759omplex @ X3)) = (uminus_uminus_real @ (re @ X3)))))). % uminus_complex.simps(1)
thf(fact_17_cmod__le, axiom,
    ((![Z : complex]: (ord_less_eq_real @ (real_V638595069omplex @ Z) @ (plus_plus_real @ (abs_abs_real @ (re @ Z)) @ (abs_abs_real @ (im @ Z))))))). % cmod_le
thf(fact_18_abs__Im__le__cmod, axiom,
    ((![X3 : complex]: (ord_less_eq_real @ (abs_abs_real @ (im @ X3)) @ (real_V638595069omplex @ X3))))). % abs_Im_le_cmod
thf(fact_19_abs__Re__le__cmod, axiom,
    ((![X3 : complex]: (ord_less_eq_real @ (abs_abs_real @ (re @ X3)) @ (real_V638595069omplex @ X3))))). % abs_Re_le_cmod
thf(fact_20_cmod__Im__le__iff, axiom,
    ((![X3 : complex, Y : complex]: (((re @ X3) = (re @ Y)) => ((ord_less_eq_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y)) = (ord_less_eq_real @ (abs_abs_real @ (im @ X3)) @ (abs_abs_real @ (im @ Y)))))))). % cmod_Im_le_iff
thf(fact_21_cmod__Re__le__iff, axiom,
    ((![X3 : complex, Y : complex]: (((im @ X3) = (im @ Y)) => ((ord_less_eq_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y)) = (ord_less_eq_real @ (abs_abs_real @ (re @ X3)) @ (abs_abs_real @ (re @ Y)))))))). % cmod_Re_le_iff
thf(fact_22_Re__def, axiom,
    ((re = (case_complex_real @ (^[X1 : real]: (^[X2 : real]: X1)))))). % Re_def
thf(fact_23_monoI1, axiom,
    ((![X : nat > real]: ((![M : nat, N3 : nat]: ((ord_less_eq_nat @ M @ N3) => (ord_less_eq_real @ (X @ M) @ (X @ N3)))) => (topolo144289241q_real @ X))))). % monoI1
thf(fact_24_monoI2, axiom,
    ((![X : nat > real]: ((![M : nat, N3 : nat]: ((ord_less_eq_nat @ M @ N3) => (ord_less_eq_real @ (X @ N3) @ (X @ M)))) => (topolo144289241q_real @ X))))). % monoI2
thf(fact_25_complex_Ocase__eq__if, axiom,
    ((case_complex_real = (^[F2 : real > real > real]: (^[Complex : complex]: (F2 @ (re @ Complex) @ (im @ Complex))))))). % complex.case_eq_if
thf(fact_26_complex__Re__le__cmod, axiom,
    ((![X3 : complex]: (ord_less_eq_real @ (re @ X3) @ (real_V638595069omplex @ X3))))). % complex_Re_le_cmod
thf(fact_27_decseqD, axiom,
    ((![F3 : nat > real, I : nat, J : nat]: ((order_106095024t_real @ F3) => ((ord_less_eq_nat @ I @ J) => (ord_less_eq_real @ (F3 @ J) @ (F3 @ I))))))). % decseqD
thf(fact_28_complex_Ocase__distrib, axiom,
    ((![H : real > real, F3 : real > real > real, Complex2 : complex]: ((H @ (case_complex_real @ F3 @ Complex2)) = (case_complex_real @ (^[X1 : real]: (^[X2 : real]: (H @ (F3 @ X1 @ X2)))) @ Complex2))))). % complex.case_distrib
thf(fact_29_decseq__def, axiom,
    ((order_106095024t_real = (^[X4 : nat > real]: (![M2 : nat]: (![N : nat]: (((ord_less_eq_nat @ M2 @ N)) => ((ord_less_eq_real @ (X4 @ N) @ (X4 @ M2)))))))))). % decseq_def
thf(fact_30_monoseq__def, axiom,
    ((topolo144289241q_real = (^[X4 : nat > real]: (((![M2 : nat]: (![N : nat]: (((ord_less_eq_nat @ M2 @ N)) => ((ord_less_eq_real @ (X4 @ M2) @ (X4 @ N))))))) | ((![M2 : nat]: (![N : nat]: (((ord_less_eq_nat @ M2 @ N)) => ((ord_less_eq_real @ (X4 @ N) @ (X4 @ M2)))))))))))). % monoseq_def
thf(fact_31_strict__mono__o, axiom,
    ((![R : nat > real, S : nat > nat]: ((order_952716343t_real @ R) => ((order_769474267at_nat @ S) => (order_952716343t_real @ (comp_nat_real_nat @ R @ S))))))). % strict_mono_o
thf(fact_32_strict__mono__o, axiom,
    ((![R : nat > nat, S : nat > nat]: ((order_769474267at_nat @ R) => ((order_769474267at_nat @ S) => (order_769474267at_nat @ (comp_nat_nat_nat @ R @ S))))))). % strict_mono_o
thf(fact_33_strict__mono__add, axiom,
    ((![K : real]: (order_1818878995l_real @ (^[N : real]: (plus_plus_real @ N @ K)))))). % strict_mono_add
thf(fact_34_strict__mono__add, axiom,
    ((![K : nat]: (order_769474267at_nat @ (^[N : nat]: (plus_plus_nat @ N @ K)))))). % strict_mono_add
thf(fact_35_strict__mono__leD, axiom,
    ((![R : real > real, M3 : real, N4 : real]: ((order_1818878995l_real @ R) => ((ord_less_eq_real @ M3 @ N4) => (ord_less_eq_real @ (R @ M3) @ (R @ N4))))))). % strict_mono_leD
thf(fact_36_strict__mono__leD, axiom,
    ((![R : nat > nat, M3 : nat, N4 : nat]: ((order_769474267at_nat @ R) => ((ord_less_eq_nat @ M3 @ N4) => (ord_less_eq_nat @ (R @ M3) @ (R @ N4))))))). % strict_mono_leD
thf(fact_37_convergent__const, axiom,
    ((![C : real]: (topolo795669587t_real @ (^[N : nat]: C))))). % convergent_const
thf(fact_38_strict__mono__compose, axiom,
    ((![R : nat > nat, S : nat > nat]: ((order_769474267at_nat @ R) => ((order_769474267at_nat @ S) => (order_769474267at_nat @ (^[X5 : nat]: (R @ (S @ X5))))))))). % strict_mono_compose
thf(fact_39_complex__mod__minus__le__complex__mod, axiom,
    ((![X3 : complex]: (ord_less_eq_real @ (uminus_uminus_real @ (real_V638595069omplex @ X3)) @ (real_V638595069omplex @ X3))))). % complex_mod_minus_le_complex_mod
thf(fact_40_convergent__subseq__convergent, axiom,
    ((![X : nat > real, F3 : nat > nat]: ((topolo795669587t_real @ X) => ((order_769474267at_nat @ F3) => (topolo795669587t_real @ (comp_nat_real_nat @ X @ F3))))))). % convergent_subseq_convergent
thf(fact_41_complex_Ocoinduct__strong, axiom,
    ((![R2 : complex > complex > $o, Complex2 : complex, Complex3 : complex]: ((R2 @ Complex2 @ Complex3) => ((![Complex4 : complex, Complex5 : complex]: ((R2 @ Complex4 @ Complex5) => (((re @ Complex4) = (re @ Complex5)) & ((im @ Complex4) = (im @ Complex5))))) => (Complex2 = Complex3)))))). % complex.coinduct_strong
thf(fact_42_complex__eq__iff, axiom,
    (((^[Y2 : complex]: (^[Z2 : complex]: (Y2 = Z2))) = (^[X5 : complex]: (^[Y3 : complex]: ((((re @ X5) = (re @ Y3))) & (((im @ X5) = (im @ Y3))))))))). % complex_eq_iff
thf(fact_43_complex_Oexpand, axiom,
    ((![Complex2 : complex, Complex3 : complex]: ((((re @ Complex2) = (re @ Complex3)) & ((im @ Complex2) = (im @ Complex3))) => (Complex2 = Complex3))))). % complex.expand
thf(fact_44_complex__eqI, axiom,
    ((![X3 : complex, Y : complex]: (((re @ X3) = (re @ Y)) => (((im @ X3) = (im @ Y)) => (X3 = Y)))))). % complex_eqI
thf(fact_45_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_46_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_47_abs__neg__one, axiom,
    (((abs_abs_real @ (uminus_uminus_real @ one_one_real)) = one_one_real))). % abs_neg_one
thf(fact_48__092_060open_062cmod_A_Is_A0_J_A_092_060le_062_Ar_092_060close_062, axiom,
    ((ord_less_eq_real @ (real_V638595069omplex @ (s @ zero_zero_nat)) @ r))). % \<open>cmod (s 0) \<le> r\<close>
thf(fact_49_abs__norm__cancel, axiom,
    ((![A : complex]: ((abs_abs_real @ (real_V638595069omplex @ A)) = (real_V638595069omplex @ A))))). % abs_norm_cancel
thf(fact_50_abs__norm__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (real_V646646907m_real @ A)) = (real_V646646907m_real @ A))))). % abs_norm_cancel
thf(fact_51_norm__minus__cancel, axiom,
    ((![X3 : complex]: ((real_V638595069omplex @ (uminus1204672759omplex @ X3)) = (real_V638595069omplex @ X3))))). % norm_minus_cancel
thf(fact_52_norm__minus__cancel, axiom,
    ((![X3 : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X3)) = (real_V646646907m_real @ X3))))). % norm_minus_cancel
thf(fact_53_abs__minus, axiom,
    ((![A : complex]: ((abs_abs_complex @ (uminus1204672759omplex @ A)) = (abs_abs_complex @ A))))). % abs_minus
thf(fact_54_abs__minus, axiom,
    ((![A : real]: ((abs_abs_real @ (uminus_uminus_real @ A)) = (abs_abs_real @ A))))). % abs_minus
thf(fact_55_abs__minus__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (uminus_uminus_real @ A)) = (abs_abs_real @ A))))). % abs_minus_cancel
thf(fact_56_abs__1, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_1
thf(fact_57_abs__1, axiom,
    (((abs_abs_complex @ one_one_complex) = one_one_complex))). % abs_1
thf(fact_58_abs__add__abs, axiom,
    ((![A : real, B : real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_add_abs
thf(fact_59_add__right__cancel, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_60_add__right__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_61_add__left__cancel, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_62_add__left__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_63_neg__equal__iff__equal, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = (uminus1204672759omplex @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_64_neg__equal__iff__equal, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_65_add_Oinverse__inverse, axiom,
    ((![A : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ A)) = A)))). % add.inverse_inverse
thf(fact_66_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_67_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_68_abs__abs, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_abs
thf(fact_69_le__zero__eq, axiom,
    ((![N4 : nat]: ((ord_less_eq_nat @ N4 @ zero_zero_nat) = (N4 = zero_zero_nat))))). % le_zero_eq
thf(fact_70_zero__eq__add__iff__both__eq__0, axiom,
    ((![X3 : nat, Y : nat]: ((zero_zero_nat = (plus_plus_nat @ X3 @ Y)) = (((X3 = zero_zero_nat)) & ((Y = zero_zero_nat))))))). % zero_eq_add_iff_both_eq_0
thf(fact_71_add__eq__0__iff__both__eq__0, axiom,
    ((![X3 : nat, Y : nat]: (((plus_plus_nat @ X3 @ Y) = zero_zero_nat) = (((X3 = zero_zero_nat)) & ((Y = zero_zero_nat))))))). % add_eq_0_iff_both_eq_0
thf(fact_72_add__cancel__right__right, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real))))). % add_cancel_right_right
thf(fact_73_add__cancel__right__right, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex))))). % add_cancel_right_right
thf(fact_74_add__cancel__right__right, axiom,
    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat))))). % add_cancel_right_right
thf(fact_75_add__cancel__right__left, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real))))). % add_cancel_right_left
thf(fact_76_add__cancel__right__left, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ B @ A)) = (B = zero_zero_complex))))). % add_cancel_right_left
thf(fact_77_add__cancel__right__left, axiom,
    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat))))). % add_cancel_right_left
thf(fact_78_add__cancel__left__right, axiom,
    ((![A : real, B : real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real))))). % add_cancel_left_right
thf(fact_79_add__cancel__left__right, axiom,
    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = A) = (B = zero_zero_complex))))). % add_cancel_left_right
thf(fact_80_add__cancel__left__right, axiom,
    ((![A : nat, B : nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat))))). % add_cancel_left_right
thf(fact_81_add__cancel__left__left, axiom,
    ((![B : real, A : real]: (((plus_plus_real @ B @ A) = A) = (B = zero_zero_real))))). % add_cancel_left_left
thf(fact_82_add__cancel__left__left, axiom,
    ((![B : complex, A : complex]: (((plus_plus_complex @ B @ A) = A) = (B = zero_zero_complex))))). % add_cancel_left_left
thf(fact_83_add__cancel__left__left, axiom,
    ((![B : nat, A : nat]: (((plus_plus_nat @ B @ A) = A) = (B = zero_zero_nat))))). % add_cancel_left_left
thf(fact_84_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_85_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_86_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_87_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_88_add_Oright__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.right_neutral
thf(fact_89_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_90_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_91_add_Oleft__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % add.left_neutral
thf(fact_92_add__le__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_right
thf(fact_93_add__le__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_left
thf(fact_94_neg__equal__zero, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real))))). % neg_equal_zero
thf(fact_95_equal__neg__zero, axiom,
    ((![A : real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real))))). % equal_neg_zero
thf(fact_96_neg__equal__0__iff__equal, axiom,
    ((![A : complex]: (((uminus1204672759omplex @ A) = zero_zero_complex) = (A = zero_zero_complex))))). % neg_equal_0_iff_equal
thf(fact_97_neg__equal__0__iff__equal, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % neg_equal_0_iff_equal
thf(fact_98_neg__0__equal__iff__equal, axiom,
    ((![A : complex]: ((zero_zero_complex = (uminus1204672759omplex @ A)) = (zero_zero_complex = A))))). % neg_0_equal_iff_equal
thf(fact_99_neg__0__equal__iff__equal, axiom,
    ((![A : real]: ((zero_zero_real = (uminus_uminus_real @ A)) = (zero_zero_real = A))))). % neg_0_equal_iff_equal
thf(fact_100_add_Oinverse__neutral, axiom,
    (((uminus1204672759omplex @ zero_zero_complex) = zero_zero_complex))). % add.inverse_neutral
thf(fact_101_add_Oinverse__neutral, axiom,
    (((uminus_uminus_real @ zero_zero_real) = zero_zero_real))). % add.inverse_neutral
thf(fact_102_neg__le__iff__le, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ B))))). % neg_le_iff_le
thf(fact_103_minus__add__distrib, axiom,
    ((![A : complex, B : complex]: ((uminus1204672759omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1204672759omplex @ A) @ (uminus1204672759omplex @ B)))))). % minus_add_distrib
thf(fact_104_minus__add__distrib, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)))))). % minus_add_distrib
thf(fact_105_minus__add__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ (plus_plus_complex @ A @ B)) = B)))). % minus_add_cancel
thf(fact_106_minus__add__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ (plus_plus_real @ A @ B)) = B)))). % minus_add_cancel
thf(fact_107_add__minus__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ (uminus1204672759omplex @ A) @ B)) = B)))). % add_minus_cancel
thf(fact_108_add__minus__cancel, axiom,
    ((![A : real, B : real]: ((plus_plus_real @ A @ (plus_plus_real @ (uminus_uminus_real @ A) @ B)) = B)))). % add_minus_cancel
thf(fact_109_abs__zero, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_zero
thf(fact_110_abs__eq__0, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0
thf(fact_111_abs__0__eq, axiom,
    ((![A : real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real))))). % abs_0_eq
thf(fact_112_abs__0, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_0
thf(fact_113_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_114_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_115_norm__eq__zero, axiom,
    ((![X3 : complex]: (((real_V638595069omplex @ X3) = zero_zero_real) = (X3 = zero_zero_complex))))). % norm_eq_zero
thf(fact_116_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_117_zero__le__double__add__iff__zero__le__single__add, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_double_add_iff_zero_le_single_add
thf(fact_118_double__add__le__zero__iff__single__add__le__zero, axiom,
    ((![A : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % double_add_le_zero_iff_single_add_le_zero
thf(fact_119_le__add__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_eq_nat @ zero_zero_nat @ B))))). % le_add_same_cancel2
thf(fact_120_le__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel2
thf(fact_121_le__add__same__cancel1, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_eq_nat @ zero_zero_nat @ B))))). % le_add_same_cancel1
thf(fact_122_le__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel1
thf(fact_123_add__le__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_eq_nat @ A @ zero_zero_nat))))). % add_le_same_cancel2
thf(fact_124_add__le__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel2
thf(fact_125_add__le__same__cancel1, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ B) = (ord_less_eq_nat @ A @ zero_zero_nat))))). % add_le_same_cancel1
thf(fact_126_add__le__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel1
thf(fact_127_neg__less__eq__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A))))). % neg_less_eq_nonneg
thf(fact_128_less__eq__neg__nonpos, axiom,
    ((![A : real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real))))). % less_eq_neg_nonpos
thf(fact_129_neg__le__0__iff__le, axiom,
    ((![A : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_eq_real @ zero_zero_real @ A))))). % neg_le_0_iff_le
thf(fact_130_neg__0__le__iff__le, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real))))). % neg_0_le_iff_le
thf(fact_131_add_Oright__inverse, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ (uminus1204672759omplex @ A)) = zero_zero_complex)))). % add.right_inverse
thf(fact_132_add_Oright__inverse, axiom,
    ((![A : real]: ((plus_plus_real @ A @ (uminus_uminus_real @ A)) = zero_zero_real)))). % add.right_inverse
thf(fact_133_add_Oleft__inverse, axiom,
    ((![A : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ A) = zero_zero_complex)))). % add.left_inverse
thf(fact_134_add_Oleft__inverse, axiom,
    ((![A : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real)))). % add.left_inverse
thf(fact_135_abs__le__zero__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ zero_zero_real) = (A = zero_zero_real))))). % abs_le_zero_iff
thf(fact_136_abs__le__self__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A))))). % abs_le_self_iff
thf(fact_137_abs__of__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_nonneg
thf(fact_138_norm__le__zero__iff, axiom,
    ((![X3 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X3) @ zero_zero_real) = (X3 = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_139_norm__le__zero__iff, axiom,
    ((![X3 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X3) @ zero_zero_real) = (X3 = zero_zero_real))))). % norm_le_zero_iff
thf(fact_140_add__neg__numeral__special_I7_J, axiom,
    (((plus_plus_complex @ one_one_complex @ (uminus1204672759omplex @ one_one_complex)) = zero_zero_complex))). % add_neg_numeral_special(7)
thf(fact_141_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_142_add__neg__numeral__special_I8_J, axiom,
    (((plus_plus_complex @ (uminus1204672759omplex @ one_one_complex) @ one_one_complex) = zero_zero_complex))). % add_neg_numeral_special(8)
thf(fact_143_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_144_abs__of__nonpos, axiom,
    ((![A : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((abs_abs_real @ A) = (uminus_uminus_real @ A)))))). % abs_of_nonpos
thf(fact_145_zero__reorient, axiom,
    ((![X3 : nat]: ((zero_zero_nat = X3) = (X3 = zero_zero_nat))))). % zero_reorient
thf(fact_146_zero__le, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ zero_zero_nat @ X3)))). % zero_le
thf(fact_147_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat))). % le_numeral_extra(3)
thf(fact_148_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_149_add_Ogroup__left__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.group_left_neutral
thf(fact_150_add_Ogroup__left__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.group_left_neutral
thf(fact_151_add_Ocomm__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.comm_neutral
thf(fact_152_add_Ocomm__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.comm_neutral
thf(fact_153_add_Ocomm__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.comm_neutral
thf(fact_154_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_155_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_156_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_157_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_158_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_159_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_160_real__norm__def, axiom,
    ((real_V646646907m_real = abs_abs_real))). % real_norm_def
thf(fact_161_abs__eq__0__iff, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0_iff
thf(fact_162_add__nonpos__eq__0__iff, axiom,
    ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ X3 @ zero_zero_nat) => ((ord_less_eq_nat @ Y @ zero_zero_nat) => (((plus_plus_nat @ X3 @ Y) = zero_zero_nat) = (((X3 = zero_zero_nat)) & ((Y = zero_zero_nat))))))))). % add_nonpos_eq_0_iff
thf(fact_163_add__nonpos__eq__0__iff, axiom,
    ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ zero_zero_real) => ((ord_less_eq_real @ Y @ zero_zero_real) => (((plus_plus_real @ X3 @ Y) = zero_zero_real) = (((X3 = zero_zero_real)) & ((Y = zero_zero_real))))))))). % add_nonpos_eq_0_iff
thf(fact_164_add__nonneg__eq__0__iff, axiom,
    ((![X3 : nat, Y : nat]: ((ord_less_eq_nat @ zero_zero_nat @ X3) => ((ord_less_eq_nat @ zero_zero_nat @ Y) => (((plus_plus_nat @ X3 @ Y) = zero_zero_nat) = (((X3 = zero_zero_nat)) & ((Y = zero_zero_nat))))))))). % add_nonneg_eq_0_iff
thf(fact_165_add__nonneg__eq__0__iff, axiom,
    ((![X3 : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ zero_zero_real @ Y) => (((plus_plus_real @ X3 @ Y) = zero_zero_real) = (((X3 = zero_zero_real)) & ((Y = zero_zero_real))))))))). % add_nonneg_eq_0_iff
thf(fact_166_add__nonpos__nonpos, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)))))). % add_nonpos_nonpos
thf(fact_167_add__nonpos__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_nonpos_nonpos
thf(fact_168_add__nonneg__nonneg, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))))))). % add_nonneg_nonneg
thf(fact_169_add__nonneg__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_nonneg_nonneg
thf(fact_170_add__increasing2, axiom,
    ((![C : nat, B : nat, A : nat]: ((ord_less_eq_nat @ zero_zero_nat @ C) => ((ord_less_eq_nat @ B @ A) => (ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C))))))). % add_increasing2
thf(fact_171_add__increasing2, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_eq_real @ zero_zero_real @ C) => ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing2
thf(fact_172_add__decreasing2, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ C @ zero_zero_nat) => ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ B)))))). % add_decreasing2
thf(fact_173_add__decreasing2, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ C @ zero_zero_real) => ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing2
thf(fact_174_add__increasing, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C))))))). % add_increasing
thf(fact_175_add__increasing, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing
thf(fact_176_add__decreasing, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ B)))))). % add_decreasing
thf(fact_177_add__decreasing, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing
thf(fact_178_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_nat @ one_one_nat @ zero_zero_nat))))). % not_one_le_zero
thf(fact_179_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_180_zero__le__one, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ one_one_nat))). % zero_le_one
thf(fact_181_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_182_neg__eq__iff__add__eq__0, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = B) = ((plus_plus_complex @ A @ B) = zero_zero_complex))))). % neg_eq_iff_add_eq_0
thf(fact_183_neg__eq__iff__add__eq__0, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((plus_plus_real @ A @ B) = zero_zero_real))))). % neg_eq_iff_add_eq_0
thf(fact_184_eq__neg__iff__add__eq__0, axiom,
    ((![A : complex, B : complex]: ((A = (uminus1204672759omplex @ B)) = ((plus_plus_complex @ A @ B) = zero_zero_complex))))). % eq_neg_iff_add_eq_0
thf(fact_185_eq__neg__iff__add__eq__0, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = ((plus_plus_real @ A @ B) = zero_zero_real))))). % eq_neg_iff_add_eq_0
thf(fact_186_add_Oinverse__unique, axiom,
    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = zero_zero_complex) => ((uminus1204672759omplex @ A) = B))))). % add.inverse_unique
thf(fact_187_add_Oinverse__unique, axiom,
    ((![A : real, B : real]: (((plus_plus_real @ A @ B) = zero_zero_real) => ((uminus_uminus_real @ A) = B))))). % add.inverse_unique
thf(fact_188_ab__group__add__class_Oab__left__minus, axiom,
    ((![A : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ A) = zero_zero_complex)))). % ab_group_add_class.ab_left_minus
thf(fact_189_ab__group__add__class_Oab__left__minus, axiom,
    ((![A : real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real)))). % ab_group_add_class.ab_left_minus
thf(fact_190_add__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = zero_zero_complex) = (B = (uminus1204672759omplex @ A)))))). % add_eq_0_iff
thf(fact_191_add__eq__0__iff, axiom,
    ((![A : real, B : real]: (((plus_plus_real @ A @ B) = zero_zero_real) = (B = (uminus_uminus_real @ A)))))). % add_eq_0_iff
thf(fact_192_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_complex = (uminus1204672759omplex @ one_one_complex)))))). % zero_neq_neg_one
thf(fact_193_zero__neq__neg__one, axiom,
    ((~ ((zero_zero_real = (uminus_uminus_real @ one_one_real)))))). % zero_neq_neg_one
thf(fact_194_abs__ge__zero, axiom,
    ((![A : real]: (ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ A))))). % abs_ge_zero
thf(fact_195_le__minus__one__simps_I1_J, axiom,
    ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real))). % le_minus_one_simps(1)
thf(fact_196_le__minus__one__simps_I3_J, axiom,
    ((~ ((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))))). % le_minus_one_simps(3)
thf(fact_197_abs__minus__le__zero, axiom,
    ((![A : real]: (ord_less_eq_real @ (uminus_uminus_real @ (abs_abs_real @ A)) @ zero_zero_real)))). % abs_minus_le_zero
thf(fact_198_eq__abs__iff_H, axiom,
    ((![A : real, B : real]: ((A = (abs_abs_real @ B)) = (((ord_less_eq_real @ zero_zero_real @ A)) & ((((B = A)) | ((B = (uminus_uminus_real @ A)))))))))). % eq_abs_iff'
thf(fact_199_abs__eq__iff_H, axiom,
    ((![A : real, B : real]: (((abs_abs_real @ A) = B) = (((ord_less_eq_real @ zero_zero_real @ B)) & ((((A = B)) | ((A = (uminus_uminus_real @ B)))))))))). % abs_eq_iff'
thf(fact_200_plus__complex_Osimps_I1_J, axiom,
    ((![X3 : complex, Y : complex]: ((re @ (plus_plus_complex @ X3 @ Y)) = (plus_plus_real @ (re @ X3) @ (re @ Y)))))). % plus_complex.simps(1)
thf(fact_201_plus__complex_Osimps_I2_J, axiom,
    ((![X3 : complex, Y : complex]: ((im @ (plus_plus_complex @ X3 @ Y)) = (plus_plus_real @ (im @ X3) @ (im @ Y)))))). % plus_complex.simps(2)
thf(fact_202_one__complex_Osimps_I1_J, axiom,
    (((re @ one_one_complex) = one_one_real))). % one_complex.simps(1)
thf(fact_203_add__right__imp__eq, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_204_add__right__imp__eq, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_205_add__left__imp__eq, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_206_add__left__imp__eq, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_207_add_Oleft__commute, axiom,
    ((![B : real, A : real, C : real]: ((plus_plus_real @ B @ (plus_plus_real @ A @ C)) = (plus_plus_real @ A @ (plus_plus_real @ B @ C)))))). % add.left_commute
thf(fact_208_add_Oleft__commute, axiom,
    ((![B : complex, A : complex, C : complex]: ((plus_plus_complex @ B @ (plus_plus_complex @ A @ C)) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.left_commute
thf(fact_209_add_Ocommute, axiom,
    ((plus_plus_real = (^[A2 : real]: (^[B2 : real]: (plus_plus_real @ B2 @ A2)))))). % add.commute
thf(fact_210_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A2 : complex]: (^[B2 : complex]: (plus_plus_complex @ B2 @ A2)))))). % add.commute
thf(fact_211_add_Oright__cancel, axiom,
    ((![B : real, A : real, C : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_212_add_Oright__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_213_add_Oleft__cancel, axiom,
    ((![A : real, B : real, C : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_214_add_Oleft__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add.left_cancel

% Conjectures (1)
thf(conj_0, conjecture,
    ((topolo144289241q_real @ (^[N : nat]: (im @ (s @ (f @ (g @ N)))))))).
